Actively Circulating Volume as a Consequence of Stochasticity within Microcirculation

Author(s)
Viktor V. Kislukhin

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.

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.

Keywords

Blood Volume, Actively Circulating Volume, Microcirculation, Vasomotion, Markov Chain, Math Model of Cardiovascular System

Blood Volume, Actively Circulating Volume, Microcirculation, Vasomotion, Markov Chain, Math Model of Cardiovascular System

Cite this paper

nullV. Kislukhin, "Actively Circulating Volume as a Consequence of Stochasticity within Microcirculation,"*Applied Mathematics*, Vol. 2 No. 4, 2011, pp. 508-513. doi: 10.4236/am.2011.24066.

nullV. Kislukhin, "Actively Circulating Volume as a Consequence of Stochasticity within Microcirculation,"

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