Blood flow in the cerebral venous system: modeling and simulation

Abstract The development of a software platform incorporating all aspects, from medical imaging data, through three-dimensional reconstruction and suitable meshing, up to simulation of blood flow in patient-specific geometries, is a crucial challenge in biomedical engineering. In the present study, a fully three-dimensional blood flow simulation is carried out through a complete rigid macrovascular circuit, namely the intracranial venous network, instead of a reduced order simulation and partial vascular network. The biomechanical modeling step is carefully analyzed and leads to the description of the flow governed by the dimensionless Navier–Stokes equations for an incompressible viscous fluid. The equations are then numerically solved with a free finite element software using five meshes of a realistic geometry obtained from medical images to prove the feasibility of the pipeline. Some features of the intracranial venous circuit in the supine position such as asymmetric behavior in merging regions are discussed.

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

[2]  Frédéric Hecht,et al.  New development in freefem++ , 2012, J. Num. Math..

[3]  Paul M. Parizel,et al.  MR angiography of the intracranial vessels: technical aspects and clinical applications , 2004, Neuroradiology.

[4]  F. Thomasset.  Finite element methods for Navier-Stokes equations , 1980 .

[5]  Marc Thiriet.  Comprar Circulatory and Ventilatory Systems: Biomathematical and Biomechanical Modeling | Thiriet, Marc | 9781441997579 | Springer , 2011 .

[6]  N. Stergiopulos,et al.  Validation of a one-dimensional model of the systemic arterial tree. , 2009, American journal of physiology. Heart and circulatory physiology.

[7]  Marc Thiriet,et al.  Biology and mechanics of blood flows , 2008 .

[8]  Lucas O. Müller,et al.  Computational haemodynamics in stenotic internal jugular veins , 2014, Journal of Mathematical Biology.

[9]  Nan Xiao,et al.  Multi-scale computational model of three-dimensional hemodynamics within a deformable full-body arterial network , 2013, J. Comput. Phys..

[10]  T. KiliÇ,et al.  Anatomy of cerebral veins and sinuses. , 2008, Frontiers of neurology and neuroscience.

[11]  F. Ståhlberg,et al.  Measurement of Blood Flow in the Superior Sagittal Sinus in Healthy Volunteers, and in Patients with Normal Pressure Hydrocephalus and Idiopathic Intracranial Hypertension with Phase-Contrast Cine MR Imaging , 1996, Acta radiologica.

[12]  Alejandro F. Frangi,et al.  Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity , 2005, IEEE Transactions on Medical Imaging.

[13]  Marcela Szopos,et al.  Hemodynamic simulations in the cerebral venous network: A study on the influence of different modeling assumptions , 2015 .

[14]  Shigehiko Ogoh,et al.  The effect of phenylephrine on arterial and venous cerebral blood flow in healthy subjects , 2011, Clinical physiology and functional imaging.

[15]  Alejandro F. Frangi,et al.  A Virtual Coiling Technique for Image-Based Aneurysm Models by Dynamic Path Planning , 2013, IEEE Transactions on Medical Imaging.

[16]  Alfio Quarteroni,et al.  A 3D/1D geometrical multiscale model of cerebral vasculature , 2009 .

[17]  David A. Steinman,et al.  Virtual angiography for visualization and validation of computational models of aneurysm hemodynamics , 2005, IEEE Transactions on Medical Imaging.

[18]  B. Schaller,et al.  Physiology of cerebral venous blood flow: from experimental data in animals to normal function in humans , 2004, Brain Research Reviews.

[19]  Lucas O. Müller,et al.  Enhanced global mathematical model for studying cerebral venous blood flow. , 2014, Journal of biomechanics.

[20]  Marek Czosnyka,et al.  A phase-contrast MRI study of physiologic cerebral venous flow. , 2009, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[21]  M. Ursino,et al.  A new hemodynamic model for the study of cerebral venous outflow. , 2015, American journal of physiology. Heart and circulatory physiology.

[22]  Jean-Jacques Bellanger,et al.  A new approach in combined modeling of MRI and blood flow: A preliminary study , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[23]  Marie Oshima,et al.  Computational fluid dynamic simulation of a giant basilar tip aneurysm with eventual rupture after Hunterian ligation. , 2014, World neurosurgery.

[24]  A. Moura,et al.  Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology. , 2011, Mathematical biosciences and engineering : MBE.

[25]  R. Löhner,et al.  Hemodynamic analysis of intracranial aneurysms with moving parent arteries: Basilar tip aneurysms , 2010, International journal for numerical methods in biomedical engineering.

[26]  Jean-Daniel Boissonnat,et al.  From arteriographies to computational flow in saccular aneurisms: the INRIA experience , 2005, Medical Image Anal..

[27]  O. Pironneau.  On the transport-diffusion algorithm and its applications to the Navier-Stokes equations , 1982 .

[28]  Peter J. Hunter,et al.  Numerical Simulation of Blood Flow in an Anatomically-Accurate Cerebral Venous Tree , 2013, IEEE Transactions on Medical Imaging.

[29]  A. Marsden,et al.  An integrated approach to patient-specific predictive modeling for single ventricle heart palliation , 2014, Computer methods in biomechanics and biomedical engineering.

[30]  J. Karemaker,et al.  Human cerebral venous outflow pathway depends on posture and central venous pressure , 2004, The Journal of physiology.

[31]  Lucas O Müller,et al.  A global multiscale mathematical model for the human circulation with emphasis on the venous system , 2014, International journal for numerical methods in biomedical engineering.

[32]  David Hasan,et al.  Stratification of a population of intracranial aneurysms using blood flow metrics , 2015, Computer methods in biomechanics and biomedical engineering.

[33]  Alfio Quarteroni,et al.  Basic mathematical models and motivations , 2009 .

[34]  Stéphanie Salmon,et al.  Extension of an MRI Simulator Software for Phase Contrast Angiography Experiments , 2014, ISBMS.

[35]  G. Karniadakis,et al.  Modeling Blood Flow Circulation in Intracranial Arterial Networks: A Comparative 3D/1D Simulation Study , 2010, Annals of Biomedical Engineering.

[36]  J. Alastruey,et al.  A systematic comparison between 1‐D and 3‐D hemodynamics in compliant arterial models , 2014, International journal for numerical methods in biomedical engineering.

[37]  V. Lee,et al.  Nonenhanced MR angiography. , 2008, Radiology.

[38]  Hugues Talbot,et al.  3D CFD in Complex Vascular Systems: A Case Study , 2014, ISBMS.

[39]  Marc Thiriet,et al.  Cell and Tissue Organization in the Circulatory and Ventilatory Systems , 2011 .

[40]  Guanghong Ding,et al.  Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement , 2011, Computer methods in biomechanics and biomedical engineering.