Fractal properties of perfusion heterogeneity in optimized arterial trees: A model study

Autor(en)

Rudolf Karch, Friederike Neumann, Bruno Karl Podesser, Martin Neumann, Paul Szawlowski, Wolfgang Schreiner

Abstrakt

Regional blood flows in the heart muscle are remarkably heterogeneous. It is very likely that the most important factor for this heterogeneity is the metabolic need of the tissue rather than flow dispersion by the branching network of the coronary vasculature. To model the contribution of tissue needs to the observed flow heterogeneities we use arterial trees generated on the computer by constrained constructive optimization. This method allows to prescribe terminal flows as independent boundary conditions, rather than obtaining these flows by the dispersive effects of the tree structure. We study two specific cases: equal terminal flows (model 1) and terminal flows set proportional to the volumes of Voronoi polyhedra used as a model for blood supply regions of terminal segments (model 2). Model 1 predicts, depending on the number Nterm of end-points, fractal dimensions D of perfusion heterogeneities in the range 1.20 to 1.40 and positively correlated nearest-neighbor regional flows, in good agreement with experimental data of the normal heart. Although model 2 yields reasonable terminal flows well approximated by a lognormal distribution, it fails to predict D and nearest-neighbor correlation coefficients r1 of regional flows under normal physiologic conditions: model 2 gives D = 1.69 ‘ 0.02 and r 1 = -0.18 ‘ 0.03 (n = 5), independent of Nterm and consistent with experimental data observed under coronary stenosis and under the reduction of coronary perfusion pressure. In conclusion, flow heterogeneity can be modeled by terminal positions compatible with an existing tree structure without resorting to the flow-dispersive effects of a specific branching tree model to assign terminal flows.

Organisation(en)

Computergestützte Physik und Physik der Weichen Materie, Forschungsgruppe Workflow Systems and Technology, Department für Biochemie und Zellbiologie

Externe Organisation(en)

Medizinische Universität Wien

Journal

Journal of General Physiology

Band

122

Seiten

307-321

Anzahl der Seiten

15

ISSN

0022-1295

DOI

https://doi.org/10.1085/jgp.200208747

Publikationsdatum

2003

Peer-reviewed

Ja

ÖFOS 2012

1030 Physik, Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/969015de-a0a6-4acf-b010-60022a291a74