Mathematical models of microcirculation: fluid-dynamics and nutrient delivery

Paola Causin, Department of Mathematics, Universita’ degli Studi di Milano

Transport and exchange of nutrients from peripheral blood circulation provide fundamental support to body organs activity. Investigation of these circulatory districts, which include thousands of microvessels with diameter less than 200mm, is often difficult even with up-to-date imaging facilities.

 

^{Microcirculatory network with deformed vessel radii, in color. Vessels deform due to transmural blood pressure (difference between internal and interstitial pressure)}

 

 

 

 

In our research, we investigate mathematical models of microcirculatory districts, capable of dealing with large, general microcirculatory networks with an affordable time of resolution.  Networks are described as graphs of distensible tubes (vessels), representative of realistic cerebral and cerebral-like arterioles, venules and capillaries. The distribution of blood flow and pressure drop within these intricate networks is a main regulatory element of nutrient supply. Flow and pressure are highly interlaced functions of vessel resistances, these latter being determined by the variable blood biophysical properties, vessel mechanical and geometrical features. Fluid-structure interaction approaches are considered to account for vessel compliance. Preliminary investigations have been carried out on autoregolatory mechanism in arterioles both with phenomenological and more detailed  representations including the dynamics of key chemical species. The different models are applied in particular to the study of eye retina circulation

Solute transport in blood is modeled via diffusion-convection-reaction equations, coupled with nutrient delivery to the surrounding tissue. In particular, oxygen dynamics is addressed by mixture theory in blood to keep into account the presence of its free form in plasma and bounded form in red blood cells. Solute profiles in tissue are also studied by diffusion-reaction equations, including the presence of delimiting membranes which possibly hinder the passage of certain chemical species. Drug delivery in the eye retina is studied as an application of this research.

This work is performed in collaboration with Francesca Malgaroli, Dept of Mathematics, Politecnico di Milano, Italy.

For further information please contact paola.causin@unimi.it

Bibliography

• Causin, G.Guidoboni, F.Malgaroli, R.Sacco, A.Harris, “Mathematical modeling of the retinal microcirculation and oxygen delivery”, apparso nel volume “Integrated multidisciplinary approaches in the study and care of the human eye. Clinical experience, mathematical modelling, new technologies”, Kugler Publications, Amsterdam, The Netherlands, (2014)
• Causin, G. Guidoboni, F. Malgaroli, R. Sacco, A. Harris. ”Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation”. Biomech Model Mechanobiol, DOI=10.1007/s10237-015-0708-7, (2015)
• Causin, F. Malgaroli, “A mathematical and computational model of blood flow regulation in microvessels: application to the eye retina circulation”, JMMB, 15(02), (2015)
• Causin, G. Guidoboni, F. Malgaroli, R. Sacco, A. Harris. “Impact of blood flow on ocular pathologies: can mathematical and numerical modeling help preventing blindness?”, The European Consortium for Mathematics in Industry, subseries of Mathematics in Industry, Series Editors: Bonilla, L.L., Günther, M., Scherzer, O., Schilders, W., (2016)
• Causin, F. Malgaroli, “Blood Flow Repartition in Distensible Microvascular Networks: Implication of Interstitial and Outflow Pressure Conditions”, to appear on J Coupled Syst Multiscale Dyn, (2016)
• Causin, F. Malgaroli. “Mathematical assessment of drug build-up in the posterior eye following trans-scleral delivery”, submitted to Journal of Mathematics in Industry, (2016)