The dynamics of vein graft remodeling induced by hemodynamic forces: a mathematical model

Although vein bypass grafting is one of the primary options for the treatment of arterial occlusive disease and provides satisfactory results at an early stage of the treatment, the patency is limited to a few months in many patients. When the vein is implanted in the arterial system, it adapts to the high flow rate and high pressure of the arterial environment by changing the sizes of its layers, and this remodeling is believed to be a precursor of future graft failure. Hemodynamic forces, such as wall shear stress (WSS) and wall tension, have been recognized as major factors impacting vein graft remodeling. Although a wide range of experimental evidence relating hemodynamic forces to vein graft remodeling has been reported, a comprehensive mathematical model describing the relationship among WSS, wall tension, and the structural adaptation of each individual layer of the vein graft wall is lacking. The current manuscript presents a comprehensive and robust framework for treating the complex interaction between the WSS, wall tension, and the structural adaptation of each individual layer of the vein graft wall. We modeled the intimal and medial area and the radius of external elastic lamina, which in combination dictate luminal narrowing and the propensity for graft occlusion. Central to our model is a logistic relationship between independent and dependent variables to describe the initial increase and later decrease in the growth rate. The detailed understanding of the temporal changes in vein graft morphology that can be extracted from the current model is critical in identifying the dominant contributions to vein graft failure and the further development of strategies to improve their longevity.