Abstract 481: Biophysical models of pattern formation in bone marrow endothelial networks
Authors: Brummer Alexander B. , Kim Young-Woong , Carlesso Nadia , Rockne Russell C. 
Published: June 2022

Abstract
In this work we aim to understand how cellular aggregation and angiogenic pattern formation develop in bone marrow endothelial networks by integrating spatial-temporal mathematical models with theory regarding how cellular metabolism scales with cell number. Presently, efforts to model angiogenic pattern formation fail to accurately predict spatial characteristics often observed.
Biological allometries, such as the scaling of metabolism to mass or cell number, have been hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to motion. Metabolic scaling theory argues that two guiding principles—optimization of motion and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Recently, metabolic scaling theory has been applied to study tumor growth rates, offering a mechanistic link between tumor growth and vascular patterning.
Remarkably, there exists two classes of spatial-temporal mathematical models where equivalent angiogenic pattern formation occurs. These two classes are determined primarily by either cellular interactions as proposed by Hillen and Painter, or biomechanical forces as proposed by Manoussaki and Murray. Examples of underlying mechanisms are chemotactic quorum-sensing and resource competition for the former, and advection-diffusion driven stresses and strains in the extra-cellular matrix for the latter. We compare these models by examining theoretical predictions for pattern forming criteria with numerical simulations. Furthermore, we identify experimentally testable predictions for angiogenic pattern formation related to the spatial configuration of the extra-cellular matrix. We test these predictions against in vitro confocal microscopy imaging data for bone marrow endothelial networks with experimental control over adhesion molecules and the resulting network structure. Specifically, we measure time-dependent geometric features in the highly reticulated endothelial networks related to steady-state equilibration, connectivity and space-filling. Example metrics are the scaling of network edge lengths and enclosed areas within the extra-cellular matrix that indicate changes to network morphology as adhesion molecules are present or absent. These metrics are informed by metabolic scaling theory and are predicted by the steady-state solutions of the underlying models. By conducting metric and model selection, this work identifies data-driven mechanisms for angiogenic pattern formation and quantifies normality in bone-marrow endothelial networks. This is an essential step for future work in quantifying and understanding abnormality in bone marrow endothelial networks.
Citation Format: Alexander B. Brummer, Young-Woong Kim, Nadia Carlesso, Russell C. Rockne. Biophysical models of pattern formation in bone marrow endothelial networks [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 481.