Search

(1) Background: Biomechanics during landing tasks, such as the kinematics and kinetics of the knee, are altered following anterior cruciate ligament (ACL) injury and reconstruction. These variables are recommended to assess prior to clearance for return to sport, but clinicians lack access to the current gold-standard laboratory-based assessment. Inertial sensors serve as a potential solution to provide a clinically feasible means to assess biomechanics and augment the return to sport testing. The purposes of this study were to (a) develop multi-sensor machine learning algorithms for predicting biomechanics and (b) quantify the accuracy of each algorithm. (2) Methods: 26 healthy young adults completed 8 trials of a double limb jump landing task. Peak vertical ground reaction force, peak knee flexion angle, peak knee extension moment, and peak sagittal knee power absorption were assessed using 3D motion capture and force plates. Shank- and thigh- mounted inertial sensors were used to collect data concurrently. Inertial data were submitted as inputs to single- and multiple- feature linear regressions to predict biomechanical variables in each limb. (3) Results: Multiple-feature models, particularly when an accelerometer and gyroscope were used together, were valid predictors of biomechanics (R2 = 0.68–0.94, normalized root mean square error = 4.6–10.2%). Single-feature models had decreased performance (R2 = 0.16–0.60, normalized root mean square error = 10.0–16.2%). (4) Conclusions: The combination of inertial sensors and machine learning provides a valid prediction of biomechanics during a double limb landing task. This is a feasible solution to assess biomechanics for both clinical and real-world settings outside the traditional biomechanics laboratory.

Summary Study aim: Oxygen Uptake (VO2) is avaluable metric for the prescription of exercise intensity and the monitoring of training progress. However, VO2 is difficult to assess in anon-laboratory setting. Recently, an artificial neural network (ANN) was used to predict VO2 responses during aset walking protocol on the treadmill [9]. The purpose of the present study was to test the ability of an ANN to predict VO2 responses during cycling at self-selected intensities using Heart Rate (HR), time derivative of HR, power output, cadence, and body mass data. Material and methods: 12 moderately-active adult males (age: 21.1 ± 2.5 years) performed a50-minute bout of cycling at a variety of exercise intensities. VO2, HR, power output, and cadence were recorded throughout the test. An ANN was trained, validated and tested using the following inputs: HR, time derivative of HR, power output, cadence, and body mass. A twelve-fold hold-out cross validation was conducted to determine the accuracy of the model. Results: The ANN accurately predicted the experimental VO2 values throughout the test (R2 = 0.91 ± 0.04, SEE = 3.34 ± 1.07 mL/kg/min). Discussion: This preliminary study demonstrates the potential for using an ANN to predict VO2 responses during cycling at varied intensities using easily accessible inputs. The predictive accuracy is promising, especially considering the large range of intensities and long duration of exercise. Expansion of these methods could allow ageneral algorithm to be developed for a more diverse population, improving the feasibility of oxygen uptake assessment.

This paper presents the results of an investigation on the dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. The full equation of motion for both rocking disks is derived from first principles. For unforced behavior, Lamb's method is used to derive the linear natural frequency of both disks, and harmonic balance is used to determine their amplitude-dependent rocking frequencies. A stability analysis then reveals that the equilibria and stability of the two disks are considerably different, as the semi-elliptical disk has a super-critical pitchfork bifurcation that enables it to exhibit bistable rocking behavior. Experimental studies were conducted to verify the trends. For vertically forced behavior, numerical investigations show the disk's responses to forward and reverse frequency sweeps. Three modes of periodicity were observed for the steady state behavior. Experiments were performed to verify the frequency responses and the presence of the three rocking modes. Comparisons between the experiments and numerical investigations show good agreement.

This study examines the viability of utilizing a dynamical system model and heuristic parameter estimation algorithm to make predictions for maximum heart rate ( $$\mathrm {HR_{max}}$$ ) and maximal oxygen uptake ( $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ ) using data collected from a submaximal testing protocol. $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ is widely considered to be the best single measurement of overall fitness in humans. When a $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ assessment is not available, $$\mathrm {HR_{max}}$$ is often used to prescribe exercise intensities for training and rehabilitation. In the absence of maximal cardiopulmonary exercise testing (CPET), $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ are typically estimated using traditional submaximal prediction methods with well-known limitations and inaccuracies. For this study, 12 regularly exercising healthy young adult males performed a bout of maximal CPET on a cycle ergometer to determine their true $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ . Participants also performed a submaximal bout of exercise at varied intensities. A dynamical system model and heuristic parameter estimation algorithm were applied to the submaximal data to estimate the participants’ $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ . The submaximal predictions were evaluated by computing the coefficient of determination $${R^2}$$ and the standard error of the estimate (SEE) through comparisons with the true maximal values for $$\mathrm {HR_{max}}$$ ( $${R^2 = 0.96}$$ , SEE = 2.4 bpm) and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ ( $${R^2 = 0.93}$$ , SEE = 2.1 mL kg $$^{-1}$$ min $$^{-1}$$ ). The results from this study suggest that a dynamical system model and heuristic parameter estimation algorithm can provide accurate predictions for $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ using data collected from a submaximal testing protocol.

Summary Study aim: Mathematical models of the relationship between training and performance facilitate the design of training protocols to achieve performance goals. However, current linear models do not account for nonlinear physiological effects such as saturation and over-training. This severely limits their practical applicability, especially for optimizing training strategies. This study describes, analyzes, and applies a new nonlinear model to account for these physiological effects. Material and methods: This study considers the equilibria and step response of the nonlinear differential equation model to show its characteristics and trends, optimizes training protocols using genetic algorithms to maximize performance by applying the model under various realistic constraints, and presents a case study fitting the model to human performance data. Results: The nonlinear model captures the saturation and over-training effects; produces realistic training protocols with training progression, a high-intensity phase, and a taper; and closely fits the experimental performance data. Fitting the model parameters to subsets of the data identifies which parameters have the largest variability but reveals that the performance predictions are relatively consistent. Conclusions: These findings provide a new mathematical foundation for modeling and optimizing athletic training routines subject to an individual’s personal physiology, constraints, and performance goals.

Prior studies have investigated heart rate dynamics from a variety of perspectives, but are often inadequate for predicting heart rate responses across a broad range of transient exercise intensities. The aim of this study was to develop a nonlinear model to describe the heart rate response of an individual during cycling and to investigate whether heart rate is more accurately predicted by a combination of power output and cadence than by power output alone. The proposed model can account for the transient fluctuations of an individual’s heart rate while they participate in exercise that varies in intensity. The participants for this study each performed a fifty minute bout of cycling on an electric-braked cycle ergometer in the laboratory. The testing protocol for the cycling bout was designed to challenge the predictive capabilities of the model and the participants therefore abruptly changed their power outputs and cadences throughout the tests, which resulted in significant transient fluctuations in their heart rate responses. Due to the nonlinear nature of the proposed heart rate model, a heuristic algorithm was developed to perform the parameter estimation. The model predictions for heart rate matched very well with the experimental heart rate responses for each of the participants, especially when considering the challenges inherent to predicting abrupt transient behavior in the heart rate response. Model comparisons also indicated that heart rate is more accurately predicted by a combination of power output and cadence than by power output alone.

This paper analyzes the dynamics of a model dinoflagellate predator-prey system and uses simulations to validate theoretical and experimental studies. A simple model for predator-prey interactions is derived by drawing upon analogies from chemical kinetics. This model is then modified to account for inefficiencies in predation. Simulation results are shown to closely match the model predictions. Additional simulations are then run which are based on experimental observations of predatory dinoflagellate behavior, and this study specifically investigates how the predatory dinoflagellate Karlodinium veneficum uses toxins to immobilize its prey and increase its feeding rate. These simulations account for complex dynamics that were not included in the basic models, and the results from these computational simulations closely match the experimentally observed predatory behavior of K. veneficum and reinforce the notion that predatory dinoflagellates utilize toxins to increase their feeding rate.

This paper investigates the use of blending functions to improve nonlinear frequency response predictions for a pendulum system. The harmonic balance method is used to generate approximate analytical solutions for the amplitude-dependent natural frequency of an unforced pendulum, as well as the frequency response behavior of a forced pendulum. For both cases, separate results are obtained and compared from two different approximations for the sine function: Taylor series expansion (evaluated at the stable equilibrium position of the pendulum) and Legendre polynomial series expansion (evaluated for the pendulum’s entire range of motion). The solutions obtained from these two approximations feature a classical trade-off, with the Taylor series predictions offering superior accuracy at small to moderate amplitudes of oscillation, while the Legendre polynomial series predictions offer superior accuracy at moderate to large amplitudes of oscillation. We propose a method for blending these two results in order to obtain a hybrid analytical expression that captures the nonlinear amplitude-dependent characteristics of the pendulum system across its entire range of motion, and we validate these results with numerical studies and experimentation. We believe that this blending approach could also be applied to more complex systems whose dynamics exhibit similar nonlinear behavior to the pendulum.

This paper presents a theoretical analysis and experimental validation of passively reconfigurable bandgaps in a 1D chain of oscillators. Nonlinearities in the system result in a morphing of the bandgap structure when the excitation amplitude passes a certain threshold. Specifically, an asymmetric bistability is used to achieve amplitude dependent filtering through passive bandgap reconfiguration. The experimental system consists of a 1D chain of axially aligned pendulums arranged in dimer unit cells with nearest neighbor coupling. Repulsive magnets are used to induce bistability in the pendulums. Comparisons between experiments and theory show good agreement.

This paper develops a nonlinear mathematical model to describe the heart rate response of an individual during cycling. The model is able to account for the fluctuations of an individual’s heart rate while they participate in exercise that varies in intensity. A method for estimating the model parameters using a genetic algorithm is presented and implemented, and the results show good agreement between the actual parameter values and the estimated values when tested using synthetic data.Copyright © 2015 by ASME

This paper investigates the dynamic behavior of a 1D array of magnetically coupled MEMS oscillators. To facilitate future research and innovation, this paper details the model used to predict wave propagation behavior in the microfabricated array. The investigations model the oscillator array as a series of clamped-clamped beams that are coupled via magnetic proof masses. The contributions to system dynamics of the beam and magnetic interactions of each oscillator are theorized. Finally, the dynamic behavior for the entire array is investigated with a series of theoretical trend studies.Copyright © 2015 by ASME

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular, parabolic, and semi-elliptical disks. Horace Lamb's method for deriving the natural frequency of an arbitrary rocking disk is applied to three shapes with semicircular, parabolic, and semi-elliptical cross sections, respectively. For the case of the semicircular disk, the system's equation of motion is derived to verify Lamb's method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the cases of the parabolic and semi-elliptical disks, this investigation reveals a supercritical pitchfork bifurcation for changes in a single geometric parameter which indicates that the systems can exhibit bistable behavior. Comparisons between experimental validation and theory show good agreement.

We demonstrate a MEMS platform for the investigation of energy propagation behavior in an array of nonlinearly coupled oscillators. The long-term objective is to experimentally demonstrate behaviors that have, until recently, only been theorized to occur in oscillator networks, such as passively reconfiguring bandgaps, energy localization, and chimera states. An improved fundamental understanding and of these phenomena could offer new capabilities for the prevention of catastrophic failures from shock loads, passive amplitude and frequency filters, and energy conversion systems. Here, we detail the design and fabrication of a coupled oscillator testbed, and then demonstrate transverse wave propagation along 1-D magnetically coupled oscillator arrays. Ongoing experiments seek to realize more complicated energy transfer behavior via design variations on this testbed.

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular and parabolic disks. Horace Lamb’s method for deriving the natural frequency of an arbitrary rocking disk is applied to two shapes with semicircular and parabolic cross sections, respectively. For the case of the semicircular disk, the system’s equation of motion is derived to verify Lamb’s method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the case of the parabolic disk, this investigation unveils a super-critical pitchfork bifurcation for changes in a single geometric parameter which reveals that the system can exhibit bistable behavior. Rapid prototyping technology was used to manufacture sample disks across a wide range of parameters, and a laser tachometer was used to experimentally determine the natural frequency of each disk. Comparisons between experiment and theory show good agreement.Copyright © 2014 by ASME

By applying an asymmetric on-site restoring force in a 1D chain of oscillators, we demonstrate experimentally that a morphing in the bandgap structure or passive bandgap reconfiguration can be triggered by an increase in environmental excitation amplitude. Recent studies on wave propagation have focused on new capabilities and behaviors resulting from intrinsic nonlinearities. This paper details a bistable experimental design that achieves amplitude dependent filtering through passive bandgap reconfiguration, which is triggered by a bifurcation. The system studied comprises a 1D chain of axially aligned pendulums in dimer unit cells with geometrically nonlinear nearest neighbor coupling where bistability is induced through repulsive magnets. When the bistability is asymmetric, each potential well has a different linear spectra. Though this paper uses mechanically coupled oscillators as an example, the phenomenon itself could be used in any wave propagation media where asymmetric bistability can be implemented.