TY - JOUR

T1 - Rigorous mathematical optimization of synthetic hepatic vascular trees

AU - Jessen, Etienne

AU - Steinbach, Marc C.

AU - Debbaut, Charlotte

AU - Schillinger, Dominik

N1 - Publisher Copyright: © 2022 Royal Society Publishing. All rights reserved.

PY - 2022/6/15

Y1 - 2022/6/15

N2 - 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 to 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.

AB - 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 to 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.

KW - Heuristic topology optimization

KW - Liver corrosion cast

KW - Nonlinear optimization problem

KW - Rigorous geometry optimization

KW - Synthetic vascular trees

KW - Validation

UR - http://www.scopus.com/inward/record.url?scp=85132082405&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2202.04406

DO - 10.48550/arXiv.2202.04406

M3 - Article

C2 - 35702863

VL - 19

JO - Journal of the Royal Society Interface

JF - Journal of the Royal Society Interface

SN - 1742-5689

IS - 191

M1 - 20220087

ER -