Modeling perfusion in the cerebral vasculature

Todem, David; Moore, Stephen

doi:10.1016/j.medengphy.2008.09.008

Cited by 27 publications

(20 citation statements)

References 65 publications

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“…However, this structure is complete in <50% of the population. 19 Of course, for the model to have an actual clinical value, parameters of the Circle of Willis should be assigned on an individual basis, for instance starting from single angiographic studies. Compliances in the ICA and the BA were computed, starting from radii and length values reported in Table 1, and using the following equation: C ¼ 3 2 p r 2 r h l E ; where r is the inner radius, l the vessel length, E the vessel Young modulus (normal values 8-16 dyn/cm 2 ), and r/h the wall/thickness ratio (normal values [8][9][10].…”

Section: Parameter Assignmentmentioning

confidence: 99%

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

Ursino

Giannessi

2010

Ann Biomed Eng

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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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Section: Parameter Assignmentmentioning

confidence: 99%

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

Ursino

Giannessi

2010

Ann Biomed Eng

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“…Detailed velocity fields in an arterial segment (i.e., a small longitudinal section of the arterial tree) can be obtained with 3-dimensional (3D) patient-specific models [2][3][4]. However, since these models are computationally expensive, and can only be feasibly applied to small to medium sized arterial segments, a 1D wave propagation model is more suitable for the computation of pressure and flow waves throughout the arterial tree [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…In order to examine inter-patient variations, three virtual patients are considered, the first having a complete circle of Willis. The other geometries tested are lacking either the anterior communicating artery or the posterior communicating artery, for those are variations of the circle of Willis commonly seen in patients [2].…”

Section: Introductionmentioning

confidence: 99%

The influence of contrast agent injection on physiological flow in the circle of Willis

Mulder

Bogaerds

Rongen

et al. 2011

Medical Engineering & Physics

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“…Full details of the phenomenological model will be presented in a forthcoming publication. David and Moore (2008), Alastruey et al (2007), David et al (2010), and Farr and David (2011) provide more background.…”

Section: Cerebrovascular Autoregulation Modelmentioning

confidence: 99%

Numerical techniques for dynamic resistive networks

Brown

2013

ANZIAMJ

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We consider approaches to the numerical difficulties posed by modelling resistive networks with dynamically changing resistances according to a set of coupled ordinary differential equations (odes). The prototype problem is autoregulation on a cerebral microvascular network. In this network the amount of perfusion, or tissue blood supply, is determined by the resistance of the vascular network. This resistance can be dynamically altered to regulate the amount of blood flow and hence maintain a balance of chemicals and nutrients in the tissue. The mechanisms responsible for this are primarily local, and are due to various chemical pathways to the vascular smooth muscle cells lining the arterioles and arteries in the vasculature. These cells contract and dilate, which alters the radii and hence resistance of the vessels. Contents C172Because of the global coupling induced by the resistive network, the resulting stiff system of odes has a dense Jacobian which precludes the direct application of traditional implicit numerical solution methods. We consider a means of remedying this problem by taking a block diagonal Jacobian approximation which allows use of an implicit method but retains the desirable property of explicit solvers of linear solution time scaling with problem size. Subject class: 65L99

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Modeling perfusion in the cerebral vasculature

Cited by 27 publications

References 65 publications

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

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

The influence of contrast agent injection on physiological flow in the circle of Willis

Numerical techniques for dynamic resistive networks

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