Modeling and Identifying the Somatic Reflex Network of the Human Neuromuscular System Akihiko MURAI, Katsu YAMANE, and Yoshihiko NAKAMURA Department of Mechano-Informatics University of Tokyo 7-3-1, Hongo, Bunkyo-ku Tokyo, 113-8656, JAPAN Email: murai@ynl.t.u-tokyo.ac.jp Abstract— In this paper, we build a mathematical model of the whole-body neuromuscular network and identify its parameters by optical motion capture, inverse kinematics, inverse dynamics computation, and statistical analysis. The model includes a skeleton, a musculotendon network, and a neuromuscular network. The skeleton is composed of 155 joints representing the inertial property and mobility of the human body. The musculotendon network includes more than 1000 muscles, tendons, and ligaments modeled as ideal wires with any number of via points. We also develop an inverse dynamics algorithm to estimate the muscle tensions required to perform a given motion sequence. Finally, we model the somatic reflex network based on the relationship between the spinal nerves and the muscle tensions by a neural network. The resulting parameters match well with the agonist-antagonist relationship of the muscles. We also demonstrate that the model inherently includes low-level somatic reflexes such as the patellar tendon reflex using the neuromuscular model. This is the attempt to build and identify the neuromuscular network based only on non- invasive motion measurements, and the result shows that the whole-body muscles can be controlled by the command signals as few as the number of spinal nerve rami. Keywords: Musculoskeletal Human Model, Neuromuscular Network, Somatic Reflex, Neural Network. I. Introduction It is still an open research issue to understand the mechanism for generating and coordinating human motions. In the brain science community, researchers have been tried to analyze and model how the brain coordinates the whole-body motion [1], [2]. In the biome- chanics community, on the other hand, the dynamics computation and motion analysis using musculoskeletal models have been investigated [3], [4], [5]. However, the ones are too line-by-line and the others are too rough, so there is still a large gap between the two approaches. In this research, we build a whole-body neuromuscular system on top of our musculoskeletal human model for somatosensory calculation (Fig. 1) [6]. We identify the parameters of the neuromuscular model through experiments using optical motion capture system, inverse kinematics, inverse dynamics computation, statistical methods, and a neural network model. This work is intended to become the jump-start to bridge the gap between the two fields. The developed model will be Fig. 1. The musculoskeletal model. applied to the fields such as biomechanics, neurology, rehabilitation, and sport science. Our model consists of a skeleton, a musculotendon network, and a neuromuscular network. We model the neuromuscular network by a neural network representing the connection between the spinal neural signals and the muscle tensions. To identify the parameters of this neural network, we first measure the human motions with an optical motion capture system. We then use our musculoskeletal model to solve the inverse dynamics, and obtain the muscle tensions required to achieve the captured motions. Independent component analysis (ICA) is applied to the muscle tension data, which indicates that the 989-dimiensional muscle tensions can be represented by as few as 120 independent signals. We train the neural network model of the neuromuscular network such that it outputs the muscle tension data when the inputs are the independent components. The neural network parameters show a clear correspondence with the agonist-antagonist relationships of the muscles. The human neuromuscular system contains complex closed-loops of the somatic reflexes. It is, however, usually very difficult to identify a system embedded in a closed-loop. In our previous work, we modeled the neuromuscular network by converting each closed- loop to an open-loop [7]. According to the research on Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 23-26, 2007. FrB08.2 1-4244-0788-5/07/$20.00 ©2007 IEEE 2717