Dynamics of pulsatile flow in fractal models of vascular branching networks

Efficient regulation of blood flow is critically important to the normal function of many organs, especially the brain. To investigate the circulation of blood in complex, multi-branching vascular networks, a computer model consisting of a virtual fractal model of the vasculature and a mathematical model describing the transport of blood has been developed. Although limited by some constraints, in particular, the use of simplistic, uniformly distributed model for cerebral vasculature and the omission of anastomosis, the proposed computer model was found to provide insights into blood circulation in the cerebral vascular branching network plus the physiological and pathological factors which may affect its functionality. The numerical study conducted on a model of the middle cerebral artery region signified the important effects of vessel compliance, blood viscosity variation as a function of the blood hematocrit, and flow velocity profile on the distributions of flow and pressure in the vascular network.

[1]  R. Karch,et al.  Optimized arterial trees supplying hollow organs. , 2006, Medical engineering & physics.

[2]  László Kocsis,et al.  Fractal Branching Pattern in the Pial Vasculature in the Cat , 2001, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[3]  C A Dawson,et al.  Branching exponent heterogeneity and wall shear stress distribution in vascular trees. , 2001, American journal of physiology. Heart and circulatory physiology.

[4]  R. Horton.  EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY , 1945 .

[5]  Prosenjit Bagchi,et al.  Mesoscale simulation of blood flow in small vessels. , 2007, Biophysical journal.

[6]  C D Murray,et al.  The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. , 1926, Proceedings of the National Academy of Sciences of the United States of America.

[7]  M. Ursino,et al.  A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics. , 1997, Journal of applied physiology.

[8]  Yi Liu,et al.  Vascular metabolic dissipation in Murray's law. , 2007, American journal of physiology. Heart and circulatory physiology.

[9]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[10]  A. Pries,et al.  Biophysical aspects of blood flow in the microvasculature. , 1996, Cardiovascular research.

[11]  Spencer J. Sherwin,et al.  Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system , 2003 .

[12]  S. Sherwin,et al.  Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements. , 2007, Journal of biomechanics.

[13]  M. Ursino.  A mathematical study of human intracranial hydrodynamics part 1—The cerebrospinal fluid pulse pressure , 2006, Annals of Biomedical Engineering.

[14]  S. Sherwin,et al.  Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements , 2011, Journal of biomechanics.

[15]  L A Taber,et al.  An optimization principle for vascular radius including the effects of smooth muscle tone. , 1998, Biophysical journal.

[16]  Yunlong Huo,et al.  Diameter asymmetry of porcine coronary arterial trees: structural and functional implications. , 2008, American journal of physiology. Heart and circulatory physiology.

[17]  T David,et al.  3D models of blood flow in the cerebral vasculature. , 2006, Journal of biomechanics.

[18]  P. S. Ramalho.  Microcirculation and hemorheology. , 1983, Acta medica portuguesa.

[19]  M. Olufsen,et al.  Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions , 2000, Annals of Biomedical Engineering.

[20]  Yunlong Huo,et al.  Pulsatile blood flow in the entire coronary arterial tree: theory and experiment. , 2006, American journal of physiology. Heart and circulatory physiology.

[21]  Arnold P. G. Hoeks,et al.  Wall shear stress as measured in vivo: consequences for the design of the arterial system , 2008, Medical & Biological Engineering & Computing.

[22]  F Henry-Le Bros,et al.  Cerebral blood flow and metabolism, L Edvinsson, E Mackenzie, J McCulloch. Raven Press, Paris (1993) , 1994 .

[23]  Jenny Dankelman,et al.  Relation between branching patterns and perfusion in stochastic generated coronary arterial trees , 2007, Medical & Biological Engineering & Computing.

[24]  A. Pries,et al.  Resistance to blood flow in microvessels in vivo. , 1994, Circulation research.

[25]  P. Marchiafava,et al.  Geometric Characteristics of Arterial Network of Rat Pial Microcirculation , 2007, Journal of Vascular Research.

[26]  Albert van der Zwan,et al.  Anatomy and Functionality of Leptomeningeal Anastomoses: A Review , 2003, Stroke.

[27]  Céline Fouard,et al.  A Novel Three‐Dimensional Computer‐Assisted Method for a Quantitative Study of Microvascular Networks of the Human Cerebral Cortex , 2006, Microcirculation.

[28]  Amir Haghighat,et al.  Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education , 2005 .

[29]  John K-J. Li,et al.  Dynamics of the vascular system , 2004 .

[30]  Sandro Rossitti,et al.  Vascular Dimensions of the Cerebral Arteries Follow the Principle of Minimum Work , 1993, Stroke.

[31]  E. Gabryś,et al.  Blood flow simulation through fractal models of circulatory system , 2006 .

[32]  W Schreiner,et al.  Anatomical variability and functional ability of vascular trees modeled by constrained constructive optimization. , 1997, Journal of theoretical biology.

[33]  W Schreiner,et al.  A three-dimensional model for arterial tree representation, generated by constrained constructive optimization , 1999, Comput. Biol. Medicine.

[34]  N. Stergiopulos,et al.  Comprar Snapshots Of Hemodynamics. An Aid For Clinical Research And Graduate Education | Nico Westerhof | 9781441963628 | Springer , 2010 .

[35]  V V Gafiychuk,et al.  On the principles of the vascular network branching. , 2001, Journal of theoretical biology.

[36]  S. Sherwin,et al.  Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. , 2007, Journal of biomechanics.

[37]  Aleksander S Popel,et al.  Microcirculation and Hemorheology. , 2005, Annual review of fluid mechanics.

[38]  S. Mayer,et al.  On the pressure and flow-rate distributions in tree-like and arterial-venous networks. , 1996, Bulletin of mathematical biology.

[39]  W Schreiner,et al.  Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. , 1996, Journal of theoretical biology.