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Research Papers

A Coupled Lumped-Parameter and Distributed Network Model for Cerebral Pulse-Wave Hemodynamics

[+] Author and Article Information
Jaiyoung Ryu

Mechanical Engineering,
University of California,
Berkeley, CA 94720

Xiao Hu

Physiological Nursing and Neurosurgery,
Institute of Computational Health Sciences,
University of California,
San Francisco, CA 94143

Shawn C. Shadden

Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: shadden@berkeley.edu

1Corresponding author.

Manuscript received May 7, 2015; final manuscript received July 27, 2015; published online September 3, 2015. Assoc. Editor: Tim David.

J Biomech Eng 137(10), 101009 (Sep 03, 2015) (13 pages) Paper No: BIO-15-1227; doi: 10.1115/1.4031331 History: Received May 07, 2015; Revised July 27, 2015

The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is necessary for cerebral blood flow (CBF) modeling, as well as investigations into pathological conditions. We discuss a one-dimensional (1D) nonlinear model of blood flow in the cerebral arteries coupled to autoregulatory lumped-parameter (LP) networks. The LP networks incorporate intracranial pressure (ICP), cerebrospinal fluid (CSF), and cortical collateral blood flow models. The overall model is used to evaluate changes in CBF due to occlusions in the middle cerebral artery (MCA) and common carotid artery (CCA). Velocity waveforms at the CCA and internal carotid artery (ICA) were examined prior and post MCA occlusion. Evident waveform changes due to the occlusion were observed, providing insight into cerebral vasospasm monitoring by morphological changes of the velocity or pressure waveforms. The role of modeling of collateral blood flows through cortical pathways and communicating arteries was also studied. When the MCA was occluded, the cortical collateral flow had an important compensatory role, whereas the communicating arteries in the circle of Willis (CoW) became more important when the CCA was occluded. To validate the model, simulations were conducted to reproduce a clinical test to assess dynamic autoregulatory function, and results demonstrated agreement with published measurements.

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Figures

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Fig. 1

(a) Schematic of the 1D arterial network. Outflow boundaries marked with ○ are coupled with the LP network in (b), and boundaries marked with • are coupled to three-element Windkessel models. Locations where A0 is varied are marked with ×. (b) Schematic of the LP network model, which includes CA. The bounding box represents intracranial space, and a single ICP model is shared by the six cerebral distal vascular bed models inside the intracranial space.

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Fig. 2

Waveforms in the RBR, RCCA, RICA, and RMCA. The first two rows compare waveforms resulting from the P1 and P2 pressure–area models, including (first row) PWV and total pulse-wave propagation speed (PWV + U), as well as (second row) full (P), forward (P+), and backward (P−) components of pressure. The third and fourth rows, respectively, plot the full, forward, and backward components for velocity and wave intensity. Horizontal lines denote the reference PWV (c0=β/2ρA01/2). Vertical lines denote aortic-valve closure.

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Fig. 3

Flow velocities at the middle sections of RICA (top left) and RCCA (bottom left), and their normalized quantities (U*=(U−min(U))/(max(U)−min(U)), right) are shown for the healthy and RMCA occlusion conditions. They are compared with (DC) and without (No-DC) distal collateral pathways.

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Fig. 6

Flow velocity at the RMCA measured in vivo using TCD with compression–decompression of right CCA (left) (Reproduced with permission from Smielewski et al. [46]. Copyright 1996 by Wolters Kluwer Health, Inc.) and predicted by the present model (right).

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Fig. 4

The changes of flow rates at the RCCA (a), RMCA (b), RACA (c), RVERT (d), all cerebral outlets (e), and velocity at the narrowed RCCA (f) due to the compression of both CCAs. Horizontal axes denote the baseline area of the narrowed portion of the RCCA compared to the initial baseline area. Solid and dashed lines represent the cases with healthy and unhealthy autoregulation cases, respectively.

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Fig. 5

The activation factor M (solid lines, left vertical axis) and active tension Tm (dashed lines, right vertical axis) (left). Distal radius (solid lines, left vertical axis) and ICP (dashed lines, right vertical axis) (right). M, Tm, and rd are from downstream of RMCA. Both healthy and impaired CA cases are shown. Horizontal axes denote the reference area of the constricted portion of the RCCA compared to the initial reference area.

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