Mathematical methods for modeling the microcirculation

Arciero, Julia; Causin, Paola; Malgaroli, Francesca

doi:10.3934/biophy.2017.3.362

Cited by 21 publications

(25 citation statements)

References 148 publications

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“…There has been extensive modelling of blood flow in the retina and surrounding ocular region, and also of the interactions of oxygen and metabolites with the surrounding tissue. A detailed review of some of these models was given by Arciero et al [2]. The focus of many of these models is the actual flow of blood in the microarteries and the changes due to the intra-ocular pressure.…”

Section: Introductionmentioning

confidence: 99%

Modelling Hydrogen Clearance From the Retina

Farrow¹,

Hocking²,

Cringle³

et al. 2018

ANZIAM J.

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The human retina is supplied by two vascular systems: the highly vascular choroidal, situated behind the retina; and the retinal, which is dependent on the restriction that the light path must be minimally disrupted. Between these two circulations, the avascular retinal layers depend on diffusion of metabolites through the tissue. Oxygen supply to these layers may be threatened by diseases affecting microvasculature, for example diabetes and hypertension, which may ultimately cause loss of sight.An accurate model of retinal blood flow will therefore facilitate the study of retinal oxygen supply and, hence, the complications caused by systemic vascular disease. Here, two simple models of the blood flow and exchange of hydrogen with the retina are presented and compared qualitatively with data obtained from experimental measurements. The models capture some interesting features of the exchange and highlight effects that will need to be considered in a more sophisticated model and in the interpretation of experimental results.

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Section: Introductionmentioning

confidence: 99%

Modelling Hydrogen Clearance From the Retina

Farrow¹,

Hocking²,

Cringle³

et al. 2018

ANZIAM J.

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show abstract

“…In addition, the current model does not consider the non‐Newtonian phenomena of blood rheology, eg, shear thinning, history effects, hysteresis, and structural aggregates. These effects can be required in accurately predicting the blood flow in the microvasculature . In this reason, the non‐Newtonian effects can be a part of future work as well.…”

Section: Discussionmentioning

confidence: 99%

A computational modeling of blood flow in asymmetrically bifurcating microvessels and its experimental validation

Lee

Hong

Yoo

et al. 2018

Numer Methods Biomed Eng

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Microvascular transport is complex due to its heterogeneity. Many researchers have been developing mathematical and computational models in predicting microvascular geometries and blood transport. However, previous works were focused on developing simulation models, not on validating suggested models with microvascular geometry and blood flow in the real microvasculature. In this paper, we suggest a computational model for microvascular transport with experimental validation in its geometry and blood flow. The geometry is generated by controlling asymmetric conditions of microvascular network. Also, the blood flow in microvascular networks is predicted by considering in vivo viscosity, Poiseuille flow model, and hematocrit redistribution by plasma skimming. The suggested model is validated by the measured data in rat mesentery. Also, the microvascular transport in a case of mouse cortex is predicted and compared against experimental data to check applicability of the suggested model.

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“…Although many fundamental aspects of vascular tissue engineering apply to both large blood vessels and capillaries, fabrication methods for one vessel type are not necessarily applicable for the other. This is due to several profound differences between large vessel modeling and microvasculature modeling: vessel diameter (centimeters and millimeters vs. micrometers), number of vessels (individual hollow tubes vs. vascular network), the role of blood rheology (Newtonian vs. corpuscular fluid models), and characteristic Reynolds and Womersley numbers (relevant vs. very low) [ 22 , 23 ]. The fabrication methods are discussed in Section 3 .…”

Section: Important Aspects Of Microvascular Tissue Engineeringmentioning

confidence: 99%

“…Great progress has been made in the mathematical and computer modeling of complex microvascular systems in the last decades [ 23 ]. The use of such an approach serves several different functions in research, such as identifying key elements, testing hypotheses and simulations, and optimizing experimental methods, thus contributing to different stages in the understanding of biological phenomena [ 136 , 137 ].…”

Section: Mathematical Modeling Of Biophysical Propertiesmentioning

confidence: 99%

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Microvascular Tissue Engineering—A Review

et al. 2021

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Tissue engineering and regenerative medicine have come a long way in recent decades, but the lack of functioning vasculature is still a major obstacle preventing the development of thicker, physiologically relevant tissue constructs. A large part of this obstacle lies in the development of the vessels on a microscale—the microvasculature—that are crucial for oxygen and nutrient delivery. In this review, we present the state of the art in the field of microvascular tissue engineering and demonstrate the challenges for future research in various sections of the field. Finally, we illustrate the potential strategies for addressing some of those challenges.

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Mathematical methods for modeling the microcirculation

Cited by 21 publications

References 148 publications

Modelling Hydrogen Clearance From the Retina

Modelling Hydrogen Clearance From the Retina

A computational modeling of blood flow in asymmetrically bifurcating microvessels and its experimental validation

Microvascular Tissue Engineering—A Review

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