Gmsh transfinite line with ruled surface
We assume that cells are sensitive to quasi-steady approximation of mechanical quantities, such as mechanical stress. Change in the anatomy takes days and mechanical stress over a slow time scale.
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It is feasible to use separated modules to approximate each scale that are weekly coupled. The time scale of the tissue adaptation is of the order of the cell cycle expressed in hours. The tissue plasticity is at the spatial scale of the individual cells, i.e. The spatial resolution is at the scale where the density of tissue is in continuum mechanic, i.e. The continuous mechanic description of flow and tissue deformation operates at the time scale of the second. Our model encompasses multiple scales in space and time. Based on both fundamental biology and the physical environment, we propose here a computational framework to develop an agent based model of vascular adaptation following acute intervention. In order to significantly advance our understanding of the function of such complex phenomena, it is necessary to integrate data from several domains and use quantitative models to predict the behavior and outcomes.
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These strategies have focused largely on linear models to separately describe the physical or biologic components of vascular disease progression. Over the past two decades, researchers have applied a wide variety of approaches to investigate the biologic mechanisms that drive a pathologic hyperplasic or vascular remodeling in an effort to identify novel therapeutic strategies to improve clinical outcomes. Vascular adaptation following local injury occurs through a combination of wall thickening (hyperplasia) and expansion or contraction of the lumen. Since many technical avenues for improved patency have been exhausted, the recent belief has been that the future of enhancing the durability of these constructions lies in a better knowledge of the biology of the vein graft healing response. Contemporary data demonstrate restenosis rates following percutaneous coronary interventions to range between 25-35% at 6 months and high grade restenosis (>75%) or occlusion of coronary vein bypass grafts approaching 50% at a year. Despite the escalating need for these often life-saving procedures, their medium and long-term durability remains compromised. Fueled by an epidemic of obesity and diabetes in the United States, substantial increases in the need for these interventions are projected over the next decade. Surgical revascularization using autologous vein also remains a frequent used treatment option, with 427,000 coronary bypass procedures performed in 2004. In 2009, cardiovascular disease was the underlying cause of death accounting for 34.1% of all 2,371,000 deaths, accounting for 1 of every 2.8 deaths in the United States. Our implementation (i) is modular, (ii) starts from basic mechano-biology principle at the cell level and (iii) facilitates the agile development of the model. Cornerstone to our model is a feedback mechanism between environmental conditions and dynamic tissue plasticity described at the cellular level with an agent based model. We propose a multiscale computational framework of vascular adaptation to develop a bridge between theory and experimental observation and to provide a method for the systematic testing of relevant clinical hypotheses.
GMSH TRANSFINITE LINE WITH RULED SURFACE DRIVERS
Despite incremental progress, specific cause/effect linkages among the primary drivers of the pathology, (hemodynamic factors, inflammatory biochemical mediators, cellular effectors) and vascular occlusive phenotype remain lacking. Over the past two decades, researchers have applied a wide variety of approaches to investigate the primary failure mechanisms, neointimal hyperplasia and aberrant remodeling of the wall, in an effort to identify novel therapeutic strategies.
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The failure rate for vascular interventions (vein bypass grafting, arterial angioplasty/stenting) remains unacceptably high.