TITLE:
Actively Circulating Volume as a Consequence of Stochasticity within Microcirculation
AUTHORS:
Viktor V. Kislukhin
KEYWORDS:
Blood Volume, Actively Circulating Volume, Microcirculation, Vasomotion, Markov Chain, Math Model of Cardiovascular System
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.4,
March
31,
2011
ABSTRACT: It is well established that in the pathology of the cardio-vascular system (CVS) only a portion of the blood volume (BV) can be in active circulation. This portion of BV is named the actively circulating volume (ACV) and is evaluated from a monotone decrease of dilution curve produced by an intravascular tracer. In given paper is presented Markov chain as a math model of the flow of a tracer throughout CVS. The consideration of CVS as a set of segments with respect to an anatomical structure and assuming the existence for CVS steady-state condition; leads to the Markov chain of the finite order with constant coefficients. The conclusions of the article are 1) there are open and closed microvessels, such that the switching from open to closed and back is a stochastic process, 2) if the switching is slow then the ACV, as the volume of heart chambers and only open for circulation vessels, can be detected.