A mathematical model of the human upper limb was developed based on high-resolution medical images of the muscles and bones obtained from the Visible Human Male (VHM) project. Three-dimensional surfaces of the muscles and bones were reconstructed from Computed Tomography (CT) images and Color Cryosection images obtained from the VHM cadaver. Thirteen degrees of freedom were used to describe the orientations of seven bones in the model: clavicle, scapula, humerus, radius, ulna, carpal bones, and hand. All of the major articulations from the shoulder girdle down to the wrist were included in the model. The model was actuated by 42 muscle bundles, which represented the actions of 26 muscle groups in the upper limb. The paths of the muscles were modeled using a new approach called the Obstacle-set Method [33]. The calculated paths of the muscles were verified by comparing the muscle moment arms computed in the model with the results of anatomical studies reported in the literature. In-vivo measurements of maximum isometric muscle torques developed at the shoulder, elbow, and wrist were also used to estimate the architectural properties of each musculotendon actuator in the model. The entire musculoskeletal model can be reconstructed using the data given in this paper, along with information presented in a companion paper which defines the kinematic structure of the model [26].

The purpose of this study was to develop and apply a general method for estimating the architectural properties of human muscles in vivo. The method consists of a two-phase, nested optimization procedure in which the values of peak isometric force, optimal muscle-fiber length, and tendon slack length are calculated for each musculotendon actuator, knowing muscle volume and the minimum and maximum physiological lengths of the actuator. In phase I, the positions of the bones and the activation levels of the muscles are found by maximizing the isometric torque developed for each degree of freedom at each joint. In phase II, the architectural properties of each musculotendon actuator are found by matching the strength profile of the model to that measured for subjects. The method is used to estimate the architectural properties of 26 major muscle groups crossing the shoulder, elbow, and wrist. Wherever possible, the model calculations are compared against measurements obtained from anatomical studies reported in the literature. Architectural data obtained from our work should be useful to researchers interested in developing musculoskeletal models of the upper limb.

A computational method is introduced for modeling the paths of muscles in the human body. The method is based on the premise that the resultant muscle force acts along the locus of the transverse cross-sectional centroids of the muscle. The path of the muscle is calculated by idealizing its centroid path as a frictionless elastic band, which moves freely over neighboring anatomical constraints such as bones and other muscles. The anatomical constraints, referred to as obstacles, are represented in the model by regular-shaped, rigid bodies such as spheres and cylinders. The obstacles, together with the muscle path, define an obstacle set. It is proposed that the path of any muscle can be modeled using one or more of the following four obstacle sets: single sphere, single cylinder, double cylinder, and sphere-capped cylinder. Assuming that the locus of the muscle centroids is known for an arbitrary joint configuration, the obstacle-set method can be used to calculate the path of the muscle for all other joint configurations. The obstacle-set method accounts not only for the interaction between a muscle and a neighboring anatomical constraint, but also for the way in which this interaction changes with joint configuration. Consequently, it is the only feasible method for representing the paths of muscles which cross joints with multiple degrees of freedom such as the deltoid at the shoulder.

A kinematic model of the arm was developed using high-resolution medical images obtained from the National Library of Medicine's Visible Human Project (VHP) dataset. The model includes seven joints and uses thirteen degrees of freedom to describe the relative movements of seven upper-extremity bones: the clavicle, scapula, humerus, ulna, radius, carpal bones, and hand. Two holonomic constraints were used to model the articulation between the scapula and the thorax. The kinematic structure of each joint was based on anatomical descriptions reported in the literature. The three joints comprising the shoulder girdle - the sternoclavicular joint, the acromioclavicular joint, and the glenohumeral joint - were each modeled as a three degree-of-freedom, ideal, ball-and-socket joint. The articulations at the elbow and wrist - humeroulnar flexion-extension, radioulnar pronation-supination, radiocarpal flexion-extension, and radiocarpal radial-ulnar deviation - were each modeled as a single degree-of-freedom, ideal, hinge joint. Locations of the joint centers and joint axes were derived by graphically inspecting the three-dimensional surfaces of the reconstructed bones. The relative positions of the bones were defined by fixing a reference frame to each bone; the position and orientation of each reference frame were based on the positions of anatomical landmarks and on the shapes of the reconstructed bone surfaces. Tables are provided which specify the positions and orientations of the joint axes and the bone-fixed reference frames for the model arm.

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To understand how humans perform non-ballistic movements, we have developed an optimal control model to simulate rising from a chair. The human body was modeled as a three-segment, articulated, planar linkage, with adjacent links joined together by frictionless revolutes. The skeleton was actuated by eight musculotendinous units with each muscle modeled as a three-element entity in series with tendon. Because rising from a chair presents a relatively ambiguous performance criterion, we chose to evaluate a number of different performance criteria, each based upon a fundamental dynamical property of movement; muscle force. Through a quantitative comparison of model and experiment, we found that neither a minimum-impulse nor a minimum-energy criterion is able to reproduce the major features of standing up. Instead, we introduce a performance criterion based upon an important and previously overlooked dynamical property of muscle: the time derivative of force. Our motivation for incorporating such a quantity into a mathematical description of the goal of a motor task is founded upon the belief that non-ballistic movements are controlled by gradual increases in muscle force rather than by rapid changes in force over time. By computing the optimal control solution for rising from a static squatting position, we show that minimizing the integral of a quantity which depends upon the time derivative of muscle force meets an important physiological requirement: it minimizes the peak forces developed by muscles throughout the movement. Furthermore, by computing the optimal control solution for rising from a chair, we demonstrate that multi-joint coordination is dictated not only by the choice of a performance criterion but by the presence of a motion constraint as well.

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