Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

Abdominal aortic aneurysm can exhibit transitional flow characteristics in laminar flow regimes. To report transitional flow characteristics, we examined the convergence of phase-averaged solutions by executing blood flow simulations of a patient-specific abdominal aortic aneurysmal model for 257 cardiac cycles with periodic, pulsatile boundary conditions. The phase-averaged solutions were computed by averaging the solutions over various numbers of cardiac cycles and compared against the ones averaged over 124 cycles. The phase-averaged solutions reported small differences when they were averaged over a large number of cardiac cycles. The instantaneous solutions, however, failed to exhibit fluctuations reported in the phase-averaged solutions. To study blood flows in the aneurysmal region we need to study phase-averaged solutions as they exhibit non-periodic, disturbed flow characteristics. Additionally, when obtaining phase-averaged solutions it is preferred to compute an average over a large number of cardiac cycles to be able to represent flow structures of the converged phase-averaged solutions.