A Mathematical and Computational Model of Blood Flow Regulation in Microvessels: Application to the Eye Retina Circulation

Causin, Paola; Malgaroli, Francesca

doi:10.1142/s0219519415400278

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…What is lost is the spatial distribution of field variables, so that relevant geometrical and physical heterogeneities of the network cannot be represented, as well as complex internal interactions (see [10] for a discussion on this topic). Spatial heterogeneity is taken into account in a different set of papers, which represent relatively small vessel graphs as a collection of 1D distensible tubes, derived from mathematical algorithms [11,12,13,14] or from medical imaging data [15]. While these models include the effect of the geometrical localization of each vessel in the network the mechanical description is absent (rigid vessels) or very simplified.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of local perfusion in large distensible microvascular networks

Causin

Malgaroli

2017

Computer Methods in Applied Mechanics and Engineering

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Microvessels -blood vessels with diameter less than 200 µm-form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced function of single vessel resistances and mutual vessel interactions. Since, it is often impossible to quantify all these aspects when collecting experimental measures, in this paper we propose a mathematical and computational model to study the behavior of microcirculatory networks subjected to different conditions. The network geometry, which can be derived from digitized images of experimental measures or constructed in silico on a computer by mathematical laws, is simplified for computational purposes into a graph of connected straight cylinders, each one representing a vessel. The blood flow and pressure drop across the single vessel, further split into smaller elements, are related through a generalized Ohm's law featuring a conductivity parameter, function of the vessel cross section area and geometry, which undergo deformations under pressure loads. The membrane theory is used for the description of the deformation of vessel lumina, tailored to the structure of thick-walled arterioles and thin-walled venules. In addition, since venules can possibly experience negative values of transmural pressure (difference between luminal and interstitial pressure), a buckling model is also included to represent vessel collapse. The complete model including arterioles, capillaries and venules represents a nonlinear coupled system of PDEs, which is approached numerically by finite element discretization and linearization techniques. As an example of application, we use the model to simulate flow in the microcirculation of the human eye retina, a terminal system with a single inlet and outlet. After a phase of validation against experimental measurements of the correctness of the blood flow and pressure fields in the network, we compute the network response to different interstitial pressure values. Such a study is carried out both for global and localized variations of the interstitial pressure. In both cases, significant redistributions of the blood flow in the network arise, highlighting the importance of considering the single vessel behavior along with its position and connectivity in the network.

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling of local perfusion in large distensible microvascular networks

Causin

Malgaroli

2017

Computer Methods in Applied Mechanics and Engineering

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Examination of Couple Stress Hybrid Nanoparticles (CuO-Cu/Blood) as a Targeted Drug Carrier with Magnetic Effects Through Porous Sheet

2021

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Application of Drug Delivery in Magnetohydrodynamics Peristaltic Blood Flow of Nanofluid in a Non-Uniform Channel

Abbas

Bai

Rashidi

et al. 2016

J. Mech. Med. Biol.

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In this paper, we have studied the application of drug delivery in magnetohydrodynamics (MHD) peristaltic blood flow of nanofluid in a non-uniform channel. The governing equation of motion and nanoparticles are modeled under the consideration of creeping flow and long wavelength. The resulting non-linear coupled differential equation is solved with the help of perturbation. Numerical Integration has been used to obtain the results for pressure rise and friction forces. The impact of various pertinent parameters on temperature profile, concentration profile such as density Grashof number, thermal Grashof number, Brownian motion parameter, thermophoresis parameter and MHD is demonstrated mathematically and graphically. The present analysis is also applicable for three-dimensional profile.

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A Mathematical and Computational Model of Blood Flow Regulation in Microvessels: Application to the Eye Retina Circulation

Cited by 3 publications

References 10 publications

Mathematical modeling of local perfusion in large distensible microvascular networks

Mathematical modeling of local perfusion in large distensible microvascular networks

Examination of Couple Stress Hybrid Nanoparticles (CuO-Cu/Blood) as a Targeted Drug Carrier with Magnetic Effects Through Porous Sheet

Application of Drug Delivery in Magnetohydrodynamics Peristaltic Blood Flow of Nanofluid in a Non-Uniform Channel

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