Mathematical methods for modeling the microcirculation

Julia C. Arciero; Paola Causin; Francesca Malgaroli; Julia C. Arciero; Paola Causin; Francesca Malgaroli

doi:10.3934/biophy.2017.3.362

AIMS Biophysics

2017, Volume 4, Issue 3: 362-399. doi: 10.3934/biophy.2017.3.362

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Review

Mathematical methods for modeling the microcirculation

1.
Department of Mathematical Sciences, IUPUI, 402 N. Blackford, LD 270, Indianapolis IN 46202, USA
2.
Department of Mathematics, University of Milan, via Saldini 50, 20133 Milano, Italy

Received: 02 March 2017 Accepted: 09 May 2017 Published: 07 June 2017

The microcirculation plays a major role in maintaining homeostasis in the body. Alterations or dysfunctions of the microcirculation can lead to several types of serious diseases. It is not surprising, then, that the microcirculation has been an object of intense theoretical and experimental study over the past few decades. Mathematical approaches offer a valuable method for quantifying the relationships between various mechanical, hemodynamic, and regulatory factors of the microcirculation and the pathophysiology of numerous diseases. This work provides an overview of several mathematical models that describe and investigate the many different aspects of the microcirculation, including geometry of the vascular bed, blood flow in the vascular networks, solute transport and delivery to the surrounding tissue, and vessel wall mechanics under passive and active stimuli. Representing relevant phenomena across multiple spatial scales remains a major challenge in modeling the microcirculation. Nevertheless, the depth and breadth of mathematical modeling with applications in the microcirculation is demonstrated in this work. A special emphasis is placed on models of the retinal circulation, including models that predict the influence of ocular hemodynamic alterations with the progression of ocular diseases such as glaucoma.
- microcirculation,
- blood flow,
- oxygen transport,
- autoregulation,
- fluid-structure interaction problems,
- mathematical model,
- retinal microcirculation
Citation: Julia C. Arciero, Paola Causin, Francesca Malgaroli. Mathematical methods for modeling the microcirculation[J]. AIMS Biophysics, 2017, 4(3): 362-399. doi: 10.3934/biophy.2017.3.362

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Abstract

The microcirculation plays a major role in maintaining homeostasis in the body. Alterations or dysfunctions of the microcirculation can lead to several types of serious diseases. It is not surprising, then, that the microcirculation has been an object of intense theoretical and experimental study over the past few decades. Mathematical approaches offer a valuable method for quantifying the relationships between various mechanical, hemodynamic, and regulatory factors of the microcirculation and the pathophysiology of numerous diseases. This work provides an overview of several mathematical models that describe and investigate the many different aspects of the microcirculation, including geometry of the vascular bed, blood flow in the vascular networks, solute transport and delivery to the surrounding tissue, and vessel wall mechanics under passive and active stimuli. Representing relevant phenomena across multiple spatial scales remains a major challenge in modeling the microcirculation. Nevertheless, the depth and breadth of mathematical modeling with applications in the microcirculation is demonstrated in this work. A special emphasis is placed on models of the retinal circulation, including models that predict the influence of ocular hemodynamic alterations with the progression of ocular diseases such as glaucoma.

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