# Blood Vessel Branching: Beyond the Standard Calculus Problem

@article{Adam2011BloodVB, title={Blood Vessel Branching: Beyond the Standard Calculus Problem}, author={John A. Adam}, journal={Mathematics Magazine}, year={2011}, volume={84}, pages={196 - 207} }

Summary Calculating the optimal angle for blood vessel branching is a standard calculus problem. However, optimality in that setting is judged by a cost functional that turns out not to give realistic results. We study a sequence of improvements to the cost functional, finally arriving at one that passes an important modeling test: From this last functional, we derive three empirical laws of blood vessel branching, originally proposed by German zoologist Wilhelm Roux.

## 20 Citations

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

- Mathematics, Computer SciencePLoS Comput. Biol.
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It is found that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material- cost optimizations for the mouse lung.

Branch order regression for modeling brain vasculature

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A novel parametrization preserves an important aspect of tree structure, namely its branch order, and is amenable to standard methods of analysis, like generalized linear/additive models.

Fluid Flow at Branching Junctions

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The flow of fluids at branching junctions plays important kinematic and dynamic roles in most biological and industrial flow systems. The present paper highlights some key issues related to the flow…

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- Physics, MedicineMicrovascular research
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This work suggests a new paradigm in microvascular blood flow properties, that vessel bifurcation itself, regardless of its angle, holds considerable influence on blood viscosity, and this phenomenon will help to develop new predictive tools inmicrovascular research.

Computational feasibility of simulating changes in blood flow through whole-organ vascular networks from radiation injury.

- Medicine, Computer ScienceBiomedical physics & engineering express
- 2020

It is demonstrated, for the first time, that it is computationally feasible to calculate radiation dose deposition in whole-organ vascular networks and the resulting change in blood flow.

Solute dispersion in bifurcating networks

- Materials ScienceJournal of Fluid Mechanics
- 2020

Abstract Advective–diffusive transport of passive scalars in confined environments (e.g. vessels and channels) within a network is of fundamental importance in a plethora of biological and…

Computational feasibility of simulating whole-organ vascular networks.

- Medicine, Computer ScienceBiomedical physics & engineering express
- 2020

It is demonstrated, for the first time, that it is feasible to computationally model the vasculature of the whole human brain using a fractal-based algorithm.

Computational feasibility of calculating the steady-state blood flow rate through the vasculature of the entire human body.

- Medicine, PhysicsBiomedical physics & engineering express
- 2020

This study designed and implemented a two-step algorithm to calculate the blood flow rates through a vasculature equal in size to that of the human body using principles of steady-state fluid dynamics.

A theoretical framework for determining cerebral vascular function and heterogeneity from dynamic susceptibility contrast MRI

- Physics, MedicineJournal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism
- 2017

A theoretical framework for determining cerebral vascular function and heterogeneity from dynamic susceptibility contrast magnetic resonance imaging (MRI), which covers realistic structural architectures for vessel branching and orientations, as well as a range of hemodynamic scenarios for blood flow, capillary transit times and oxygenation is presented.

Analysis of Coronary Contrast Agent Transport in Bolus-Based Quantitative Myocardial Perfusion MRI Measurements with Computational Fluid Dynamics Simulations

- Materials Science, Computer ScienceFIMH
- 2017

The analysis of contrast agent dispersion in bolus-based quantitative myocardial perfusion MRI measurements finds multi-faceted influences on bolus shape from length of traversed vessels to bifurcation angles and vessel curvature.

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