Development of a mathematical model for predicting electrically elicited quadriceps femoris muscle forces during isovelocity knee joint motion

Computational Design of FastFES Treatment to Improve Propulsive Force Symmetry During Post-stroke Gait: A Feasibility Study

Stroke is a leading cause of long-term disability worldwide and often impairs walking ability. To improve recovery of walking function post-stroke, researchers have investigated the use of treatments such as fast functional electrical stimulation (FastFES). During FastFES treatments, individuals post-stroke walk on a treadmill at their fastest comfortable speed while electrical stimulation is delivered to two muscles of the paretic ankle, ideally to improve paretic leg propulsion and toe clearance. However, muscle selection and stimulation timing are currently standardized based on clinical intuition and a one-size-fits-all approach, which may explain in part why some patients respond to FastFES training while others do not. This study explores how personalized neuromusculoskeletal models could potentially be used to enable individual-specific selection of target muscles and stimulation timing to address unique functional limitations of individual patients post-stroke. Treadmill gait data, including EMG, surface marker positions, and ground reactions, were collected from an individual post-stroke who was a non-responder to FastFES treatment. The patient's gait data were used to personalize key aspects of a full-body neuromusculoskeletal walking model, including lower-body joint functional axes, lower-body muscle force generating properties, deformable foot-ground contact properties, and paretic and non-paretic leg neural control properties. The personalized model was utilized within a direct collocation optimal control framework to reproduce the patient's unstimulated treadmill gait data (verification problem) and to generate three stimulated walking predictions that sought to minimize inter-limb propulsive force asymmetry (prediction problems). The three predictions used: (1) Standard muscle selection (gastrocnemius and tibialis anterior) with standard stimulation timing, (2) Standard muscle selection with optimized stimulation timing, and (3) Optimized muscle selection (soleus and semimembranosus) with optimized stimulation timing. Relative to unstimulated walking, the optimal control problems predicted a 41% reduction in propulsive force asymmetry for scenario (1), a 45% reduction for scenario (2), and a 64% reduction for scenario (3), suggesting that non-standard muscle selection may be superior for this patient. Despite these predicted improvements, kinematic symmetry was not noticeably improved for any of the walking predictions. These results suggest that personalized neuromusculoskeletal models may be able to predict personalized FastFES training prescriptions that could improve propulsive force symmetry, though inclusion of kinematic requirements would be necessary to improve kinematic symmetry as well.

Dynamic optimization of stimulation frequency to reduce isometric muscle fatigue using a modified Hill-Huxley model

INTRODUCTION

Optimal frequency modulation during functional electrical stimulation (FES) may minimize or delay the onset of FES-induced muscle fatigue.

METHODS

An offline dynamic optimization method, constrained to a modified Hill-Huxley model, was used to determine the minimum number of pulses that would maintain a constant desired isometric contraction force.

RESULTS

Six able-bodied participants were recruited for the experiments, and their quadriceps muscles were stimulated while they sat on a leg extension machine. The force-time (F-T) integrals and peak forces after the pulse train was delivered were found to be statistically significantly greater than the force-time integrals and peak forces obtained after a constant frequency train was delivered.

DISCUSSION

Experimental results indicated that the optimized pulse trains induced lower levels of muscle fatigue compared with constant frequency pulse trains. This could have a potential advantage over current FES methods that often choose a constant frequency stimulation train. Muscle Nerve 57: 634-641, 2018.

An Energetic Model of Low Frequency Isometric Neuromuscular Electrical Stimulation

The objective of this study was to evaluate whether an adapted Hill-type model of muscle energetics could account for the relatively high energy turnover observed during low frequency isometric Neuromuscular Electrical Stimulation (NMES). A previously validated Hill-based model was adapted to estimate the energy consumption due to muscle activation, force maintenance and internal shortening of the muscle during isometric NMES. Quadriceps muscle model parameters were identified for 10 healthy subjects based on the experimentally measured torque response to isometric stimulation at 8 Hz. Model predictions of torque and energy consumption rates across the stimulation range 1-12 Hz were compared with experimental data recorded from the same subjects. The model provided estimates in close agreement with the experimental values for the group mean energy consumption rate across the frequency range tested, (R adj (2) = 0.98), although prediction of individual data points for all frequencies and all subjects was more variable, (R adj (2) = 0.70). The model suggests that approximately one-third of the energy between 4 and 6 Hz is due to shortening heat. The model provides a means of identifying optimal therapeutic stimulation patterns for sustained incremental oxygen uptake at minimum torque output for a given muscle and provides insight into the energetic components involved.

Comparison of two stretching methods and optimization of stretching protocol for the piriformis muscle

Piriformis syndrome is an uncommon diagnosis for a non-discogenic form of sciatica whose treatment has traditionally focused on stretching the piriformis muscle (PiM). Conventional stretches include hip flexion, adduction, and external rotation. Using three-dimensional modeling, we quantified the amount of (PiM) elongation resulting from two conventional stretches and we investigated by use of a computational model alternate stretching protocols that would optimize PiM stretching. Seven subjects underwent three CT scans: one supine, one with hip flexion, adduction, then external rotation (ADD stretch), and one with hip flexion, external rotation, then adduction (ExR stretch). Three-dimensional bone models were constructed from the CT scans. PiM elongation during these stretches, femoral neck inclination, femoral head anteversion, and trochanteric anteversion were measured. A computer program was developed to map PiM length over a range of hip joint positions and was validated against the measured scans. ExR and ADD stretches elongated the PiM similarly by approximately 12%. Femoral head and greater trochanter anteversion influenced PiM elongation. Placing the hip joints in 115° of hip flexion, 40° of external rotation and 25° of adduction or 120° of hip flexion, 50° of external rotation and 30° of adduction increased PiM elongation by 30-40% compared to conventional stretches (15.1 and 15.3% increases in PiM muscle length, respectively). ExR and ADD stretches elongate the PiM similarly and therefore may have similar clinical effectiveness. The optimized stretches led to larger increases in PiM length and may be more easily performed by some patients due to increased hip flexion.

Predicting non-isometric fatigue induced by electrical stimulation pulse trains as a function of pulse duration

Background

Our previous model of the non-isometric muscle fatigue that occurs during repetitive functional electrical stimulation included models of force, motion, and fatigue and accounted for applied load but not stimulation pulse duration. Our objectives were to: 1) further develop, 2) validate, and 3) present outcome measures for a non-isometric fatigue model that can predict the effect of a range of pulse durations on muscle fatigue.

Methods

A computer-controlled stimulator sent electrical pulses to electrodes on the thighs of 25 able-bodied human subjects. Isometric and non-isometric non-fatiguing and fatiguing knee torques and/or angles were measured. Pulse duration (170–600 μs) was the independent variable. Measurements were divided into parameter identification and model validation subsets.

Results

The fatigue model was simplified by removing two of three non-isometric parameters. The third remained a function of other model parameters. Between 66% and 77% of the variability in the angle measurements was explained by the new model.

Conclusion

Muscle fatigue in response to different stimulation pulse durations can be predicted during non-isometric repetitive contractions.

Predicting fatigue during electrically stimulated non-isometric contractions

Mathematical prediction of power loss during electrically stimulated contractions is of value to those trying to minimize fatigue and to those trying to decipher the relative contributions of force and velocity. Our objectives were to: (1) develop a model of non-isometric fatigue for electrical stimulation-induced, open-chain, repeated extensions of the leg at the knee; and (2) experimentally validate the model. A computer-controlled stimulator sent electrical pulses to surface electrodes on the thighs of 17 able-bodied subjects. Isometric and non-isometric non-fatiguing and fatiguing leg extension torque and/or angle at the knee were measured. Two existing mathematical models, one of non-isometric force and the other of isometric fatigue, were combined to develop the non-isometric force-fatigue model. Angular velocity and 3 new parameters were added to the isometric fatigue model. The new parameters are functions of parameters within the force model, and therefore additional measurements from the subject are not needed. More than 60% of the variability in the measurements was explained by the new force-fatigue model. This model can help scientists investigate the etiology of non-isometric fatigue and help engineers to improve the task performance of functional electrical stimulation systems.