8th. World Congress on Computational Mechanics (WCCM8) 5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30 – July 5, 2008 Venice, Italy MULTI-SCALE MODELING OF BLOOD VESSELS USING A FLUID-SOLID GROWTH FRAMEWORK *C. Alberto Figueroa¹, Seungik Baek ² , Charles A. Taylor¹ and Jay D. Humphrey³ ¹ Stanford University 318 Campus Drive, Stanford CA 94305 cafa@stanford.edu, taylorca@stanford.edu ² Michigan State University 2457 Eng. building, East Lansing, MI 48824 sbaek@egr.msu.edu ³ Texas A&M University 335L Zachry Eng. Ctr College Station, TX 77843 jhumphrey@tamu.edu Key Words: Vascular, Multi-scale, Growth and Remodeling, Fluid-solid interactions. ABSTRACT Introduction: Blood vessels adapt and remodel in response to changes in their biomechanical and biochemical environment during development and aging, and with diseases including atherosclerosis, aneurysms, and hypertension to name a few examples. While computational methods have been utilized separately to quantify hemodynamic conditions and to simulate growth and remodeling processes, there is a pressing need for a unified approach to model vascular adaptation and disease progression in response to biomechanical and biochemical stimuli. This class of Fluid- Solid Growth (FSG) problems is inherently multi-scale in time since the biomechanical forces due to the heart beat change over seconds whereas vascular adaptation can occur over days to weeks and diseases progress over months to years. In addition, FSG problems are multi-scale in space since biomechanical forces and biochemical stimuli, sensed at a molecular and cellular scale, elicit adaptive and maladaptive responses from molecular (nm) to organ (cm) scales. We describe herein a novel computational method to model fluid-solid growth problems and illustrate this method by applying it to simulate the enlargement of a cerebral aneurysm in response to shear and tensile stress. Methods: We have developed a computational framework to simulate FSG mechanics in the vasculature [1] that incorporates some of the key multi-scale temporal and spatial processes that play a role in arterial adaptation. This unified framework couples modules that represent Growth and Remodeling (G&R) [2] and Fluid-Structure Interaction (FSI) [4] by exploiting a theory of small on large [5] to resolve differences in temporal and spatial scales. The G&R module uses a constrained mixture theory [3] to model the turnover of individual structurally significant constituents of the vascular wall, including changes in the production and removal of separate families of collagen fibers and changes in the vasoactive behavior of smooth muscle cells in response to deviations from a homeostatic state. The G&R module incorporates biochemical and biomechanical processes from molecular to tissue scales, but these phenomena occur over long time scales. The FSI module utilizes the Coupled Momentum Method for Fluid-Solid Interaction (CMM-FSI) to quantify shear and tensile forces acting on the vascular wall in geometrically accurate patient-specific models [4]. The FSI module