The Optimal Form of Distribution Networks Applied to the Kidney and Lung

TL;DR

This paper presents a model to optimize the shape of organ distribution networks, revealing that a modified ellipsoid form minimizes volume and closely resembles the natural anatomy of kidneys and lungs.

Contribution

It introduces a variational model that predicts the optimal organ shape for distribution networks, aligning with biological forms.

Findings

Distribution networks are optimally shaped as modified ellipsoids.

The model closely matches the external anatomy of kidneys and lungs.

Uses a geometric variational approach similar to isoperimetric theorems.

Abstract

A model is proposed to minimize the total volume of the main distribution networks of fluids in relation to the organ form. The minimization analysis shows that the overall exterior form of distribution networks is a modified ellipsoid, a geometric form that is a good approximation to the external anatomy of the kidney and lung. The variational procedure implementing this minimization is similar to the traditional isoperimetric theorems of geometry. A revised version of this preprint that expands Section 4 will be published in the Journal of Biological Systems, World Scientific Publishing.