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MODELLING OF CHRONIC CEREBRO SPINAL VENOUS
INSUFFICIENCY (CCSVI)

Abstract. Recently, Zamboni (2009) and collaborators have empirically discovered that a signiffcant number of Multiple Sclerosis (MS) patients suffer from malformations in the veins that drain blood from the brain and the spinal cord. Such condition has become known as Chronic Cerebro Spinal Venous Insuciency, or CCSVI for short. Zamboni and collaborators go further, see Singh and Zamboni (2009). They have put forward the hypothesis that anomalous venous haemodynamics could ultimately be the triggering mechanism of axon demyelination and MS.

In this presentation we describe our current work that aims at the construction of a closed-loop mathematical model of the human circulatory system to study the haemodynamical implications observed by Zamboni. Based on MRI data we have been able to construct a complex vascular network treated in multi-scale fashion as a combination of 0D (ODEs) and 1D hyperbolic systems. Here we address some of the mathematical and numerical challenges posed by the problem of interest. See Mueller et al. (2012). Preliminary results will be shown.

Computer simulation of blood flow in the intra/extra cranial venous
system in humans with multiple sclerosis and the CCSVI condition

Summary and aims of the research programme

This research programme is motivated by the recently proposed association between multiple sclerosis (MS) and a vascular anomaly termed chronic cerebro-spinal venous insufficiency (CCSVI) by Zamboni and collaborators. The CCSVI condition is characterized by the presence of obstructions of various kinds in the extracranial veins. Such obstructions prevent a normal drainage of blood from the brain to the heart. CCSVI is present in a relevant number of MS patients and such occurrence is of great clinical interest. However such association does not yet explain the gestation of MS, although it has been hypothesized a potential link between the altered fluid dynamics, transport and deposition of iron, disruption of the brain- blood barrier and penetration of autoaggressive immune cells into the CNS, with the known consequences of demyelization of the nerve’s sheath.

This research programme is limited to a theoretical study of the bio-fluid dynamical aspects of the CCSVI condition by means of a mathematical model. The aim is to further investigate the physical phenomena observed empirically by Zamboni and collaborators by means of colour Doppler sonography measurements. The research programme has several distinct parts, including (1) the determination of the computational domain, (2) the construction of a mathematical model for the fluid dynamical problem and (3) the development of computational methods that would allow a computer simulation of the phenomena of interest. There would follow a (4) comparison between theoretical simulation and empirical measurements, (5) use of the theoretical model to study of Zamboni's protocol for testing the CCSVI condition and (6) the formulation of recommendations. If successful, the theoretical tool developed could subsequently be used as the basis for further research, for example to assist potential surgery and to perhaps even associate the anomalous fluid dynamics to the anomalous behaviour of the brain blood barrier, an accepted component of multiple sclerosis.

REMISSION: a long-term research project on REsearch into Mathematical modelling of multIple SclerosiS and its vascular connectION
Professor Eleuterio Toro

The aim is to further investigate the physical phenomena observed empirically by Zamboni and collaborators by means of colour Doppler sonography measurements.

Based on MRI data we have been able to construct a complex vascular network treated in multi-scale fashion as a combination of 0D (ODEs) and 1D hyperbolic systems.

I expect this approach should be able to calculate the dynamic pressure distributions in the venules and hopefully relate the over-pressures to BBB disruption.

I understand only enough of this to wonder why CSF is not being included in a study of the fluid dynamics of the brain. CSF and it's flow (or lack of) affects pressure in the brain and venous system.

Our findings, demonstrating that CCSVI has a significant impact on brain pathophysiology, and particularly on the balance of intracranial fluids, could provide stimulation for the development, in the future, of mathematical models currently lacking (probably because the description of CCSVI is so recent). A model is needed in which increased resistance of venous outflow is partially corrected by the development of collateral circulations (2, 19). Speculatively the imbalance in CSF filtration-reabsorption processes might be related to increased transmural pressure in the condition of CCSVI (1,5,23,24).

My research includes the construction of computational methods for solving differential equations, with particular emphasis on hyperbolic balance laws. Scientists world-wide have applied these methods to many areas, such as astrophysics, shock-wave physics, relativity, meteorology, combustion, propulsion, aerodynamics, environmental sciences, industrial and biomedical problems.

For the last 20 years I have been working on the construction of non-linear numerical methods of arbitrary order of accuracy in space and time, the ADER methods. Very high order methods have a huge efficiency gain that increases the power of mathematical modelling and simulation in science and engineering. The ADER numerical techniques have so far been found to be relevant in astrophysics, aero-acoustics, seismology, tsunami wave propagation and biomedical applications.

I am currently focused on the study of the physics of neurodegenerative diseases and their potential link to venous haemodynamics. Of particular interest is the theoretical elucidation of the link between Multiple Sclerosis and vascular anomalies, such as Chronic Cerebro-Spinal Venous Insufficiency (CCSVI), empirically discovered by Zamboni (2009). We are making progress on this very timely theme of practical relevance to so many people around the world. Advances are possible thanks to the contribution of PhD students, post-doctoral fellows, colleagues in Trento and collaboration with academics and medical doctors in Europe, USA and elsewhere.

14:00-14:15. Professor Eleuterio Toro. Welcome address and introduction
14:15-15:15. Dr. MD Franz Schelling. Invited Speaker. Predictable outcomes of interventions for CCSVI in Multiple Sclerosis?
15:15-16:00. Lucas Mueller. Introduction by Professor Eleuterio Toro. Construction of a mathematical model for the study of haemodynamical aspects of CCSVI
16:00-16:15. Break
16:15-16:45. Dr. Alfonso Caiazzo and Gino Montecinos. Computational haemodynamics in stenotic internal jugular veins.
16:45-17:15. Miss Laura Facchini. Introduction by Professor Alberto Bellin. The impact of pressure disorder on solute exchange across micro-vessel walls.
17:15-17:30. Discussion.
Everyone welcome!
Contact: Professor E F Toro.

COMPUTATIONAL HAEMODYNAMICS IN STENOTIC INTERNAL JUGULAR VEINS

Alfonso Caiazzo, PhD1, Gino Montecinos, MS1, Lucas Mueller Omar, MS1, Eleuterio
Toro Francisco, PhD1, Ewart Haacke Mark, PhD2

1 Universita di Trento, via Mesiano 77, Trento, TN, Trento, Italy
2 Wayne State University, 3990 John R Road, Detroit, MI 48201, USA.

Figure 1 shows a set of preliminary results for a stenotic LIJV. In particular, in the original configuration (Fig.1, left) the pressure difference between LIJVs inlet and outlet is around 1 mmHg, while, in the case of a stenosis, we observe that a significant increase in IJV pressure drop (above 1.5 mmHg) is achieved with a reduction of the CSA of more than 50% (Fig. 1, center and right). Further results will be presented during the conference.

This work represents a first step towards a computer-aided understanding of CCSVI haemodynamics in a patient-specific context. Future developments will focus on the implementation of Fluid-Structure Interaction models to account for veins compliance, and on the incorporation of this framework into a multi-scale global model of the cardiovascular system.