A Stochastic Delay Differential Model of Cerebral Autoregulation

Simona Panunzi,Laura D’Orsi,Andrea De Gaetano,Daniela Iacoviello,Heye Zhang

doi:10.1371/journal.pone.0118456

Abstract

Mathematical models of the cardiovascular system and of cerebral autoregulation (CAR) have been employed for several years in order to describe the time course of pressures and flows changes subsequent to postural changes. The assessment of the degree of efficiency of cerebral auto regulation has indeed importance in the prognosis of such conditions as cerebro-vascular accidents or Alzheimer. In the quest for a simple but realistic mathematical description of cardiovascular control, which may be fitted onto non-invasive experimental observations after postural changes, the present work proposes a first version of an empirical Stochastic Delay Differential Equations (SDDEs) model. The model consists of a total of four SDDEs and two ancillary algebraic equations, incorporates four distinct delayed controls from the brain onto different components of the circulation, and is able to accurately capture the time course of mean arterial pressure and cerebral blood flow velocity signals, reproducing observed auto-correlated error around the expected drift.

Highlights

Autoregulation of blood flow denotes the intrinsic ability of an organ or a vascular bed to maintain a constant perfusion in the face of blood pressure changes [1]}
We aim to show that this model is able to reliably reproduce the time course of mean arterial pressure (AP) and cerebral blood flow velocity (CBFV) time courses after changes in posture, inclusive of some auto-correlated oscillations around the expected signals
Some of parameters affect more than others the behaviour of brain arterial pressure (BAP) or arterial pressure (AP) and cerebral blood flow velocity, as shown in Fig. 4 and Fig. 5

Summary

Introduction

Autoregulation of blood flow denotes the intrinsic ability of an organ or a vascular bed to maintain a constant perfusion in the face of blood pressure changes [1]}. For the assessment and prognosis of the progression of some diseases, such as cerebrovascular accidents, Alzheimer and others [2,3,4,5,6,7,8,9], the evaluation of the adequacy of cerebral autoregulation provides important information Compromised cerebral hemodynamics, such as reduced vasodilation, reaction to CO2 and other stimuli, may be related to reduced post-stenotic perfusion pressure. A comprehensive, deterministic mechanistic model of the interplay of cerebral blood flow, cerebral blood volume, intracranial pressures and regulatory mechanisms, had been proposed by Ursino and Lodi [13]. This model, using measured arterial pressure (AP) as driving or input

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