ArborSim: Articulated, branching, OpenSim routing for constructing models of multi-jointed appendages with complex muscle-tendon architecture

Abstract

Computational models of musculoskeletal systems are essential tools for understanding how muscles, tendons, bones, and actuation signals generate motion. In particular, the OpenSim family of models has facilitated a wide range of studies on diverse human motions, clinical studies of gait, and even non-human locomotion. However, biological structures with many joints, such as fingers, necks, tails, and spines, have been a longstanding challenge to the OpenSim modeling community, especially because these structures comprise numerous bones and are frequently actuated by extrinsic muscles that span multiple joints—often more than three—and act through a complex network of branching tendons. Existing model building software, typically optimized for limb structures, makes it difficult to build OpenSim models that accurately reflect these intricacies. Here, we introduce ArborSim, customized software that efficiently creates musculoskeletal models of highly jointed structures and can build branched muscle-tendon architectures. We used ArborSim to construct toy models of articulated structures to determine which morphological features make a structure most sensitive to branching. By comparing the joint kinematics of models constructed with branched and parallel muscle-tendon units, we found that among various parameters—the number of tendon branches, the number of joints between branches, and the ratio of muscle fiber length to muscle tendon unit length—the number of tendon branches and the number of joints between branches are most sensitive to branching modeling method. Notably, the differences between these models showed no predictable pattern with increased complexity. As the proportion of muscle increased, the kinematic differences between branched and parallel models units also increased. Our findings suggest that stress and strain interactions between distal tendon branches and proximal tendon and muscle greatly affect the overall kinematics of a musculoskeletal system. By incorporating complex muscle-tendon branching into OpenSim models using ArborSim, we can gain deeper insight into the interactions between the axial and appendicular skeleton, model the evolution and function of diverse animal tails, and understand the mechanics of more complex motions and tasks.

Author summary

OpenSim models of musculoskeletal systems are valuable tools for understanding the mechanisms underlying biological movement. However, highly jointed structures, like necks and tails, have been difficult to model, likely due to the presence of numerous bones, and their complex network of branched muscle-tendon units that span many joints. We introduce ArborSim, a modeling tool that facilitates construction of branched muscle-tendon units. Our comparisons of equivalent branched and unbranched models suggest that the modeling approach greatly affects the model predictions, which thereby indicates the importance of accurately modeling branching in multi-jointed structures. With ArborSim, we provide a unified framework that not only streamlines the creation of the complex musculoskeletal models of these structures but also paves the way for more in-depth investigations into the biomechanical behavior of branched muscle-tendon networks. This encourages more detailed study of the material properties and mechanics of complex muscle-tendon branching networks and highly jointed structures.