Mathematical Reconstruction of Patient-Specific Vascular Networks Based on Clinical Images and Global Optimization

Abstract

Cancer is a major cause of death worldwide and becomes particularly threatening once it begins to metastasize. During metastasis, the blood vessels serve as pathways for cancerous cell transportation and hence are crucial for understanding cancer growth. Existing medical imaging modalities can provide 3-D contrast images of the vascular tissues but with limited quality and detailedness. A much-needed tool for cancer research is thus one that can reconstruct vascular networks from low-quality clinical images. To this end, we developed a computational framework that takes 3-D medical images as input and reconstructs complete, patient-specific vascular network models using a mathematical optimization procedure. Our framework extracts major vessels from the images and uses the organ geometry to select vessel termination points. Then, it generates the remainder network based on physiological optimality principles. Using the framework, we obtained a set of network models with over 3000 terminal segments from a brain MRA scan. We analyzed the Strahler order, vessel radius, and branch length distributions of the models, which match with actual human data. We also performed fluid dynamics simulation inside the reconstructed vessels and showed that the pressure and shear stress distributions agree with existing in vivo measurements. The qualitative and quantitative agreements in vessel morphometry and hemodynamics demonstrate the effectiveness of the framework. Our method bridges the gap between image-based vessel models, accuracy of which is limited by the resolution of clinical images, and hypothetical models.