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Rigorous mathematical optimization of synthetic hepatic vascular trees

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical...

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Autores principales: Jessen, Etienne, Steinbach, Marc C., Debbaut, Charlotte, Schillinger, Dominik
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9198513/
https://www.ncbi.nlm.nih.gov/pubmed/35702863
http://dx.doi.org/10.1098/rsif.2022.0087
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author Jessen, Etienne
Steinbach, Marc C.
Debbaut, Charlotte
Schillinger, Dominik
author_facet Jessen, Etienne
Steinbach, Marc C.
Debbaut, Charlotte
Schillinger, Dominik
author_sort Jessen, Etienne
collection PubMed
description In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach.
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spelling pubmed-91985132022-06-15 Rigorous mathematical optimization of synthetic hepatic vascular trees Jessen, Etienne Steinbach, Marc C. Debbaut, Charlotte Schillinger, Dominik J R Soc Interface Life Sciences–Mathematics interface In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach. The Royal Society 2022-06-15 /pmc/articles/PMC9198513/ /pubmed/35702863 http://dx.doi.org/10.1098/rsif.2022.0087 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Life Sciences–Mathematics interface
Jessen, Etienne
Steinbach, Marc C.
Debbaut, Charlotte
Schillinger, Dominik
Rigorous mathematical optimization of synthetic hepatic vascular trees
title Rigorous mathematical optimization of synthetic hepatic vascular trees
title_full Rigorous mathematical optimization of synthetic hepatic vascular trees
title_fullStr Rigorous mathematical optimization of synthetic hepatic vascular trees
title_full_unstemmed Rigorous mathematical optimization of synthetic hepatic vascular trees
title_short Rigorous mathematical optimization of synthetic hepatic vascular trees
title_sort rigorous mathematical optimization of synthetic hepatic vascular trees
topic Life Sciences–Mathematics interface
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9198513/
https://www.ncbi.nlm.nih.gov/pubmed/35702863
http://dx.doi.org/10.1098/rsif.2022.0087
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