Optimal Control of Isometric Muscle Dynamics

We use an indirect optimal control approach to calculate the optimal neural stimulation needed to obtain measured isometric muscle forces. The neural stimulation of the nerve system is hereby considered to be a control function (input) of the system 'muscle' that solely determines the muscle force (output). We use a well-established muscle  model and experimental data of isometric contractions. The model consists of coupled activation and contraction dynamics described by ordinary differential equations. To validate our results, we perform a comparison with commercial optimal control software

Implementation and validation of the extended Hill-type muscle model with robust routing capabilities in LS-DYNA for active human body models

In the state of the art finite element AHBMs for car crash analysis in the LS-DYNA software material named *MAT_MUSCLE (*MAT_156) is used for active muscles modeling. It has three elements in parallel configuration, which has several major drawbacks: restraint approximation of the physical reality, complicated parameterization and absence of the integrated activation dynamics. This study presents implementation of the extended four element Hill-type muscle model with serial damping and eccentric force-velocity relation including Ca2+ dependent activation dynamics and internal method for physiological muscle routing

Improving Precision Force Control With Low-Frequency Error Amplification Feedback: Behavioral and Neurophysiological Mechanisms

Although error amplification (EA) feedback has been shown to improve performance on visuomotor tasks, the challenge of EA is that it concurrently magnifies task-irrelevant information that may impair visuomotor control. The purpose of this study was to improve the force control in a static task by preclusion of high-oscillatory components in EA feedback that cannot be timely used for error correction by the visuomotor system. Along with motor unit behaviors and corticomuscular coherence, force fluctuations (Fc) were modeled with non-linear SDA to contrast the reliance of the feedback process and underlying neurophysiological mechanisms by using real feedback, EA, and low-frequency error amplification (LF-EA). During the static force task in the experiment, the EA feedback virtually potentiated the size of visual error, whereas the LF-EA did not channel high-frequency errors above 0.8 Hz into the amplification process. The results showed that task accuracy was greater with the LF-EA than with the real and EA feedback modes, and that LF-EA led to smaller and more complex Fc. LF-EA generally led to smaller SDA variables of Fc (critical time points, critical point of Fc, the short-term effective diffusion coefficient, and short-term exponent scaling) than did real feedback and EA. The use of LF-EA feedback increased the irregularity of the ISIs of MUs but decreased the RMS of the mean discharge rate, estimated with pooled MU spike trains. Beta-range EEG–EMG coherence spectra (13–35 Hz) in the LF-EA condition were the greatest among the three feedback conditions. In summary, amplification of low-frequency errors improves force control by shifting the relative significances of the feedforward and feedback processes. The functional benefit arises from the increase in the common descending drive to promote a stable state of MU discharges

Occupant Neck Muscle Modelling in Rear-End Crashes

The ultimate goal of the present research is to incorporate active and passive neck muscle effects in a female Finite Element (FE) Human Body Model (HBM). The application of interest is Whiplash Associated Disorders (WAD), which can occur in a low-speed rear-end impact. Two reflex mechanisms, the Vestibulocollic reflex (VCR) and the Cervicocollic reflex (CCR), are integral to maintaining head orientation. Therefore, active muscle modelling in HBMs should address the behaviour of these reflex mechanisms. Female FE HBMs are the focus of the present thesis because of their higher risk of sustaining WAD than males. This model should reproduce kinematics that can be used for global and local tissue injury prediction of WAD. The present thesis was arranged to address the main objective systematically and consists of six studies addressing five research questions. Two human body models representing the 50th percentile population, the VIVA OpenHBM and VIVA+ HBM, were used. The model was developed with and benchmarked against volunteer test data. Based on the collective studies in this thesis, the isolated head-neck model can be used to develop an active muscle controller. A simple, single-link approach was used to design a Proportional-Derivative (PD) controller called Angular Positioned Feedback (APF). This simple controller was convenient to implement and calibrate with available experimental data. Furthermore, reliable parameter identification, such as active muscle controller gains, were obtained via optimization using both head and cervical vertebral kinematics as objectives. A parameter study of different control strategies confirmed that the APF control strategy, combined with parallel damping elements (PDE), was the most effective for recreating volunteer kinematic responses compared to the model with only passive elements, particularly when impact severity was varied. Real-world collision data was used to evaluate the model’s usefulness using injury outcome data for known collision severities. The inclusion of neck muscle responses considerably influenced the cervical vertebral kinematics but only slightly influenced head kinematics before the rebound phase, depending on the head-to-headrest offset. Consequently, a slight difference in global kinematic-based injury criteria such as Neck Injury Criteria (NIC) was observed between a model with and without neck muscle responses. In contrast, significant differences between the two groups were observed for local, tissue-based, whiplash injury prediction. Hypotheses, such as Aldman pressure, require cervical spine kinematics and place higher requirements on the model’s performance. This analysis revealed the need for both global-based injury criteria and local, tissue level analysis to understand how WAD occur. Therefore, whiplash injury prediction would be more reliable using a model with the APF control strategy combined with PDE developed herein, than a model without active neck muscle responses. The FE HBMs with neck muscle responses have been developed and validated for low-speed rear-end impact and WAD analyses. The models have been shown to be robust and able to replicate volunteer head-neck kinematics

A Novel Framework to Model the Short and Medium Term Mechanical Response of the Medial Gastrocnemius

Musculoskeletal disorders (MSDs) are the second largest cause of disability worldwide and cost the UK National Health Service (NHS) over £4.7 billion yearly. One holistic approach to alleviate this burden is to create in silico models that provide insight into MSDs which will improve diagnostic and therapeutic procedures. This thesis presents a modelling framework that analyses the mechanical behaviour of anatomical skeletal muscles. The anatomical geometry and fibre paths of the medial gastrocnemius muscle were acquired from the Living Human Data Library (LHDL). The medial gastrocnemius model was further sophisticated by incorporating morphological representations of the aponeurosis and myotendon transition region. Having carried out a finite element analysis on the medial gastrocnemius, it was found that the morphology and size of the transition region significantly affected the mechanical response of the muscle. Three illustrative simulations were subsequently carried out on the model, to better understand the muscle’s mechanical response in differing mechanical environments: (1) the effects of high extensions on the muscle’s mechanical response, (2) lengthening of the aponeurosis - a phenomenon often observed following aponeurosis regression - and (3) the stress-strain regime of the muscle when the tendon experiences a laceration and heals over 21 days. These models show the regions that experienced the highest strains were the muscle-tendon transition regions. As MSDs tend to be of a degenerative nature and progress over time, the temporal changes of the mechanical response of skeletal muscle tissue is of great interest. In the penultimate chapter, the medial gastrocnemius was assessed across various remodelling regimes. It was found that the muscle returned to homeostasis only when both the muscle and tendon remodelled – albeit, at different remodelling rates. Whilst this observation seems intuitive, most other growth and remodelling models of skeletal muscles have only remodelled either the muscle or tendon constituent. The model developed in this thesis therefore has the potential to inform multi-scale musculo-skeletal muscle models thus providing a significant contribution to understanding MSDs