Vasomotion model explanation for urea rebound

Urea rebound after hemodialysis is generally attributed to urea entering the circulation from poorly perfused tissue and/or entering from regions with low membrane permeability for urea. Another explanation for rebound is based on disorders in the microcirculation, connected with the phenomenon of vasomotion, i.e., cyclic opening and closing of microvessels. The purpose of the following mathematical model is to explain observed urea rebound by the vasomotion phenomenon. The significance of vasomotion is related to the fact that a significant fraction, up to 80-95%, of all microvessels are closed while others are being perfused. The rate with which open microvessels "migrate" through the tissue determines quality of perfusion. A stochastic scheme for describing vasomotion is developed. Probabilities to change the state of microvessels are defined as follows: alpha = probability to be open and remain open; beta = to be open and become closed; v = to be closed and remain closed; mu = to be closed and become open. The activity of vasomotion is defined by the rate of vasomotion, R, R = beta + mu, and can be measured using a curve of urea concentration.