Introduction: Pes equinus with increased ankle joint stiffness is a common impairment in stroke and Cerebral Palsy (CP) patients with structural and/or neural deficits of the ankle muscles. Equinus gait is characterized by toe-strike, abnormal ankle plantarflexion and decreased ankle range of motion (ROM). A new ankle-foot orthosis (AFO) with negative stiffness was previously developed to compensate for the increased ankle joint stiffness and improve equinus gait, reducing plantarflexion and increasing ankle ROM. The goal of this project was to predict the effects of ankle stiffness compensation on equinus gait simulations.

Methods: Forward simulations of unimpaired and equinus gait were generated in
the sagittal plane with a musculoskeletal model implemented in OpenSim and a
neural controller implemented in SCONE. After validation of the unimpaired gait
simulation, a sensitivity analysis on ankle kinematics was performed, introducing
structural and/or neural alterations of the ankle muscles to achieve an equinus gait. Consecutively, equinus gait simulations were validated with previously collected data of CP patients. Finally, an AFO model was developed in OpenSim to simulate AFO-assisted gait.

Results: The unimpaired gait simulation yielded realistic results, and was robust to all alterations, generating stable gaits. Shorter Gastrocnemius fiber length and/or increased plantarflexor muscles activations, with Tibialis Anterior weakness, had the largest effect on the ankle joint kinematics and resulted in realistic CP equinus gaits. Simulations of AFO-assisted gait resulted in reduced abnormal plantarflexion, and increased ankle ROM in the condition with shorter Gastrocnemius.

Discussion and Conclusion: This study presented realistic simulations of equinus
gait, by modelling structural and/or neural alterations of the ankle muscles and
predicted improved ankle function when compensating ankle stiffness with an external force. Although higher stiffness compensation and more simulations should be obtained, this study provides a solid ground for further investigation of the AFO effects. These results can ultimately assist in the prescription and tuning of the new AFO for patients with equinus.

To objectively diagnose the severity of spasticity, it is important to measure the muscle activity accurately. Filtered EMG has an offset above zero which is part noise and part background activity. The goal of this study is to separate these two parts, using a non-linear neuromuscular ankle model. The model uses positional and EMG data as inputs to make a prediction of the output torque around the ankle, optimizing several muscle parameters. It was assumed model error was partly caused by the lack of separation of background activity and noise in the EMG offset. The correlation between model error and the force-length relationship of the muscle was investigated, as it was hypothesized that the force-length relationship could be used to separate background activity from noise in EMG.Twelve subjects (11 male, 1 female, mean age 25.21.7 years) participated in the study, which was approved by the TU Delft Human Research Ethics Committee. The Achilles ankle perturbator and the TMSi Porti7 EMG system were used to obtain positional and EMG data around the ankle. The subjects performed several trials containing multiple ramp-and-hold phases. The trials were performed while relaxed, and while performing co-contraction at 5% and 10% of maximum voluntary co-contraction. Model validity was judged on robustness and fit. Model fit shows how close the predicted torque resembles the measured torque. High robustness is defined as a low variance of the model parameters per subject, between trials. To improve robustness, two model configurations, one using averaged data and one simplified model configuration, were compared with the original model. The most robust model configuration was used as a basis for an alternative model, which added a parameter for each EMG signal, that subtracted part of the EMG offset. This EMG offset subtraction parameter was added to remove the constant part of the noise in the EMG offset. The correlation between model error and the force-length relationship of the model was calculated for the model with the best robustness, and the alternative model.Model robustness was not improved in the averaged data model configuration or the simplified model configuration, compared to the original model. The original model was therefore used for the rest of the study. The EMG offset subtraction parameter did not yield to desired reduction of noise in the EMG offset. This was likely a result of difficulties with determining the EMG offset. Only weak correlations (R<<0.3) were found between the model error and the force-length relationship of the muscles, for both the original model and the alternative model configuration.

Subjectivity, lack of precision, and accuracy are the challenges in the spasticity clinical measurement. One of the causes is the unwell standardization of the measurements that cause temporary changes in muscle resistance termed as muscle thixotropy. This temporary changes can affect the accuracy of the result that may lead to a wrong diagnosis. Unfortunately, resting period between the measurements, as one of the factors generating the thixotropic effect, is still not well considered. The present study investigates the effect of resting period on the short-range stiffness and the resting torque in muscle thixotropy around the human ankle joint. Twenty participants were seated on a chair with the foot placed onto the footplate connected to the Achilles Rehabilitation Device(ARD). The experimental procedure was done using segmental passive slow movements (v=5° /s) applied to the ankle with each segment consisting of multiple dorsi-plantarfexion cycles (Amplitude 15° in dorsiflexion direction) controlled by the ARD. Six different resting period durations (1s, 2s, 4s, 8s, 16s, 32s) were applied to the segments with Balance Latin Square randomization rule. The results clearly showed the time dependency of the Short-range stiffness (SRS) (RM ANOVA, F(1.702,32.399)=210.776, p<0.0005) and the resting torque (RM ANOVA, F(1.709,32.472)=210.776, p<0.0005) with a negative exponential pattern. We suggested that the most responsible structures for SRS and resting torque were the cross-bridges. We found that the resting torque was significantly affected by the multiple movements in the primary procedure (Wilcoxon Signed-Rank test, Z=-3920, p<0.0005) which had not recovered to its initial value. However, the insignificant effect was found in SRS (dependent t-test, t(19)=1.512, and p=0.147). We suggested that the SRS was generated as long as having enough resting period whereas resting torque was not. Our interpretation is that the resting torque was influenced by the mechanical-history of both dorsi- and plantar flexor muscles. The compliance of the tendon and the parallel connective tissue of plantarflexors, as well as the stiffness recovery of the dorsiflexor muscles, caused the slow resting torque recovery even though the cross-bridges in plantarflexors already started reforming.

Relevance: To enhance our understanding of motor impairments (e.g. post-stroke or due to Parkinson's Disease), objective measures for communication in the nervous system are required. By applying system identification techniques to oscillations in brain and muscle activity, we can objectively quantify the coupling between these areas.

Gap: Unfortunately, none of the existing techniques combine the ability to assess nonlinear behavior and to detect causality in a closed-loop, which is necessary to fully characterize communication in the nervous system.

Methods: In this study, a new connectivity measure, the Nonlinear Directed Transfer Function (NDTF) is introduced. The NDTF is derived by mapping a nonlinear autoregressive model (i.e. NARX model) to the frequency domain, and provides an approximation of the linear and nonlinear causal influences on the output spectrum.

Results: The NDTF was validated using simulated data of a bidirectional, nonlinear system. Additionally, NDTF was applied to simultaneously recorded EEG-EMG of a wrist flexion task. For the experimental data, the NDTF results were dominated by linear interactions.

Conclusions: The NDTF has proven advantages above existing connectivity measures. However, it is sensitive to changes in the sampling frequency and segmentation, making interpretation difficult. The mainly linear interaction found in the EEG-EMG data implies limited sensory feedback, since the ascending pathways are known to act nonlinear.

Ultrasound gives the opportunity to look at muscles and observe their change in length. This tool has increased the knowledge about muscle-tendon dynamics and sometimes revealed surprising muscle stretch behaviour. System identification experiments use robots to disturb the ankle and measure its torque and angle. Muscle movement is derived from the measured joint angle and their assumed relationship. This study uses plane-wave ultrasound imaging to investigate the relation between ankle angle and muscle length during system identification experiments. The first goal is to determine the feasibility of using ultrasound measurements for system identification.  The second goal is to investigate the validity of the assumption that muscle stretch is proportional to ankle angle and the effect of this assumption on the prediction of reflex size. Transient and continuous disturbances were applied to the ankle, while images of the soleus and gastrocnemius were recorded with ultrasound and processed with an image tracking algorithm. For small (1° SD) continuous perturbations ankle angle and muscle length can be assumed proportional during a relax task. However, a conclusion cannot be drawn for the position task due to the low coherence of the muscle length measurements. For transient perturbations with a high velocity (>90°/s) the muscle length showed oscillations that were not present in the ankle angle, demonstrating a non-proportional relationship. The gastrocnemius velocity predicted the size of the short latency reflex better than the perturbation velocity of the ankle robot. Using plane-wave ultrasound imaging for system identification experiments was feasible.