Mathematical modelling in physiology and medicine: neurological diseases

Eleuterio Toro (University of Trento)

Thursday 3rd May, 2018 14:00-15:00 311B Mathematics and Statistics Building


There is increasing evidence of the involvement of the dynamics of fluid compartments of the central nervous system (CNS) in the pathophysiology of neurological diseases [1], [2]. Supportive, recent advances in human physiology include the discovery of a meningeal lymphatic system [3], [4]. A feasible multidisciplinary holistic approach to understand the basic mechanisms at work is offered by mathematical modelling. In this talk I first give a brief review of some neurological diseases thought to be associated to malfunctions of CNS fluid compartments, such as Multiple Sclerosis, Meniere’s Disease, Idiopathic Parkinson’s Disease, Alzheimer’s Disease and Idiopathic Intracranial Hypertension. I then describe a global, closed loop mathematical model for the entire human circulation [5-6] coupled to the dynamics of cerebrospinal fluid (CSF) and brain dynamics [7]. Sample computations on the effect of extracranial venous strictures on CNS haemodynamics and CSF dynamics are presented. Intracranial venous hypertension and disturbed CSF dynamics are predicted. These computational results support recent medical hypotheses and may help to unravel some of the underlying mechanisms of some of these diseases, paving the way to treatment strategies. I then point out some of the limitations of our present mathematical model and describe current work aimed at enhancing it, to include the peripheral as well as the newly discovered brain lymphatic system. Some unresolved mathematical and numerical challenges are briefly described.

[1] Thomas Brinker, Edward Stopa, John Morrison and Petra Klinge. A new look at cerebrospinal fluid circulation. Fluids and Barriers of the CNS 2014, 11:10. Published online 2014 May 1. doi: 10.1186/2045-8118-11-10
[2] Eleuterio F. Toro. Brain Venous Haemodynamics, Neurological Diseases and Mathematical Modelling. A Review. Applied Mathematics and Computation, Vol. 272, pp 542-579, 2016.
[3] Antoine Louveau, Igor Smirnov, Timothy J. Keyes, Jacob D. Eccles, Sherin J. Rouhani, J. David Peske, Noel C. Derecki, David Castle, James W. Mandell, Kevin S. Lee, Tajie H. Harris & Jonathan Kipnis. Structural and functional features of central nervous system lymphatic vessel. Nature 523, 337–341 (16 July 2015) doi:10.1038/nature14432
[4] Aleksanteri Aspelund, Salli Antila, Steven T. Proulx, Tine Veronica Karlsen, Sinem Karaman, Michael Detmar, Helge Wiig, and Kari Alitalo. A dural lymphatic vascular system that drains brain interstitial fluid and macromolecules. The J. Exp. Medicine, Vol. 212 (7), pp 991-999, 2015
[5] Lucas O. Mueller and Eleuterio F. Toro. A global multi-scale model for the human circulation with emphasis on the venous system. International Journal for Numerical Methods in Biomedical Engineering. Volume 30, Issue 7, pages 681-725, July 2014
[6] Lucas O. Mueller and Eleuterio F. Toro. Enhanced global mathematical model for studying cerebral  venous blood. Journal of Biomechanics. Volume 47, Issue 13, 17 October 2014, Pages 3361-3372
[7] Eleuterio Toro, Andreas Linninger, Qinghui Zhang, Lucas O Mueller and Christian Contarino. Holistic multi-fluid mathematical model for the central nervous system. In preparation 2018.

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