PROJECT SUMMARY The vascular system plays a crucial role in diagnostics, treatment, and surgical planning in a wide array of diseases. Historically, practitioners locate vessel manually on each image of a CT scan. This is a tedious process that can vary highly depending on the individual's experience and ability. Recently, there has been motivation to automate this process to save time and increase accuracy. This process, vessel segmentation, is challenging because of the small size of the vessel structure and the varying contrast and noise in medical images. Current image processing techniques have not been successful in resolving the full vascular systems in humans because of these challenges. However, a novel neural network algorithm has shown potential to reduce training times and increase accuracy per degree of freedom in medical imaging segmentation. Applying this algorithm in the liver vessel segmentation, and eventually other organs' vascular system segmentation shows great promise. In addition to achieving successful vessel segmentation of the full vascular system, there is motivation to create a model that simulates blood flow and mass transportation in the vascular system. This is accomplished by using coupled multidimensional computational models for the flow and transport within the blood vessels. The combination of these two aims will give a complete overview of the location and function of a patient's circulatory system. This research will be completed by the joint effort of the Computational and Applied Mathematics Department at Rice University and the Department of Imaging Physics, Division of Diagnostic Imaging at The University of Texas MD Anderson Cancer Center. The collaborative nature of this project allows mathematicians to work with physicians who are experienced in the diagnosis and treatment of many diseases. Leveraging everyone's strengths and background will allow for a successful development and implementation of this project.