3D hybrid modeling of vascular network formation

Perfahl, Holger; Hughes, Barry D.; Tomas, Alaracon,; Maini, Philip K.; Lloyd, Mark C.; Reuß, Matthias; Byrne, Helen M.

doi:10.48550/arxiv.1610.00661

Cited by 2 publications

(4 citation statements)

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“…While at this stage, differences in the spatial distribution of tortuosity or loops are not apparent, in future work, we will investigate these observations further by applying statistical analyses to the full dataset. At the same time, we will use our existing multiscale models of vascular tumour growth to generate artificial networks for analysis with TDA [9,10,19]. In this way, we aim to establish whether observed patterns (such as persistence of cycles in the topological description of the network) can be related to specific biophysical mechanisms used to construct the vessel networks, to investigate how the barcode associated with a particular tumour changes as the tumour and its vasculature evolve.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…A large number of mathematical models have been developed over the past 30 years to study tumour-induced angiogenesis [15,18,20] and to simulate artificial vessel networks. For example, now we have multiscale, agent-based models that simulate angiogenesis and vascular tumour growth [9,10,19]. These models have been used to investigate how vessel networks respond to anti-angiogenic and other vascular targeting agents.…”

Section: Mathematical Models Of Artificial Vessel Networkmentioning

confidence: 99%

“…An observed summary outside the range, or close to the boundary of this range, of these simulated summaries, indicates deviation from the expectation. For vascular networks, theoretical models have been investigated for example in [19], but depending on the complexity of the simulations, simpler models based on branching processes may be more appropriate. If it is not possible to simulate from appropriate models, then statistical machine learning offers a model-free approach to classify data through using TDA summaries as features in an automated learning method such as random forests.…”

Section: 2mentioning

confidence: 99%

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Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature

Byrne,

Harrington,

Muschel

et al. 2019

Preprint

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Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate multiple, high-resolution images of the same tissue region, and show how vessel networks evolve during disease onset and treatment. Such experimental advances have created an exciting opportunity for discovering new links between vessel structure and disease through the development of mathematical tools that can analyse these rich datasets. Here we explain how topological data analysis (TDA) can be used to study vessel network structures. TDA is a growing field in the mathematical and computational sciences, that consists of algorithmic methods for identifying global and multi-scale structures in high-dimensional data sets that may be noisy and incomplete [4,7,24]. TDA has identified the effect of ageing on vessel networks in the brain [21] and more recently proposed to study blood flow and stenosis [16]. Here we present preliminary work which shows how TDA of spatial network structure can be used to characterise tumour vasculature.

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Section: Discussion and Outlookmentioning

confidence: 99%

Section: Mathematical Models Of Artificial Vessel Networkmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

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Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature

Byrne,

Harrington,

Muschel

et al. 2019

Preprint

Self Cite

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“…Synthetic tree generation relies on the principle that the blood vessels supply the tissues by filling the tissue volume while minimizing required work. Previous tree generation strategies include constrained constructive optimization, staged growth-based constrained constructive optimization, nonlinear programming based constrained constructive optimization, and supply-demand relationship based tree generation methods (Blanco et al 2021;Capasso et al 2013;Coppini et al 1997;Heck et al 2015;Jaquet et al 2019;Jessen et al 2022;Karch et al 1999Karch et al , 2000Levine et al 2001;Milde et al 2013;Mittal et al 2005;Perfahl et al 2017;Shen et al 2021;Schreiner et al 2006;Smith et al 2000;Spill et al 2015;Tawhai et al 2000;Talou et al 2021;Wang and Bassingthwaighte 1990;Yang and Wang 2013). The constrained constructive optimization (CCO) methods are the most widely used tree generation algorithms so far (Blanco et al 2021;Jaquet et al 2019;Karch et al 1999Karch et al , 2000Schreiner et al 2006;Talou et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Tissue-growth-based synthetic tree generation and perfusion simulation

Kim

Rundfeldt²,

Lee³

2023

Biomech Model Mechanobiol

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Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

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3D hybrid modeling of vascular network formation

Cited by 2 publications

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Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature

Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature

Tissue-growth-based synthetic tree generation and perfusion simulation

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