Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

Causin, Paola; Guidoboni, Giovanna; Malgaroli, Francesca; Sacco, Riccardo; Harris, Alon

doi:10.1007/s10237-015-0708-7

Cited by 55 publications

(50 citation statements)

References 85 publications

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“…This similarity indicates that the blood flow rates in the retinal microcirculation scale similarly with diameter regardless of the chosen pressure drop. This scaling is also consistent with power law relationships between flow and diameter in arterial and venous networks obtained by a mathematical model by Causin et al [11] and experimental findings by Riva et al [35], which found k values of 2.76 and 2.84 for the two networks, respectively.…”

Section: Discussionsupporting

confidence: 91%

“…These predictions are within range of previous modeling studies byCausin et al [11] andLiu et al [10]. Causin et al[11] predicted an average arteriolar PO 2 between 49 and 77 mmHg for an oxygen demand of 3.6 cm 3 O 2 /100 cm 3 /min, and Liu et al[10] predicted PO 2 values between 65 and 108 mmHg in an arteriolar network.…”

supporting

confidence: 88%

“…The model is used to predict oxygen saturation in arterioles, but does not include venous saturation predictions or any aspects of flow regulation. Causin et al [11] developed a 6-layer model (3 layers for the inner retina and 3 layers for the outer retina) that couples blood flow mechanics to a vascular network model for oxygen distribution in tissue. The vascular network model consists of arterioles and venules represented as discrete fractal trees and a capillary plexus represented as a set of parallel pipes.…”

Section: Introductionmentioning

confidence: 99%

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Predicting retinal tissue oxygenation using an image-based theoretical model

Fry

Coburn

Whiteman

et al. 2018

Mathematical Biosciences

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Impaired oxygen delivery and tissue perfusion have been identified as significant factors that contribute to the loss of retinal ganglion cells in glaucoma patients. This study predicts retinal blood and tissue oxygenation using a theoretical model of the retinal vasculature based on confocal microscopy images of the mouse retina. These images reveal a complex and heterogeneous geometry of vessels that are distributed non-uniformly into multiple distinct retinal layers at varying depths. Predicting oxygen delivery and distribution in this irregular arrangement of retinal microvessels requires the use of an efficient theoretical model. The model employed in this work utilizes numerical methods based on a Green's function approach to simulate the spatial distribution of oxygen levels in a network of retinal blood vessels and the tissue surrounding them. Model simulations also predict the blood flow rates and pressures in each of the microvessels throughout the entire network. As expected, the model predicts that average vessel PO decreases as oxygen demand is increased. However, the standard deviation of PO in the vessels nearly doubles as oxygen demand is increased from 1 to 8 cm O/100 cm/min, indicating a very wide spread in the predicted PO levels, suggesting that average PO is not a sufficient indicator of oxygenation in a heterogeneous vascular network. Ultimately, the development of this mathematical model will help to elucidate the important factors associated with blood flow and metabolism that contribute to the vision loss characteristic of glaucoma.

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Section: Discussionsupporting

confidence: 91%

supporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Predicting retinal tissue oxygenation using an image-based theoretical model

Fry

Coburn

Whiteman

et al. 2018

Mathematical Biosciences

Self Cite

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“…In this paper, each candidate tree was treated as arterial tree. To compute the fluid-dynamic parameters, at the inlets a pressure value of 40 mmHg, which reflects the hydrostatic and frictional pressure losses from the aorta to the Central Retinal Artery (CRA) (Causin et al [16]), was specified. To prevent vessels from collapse, a pressure slightly higher than the intraocular pressure in normal conditions (15 mmHg) was enforced at the outlet.…”

Section: -D Vascular Modelmentioning

confidence: 99%

A fluid-dynamic based approach to reconnect the retinal vessels in fundus photography

Calivá

Hunter

Chudzik

et al. 2017

2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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Abstract-This paper introduces the use of fluid-dynamic modeling to determine the connectivity of overlapping venous and arterial vessels in fundus images. Analysis of the retinal vascular network may provide information related to systemic and local disorders. However, the automated identification of the vascular trees in retinal images is a challenging task due to the low signal-to-noise ratio, nonuniform illumination and the fact that fundus photography is a projection on to the imaging plane of three-dimensional retinal tissue. A zero-dimensional model was created to estimate the hemodynamic status of candidate tree configurations. Simulated annealing was used to search for an optimal configuration. Experimental results indicate that simulated annealing was very efficient on test cases that range from small to medium size networks, while ineffective on large networks. Although for large networks the nonconvexity of the cost function and the large solution space made searching for the optimal solution difficult, the accuracy (average success rate = 98.35%), and simplicity of our novel approach demonstrate its potential effectiveness in segmenting retinal vascular trees.

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“…Experimental results have indicated disordered spatial distribution of blood vessels [21]. In retinal vascular network, the arterioles and venules reach out from the center to the periphery, forming a roughly radial skeleton, while capillaries form a vessel network that links the arterioles and venules [22]. It is also observed that the microcirculation in tumor tissue presents a chaotic geometry [23].…”

Section: Introductionmentioning

confidence: 99%

A fast numerical method for oxygen supply in tissue with complex blood vessel network

Huang

Ying

2020

Preprint

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AbstractOxygen field evaluation is important in modeling and simulation of many important physiological processes of animals, such as angiogenesis. However, numerical simulation of the oxygen field in animal tissue is usually limited by the unusual coupling of different mechanisms, the nonlinearity of the model, and the complex geometry of refined blood vessel networks. In this work, a fast numerical method is designed for the simulation of oxygen supply in tissue with a large-scale complex vessel network. This method employs an implicit finite-difference scheme to compute the oxygen field. By virtue of an oxygen source distribution technique from vessel center lines to mesh points and a corresponding post-processing technique that eliminate the local numerical error induced by source distribution, square mesh with relatively large mesh sizes can be applied while sufficient numerical accuracy is maintained. The new method has computational complexity which is slightly higher than linear with respect to the number of mesh points and has a convergence order which is slightly lower than second order with respect to the mesh size. As an example, the oxygen field of a tissue irrigated by a blood vessel network with more than four thousand blood vessels can be accurately computed within one minute with our new method. The new method will definitely promote further researches based on evaluation of oxygen field, such as modeling of angiogenesis and pathogenesis of many cardiovascular diseases.

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Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

Cited by 55 publications

References 85 publications

Predicting retinal tissue oxygenation using an image-based theoretical model

Predicting retinal tissue oxygenation using an image-based theoretical model

A fluid-dynamic based approach to reconnect the retinal vessels in fundus photography

A fast numerical method for oxygen supply in tissue with complex blood vessel network

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