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Remnant livers will be regenerated in live donors after a large volume resection for transplantation. How the structures and hemodynamics of portal vein will evolve with liver regeneration remains unknown. This prompts the present hemodynamic simulation for a 25 year-old man who received a right donor lobectomy. According to the magnetic resonance imaging/computed tomography images taken prior to the operation and one month after the operation, three sequential models of portal veins (pre-op, immediately after the operation, and one-month post-op) were constructed by AMIRA and HYPERMESH, while the immediately after the operation model was generated by removing the right branch in the pre-op model. Hemodynamic equations were solved subject to the sonographically measured inlet velocity. The simulated branch velocities were compared with the measured ones. The predicted overall pressure in the portal vein after resection was found to increase to a magnitude that has not reached to an extent possibly leading to portal hypertension. As expected, blood pressure has a large change only in the vicinity of the resection region. The branches grew considerably different from the original one as the liver is regenerated. Results provide useful evidence to justify the current computer simulation.

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Abstract. Development of a stable finite element model for solving steady incompressible viscous fluid flows in three dimensions is the main theme of the present study. For stability reasons, weighting functions are designed in favor of field variables on the upstream side. For accuracy reasons, it is required that weighting functions be equipped with the streamline operator so that false diffusion errors can be largely suppressed. In the steady-state analysis of Navier-Stokes equations, we adopt the mixed formulation to preserve mass conservation on quadratic elements which accommodate the Ladyzhenskaya-Babǔska-Brezzi (LBB) stability condition. To resolve difficulties arising from asymmetry and indefiniteness in the resulting large-size matrix equations, we abandon the elimination-like solution solver because the storage demand exceeds the ability of our hardware to solve for three-dimensional problems. A modern iteration solver, known as the biconjugate gradiant stabilized (BICGSTAB) solution solver, is thus implemented in an element-by-element fashion to effectively alleviate the problem. For performance reasons, the finite element code developed here should be implemented in a hardware environment which is suited to the use of an iterative solver. To this end, our analysis is implemented in shared memory parallel architectures, CRAY C-90 and J-90. We benchmark the parallel computing performance through a lid-driven cavity flow problem and a problem amenable to analytic solution.