Otto-von-Guericke-Universität Magdeburg


Prof. Dr. hc. Eleuterio Toro, Ph.D.


On the dynamics of interacting fluid compartments of the central nervous system: a mathematical modeling approach


Body-fluid compartments that are relevant to the understanding of the physiology of the central nervous system (CNS) are first reviewed [1], emphasising very recent biomedical research that includes the discovery of a brain lymphatic system [2], strenuously denied in the classical medical literature. There follows a brief review of some neurodegenerative diseases thought to be associated to malfunctions of CNS fluid compartments, such as multiple sclerosis, Meniere’s disease, Parkinson’s disease and Alzheimer’s disease [3]. I then describe a global, closed loop mathematical model for the entire human circulation [4], [5] coupled to the dynamics of cerebrospinal fluid (CSF) and brain dynamics [6]. Sample computations on the effect of extracranial venous strictures on brain haemodynamics and CSF dynamics are presented. Intracranial venous hypertension is predicted as well disturbed CSF dynamics. These computational results support recent medical hypotheses and may help to unravel some of the underlying mechanisms of some of these diseases. Current/future work is concerned with the enhancement of our global model to include the peripheral as well as the newly discovered brain lymphatic system.


[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] 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

[3] Eleuterio F. Toro. Brain Venous Haemodynamics, Neurological Diseases and Mathematical Modelling. A Review. Applied Mathematics and Computation, Vol. 272, pp 542-579, 2016. doi:10.1016/j.amc.2015.06.0662015.

[4] 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.

[5] 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.

[6] Eleuterio Toro, Andreas Linninger, Qinghui Zhang, Lucas O Mueller and Christian Contarino. Holistic multi-fluid mathematical model for the central nervous system. In preparation 2016.

Datum: 08.09.2016, Raum: G05-205 (Senatssaal), Zeit: 17:15
Letzte Änderung: 16.11.2016 - Ansprechpartner:
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