0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lassen, N. A. , 1959, “ Cerebral Blood Flow and Oxygen Consumption in Man,” Physiol. Rev., 39(2), pp. 183–238. [PubMed]
Paulson, O. B. , Strandgaard, S. , and Edvinsson, L. , 1989, “ Cerebral Autoregulation,” Cerebrovasc. Brain Metab. Rev., 2(2), pp. 161–192.
Van Beek, A. H. , Claassen, J. A. , Rikkert, M. G. O. , and Jansen, R. W. , 2008, “ Cerebral Autoregulation: An Overview of Current Concepts and Methodology With Special Focus on the Elderly,” J. Cereb. Blood Flow Metab., 28(6), pp. 1071–1085. [CrossRef] [PubMed]
Westerhof, N. , Lankhaar, J.-W. , and Westerhof, B. E. , 2009, “ The Arterial Windkessel,” Med. Biol. Eng. Comput., 47(2), pp. 131–141. [CrossRef] [PubMed]
Ursino, M. , and Giannessi, M. , 2010, “ A Model of Cerebrovascular Reactivity Including the Circle of Willis and Cortical Anastomoses,” Ann. Biomed. Eng., 38(3), pp. 955–974. [CrossRef] [PubMed]
Gonzalez-Fernandez, J. M. , and Ermentrout, B. , 1994, “ On the Origin and Dynamics of the Vasomotion of Small Arteries,” Math. Biosci., 119(2), pp. 127–167. [CrossRef] [PubMed]
Harder, D. R. , 1984, “ Pressure-Dependent Membrane Depolarization in Cat Middle Cerebral Artery,” Circ. Res., 55(2), pp. 197–202. [CrossRef] [PubMed]
Harder, D. R. , 1987, “ Pressure-Induced Myogenic Activation of Cat Cerebral Arteries is Dependent on Intact Endothelium,” Circ. Res., 60(1), pp. 102–107. [CrossRef] [PubMed]
David, T. , Alzaidi, S. , and Farr, H. , 2009, “ Coupled Autoregulation Models in the Cerebro-Vasculature,” J. Eng. Math., 64(4), pp. 403–415. [CrossRef]
van de Vosse, F. N. , and Stergiopulos, N. , 2011, “ Pulse Wave Propagation in the Arterial Tree,” Annu. Rev. Fluid Mech., 43(1), pp. 467–499. [CrossRef]
Alastruey, J. , Parker, K. H. , Peiró, J. , Byrd, S. M. , and Sherwin, S. J. , 2007, “ Modelling the Circle of Willis to Assess the Effects of Anatomical Variations and Occlusions on Cerebral Flows,” J. Biomech., 40(8), pp. 1794–1805. [CrossRef] [PubMed]
Alastruey, J. , Moore, S. M. , Parker, K. H. , David, T. , Peiró, J. , and Sherwin, S. J. , 2008, “ Reduced Modelling of Blood Flow in the Cerebral Circulation: Coupling 1-D, 0-D and Cerebral Auto-Regulation Models,” Int. J. Numer. Methods Fluids, 56(8), pp. 1061–1067. [CrossRef]
Köppl, T. , Schneider, M. , Pohl, U. , and Wohlmuth, B. , 2014, “ The Influence of an Unilateral Carotid Artery Stenosis on Brain Oxygenation,” Med. Eng. Phys., 36(7), pp. 905–914. [CrossRef] [PubMed]
Liang, F. , Fukasaku, K. , Liu, H. , and Takagi, S. A. , 2011, “ Computational Model Study of the Influence of the Anatomy of the Circle of Willis on Cerebral Hyperperfusion Following Carotid Artery Surgery,” Biomed. Eng. Online, 10(84), pp. 1–22. [PubMed]
David, T. , and Moore, S. , 2008, “ Modeling Perfusion in the Cerebral Vasculature,” Med. Eng. Phys., 30(10), pp. 1227–1245. [CrossRef] [PubMed]
Connolly, M. , He, X. , Gonzalez, N. , Vespa, P. , DiStefano, J., III , and Hu, X. , 2014, “ Reproduction of Consistent Pulse-Waveform Changes Using a Computational Model of the Cerebral Circulatory System,” Med. Eng. Phys., 36(3), pp. 354–363. [CrossRef] [PubMed]
Lodi, C. A. , and Ursino, M. , 1999, “ Hemodynamic Effect of Cerebral Vasospasm in Humans: A Modeling Study,” Ann. Biomed. Eng., 27(2), pp. 257–273. [CrossRef] [PubMed]
Ursino, M. , and Lodi, C. A. , 1998, “ Interaction Among Autoregulation, CO2 Reactivity, and Intracranial Pressure: A Mathematical Model,” Am. J. Physiol.: Heart Circ. Physiol., 274(5), pp. H1715–H1728.
Giller, C. A. , 1991, “ A Bedside Test for Cerebral Autoregulation Using Transcranial Doppler Ultrasound,” Acta Neurochir., 108(1–2), pp. 7–14. [CrossRef]
Fahrig, R. , Nikolov, H. , Fox, A. J. , and Holdsworth, D. W. , 1999, “ A Three-Dimensional Cerebrovascular Flow Phantom,” Med. Phys., 26(8), pp. 1589–1599. [CrossRef] [PubMed]
Moore, S. , David, T. , Chase, J. G. , Arnold, J. , and Fink, J. , 2006, “ 3D Models of Blood Flow in the Cerebral Vasculature,” J. Biomech., 39(8), pp. 1454–1463. [CrossRef] [PubMed]
Stergiopulos, N. , Young, D. F. , and Rogge, T. R. , 1992, “ Computer Simulation of Arterial Flow With Applications to Arterial and Aortic Stenoses,” J. Biomech., 25(12), pp. 1477–1488. [CrossRef] [PubMed]
Barnard, A. C. L. , Hunt, W. A. , Timlake, W. P. , and Varley, E. A. , 1966, “ Theory of Fluid Flow in Compliant Tubes,” Biophys. J., 6(6), pp. 717–724. [CrossRef] [PubMed]
Hughes, T. J. R. , and Lubliner, J. , 1973, “ On the One-Dimensional Theory of Blood Flow in the Large Vessels,” Math. Biosci., 18(1–2), pp. 161–170. [CrossRef]
Formaggia, L. , Lamponi, D. , and Quarteroni, A. , 2003, “ One-Dimensional Models for Blood Flow in Arteries,” J. Eng. Math., 47(3–4), pp. 251–276. [CrossRef]
Smith, N. P. , Pullan, A. J. , and Hunter, P. J. , 2002, “ An Anatomically Based Model of Transient Coronary Blood Flow in the Heart,” SIAM J. Appl. Math., 62(3), pp. 990–1018. [CrossRef]
Sherwin, S. J. , Franke, V. , Peiró, J. , and Parker, K. , 2003, “ One-Dimensional Modelling of a Vascular Network in Space-Time Variables,” J. Eng. Math., 47(3–4), pp. 217–250. [CrossRef]
Olufsen, M. S. , Peskin, C. S. , Kim, W. Y. , Pedersen, E. M. , Nadim, A. , and Larsen, J. , 2000, “ Numerical Simulation and Experimental Validation of Blood Flow in Arteries With Structured-Tree Outflow Conditions,” Ann. Biomed. Eng., 28(11), pp. 1281–1299. [CrossRef] [PubMed]
Steele, B. N. , Wan, J. , Ku, J. P. , Hughes, T. J. , and Taylor, C. A. , 2003, “ In Vivo Validation of a One-Dimensional Finite-Element Method for Predicting Blood Flow in Cardiovascular Bypass Grafts,” IEEE Trans. Biomed. Eng., 50(6), pp. 649–656. [CrossRef] [PubMed]
Parker, K. H. , 2009, “ An Introduction to Wave Intensity Analysis,” Med. Biol. Eng. Comput., 47(2), pp. 175–188. [CrossRef] [PubMed]
Alastruey, J. , Hunt, A. A. E. , and Weinberg, P. D. , 2014, “ Novel Wave Intensity Analysis of Arterial Pulse Wave Propagation Accounting for Peripheral Reflections,” Int. J. Numer. Methods Biomed. Eng., 30(2), pp. 249–279. [CrossRef]
Formaggia, L. , Lamponi, D. , Tuveri, M. , and Veneziani, A. , 2006, “ Numerical Modeling of 1D Arterial Networks Coupled With a Lumped Parameters Description of the Heart,” Comput. Methods Biomech. Biomed. Eng., 9(5), pp. 273–288. [CrossRef]
Alastruey, J. , Parker, K. H. , Peiró, J. , and Sherwin, S. J. , 2008, “ Lumped Parameter Outflow Models for 1-D Blood Flow Simulations: Effect on Pulse Waves and Parameter Estimation,” Commun. Comput. Phys., 4(2), pp. 317–336.
Liang, F. , Takagi, S. , Himeno, R. , and Liu, H. , 2009, “ Multi-Scale Modeling of the Human Cardiovascular System With Applications to Aortic Valvular and Arterial Stenoses,” Med. Biol. Eng. Comput., 47(7), pp. 743–755. [CrossRef] [PubMed]
Huang, P. , and Muller, L. , 2015, “ Simulation of One-Dimensional Blood Flow in Networks of Human Vessels Using a Novel TVD Scheme,” Int. J. Numer. Methods Biomed. Eng., 31(5), p. e02701. [CrossRef]
Hu, X. , Nenov, V. , Bergsneider, M. , Glenn, T. , Vespa, P. , and Martin, N. , 2007, “ Estimation of Hidden State Variables of the Intracranial System Using Constrained Nonlinear Kalman Filters,” IEEE Trans. Biomed. Eng., 54(4), pp. 597–610. [CrossRef] [PubMed]
Blacher, J. , Asmar, R. , Djane, S. , London, G. M. , and Safar, M. E. , 1999, “ Aortic Pulse Wave Velocity as a Marker of Cardiovascular Risk in Hypertensive Patients,” Hypertension, 33(5), pp. 1111–1117. [CrossRef] [PubMed]
Sutton-Tyrrell, K. , Najjar, S. S. , Boudreau, R. M. , Venkitachalam, L. , Kupelian, V. , Simonsick, E. M. , Havlik, R. , Lakatta, E. G. , Spurgeon, H. , Kritchevsky, S. , Pahor, M. , Bauer, D. , and Newman, A. , 2005, “ Elevated Aortic Pulse Wave Velocity, A Marker of Arterial Stiffness, Predicts Cardiovascular Events in Well-Functioning Older Adults,” Circulation, 111(25), pp. 3384–3390. [CrossRef] [PubMed]
Latham, R. D. , Westerhof, N. , Sipkema, P. , Rubal, B. J. , Reuderink, P. , and Murgo, J. P. , 1985, “ Regional Wave Travel and Reflections Along the Human Aorta: A Study With Six Simultaneous Micromanometric Pressures,” Circulation, 72(6), pp. 1257–1269. [CrossRef] [PubMed]
Willemet, M. , and Alastruey, J. , 2015, “ Arterial Pressure and Flow Wave Analysis Using Time-Domain 1-D Hemodynamics,” Ann. Biomed. Eng., 43(1), pp. 190–206. [CrossRef] [PubMed]
Parker, K. H. , and Jones, C. , 1990, “ Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics,” ASME J. Biomech. Eng., 112(3), pp. 322–326. [CrossRef]
Niki, K. , Sugawara, M. , Chang, D. , Harada, A. , Okada, T. , Sakai, R. , Uchida, K. , Tanaka, R. , and Mumford, C. E. , 2002, “ A New Noninvasive Measurement System for Wave Intensity: Evaluation of Carotid Arterial Wave Intensity and Reproducibility,” Heart Vessels, 17(1), pp. 12–21. [CrossRef] [PubMed]
Asgari, S. , Gonzalez, N. , Subudhi, A. W. , Hamilton, R. , Vespa, P. , Bergsneider, M. , Roach, R. C. , and Hu, X. , 2012, “ Continuous Detection of Cerebral Vasodilatation and Vasoconstriction Using Intracranial Pulse Morphological Template Matching,” PLoS One, 7(11), p. e50795. [CrossRef] [PubMed]
Czosnyka, M. , Smielewski, P. , Kirkpatrick, P. , Menon, D. K. , and Pickard, J. D. , 1996, “ Monitoring of Cerebral Autoregulation in Head-Injured Patients,” Stroke, 27(10), pp. 1829–1834. [CrossRef] [PubMed]
Miller, J. D. , and Becker, D. P. , 1982, “ Secondary Insults to the Injured Brain,” J. R. Coll. Surg. Edinburgh, 27(5), pp. 292–298.
Smielewski, P. , Czosnyka, M. , Kirkpatrick, P. , McEroy, H. , Rutkowska, H. , and Pickard, J. D. , 1996, “ Assessment of Cerebral Autoregulation Using Carotid Artery Compression,” Stroke, 27(12), pp. 2197–2208. [CrossRef] [PubMed]
Liang, F. , Takagi, S. , Himeno, R. , and Liu, H. , 2009, “ Biomechanical Characterization of Ventricular–Arterial Coupling During Aging: A Multi-Scale Model Study,” J. Biomech., 42(6), pp. 692–704. [CrossRef] [PubMed]
Epstein, S. , Willemet, M. , Chowienczyk, P. , and Alastruey, J. , 2015, “ Reducing the Number of Parameters in 1D Arterial Blood Flow Modelling: Less is More for Patient-Specific Simulations,” Am. J. Physiol.: Heart Circ. Physiol., 309(1), pp. H222–H234. [CrossRef] [PubMed]
Alastruey, J. , Khir, A. W. , Matthys, K. S. , Segers, P. , Sherwin, S. J. , Verdonck, P. R. , Parker, K. H. , and Peiró, J. , 2011, “ Pulse Wave Propagation in a Model Human Arterial Network: Assessment of 1-D Visco-Elastic Simulations Against In Vitro Measurements,” J. Biomech., 44(12), pp. 2250–2258. [CrossRef] [PubMed]
Reymond, P. , Merenda, F. , Perren, F. , Rüfenacht, D. , and Stergiopulos, N. , 2009, “ Validation of a One-Dimensional Model of the Systemic Arterial Tree,” Am. J. Physiol.: Heart Circ. Physiol., 297(1), pp. H208–H222. [CrossRef] [PubMed]
Valdez-Jasso, D. , Bia, D. , Zócalo, Y. , Armentano, R. L. , Haider, M. A. , and Olufsen, M. S. , 2011, “ Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure–Area Dynamics Under In Vivo and Ex Vivo Conditions,” Ann. Biomed. Eng., 39(5), pp. 1438–1456. [CrossRef] [PubMed]
Coyle, P. , and Heistad, D. , 1991, “ Development of Collaterals in the Cerebral Circulation,” J. Vasc. Res., 28(1–3), pp. 183–189.
Coyle, P. , and Heistad, D. D. , 1987, “ Blood Flow Through Cerebral Collateral Vessels One Month After Middle Cerebral Artery Occlusion,” Stroke, 18(2), pp. 407–411. [CrossRef] [PubMed]
Alpers, B. , Berry, R. , and Paddison, R. , 1959, “ Anatomical Studies of the Circle of Willis in Normal Brain,” AMA Arch. Neurol. Psychiatry, 81(4), pp. 409–418. [CrossRef] [PubMed]
Kahlert, P. , Al-Rashid, F. , Döttger, P. , Mori, K. , Plicht, B. , Wendt, D. , Bergmann, L. , Kottenberg, E. , Schlamann, M. , Mummel, P. , Holle, D. , Thielmann, M. , Jakob, H. G. , Konorza, T. , Heusch, G. , Erbel, R. , and Eggebrecht, H. , 2012, “ Cerebral Embolization During Transcatheter Aortic Valve Implantation: A Transcranial Doppler Study,” Circulation, 126(10), pp. 1245–1255. [CrossRef] [PubMed]
Hu, X. , Xu, P. , Scalzo, F. , Vespa, P. , and Bergsneider, M. , 2009, “ Morphological Clustering and Analysis of Continuous Intracranial Pressure,” IEEE Trans. Biomed. Eng., 56(3), pp. 696–705. [CrossRef] [PubMed]
Hu, X. , Xu, P. , Asgari, S. , Vespa, P. , and Bergsneider, M. , 2010, “ Forecasting ICP Elevation Based on Prescient Changes of Intracranial Pressure Waveform Morphology,” IEEE Trans. Biomed. Eng., 57(5), pp. 1070–1078. [CrossRef] [PubMed]

Figures

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In