A mathematical model of venous neointimal hyperplasia formation

In this work, we construct a mathematical model which analyzes the role that growth factors might play in the stenosis at the venous anastomosis. The model consists of a system of partial differential equations describing the influence of oxidative stress and turbulent flow on growth factors, the interaction among growth factors, smooth muscle cells, and extracellular matrix, and the subsequent effect on the stenosis at the venous anastomosis, which, in turn, affects the level of oxidative stress and degree of turbulent flow. Computer simulations suggest that our model can be used to predict access stenosis as a function of the initial concentration of the growth factors inside the intimal-luminal space.The proposed model describes the formation of venous neointimal hyperplasia, based on pathogenic mechanisms. The results suggest that interventions aimed at specific growth factors may be successful in prolonging the life of the vascular access, while reducing the costs of vascular access maintenance. The model may also provide indication of when invasive access surveillance to repair stenosis should be undertaken.Healthy kidneys filter wastes from blood and regulate electrolyte, acid-base, and volume homeostasis. When the kidneys fail, one needs treatment to replace the work the kidneys normally perform. One available treatment is hemodialysis, which utilizes an artificial kidney. The patients' blood is pumped into the artificial kidney where metabolic waste products diffuse out of the blood, and the cleansed blood is then returned back to the body. In order to perform hemodialysis, the patient must have suitable vascular access to allow adequate flow of blood to the hemodialysis circuit.The most common types of vascular access used for hemodialysis are the arteriovenous (AV) fistula and the expanded polytetrafluoroethylene (ePTFE) graft. A surgeon creates an AV fistula by directly connecting an artery to a vein, usually in the forearm. The increased blood flow caus