Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Impact of extra-cranial venous anomalies on cerebral haemodynamics. Numerical study via a global model
Eleuterio Francisco Toro, Lucas Omar Muller

Last modified: 2014-06-09


Impact of extra-cranial venous anomalies on cerebral haemodynamics.

Numerical study via a global model


Eleuterio Toro and Lucas Mueller

University of Trento, Italy

By means of global mathematical model for the entire human circulation we study the physical aspects of cerebral venous haemodynamics resulting from anomalous extra-cranial venous malformations.

The mathematical model. Starting from first principles, we have constructed a global, closed-loop, multi-scale mathematical model for the entire human circulation, including the arterial system, the venous system, the heart, the pulmonary circulation, the cerebrospinal fluid system and the microcirculation [1]. The model includes a detailed description of intracranial and extra-cranial veins. Medium to large vessels are described by partial differential equations and the remaining components by systems of differential-algebraic equations. State-of-the art numerical methods are used to solve the equations. Patient-specific characterization of major veins of the head and neck is carried out using MRI data. Thorough validation of the model is carried out through the use of published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. The mathematical model is then used to study the CCSVI condition as described by Zamboni et al. [2]. Results from our study will be presented in this talk.

Preliminary results. Our computations so far reveal that stenotic extra-cranial veins cause a pressure increase upstream of their location, with the pressure drop across the stenosis being around 1.5 mmHg. This pressure increase has a direct impact on the dural sinuses, effect that is strongly influenced by the specific configuration of the confluence of sinuses. However, due to the Starling resistor mechanism, the impact of the pressure increase on intracranial-vein pressure appears to be indirect and proceeds as follows: increased dural sinus pressure reduces CSF reabsorption rates leading to an increase in intracranial pressure. Intracranial pressure will increase until a new balance between CSF generation and absorption is reached. Then, the increased intracranial pressure will be directly transmitted to intracranial veins.

Acknowledgements . The authors warmly thank Prof. E. M. Haacke (MR Research Facility Wayne State University, Detroit, USA) for providing MRI data used in this study. This work has been partially supported by CARITRO (Fondazione Cassa di Risparmio di Trento e Rovereto, Italy), project No. 2011.0214.


[1] Lucas O. Mueller and Eleuterio F. Toro. A global multi-scale model for the human circulation with emphasis on the venous system. Interna- tional Journal for Numerical Methods in Biomedical Engineering. In press, 2013. 
Also published on line as pre-print. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK.

[2] Zamboni P. Zamboni, R. Galeotti, E. Menegatti, A. M. Malagoni, G. Tacconi, S. Dall’Ara, I. Bar- tolomei, and F. Salvi. Chronic cerebrospinal venous insufficiency in patients with multiple sclerosis. Journal of Neurology, Neurosurgery and Psychiatry, 80:392–399, 2009.


1D blood flow models; venous system; extracranial venous anomalies