Sensitivity of medial and lateral knee contact force predictions to frontal plane alignment and contact locations

Musculoskeletal models are increasingly used to estimate medial and lateral knee contact forces, which are difficult to measure in vivo. The sensitivity of contact force predictions to modeling parameters is important to the interpretation and implication of results generated by the model. The purpose of this study was to quantify the sensitivity of knee contact force predictions to simultaneous errors in frontal plane knee alignment and contact locations under different dynamic conditions. We scaled a generic musculoskeletal model for N = 23 subjects’ stature and radiographic knee alignment, then perturbed frontal plane alignment and mediolateral contact locations within experimentally-possible ranges of 10° to −10° and 10 to −10 mm, respectively. The sensitivity of first peak, second peak, and mean medial and lateral knee contact forces to knee adduction angle and contact locations was modeled using linear regression. Medial loads increased, and lateral loads decreased, by between 3% and 6% bodyweight for each degree of varus perturbation. Shifting the medial contact point medially increased medial loads and decreased lateral loads by between 1% and 4% bodyweight per millimeter. This study demonstrates that realistic measurement errors of 5 mm (contact distance) or 5° (frontal plane alignment) could result in a combined 50% BW error in subject specific contact force estimates. We also show that model sensitivity varies between subjects as a result of differences in gait dynamics. These results demonstrate that predicted knee joint contact forces should be considered as a range of possible values determined by model uncertainty.     

Meta-analysis reveals impacts of disturbance on reptile and amphibian body condition

Ecosystem disturbance is increasing in extent, severity and frequency across the globe. To date, research has largely focussed on the impacts of disturbance on animal population size, extinction risk and species richness. However, individual responses, such as changes in body condition, can act as more sensitive metrics and may provide early warning signs of reduced fitness and population declines. We conducted the first global systematic review and meta-analysis investigating the impacts of ecosystem disturbance on reptile and amphibian body condition. We collated 384 effect sizes representing 137 species from 133 studies. We tested how disturbance type, species traits, biome and taxon moderate the impacts of disturbance on body condition. We found an overall negative effect of disturbance on herpetofauna body condition (Hedges' g = −0.37, 95% CI: −0.57, −0.18). Disturbance type was an influential predictor of body condition response and all disturbance types had a negative mean effect. Drought, invasive species and agriculture had the largest effects. The impact of disturbance varied in strength and direction across biomes, with the largest negative effects found within Mediterranean and temperate biomes. In contrast, taxon, body size, habitat specialisation and conservation status were not influential predictors of disturbance effects. Our findings reveal the widespread effects of disturbance on herpetofauna body condition and highlight the potential role of individual-level response metrics in enhancing wildlife monitoring. The use of individual response metrics alongside population and community metrics would deepen our understanding of disturbance impacts by revealing both early impacts and chronic effects within affected populations. This could enable early and more informed conservation management.     

Dynamic regulation of heart rate during acute hypotension: new insight into baroreflex function

To examine the dynamic properties of baroreflex function, we measured beat-to-beat changes in arterial blood pressure (ABP) and heart rate (HR) during acute hypotension induced by thigh cuff deflation in 10 healthy subjects under supine resting conditions and during progressive lower body negative pressure (LBNP). The quantitative, temporal relationship between ABP and HR was fitted by a second-order autoregressive (AR) model. The frequency response was evaluated by transfer function analysis. Results: HR changes during acute hypotension appear to be controlled by an ABP error signal between baseline and induced hypotension. The quantitative relationship between changes in ABP and HR is characterized by a second-order AR model with a pure time delay of 0.75 s containing low-pass filter properties. During LBNP, the change in HR/change in ABP during induced hypotension significantly decreased, as did the numerator coefficients of the AR model and transfer function gain. Conclusions: 1) Beat-to-beat HR responses to dynamic changes in ABP may be controlled by an error signal rather than directional changes in pressure, suggesting a "set point" mechanism in short-term ABP control. 2) The quantitative relationship between dynamic changes in ABP and HR can be described by a second-order AR model with a pure time delay. 3) The ability of the baroreflex to evoke a HR response to transient changes in pressure was reduced during LBNP, which was due primarily to a reduction of the static gain of the baroreflex.     

Frequency response model of skeletal muscle and its association with contractile properties of skeletal muscle

The aims of the present study were to develop a mathematical model of the skeletal muscle based on the frequency transfer function, referred to as frequency response model, and to presume the relationship between the model elements and skeletal muscle contractile properties. Twitch force in elbow flexion was elicited by applying a single electrical stimulation to the motor point of biceps brachii muscles, and then analyzed visually by the Bode gain and phase diagram of the force signal. The frequency response model was represented by a frequency transfer function consisting of five basic control elements (proportional element, dead time element, and three first-order lag elements). The model element constants were estimated by best-fitting to the Bode gain and phase diagram of the twitch force signal. The proportional constant and the dead time in the frequency response model correlated significantly with the peak torque and the latency in the actual twitch force, respectively. In addition, the time constants of the three first-order lag elements in the model correlated strongly with the contraction time and the half relaxation time in the actual twitch force. The results suggested a possibility that the individual elements in the frequency response model would reflect the biochemical and biomechanical properties in the excitation–contraction coupling process of skeletal muscle.     

Local Viscoelastic Properties of Live Cells Investigated Using Dynamic and Quasi-Static Atomic Force Microscopy Methods

The measurement of viscoelasticity of cells in physiological environments with high spatio-temporal resolution is a key goal in cell mechanobiology. Traditionally only the elastic properties have been measured from quasi-static force-distance curves using the atomic force microscope (AFM). Recently, dynamic AFM-based methods have been proposed to map the local in vitro viscoelastic properties of living cells with nanoscale resolution. However, the differences in viscoelastic properties estimated from such dynamic and traditional quasi-static techniques are poorly understood. In this work we quantitatively reconstruct the local force and dissipation gradients (viscoelasticity) on live fibroblast cells in buffer solutions using Lorentz force excited cantilevers and present a careful comparison between mechanical properties (local stiffness and damping) extracted using dynamic and quasi-static force spectroscopy methods. The results highlight the dependence of measured viscoelastic properties on both the frequency at which the chosen technique operates as well as the interactions with subcellular components beyond certain indentation depth, both of which are responsible for differences between the viscoelasticity property maps acquired using the dynamic AFM method against the quasi-static measurements.     

Local Viscoelastic Properties of Live Cells Investigated Using Dynamic and Quasi-Static Atomic Force Microscopy Methods

The measurement of viscoelasticity of cells in physiological environments with high spatio-temporal resolution is a key goal in cell mechanobiology. Traditionally only the elastic properties have been measured from quasi-static force-distance curves using the atomic force microscope (AFM). Recently, dynamic AFM-based methods have been proposed to map the local in vitro viscoelastic properties of living cells with nanoscale resolution. However, the differences in viscoelastic properties estimated from such dynamic and traditional quasi-static techniques are poorly understood. In this work we quantitatively reconstruct the local force and dissipation gradients (viscoelasticity) on live fibroblast cells in buffer solutions using Lorentz force excited cantilevers and present a careful comparison between mechanical properties (local stiffness and damping) extracted using dynamic and quasi-static force spectroscopy methods. The results highlight the dependence of measured viscoelastic properties on both the frequency at which the chosen technique operates as well as the interactions with subcellular components beyond certain indentation depth, both of which are responsible for differences between the viscoelasticity property maps acquired using the dynamic AFM method against the quasi-static measurements.     

The effects of pH on force and stiffness development in mouse muscles

Changes in force and stiffness during contractions of mouse extensor digitorum longus and soleus muscles were measured over a range of extracellular pH from 6.4 to 7.4. Muscle stiffness was measured using small amplitude (less than 0.1% of muscle length), high frequency (1.5 kHz) oscillations in length. Twitch force was not significantly affected by changes in pH, but the peak force during repetitive stimulation (2, 3, and 20 pulses) was decreased significantly as the pH was reduced. Changes in muscle stiffness with pH were in the same direction, but smaller in extent. If the number of attached cross-bridges in the muscle can be determined from the measurement of small amplitude, high frequency muscle stiffness, then these findings suggest that (a) the number of cross-bridges between thick and thin filaments declines in low pH and (b) the average force per cross-bridge also declines in low pH. The decline in force per cross-bridge could arise from a reduction in the ability of cross-bridges to generate force during their state of active force production and (or) in an increased percentage of bonds in a low force, "rigor" state.     

Dynamics of the Coiled-Coil Unfolding Transition of Myosin Rod Probed by Dissipation Force Spectrum

The motor protein myosin II plays a crucial role in muscle contraction. The mechanical properties of its coiled-coil region, the myosin rod, are important for effective force transduction during muscle function. Previous studies have investigated the static elastic response of the myosin rod. However, analogous to the study of macroscopic complex fluids, how myosin will respond to physiological time-dependent loads can only be understood from its viscoelastic response. Here, we apply atomic force microscopy using a magnetically driven oscillating cantilever to measure the dissipative properties of single myosin rods that provide unique dynamical information about the coiled-coil structure as a function of force. We find that the friction constant of the single myosin rod has a highly nontrivial variation with force; in particular, the single-molecule friction constant is reduced dramatically and increases again as it passes through the coiled-uncoiled transition. This is a direct indication of a large free-energy barrier to uncoiling, which may be related to a fine-tuned dynamic mechanosignaling response to large and unexpected physiological loads. Further, from the critical force at which the minimum in friction occurs we determine the asymmetry of the bistable landscape that controls uncoiling of the coiled coil. This work highlights the sensitivity of the dissipative signal in force unfolding to dynamic molecular structure that is hidden to the elastic signal.     

Determining the effect of hydration upon the properties of ligaments using pseudo Gaussian stress stimuli

The level of tissue hydration is known to effect viscoelastic material properties. However, prior studies have not fully investigated the effect of hydration on dynamic behavior nor compared the results of transient and dynamic behavior. The material properties of medial collateral rat knee ligaments were studied in relation to hydration, using (sequentially) 0.3 osmolar artificial interstitial fluid (AIF), solutions of AIF plus sucrose with osmolarity 1.05, 1.80 or 2.55, and then AIF. In each solution, the complex compliance was determined as a function of frequency, and the creep response was measured. Complex compliance was determined from a constitutive model created by applying a 0.4+/-0.2 MPa pseudo Gaussian (PGN) stress stimulus to the ligament. Dehydration caused a reduction in cross-sectional area that was linearly related to the osmolarity of the solution. Reductions of up to 52% were observed and were reversible upon rehydration. Dehydration caused a reduction in the creep rate that was not immediately recovered upon rehydration. The storage compliance was reduced by up to 50% with dehydration; these changes were reversed upon rehydration. The loss compliance and phase angle were not affected by dehydration. Transient and dynamic experiments examine different viscoelastic characteristics and both types of tests appear to be necessary to fully characterize the effects of hydration.     

A simple force platform.

The force platform consists of a sandwhich of steel, Rockwool and concrete plates about 900 X 700 mm in surface. Four steel rings were bolted to the under side of the steel plate in each corner. Each steel ring was furnished with only one strain gauge, two of which were placed on the outer- respectively on the inner side of each ring. The four strain gauges were connected to a measuring bridge. Before mounting the rings on the steel plate, the sensitivity to pressure of each ring was adjusted in such a way that they were all similar. Because of this the platform responded with a signal which was independent of where a pressure was applied within the surface of the platform. The platform showed a rectilinear response for static forces up to 500 kp with a stable zero value. In response to dynamic forces the platform showed a resononance frequency of about 50 Hz, with a damping factor of 0.15. Calibration of dynamic forces was carried out by calculation of the forces during a vertical jump compared with what would be expected from the time of flight also registered by the platform-measuring-bridge-ink-writer-set-up. The time of flight was significantly higher (11%) than exected from the time-force relations beforetake-off. This was esplained partly by the relatively low damping factor in the system, partly by the subjects not extending their knees at landing on the platform.     

Comparison between kinematic and kinetic methods for computing the vertical displacement of the center of mass during human hopping at different frequencies

Kinematic and kinetic methods (sacral marker, reconstructed pelvis, segmental analysis, and force platform methods) have been used to calculate the vertical excursion of the center of mass (COM) during movement. In this study we compared the measurement of vertical COM displacement yielded by different methods during able-bodied subjects' hopping at different frequencies (varying between 1.2 and 3.2 Hz). ANOVA revealed a significant interaction between hopping frequency and method (p < 0.001), showing that increasing hopping frequency reduced the differences between methods. A post hoc analysis revealed a significant difference between all methods at the lowest hopping frequency and between the force platform and both the sacral marker and reconstructed pelvis methods at the intermediate hopping frequencies, with differences ranging from 16 to 67 millimeters (all p < 0.05). Results are discussed in view of each methods' limits. We conclude that the segmental analysis and force platform methods can be considered to provide the most accurate results for COM vertical excursion during human hopping in a large range of hopping frequency.     

Validating a low-cost,consumer force-measuring platform as an accessible alternative for measuring postural sway

The Zibrio SmartScale is a low-cost, portable force platform designed to perform an objective assessment of postural stability. The purpose of the present study was to validate the center of pressure (COP) measurements in the Zibrio SmartScale. Simultaneous COP data was collected by a Zibrio SmartScale and a laboratory-grade force platform (LFP) under the dynamic motion of an inverted pendulum device intended to mimic the sway of a standing human. The inverted pendulum was placed on the Zibrio SmartScale which was placed on the LFP. The pendulum was then displaced to angles of 3° and 5° in both the anterior-posterior (AP) and medial–lateral (ML) directions. The findings of this study show low mean average error (MAE) among the measures taken simultaneously upon the LFP and Zibrio SmartScale with no appreciable difference in error in either AP or ML COP directions. Averaged over repeated trials, the MAE did not surpass 0.5 mm. This represented 0.4% of the total range (±50 to 60 mm in 5° displacement trials) of simulated COP. The results of this study strongly indicate that the Zibrio SmartScale can perform adequately as a light-weight and low-cost alternative method of COP measurement in comparison to a traditional LFP.     

Reliability of assessing trunk motor control using position and force tracking and stabilization tasks

System-based methods have been applied to assess trunk motor control in people with and without back pain, although the reliability of these methods has yet to be established. Therefore, the goal of this study was to quantify within- and between-day reliability using systems-based methods involving position and force tracking and stabilization tasks. Ten healthy subjects performed six tasks, involving tracking and stabilizing of trunk angular position in the sagittal plane, and trunk flexion and extension force. Tracking tasks involved following a one-dimensional, time-varying input signal displayed on a screen by changing trunk position (position tracking) or trunk force (force tracking). Stabilization tasks involved maintaining a constant trunk position (position stabilization) or constant trunk force (force stabilization) while a sagittal plane disturbance input was applied to the pelvis using a robotic platform. Time and frequency domain assessments of error (root mean square and H₂ norm, respectively) were computed for each task on two separate days. Intra-class correlation coefficients (ICC) for error and coefficients of multiple correlations (CMC) for frequency response curves were used to quantify reliability of each task. Reliability for all tasks was excellent (between-day ICC≥0.8 and CMC>0.75, within-day CMC>0.85). Therefore, position and force control tasks used to assess trunk motor control can be deemed reliable.     

Methods and estimations of uncertainties in single-molecule dynamic force spectroscopy

In dynamic force spectroscopy, access to the characteristic parameters of single molecular bonds requires nontrivial measurements and data processing as the rupture forces are found not only to be distributed over a wide range, but are also dependent on the loading rate. The choice of measurement procedure and data processing methods has a considerable impact on the accuracy and precision of the final results. We analyze, by means of numerical simulations, methods to minimize and assess the magnitude of the expected errors for different combinations of experimental and evaluation methods. It was found that the choice of fitting function is crucial to extract correct parameter values. Applying a Gaussian function, which is a common practice, is equivalent to introducing a systematic error, and leads to a consequent overestimation of the thermal off-rate by more than 30%. We found that the precision of the bond length and the thermal off-rate, in presence of unbiased noise, were improved by reducing the number of loading rates for a given number of measurements. Finally, the results suggest that the minimum number of measurements needed to obtain the bond strength, with acceptable precision, exceeds the common number of ~100 reported in literature.     

Ratio estimation with measurement error in the auxiliary variate

Summary .  With auxiliary information that is well correlated with the primary variable of interest, ratio estimation of the finite population total may be much more efficient than alternative estimators that do not make use of the auxiliary variate. The well-known properties of ratio estimators are perturbed when the auxiliary variate is measured with error. In this contribution we examine the effect of measurement error in the auxiliary variate on the design-based statistical properties of three common ratio estimators. We examine the case of systematic measurement error as well as measurement error that varies according to a fixed distribution. Aside from presenting expressions for the bias and variance of these estimators when they are contaminated with measurement error we provide numerical results based on a specific population. Under systematic measurement error, the biasing effect is asymmetric around zero, and precision may be improved or degraded depending on the magnitude of the error. Under variable measurement error, bias of the conventional ratio-of-means estimator increased slightly with increasing error dispersion, but far less than the increased bias of the conventional mean-of-ratios estimator. In similar fashion, the variance of the mean-of-ratios estimator incurs a greater loss of precision with increasing error dispersion compared with the other estimators we examine. Overall, the ratio-of-means estimator appears to be remarkably resistant to the effects of measurement error in the auxiliary variate.     

A new method for wide frequency range dynamic olfactory stimulation and characterization

Sensory receptors often receive strongly dynamic, or time varying, inputs in their natural environments. Characterizing their dynamic properties requires control and measurement of the stimulus over a frequency range that equals or exceeds the receptor response. Techniques for dynamic stimulation of olfactory receptors have lagged behind other major sensory modalities because of difficulties in controlling and measuring the concentration of odorants at the receptor. We present a new method for delivering olfactory stimulation that gives linear, low-noise, wide frequency range control of odorant concentration. A servo-controlled moving bead of silicone elastomer occludes the tip of a Pasteur pipette that releases odorant plus tracer gas into a flow tube. Tracer gas serves as a surrogate indicator of odorant concentration and is measured by a photoionization detector. The system has well-defined time-dependent behavior (frequency response and impulse response functions) and gives predictable control of odorant over a significant volume surrounding the animal. The frequency range of the system is about 0-100 Hz. System characterization was based on random (white noise) stimulation, which allows more rapid and accurate estimation of dynamic behavior than deterministic signals such as sinusoids or step functions. Frequency response functions of Drosophila electroantennograms stimulated by fruit odors were used to demonstrate a typical application of the system.     

Sensory transduction in an insect mechanoreceptor: extended bandwidth measurements and sensitivity to simulus strenght

The dynamic properties of sensory transduction in an insect mechanoreceptor, the femoral tactile spine of the cockroach, Periplaneta americana, have been studied by measurement of the frequency response function between randomly varying movement of the tactile spine and afferent action potentials from the sensory neuron which innervates it. The frequency response function of the mechanoreceptor has been characterized over a frequency range which is more than ten times larger than has previously been used for this preparation. Also the effects of varying the amplitude of the stimulating signal have been studied by the use of a range of input signal strengths from about 0.5 to 10 m R.M.S. displacement. The measured frequency response functions can all be well fitted by a theoretical relationship which is a fractional exponent of complex frequency, provided that the time delay caused by conduction of the action potentials from the sensory dendrite to the recording electrodes is taken into account. Under small signal conditions the exponent of complex frequency is close to 0.5 but with larger displacements its value decreases to about half this value. The overall sensitivity of the receptor, as measured by the gain of the frequency response function at a natural frequency of 1 radian/s, is not significantly altered by changes in the input movement amplitude, so that the receptor behaves linearly in this respect. However, the mean rate of action potential occurrence is not linearly related to input movement amplitude. These results are discussed in terms of current theories of sensory transduction and the possible role of tubular bodies in the dynamic behaviour of insect cuticular mechanoreceptors.     

Muscle activity in the leg is tuned in response to impact force characteristics

Based on results from quasi-static experiments, it has been suggested that the lower extremity muscle activity is adjusted in reaction to impact forces with the goal of minimizing soft-tissue vibrations. It is not known whether a similar muscle tuning occurs during dynamic activities. Thus, the purpose of this study was to determine the effect of changes in the input signal on (a) vibrations of lower extremity soft-tissue packages and (b) EMG activity of related muscles during heel-toe running. Subjects performed heel-toe running in five different shoe conditions. Ground reaction forces were measured with a KISTLER force platform, soft-tissue vibrations were measured with tri-axial accelerometers and muscle activity was measured using surface EMG from the quadriceps, hamstrings, tibialis anterior and triceps surae groups from 10 subjects. By changing both the speed of running and the shoe midsole material the impact force characteristics were changed. There was no effect of changes in the input signal on the soft-tissue peak acceleration following impact. A significant correlation (R2=0.819) between the EMG pre-activation intensity and the impact loading rate changes was found for the quadriceps. In addition, the input frequency was shown to approach the vibration frequency of the quadriceps. This evidence supports the proposed paradigm that muscle activity is tuned to impact force characteristics to control the soft-tissue vibrations.     

Compensation for inertial and gravity effects in a moving force platform

Force plates for human movement analysis provide accurate measurements when mounted rigidly on an inertial reference frame. Large measurement errors occur, however, when the force plate is accelerated, or tilted relative to gravity. This prohibits the use of force plates in human perturbation studies with controlled surface movements, or in conditions where the foundation is moving or not sufficiently rigid. Here we present a linear model to predict the inertial and gravitational artifacts using accelerometer signals. The model is first calibrated with data collected from random movements of the unloaded system and then used to compensate for the errors in another trial. The method was tested experimentally on an instrumented force treadmill capable of dynamic mediolateral translation and sagittal pitch. The compensation was evaluated in five experimental conditions, including platform motions induced by actuators, by motor vibration, and by human ground reaction forces. In the test that included all sources of platform motion, the root-mean-square (RMS) errors were 39.0 N and 15.3 N m in force and moment, before compensation, and 1.6 N and 1.1 N m, after compensation. A sensitivity analysis was performed to determine the effect on estimating joint moments during human gait. Joint moment errors in hip, knee, and ankle were initially 53.80 N m, 32.69 N m, and 19.10 N m, and reduced to 1.67 N m, 1.37 N m, and 1.13 N m with our method. It was concluded that the compensation method can reduce the inertial and gravitational artifacts to an acceptable level for human gait analysis.     

Measurement error in covariates in the marginal hazards model for multivariate failure time data

We consider measurement error in covariates in the marginal hazards model for multivariate failure time data. We explore the bias implications of normal additive measurement error without assuming a distribution for the underlying true covariate. To correct measurement-error-induced bias in the regression coefficient of the marginal model, we propose to apply the SIMEX procedure and demonstrate its large and small sample properties for both known and estimated measurement error variance. We illustrate this method using the Lipid Research Clinics Coronary Primary Prevention Trial data with total cholesterol as the covariate measured with error and time until angina and time until nonfatal myocardial infarction as the correlated outcomes of interest.