Wendy M. Murray

A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control.

Biomechanical models of the musculoskeletal system are frequently used to study neuromuscular control and simulate surgical procedures. To be broadly applicable, a model must be accessible to users, provide accurate representations of muscles and joints, and capture important interactions between joints. We have developed a model of the upper extremity that includes 15 degrees of freedom representing the shoulder, elbow, forearm, wrist, thumb, and index finger, and 50 muscle compartments crossing these joints. The kinematics of each joint and the force-generating parameters for each muscle were derived from experimental data. The model estimates the muscle–tendon lengths and moment arms for each of the muscles over a wide range of postures. Given a pattern of muscle activations, the model also estimates muscle forces and joint moments. The moment arms and maximum moment-generating capacity of each muscle group (e.g., elbow flexors) were compared to experimental data to assess the accuracy of the model. These comparisons showed that moment arms and joint moments estimated using the model captured important features of upper extremity geometry and mechanics. The model also revealed coupling between joints, such as increased passive finger flexion moment with wrist extension. The computer model is available to researchers at http://nmbl.stanford.edu.

Variation of muscle moment arms with elbow and forearm position

We hypothesized that the moment arms of muscles crossing the elbow vary substantially with forearm and elbow position and that these variations could be represented using a three-dimensional computer model. Flexion/extension and pronation/supination moment arms of the brachioradialis, biceps, brachialis, pronator teres, and triceps were calculated from measurements of tendon displacement and joint angle in two anatomic specimens and were estimated using a computer model of the elbow joint. The anatomical measurements revealed that the flexion/extension moment arms varied by at least 30% over a 95 degrees range of motion. The changes in flexion/extension moment arm magnitudes with elbow flexion angle were represented well by the computer model. The anatomical studies and the computer model demonstrate that the biceps flexion moment arm peaks in a more extended elbow position and has a larger peak when the forearm is supinated. Also, the peak biceps supination moment arm decreases as the elbow is extended. These results emphasize the need to account for the variation of muscle moment arms with elbow flexion and forearm position.

The isometric functional capacity of muscles that cross the elbow

We hypothesized that muscles crossing the elbow have fundamental differences in their capacity for excursion, force generation, and moment generation due to differences in their architecture, moment arm, and the combination of their architecture and moment arm. Muscle fascicle length, sarcomere length, pennation angle, mass, and tendon displacement with elbow flexion were measured for the major elbow muscles in 10 upper extremity specimens. Optimal fascicle length, physiological cross-sectional area (PCSA), moment arm, operating range on the force-length curve, and moment-generating capacity were estimated from these data. Brachioradialis and pronator teres had the longest (17.7cm) and shortest (5.5cm) fascicles, respectively. Triceps brachii (combined heads) and brachioradialis had the greatest (14.9cm(2)) and smallest (1.2cm(2)) PCSAs, respectively. Despite a comparable fascicle length, long head of biceps brachii operates over a broader range of the force-length curve (length change=56% of optimal length, 12.8cm) than the long head of triceps brachii (length change=28% of optimal length, 12. 7cm) because of its larger moment arm (4.7cm vs. 2.3cm). Although brachioradialis has a small PCSA, it has a relatively large moment-generating capacity (6.8cm(3)) due to its large moment arm (average peak=7.7cm). These results emphasize the need to consider the interplay of architecture and moment arm when evaluating the functional capabilities of a muscle.

Identification of key pinch forces required to complete functional tasks

Reconstructive hand surgeries restore key pinch to individuals with pinch force deficits caused by tetraplegia. Data that define the magnitudes of force necessary to complete functional key pinch tasks are limited. This study aims to establish target pinch forces for completing selected tasks that represent a range of useful functional activities. A robot arm instrumented with a force sensor completed the tasks and simultaneously measured the forces applied to the task objects. Lateral pinch force requirements were calculated from these measured object forces. Pinch force requirements ranged from 1.4 N to push a button on a remote to 31.4 N to insert a plug into an outlet. Of the tasks studied, 9 of 12 required less than 10.5 N. These pinch force requirements, when compared to pinch forces produced by 14 individuals with spinal cord injuries (with and without surgical reconstruction of pinch), accurately predicted success or failure in 81% of subject trials. The prediction errors indicate a need to measure other factors such as pinch opening, force location, force direction, and proximal joint control.

Architecture of the rectus abdominis, quadratus lumborum, and erector spinae

Quantitative descriptions of muscle architecture are needed to characterize the force-generating capabilities of muscles. This study reports the architecture of three major trunk muscles: the rectus abdominis, quadratus lumborum, and three columns of the erector spinae (spinalis thoracis, longissimus thoracis and iliocostalis lumborum). Musculotendon lengths, muscle lengths, fascicle lengths, sarcomere lengths, pennation angles, and muscle masses were measured in five cadavers. Optimal fascicle lengths (the fascicle length at which the muscle generates maximum force) and physiologic cross-sectional areas (the ratio of muscle volume to optimal fascicle length) were computed from these measurements. The rectus abdominis had the longest fascicles of the muscles studied, with a mean (S.D.) optimal fascicle length of 28.3 (4.2)cm. The three columns of the erector spinae had mean optimal fascicle lengths that ranged from 6.4 (0.6)cm in the spinalis thoracis to 14.2 (2.1)cm in the iliocostalis lumborum. The proximal portion of the quadratus lumborum had a mean optimal fascicle length of 8.5 (1.5)cm and the distal segment of this muscle had a mean optimal fascicle length of 5.6 (0.9)cm. The physiologic cross-sectional area of the rectus abdominis was 2.6 (0.9)cm(2), the combined physiologic cross-sectional area of the erector spinae was 11.6 (1.8)cm(2), and the physiologic cross-sectional area of the quadratus lumborum was 2.8 (0.5)cm(2). These data provide the basis for estimation of the force-generating potential of these muscles.

Muscle short-range stiffness can be used to estimate the endpoint stiffness of the human arm

The mechanical properties of the human arm are regulated to maintain stability across many tasks. The static mechanics of the arm can be characterized by estimates of endpoint stiffness, considered especially relevant for the maintenance of posture. At a fixed posture, endpoint stiffness can be regulated by changes in muscle activation, but which activation-dependent muscle properties contribute to this global measure of limb mechanics remains unclear. We evaluated the role of muscle properties in the regulation of endpoint stiffness by incorporating scalable models of muscle stiffness into a three-dimensional musculoskeletal model of the human arm. Two classes of muscle models were tested: one characterizing short-range stiffness and two estimating stiffness from the slope of the force-length curve. All models were compared with previously collected experimental data describing how endpoint stiffness varies with changes in voluntary force. Importantly, muscle properties were not fit to the experimental data but scaled only by the geometry of individual muscles in the model. We found that force-dependent variations in endpoint stiffness were accurately described by the short-range stiffness of active arm muscles. Over the wide range of evaluated arm postures and voluntary forces, the musculoskeletal model incorporating short-range stiffness accounted for 98 ± 2, 91 ± 4, and 82 ± 12% of the variance in stiffness orientation, shape, and area, respectively, across all simulated subjects. In contrast, estimates based on muscle force-length curves were less accurate in all measures, especially stiffness area. These results suggest that muscle short-range stiffness is a major contributor to endpoint stiffness of the human arm. Furthermore, the developed model provides an important tool for assessing how the nervous system may regulate endpoint stiffness via changes in muscle activation.

Benchmarking of dynamic simulation predictions in two software platforms using an upper limb musculoskeletal model

Several opensource or commercially available software platforms are widely used to develop dynamic simulations of movement. While computational approaches are conceptually similar across platforms, technical differences in implementation may influence output. We present a new upper limb dynamic model as a tool to evaluate potential differences in predictive behavior between platforms. We evaluated to what extent differences in technical implementations in popular simulation software environments result in differences in kinematic predictions for single and multijoint movements using EMG- and optimization-based approaches for deriving control signals. We illustrate the benchmarking comparison using SIMM–Dynamics Pipeline–SD/Fast and OpenSim platforms. The most substantial divergence results from differences in muscle model and actuator paths. This model is a valuable resource and is available for download by other researchers. The model, data, and simulation results presented here can be used by future researchers to benchmark other software platforms and software upgrades for these two platforms.

The Influence of Elbow Position on the Range of Motion of the Wrist Following Transfer of the Brachioradialis to the Extensor Carpi Radialis Brevis Tendon

Background: In patients who have an injury of the cervical spinal cord, the brachioradialis tendon may be transferred to the extensor carpi radialis brevis tendon to restore voluntary wrist extension. We hypothesized that the active range of motion of the wrist depends on the position of the elbow after this transfer because the brachioradialis changes length substantially during elbow flexion, which implies the maximum force that the muscle can produce varies with elbow position. The objectives of this study were to determine whether the position of the elbow influences the range of motion of the wrist following transfer of the brachioradialis to the extensor carpi radialis brevis tendon and to evaluate the effect of surgical tensioning.Methods: The range of motion of eight wrists was assessed after brachioradialis transfer. Two positions of the elbow were tested, the passive limit of elbow extension and 120° of flexion. The range of motion of the wrist was also simulated with use of a biomechanical model. Using the model, we compared the active range of motion of the wrist, with the elbow at 0° and 120° of flexion, following three different approaches to surgical tensioning. The simulations were also repeated to evaluate how muscle strength influences outcomes.Results: Wrist extension decreased and passive flexion increased when the elbow was flexed. Maximum wrist extension was significantly correlated with passive flexion in all subjects (r = 0.95 and p < 0.001 when the elbow was extended and r = 0.82 and p < 0.03 when the elbow was flexed). The biomechanical model suggested that tensioning the tendon transfer so that the fibers of the brachioradialis do not become excessively short when the elbow is flexed may improve outcomes. The simulations also revealed that it is more difficult to maintain a consistent wrist position with the elbow in different postures when a weaker muscle is transferred.Conclusions: The model suggests that altering the surgical tension could improve wrist extension when the elbow is flexed. However, the ultimate result is sensitive to the strength of the brachioradialis.Clinical Relevance: The brachioradialis is the donor muscle most commonly used to restore the function of the wrist and hand in tetraplegia. Because many self-care activities involve acquiring an object at a distance from the body and then bringing the object close to the body, it is important to consider the influence of the position of the elbow on the function of the transferred brachioradialis.

The unoperated hand: the role of passive forces in hand function after tetraplegia

Passive forces play a large role in hand function after tetraplegia. Most individuals with tetraplegia choose not to undergo surgical reconstruction of hand function and, therefore, depend on the passive properties of their musculoskeletal system to perform functional tasks. Knowledge of the levels of force needed to perform many of these tasks is lacking. Understanding the mechanics of producing passive force is important for designing adaptive tools and other devices for tetraplegic individuals. Knowledge of the passive properties of the upper extremity is important in forming treatment strategies. The passive forces produced for change to the tenodesis grasp are small but useful to the individual. Since these forces arise from basic anatomy and muscle function, they are important even after surgical restoration of hand function. Compensatory strategies for the unoperated hand probably play a role in the operated hand. The approach to surgical restoration of grasp must consider how passive forces contribute to functional outcome.

Biomechanics of the Steindler Flexorplasty Surgery: A Computer Simulation Study

PURPOSE Our goal was to investigate the capacity of a Steindler flexorplasty to restore elbow flexion to persons with C5-C6 brachial plexus palsy. In this procedure the origin of the flexor-pronator mass is moved proximally onto the humeral shaft. We examined how the choice of the proximal attachment site for the flexor-pronator mass affects elbow flexion restoration, especially considering possible side effects including limited wrist and forearm motion owing to passive restraint from stretched muscles. METHODS A computer model of the upper extremity was used to simulate the biomechanical consequences of various surgical alterations. Unimpaired, preoperative, and postoperative conditions were simulated. Seven possible transfer locations were used to investigate the effects of choice of transfer location. RESULTS Each transfer site produced a large increase in elbow flexion strength. Transfer to more proximal attachment sites also produced large increases in passive resistance to wrist extension and forearm supination. CONCLUSIONS To reduce detrimental side effects while achieving clinical goals our theoretical analysis suggests a transfer to the distal limit of the traditional transfer region.