A computational model for microcirculation including Fahraeus‐Lindqvist effect, plasma skimming and fluid exchange with the tissue interstitium. (20th November 2018)

• Record Type: Journal Article
• Authors: Possenti, Luca; di Gregorio, Simone; Gerosa, Fannie Maria; Raimondi, Giorgio; Casagrande, Giustina; Costantino, Maria Laura; Zunino, Paolo
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 35:Number 3(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-11-20
• Subjects: capillary leakage -- Fahraeus‐Lindqvist -- microcirculation -- plasma skimming; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3165
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: We present a two‐phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus‐Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one‐dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation, and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus‐Lindqvist, plasma skimming, and capillary leakage effects on the distribution of flow in a microvascular network. Abstract : We develop a mathematical model of microcirculation that combines nonlinear rheology, hematocrit distribution, arbitrary vascular morphology, and interaction with the tissue interstitium. The model is derived from the fundamental governing principles by means of dimensional (topological) reduction techniques. We validate the model on the basis of semi‐analytical solutions and we propose an algorithm to computationally generate microvascular morphologies on the basis of biomimetic principles. Finally, we address the application of the model to realistic cases.