Enhanced global mathematical model for studying cerebral venous blood flow.

Here we extend the global, closed-loop, mathematical model for the cardiovascular system in Müller and Toro (2014) to account for fundamental mechanisms affecting cerebral venous haemodynamics: the interaction between intracranial pressure and cerebral vasculature and the Starling-resistor like behaviour of intracranial veins. Computational results are compared with flow measurements obtained from Magnetic Resonance Imaging (MRI), showing overall satisfactory agreement. The role played by each model component in shaping cerebral venous flow waveforms is investigated. Our results are discussed in light of current physiological concepts and model-driven considerations, indicating that the Starling-resistor like behaviour of intracranial veins at the point where they join dural sinuses is the leading mechanism. Moreover, we present preliminary results on the impact of neck vein strictures on cerebral venous hemodynamics. These results show that such anomalies cause a pressure increment in intracranial cerebral veins, even if the shielding effect of the Starling-resistor like behaviour of cerebral veins is taken into account.

[1]  N A Thacker,et al.  Prediction of the jugular venous waveform using a model of CSF dynamics. , 2007, AJNR. American journal of neuroradiology.

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

[3]  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.

[4]  W. Conrad,et al.  Pressure--flow relationships in collapsible tubes. , 1969, IEEE transactions on bio-medical engineering.

[5]  J Ekstedt,et al.  CSF hydrodynamic studies in man. 2 . Normal hydrodynamic variables related to CSF pressure and flow. , 1978, Journal of neurology, neurosurgery, and psychiatry.

[6]  R. Himeno,et al.  Biomechanical characterization of ventricular-arterial coupling during aging: a multi-scale model study. , 2009, Journal of biomechanics.

[7]  Jean-Rodolphe Vignes,et al.  A hypothesis of cerebral venous system regulation based on a study of the junction between the cortical bridging veins and the superior sagittal sinus. Laboratory investigation. , 2007, Journal of neurosurgery.

[8]  J O Rowan,et al.  Raised intracranial pressure and cerebral blood flow , 1972, Journal of Neurology Neurosurgery & Psychiatry.

[9]  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.

[10]  Q. Pang,et al.  Biological characteristics of the cerebral venous system and its hemodynamic response to intracranial hypertension. , 2012, Chinese medical journal.

[11]  C. Lee.  Chronic Cerebrospinal Venous Insufficiency: A Failed Concept , 2015, Vascular specialist international.

[12]  Eleuterio F. Toro,et al.  Flow in Collapsible Tubes with Discontinuous Mechanical Properties: Mathematical Model and Exact Solutions , 2013 .

[13]  R. Penn,et al.  A mathematical model of blood, cerebrospinal fluid and brain dynamics , 2009, Journal of mathematical biology.

[14]  A. Shapiro.  Steady Flow in Collapsible Tubes , 1977 .

[15]  J. Luce,et al.  A Starling resistor regulates cerebral venous outflow in dogs. , 1982, Journal of applied physiology: respiratory, environmental and exercise physiology.

[16]  C. Avezaat,et al.  The role of the pulsatile pressure variations in intracranial pressure monitoring , 2005, Neurosurgical Review.

[17]  S. Rossitti.  Pathophysiology of increased cerebrospinal fluid pressure associated to brain arteriovenous malformations: The hydraulic hypothesis , 2013, Surgical neurology international.

[18]  J P Mynard,et al.  A simple, versatile valve model for use in lumped parameter and one‐dimensional cardiovascular models , 2012, International journal for numerical methods in biomedical engineering.

[19]  F. Salvi,et al.  Changes of cine cerebrospinal fluid dynamics in patients with multiple sclerosis treated with percutaneous transluminal angioplasty: a case-control study. , 2013, Journal of vascular and interventional radiology : JVIR.

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

[21]  M. Dwyer,et al.  Cine cerebrospinal fluid imaging in multiple sclerosis , 2012, Journal of magnetic resonance imaging : JMRI.

[22]  Q. Pang,et al.  The Hemodynamic Response of the Cerebral Bridging Veins to Changes in ICP , 2010, Neurocritical care.

[23]  Lucas O. Müller,et al.  Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties , 2013, International journal for numerical methods in biomedical engineering.

[24]  C. Avezaat,et al.  Cerebral blood flow autoregulation during intracranial hypertension: a simple, purely hydraulic mechanism? , 2009, Child's Nervous System.

[25]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[26]  D. F. Young,et al.  Effect of geometry on pressure losses across models of arterial stenoses. , 1976, Journal of biomechanics.

[27]  I. Kanno,et al.  Arterial fraction of cerebral blood volume in humans measured by positron emission tomography , 2001, Annals of nuclear medicine.

[28]  Jonathan P. Mynard,et al.  Computer modelling and wave intensity analysis of perinatal cardiovascular function and dysfunction , 2011 .

[29]  E. Starling,et al.  The influence of variations in temperature and blood‐pressure on the performance of the isolated mammalian heart , 1912, The Journal of physiology.

[30]  L. Kramer,et al.  Chronic Cerebrospinal Venous Insufficiency: Case–Control Neurosonography Results , 2013, Annals of neurology.

[31]  F. Salvi,et al.  patients with multiple sclerosis Chronic cerebrospinal venous insufficiency in , 2009 .

[32]  J. Rowan,et al.  Raised intracranial pressure and cerebral blood flow , 1973, Journal of Neurology Neurosurgery & Psychiatry.

[33]  M. Gulisano,et al.  Internal jugular vein valves: an assessment of prevalence, morphology and competence by color Doppler echography in 240 healthy subjects. , 2010, Italian journal of anatomy and embryology = Archivio italiano di anatomia ed embriologia.