Blood Vessel Branching: Beyond the Standard Calculus Problem

2011/06/01 by John Adam · 1 citation
Medicine · #Platelet Disorders and Treatments #Lipid metabolism and disorders #Diabetes, Cardiovascular Risks, and Lipoproteins

paper · doi:10.4169/math.mag.84.3.196

openalex publication_date 2011/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/30

Abstract

SummaryCalculating 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.

Citations

• Mathematics in nature. modeling patterns in the natural world

Cited by

• Calculus [wikipedia]

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