Computer Generation of Three Dimensional Human Cerebral Vasculature Models
Recent clinical findings suggest changes in vasculature compliance may be responsible for abnormal brain dynamics in diseases like hydrocephalus. Understanding and treating pathological brain dynamics requires a quantitative understanding of the complex interaction between pulsating vasculature, cerebrospinal fluid, and brain tissue. Models addressing anatomically correct geometry, physiological haemodynamics and complete interactions of vasculature and brain tissue are required for this purpose. In this article, a geometrical model of the cerebral vasculature is presented as a first step in the development of a fully distributed mathematical model for quantitative analysis of intracranial dynamics. We present two- and three- dimensional models of the human cerebral vasculature network. The model was generated in two phases. First, the major extracerebral arteries were reconstructed using patient-specific MRI images. Then in step two a special modified algorithm of Beard & Bassingthwaighte generated the microvasculature, starting from the major arteries of step one. This fractal-based growth algorithm incorporates vessel and complex domain boundary avoidance to create the vasculature. Significant findings are: (1) MRI imaging was successful in generating patient specific geometry of the brain cerebral arteries including carotid artery, basilar artery, Circle of Willis and vertebral arteries; (2) a microvasculature below the medical imaging resolution was successfully created by the computer algorithm; (3) vessels consistently remained inside the domain boundary and avoided overlap; (4) model capillary density agrees qualitatively with actual human capillary density. However, there were some limitations to the model. The model is not completely consistent with the cerebral vasculature anatomy due to limited MRI resolution and the absence of physiological driving forces for the vessel growth in the algorithm. Future work will focus on acquiring quantitatively accurate capillary density in the model by incorporating growth factors in the algorithm. Work is being done toward incorporating blood vessel branching factors and constrained optimization techniques into the algorithm. Moreover, in the next step blood flow simulations need to be performed to predict blood flow and vessel dilations.