Blood Flow in the Circle of Willis: Modeling and Calibration

DeVault, Kristen J.; Gremaud, Pierre A.; Novak, Vera; Olufsen, Mette S.; Vernières, Guillaume; Zhao, Peng

doi:10.1137/07070231x

Cited by 106 publications

(102 citation statements)

References 63 publications

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“…This is, therefore, a limitation of our study, and a full verification of our results using in vivo data remains to be done in future work. Future work could also carry out a similar analysis using more complex visco-elastic models of the arterial wall that account for stress relaxation [10,23,24] and the nonlinear behaviour of the arterial wall [25,26].…”

Section: Discussionmentioning

confidence: 99%

“…For patient-specific 1-D simulations we also need arterial lengths and mean cross-sectional areas, which can be obtained from medical images, such as MR imaging [10,48,49]. The wall thickness is necessary to calculate the local Young's modulus, Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Optimisation techniques as those proposed in [10,11] can be used to calculate the rest of parameters. We believe, however, that mechanical-based algorithms, as those described here, should first be used to determine the total compliance and net resistance of the system, outflow pressures, and local compliances and viscous moduli at as many locations as possible.…”

Section: Discussionmentioning

confidence: 99%

“…There are, however, more complex models that also account for stress relaxation [10,23,24] and the nonlinear behaviour of the wall [25,26]. Here we use a Voigt-type visco-elastic model since it is the simplest model to reproduce, to first approximation, the main features of visco-elastic effects on blood flow in large arteries [9,16,[20][21][22].…”

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confidence: 99%

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Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

et al. 2012

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The shape of the arterial pulse waveform is intimately related to the physical properties of the cardiovascular system. It is clinically relevant to measure those properties that are related to cardiovascular function, such as the local elasticity and viscosity of the arterial wall, total compliance and net peripheral resistance of the systemic arterial tree. Most of these properties cannot be directly measured in vivo, but they can be calculated from pressure, flow and wall displacement measurements that can be obtained in vivo. We carry out a linear analysis of the one-dimensional (1-D) equations of blood flow in Voigt-type visco-elastic vessels to study the effects on pulse wave propagation of blood viscosity, flow inertia, wall visco-elasticity, total arterial compliance, net resistance, peripheral outflow pressure, and flow rate at the aortic root. Based on our analysis, we derive methods to calculate the local elastic and viscous moduli of the arterial wall, and the total arterial compliance, net resistance, time constant and peripheral outflow pressure of the systemic arterial tree from pressure, flow and wall displacement data that can be measured in vivo. Analysis of in vivo data is beyond the scope of this study, and therefore, we verify the results of our linear analysis and assess the accuracy of our estimation methods using pulse waveforms simulated in a nonlinear visco-elastic 1-D model of the larger conduit arteries of the upper body, which includes the circle of Willis in the cerebral circulation.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

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Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

et al. 2012

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“…Elasticity of the vessel is described by the quantity f(r 0 ) with relaxed vessel radius r 0 (z), A 0 (z) is the relaxed cross-sectional vessel area, R(z, t) the vessel radius, δ b is the boundary layer thickness and Re is the Reynold's number. Although these equations have been commonly used by various groups [1,4,5,14], no publicly accessible implementation of the solution to (4) could be found, meaning that each publication from a separate group resulted in the reimplementation of the same or very similar methods and equations. Therefore, the Vascular Modelling in Python toolkit (VaMpy) was developed and published on GitHub 1 with the documentation available on GitHub Pages.…”

Section: Introductionmentioning

confidence: 99%

VaMpy: A Python Package to Solve 1D Blood Flow Problems

Diem¹,

Bressloff

2017

JORS

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Finite-differences methods such as the Lax-Wendroff method (LW) are commonly used to solve 1D models of blood flow. These models solve for blood flow and lumen area and are useful in disease research, such as hypertension and atherosclerosis, where flow and pressure are good indicators for the presence of disease. Despite the popularity of the LW method to solve the blood flow equations, no implementation of a LW solver for these equations has been published and made publicly available. This leads to the reimplementation of the same methods within different research groups and makes verification of results more difficult. The Vascular Modelling in Python (VaMpy) toolkit is a Python package that aims to fill this gap. It implements Richtmyer's two-step Lax-Wendroff scheme to solve 1D model equations of blood flow in arterial trees and aims at facilitating the solution of blood flow problems for various medical applications.

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Vessel distance mapping: a novel methodology for assessing vascular‐induced cognitive resilience

Garcia-Garcia

Mattern

Vockert

et al. 2022

Alzheimer's & Dementia

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BackgroundThe association between cerebral blood supply and cognition has gained increasing interest, considering the remarkable anatomical variability of the circle of Willis. Thus, qualitative classifications of the arteries contributing to the hippocampal supply has been performed in previous studies to determine whether the additional presence of vessels might translate into cognitive differences and cerebral structural changes when coexisting with vascular pathology, to the extent of constituting a cognitive reserve. Nevertheless, the promising results in these regards are not without controversy. Hence, Vessel Distance Mapping (VDM) is here introduced, in order to ascertain the correlation of VDM‐metrics with each other and with cognitive status, as well as to elucidate which metrics have the greatest impact on cognition.MethodA battery of cognitive tests was used (including ADAScog and MoCA) in 51 subjects (71 ± 8.5yrs) with (n=20) and without (n=31) cerebral small vessel disease. Their hippocampal‐related vessels were manually segmented by using high‐resolution 7T Time‐of‐Flight‐MRI. Vessel distance maps were generated by computing the distances of each voxel to its nearest vessel, obtaining 3 VDM‐metrics: global‐VDM (vessel density surrogate), VS‐VDM (vessel‐specific supply), and COMD (distance to the center of mass, reflecting vessel distribution). Hippocampal masks were used to assess the whole and subregional hippocampus. Regression models were applied for evaluating the interrelation among the metrics, and their association with cognition.ResultHigh correlations were observed for intra‐metric comparisons, as well as when comparing whole hippocampal vs. sub‐hippocampal metrics. Greater values of VDM‐metrics reflecting higher distances among vessels were associated with poorer cognitive outcomes only in subjects affected by vascular pathology (global‐VDM R²=0.7248, p=0.0054; COMD R²=0.7248, p=0.0013). Metrics revealing vascular distribution (p=0,0053) and density (p=0,0169) were the most influential on cognition, and in this context those for the whole hippocampus predominated over the subregional ones.ConclusionA mixed contribution of vessel distribution and density is proposed to confer cognitive resilience, in a way consistent with anatomical fundamentals and with previous research findings. VDM provides a new, structure‐driven approach on which to raise new questions supported by the statistical robustness of a quantitative method with potential clinical implications.

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Blood Flow in the Circle of Willis: Modeling and Calibration

Cited by 106 publications

References 63 publications

Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

VaMpy: A Python Package to Solve 1D Blood Flow Problems

Vessel distance mapping: a novel methodology for assessing vascular‐induced cognitive resilience

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