Novel Computational Methods for Simulation of Wound Healing and Analysis of Arterial and Metabolic Disease
Pinhas Bar-Yoseph
Faculty of Mechanical Engineering, Technion-IIT, Haifa, Israel
Abstract:
The following summarizes our work on the application of novel computational methods to analyzing arterial and metabolic diseases and to healing wounds.
Analysis of Arterial Disease Treatment:
Arterial diseases are of special interest in computational biomechanics. Such diseases originate inside the vessel wall and thus change the local geometric configuration. Specifically, vessel occlusion can occur due to the rapid formation of thrombi near areas of significant intimal thickening, greatly reducing blood flow. Alternatively, the locally weakened arterial wall can dilate and form a balloon-like vessel section (aneurysm), possibly leading to rupture. Understanding and simulating coagulationbased mechanisms and pathologies can contribute to assessing the effectiveness, operation and safety of practically any implant that comes in contact with the blood stream or is placed in a blood vessel. In effect, this knowledge can be applied to any blood-flow related device and procedure. The virtual particle integration method we have developed can be used to approximate the Lagrangian integral in real time for any point in space and time for the entire domain and can be easily integrated into the Lattice-Boltzman method. To illustrate,
we applied our method to a blood coagulation model. The method was shown to accurately capture the coagulation characteristics observed in experiments.
Simulation of Wound Healing:
Collective migration of cells plays an important role in many physiological processes, among them metastasis, morphogenesis, bone remodeling, and wound and fracture healing. The classical approach to modeling collective cell movement uses coupled nonlinear reaction-diffusion equations for biological cells and diffusive chemicals that interact with these. This approach takes into account cell diffusion, cell proliferation, cell death, and chemotaxis, but fails to consider many factors that affect stochastic collective movement of cells. Our multi-scale approach, based on the Glazier Graner Hogeweg model, has been implemented for biological cells, together with the finite element method for a diffusive chemical. The approach assumes that the cells secrete a diffusive chemical when they sense a wound in the region and that the cells are attracted by this released chemical. Fingering morphology can occur with a certain combination of characteristic parameters. The approach also considers the effects of a polarized substrate.
Analysis of Metabolic Bone Disease Treatment:
Micro-architectural deterioration of bone tissue is characteristic of metabolic bone diseases such as osteoporosis, which are marked by increased bone fragility. Because this deterioration can lead to micro fractures, early diagnosis is a key to intervention. Today the biomedical community is interested in developing accurate and noninvasive means for evaluating bone micro-structure and bone quality. We propose a new approach for multi-scale finite element analysis. This approach will provide physicians with a "digital magnifying glass" offering continuous transition between macro- and micro- scales, thus acting as a computational biopsy. Two domain decompositions approaches are being investigated as a basis for finite element analysis at the micro-scale level.