3D Musculoskeletal Simulation




			The Department of Orthopaedic Surgery and Rehabilitation Biomechanics Laboratory Simulation Development Introduction In order to obtain a visual and quantitative verification of the appropriateness of one, two, and three degree of freedom models for motion, we have developed an interactive system for the independent adjustment and definition of multiple degree-of-freedom linkage systems representative of human leg and arm motion. The system is built so that, once the kinematic structure is defined, control points for interactive definition of muscle-tendon and ligament paths may be manually adjusted and refined, providing a tool for interactive musculoskeletal modeling and simulation. All kinematic transformation nodes are built as linkages within an openGL hierarchical structure. The structure for independent adjustment of each axis of motion required tracking the inverse of all transformations applied to the axis during visualization and adjustment. The inverse is applied to all structures below the axis of interest so that only the axis is effected during 3D adjustment. The system allows for the visual adjustment and verification of the placement of an axis or axes. This interactive task is carried out through control of point of view of the observer, the position and orientation of the view, and the position and orientation of each axis. These dynamic view and control commands are carried out simultaneously with rotational control of distal joint segments about their defined axis or axes. With such immediate and interactive flexibility, the user is able to rapidly iterate upon appropriate axis placement based upon a 3D visual verification of joint congruence throughout joint range-of-motion. (Click for larger version) Methods The current development environment is a dual processor 700 Mhz Pentium III Windows 2000 system using Visual C++ v6.0, and OpenGL with the GLUT Library. The graphics driver is the Evans & Sutherland Tornado using Realimage technology. In addition to mouse and keyboard interactive methods, this system utilizes pop-up menus with control widgets and 6 DOF control using a Spaceball (Spaceball model 3003, Spacetec IMC Corp., Lowell, MA). Structures for this kinematic model are derived from axial computerized tomography (CT) slices of fresh-frozen cadaver specimens. One mm thick slices spaced at 1 mm are used for the joint areas which require the greatest resolution. One mm thick slices spaced 5 mm apart are used for the mid shaft areas of bones. This approach helps to maintain highest detail in critical areas and save on structure size where such detail is not needed. The limbs used in the model were scanned on a General Electric Computerized Tomography scanner (GE Model 9800). The images are processed with Mimics software to yield standard stereolithography files describing each individual bone as a triangulated surface. The simulation software is then used to read in each stereolithography according to a kinematic hierarchy. Axes (up to three per diarthroidal joint) positions and orientations must initially be manually adjusted per literature references when available, or visual approximation when they are not. nd model. Various display modes (shading, wireframe, 3D stereo) and control methods ranging from keyboard to GUI to spaceball are available. Muscle-tendon and ligament paths may be described in terms of a sequence of manually positioned control points, some in a fixed position relative to a particular bone, others designed to slide smoothly over the surface of the bone. Once a path has been defined, it may be modeled as either a line segment or one of a variety of spline curves, and the moment arm as a function of joint angle may be viewed in real-time or recorded. (Click for larger version) Recent progress Here is a summary of progress over the past year in MS Word format. Related Research Many papers, posters, and conference presentations have been based upon this simulation. Much current work revolves around studies of muscle-tendon paths and moment arms, the correlation between the simulation and physiology, and particularly the use of the simulation as a predicting tool and hypothesis generator. A detailed list of publications may be added later. The Parametric Ellipse In the context of simulation development, the software developer derived this 3D parametric equation of an arbitrarily oriented ellipse: Here, theta is in radians, C is the center, and rho and phi are constants. As this does not appear to have been published elsewhere, a paper is in preparation. Some related information in the form of Mathematica worksheets: Proof that the path described by the parametric function is indeed an ellipse Proof that the path is coplanar The relation of rho and phi to the orientation and size of the ellipse Finding the vertices of the ellipse when rho and phi are known Here's a Word document discussing the determination of rho and phi to generate an ellipse with a particular semimajor and semiminor axes, and normal. Pseudo-Gaussian Model for Articulating Surfaces Challenged to come up with a surface-following model of the patella's motion over the femur, the developer noticed that the relevant articular surfaces had axial-parallel cross-sections which resembled a Gaussian (bell) curve. To avoid the mathematical difficulties of a true Gaussian function (not symbolically integrable), a pseudo-gaussian function was derived to model these articular surface cross-sections. Here, the x axis is a fixed rotational axis, and the y axis is the radial distance from that axis to the articular surface. This model is found to fit the articular surfaces extremely well, albeit via a nonlinear regression (performed by NLREG software). Although intended as a model for the patella and distal femur surfaces, this function turns out to be a surprisingly accurate model for nearly every articular joint surface in the body. The one exception found so far is the proximal head of the femur, which curves back on itself in a non-functional manner, better modeled by a sphere. A paper summarizing these results is in progress. Acknowledgments This project was supported by a grant provided by the Texas Advanced Technology Program (Project Number: 004952-0011-1999), with additional support from Sulzer Orthopedics, Inc., Austin, TX.

			Department Homepage \| Clinical Services \| Orthopaedic Residency \| Academics \| Research \| Administrative UTMB \| Search \| Directory \| Toolbox \| News \| Jobs \| Contact \| Sitemap UT System \| Reports to the State \| Compact With Texans \| Statewide Search This site published by Randal Morris (rmorris@utmb.edu) for The Department of Orthopaedic Surgery and Rehabilitation. Copyright © 2004-05 The University of Texas Medical Branch. Please review our privacy policy and Internet guidelines.

The Parametric Ellipse

Pseudo-Gaussian Model for Articulating Surfaces