Abstract
Computational tools for the study of the biomechanical regulation of tissue morphology and function across length scales.Mechanical feedback at the cellular level is an important regulator of morphogenesis and proper function of biological tissues and organs. Tissue morphology and function is usually studied at the macroscale, while the regulation of cellular behavior is studied at the microscale. However, very little is known about the dynamic relationship between these two scales and how they interact with each other in order to create and maintain a healthy macroorganism. This presentation will be split in to two different portions. For the first part, I will present an example of the regulation of morphogenesis across length scales with the case of angiogenesis, the process by which new blood vessels sprout from existing vessels. Mechanical interactions during angiogenesis, i.e. traction forces applied by neovessels and the corresponding deformation of the extracellular matrix (ECM), are important regulators of growth and neovascularization and the dynamic relationship between these components and vascular topology are poorly understood. Our goal during this research was to develop, implement, and validate a computational framework that simulates the dynamic mechanical interaction between angiogenic neovessels and the ECM. I will present a novel continuous-discrete finite element (FE) model with angiogenic growth coupled with matrix deformation. Angiogenesis was simulated using a discrete growth model. This model uses properties of the ECM, represented by a continuous FE mesh, to regulate angiogenic growth and branching and was capable of accurately predicting vascular morphometric data when simulating growth in various matrix conditions. To couple growth with matrix deformation, sprout forces were applied to the mesh and the corresponding deformation of the matrix was determined using the nonlinear FE software FEBio. This deformation was then used to update the ECM into the current configuration before calculating the next growth step. These methods provide a flexible computational platform to investigate the mechanisms by which the biomechanical interaction between cells and the ECM regulates the structure and composition of the emerging tissue during morphogenesis and induce patterns and organization. However, this model homogenized microscale properties across the macroscale using mixture theory, which among other things does not allow to the explicit calculation of stress/strain along the surface of microvessels which may be an important component to regulating vascular behavior. For the remainder of the presentation I will present alternate approaches for using the FE method to study biomechanics across the micro- and macroscale including 1st and 2nd order computational homogenization schemes that could be utilized to overcome these limitations.