A mathematical model of venous neointimal hyperplasia formation

Paula Budu-Grajdeanu¹ , Richard C Schugart¹ , Avner Friedman¹ , Christopher Valentine² , Anil K Agarwal² and Brad H Rovin²

¹Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA

²Division of Nephrology, Department of Internal Medicine at The Ohio State University College of Medicine, Columbus, OH, USA

author email corresponding author email

Theoretical Biology and Medical Modelling 2008, 5:2doi:10.1186/1742-4682-5-2


Published:	23 January 2008

Abstract

Background

In hemodialysis patients, the most common cause of vascular access failure is neointimal hyperplasia of vascular smooth muscle cells at the venous anastomosis of arteriovenous fistulas and grafts. The release of growth factors due to surgical injury, oxidative stress and turbulent flow has been suggested as a possible mechanism for neointimal hyperplasia.

Results

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.

Conclusion

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.