Image-Based Tissue Growth Modeling and Prediction

The goal of this research is to study tissue growth via developing mathematical formulations and computational modeling. Tissue growth modeling has many applications --- including tumor growth, wound healing, bone remodeling, epithelial tissue remodeling, and other problems in developmental biology. Key to this study is incorporating the results of the analysis of non-destructive medical images that augment the models. Quantitative image analysis for the purpose of providing input parameters for and validation of tumor growth models (TGMs) is discussed. Two types of computational TGMs are studied in detail: one is based on the logistic equation, the other is based on the theory of porous media, or mixture theory. For the mixture-based model, we developed an algorithm that couples a level set method to track tumor boundaries while the tissues themselves are treated as a perfused mixture. After the mathematical foundation of each of the TGMs is formulated, we discuss implementation aspects, along with computational results. Finally, we validate the computational results with experimental observations of tumor volume versus time via imaging data acquired from animal models. The RMS deviation between predicted and observed values is as close as 11% of the time-averaged volume.