Multiscale Modelling for Cerebrospinal Fluid Dynamics: Multicompartmental Poroelacticity and the Role of AQP4

Dean Chou, John C. Vardakis, Yiannis Ventikos

1Institute of Biomedical Engineering, University of Oxford, Oxford, UK 2Department of Engineering Science, University of Oxford, Oxford, UK.
Department of Mechanical Engineering, University College London, London, UK.

DOI: 10.4236/jbm.2014.22001                

Abstract

Cerebrospinal fluid (CSF) is recognized to play an important role in the brain environment and central nerv-ous system (CNS). At the microscopic level, glial cells and water channel proteins (WCPs), also known as aquaporins (AQPs), are believed to be central in regulating CSF. Furthermore, such elements are postulated to associate with numerous cerebral and neurological pathologies. The novelty of the present research is the attempt to investigate such pathophysi-ological phenomena via a multi scale physical model incorporating mechanisms across all scales, including the AQP effects. The proposed physical multiscale model can explore the relationship between CSF and glial cells via the incorporation of AQPs (as microscopic channels) and elaborate on the macroscopic manifestations of this interplay. This study aims to make a tangible contribution to the understanding of cerebral or neurological pathologies via virtual physiological human (VPH) in silico.

Keywords

Aquaporin; Hydrocephalus; Cerebrospinal Fluid; Computational Fluid Dynamics

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Rosenberg, G.A. (1999) Ischemic Brain Edema. Progress in Cardiovascular Diseases, 42, 209-216. http://dx.doi.org/10.1016/S0033-0620(99)70003-4
[2]	Rockwood, K., et al. (2007) Toward a Revision of Criteria for the Dementias. Alzheimer’s & Dementia, 3, 428-440. http://dx.doi.org/10.1016/j.jalz.2007.07.014
[3]	Hasegawa, H., et al. (1994) Molecular Cloning of a Mercuri-al-Insensitive Water Channel Expressed in Selected Water-Transporting Tissues. Journal of Biological Chemistry, 269, 5497-500.
[4]	Jung, J.S., et al. (1994) Molecular Characterization of an Aquaporin cDNA from Brain: Candidate Osmoreceptor and Regulator of Water Balance. Proceedings of the National Academy of the United States of America, 91, 13052-13056. http://dx.doi.org/10.1073/pnas.91.26.13052
[5]	Terzaghi, K. (1923) Die berechnung der durchlassigkeitzifer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen, Mathematish-naturwissenschaftliche, Klasse. Akademie der Wissenschaften, Vienna, 125-138.
[6]	Biot, M.A. (1941) General Theory of Three-Dimensional Con-solidation. Journal of Applied Physics, 12, 155-164. http://dx.doi.org/10.1063/1.1712886
[7]	Mendes, M.A., Murad, M.A. and Pereira, F. (2012) A New Computational Strategy for Solving Two-Phase Flow in Strongly Heterogeneous Poroelastic Media of Evolving Scales. International Journal for Numerical and Analytical Methods in Geomechanics, 36, 1683-1716. http://dx.doi.org/10.1002/nag.1067
[8]	Carcione, J.M., Morency, C. and Santos, J.E. (2010) Computational Poroelas-ticity—A Review. Geophysics, 75, A229- A243.
[9]	Pena, A., Bolton, M.D. and Pickard, J.D. (1998) Cellular Poroe-lasticity: A Theoretical Model for Soft Tissue Mechanics. http://www-civ.eng.cam.ac.uk/geotech_new/people/bolton/mdb_pub/76_poromechanics98_475_480.PDF
[10]	Stokes, I.A., et al. (2010) Limitation of Finite Element Analysis of Poroelastic Behavior of Biological Tissues Undergoing Rapid Loading. Annals of Biomedical Engineering, 38, 1780-1788. http://dx.doi.org/10.1007/s10439-010-9938-0
[11]	Wang, X. and Hong, W. (2012) A Visco-Poroelastic Theory for Polymeric Gels. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science.
[12]	Polzer, S., et al. (2012) Impact of Poroelasticity of Intraluminal Thrombus on Wall Stress of Abdominal Aortic Aneurysms. Bio-Medical Engineering OnLine, 11, 62. http://dx.doi.org/10.1186/1475-925X-11-62
[13]	Nia, H.T., et al. (2011) Poroe-lasticity of Cartilage at the Nanoscale. Biophysical Journal, 101, 2304-2313. http://dx.doi.org/10.1016/j.bpj.2011.09.011
[14]	Wan, X.C., Steudle, E. and Hartung, W. (2004) Gating of Water Channels (Aquaporins) in Cortical Cells of Young Corn Roots by Mechanical Stimuli (pressure pulses): Effects of ABA and of HgCl2. Journal of Experimental Botany, 55, 411-422. http://dx.doi.org/10.1093/jxb/erh051
[15]	Kimelberg, H.K. (2004) Water Homeostasis in the Brain: Basic Concepts. Neuroscience, 129, 851-860. http://dx.doi.org/10.1016/j.neuroscience.2004.07.033
[16]	Tully, B. and Ventikos, Y. (2011) Cerebral Water Transport Using Multiple-Network Poroelastic Theory: Application to Normal Pressure Hydrocephalus. Journal of Fluid Mechanics, 667, 188-215. http://dx.doi.org/10.1017/S0022112010004428
[17]	Tully, B. and Ventikos, Y. (2009) Coupling Poroelasticity and CFD for Cerebrospinal Fluid Hydrodynamics. IEEE Transactions on Biomedical Engineering, 56, 1644-1651. http://dx.doi.org/10.1109/TBME.2009.2016427
[18]	Vandoormaal, J.P. and Raithby, G.D. (1984) Enhancements of the Simple Method for Predicting Incompressible Fluid- Flows. Numerical Heat Transfer, 7, 147-163.
[19]	Badaut, J., Brunet, J.F. and Regli, L. (2007) Aquawporins in the Brain: From Aqueduct to “Multi-Duct”. Metabolic Brain Disease, 22, 251-263. http://dx.doi.org/10.1007/s11011-007-9057-2