Marc-Oliver Gewaltig

From the computational point of view, musculoskeletal control is the problem of controlling high degrees of freedom and dynamic multi-body system that is driven by redundant muscle units. A critical challenge in the control perspective of skeletal joints with antagonistic muscle pairs is finding methods robust to address this ill-posed nonlinear problem. To address this computational problem, we implemented a twofold optimization and learning framework to be specialized in addressing the redundancies in the muscle control . In the first part, we used model predictive control to obtain energy efficient skeletal trajectories to mimick human movements. The second part is to use deep reinforcement learning to obtain a sequence of stimulus to be given to muscles in order to obtain the skeletal trajectories with muscle control. We observed that the desired stimulus to muscles is only efficiently constructed by integrating the state and control input in a closed-loop setting as it resembles the proprioceptive integration in the spinal cord circuits. In this work, we showed how a variety of different reference trajectories can be obtained with optimal control and how these reference trajectories are mapped to the musculoskeletal control with deep reinforcement learning. Starting from the characteristics of human arm movement to obstacle avoidance experiment, our simulation results confirm the capabilities of our optimization and learning framework for a variety of dynamic movement trajectories. In summary, the proposed framework is offering a pipeline to complement the lack of experiments to record human motion-capture data as well as study the activation range of muscles to replicate the specific trajectory of interest. Using the trajectories from optimal control as a reference signal for reinforcement learning implementation has allowed us to acquire optimum and human-like behaviour of the musculoskeletal system which provides a framework to study human movement in-silico experiments. The present framework can also allow studying upper-arm rehabilitation with assistive robots given that one can use healthy subject movement recordings as reference to work on the control architecture of assistive robotics in order to compensate behavioural deficiencies. Hence, the framework opens to possibility of replicating or complementing labour-intensive, time-consuming and costly experiments with human subjects in the field of movement studies and digital twin of rehabilitation.

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

The dendritic trees of neurons play an important role in the information processing in the brain. While it is tacitly assumed that dendrites require independent compartments to perform most of their computational functions, it is still not understood how they compartmentalize into functional subunits. Here we show how these subunits can be deduced from the structural and electrical properties of dendrites. We devised a mathematical formalism that links the dendritic arborization to an impedance-based tree-graph and show how the topology of this tree-graph reveals independent dendritic compartments. This analysis reveals that coopera-tivity between synapses decreases less than depolarization with increasing electrical separation, and thus that surprisingly few independent subunits coexist on dendritic trees. We nevertheless find that balanced inputs or shunting inhibition can modify this topology and increase the number and size of compartments in a context-dependent, temporal manner. We also find that this dynamic recompartmentalization can enable branch-specific learning of stimulus features.

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green’s function (GF) formalism can be rewritten to scale as [ ] with the number n of inputs locations, contrary to the previously reported [ ] scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.