Publications 2003-2005
Introduction:
We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. Many practitioners solve these types of problems using reduced coordinate (or generalized coordinate) formulations that parameterize the degrees of freedom in a manner consistent with the constraints of articulation, effectively reducing the overall degrees of freedom, eliminating those that could violate the constraints. However, consistency conditions are required to ensure that closed loops are actually closed adding a nonlocal constraint to the system. Moreover, unpredictable contact and collision can pose serious difficulties. We have found it easier to design algorithms that treat closed loops and frequent contact and collision in maximal coordinates, and propose a novel maximal coordinates approach that builds on the previous work of [Guendelman et al. 2003]. Our approach works with any black box method for specifying valid joint constraints, and no special considerations are required for arbitrary closed loops and/or branching. Moreover, our technique is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies but not in the number of auxiliary constraints.
Abstract:
We present a tetrahedral mesh generation algorithm designed for the Lagrangian simulation of deformable bodies. The algorithm’s input is a level set (i.e., a signed distance function on a Cartesian grid or octree). First a bounding box of the object is covered with a uniform lattice of subdivision-invariant tetrahedra. The level set is then used to guide a red green adaptive subdivision procedure that is based on both the local curvature and the proximity to the object boundary. The final topology is carefully chosen so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, this candidate mesh is compressed to match the object boundary. To maintain element quality during this compression phase we relax the positions of the nodes using finite elements, masses and springs, or an optimization procedure. The resulting mesh is well suited for simulation since it is highly structured, has topology chosen specifically for large deformations, and is readily refined if required during subsequent simulation.We then use this algorithm to generate meshes for the simulation of skeletal muscle from level set representations of the anatomy. The geometric complexity of biological materials makes it very difficult to generate these models procedurally and as a result we obtain most if not all data from an actual human subject. Our current method involves using voxelized data from the Visible Male [1] to create level set representations of muscle and bone geometries. Given this representation, we use simple level set operations to rebuild and repair errors in the segmented data as well as to smooth aliasing inherent in the voxelized data.
Abstract:
Computer models of the musculoskeletal system generally represent muscle geometry using a series of line segments. This simplification limits the ability of models to accurately represent the paths of muscles with complex geometry and assumes that moment arms are equivalent for all fibers within a muscle (or muscle compartment). Recently Blemker and Delp demonstrated that three-dimensional (3D) finite-element models of muscle can improve representations of muscles with complex geometry, like the gluteus maximus, which has broad attachments and wraps around underlying structures. 3D muscle modeling has the potential to improve our ability to represent complex musculoskeletal structures, including the shoulder and neck. However, the applicability of 3D muscle modeling to these problems is limited due to computational expense. Solutions take over three hours for one or two muscles using a standard nonlinear finite-element formulation. Recently, Teran et al introduced a new quasi-static invertible finite-element algorithm that allows for major improvements in simulation times over traditional techniques. The goal of the present work is to evaluate the accuracy of this new finite-element solution strategy for representing skeletal muscle behavior. To do this, we created a 3D model of the gluteus maximus (a complex muscle that has broad attachments and wraps around underlying structures), simulated the motion of the muscle through hip flexionextension using new the formulation as well as the standard formulation, and compared the results from the two methods.
Abstract:
Quasistatic and implicit time integration schemes are typically employed to alleviate the stringent time step restrictions imposed by their explicit counterparts. However, both quasistatic and implicit methods are subject to hidden time step restrictions associated with both the prevention of element inversion and the effects of discontinuous contact forces. Furthermore, although fast iterative solvers typically require a symmetric positive definite global stiffness matrix, a number of factors can lead to indefiniteness such as large jumps in boundary conditions, heavy compression, etc. We present a novel quasistatic algorithm that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration. Additionally, we robustly compute smooth elastic forces in the presence of highly deformed, inverted elements alleviating artificial time step restrictions typically required to prevent such states. Finally, we propose a novel strategy for treating both collision and self-collision in this context.
Abstract:
Simulation of the musculoskeletal system has important applications in biomechanics, biomedical engineering, surgery simulation, and computer graphics. The accuracy of the muscle, bone, and tendon geometry as well as the accuracy of muscle and tendon dynamic deformation are of paramount importance in all these applications. We present a framework for extracting and simulating high resolution musculoskeletal geometry from the segmented visible human data set. We simulate 30 contact/collision coupled muscles in the upper limb and describe a computationally tractable implementation using an embedded mesh framework. Muscle geometry is embedded in a nonmanifold, connectivity preserving simulation mesh molded out of a lower resolution BCC lattice containing identical, well-shaped elements, leading to a relaxed time step restriction for stability and, thus, reduced computational cost. The muscles are endowed with a transversely isotropic, quasi-incompressible constitutive model that incorporates muscle fiber fields as well as passive and active components. The simulation takes advantage of a new robust finite element technique that handles both degenerate and inverted tetrahedra.
Abstract:
We present an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, our model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also provide a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior. Finally, we present an improved method for rigid body collision handling in the context of mixed explicit/implicit time-stepping.
Abstract:
Motivated by Lagrangian simulation of elastic deformation, we propose a new tetrahedral mesh generation algorithm that produces both high quality elements and a mesh that is well conditioned for subsequent large deformations. We use a signed distance function defined on a Cartesian grid in order to represent the object geometry. After tiling spacewith a uniform lattice based on crystallography, we use the signed distance function or other user defined criteria toguide a red green mesh subdivision algorithm that results in a candidate mesh with the appropriate level of detail.Then, we carefully select the final topology so that the connectivity is suitable for large deformation and the meshapproximates the desired shape. Finally, we compress the mesh to tightly fit the object boundary using either massesand springs, the finite element method or an optimization approach to relax the positions of the nodes. The resultingmesh is well suited for simulation since it is highly structured, has robust topological connectivity in the face of largedeformations, and is readily refined if deemed necessary during subsequent simulation.
Abstract:
Since it relies on a geometrical rather than a variational framework, many find the finite volume method (FVM) more intuitive than the finite element method (FEM). We show that the FVM allows one to interpret the stress inside a tetrahedron as a simple "multidimensional force" pushing on each face. Moreover, this interpretation leads to a heuristic method for calculating the force on each node, which is as simple to implement and comprehend as masses and springs. In the finite volume spirit, we also present a geometric rather than interpolating function definition of strain. We use the FVM and a quasi-incompressible, transversely isotropic, hyperelastic constitutive model to simulate contracting muscle tissue. B-spline solids are used to model fiber directions, and the muscle activation levels are derived from key frame animations.