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Scientific Reports volume 12, Article number: 19047 (2022) Cite this article
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In underground engineering, disturbance of dynamic load can change layered rock mass stress state and induce accidents. Traditional elastic mechanics can’t effectively solve the complex deformation problem. However, Hamiltonian mechanics system can overcome this problem. Dual variables are introduced in symplectic space to solve the deflection equations of single-layered thin plate rock mass. Comparing vibration parameters, it’s found the 1st, 5th and 6th order are effective vibration modes. The resonance characteristics of thin plate are obtained with three dynamic loads. It’s found the thin plate is most likely to resonate and damage due to the smallest resonance frequency interval and the largest vibration amplitude by impact wave and rectangular wave respectively. Then, the vibration mode of multi-layered rock mass is analyzed through Multiple Reference Impact Testing. The failure of fine sandstone is caused by the resonance of effective vibration modes by hammer excitation. Finally, the failure mechanism of thin plate is obtained by the failure theory and LS-DYNA. It’s found the four sides and corners suffer tensile shear failure and shear failure respectively. When tensile failure occurs in central, the main crack and secondary crack propagate along long axis and short axis to form “O-十” failure mode.
In the process of geological deposition, sedimentary rocks with bedding structure are formed due to gravity. The sedimentary rocks with obvious bedding structure can also be considered as multi-layered rock mass^1,2,3,4. The layered rock mass can maintain good mechanical properties and strong stability without external disturbance^5,6, but with the development of underground engineering, the stress state of deep buried layered rock mass will change and cause deformation and failure^7,8,9. Therefore, the study on mechanical properties of layered rock mass is urgent. Multi-layered rock mass can be regarded as formed by cementation of single rock mass with various properties. So, the material properties of layered rock mass are heterogeneous, which leads its nonlinear mechanical properties^10,11. In order to clarify the mechanical properties of layered rock mass, several scholars have carried out a series of mechanical experiments. Zuo prepared coal-rock combination specimens with different lithologies by adhesive tape^12,13,14, they established nonlinear theoretical model of coal-rock combination, pre-peak and post-peak stress–strain models under uniaxial compression^15,16. Zhang discussed relationship between layers and mechanical parameters of multi-layered rock mass by true triaxial compression tests. It was found the peak strength and peak strain increases along with confining pressure increases. The mechanical properties and statistical damage constitutive model under hydraulic-mechanical coupling rock mass was established by comparing the deformation characteristics and failure modes². Wang studied the effect of interlayer thickness and strength on mechanical behavior and failure processes of layered rock mass with holes through uniaxial compression experiments. They found interlayer thickness and strength would lead the change of peak strength and elastic modulus of rock mass¹⁷. Liu conducted true triaxial compression experiments on two types of foliation orientation according to the large anisotropic deformation caused by the change of original rock stress state. They found the strength and failure modes of layered rocks greatly due to the lateral stress differences (({sigma }_{2}-{sigma }_{3})) has great influence on different foliation directions. Correspondingly, in order to avoid large anisotropic deformation, the angle between the tunnel axis and foliation strike should be as large as possible¹⁸. Cai considered the influence of intermediate principal stress on rock fracture and strength, the developed path of microcracks and fractures in rock was analyzed by using numerical simulation (FEM/DEM). Stress-induced fracturing and microcracking leading to onion-skin fractures, spalling and slabbing in layered rock mass were revealed¹⁹. In order to study mechanical properties of composite rock mass, Zienkiewicz proposed multilayered rock mass model which considered viscoplastic strain rate as the sum of each joint group and rock material²⁰. Further Wu proposed an anisotropic composite model based on the Drucker-Prager criterion. The model not only can describe anisotropic characteristics of rock strength and deformation, but also can realize nonlinear operation²¹. Several researchers studied rock mechanical properties and failure modes through uniaxial or triaxial compression experiments from macroscopic perspective, which is not comprehensive for considering the mesoscopic evolution of the creep fracture in layered rock mass. Zhao obtained the influence of inclination, thickness, weak layers on creep failure mode through analyzing the initiation, propagation, penetration process of cracks in layered rock mass²². Wang studied two curved failure mechanisms for single and multiple rock layers in high-pressure gas storage tunnel based on the upper bound theorem and variational principle. The analytical solutions of critical uplift pressure and failure surface were solved, which can provide theoretical references for tunnels design and construction²³. By analyzing the stress–strain characteristics and failure characteristics of layered rock mass in these researches, they established the damage constitutive model which can provide strong support for deformation and failure of roadway surrounding rock^4,24,25. However, the low strain rate loading condition is not suitable for all cases. In roadway excavation and tunnel excavation, the dynamic impact load with high strain rate can be generated when using mechanical tools and blasting excavation^26,27. The rock failure modes caused by the two loading conditions are quite different, the fundamental reason is the rock failure mechanisms under the two loading conditions are different. In underground engineering, layered rock mass will be damaged by impact load with high strain rate, so it is necessary to study the deformation and failure characteristics of layered rock mass under dynamic impact load.
Because the depletion of coal resources in shallow strata, coal mines enter deep strata mining. With the depth increase, the ground stress and gas stress of coal seam increase. The stress state of layered rock mass became more complicated, dynamic disasters such as gas outburst and rock burst occur more frequently^28,29,30. Under strong dynamic disturbances, the damage of multi-layered rock mass in the upper part of the roadway is fatal to the safety production in mines^27,31,32. Now most failure mode studies of layered rock mass are focusing on the quasi-static loading conditions with low strain rate, while the failure modes under impact load and quasi-static load are quite different³³. But there are few studies on the layered coal rock mass under impact load, which have great significance for dynamic disaster control in mine. Braunagel studied the effect of rapid stress cycles on dynamic compressive strength using modified split Hopkinson pressure bar (SHPB). They found the failure mode of rock changes from localized failure along discrete fractures to distributed fracturing, the compressive strength of granite decreases twice under cyclic loading³⁴. Xie constructed the dynamic mechanical constitutive model of the coal-rock combination specimens by SHPB. They found the strain softening effect were stronger than the hardening effect in coal-rock combination specimens, main damage location was in the coal body³⁵. According to the experiment result, Wen studied the dynamic compression characteristics of layered rock mass with significant strength changes. They found the dynamic compressive strength of layered rock mass increases approximately linearly with loading strain rate increased. Recording crack propagation paths by high-speed camera, it was found the bedding plane dip angle control the failure mode for parallel or near-parallel to the dynamic wave trans-mitting direction³⁶.Han found the localized slabbing degree of composite rock mass was sensitive to the filled joint thickness, but all specimens ultimately exhibited an axial splitting failure³⁷. Furthermore, Han studied the influence of interlayer strength on stress propagation, crack propagation mechanism and failure mode in composite rock-mortar specimens by SHPB and DIC. It was determined that tensile cracks initiate at the rock-mortar interface along the loading direction eventually leading to tensile failure³⁸. Qiu studied the influence of interfacial roughness and loading rates effect on crack extension velocity. The results showed that the larger the interfacial roughness, the easier the crack penetrates the composite rock mass, and the average crack propagation speeds increase with loading rate^39,40. Zheng proposed a numerical 3D mesoscopic approach based on the discrete element method combined with XCT images to characterize the dynamic impact behavior of heterogeneous coal-rock. According to the model, the meso-damage mode and fracture mechanism of heterogeneous coal-rock under different impact modes and impact velocities were studied^41,42. Since the existing phase field mode can only model the tensile-induced fracture which can’t well reproduce the diversity of dynamic fracture, Duan proposed a new phase field model which involved all the commonly seen dynamic fracture mechanisms to reflect dynamic rock diversity under impact loading. Through this model, crack initiation and propagation can be automatically characterized by phase field evolution equation, and different fracture modes of layered rock can be predicted⁴³. In addition, some scholars used thin plate theory to study the breaking form and caving law of the gob roof. Zuo simulated the roof fracture experiment of goaf by thin plates, which explained the O–X failure mode of thin plate was initiated by tensile-shear stress⁴⁴. Because of transverse shear stress strengthened with plate thickness increase, the failure mode of “O − *” appear. These studies provide good foundation for exploring the dynamic mechanical properties of layered rock mass, but now the complex deformation characteristics and failure mode of layered rock mass are still unclear using traditional elastic mechanics. However, the failure characteristics of layered rock mass are very important for underground engineering. So, further research on this aspect is required.
Now, the fracture research on thin plates is based on the traditional elastic mechanics, it’s difficult to find all solutions which strictly meet the boundary conditions in the solution process. So, the boundary conditions are often given by saint venant principle^45,46,47. However, the substitution method will lead large errors in the boundary calculation results, which is difficult to reflect the real situation^48,49. Hamilton mechanical system can overcome the shortcomings of some boundary conditions in traditional elastic mechanics^50,51,52. During solving process, this method can reduce the order of high-order differential equations to decrease the difficulty of solving by introduce the dual variables in symplectic space^53,54.So the Hamiltonian mechanics system can solve the end, local complex deformation problems which are difficult to deal by traditional elastic mechanics⁵⁵. In order to clarify the failure characteristics of multi-layered rock mass, it’s necessary to clarify the failure characteristics of single-layered thin plate rock mass. In this paper, the mechanical problem of single-layered thin plate rock mass is transformed into solving the eigenvalue and eigenvector of Hamiltonian. Based on the separation variable method, the deflection vibration mode function of single-layered thin plate rock mass is derived, the controlling equations of thin plate are solved by the Duhame integral. Subsequently, the resonance characteristics of single-layered thin plate rock mass under different dynamic loads are discussed, which the correctness of the theoretical derivation is verified by analyzing the effective vibration mode parameters in MRIT. Finally, the failure characteristics of single-layered thin plate rock mass under impact load are obtained through failure theory and numerical simulation.
As shown in Fig. 1, in this paper the single-layered thin plate rock mass is transversely isotropic in mechanical properties. The density of the rock mass is ρ, the thickness is h, the size is a × b, the elastic modulus is E, the Poisson’s ratio is υ, the x–y plane is neutral plane.
Mechanical calculation model of single layered thin plate rock mass.
Based on the transient equilibrium conditions of the internal mechanics of thin plate rock mass, the differential equation of single-layered thin plate rock mass can be derived under forced vibration⁵⁶:
where w (x, y, t) is the deflection; D is the bending stiffness of single-layered thin plate rock mass; ρ is the density of single-layered thin plate rock mass; q(t) is external dynamic load.
To solve the homogeneous Eq. (1), set q(t) = 0, the free vibration differential equation of single-layered thin plate rock mass as follows⁵⁰:
In this paper, we assume that the vibration of single-layered thin plate rock mass has the following harmonic oscillator with time as:
where ω is the natural frequency; W(x,y) is the deflection mode function.
Bring Formula (3) into Formula (2), we can get:
where k⁴ = ρhω²/D.
It is necessary to decouple the physical parameters in (4) using the Hamilton dual equations. If set θ = ∂W/∂x, the relationship between the physical parameters as follows⁵⁷:
If vector v = [W, θ, − V_x, M_x], the dual equation in Hamilton system as follows⁵⁸:
The Eq. (8) can also be expressed as:
Based on the symplectic geometry method and separation of variables, the solutions of (9) can be obtained. W(x) and W(y) are the deflection modes along the x and y directions respectively, the specific forms as follows^58,59,60:
where α₁ and α₂ are the eigenvalues in the x direction, β₁ and β₂ are eigenvalues in the y direction, α₁, α₂, β₁, β₂ satisfy the following rules:
(alpha_{1}^{2} + alpha_{2}^{2} = beta_{1}^{2} + beta_{2}^{2} = 2k^{2}), (alpha_{1}^{2} + beta_{1}^{2} = k^{2}), (alpha_{2}^{2} + beta_{2}^{2} = 3k^{2}), (alpha_{2}^{2} – beta_{1}^{2} = k^{2}).
In order to obtain the deflection equation of single-layered thin plate rock mass under free vibration, the boundary conditions should be determined. In this section, single-layered thin plate rock mass in a state of four edges fixed and isn’t disturbed by external load.
In the y direction of thin plate rock mass, there are the following relations:
W(x,0) = 0, ∂W(x,0)/∂y = 0; W(x,b) = 0, ∂W(x,b)/∂y = 0.
Combined with (9), we can get:
With (11), the frequency equation along the y direction can be obtained as:
The deflection equation as follows:
where
(k_{1} = frac{{cos alpha_{1} b – cosh alpha_{2} b}}{{frac{{alpha_{2} }}{{alpha_{1} }}sin alpha_{1} b – sinh alpha_{2} b}}), (k_{2} = frac{{cos beta_{1} a – cosh beta_{2} a}}{{frac{{beta_{2} }}{{beta_{1} }}sin beta_{1} a – sinh beta_{2} a}}).
The solutions’ form of the non-homogeneous control Eq. (1) can be expressed as follows:
Insert (15) into (1):
With (4),
Then,
The orthogonality of the deflection equations as follows⁶¹:
We multiply both sides of (18) by W_m(x,y) and do integral over the thin plate:
Set
Then,
Based on Duhamel’ Integral, the solutions can be expressed as follows:
And then,
Combining the frequency equation of single-layered thin plate rock mass, the main vibration mode is solved by Newton’s iterative method and the calculated values of the first 10 order vibration modal parameters are shown in Table 1. It’s found that the 1st order,5th order and 6th order vibration functions are the main vibration modes by comparing the first 10 order vibration modal parameters (Table 2).
Fourier transform can be used to obtain the Fourier series expressions and waveforms of rectangular waves, triangular wave and impact wave. The Fourier series expressions and waveforms of dynamic loading with amplitude A = 1, period T = 2 s as shown in Table 3. When the Fourier series expressions are inserted in Eq. (4), the time harmonic vibration term φ_m(t) of thin plate rock mass as shown in Table 4. Then, the vibration equation of thin plate rock mass can be obtained with Eq. (3). When the vibration frequency of dynamic loading and the main vibration mode (ω_m) of thin plate rock mass satisfy Eq. (25), resonance phenomenon occurs.
The vibration frequency and period of the dynamic load is ω = π rad/s (0.5 Hz), T = 2 s. By plotting φ_m(t) versus ω_m under three different dynamic loads, the resonant frequency characteristics of thin plate rock mass are revealed at t = 0–20 s, 0.01 s interval, algebraic and term n = 150.
Under the rectangular wave, the time harmonic vibration term φ_m(t) of effective modes which the 1st, 5th and 6th orders are analyzed and the vibration patterns as shown in Fig. 2. It’s found that the resonance frequency interval caused by rectangular wave is 2π (2ω), the resonant amplitude φ_m(t) distributed in ω_m = π–15π rad/s (ω–15ω). According to (25), the thin plate rock mass will resonate when ω_m = nω. With rectangular wave, when n is odd number, the resonance phenomenon is obvious. When n is even number, the resonance phenomenon is not obvious. The amplitude of resonance decreases exponentially with the resonance frequency increases.
The vibration of φ_m(t) of ω_m under rectangular wave.
Under the triangular wave, the time harmonic vibration term φ_m(t) of effective modes which the 1st, 5th and 6th orders are analyzed and the vibration patterns as shown in Fig. 3. Like the effect of rectangular wave, the resonance frequency interval caused by triangular wave is 2π (2ω), the resonant amplitude φ_m(t) distributed in ω_m = π–15π rad/s (ω–15ω). With triangular wave, when n is odd number, the resonance phenomenon is obvious. When n is even number, the resonance phenomenon is not obvious. The amplitude of resonance decreases exponentially with the resonance frequency increases.
The vibration of φ_m(t) of ω_m under triangular wave.
Under the impact wave, the time harmonic vibration term φ_m(t) of effective modes which the 1st, 5th and 6th orders are analyzed and the vibration patterns as shown in Fig. 4. Different from the rectangular wave and triangular wave, the resonance frequency interval caused by impact wave is π (ω), the resonant amplitude φ_m (t) relatively small. With impact wave, single-layered thin plate rock mass will resonate when n is positive integer. The amplitude of resonance keeps constant with the resonance frequency increases.
The vibration of φ_m(t) of ω_m under impact wave.
By analyzing the resonance parameters generated from different dynamic loads. On the one hand, the resonance frequency interval caused by impact wave is the smallest in dynamic loads, so that single-layered thin plate rock mass will resonate easily by impact wave. On the other hand, the resonant amplitude of rectangular wave is the biggest in dynamic loads, so that the resonance effect caused by rectangular wave is the most obvious. Correspondingly, the damage effect by rectangular wave acting on thin plate rock mass is the most significant.
The similarity simulation experiment is widely used to simulate the deformation and failure laws of overlying strata in mining. In this paper, the similarity simulation experiment platform is 1800 mm × 160 mm × 1100 mm. We use five types rock mass to simulate multi-layer coal and rock mass, the rock mass from the top to the bottom of the model are fine sandstone, medium sandstone, coal, coarse sandstone, mudstone respectively. The thickness of each rock mass is 200 mm and the bulk density similarity ratio is 1:1.6. The composition and ratio of similar materials in each layer rock mass as shown in Table 5.
In the traditional experimental modal analysis, the force hammer is used as the excitation device. Hammering method is the most widely used modal test method due to its convenient installation, strong mobility and less channel requirements. According to the number of data acquisition equipment channels, hammering method can be divided into Single Reference Impact Testing (SRIT) and Multiple Reference Impact Testing (MRIT)^62,63. MRIT can obtain more row or column matrix parameters for spectral analysis, MRIT is more convenient than SRIT^64,65. So MRIT is used in this paper, 9 hammer action points are arranged in turn on the top surface of fine sandstone, 100 mm apart from two adjacent action points. In order to reduce the damage of fine sandstone structure caused by the force hammer, iron blocks with size of 80 mm × 80 mm are placed at each action point as shown in Fig. 5. The 1#–5# action point is arranged vertically at the top plane center of fine sandstone, the action points 6#, 8# and 7#, 9# are located on the left and right sides of the top of fine sandstone, which arranged at 45° and 135° in the horizontal direction. The vibration amplitude which caused by force hammer is measured by magnetoelectric speed sensors (2D001), the No.1-No.4 sensors are distributed respectively at the interfaces of each layer rock mass, the surface of the sensor (signal receiving surface) attached the interface of each rock mass. The magnetoelectric signal is transmitted to the distributed network dynamic signal test system (DH5981), which is used for data acquisition and analysis.
Experimental model and data acquisition system.
When 2# action point is acted by the force hammer, the amplitude curve of each layer rock mass obtained by No.1–No.4 sensors as shown Fig. 6. It’s found that, the vibration trends measured by four sensors are similar. When t₁ = 15 ms, the No.1 sensor reaches the first extreme value s₁ = − 0.005 mm; When t₆ = 51 ms, the No.1 sensor reaches the peak s₆ = 0.014 mm. When the 2#, 4# and 6# action points are respectively acted by the force hammer, the extreme points and corresponding time points of amplitude curve as shown in Table 6. Under the disturbance of impact load, the vibration period of each layer rock mass is T₁ = 18–21 ms, the vibration frequency is 45–52.5 Hz.
Amplitude time-history curves under 2# action point excited alone.
When 2# action point is acted by the force hammer, the amplitude-frequency distributions of each sensor as shown Fig. 7. It’s found that the amplitude vibration trends measured by four sensors are similar. When p₁ = 50.5 Hz, the No.1 sensor reaches peak 7.2 × 10⁻³ mm, other sensors reach peak at this nearby frequency. Based on Hilbert Huang transform (HHT), the interface vibration waveforms are decomposed by EEMD^27,29,32. Combined with energy formula: ({int }_{-infty }^{infty }{x}^{2}(t)dt), the energy distributions and marginal spectrum of the decomposed waveforms are obtained^30,56.
Amplitude-frequency distribution of interface vibration under 2# action point excitation.
With 2# action point is excited, the vibration waveform is decomposed into five vibration modes (IMF1–IMF5) as shown in Fig. 8a. IMF1, IMF2 and IMF3 occupy most energy of the vibration waveform in Fig. 8b, so they are called effective vibration modes. IMF2 is called the main vibration mode due to it takes up 96% of the total energy. It’s found that the vibration frequency of the original waveform in 40.0–90.0 Hz (P₁–P₃) by analyzing the marginal spectrum in Fig. 8c. When the vibration frequency P₂ = 50.5 Hz, the marginal spectral amplitude reaches the maximum value. By analyzing the marginal spectrum of effective vibration modes (IMF1, IMF2 and IMF3), the predominant frequencies of IMF1、IMF2 and IMF3 are P₄ = 236.8 Hz, P₅ = 50.2 Hz and P₆ = 45.9 Hz respectively. The resonance frequency range caused by impact load is 225–262.5 Hz and 45–52.5 Hz. According to Table 2, it’s found that the main vibration modes frequency of fine sandstone is 30.1–128.3 Hz which is similar to the disturbance frequency of impact load. This cause resonance and enhance the failure effect of fine sandstone under impact load.
The waveform decomposition under 2# action point excitation.
Based on the first strength theory and third strength theory⁶⁶, the maximum shear stress(τ_max) distribution of the 1st, 5th and 6th mode as shown in Fig. 9. In 1st mode, the maximum shear stress concentrates at the middle of the four sides, which is symmetrical along the long and short central axis. The maximum shear stress of the 5th mode distributes in the long central axis and the middle of the two short sides, which are symmetrical along the long central axis. The maximum shear stress of the 6th mode distributes in the short central axis and the middle of the two long sides, which are symmetrical along the short central axis. It’s found that the stress σ_x of the 1st and 6th effective mode are greater than the stress σ_y, the stress σ_y of the 5th effective mode is greater than the stress σ_x, the shear stress is relatively small. So that the tensile failure is the main failure pattern in the center of thin plate rock mass. At the middle of the four sides on the thin plate rock mass, the stress σ_x, σ_y and τ_max concentrate together. The shear stress τ_xy of the 1st, 5th and 6th modes and stress σ_y of the 6th mode are concentrated at four corners. Therefore, four sides of the thin plate rock mass are the tensile-shear failure caused by the combined action of tensile stress and shear stress, four corners are the shear failure caused by the shear stress. On the area outside the four sides and four corners, τ_max of the 1st mode is relatively small, τ_max of the 5th and 6th modes concentrate along the long central axis and short central axis of the thin plate respectively. When thin plate rock mass subjected to dynamic load, many main cracks are formed along the long central axis, a small number of secondary cracks are formed along the short central axis of thin plate.
The maximum shear stress(τ_max) distribution of the 1st, 5th and 6th mode.
In LS-DYNA, the PLASTIC_KINEMATIC material model and Cowper Symonds model are used to simulate the failure of the thin plate rock mass under the dynamic load⁶⁷. The dynamic damage and failure process of thin plate rock mass as shown in Fig. 10. From Fig. 10a, it’s found that cracks first appear in the middle and corners of the four sides on the thin plate, these cracks develop further along the boundary. Subsequently, cracks are generated in the center of the thin plate, the cracks extend outward along the long and short central axes of the thin plate in Fig. 10b. And the number of cracks along the long central axis is much larger than the cracks along the short central axis in Fig. 10c. The numerical simulation results are consistent with theoretical derivation in Fig. 9. So that, the failure position can be determined by 1st effective mode which in the middle of the four sides, four corners and central area of the thin plate. The trend of the cracks can be determined by the 5th and 6th effective modes, which along the long central axis and short central axis.
The dynamic damage and failure process of single-layered thin plate rock mass.
The failure patterns of single-layered thin plate rock mass with thickness of 2 cm and critical thickness of 4.5 cm were studied under static load by the simulation experiment device for roof breakage in goaf as shown in Fig. 11⁴⁴. The results showed that: (1) With static load in Fig. 11a, the four sides of single-layered thin plate rock mass were subjected to the combined action of shear stress and tensile stress. The shear stress caused tensile shear failure on the four sides and formed an “O” ring. (2) The tensile failure not only occurred in the central area of single-layered thin plate rock mass, but also formed main vertical crack which propagated along the long axis. The main vertical crack splitted into “X” type crack, when it extended to the four corners. Finally, the “O-X” failure pattern was formed. (3) With the thickness of rock mass increases(critical thickness is 4.5 cm), it’s quite clear that there has a horizontal crack along the short central axis, which made the thin plate rock mass formed “O-❋” failure pattern in Fig. 11b.
The failure pattern of single-layered thin plate rock mass under static load.
According to the Figs. 9 and 10, four sides and four corners of single-layered thin plate rock mass occur tensile shear failure and shear failure under dynamic load. The main crack along the long central axis and the secondary crack along the short central axis are formed in the center of thin plate due to tensile-shear failure and shear failure. So the “O-十” failure pattern of single-layered thin plate rock mass is formed. Therefore, it’s obvious that the fracture mechanism of thin plate rock mass under dynamic load and static load is different, and the fracture characteristics are also different.The reason for the difference of fracture characteristics in thin plate rock mass is the stress loading condition in different ways. In Zuo’s study, the stress is mainly loaded to the rock mass under static loading conditions with low strain rate^12,13,14,44, the failure mechanism is like the rock failure criterion which established by other scholars. However, the main content of this paper is the failure characteristics of layered rock under dynamic impact load with high strain rate. Based on the vibration characteristics, the deflection equation and effective vibration mode are deduced by Hamilton mechanical system. Combined with experiment and numerical simulation, the failure of single-layer thin rock mass is caused by the resonance which is induced by the effective vibration mode under dynamic impact load. On the one hand, the research results can use the resonance effect to accelerate the rock breaking process, reduce the energy consumption of rock breaking and improve the rock breaking efficiency; on the other hand, it can provide new ideas for the use and maintenance of built roadways and tunnels.
In this paper Hamiltonian mechanics system is used to solve the deflection equations of single-layered thin plate rock mass, the main vibration modes and resonance characteristics under different dynamic loads can be obtained. Through theoretical analysis and numerical simulation, the failure mode of single-layered thin plate rock mass is obtained. The specific conclusions are as follows:
Based on the dual equation and Duhamel’s integral, the mechanical model of single-layered thin plate rock mass is established. The main vibration modes (1st, 5th, and 6th modes) and the frequencies of thin plate rock mass are verified.
The resonance frequency interval and resonant amplitude φ_m(t) caused by rectangular wave, triangular wave and impact wave can be obtained. With resonance frequency increase, the amplitude of resonance initiated by rectangular wave, triangular wave decreases exponentially, the amplitude of resonance initiated by impact wave keeps constant.
The thin plate is most likely to resonate and damage due to the smallest resonance frequency interval and the largest vibration amplitude by impact wave and rectangular wave respectively.
According to the MRIT, the vibration waveform can be decomposed into five vibration modes, the main vibration mode and the effective vibration modes are determined by energy analysis. Comparing main vibration modes parameters, it’s concluded the rock mass failure is caused by effective vibration modes of dynamic load.
Combining the first and third strength theory, it’s found that the failure of thin plate at the central area, four corners and the middle of the four sides, which determined by tensile stress and shear stress of 1st mode. Main cracks and secondary cracks formed along the long axis and short axis, which determined by τ_max of 5th and 6th modes.
Through numerical simulation, when tensile failure occurs in the center of thin plate rock mass, the cracks expand along the long axis and the short axis respectively to become the main crack and the secondary crack. finally the “O-十” failure pattern is formed which is different from the failure pattern formed by static load.
ThE data used to support the findings of this study are available from the corresponding authors upon request.
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This research was conducted with financial support from the National Natural Science Foundation of China (52064046, 51804311). Department of Science and Technology of Xinjiang Uygur Autonomous Region (science and technology aid Xinxiang) (2020E0258). China Scholarship Council (CSC) and the Fundamental Research Funds for the Central Universities (2020YJSAQ13).
School of Emergency Management and Safety Engineering, China University of Mining and Technology (Beijing), Ding No.11, Xueyuan Road, Haidian District, Beijing, 100083, China
Feng Li, Chenchen Wang, Runchuan Sun, Guangyou Xiang, Baorui Ren & Zhao Zhang
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China
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F.L. carries out formula derivation and theoretical analysis, in addition he provides writing ideas and financial support. C.W. conducts data analysis and writes main manuscript text. R.S. carries out Multiple Reference Impact Testing. G.X. conducts numerical simulation.
Correspondence to Chenchen Wang.
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Republicans went into Tuesday’s midterm election bullish about their chances about a “red wave” carrying them to huge majorities in the House and Senate, after spending months bashing Democrats about issues like inflation, crime and education.
But the so-called red wave ultimately did not materialize, with Democratic incumbents showing resilience in key races — and even making key pickups, like John Fetterman flipping Pennsylvania’s U.S. Senate seat from red to blue.
The balance of power of Congress is still up in the air, and Republicans could still win control, as Republican leader Kevin McCarthy told supporters in the early hours of Wednesday morning: “When you wake up tomorrow, we will be in the majority.”
But even with some key races like outstanding, it’s clear that Tuesday’s election defied historical trends. While Republicans had massive double-digit victories in states like Florida, Democrats held on to key House seats in states from Virginia to Kansas and claimed governors’ races in battleground states like Michigan, Wisconsin and Pennsylvania.
“While many races remain too close to call, it is clear that House Democratic Members and candidates are strongly outperforming expectations across the country,” House Speaker Nancy Pelosi said.
But as one defeated GOP candidate put it early Wednesday morning: “The RED WAVE did not happen.”
Here are a few takeaways from this year’s midterms so far:
Republicans started off Tuesday evening strong, with early results showing a rout in Florida. 
Incumbent Gov. Ron DeSantis — who only won the governor’s race in 2018 by roughly 30,000 votes — swept to a massive re-election victory, including winning the once-Democratic stronghold of Miami-Dade County, which Hillary Clinton won by nearly 30 points in 2016.
Coupled with fellow GOP Sen. Marco Rubio cruising to victory against a strong Democratic challenger, Rep. Val Demings, more and more evidence appears to show that Florida may no longer be a “swing state.” 
Despite the fact that former President Barack Obama carried the state twice — in 2008 and 2012 — and registered Democrats exceeded Republicans in 2020, the state has shifted rightward in recent years, thanks in part to an influx of new residents and the GOP making inroads with Latino voters.
Carlos Curbelo, a Republican former member of Congress, told The Associated Press that Florida is “off the map” for Democrats “for the foreseeable future.”
“Democrats really have to think about how they are going to rebuild there,” Curbelo said. “The Obama coalition no longer exists.”
DeSantis was not the only Republican governor to have a good night on Tuesday.
In Texas, Gov. Greg Abbott won a third term decisively, delivering Democrat Beto O’Rourke a devastating defeat — his third failed run for office in four years — despite record fundraising.
“Tonight, Texans sent a very resounding message,” Abbott said in a victory speech.
And Georgia Gov. Brian Kemp delivered Democrat Stacey Abrams a resounding defeat in a rematch of their high-profile 2018 race.
“It looks like the reports of my political death have been greatly exaggerated,” Kemp said, adding: “This election proves that when Republicans stay focused on real world solutions that put hard-working people first, we can win now, but also in the future.”
On the other side of the coin, Democrats claimed governorships in three key states that President Biden won in 2020, which may prove crucial in the battle for abortion rights and oversight of the 2024 presidential election.
In Michigan, Gov. Gretchen Whitmer won a second four-year term in Lansing, defeating far-right GOP candidate Tudor Dixon, a former political commentator and horror-film actress, in a re-election battle where abortion rights proved crucial. Whitmer led a statewide Democratic ticket that featured abortion as a centerpiece in the aftermath of the Supreme Court overturning Roe v. Wade over the summer.
"Whe prospect of leading this state for four more years is a privilege which we are incredibly grateful and excited about," Whitmer told supporters in Detroit. "We will always work with anyone who actually wants to solve a problem because there’s nothing more important than the people of this state to us — all of the people of this state."
Whitmer also threw her support behind a ballot measure enshrining abortion rights into the state’s constitution, which voters approved.
In neighboring Wisconsin, incumbent Gov. Tony Evers defeated Republican Tim Michels, a Trump-backed candidate who espoused the former president’s false claims of voter fraud in the 2020 election, to win another term in the statehouse.
Evers’ win keeps a Democrat in power in battleground Wisconsin ahead of the 2024 election. In an audio recording released by a left-leaning political group, Michels was heard saying that "Republicans will never lose another election" if he was elected governor; Evers called Michels "a danger to our democracy" in a Twitter post in response to the comment. (Michels’ campaign later clarified in a statement to Insider that 
Michels favored disbanding the state’s bipartisan elections commission and had promised to sign bills vetoed by Evers that would make it harder to vote absentee.
Evers said his victory was a win for reproductive rights, public schools, clean energy and continuing to invest in the state’s infrastructure.
“You showed up because you saw our democracy was on the brink of existence and you decided to do a damn thing about it,” Evers told supporters in his victory speech.
Evers’ victory stood to guarantee that Democrats would still have a check on Republican power in the Legislature, as GOP attempts of winning enough seats to have a veto-proof supermajority looked to be unsuccessful.
In Pennsylvania, Democrat Josh Shapiro clinched victory in Pennsylvania’s gubernatorial race, a key Democratic hold in the Keystone State.
Shapiro, who faced off against Republican Doug Mastriano, served as the state’s attorney general for two terms before running for the governor’s seat. The Democrat smashed Pennsylvania’s campaign finance record in a powerhouse campaign in a year in which Democrats nationally faced headwinds, including high inflation.
“Tonight, voters from Gen Z to our seniors, voters from all walks of life, have given me the honor of a lifetime, given me the chance to serve you as Pennsylvania’s next governor,” Shapiro told a cheering crowd of hundreds in his victory speech.
Shapiro thanked his family and supporters and went on to tell the crowd that “real freedom won tonight” and “Democracy endured” in a race he characterized as a fight for the right to vote and the right to abortion.
At stake in the Keystone State’s gubernatorial elections were abortion rights, as well as management of the 2024 presidential election in a swing state that is often decisive. The governor’s office appoints the top election official for the state, which can affect major issues like the economy and abortion.
Shapiro’s victory makes him the first governor of Pennsylvania elected to succeed a member of his party since 1966.
Pennsylvania’s stature has risen in the U.S. Senate — by about 6 feet, 8 inches.
The Associated Press projected Wednesday that Pennsylvania’s Lt. Gov. John Fetterman defeated Republican Mehmet Oz in the state’s U.S. Senate race, giving Democrats a key pickup in the chamber and delivering the first Senate flip of the 2022 midterms.
“It’s official,” Fetterman wrote on Twitter early Wednesday morning. “I will be the next U.S. Senator from Pennsylvania. We bet on the people of Pennsylvania – and you didn’t let us down And I won’t let you down. Thank you.”
In a speech early Wednesday morning, Fetterman told supporters he was "humbled" by their support and evoked his campaign slogan, "every county, every vote."
"And that’s exactly what happened," he said. "We jammed them up. We held the line. I never expected that we were going to turn these red counties blue,  but we did what we needed to do."
"This campaign has always been about fighting for everyone who has ever been knocked down, that ever got back up," Fetterman said. "This race is for the future of every community across Pennsylvania, for every small town, or person that ever felt left behind, for every job that has ever been lost, for every factory that was ever closed, for every person that works hard but never got ahead."
"I’m proud of what we ran on: Protecting a woman’s right to choose, raising our minimum wage, fighting [for] the union way of life, healthcare is a fundamental human right," Fetterman said. "It saved my life, and it should all be there for you, if you ever should need it."
The election night win calls an end to a long, contentious contest, marked both by social media sniping and questions about Fetterman’s ability to handle the office after suffering a stroke on the campaign trail.
Fetterman began the race with a hefty lead in the polls, an edge that dwindled in the wake of a May stroke that kept him from the campaign trail and a debate performance that concerned some viewers due to his use of a captioning device – a move that Oz and his supporters used to try and paint Fetterman as unfit for office.
According to AP VoteCast data collected from likely voters ahead of Election Day,  52% of respondents said they were very or somewhat confident in Fetterman’s ability to serve in Congress after suffering a stroke earlier this year, compared to 47% who were not.
But Fetterman’s campaign, which portrayed Oz as an outsider out of touch with Pennsylvanian’s everyday struggles, was effective enough to sway the election in his favor, as well as his positions on abortion and healthcare. 
Republicans went into Tuesday’s election predicting a massive "red wave" would sweep them into a dominant House majority, and possibly even swing the Senate. At one point last year, Republican leader McCarthy predicted the GOP could flip as many as 60 seats.
But as the results started to roll in, it was clear that the GOP would not get the Democratic wipeout they had hoped for.
Democratic Reps. Abigail Spanberger and Jennifer Wexton held off spirited Republican challengers in Virginia districts the GOP had hoped to flip. Ohio Rep. Marcy Kaptur held off a challenge from Republican J.R. Majewski, who was at the U.S. Capitol during the deadly Jan. 6, 2021, riot and who misrepresented his military service. 
Democrats held House seats in Rhode Island, Ohio, Kansas and New Hampshire that Republicans were targeting. They also flipped some seats, including a suburban Illinois district, from Republicans.
Republicans needed a net of just five seats to reach a 218-seat House majority, which they appeared poised to accomplish.
They picked up a Nashville, Tennessee-area seat long held by Democrats. And in a dramatic example of the difficult political environment for Democrats, the party’s House campaign chairman Rep. Sean Patrick Maloney was fighting for political survival against Republican state legislator Mike Lawler in New York’s Hudson Valley. He would be the first Democratic campaign chief to suffer defeat in two decades.
But it’s far from the "bloodbath" that some officials predicted.
Once again, a U.S. Senate race in Georgia is heading to a runoff election, with control of the chamber potentially on the line.
The top two candidates in Tuesday’s race — Incumbent Sen. Raphael Warnock, a Democrat, and Republican challenger Herschel Walker — will face off on Dec. 6 since neither candidate received 50% of the vote, Georgia secretary of state Brad Raffensperger said on Wednesday.
"There’s one race in our state that is going to be moving to the December 6 runoff," he said. "That is the race for the United States Senate, between Senator Raphael Warnock and Herschel Walker. Our office has already begun the behind-the-scenes work to start building the ballots."
"It’s a lot of work, but that’s how the machinery of our democratic republic works," Raffensperger added. "We welcome it, because we know at the end of the day, everyone wants to know that we have honest and fair elections. And we do ask the voters to come out and vote one last time."
It’s a familiar position for Warnock, who was first elected to the Senate on Jan. 5, 2021, in a runoff election after neither he nor then-incumbent Sen. Kelly Loeffler garnered a majority of the vote in the general election on Nov. 3, 2020. Warnock ultimately won the race to fill the remaining two years of Republican Johnny Isaacson’s term by roughly 93,000 votes.
“We’re not sure if this journey is over tonight or if there’s still a little work yet to do,” Warnock told voters in the early morning hours of Wednesday. “I understand that at this late hour you may be a little tired, but whether it’s later tonight or tomorrow or four weeks from now, we will hear from the people of Georgia.”
Similarly, Walker urged his supporters to "hang in there a little bit longer." 
"I’m telling you right now: I didn’t come to lose," he added.
As of Wednesday, Warnock leads Walker by roughly 35,000 votes. Libertarian candidate Chase Oliver garnered a little more than 81,000 votes.
Looking back on 2020, victories from Warnock and his de facto “running mate,” Sen. Jon Ossoff, D-Ga., gave Democrats their 50-50 majority thanks to Vice President Kamala Harris’ tie breaking vote.
Georgia’s other high-profile race, the 2018 gubernatorial rematch between Democrat Stacey Abrams and Republican Gov. Brian Kemp was decided quickly, with the GOP incumbent surpassing 53% of the vote.
Aside from Georgia, a number of key races that will determine control of Congress for the remainder of President Biden’s first term were still outstanding.
In Arizona, incumbent Sen. Mark Kelly leads Republican rival Blake Masters, a venture capitalist, but the race is still too close to call.
Kelly’s 2020 special election victory gave Democrats both of Arizona’s Senate seats for the first time in 70 years. It was propelled by the state’s fast-changing demographics and the unpopularity of then-President Donald Trump.
Kelly, who flew in space as a NASA astronaut and is married to former Rep. Gabby Giffords, thanked his family and supporters gathered in Tucson and said he was confident he would prevail once all ballots are counted.
“It’s been the honor of my life to represent Arizona in the United States Senate,” Kelly said. “And for as long as I’m there, I’ll be honest with you, I will protect our country and our democracy.”
The nail-biting race between Democratic incumbent Sen. Catherine Cortez Masto and Republican challenger Adam Laxalt remained too early to call after polls closed across Nevada Tuesday night.
Laxalt and Cortez Masto have been locked in a tight race for weeks, both hitting hard on national party talking points: Laxalt blaming inflation and illegal immigration on Democratic policies, and Cortez Masto promising to block GOP-led attempts at a nationwide abortion ban and to fight for a pathway to permanent citizenship for undocumented immigrants who came to the country as children.
Hours after the polls closed, both candidates told supporters that they expected to come out ahead.
“Our positive energy got us here today, and our positive energy is going to continue to flow this week,” Cortez Masto said from a Democratic watch party on the Las Vegas strip. “We are gonna get this done.”
“We are exactly where we want to be in this race. We have a lot of votes coming in across the state yet,” Laxalt told supporters at a Las Vegas casino. “We are going to win this race.”
The outcome of the two Arizona and Nevada races may not be known for days because both states conduct elections in part by mail ballots, which take a long time to count.
The Associated Press projected that Wisconsin Sen. Ron Johnson eked out a win over Democrat Mandela Barnes, bolstering Republicans’ figures in the chamber. And while Alaska’s Senate race has not yet been called, the contest is expected to be won by one of the two leading Republican candidates.
After Fetterman’s flip, Republicans need to win two of Georgia, Nevada or Arizona in order to win control of the Senate.
The Associated Press contributed to this report.
Spectrum News’ Austin Landis, Rachel Tillman, Eden Harris, David Mendez and Justin Tasolides contributed to this report.

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I have thought all this time that Justin Bieber was the marketing genius. Remember how he was cancelled by his own country Canada for his then obnoxious behavior? Bieber turned that around to become a respected pop star. But it has now turned out that Taylor Swift is the true genius, not only in marketing but also in music production and in being able to turn painful memories into moneymakers.
Take a look at what has happened since she released her latest album Midnights at the stroke of what else, but midnight, last Oct. 21. Spotify crashed. Midnights became the most streamed album in a single day. Three hours later, Taylor released the Midnights 3:AM version with seven additional songs, tunes that were short-listed for the album but did not make the final cut.  Swifties, as her fans are called, went doubly crazy. So a week later, Midnights became the most streamed album ever. It also made No. 1 in Billboard’s Top 200 Albums hit list.
That is not all. Pop music history continued to unfold before our eyes or I should say in our ears, courtesy of Taylor. For the first time ever, 10 tracks by one artist made it to the Top 10 of Billboard’s Hot 100 chart for an entire week. That was Swiftie and her Midnights, of course.  The last time something like this happened was in September 2021. Drake aced the feat but he had only nine singles in the Top 10 from his album Certified Lover Boy. Taylor has now broken that record with 10.
Take a look at the Top 20 songs in the latest edition of the Hot 100: Anti-Hero; Lavender Hope; Maroon; Snow on the Beach featuring Lana del Rey; Midnight Rain; Bejeweled; Question…?; You’re on your Own, Kid; Karma; Vigilante Shit, all of these tracks are by Taylor Swift.
Take note, Swiftie has more songs in the next 20 listing. Unholy by Sam Smith and Kim Petras; Bad Habit by Steve Lacy; Mastermind by Taylor; Labyrinth by Taylor; Sweet Nothing by Taylor; As It Was by Harry Styles; I Like You (A Happier Day) by Post Malone and Doja Cat; I Ain’t Worried by One Republic; Your Proof by Morgan Wallen; and Would’ve, Could’ve, Should’ve by Taylor.
Not only that. Swiftie still has more songs from Midnights in the Top 50: 21.) Bigger Than the Whole Sky; 26.) The Great War; 32.) Paris; 33.) High Infidelity; 41.) Glitch; and 45.) Dear Reader.
Midnights is Taylor’s 10th studio album. It contains new original compositions about 13 sleepless nights in her life. Unless caused by joy or too much excitement, sleepless nights are not pleasant experiences. The tossing and turning all night are caused by tears, boo-hoo, heartaches, fears, Eeek!, monsters under my bed!, pain, is it a heart attack or heartburn, and a lot of times by that man who left you, who betrayed you or didn’t love you at all.
Taylor has taken all those feelings and turned them into songs that are now making so much money, she will remain rich, overly solvent all her life. Nyanyanyananah! Eat your hearts out Scooter Braun for wanting to own my songs. Take this Kanye West, for picking a fight with me. Take this, John Mayer, Jake Gyllenhaal, Calvin Harris, Harry Styles, etc., all you guys who could have been nicer to Swiftie. Thank heavens, she has now found true love.
Pop rock Anti-Hero with its nightmare nods is interesting. Lavender Haze is dreamy disco. Bejeweled with its lush star-studded Cinderella-inspired video is fun. But Midnights has no stand-out single. Taylor meanders. The content is disjointed. Just like what happens with thoughts during sleepless nights. If this was her intent, then it is an excellent album.
What I see in Midnights is everything that Taylor has learned all these past years. That is what I find so remarkable about her. She is continuously learning the ropes about making and marketing music and putting all those into wonderful use. Now the question is if she has reached her peak. Not likely. She is still young. So, I wonder, what will she come up with next?
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WAVERLY, Ohio (WXIX) – The jury in George Wagner IV’s murder trial listened Wednesday to secret recordings of the Wagner family.
The recordings are from wiretaps on their phones and one of their vehicles more than four years ago before the Wagners were arrested for the 2016 Pike County massacre.
Pike County massacre: Complete trial coverage
The first ones played for jurors on Wednesday morning captured May 2018 telephone conversations between George Wagner IV’s younger brother, Jake Wagner, and his then-wife, Beth Ann.
The couple discussed his mother, Angela Wagner and Beth Ann’s struggles daily living with her while Jake Wagner traveled most of the week as a truck driver with his older brother. The two women were in the home alone caring for Jake and George’s young children.
Beth Ann testified last month that Angela Wagner ran things and accused of inappropriately touching Jake Wagner’s then-2-year-old daughter, Sophia, and then she was forbidden to be alone with her step-daughter and George Wagner IV’s toddler son, Bulvine.
“I feel like I’m living in Nazi Germany,” Beth Ann told Jake Wagner in the second recording played in court.
In other recorded calls played for the jury, a terse argument between Jake Wagner and his mother over her issues with his wife erupted into a shouting match when he told his mother she was being “delusional” and “going off the deep end.”
“Don’t you insult me,” Angela Wagner ordered her son. “You’ve done enough damage around here.”
The dispute escalated even further as Angela Wagner complained that her granddaughter knew (with Jake’s wife there) that Angela Wagner was her grandmother, not her mother. This clearly upset Angela Wagner, who was still convinced Beth Ann inappropriately touched her granddaughter.
Jake Wagner shouts at one point about his daughter: “You are not her mother, you are her grandmother!” He also his mother that she insults his wife “every day. You can’t stop insulting her.
In another batch of recordings played for the jury, Jake Wagner and his brother screamed at each other as they traveled in the “R&L Truck” as part of their jobs, according to evidence introduced Wednesday.
They also viciously argued over Jake Wagner’s wife. George Wagner IV accused his brother of believing his wife over his daughter.
He called Jake Wagner’s wife a “whore,” which Jake Wagner bitterly denied. The brothers screamed back and forth about that and then what God would want. Their dispute was laced with profanity and racial and anti-gay slurs.
George Wagner asked his brother if he would want Beth Ann to have his daughter while they were in jail. Jake Wagner responded no because his wife hasn’t been around long enough to know how to do things with his daughter the way he would want them. But, he told his brother “I sure as s— trust her.”
“If we all go to the electric chair, would you want Beth to tell (Sophia) about it?” George Wagner responded.
Most of the tapes do not point directly to George IV’s involvement in the Pike County Massacre.
His attorneys say he wasn’t ever there on the night of April 21, 2016.
Jurors are being provided transcripts of the recordings as they listen.
Pike County Common Pleas Court Judge Randy Deering stressed the documents are simply listening aids.
The transcripts are not considered evidence, the recordings are, he ruled, adding that the jury will not have access to the transcripts during deliberations.
The recordings between the Wagners began in May 2018 and lasted into August 2018.
The Ohio Bureau of Criminal Investigation sought the warrant for the wiretaps only after “exhausting” all other investigative techniques, the lead agent on the case testified Tuesday.
The entire investigative team agreed it was a necessary step to obtain the wiretaps, Special Agent Ryan Scheiderer said, pointing out how close-knit the Wagners were and kept discussions amongst themselves.
It also was a way for BCI to become aware of new or known associates and/or relatives of the Wagners so BCI could interview them, he testified.
On Wednesday, BCI Criminal Intelligence Analyst Julia Eveslage told the jury BCI had extensive legal training before using the wiretaps.
These recordings have been the subject of much debate in recent days between the state and defense. The attorneys got into a heated argument Tuesday and Friday, prompting the judge to send the jury home and cancel court on Friday.
Special Prosecutor Angela Canepa and John Parker, George IV’s attorney, both want to play audio recordings, but they disagreed over which ones and when the state informed the defense.
George Wagner IV and his brother and their parents, Billy Wagner, 51, and Angela Wagner, 52, were all indicted in November 2018 for the killings.
Prosecutors long have said custody and control over the then-2-year-old daughter of Jake Wagner and one of the victims, Hanna May Rhoden, 19, was the motive behind the slayings.
Angela Wagner and Jake Wagner both testified recently against George Wagner IV as part of their plea deals with the state after admitting their roles.
George Wagner, 31, and his father have pleaded not guilty and continue to fight all charges, including eight counts of aggravated murder.
Billy Wagner’s trial is expected to be held in Pike County next year.
Jake Wagner and Angela Wagner both testified that the entire family participated in the massacre.
Jake Wagner calmly recounted in graphic detail how he killed five of the eight victims, including the mother of his child, and shot and wounded a sixth.
He implicated his father in killing three of the victims and confirmed on the stand his brother George killed no one, shot no one and, in fact, never once fired his gun.
George Wagner’s attorneys unsuccessfully tried to have the murder charges thrown out against their client earlier this year before the trial started.
His brother and mother’s confessions prove he didn’t kill or even shoot anyone, they argued in court records and in person before the judge, but Deering refused to dismiss the charges.
The judge sided with the state, who contends George Wagner should be convicted of the murder charges because he actively participated in the planning, preparation and cover-up of the massacre.
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Free Plug-in For Adding Depth To Music  Sonic State
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Professional audio products brand Mackie has acquired Babelson Audio’s catalogue of plugins.
Keep up to date with the latest industry news here.
Founded back in the ’70s, Mackie has made quite a name for itself across the years as a leader in audio engineering, known among audio professionals for their power, performance, versatility, and sonic signature.
Babelson Founder Thomas Ceyhan said that the Mackie brand “has always been synonymous with creativity, great sound, and great value”. In reference to acquisition of Babelson Audio’s catalogue, “I can think of no better partner for bringing these great products to a broader audience”.
Mackie has built a name for itself as a driver of audio innovation and reliability, with their Onyx Series sitting as the “benchmark for legendary sonic performance”.
Existing Babelson plugin users don’t need to worry either, with a seamless transition planned.
Users will still have access to all previous purchases, with plans from Mackie to continue to support updates and new versions of existing Babelson plugins, in addition to introducing brand new plugins under the new acquisition.
Babelson’s plugins are compatible across all major DAW software, enabling versatility and range in production.
“With the addition of Babelson plugins to the Mackie family, we are excited to be able to offer our users some of the most powerful, versatile, and best sounding tools available for their music production needs,” said Mackie CEO Alex Nelson.
“Just as importantly, it deepens our bench for hardware-based processing in future products.”
This acquisition will enable a much broader reach for Babelson’s highly acclaimed plugins, and provides new solutions for customers using DAW software.
In order to authorise Babelson plugins, users will first need to install the iLok License Manager, which can be downloaded for free from the iLok website.
Head to Mackie for more information. For local enquiries on Mackie products, reach out to Dynamic Music.

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Scranton is a private Catholic and Jesuit institution that delivers a transformative education, grounded in the liberal arts.
Scranton is a private Catholic and Jesuit institution that delivers a transformative education, grounded in the liberal arts.
At The University of Scranton, our rigorous, in-depth education provides the field-specific knowledge and competencies needed for professional success.
At The University of Scranton, our rigorous, in-depth education provides the field-specific knowledge and competencies needed for professional success.
Become a Royal! Scranton offers the perfect combination of academic environment, social experience, and personal support our students need to build successful lives and careers.
Become a Royal! Scranton offers the perfect combination of academic environment, social experience, and personal support our students need to build successful lives and careers.
Student Life is vibrant and varied, from ministries-based programs and leadership initiatives to student-run activities, clubs and organizations.
Student Life is vibrant and varied, from ministries-based programs and leadership initiatives to student-run activities, clubs and organizations.
With more than 51,000 Scranton graduates out there, connecting with fellow alumni couldn’t be easier, and we’re here to help!
With more than 51,000 Scranton graduates out there, connecting with fellow alumni couldn’t be easier, and we’re here to help!
 Please use the following site map to locate the information you are looking for, or search our web archives for past versions of the page. 
Scranton is a private Catholic and Jesuit institution that delivers a transformative education, grounded in the liberal arts.
Scranton is a private Catholic and Jesuit institution that delivers a transformative education, grounded in the liberal arts.
At The University of Scranton, our rigorous, in-depth education provides the field-specific knowledge and competencies needed for professional success.
At The University of Scranton, our rigorous, in-depth education provides the field-specific knowledge and competencies needed for professional success.
Become a Royal! Scranton offers the perfect combination of academic environment, social experience, and personal support our students need to build successful lives and careers.
Become a Royal! Scranton offers the perfect combination of academic environment, social experience, and personal support our students need to build successful lives and careers.
Student Life is vibrant and varied, from ministries-based programs and leadership initiatives to student-run activities, clubs and organizations.
Student Life is vibrant and varied, from ministries-based programs and leadership initiatives to student-run activities, clubs and organizations.
With more than 51,000 Scranton graduates out there, connecting with fellow alumni couldn’t be easier, and we’re here to help!
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Scientific Reports volume 12, Article number: 19045 (2022) Cite this article
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Spider webs are finely tuned multifunctional structures, widely studied for their prey capture functionalities such as impact strength and stickiness. However, they are also sophisticated sensing tools that enable the spider to precisely determine the location of impact and capture the prey before it escapes. In this paper, we suggest a new mechanism for this detection process, based on potential modal analysis capabilities of the spider, using its legs as distinct distributed point sensors. To do this, we consider a numerical model of the web structure, including asymmetry in the design, prestress, and geometrical nonlinearity effects. We show how vibration signals deriving from impacts can be decomposed into web eigenmode components, through which the spider can efficiently trace the source location. Based on this numerical analysis, we discuss the role of the web structure, asymmetry, and prestress in the imaging mechanism, confirming the role of the latter in tuning the web response to achieve an efficient prey detection instrument. The results can be relevant for efficient distributed impact sensing applications.
Many natural structures have fascinated and inspired researchers over the years for their optimized characteristics. Spider webs are a particularly prominent example, due to their various functions, their versatility and efficiency. Spider webs occur in different shapes and geometries, and allow arachnids to perform a vast variety of tasks such as capturing prey, lifting heavy objects and throwing themselves at accelerations around 80g^1,2. Of all the types of webs, however, two dimensional orb webs are probably the most renowned. These particular structures are typically composed of radial and frame threads produced with major ampullate silk³, which are secured to surfaces through the cement-like piriform silk⁴. The radial threads are intercepted with the sticky spirals threads of the web that are produced with aggregate and flagelliform silk and efficiently adhere to the prey^5,6,7,8.
From a mechanical point of view, spider webs display multiple excellent properties in terms of strength and toughness of the single silk threads, adhesion of the anchorages with the surfaces, and impact resistance⁹. These web characteristics also translate into an outstanding mechanical efficiency in localizing and catching prey^10,11, a process that benefits from the mechanical properties of the silk and the vibration properties of the web^12,13. Recent studies based on transient response analysis have indicated that prestressing is used to tune the sonic properties of webs^13,14, which has a great influence on flexural wave propagation that may be used by spiders as a means to localize prey^15,16. Laser vibrometry measurements have shown that radial threads are able to efficiently transmit the entire frequency range between 1 and 10 kHz^17,18, frequencies that are detected by the cuticular vibration receptors of the spiders¹⁹. These threads can undergo transverse (perpendicular to the thread and the plane of the web), lateral (perpendicular to the thread and in the plane of the web), and longitudinal (along the thread axis) motions¹⁷. The propagation of transverse and longitudinal waves are governed by distinct mechanisms^20,21,22, giving rise to different propagation speeds and damping mechanisms^12,18,23. The overall transmitted frequency by a web may vary from around 100 Hz, which is typical of insect impacts, to peaks ranging from 5 Hz to 50 Hz due to the leg movements of trapped insects, and between 100 Hz and 300 Hz due to fluttering bees and flies. The frequency contents of such signals differ considerably from those that may arise due to wind loading, typically below 10 Hz. The unique wave transmission characteristics of spider orb webs must therefore be able to act as mechanical filters for a wide variety of inputs.
In this work, we discuss a possible vibration detection mechanism used by a spider to sense prey impacts using modal decomposition of the web motion. Vibrations are one of many physical quantities used by spiders for sensing¹⁵. Without wishing to address the details of the biology of spider sensing, here, we aim to demonstrate through mathematical and physical considerations the feasibility of using vibrations in a spider orb web for effective prey impact localization, and its compatibility with existing experimental data⁶. We use the modal expansion of Green’s function to construct a semi-analytical source signal created by an impact. . Then, the visibility of the spider to this signal is addressed with Green’s function composition methods, allowing the web motion to be analyzed at the location of the spider legs. This imaging method has recently been validated with experiments on thin elastic plates²⁴. In the present study, the designed numerical web uses prestressed truss elements and nonlinear geometry effects to model realistic transverse elastic properties for such structures. We show that this approach can clearly highlight the influence of prestress, which drives the transverse rigidity; we also assess the role of imperfections within the web geometry, which help to split the degenerate modes of the structure; finally, we discuss the role of the spider position in terms of the overall imaging capabilities of the spider/web system. This work complements an extensive body of evidence that documents the optimization of structures for vibration control found in Nature²⁵.
The orb web model is built using thin threads, combining various structural elements in a deliberately asymmetrical (i.e. more realistic) assembly. The first element is a structural frame that surrounds the web, built in an irregular octagonal shape, included in a 40 cm diameter circle (the 8 corner points of the octagon are at equal distances from the center). The second element of the assembly is an ensemble of radial threads built from an off-center small circle inside the previously designed octagonal shape, connected to the surrounding structure (light brown in Fig. 1a) with a constant angular distribution of the threads. The third element of the assembly are the spiral threads (light blue in Fig. 1a), built as a spiral of maximum radius of 30 cm, starting at the small off-center circle, with an angle-varying radius, allowing a smaller step in the outer part of the spiral than in the center, with an additional randomness value, conferring a more realistic appearance to the obtained orb web. The overall resulting geometry is depicted in Fig. 1a. This is the original, unstrained geometry, i.e., before any applied prestress.
The web structure is mechanically modeled with the Finite Element software COMSOL Multiphysics using prestressed truss elements, with the inclusion of geometrical nonlinearity effects. Prestress values induce a “stress stiffening” effect, where the transverse elasticity of a thread is directly proportional to the tensile force acting on it. Geometrical nonlinearity allows the inclusion of large strain values and geometrical deformations. Similar to the case of a string, if the axial stress is zero or negative, the transverse stiffness of a truss is zero²⁶. The final stretched web acts, therefore, as a transverse resonator. The overall modal response of the web is investigated using eigenvalue analysis. The numerical modeling is thus based on the hypothesis that the original nonlinear problem can be treated as a linear eigenvalue problem: despite the large displacement amplitude induced by the prestress and geometrical nonlinearity, the modal vibrations occur around this new deformed state with small vibration amplitudes (i.e., dynamic displacements are small compared to the prestress-induced static displacements). This means that the dynamic amplitude does not affect the rigidity of the structure, which is essentially due to static forces. In order to include a representative mechanical response of the numerically designed orb-web, we associate for the surrounding frame and axial threads elements (light-brown color in Fig. 1a) and to the spiral threads (light-blue color in Fig. 1a) the mechanical and structural parameters indicated in Table 1.
From²⁷, the nonlinear stress/strain law for the silk suggests a non-constant value for the Young’s modulus, with an early transition to plasticity. The use of realistic stress values and elastic properties for the silk requires the integration of a complete nonlinear material law in order to obtain the global deformation and stress of the total structure observed in Nature. In the present study, we use the Young’s modulus value in the plastic zone, i.e., around 100 MPa. In this manner, the final stress value supported by the thread is coherent with previously published results²⁸, with no need to add more complexity to the simulation box. In addition, the selected value for the Poisson’s ratio does not influence the simulations, as the transverse elastic properties of the web are only determined by the stress values in the truss and thus, by its Young’s modulus.
The structure is initially stretched from the eight points that surround the structure (black dots in Fig. 1a) by a set of pre-determined forces, acting from the center of the web to the exterior. As the pulling points are not equally spaced, the set of forces needs to be determined so that their sum is zero, to avoid rigid-body motion. The following expression for the set of forces acting on the web is considered,
where (x_i) values are the equilibrium parameters that we choose to fix in the ]0.81.2[ interval and (F_0) is the global force amplitude. Projection on the x and y axes of this cumulative set of forces should be zero, which leads to the following cost function to be minimized:
Figure 1b provides the graphical representation of this set of forces after determining the 8 parameters (x_i) in a geometrical frame, centered on the radial thread origin (off-center circle). To find the solution, we use a stochastic population-based algorithm (i.e., a genetic algorithm) that searches randomly by mutation and crossover among population members. The solution is not unique, however, once one set of (x_i) is found, the global force amplitude can be adapted with the (F_0) parameter.
After applying with the calculated forces on the structure with a 2 mN amplitude for the (F_0) value, the final geometrical state of the web differs from initial one. In Nature, a spider will construct the radial threads and apply a stress to them before adding the spiral threads. This differs from our procedure where the entire structure is built simultaneously. However, this should not influence the numerical results significantly. To prevent local compression arising during the pulling phase of the web, an initial and homogeneous prestress is globally applied to all of the threads of the structure with a small value (additional to the final stress) of (sigma _0 =) 10 kPa. The final geometry and stress state for the structure are depicted in Fig. 1c. The curved profiles of the threads that appear around the web are due to nonlinear geometrical effects. The stress distribution inside the web is influenced by both global prestress and applied forces. A high level of stresses (up to 60 MPa) is reached.
(Color online) Design of the orb web. Light blue lines are the spiral threads (r_t). The light brown line is the radial thread (s_t). (a) Initial, unstressed geometry. (b) Radial force distribution in the web. The equilibrium point should satisfy (Sigma _i {mathbf {F}}_i = {mathbf {0}}), with i=1..8. (c) Final equilibrium configuration considering geometrical nonlinearity and stress values in color scale. Pictures and maps are made with (hbox {COMSOL}^{{mathrm{TM}}}) 6.0 and (hbox {MATLAB}^{{mathrm{TM}}}) R2022b softwares https://www.comsol.com/livelink-for-matlab.
Eigenfrequency analysis is performed on the prestressed structure, after the quasi-static traction. The final outputs for this study step are then the resonant frequencies (f_n) and the orthonormal modal shapes (phi _{in}), where n indicates the mode index, and i a mesh point index in the discretized and unstrained web domain. Both quantities are dependent of the applied forces from the previous study. Summing over repeated i indices, the modal orthogonality implies that (phi _{ni}^{scriptscriptstyle dag }phi _{in’} = delta _{nn’}) where ((cdot )^{scriptscriptstyle dag }) indicates the complex conjugate transpose and (delta _{nn’}) is the Kronecker delta function. Figure 2 shows the first 16 eigenmodes of the simulated structure in a prestressed state. The image displays the motion of the orb web in the deformed geometry frame considering the transverse normalized displacement field. The frequency range of the modes predicted with the simulation box agrees with in-situ experimental work on real orb webs^29,30.
(Color online) Vibration eigenmodes of the spider web, modeled by pre-stressed trusses with geometrical nonlinearity. Pictures and maps are made with (hbox {COMSOL}^{{mathrm{TM}}}) 6.0 and (hbox {MATLAB}^{{mathrm{TM}}}) R2022b softwares.https://www.comsol.com/livelink-for-matlab.
To highlight the limitations of neglecting the changes in geometry in the eigenvalue analysis, we can consider the analytical expression of the fundamental resonant frequency for a string:
where L is the string length, (rho _l) is its mass per unit length, and T the tension acting on it. If the pulling force increases, the relative change of frequency (f_0) can be estimated (neglecting the changes in the bulk density due to deformation) as follows:
As a consequence, two opposite effects appear when increasing the pulling forces on the web: an increase of stress that leads to an increase stiffness and hence resonant frequency, and an increase of strain, i.e. in the structure length, which tends to decrease the resonant frequency. This last term is not taken into account in the simulation box, as the modal analysis is performed in the reference frame attached to the material. With the large deformations of the web, we estimate that around 10(%) of the relative variations of the eigenfrequencies are due to the geometric deformation ((delta L /L simeq 0.1)). In addition, silk is a highly nonlinear material, which suggests various possibilities for the tunability of the structure. The term (delta T/T) is also simplified here to linear prestress. This simplification may be justified with the following remark: at the beginning of the plastic zone, the apparent Young’s modulus of the silk is constant in the 0.15-0.25 strain range²⁷, meaning that material nonlinear effects should be negligible in this zone. In conclusion, although the exact strain and stress states in the web cannot be derived, we will suppose that modal analysis can accurately describe its dynamical response, for a given prestress state.
To further study the vibration transmission properties of the web, an imaging method, based on a modal expansion and Green’s function composition³¹, allows us to place ourselves from the spider’s point of view. This approach is based on the fact that a spider has 8 legs and is extremely sensitive to vibrations^32,33,34. By treating each leg as an independent sensor, the spider can accumulate the information from several modes of vibration of the web, excited following the impact of a prey.
The mode shapes (phi _{in}) (Fig.2) can be used a posteriori to compute virtual sources and estimate their visibility to the spider as a function of its position on the web. For a source located at point i, the broadband motion induced in a point indexed j can generally be expressed as^31,35,36,37:
where (phi _{i n}) denotes the motion induced by the mode n at point i. This is a real function, representing a standing wave in space. As Eq. (5) remains true for complex mode shapes, we use here complex conjugate notation (^{scriptscriptstyle dag }). We also remove time dependency in Eq. (5) and neglect damping effects, meaning that this equation is valid equivalently for particle displacement, velocity or acceleration. The number of modes n dictates the spatial resolution. With an infinite number of modes, the Green function tends to a Dirac function in space. With a finite number of modes, the spatial resolution decrease drastically. Although this approach does not attempt to model the temporal evolution of a real mechanical impact, focusing only on its kinematic consequences, the theoretical expansion in Eq. (5) remains exploitable in real experiments for active source localization²⁴. The capability of the spider to detect sources can then be estimated using a composition of the Green’s function between the source i, a subset of points r and the set of points j of the domain defined by the web. This composition, according to the notations used in Eq. (5), is written as:
where (B_{nn’}) is the so-called visibility matrix. If the implicit summation in Eq. (6) is performed on the whole domain, the spatial orthogonality of the eigenmodes implies that (B_{nn’}) is an identity matrix. Instead, when only a limited number of points “r” is used for the composition of Eq. (6), an artificial coupling appears between the modes, affecting the reconstruction of the source image. In addition, the number of modes n dictates the spatial resolution. With an infinite number of modes, the Green function tends to a Dirac function in space. With a finite number of modes, the spatial resolution decreases drastically. In the case of the spider/spiderweb system, Eq. (6) is evaluated for a limited number of measurement points r, coinciding with the contact points of the eight legs and in our case using only sixteen modes. The expected spatial resolution is therefore imperfect, but sufficient for the purpose of prey localization. It is therefore possible to simulate the spider’s ability to localize prey as a function of its position on the web. To summarize, Eq. (6) combine two Green functions which correspond: i) to the vibration signal induced by the prey’s impact ((G_{ir})) and ii) to the mechanical representation that the spider produces of the web from its leg locations ((G_{rj})). The matrix (B_{nn’}) may be seen as an autoMAC criterion³⁸. It gathers the conditions for the source reconstruction from the spider’s point of view.
Figure 3 shows the calculated imaging results (in terms of normalized displacements) for an off-center impact point in two cases, i.e. when the spider is located centrally in the web, and when its position is off-center. In both cases, the spider legs are chosen to lie around the spider location with a constant azimuthal distribution ((simeq 2pi /9)) and they are considered perfectly attached to the radial threads. The color map illustrates the reconstructed amplitude of the elastic source created by the impact of a prey with the vibration amplitude reported in the −1/1 range. As only 16 modes are used, the spatial resolution is better over the azimuthal direction than along the radial one, creating this red cone in Fig. 31-a. Increasing the number of modes could help to better localize the prey, but would also increase outer diagonal values in the (B_{nn’}) matrix, leading to additional errors in the source reconstruction. In the first case, the prey impact point (indicated by a black dot) is faithfully reproduced, with a spatial uncertainty that is related to the finite number of modes used to build the image. Indeed, only one web aperture is highlight by the imaging process (in red on Fig. 31-a). In the second case, the prey position cannot be properly reconstructed with many apertures created by the imaging on Fig. 31-b. In Figs. 31-a and 2-a, the graphical representation of the spider is visual and is not included in the simulation. The positions of its eight legs are used as analysis points. A slight eccentricity of the web is accompanied by a deterioration of the virtual source reconstruction. The quality of the image can quantitatively be accessed with the (B_{nn’}) matrix, defined in Eq. (6) and represented graphically in Fig. 31-b, 2-b for the two considered cases. Large non-diagonal values indicate cross-talk between modes and thus incorrect imaging of the source.
(Color online) Effect of the position of the spider on its detection capacity. Case 1, panel (1-a) the spider is in the center and the source (black dot) is correctly detected. The color code and the web deformation quantify the normalized displacement field, induced by the source, as reinterpreted by the spider. The absolute value of the visibility matrix (vert B_{nn’} vert) in panel (1-b) shows small out-of-diagonal values. In Case 2, panel (2-a) the spider is off-center and the source is not correctly imaged. The visibility matrix (in absolute value) in panel (2-b) shows larger out-of-diagonal values, indicating cross-talk between modes. Pictures and maps are made with (hbox {COMSOL}^{{mathrm{TM}}}) 6.0 and (hbox {MATLAB}^{{mathrm{TM}}}) R2022b softwares. https://www.comsol.com/livelink-for-matlab.
Although vibration sensing is by no means the only source of information for spiders in hunting prey, and possibly not even the most important, the results presented above suggest that spiders are capable of recognizing the different vibration modes supported by the web. The very structure of the web could be somehow related to the modal distribution required for optimal structural monitoring.
In particular, from the developed simulation box and proposed data analysis, we observe that the fundamental mode of the web does not contribute to the final image of the prey. From Fig. 2, one can see that if the fundamental mode is well isolated in frequency from other modes (around 40 Hz, in our case), the modal density subsequently increases, and can be estimated as around 1 mode / 2 Hz. This particular modal density could occur by design. Indeed, as the fundamental mode is not necessary to construct an image, it may be used only to capture the prey after impact, exploiting its large damping properties, without overlapping with higher modes that are used to locate the prey. This first mode may also be used for environmental monitoring. Indeed, it is the only mode that presents maximum vibration amplitude at the center and thus, at the spider location. Therefore, it may be used to amplify external sources of noise, increasing the spider sensitivity to its environment⁹.
The actual effect of the spider on the vibration response of the web is neglected in this work. The spider introduces additional mass to the system, but also additional stiffness, since its legs are much more rigid in flexion than the silk. Analysis of the modal participation factor associated for each mode indicates that the fundamental mode at 40Hz is the most affected by the mass of the spider, whereas the other modes may be more affected by the additional rigidity. Indeed, the web center corresponds to a maximum of vibration for the fundamental mode but is at a node location for all other modes. Thus the modeling of the spider is possible but would add complexity to the system and require the use of further hypotheses in its physical description, i.e., of the silk as pre-stressed truss elements and of the spider in terms of beams subjected to bending. This will be the object of a future study.
In this work, we have constructed a qualitative mechanical model of a spider orb web, including prestress and geometrical nonlinearity. We have shown that this system acts as a multimodal transverse resonator system, naturally designed for prey impact detection. The resulting outputs of the modeling, such as resonance frequencies and prestress values within the structure are consistent with previously reported experimental data. Then, using modal expansion and Green’s function composition methods, we have proposed an imaging mechanism that could be used by the spider to exploit the vibration of its web, measured by its eight independent legs, to detect and localize prey. These results can be adapted both for practical applications in elastic wave imaging (e.g. real-time impact detection for structural health monitoring in frame-like structures) and material design problems. They also provide additional insight and understanding of the fascinating ways in which vibration phenomena are exploited in Nature.
The datasets used and analyzed during the current study available from the corresponding author on reasonable request.
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All authors are supported by the EU H2020 FET Open “Boheme” Grant No. 863179. G.G. was supported by Caritro Foundation (Prot. U1277.2020/SG.1130).
Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy
Martin Lott & Federico Bosia
Laboratory for Bioinspired, Bionic, Nano, Meta Materials and Mechanics, University of Trento, Trento, Italy
Vinicius F. Dal Poggetto, Gabriele Greco & Nicola M. Pugno
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M.L. conceived the simulation box and the source detection model. All authors contributed to the discussions and to the review of the manuscript.
Correspondence to Martin Lott.
The authors declare no competing interests.
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Lott, M., Poggetto, V.F.D., Greco, G. et al. Prey localization in spider orb webs using modal vibration analysis. Sci Rep 12, 19045 (2022). https://doi.org/10.1038/s41598-022-22898-3
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Mark Henry – senior mixer – was also kind enough to offer some insight, “We’re already feeling the benefits of our new system while we complete mixing on Smother Season 3 for RTE and BBC. Workflows have been streamlined allowing us more time to get creative in the mix. Exporting of files for remote approval has never been quicker and easier which is so helpful post Covid as we’re all adjusting to newer and more efficient ways of working.”
“We’re really excited about starting season two of Kin for RTE and AMC shortly.”
“Our newly upgraded ADR/VO booths with dedicated lipstick cams and Zoom feeds for the talent make it easier to run remote sessions and we’ve already ran ADR and animation record sessions for an impressive roster of clients including HBO, Netflix and Paramount.”

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Physical health status defines an individual’s ability to perform normal activities of daily living and is usually assessed in clinical settings by questionnaires and/or by validated tests, e.g. timed walk tests. These measurements have relatively low information content and are usually limited in frequency. Wearable sensors, such as activity monitors, enable remote measurement of parameters associated with physical activity but have not been widely explored beyond measurement of daily step count. Here we report on results from a cohort of 22 individuals with Pulmonary Arterial Hypertension (PAH) who were provided with a Fitbit activity monitor (Fitbit Charge HR^®) between two clinic visits (18.4 ± 12.2 weeks). At each clinical visit, a maximum of 26 measurements were recorded (19 categorical and 7 continuous). From analysis of the minute-to-minute step rate and heart rate we derive several metrics associated with physical activity and cardiovascular function. These metrics are used to identify subgroups within the cohort and to compare to clinical parameters. Several Fitbit metrics are strongly correlated to continuous clinical parameters. Using a thresholding approach, we show that many Fitbit metrics result in statistically significant differences in clinical parameters between subgroups, including those associated with physical status, cardiovascular function, pulmonary function, as well as biomarkers from blood tests. These results highlight the fact that daily step count is only one of many metrics that can be derived from activity monitors.
Wearable activity sensors enable remote monitoring of an individual’s physical activity, but have been largely limited to assessment of average daily step count. Walking, or ambulating, is a fundamental movement of daily life and has become an important metric in promoting human health¹. For example, increasing daily step count (from <4000 to ≥12,000) is associated with a decrease in all-cause mortality^2,3. In hospitalized patients, daily step count thresholds (typically < 1000 steps per day) have been associated with poor outcomes, such as readmissions^4,5,6. Related ambulation parameters, such as gait speed^7,8,9 and timed walk tests^10,11, have also been found to be predictive of clinically relevant outcomes.
Historically, remote monitoring of an individual’s physical status has been challenging, however, advances in wearable technology have enabled continuous assessment following surgery, or between clinic visits for patients with chronic diseases. Wearable inertial measurement units (IMUs), such as Fitbit devices, record step count along with other metrics derived from the IMU signals (e.g. sleep) that can be viewed in the associated smart phone app. In addition, many wearable devices, such as Fitbit, use photoplethysmography to measure heart rate.
Step count, and particularly daily step count, remains the most common metric for remote assessment of physical activity, however, minute-to-minute step count and heart rate data can be downloaded from the Fitbit server using their application programming interface (API). Therefore, for an individual who wears a Fibit continuously, 10,080 values of step rate (units: steps per minute, SPM) and heart rate (units: beats per minute, BPM) can be obtained over one week, each point representing the average value of step rate and heart rate for that minute. While the accuracy of step count measurements in free-living settings and in patient populations with atypical gait patterns remains a concern^12,13, studies in individuals with cancer, cardiovascular disease, pulmonary arterial hypertension, and multiple sclerosis suggest that these devices can provide accurate and clinically relevant data^14,15,16,17. Similarly, in comparison studies, heart rate measurements from Fitbit devices general show good agreement with electrocardiograms for individuals at rest or at low activity levels^18,19. However, other factors such as skin pigmentation may also influence measurement accuracy²⁰.
The objective of this study was to show that clinically-relevant metrics, beyond daily step count, can be derived from wearable activity monitors. There is a large resource of untapped information contained within the data from these devices, enabling a much more granular fingerprint of an individual’s activities of daily life. Here we present results from analysis of 22 individuals with Pulmonary Arterial Hypertension (PAH) who were each provided with a Fitbit device between two clinic visits. From minute-to-minute step rate and heart rate data we derived a range of parameters associated with physical activity during free-living, including metrics associated with the weekly heart rate and step rate distributions, parameters related to the intensity, length, and frequency of ambulations, an analog of the Physical Working Capacity test to assess fitness, a free-living 6-minute walk distance (FL6MWD), as well as weekly usage metrics. We also considered a metric of health state based on comparison of the FL6MWD to predicted values for healthy individuals with the same age, gender, and BMI as the subject. Principal Component Analysis and Latent Profile Analysis were used to identify subgroups of patients based on Fitbit metrics.
At the clinic visits a maximum of 26 measurements were recorded (7 continuous and 19 categorical), including assessment of health related quality of life (HRQOL) and WHO Functional Class, the presence or absence of various symptoms, and assessments of organ function. Continuous variables included heart rate measurements, six minute walk test (6MWT), right ventricular systolic pressure (RVSP), and three biomarkers from blood tests. To assess the potential for clinical relevance, we used a thresholding approach to compare clinical parameters between the two subgroups. We show that many Fitbit-derived metrics can be used to identify subgroups with differences in clinical parameters associated with physical status, cardiovascular function, pulmonary function, as well as biomarkers from blood tests. In addition, we show that several of the Fitbit metrics were strongly correlated with continuous clinical parameters. Overall, we show that Fitbit-derived metrics can provide insight into an individual’s activities of daily life, and have the potential to support decision making and clinical care.
We analyzed 3.5 × 10⁶ min of Fitbit data for 22 individuals with PAH between two outpatient clinic visits with an average of 18.4 ± 12.2 weeks for each subject (total 405 weeks). The average age of the subjects was 50.6 ± 13.4 years old (mean ± SD), with 3 males and 19 females. In most cases, data were analyzed in weekly blocks from Sunday to Saturday. From the weekly data we obtained a maximum of 10,080 values (100% usage) of step rate (units: steps per minute, SPM) and heart rate (units: beats per minute, BPM). The distribution of step rates (SR) over each week (excluding SR = 0) typically followed a log normal distribution (Fig. 1a), from which we extracted mean, standard deviation, and skewness. For these subjects, the maximum step rate was typically around 100 SPM, spanning medium walking (80–99 SPM) and brisk walking (100–119 SPM)²¹. For active healthy individuals additional peaks are usually observed in the step rate histograms in the 100–120 SPM range, corresponding to brisk walking, and in the 150–180 SPM range, corresponding to running²¹. We note that cadence analysis is widely used to assess exercise intensity in free living environments in a wide range of populations^21,22,23. The means of the weekly step rate histograms for each subject were 13.6–32.8 SPM, with a standard deviation in the range 10.2–30.3 SPM. The skewness varied from 1.19–2.55, showing that there was a moderate to large increase in density to the right of the most probable value. As a comparison to the commonly used daily step count, the average daily step count was in the range 1338–10,679 steps, with an average of 5729 steps per day (Supplementary Fig. 1).
a Distribution of minute-to-minute step rate (SR) (units: steps per minute, SPM). Red line shows a log normal fit. b Distribution of heart rate (BPM) for all minutes where SR = 0. Red line shows a normal fit. c Distribution of heart rate (BPM) for all minutes where SR > 0. Red line shows a normal fit. d Weekly activity map: scatter plot showing heart rate versus step rate. Each point represents one minute where a physiological heart rate was recorded. The grey lines show the upper and lower envelopes of the activity map. The blue line shows a linear least squares fit to the data.
To assess the potential for clinical significance, we used a thresholding approach. We first divided the subjects into two groups based on a threshold value, and then compared the 26 clinical parameters (Supplementary Table 1) between groups. We compared individuals with average daily step counts >5000 steps (14/22) to those with <5000 steps (8/22). This arbitrary threshold resulted in 6 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 2). Subjects with <5000 steps per day had lower 6MWD at visit 1, lower hemoglobin levels at visit 2, poorer pulmonary health (higher physician-assessed WHO FC) at visit 1, and experienced more pedal edema (Pedal Edema score) at visit 2. Two subjects had average daily step counts >10,000 steps per day (PAH 1, 19), but had no other similarities. Sensitivity analysis of threshold values and the number of statistically significant clinical parameters for all Fitbit metrics are provided in Supplementary Figs. 3 and 4.
The minute-to-minute heart rate data for each week were separated into heart rate at SR = 0 (HR(SR = 0), i.e. no physical activity) and heart rate at SR > 0 (HR(SR = 0), i.e. active). Histograms for HR(SR = 0) (Fig. 1b) and HR(SR > 0) (Fig. 1c) were described by normal distributions, from which we obtained the mean, standard deviation, and skewness. The range of mean HR(SR = 0) was 66.2–111.8 BPM, with standard deviations of 6.4–13.7 BPM (Supplementary Fig. 5). The skewness varied from −0.75 to 2.30, highlighting a broad range of behavior with relatively large tails to the left and right of the peak (Supplementary Figs. 6 and 7).
The distribution of HR(SR = 0) represents all occurrences of zero step rate and may represent various postures under a range of resting conditions (e.g. transient or sustained). To relate HR(SR = 0) to resting heart rate (RHR), we considered two conditions: the mean value and the average of the lowest 10 values of HR(SR = 0). A previous study found that individuals with PAH with RHR below 82 BPM had significantly longer overall event-free survival during a median follow-up period of 37 (18–64) months²⁴. In the study, the RHR was measured at a clinic visit during a stable period of at least 15 min of recumbent rest, but is likely higher than the true resting heart rate (see below). We compared subjects with mean values of HR(SR = 0) <82 BPM (14/22) to those with >82 BPM (8/22). This resulted in 8 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 8). Subjects with lower mean values of HR(SR = 0) had lower RHR at visits 1 and 2, and lower peak heart rate at visit 2, but experienced more pedal edema (Pedal Edema score) and more palpitations (Palpitation score) at visit 1, were less able to perform usual activities (lower EQ-5D Usual Activity scores) at visit 1, and experienced more pain/discomfort (lower EQ-5D pain/discomfort scores) at visit 1.
Two subjects (PAH 1,4) had a mean HR(SR = 0) >100 BPM. Both subjects had low fitness slopes (see below), suggesting that they did not access a wide range of heart rate during daily activities. However, PAH 1 had the highest average daily step count in the dataset. We note that 3 subjects (PAH 4, 20, 27) removed the device overnight (see below), which may have resulted in higher mean HR(SR = 0) values since heart rate values during sleeping were likely not included.
The true resting heart rate (RHR) is usually defined as the value obtained in a supine position immediately after waking but before getting out of bed²⁵. To obtain a value similar to the true RHR we calculated the average of the lowest 10 values of HR(SR = 0); we assumed that the 10 lowest values recorded during each week are most likely obtained while supine and resting for an extended period. The range of the average lowest weekly HR values was 50.3–69.2 BPM (Supplementary Fig. 5). A recent study of >90,000 individuals over 35 weeks, reported that the RHR (assumed to be the true RHR) was dependent on age, BMI and sleep duration, with daily values of RHR from 40–108 BPM²⁵, although 95% of men and women had RHR values between 50–80 BPM, similar to the range found here.
We compared individuals with skewness of HR(SR = 0) <1 (11/22) to those with skewness >1. This resulted in 4 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 9). Subjects with lower skewness values were more likely to have higher resting heart rate at visits 1 and 2, experienced less pain/discomfort (lower EQ-5D pain/discomfort scores) at visit 1 and were more likely to be in better health (higher EQ-5D Index) at visit 1. Two subjects had skewness of HR(SR = 0) values >1.9 (PAH 27, 28): both subjects also had relatively low resting heart rates, longer free-living 6MWD, and higher fitness plot slopes.
The heart rate at SR > 0 represents HR values while subjects were active. The mean values of HR(SR > 0) were 78.6–121.0 BPM (mean 94.4 BPM), and the standard deviation was 6.5–14.0 BPM (Supplementary Fig. 10). The mean values were only slightly higher than the mean values of HR(SR = 0), although the standard deviations were similar. The mean skewness values for HR(SR > 0) were from −0.57 to 1.35, similar to the range for HR(SR = 0). We compared individuals with mean values of HR(SR > 0) <95 BPM (12/22) to those with >95 BPM, resulting in 4 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 11). Subjects with lower mean values of HR(SR > 0) had lower RHR at visits 1 and 2, lower albumin levels at visit 1, and experienced more palpitations (lower Palpitation score) at visit 1.
All of the weekly data can be represented on a scatter plot which maps out an individual’s weekly activity on a minute-to-minute basis (Fig. 1d). These activity maps are approximately triangular with relatively high density of points at low step rates and decreasing density as the step rate increases. Other parameters derived from the minute-to-minute data included assessment of fitness based on the Physical Working Capacity 170 (PWC 170) test, metrics associated with weekly ambulation, free-living 6-minute walk distance (FL6MWD), and device usage.
To identify subgroups within the subject population we performed principal component analysis (PCA). Five parameters were selected for analysis: the mean and standard deviation of the step rate histogram, the standard deviation of HR at SR > 0, the mean HR at SR = 0, and the fraction of time inactive (Fig. 2a). The data points for each week for most subjects were tightly clustered in distinct regions. From the loading plot (Fig. 2b), PC1 is dominated by the step rate parameters (+PC1) and the fraction of time inactive (−PC1). PC2 is dominated by the mean heart rate at SR = 0 (+PC2) and the standard deviation of the heart rate for SR > 0 (−PC2). The group of subjects in the fourth quadrant (PAH 3, 9, 12, 19, 23, 27) are characterized by high mean and standard deviation of the step rate, and a high value of the standard deviation of the heart rate at SR > 0. This implies that these individuals exhibit a wide range of step rates and a wide range of heart rates during normal activities of daily life. The group of subjects along the positive y-axis (PAH 1, 10, 14, 17) are characterized by high mean heart rate at SR = 0. High values of HR(SR = 0) imply that these individuals have a high resting heart rate and are unlikely to access a wide range of heart rates during normal activities, even if they have the capacity for moderate or high step rates. The group of subjects along the negative x-axis (PAH 2, 7, 11, 13, 20, 21, 30) are characterized by a large fraction of time inactive. Three subjects (PAH 15, 26, 28) are clustered around the origin. The PCA plot suggests a range of behavior with distinct combinations of metrics associated with heart rate and step rate. To explore these relationships in more detail, we assessed several derived parameters. Distinct groupings of subjects were found for mean HR(SR = 0) >82 BPM, skewness of HR(SR = 0) <1, ambulation product, P > 1000, and fitness slope >0.15 (Supplementary Fig. 12).
a PCA scatter plot of the first two principal components. For each subject (N = 20), 10 weeks were randomly selected from the dataset. The variance for the first two principal components were 48.6% and 30.0%, respectively. For 100 independent runs, the mean variance of PC1 and PC2 was 77.5 ± 0.58%. Numbers represent subject IDs. Each point represents one week of data. b Loading plot. HR(SR = 0):mean is the mean value of the heart rate at SR = 0; HR(SR > 0):SD is the standard deviation of the heart rate at SR > 0; SR(SR > 0):mean is the mean step count for SR>0; SR(SR>0):SD is the standard deviation of the step rate for SR > 0; time active is the fraction of minutes with SR = 0.
To derive a metric related to physical fitness from the Fitbit data we determined the mean step rate, in 20 SPM bins, and the mean heart rate in that bin. Assuming that the step rate is related to power output, this approach is similar to the Physical Working Capacity PWC170 protocol, where the slope of a power vs. heart rate curve is used to predict the power output at 170 BPM as a measure of fitness. An example from a weekly data set shows that the mean heart rate generally increases with increasing step rate (Fig. 3a). It is also evident that the extrapolated heart rate at SR = 0 is relatively high, about 103 BPM. The fitness plot averaged over all weeks of data was almost identical to the example week (Fig. 3b), showing that there was only small weekly variation. The fitness plots for all subjects (Fig. 3b) spanned a wide range, with intercepts from 73–120 BPM (Fig. 3c) and slopes of 0.02–0.31 BPM/SPM (average = 0.15 BPM/SPM) (Fig. 3d). In general, individuals with a low heart rate at SR = 0 accessed a broader range of heart rates with increasing activity level (step rate) and hence had higher slopes.
a The average step rate and corresponding average heart rate in 20 SPM bins for PAH 14 in week 11. Bars represent mean ± SD. b Mean step rate versus mean heart rate plots averaged over all weeks for each individual. c Fitness intercept (BPM) and d fitness slope (BPM/SPM) obtained from a linear least-squares fit to the HR-SR plots for each individual. Blue bar–mean; green bars–upper and lower quartiles.
Comparison of subjects with fitness slope >0.15 (11/22) to those with slope <0.15, resulted in 3 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 13). Notably, subjects with slopes >0.15 had lower NT-proBNP levels at visits 1 and 2. B-type natriuretic peptide (BNP) and N-terminal pro b-type natriuretic peptide (NT-proBNP) are biomarkers for cardiac stress, and PAH patients with NT-proBNP levels below about 300 pg L⁻¹ are considered low risk for heart failure²⁶. The mean levels for subjects with slope >0.15 at visits 1 and 2 were 188 ± 180 and 145 ± 165 pg mL⁻¹, respectively. These results suggest that the fitness slope may be a useful indicator of NT-proBNP levels and risk for heart failure. Comparison of subjects with fitness intercepts above (10/22) and below (12/22) the mean (91 BPM) were similar to results for subgroups with HR(SR = 0) above and below 95 BPM.
We defined an ambulation as a period of at least 2 min with SR ≥ 60 SPM, which corresponds to slow walking or faster²³. A 2-minute duration was selected since the 2-minute walk test (2MWT) is widely used to assess functional capacity^27,28. From the number of weekly ambulations we obtained metrics for frequency, endurance, and intensity. The average ambulation frequency for all subjects was in the range 1.6–96 ambulations per week. A measure of a subject’s endurance was obtained from the 1/e value of an exponential fit to the histogram of weekly ambulation durations (Fig. 4a). Therefore, individuals with longer duration ambulations would be considered to have greater endurance. Endurance (1/e) values were between 2.2–7.0 min. The longest individual ambulation duration was 70 min (PAH 9). A measure of ambulation intensity was obtained from the standard deviation of the weekly step rate histogram (Fig. 4b), i.e. how far above the mean value: values ranged from 10–30 SPM. In general, the ambulation frequency was higher for shorter durations and intermediate values of step rate (Fig. 4c).
Representative ambulation metrics for PAH 14 in week 11. a Frequency of weekly ambulations of ≥2 min with sustained SR ≥ 60 SPM. Endurance was defined by the 1/e value of an exponential fit to the histogram. b Ambulation intensity was defined by the standard deviation of the step rate distribution. c Heat map showing ambulation frequency on a plot of step rate versus ambulation duration. d Violin plot showing average values of ambulation product P (=frequency × endurance × intensity) for all subjects. Blue bar–mean; green bars–upper and lower quartiles.
To compare individuals, we defined the ambulation product P as frequency × endurance × intensity. Average values for all subjects varied from 42.8 to 10,845.3 (P_mean = 1910) (Fig. 4d). Comparison of subjects with P > 1000 (12/22) to those with P < 1000, resulted in 7 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 14). An ambulation product value of 1000 was selected as it was close to the median value (1079), and represented a well-defined separation between the two groups (Fig. 4d). Subjects with P < 1000 had lower 6MWD at visits 1 and 2, and experienced more pedal edema (Pedal Edema score) at visit 1. Two subjects had ambulation product values > 5000 (PAH 9, 19). Both subjects had a high ambulation frequency and walked more than 5000 steps per day on average. Both subjects also had relatively lower resting heart rates, longer free-living 6MWD (see below), and higher fitness plot slopes. PAH 1, despite having the highest step count, ranked fourth in ambulation product value as a result of having relatively lower endurance and intensity values.
Usability and compliance with usage are critically important in deploying devices in free-living settings. Since a measured heart rate (i.e. 20 ≤ HR ≤ age predicted maximum heart rate) implies that the device is worn, we defined usage as the fraction of minutes during a week with a physiological heart rate value (i.e. minutes worn/10,080). The fraction of minutes outside this range was very small (4.2 × 10^–7%), and hence in most cases it may be reasonable to use all recorded data points (i.e. HR > 0) for analysis. In this study the average weekly usage was 0.44–0.97. Note that charging the device overnight (e.g. 8 h) once a week results in a weekly usage of 0.95. We also defined the maximum off-time as the longest continuous time during the week that the device was not worn, which varied from less than 1 h to more than 12 h. From heat maps of usage and the maximum off-times for all subjects (Supplementary Figs. 15 and 16) we can further infer how the device was used.
As an example, the usage heat map for PAH27 (average usage = 0.49) (Fig. 5a) shows that the device was consistently not worn overnight but was routinely worn during the day, resulting in a maximum off-time of around 12 h for each week (Fig. 5b). The heat map for PAH30 (average usage = 0.90) (Fig. 5c) shows that the device was not worn overnight approximately every 7 days, likely for overnight charging. The maximum off time (Fig. 5d) varied from 2–20 h, but for most weeks was 7–12 h, consistent with overnight charging. For PAH10 (average usage = 0.97) the heat map (Fig. 5e) indicates that the device was worn almost continuously except for 2 h in week 10 and 24 h in week 13 (Fig. 5f). The frequent partial usage hours from 06:00 to 07:00 suggest that the device was taken off to charge for less than one hour in the morning. Many subjects removed the device overnight approximately every 7 to 10 days, presumably for charging. Three subjects (PAH 14, 20, 27) consistently removed the device overnight. Three subjects (PAH 10, 19, 26) showed regular partial usage for about an hour, either in the morning or the evening, likely for charging.
Heat maps show usage for each hour of each day during the trial. The legend indicates the fraction of an hour that the device was worn with HR > 0. Yellow cells indicate that the device was worn continuously for the full hour. White cells indicate that the device was not worn (no HR recorded) for the full hour. a Heat map for PAH27 (13 weeks of data), showing low usage (average = 0.49) with the device not worn overnight. b The maximum off time for each week for PAH27 is consistently around 12 h overnight. Each point represents the maximum off-time for each week in the trial. c Heat map for PAH30 (22 weeks of data), showing relatively high usage (0.90), with the device removed for several hours every few days. d The maximum off time for PAH30 is typically 8–20 h and includes overnight hours. e Heat map for PAH10 (13 weeks of data), showing high usage (0.97). For the first 10 weeks the maximum off-time is less than 1 h. f The maximum off time for PAH10 is usually less than 1 h.
From the distribution of average usage (Supplementary Fig. 17), 7 of 22 subjects had usage >0.94, which corresponds approximately to the 75th percentile. Comparison of usage, resulted in 4 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 18). Subjects with average weekly usage < 0.94 (15/22) were more likely to have more severe PAH (higher EQ VAS score) at visit 1, worse pulmonary health (higher physician assessed WHO FC score) at visit 1, and experienced more difficulty breathing (modified Borg dyspnea score) at visit 2. Two subjects had average usage < 0.5 (PAH 4, 27), however, both of these subjects removed the device overnight. The third subject who removed the device overnight (PAH 20) also had low average usage (0.60). (Changes in device usage over time are summarized in Supplementary Figs. 19 and 20).
The 6MWT is a sub-maximal exercise test used to assess aerobic capacity and endurance, and was introduced by the American Thoracic Society in 2002²⁹. The 6MWT is widely used in different patient populations^30,31,32, with thresholds for prediction of survival typically in the range 300–350 m for individuals with chronic respiratory diseases, including individuals with PAH³³. Timed walk tests provide information on distance and speed^10,11, but are labor intensive and hence are impractical to implement at high frequency during hospitalization or outside the clinic. At the research level, apps for self-administered 6MWTs have been tested with wearable accelerometers³⁴. We have developed a novel approach for assessment of a free-living 6MWD (FL6MWD) by searching the weekly data for the continuous 6-min block of time with the highest cumulative step count. Step count was converted to distance based on a subject’s gender and height (Supplementary Figs. 21 and 22).
The average values of FL6MWD ranged from 164 m (PAH30) to 478 m (PAH23) (Fig. 6a). The lowest weekly FL6MWD was 85.7 m (PAH30, week 23) and the highest weekly value was 683.1 m (PAH23, week 11). 14/22 subjects had average values >320 m (PAH1, 3, 9, 10, 11, 12, 14, 17, 19, 22, 23, 26, 27, 28). Comparison of FL6MWD resulted in 6 statistically significant clinical parameters (Supplementary Table 2 and Supplementary Fig. 23). Notably, subjects with average FL6MWD < 320 m had lower 6MWD at visit 1 and visit 2, experienced more pedal edema (Pedal Edema score) at visit 2, had worse pulmonary health (higher physician-assessed WHO FC) at visit 1, and had lower hemoglobin at visit 2.
a Violin plot showing distribution of average values of FL6MWD for all subjects. Mean = 344 m. Blue bar–mean; green bars–upper and lower quartiles. b Example of a subject with good agreement between FL6MWD and interpolated clinic values (group 1, “performer”). (Triangles) clinic values, (circles) FL6MWD. The grey line shows the linear interpolation of the clinic values. c Example of a subject where the FL6MWD was lower than the interpolated clinic values (group 2, “underperformer”). (Triangles) clinic values, (circles) FL6MWD. The grey line shows the linear interpolation of the clinic values. d Violin plot of the slope of the FL6MWD (m/week) over time for all subjects. Blue bar–mean; green bars–upper and lower quartiles.
The lowest average FL6MWD was 164 m (PAH30). This subject was the second heaviest (108.7 kg), and had an ambulation P value < 1000. Two subjects had average FL6MWD values > 480 m (PAH3, 23). These subjects were in the fourth quadrant of the PCA plot, which implies that they had a wide range of step rates and heart rates during normal weekly activity, and had ambulation product P values > 1000.
As described above, 6MWD threshold values of around 320 m are predictive of poor survival in PAH patients. In the context of treatment goals, a 6MWD of ≥380–440 m has been proposed for PAH patients^35,36,37. Subjects with average FL6MWD > 400 m (12/22) had higher 6MWD at visit 2, lower NTpro-BNP at visit 2, experienced less chest pain (Angina score) at visit 1, and had better pulmonary health (lower physician-assessed WHO FC) at visit 2 (Supplementary Table 2 and Supplementary Fig. 24).
From comparison of FL6MWD to the values measured at the two clinic visits (see Methods and Supplementary Fig. 25 for details), we identified two distinct groups of individuals. In one group (group 1: “performers”), we found excellent agreement between the FL6MWD and the interpolated value of the clinic 6MWD (Fig. 6b), whereas in the second group (group 2: “underperformers”), the FL6MWD was lower than the clinical values (Fig. 6c). Subjects in group 1 were older and shorter, had lower 6MWD at visits 1 and 2, and had fewer problems in walking (lower EQ-5D Mobility score) at visit 2 (Supplementary Fig. 26). These results suggest that the daily activity for the “underperformers” was below their physical capacity.
To assess changes over time during the trial, we determined the slope of the FL6MWD (see Methods and Supplementary Fig. 27 for details). Values ranged from −17.9 m/week to +10.2 m/week (mean + 1.0 ± 5.4 m/week) (Fig. 6d). The subject with the most negative slope (PAH23) initially maintained high values of FL6MWD for the first 13 weeks, but then recorded a much lower value in subsequent weeks (Supplementary Fig. 22), suggesting a significant change in lifestyle or health state. Three subjects had a large positive slope (>4.0 m/week) (PAH3, 10, 20), and four subjects had a large negative slope (<4.0 m/week) (PAH1, 13, 21, 23).
To estimate a subject’s physical health state (PHS), we calculated the predicted 6MWD for an equivalent healthy individual (H6MWD) with the same age, gender, and BMI as the subject (see Methods for details). We defined a subject’s physical health state as the ratio of FL6MWD/H6MWD. A plot of the FL6MWD in week 1 versus the predicted H6MWD shows a wide range of values of PHS, from about 0.25 to more than 1 (Fig. 7a). 13/22 subjects had PHS values of about 0.7–0.8 (i.e. values of FL6MWD in the range of 70–80% of the equivalent healthy individual), 3 subjects had values around 0.6, and 5 subjects had values below 0.5. Subject 23 had a ratio > 1 but, as described previously, this subject recorded high FL6MWD values during the first 13 weeks, but then maintained a much lower value in subsequent weeks. It is evident that there is no correlation between the FL6MWD in week 1 and the predicted 6MWD (H6MWD) for an equivalent healthy individual (Fig. 7a).
a Data for all subjects in week 1. Each point represents the value of FLWD in week 1. The dotted lines represent constant values of physical health state (PHS = FL6MWD/H6MWD). Numbers represent subject IDs. b PHS in the first and last week. The values of FL6MWD in the last week were obtained from the value in week 1 and the slope of a linear fit to the weekly FL6MWD following smoothing. Numbers represent subject IDs. The arrows represent the change during the trial. Red arrows represent a decrease in PHS, green arrows represent an increase in PHS. c Violin plot showing the change in PHS during the trial. d Normalized change in PHS. Blue bar–mean; green bars–upper and lower quartiles.
We next assessed the change in PHS for each subject based on the values of FL6MWD in week 1 and in the last week prior to the second clinic visit (Fig. 7b). 11/22 subjects showed an increase in health state, and 11/22 subjects showed a decrease (Fig. 7c). The change in PHS was less than 10% for 15/22 subjects, and the normalized change in PHS was less that 1%/week for 18/22 subjects (Fig. 7d).
Two subjects showed an increase in PHS of more than 1%/week (PAH 3, 20), and two subjects showed a decrease of more than 1%/week (PAH 21, 23). Five subjects (PAH 3, 9, 19, 12, 27) maintained health state values greater than 0.72 for their first and last weeks. These subjects were in the fourth quadrant of the PCA plot with high mean and standard deviation of the step rate, and a high value of the standard deviation of the heart rate at SR > 0. Three subjects (PAH 30, 2, 20, 11) had health state values below 0.52 in their first and last weeks. These subjects were located along the negative x-axis of the PCA plot, characterized by a large fraction of time inactive.
Comparison of 23 Fitbit-derived metrics (Fig. 8a) revealed that relatively few of the heart rate parameters were strongly correlated with other parameters, suggesting that they measure diverse aspects of health status. Although several of the metrics derived from step rate were highly correlated to each other, there were also significant differences. For example, the mean weekly step rate was strongly correlated to three of the ambulation-related metrics but less well correlated to the FL6MWD metric. In addition, metrics such as the fitness slope were only weakly correlated to other metrics. The skewness of the step rate was strongly anticorrelated to the mean and standard deviation of the step rate, ambulation intensity, and ambulation frequency. This suggests that an increase in the mean weekly step rate introduces asymmetry into the distribution. This rich and diverse landscape suggests that the Fitbit metrics capture many different facets of health status.
a Correlation matrix (Pearson r value) of all the Fitbit-derived parameters and demographic variables (age, height, and BMI). b Correlation matrix (Pearson r value) for statistically significant continuous clinical parameters (y-axis) for subgroups identified from Fitbit parameters (x-axis).
To determine whether we could identify subgroups amongst the patients based on Fitbit metrics we performed Latent Profile Analysis. 8 Fitbit metrics were used as input: daily step count, HR(SR = 0), HR(SR = 0)sk, HR(SR > 0), ambulation P value, fitness slope. Based on the maximum Bayesian Information Criterion (BIC) (Supplementary Table 3), the subjects were categorized into three groups (Supplementary Fig. 28). Group 1 had high ambulation metrics (steps/day, ambulation product P, and FL6MWD), high HR(SR > 0), and high fitness slope (Supplementary Table 4). Group 2 were characterized by the lowest ambulation metrics (steps/day, ambulation product P, FL6MWD), the lowest HR(SR = 0) and HR(SR > 0), and the highest HR(SR = 0)sk. Group 3 had the highest HR(SR = 0) and HR(SR > 0), the lowest HR(SR = 0)sk and fitness slope. The three groups identified from LPA analysis occupied distinct regions of the PCA plot, with the exception of PAH 10 who was in Group 2 (Supplementary Fig. 29).
To further explore the relationship between Fitbit metrics and clinical parameters, we determined the correlation between 8 Fitbit metrics and the seven continuous clinical variables at the two clinic visits (see Fig. 8b). Five Fitbit metrics had strong correlations (Pearson r values > ±0.5). Albumin was correlated with HR(SR = 0) and HR(SR > 0) at visit 1 (r = 0.565 and 0.627, respectively). NT-proBNP was also correlated with HR(SR = 0) at visit 1 (r = 0.585), and was inversely correlated with fitness slope at visit 1 (r = −0.585). RHR at visits 1 and 2 were correlated with HR(SR = 0), HR(SR = 0)sk, and HR(SR > 0). 6MWD at visits 1 and 2 were correlated with FL6MWD. RVSP at visit 1 was inversely correlated with fitness slope. Notably, steps/day and ambulation P did not have strong correlations to the continuous clinical parameters.
Daily step count is a ubiquitous metric associated with wearable activity monitors. However, the underlying minute-to-minute heart rate and step rate measurements contain a rich array of data associated with physical and cardiovascular function and have the potential to provide much more detailed insight into an individual’s health status based on activities of daily living. In addition to metrics derived from the weekly distribution of minute-to-minute heart rate and step rate data, we derived several others, including: (1) an analog of the widely-used 6MWD, which we termed the free-living 6 min walk distance (FL6MWD), (2) an analog of the Physical Working Capacity test used to assess physical fitness, (3) metrics associated with the frequency, intensity, and duration of weekly ambulations, (4) metrics describing usage patterns, and (5) metrics associated with physical health status based on the FL6MWD and the predicted 6MWD for a healthy individual with the same gender, age, and BMI. These metrics are derived from a single wearable activity monitor during normal daily life and do not require any prescribed activities or external monitoring. Together these parameters provide weekly signature of an individual’s status that could be used for identifying subgroups within patient populations or assessing changes over time.
Principle component analysis showed that subjects could be grouped by parameters broadly associated with physical activity and cardiovascular function. Physical status was defined by step rate parameters (+x axis) or fraction of time inactive (−x axis). Cardiovascular status was defined by resting heart rate while inactive (+y axis) and the range of heart rates accessed during normal daily activities (−y axis). Subjects were clustered in different regions of the PCA plot both along the axes, indicating that their status was dominated by either physical or cardiovascular factors, or within a quadrant, indicating an influence of a combination of physical or cardiovascular factors. Latent Profile Analysis identified 3 groups located in distinct regions in the PCA plot, with characteristics consistent with the interpretation described above. For example, LPA Group 2 were located in the third quadrant in the PCA plot and were characterized by the lowest ambulation metrics and low heart rate metrics.
Device usage is an important factor in analyzing data from wearable devices. Using physiological values of heart rate as a proxy for a device being worn for each minute of a week enabled detailed analysis of usage patterns. Heat maps revealed a range of different usage patterns, such as removing the device overnight or wearing the device almost continuously. Usage patterns are also important in analyzing metrics related to activity. For example, daily step count may not be significantly influenced by removing the device overnight, whereas derived metrics such as fraction of time inactive may be subject to error. There are three key factors that contribute to the relatively high usage in this study: (1) the device is wrist worn and has a small form factor, (2) the battery life is up to 7–10 days, (3) many models are waterproof and hence do not need to be taken off between charges. Usage patterns and changes in usage patterns may contain additional information about an individual’s health state.
To establish the potential for clinical relevance, we used a thresholding approach to identify statistically significant differences between subgroups. Even within this relatively small population we found statistically significant differences in 18 parameters recorded at the initial or final clinic visits and based on 8 of the Fitbit-derived metrics. Clinical parameters included those associated with physical status, cardiovascular function, pulmonary function, as well as biomarkers from blood tests. The identification of statistically significant differences in a wide range of clinical parameters suggests that it may be possible to identify surrogate markers of disease severity in PAH. For example, ambulation product P < 1,000, and FL6MWD < 320 m were correlated with lower clinic measured 6MWD at visits 1 and 2. Subjects with fitness slope > 0.15 had lower NT-proBNP levels, an important biomarker of cardiac stress, at visits 1 and 2. In addition, this approach may contribute to identification of individuals who would benefit from more frequent clinic visits or specific medications.
Activity monitors can provide insight into an individual’s physical capacity in terms of activities of daily living. Many of these devices are relatively low cost and low maintenance following deployment. Long battery life and low form factor appear to be important in achieving high levels of compliance. Metrics derived from the raw data can be easily displayed in a dashboard and provide an additional tool for telemedicine.
In summary, we used the minute-to-minute step rate and heart rate data from a Fitbit device to derive a wide range of metrics associated with physical activity and cardiovascular function. These metrics were used to identify clusters of subjects with common characteristics. In addition, several Fitbit metrics were strongly correlated to continuous clinical parameters. Using a thresholding approach we showed that many Fitbit metrics resulted in statistically significant differences in clinical parameters between subgroups, including those associated with physical status, cardiovascular function, pulmonary function, as well as biomarkers from blood tests. These results highlight the fact that daily step count is only one of many metrics that can be derived from activity monitors. Importantly, this approach is generally applicable to remote monitoring of many patient populations.
There are several limitations in this study. (1) Although heart rate can be used to verify that a device is worn, independent validation of specific activities of daily life remains to be established. Ultimately, AI could be used to indicate the likelihood of specific types of activity. (2) Neither heart rate nor step rate measurements were independently validated. One approach to address this issue would be to perform independent measurements of resting heart rate while ambulating at fixed gait speed at the beginning of a trial. Independent laboratory studies of heart rate and step rate signatures in response to specific types of activities of daily life will also be important in refining data analysis. However, we note that comparison of Fitbit data to parameters from the two clinic visits (e.g. resting heart rate and 6MWD) provide support for the validity of the measurements. (3) In comparing Fitbit parameters to clinical parameters we did not consider factors such as a patient’s medication, or adjust for other covariates. Incorporating factors such as medications would likely improve the correlations to clinical parameters and provide insight into the role of these factors in activities of daily life, however, the sample size was too small. The threshold values used for comparison of clinical parameters were either guided by previous studies or selected arbitrarily. Studies in larger cohorts and in other patient populations will be essential to establishing the clinical relevance of this approach. (4) This is a small, single center study and the results remain to be reproduced in other patient populations. Nonetheless, these results show the potential for defining metrics beyond daily step count that can contribute to assessing an individual’s health status.
Data were obtained from a prospective, observational study where PAH patients wore a wrist worn activity monitor (Fitbit Charge HR^®) between two outpatient visits. The study was approved by the IRB at the Cleveland Clinic (IRB number 15–1392). Participants provided written informed consent. Thirty subjects were enrolled in the study; two patients withdrew consent after enrollment. Study details have been published elsewhere¹⁷. Outpatient visits occurred during two consecutive routine appointments where patients received various tests. Overall, the clinical data included 19 categorical and 7 continuous variables. Categorical variables included eight scores from questionnaires associated with health related quality of life (HRQOL), modified Borg dsypnea score, and RV function scores, physician and patient assessed WHO Functional Class, and seven binary scores associated with presence or absence of a symptom, and six assessments of organ function. Continuous measurements included heart rate measurements, six minute walk distance (6MWD), right ventricular systolic pressure (RVSP), and three biomarkers from blood tests. A complete list of clinical parameters is provided in Supplementary Table 1.
For each subject the minute-to-minute heart rate and step rate data were obtained from the Fitbit server. 22 of 30 data sets were included for analysis: these data sets had clinical data for both visits and at least 4 weeks of Fitbit data between the two visits. 3 subjects were excluded because they had no data on the Fitbit server, 3 subjects did not have a second clinic visit, and 2 subjects had only 1 week of Fitbit data. Data were analyzed in weekly blocks from 00:00 on Sunday to 23:59 on Saturday. Therefore, depending on the day of the week of the clinic visits, there is a gap between the clinic visit and the first and last week of Fitbit data. Each data point represents the step rate (SPM) and average heart rate (BPM) over one minute. The device was considered worn if the average heart rate for any minute was greater than or equal to 20 BPM and less than or equal to the age predicted maximal heart rate (HR_max(BPM) = 208–0.7 × age)³⁸. The number weeks of Fitbit data between the two clinic visits was 18.4 ± 12.2 (range from 7 to 65 weeks). In total we analyzed 3.5 × 10⁶ min of data over 405 weeks. Overall, this corresponds to 85% of the total time.
Baseline metrics from the week-long blocks of data were derived from the weekly values of step rate (SR), heart rate at step count equal zero (HR(SR = 0), i.e. no activity), and heart rate at step rate greater than zero (HR(SR > 0), i.e. active). From the distributions of these three metrics we obtained the mean, standard deviation, and the skewness. The heart rates were fit to a normal distribution, and the step rate was fit to a log normal distribution. A scatter plot of step rate versus heart rate provided a weekly signature of cardiovascular activity for each individual. From a linear least-squares fit to the data we obtained the slope (heart rate per step rate (BPM/SPM)). The effective area of the heart rate versus step rate (HR vs. SR) plot was determined by first calculating the upper (lower) envelopes. Each point in the upper and lower envelopes represents the average of the maximum (or minimum) HR values at each value of step count in a bin width of 10 SPM. The envelope point is located at the average step rate for all values with HR values. Step rates with no HR values are omitted from the calculation. Bins with no HR values do not have an envelope point. We then performed a linear least-squares fit to the envelopes to determine the area of the HR-SC plot.
The skewness of the step rate and heart rate distributions were obtained from:
where (bar x) is the mean, (sigma) is the standard deviation, N is the number of points, and (x_i) is the value. The skewness can be positive or negative. A positive skewness has an extended tail to the right of the distribution (median and mean to the right of the most probable value), and a negative skewness has an extended tail to the left of the distribution (median and mean to the left of the most probable value). (Sk = 0) indicates a perfect fit to the distribution. In general, (|Sk| ,< ,0.5) is considered small, (left| {Sk} right|) from 0.5–1.0 is considered moderate and (left| {Sk} right|, > ,1.0) is considered large.
To assess how heart rate and step rate metrics were distributed across the subjects we performed principal component analysis (PCA). Analysis was performed using the PCA function in MATLAB, and for all parameters the mean was set to 0 and standard deviation = 1 using the “Normalize” function. Patients with at least 10 weeks of data were included in the analysis (N = 20). Two subjects (PAH4 and 22) were excluded as they had 8 and 7 weeks of data, respectively. Here we report analysis based on 5 metrics: HR(SR = 0):mean, HR(SR > 0):SD, SR(SR > 0):mean, SR(SR > 0):SD, time inactive (fraction of minutes with SR = 0). These parameters were selected to represent heart rate and ambulation metrics and to avoid redundancy. For each parameter we used the average weekly value. The variance for the first two principal components were 48.6% and 30.0%, respectively. For 100 independent runs where we randomly selected different weeks, the mean variance of PC1 and PC2 was 77.5 ± 0.58%.
LPA was used to identify the clusters of individuals (i.e. latent profiles) based 8 Fitbit metrics: daily step count, HR(SR = 0), HR(SR = 0)sk, HR(SR > 0), ambulation P value, fitness slope, FL6MWD, and usage. LPA was performed through package ‘mclust’ (version 5.4.10) in R (version 4.2.1). The optimal number of clusters was determined based on the maximum Bayesian Information Criterion (BIC) through the function ‘mclustBIC’.
From the baseline metrics for step rate and heart rate we obtained the following derived parameters.
The subjects were instructed to wear the device on the non-dominant wrist, for as long as possible, except during exposure to water. The device was considered worn for any given minute if the average heart rate was within the defined range from 20 to the age-determined maximal heart rate. From the complete data set (3.5 × 10⁶ min) there were no HR values less than 20, and only 148 values (4.2 × 10⁻⁷%) above the age predicted heart rate maximum. To visualize the usage for each individual we created heat maps showing the average usage over each hour of each day between the two clinic visits. We also determined the maximum length of time during the week when the device was not worn, which varied from less than one hour to more than 12 h. The change in weekly usage was determined from a linear least-squares fit to the weekly usage following smoothing using single exponential smoothing with α = 0.3. To assess whether there was a linear relationship between Fitbit parameters we used the Pearson correlation method.
We assessed the fraction time that a subject was inactive each week from the number of minutes with SR = 0 divided by the total number of minutes that the device was worn, based on the criteria described above.
A proxy of the standard 6MWD was obtained by identifying the 6-minute window with the maximum cumulative number of steps during a given week. The step count was converted to a distance from the following relations: step length (m) = 0.413 x height (m) for females and 0.415 x height (m) for males³⁹. The free-living 6MWD (FL6MWD) was then obtained from the step length and the total number of steps in the 6 min window. Comparison of step length from different methods is provided in Supplementary Fig. 19.
To compare the FL6MWD to the 6MWD obtained at the clinical visits, we used the k-means algorithm (Python 3.8, sklearn.cluster.KMeans). For every week i, we determined the difference, (Delta y_i) (m), between the FL6MWD and the interpolated clinic value. The average difference over all weeks for an individual was defined as (overline {Delta y}). Using the silhouette method (Python 3.8, sklearn.metrics module), we identified two sub-groups: subjects with FL6MWD close to the interpolated clinic values (small (overline {Delta y}), group 1: “performers”), and those with FL6MWD values below the interpolated clinic values (large (overline {Delta y}), group 2: “underperformers”). An example is provided in Supplementary Fig. 25. The change in weekly FL6MWD with time between the two clinic visits was determined from a linear least-squares fit to the weekly values following smoothing using an exponential smoothing function with α = 0.3 (see Supplementary Fig. 27 for details).
Parameters related to intensity, endurance, and frequency of ambulations were obtained from analysis of the weekly step rate data. An ambulation event was defined by a sustained step rate of ≥60 SPM for at least 2 min. For a healthy individual, a step rate of 60–79 SPM is considered slow walking²³. The ambulation intensity was defined as the standard deviation of a lognormal fit to the weekly step rate histogram. We defined endurance as the 1/e value of an exponential fit (starting at 2 min) to a histogram of the ambulation duration. Ambulation frequency was defined as the total number of ambulations during the week. Finally, we defined a characteristic ambulation parameter P for each subject, based on the product of the average values of intensity, endurance, frequency.
A proxy of fitness was obtained using an approach similar to the Physical Working Capacity PWC170 protocol⁴⁰. In the submaximal PWC170 test, an individual is asked to spin on a stationary bike at two or more power outputs that maintain the heart rate within a defined range. The power output at an extrapolated heart rate of 170 bpm is then considered a proxy of VO_2,max. We used a similar approach to define a metric of fitness, taking the step rate as a proxy for level of effort, and hence assuming that that higher step count corresponds to higher power output. The mean and standard deviation of the step count per minute in 20 SPM bins was plotted versus the mean and standard deviation of the heart rate in that bin for each week. We then determined the slope (HR/SPM) and intercept (HR at SR = 0) from the weekly plots. To compare subjects, we plotted the mean and standard deviation of step rate and heart rate in each bin for each subject averaged over all weeks. We then identified the mean and standard deviation for all subjects within each bin.
An estimate of the physical health state of each individual was determined from FL6MWD/H6MWD, where H6MWD is the value of the 6MWD predicted for an equivalent healthy individual. Various studies have shown that 6MWD values for healthy individuals are dependent on age, gender and BMI (height and weight)^33,41. H6MWD (m) was calculated from⁴¹:
where age is in years, gender = 0 (female) and 1 (male), and BMI is in units of kg m⁻². This empirical relation was derived from measurements of 617 subjects (52% female) aged 29–79 with BMI in the range of 18 kg m⁻²–40 kg m⁻² who completed two 6MWTs. The fit to the data captured 46% of the variance. Other studies of healthy individuals were excluded because they had a narrower age range^42,43 or a narrower range of BMI⁴⁴.
To identify clinical parameters that were statistically significant between sub-groups determined from Fitbit-derived metrics we used a Mann-Whitney test. If a subject did not have a value for a specific clinical parameter, then that parameter was excluded from the analysis. Comparisons between groups were only made if there were at least 5 subjects in each group. No other corrections were made.
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
The data that support the findings of this prospective, observational study are not openly available but are available from the authors upon reasonable request. The data presented here are available within the article or supplementary materials.
Scripts for data analysis are available at https://github.com/peterxu1991/PAH-Fitbit-Paper.
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The authors gratefully acknowledge support from Johns Hopkins inHealth.
Measurement Corps, In Health, Johns Hopkins University School of Medicine, Baltimore, MA, USA
Zheng Xu, Nicole Zahradka, Seyvonne Ip, Amir Koneshloo & Peter C. Searson
Institute of Nanobiotechnology, Johns Hopkins University, Baltimore, MA, USA
Zheng Xu, Nicole Zahradka, Seyvonne Ip, Amir Koneshloo & Peter C. Searson
Center for Movement Studies, Kennedy Krieger Institute, Baltimore, MA, USA
Ryan T. Roemmich & Peter C. Searson
Department of Physical Medicine and Rehabilitation, Johns Hopkins University School of Medicine, Baltimore, MA, USA
Ryan T. Roemmich
Respiratory Institute, Cleveland Clinic, Cleveland, OH, USA
Sameep Sehgal & Kristin B. Highland
Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MA, USA
Peter C. Searson
Department of Materials Science & Engineering, Johns Hopkins University, Baltimore, MA, USA
Peter C. Searson
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Z.X., N.Z., S.I., A.K., R.T.R., and P.C.S. conceived the approach. S.S. and K.B.H. provided the data set. Z.X., N.Z., S.I., and A.K. analyzed the data. All authors discussed the results. P.C.S. wrote the manuscript. All authors edited the final manuscript.
Correspondence to Peter C. Searson.
The authors declare no competing interests.
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Xu, Z., Zahradka, N., Ip, S. et al. Evaluation of physical health status beyond daily step count using a wearable activity sensor. npj Digit. Med. 5, 164 (2022). https://doi.org/10.1038/s41746-022-00696-5
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STONY POINT — A weathered rock wall running along West Main Street conceals a converted 1930s barn tucked into a thickly wooded hillside.
The rustic home’s former owner liked it that way.
Jasper Johns has long been known as private, if not reclusive. It’s not surprising the town’s historian barely knew the man widely considered one of America’s greatest living artists was living just a half-mile away in the 1970s and 80s.
Johns, who bought the home in 1973 for $48,000, proceeded to expand the space and install four floor-to-ceiling garage-door style rollup windows that allowed sunlight to pour into his second-floor studio and living room below.
“I do most of my work here,” he told The Journal News in 1976. “That’s why I had to add this space. Since I made the addition and have been here full time, I’m beginning to enjoy it.”
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Johns, whose paintings using abstract images of American flags and targets brought him to prominence in the 1950s, has produced some of this country’s most iconic artworks and influenced generations of artists.
His painting Three Flags, which he sold to a gallery in 1959 for $600, was resold by a private owner to the Whitney Museum of American Art for $1 million in 1980 — at the time the highest price ever paid to a living artist. Johns expressed amusement at the price tag in a 1980 Journal News interview. “But of course, it has nothing to do with painting,” he said.
His neighbors might not have been aware of his presence, but the home caught the attention of burglars who made off with some whiskey but ignored potentially priceless paintings and prints.
“They had otherwise excellent taste in liquor,” he said in the 1976 interview, provided by the Rockland Room at the New City Library. “They took only the best Scotches and left a lot of the other bottles.”
Johns, who moved back to Manhattan in 1987, sold the Stony Point home in 1995, according to county records. Now 92, he lives in Connecticut.
Nowadays the 1.3-acre property’s rustic vibe inspires fashion photographers and filmmakers, as well as welcoming overnight guests to a converted studio apartment in the standalone wooden garage.
Stephanie Gutmann, who’s owned the property for nearly a decade, has been pitching it on home-sharing websites and Instagram as a location/vacation spot, albeit one that’s showing its age.
In one online listing she describes it as “a real old country house with all the quirks (and unique beauty) that implies,” and advises prospective visitors to “think ‘Grey Gardens’ not Better Homes and Gardens.”
The main features of the two-floor, two-bedroom 2,100-square-foot house are much the same as when Johns lived there. The exposed wooden beams, plank walls and tile and wood floors have been preserved. A wooden deck runs along the south-facing rear of the house.
Gone, however, is the backyard picnic table where Johns welcomed avant-garde composer John Cage and choreographer Merce Cunningham, who lived close by at the Gatehill Cooperative, also known as The Land.
Large windows in many rooms look out onto the bucolic parcel’s forested land, rock walls and the winding Cedar Pond Brook running along the periphery.
“He created light all over the place that he could paint by, and in doing so he created fantastic light for photography,” Gutmann said one recent morning. “People are very inspired by the light they get pretty much everywhere, particularly in the studio room because you have light streaming in from above and from virtually all sides.”
Another clue to the home’s past that remains in place is an old-fashioned bathtub whose faucets are depicted in Johns’ artworks, including Racing Thoughts, which art critic Deborah Solomon placed among her favorites from his Stony Point period.
The 1983 painting, which is owned by the Whitney, is set in the small upstairs bathroom, whose wooden door is recognizable.
“Interestingly, Jasper set some of his most remarkable paintings in the smallest room in the Stony Point house — the bathroom,” Solomon, who is writing a biography about the artist, wrote in an email.
“In the painting, you cannot see the bathtub, only the faucets on the tub,” Solomon said. “If there is a bather, he or she is hidden. But we do see, in vibrant colors, a wall collaged with emblems of the artist’s past, including a print by Barnett Newman, a reproduction of the Mona Lisa, and a black-and-white puzzle picturing the art dealer Leo Castelli.”
Stephanie Gutmann and her husband, William Tucker, bought the home in 2013 for $380,000, according to records. Tucker became “obsessed with owning it” and outbid another buyer, she said.
The husband-and-wife journalists had lived there only a few weeks when Tucker was diagnosed with cancer. “We still managed to have two great parties here,” she said, before Tucker died in 2016.
Needing to find a way to pay mounting expenses, Gutmann, a self-described semi-trained photographer, realized Johns’ studio would make an ideal location for photographers, videographers and filmmakers. Magazines have done fashion shoots here, and the musician Surf Mesa filmed a music video on the property.
The emotional and financial challenges of living in the home have been difficult, said Gutmann, who stays busy with upkeep the old house demands.
“A period that could’ve been very, very hard, and was hard, was really redeemed by having this house to work on, because I like to do carpentry and stuff like that,” Gutmann said, standing outside by a ladder she’d been using while painting one of the barn board walls.
“And then also very redeeming for me was this little piece of land with the stream and the different levels and the old trees,” she added.
Deer, hawks, egrets, wild turkeys and the occasional fox and coyote wander freely through the bushes and towering trees. “It’s almost like a little animal sanctuary, so you’ll get deer wandering right up to the windows and peering in,” she said.
Robert Brum is a freelance journalist who writes about the Hudson Valley. Contact him at [email protected]. Read his work atrobertbrum.com.

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Black Friday is quite a major occasion for the music industry as many producers look forward to purchasing some plugins of their choice enlarging their software toolkit. Retailers, plugin manufacturers & sample pack companies often kick off with their major Black Friday deals a week or two early offering lucrative discounts and offers on their products. You’ll notice almost every outlet running some sort of black Friday deals. With the vast number of plugin manufacturers and sample pack companies out there it’s quite tough as a music producer to figure out which Black Friday deals are the best and the most beneficial for you. In an attempt to reduce your problems we have shortlisted a list of plugins, sample packs, bundles, and courses you should watch out for this Black Friday. Some of these deals aren’t on sale yet but are likely to have by the time we reach Black Friday. Also, don’t forget to check out our dedicated Black Friday landing page where we list the best Black Friday deals on plugins, sample packs, bundles, presets, & courses.
 
Diva is one of the most popular synth plugins out there. It falls right into the elite category shared by other synths such as Sylenth1, Serum & Omnisphere. The analog character of Diva is what it makes such a good VST plugin. At the moment there is no Black Friday deal on Diva.
 
The Moogerfooger Effects Plug-ins are a redesign of the iconic analogue effects pedals from Moog, bringing to your digital music creation environment the legendary tone, musicality, and interconnection of the original hardware effects. The Fx bundle is currently available for 40% off during their special Black Friday Sale.
 
 
Waves have already launched the first edition of its Black Friday deals. They usually carry out their Black Friday deals in multiple phases. At the moment you can get 10% off on your 2nd plugin purchase, 30% on 3rd & 4th plugin & 50% on 5th and subsequent purchases. We would suggest keeping an eye on various different deals that pop up on their platform in the coming weeks.
 
This collection features 28 VST plugins including analogue synths, digital synths, organs, acoustic pianos, electric pianos, and string machines. All the plugins are digital emulations of some of the greatest hardware gear ever produced. One of the most anticipated deals for Black Friday 2022.
 
 

 
ShaperBox is an amazing effect plugin that allows you to completely manipulate your sounds and make interesting arrangements out of it. The ShaperBox bundle includes TimeShaper 2, VolumeShaper 6, NoiseShaper, FilterShaper Core 2, PanShaper 3, WidthShaper 2, CrushShaper and DriveShaper. There are endless possibilities of what you can achieve with a combination of these modules. It also received the support of producers such as Camelphat, and David Guetta. Definitely, one to watch out for on Black Friday.
 
Fabfilter plugins have gained the status of industry-standard among music producers. Their plugins such as Pro Q3, Saturn, Pro MB, Pro L2 are considered some of the must-haves by the community. Last year we did witness a black Friday sale on Fabfilter plugins for a week’s duration and expect to see a similar deal this year.
 
RX is a post-production plugin utilized for cleaning recorded audio samples and making acapella’s and instrumentals out of existing songs. iZotope recently launched the latest edition of the RX series, the RX 9. In case this plugin has been on your radar, do watch out for any deals that may follow in the coming weeks.
 
Phase Plant is a synth VST plugin. Phase Plant always starts with a blank template providing you endless possibilities for creating new sounds. You can add as many wavetables, oscillators as you want. Individually map them to any of the effects, lfos, triggers, envelopes etc. Once you understand this plugin completely, its a total beast. Black Friday deals are likely on Phase Plant similar to what we saw in 2020.
 
The Komplete 13 bundle features 68 instruments and effects, plus 24 Expansions. Included within are some of Native Instruments’ best Kontakt libraries & instruments such as  Guitar Rig 6, Cremona Quartet, Arkhis, Super 8 synthesizer, Noire piano, Mysteria vocal textures, Session guitars library, and a lot more. A black Friday sale on Native Instruments’ libraries & plugins is likely to be released in the coming weeks.
 
This one seems a bit ambitious as Serum is one of those plugins on which you’ll hardly find any deals, sales, coupon codes etc. We might be extremely lucky if something pops up on Black Friday 2021 so fingers crossed!
 
 
Soundtoys has an exquisite collection of mixing plugins. You might have already heard of plugins such as Decapitator, Echoboy, Alter Boy from various professionals. Similar to Black Friday 2021, Soundtoys have launched their Black Friday deals for 2022. Individual effects are up to 70% off and bundles up to 55% off. Definitely, the best time to buy if you are looking to add Soundtoys to your production toolkit.
 
 
Mastering The Mix has a very concise catalog of plugins however each of them is an excellent piece of software to drastically improve your mix and masters. If you are a mixing/mastering engineer or a music producer, they have some amazing plugins such as Reference, Bass Room, Levels, Mix Room.
 
 
 
 
Read Next: Best Early Black Friday Deals on AU/VST Plugins from Waves
Image Credits: Moog music
 
Hemant has been actively involved in the dance music industry with over 2 years of experience. Currently working as a Project Manager and heading the We Rave You Tech division. Get in touch via email or Instagram
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