A Computational Approach for Contactless Muscle Force and Strain Estimations in Distributed Actuation Biohybrid Mesh Constructs

Abstract

Biological muscle tissue can adapt to mechanical stimuli such as strain and become stronger. While this property has been explored for single, independent muscle actuators, it is still not well understood for more complex, distributed actuation architectures, which are needed for more complex biohybrid robotic systems. This study presents a computational approach for contactless methods to estimate individual muscle actuator strains and individual muscle forces on a distributed-actuator biohybrid mesh substrate. The methods presented in this work estimate the strain each muscle experiences as the substrate is stretched by creating a finite element model of our distributed muscle actuator biohybrid mesh, taking $79.8 \pm 51.9$ s to compute. Additionally, two contactless methods for muscle force estimation based on patterned substrate deformation are presented and compared: 1) Response Surface optimization, and 2) Direct Optimization. Both force estimation methods extract distributed muscle forces based on global substrate deformations. The Response Surface optimization resulted in a prediction error of $321 \pm 219\,\upmu$m with a runtime after model creation of $26 \pm 1.3$ s. The Direct Optimization method resulted in a prediction error of 0 $\upmu$m but took a long, highly-variable runtime of $663.4 \pm 918.5$ s. Directions for further improvement are discussed. Towards experimental validation of the outlined computational tools, a biaxial stretcher was constructed, and the ability to command desired displacements with the apparatus was characterized. The biaxial stretching platform achieved an average precision error of 3.10 ± 5.92% and 5.34 ± 2.38% for the x- and y-bars, respectively. Our methods aim to fill a critical gap in the design and analysis capabilities available to biohybrid robotics researchers. These preliminary estimation methods indicate the feasibility of our contactless muscle strain and muscle force estimation paradigm, which will be used to inform future in vitro experiments.