Finite Element Modeling of Active and Passive Behavior of the Human Tibialis Anterior: A Preliminary Approach

This research project serves as exploratory work in the field of computational human biomechanics. A connection between muscular force and intramuscular pressure (IMP) has been uncovered that could prove invaluable in medical diagnostics as a method to circumvent the use of electromyography. Preliminary finite element simulations were conducted to model the human tibialis anterior muscle in passive lengthening and active contraction. These simulations, totaling over 50 unique runs, utilized a novel constitutive model developed within the IMP research group. Volumetric strain, reaction forces, and pressure gradients were compared to data acquired from ongoing in vivo human experiments. A mechanism for passive stretching and active contraction was theorized, with the aponeuroses bearing the majority of the load due to their high stiffness. Though the model will require future iterations to make adjustments, several promising conclusions were drawn during analysis. Fluid pressure distributions mimic those of the volumetric strain, and provide a better prediction of IMP than hydrostatic pressure. Reaction forces and pressure readings can be iterated to a reasonable level of accuracy. A thorough list of recommendations was compiled in order to guide the future direction of the model. Fluid pressures for the active contractile simulations were higher than the expected IMP values, likely owing to the stiffness of the aponeuroses being greater than necessary. Several options for addressing this issue were proposed, such as decreased aponeurosis length and graduated thickness and stiffness of the elements in the extremes of the parts

A quasi-incompressible and quasi-inextensible element formulation for transversely isotropic materials

The contribution presents a new finite element formulation for quasi-inextensible and quasi-incompressible finite hyperelastic behavior of transeversely isotropic materials and addresses its computational aspects. The material formulation is presented in purely Eulerian setting and based on the additive decomposition of the free energy function into isotropic and anisotropic parts, where the former is further decomposed into isochoric and volumetric parts. For the quasi-incompressible response, the Q1P0 element formulation is outlined briefly, where the pressure-type Lagrange multiplier and its conjugate enter the variational formulation as an extended set of variables. Using the similar argumentation, an extended Hu-Washizu-type mixed variational potential is introduced, where the volume averaged fiber stretch and fiber stress are additional field variables. Within this context, the resulting Euler-Lagrange equations and the element formulation resulting from the extended variational principle are derived. The numerical implementation exploits the underlying variational structure, leading to a canonical symmetric structure. The efficiency of the proposed approached is demonstrated through representative boundary value problems. The superiority of the proposed element formulation over the standard Q1 and Q1P0 element formulation is studied through convergence analyses. The proposed finite element formulation is modular and exhibits very robust performance for fiber reinforced elastomers in the inextensibility limit

IMPACT OF VAGINAL SYNTHETIC PROLAPSE MESHES ON THE MECHANICS OF THE HOST TISSUE RESPONSE

The vagina helps support the bladder, urethra, uterus, and rectum. A lack of support leads to pelvic organ prolapse, and vaginal delivery is a prevalent risk factor; however, there is little research on vaginal biomechanical properties. Despite numerous complications, clinical practice involves surgical repair with synthetic meshes. Complications can be partially attributed to our lack of knowledge regarding the mesh-tissue complex (MTC) after implantation. However, it is difficult to perform rigorous studies without utilizing animal models. Therefore, we evaluated how parity affected the mechanical properties of vaginal tissue in three animal models: rodent, sheep, and non-human primate (NHP) to compare their mechanically properties to parous women who typically undergo prolapse surgery. Parity negatively impacted the mechanical properties of the vagina in NHP, which were biomechanically similar to parous women, making it a suitable model for studying the effects of mesh implantation. Second, we examined the textile and structural properties of commonly used meshes (Gynemesh, UltraPro, SmartMesh, Novasilk, and Polyform) utilizing uniaxial and ball-burst tests. These meshes had significantly different porosity and structural properties. To investigate the host response, three meshes were implanted into the abdominal wall of the rodent and NHP, and on the vagina in the NHP. The MTC was removed, and the tissue contribution was calculated. We did not observe notable changes in the tissue properties following mesh implantation in the rodent; however, implantation of the stiffest mesh (Gynemesh) in the NHP resulted in an exhibition of a stress-shielding response manifested by inferior biomechanical properties of the abdominal and vaginal tissues. Less stiff meshes (UltraPro and SmartMesh) resulted in preservation of tissue properties. To gain insight into how mesh properties affect the tissue contribution, we began developing a finite element model. Utilizing the co-rotational theory with a fiber-recruitment stress-strain relationship, we could describe the behavior of SmartMesh and UltraPro. While an in-depth characterization of these meshes revealed multiple fiber populations, further development of modeling may be instrumental in closing the current knowledge gap. Ultimately, understanding the mesh-tissue interaction will improve clinical outcomes by identifying mesh properties that are essential for providing structural support while maintaining tissue integrity

Data-driven finite elements for geometry and material design

Crafting the behavior of a deformable object is difficult---whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, Previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensive precomputation stages that rely on a priori knowledge of the object's geometry and material composition. In this paper we introduce Data-Driven Finite Elements as a solution to this problem. Given a material palette, our method constructs a metamaterial library which is reusable for subsequent simulations, regardless of object geometry and/or material composition. At runtime, we perform fast coarsening of a simulation mesh using a simple table lookup to select the appropriate metamaterial model for the coarsened elements. When the object's material distribution or geometry changes, we do not need to update the metamaterial library---we simply need to update the metamaterial assignments to the coarsened elements. An important advantage of our approach is that it is applicable to non-linear material models. This is important for designing objects that undergo finite deformation (such as those produced by multimaterial 3D printing). Our method yields speed gains of up to two orders of magnitude while maintaining good accuracy. We demonstrate the effectiveness of the method on both virtual and 3D printed examples in order to show its utility as a tool for deformable object design.National Science Foundation (U.S.) (Grant CCF-1138967)United States. Defense Advanced Research Projects Agency (N66001-12-1-4242

Institute for Computational Mechanics in Propulsion (ICOMP) fourth annual review, 1989

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated jointly by Case Western Reserve University and the NASA Lewis Research Center. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1989 are described

Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium

We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p ≥ 1 and globally C k -continuous, with k = 0 or p − 1, to find the most accurate approximation of a propagating front with the minimal number of degrees of freedom. We show that B-spline basis functions of degree p ≥ 1, which are C p−1 -continuous capture accurately the front velocity of the transmembrane potential even with moderately refined meshes; similarly, we show that, for accurate tracking of curved fronts, high-order continuous B-spline basis functions should be used. Finally, we apply Isogeometric Analysis to an idealized human left atrial geometry described by NURBS with physiologically sound fiber directions and anisotropic conductivity tensor to demonstrate that the numerical scheme retains its favorable approximation properties also in a more realistic setting

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented