Wrist Motion Simulation With a Rigid Body Spring Model Comparing Different Elements Modeling Approaches
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A rigid body spring model was used to simulate wrist motions. The carpal bones were constructed based on a computed tomography of a cadaver wrist. Bony structures were assembled as a wrist model in the simulation software, RecurDyn. Articulations between wrist joint bones were modeled using gliding surfaces, each was attached to its bone surface and this articulation was controlled by contact forces in the simulation software. Wrist ligaments were modeled by either one or two spring elements for each ligament or major component. Muscles of the wrist were represented by axial force elements. The force exerted by each tendon in each wrist movement was computed using either exponential function or sigmoid function in two different models. Each of these force functions were proportional to the distance between the simulation capitate and the capitate in the desired position. Capitate was chosen as tracking marker because the common center of rotation of wrist is within the capitate head. Each of these approaches were simulated alone or with addition of a time factor. Eight wrist models were created. Each model simulated 34° extension, 57° extension, 30° flexion, 65° flexion, radial deviation and ulnar deviation. The root mean square error was calculated for linear and angular position for each carpal bone, each wrist movement, and for each model. The combined overall RMS errors for each model were calculated. The double spring ligament model with sigmoid force function considering time factor showed the least overall RMS error and most joint stability. The single spring ligament model with exponential force function without the time factor showed the highest RMS error and joint instability in some wrist motion simulations. The different modeling approaches used in this study helped in understanding the kinematics of the wrist joint and the wrist ligaments and tendons. The results of this work encourage using these models for further kinematic studies in tandem with in vivo or in vitro studies for further validation. These models can be helpful in simulating non-physiological conditions of the wrist. Further work related to result validation using data from multiple wrists, further enhancements of ligaments and muscles modeling will improve the accuracy of these wrist models.