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A Model of Cerebrovascular Reactivity Including the Circle of Willis and Cortical Anastomoses

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Abstract

Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral hemodynamics. In this work, a mathematical model of cerebral hemodynamics and intracranial pressure (ICP) dynamics, developed in previous years, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the ICP–volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular hemodynamics and cannot only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions.

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Abbreviations

ACA:

Anterior cerebral artery

ACA1 :

Precommunicating portion of the ACA

ACA2 :

Postcommunicating portion of ACA

ACoA:

Anterior communicating artery

BA:

Basilar artery

CBF:

Cerebral blood flow

CPP:

Cerebral perfusion pressure

CSF:

Cerebrospinal fluid

ICA:

Internal carotid artery

ICP:

Intracranial pressure

MAP:

Mean systemic pressure

MCA:

Middle cerebral artery

\(P_{{\text{aCO}}_{2}}\) :

Arterial CO2 partial pressure

PCA:

Posterior cerebral artery

PCA1 :

Precommunicating portion of the PCA

PCA2 :

Postcommunicating portion of PCA

PCoA:

Posterior communicating artery

THR:

Transient hyperemic response

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  1. Department of Electronics, Computer Science, and Systems, University of Bologna, via Venezia 52, 47023, Cesena, FC, Italy

    Mauro Ursino & Massimo Giannessi

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  1. Mauro Ursino
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Associate Editor Larry V. McIntire oversaw the review of this article.

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Ursino, M., Giannessi, M. A Model of Cerebrovascular Reactivity Including the Circle of Willis and Cortical Anastomoses. Ann Biomed Eng 38, 955–974 (2010). https://doi.org/10.1007/s10439-010-9923-7

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