# 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

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## References

SHOWING 1-10 OF 14 REFERENCES

Mathematics in Nature : Modeling Patterns in the Natural World

- Mathematics
- 2005

And while I have sought to shew the naturalist how a few mathematical concepts and dynamical principles may help and guide him, I have tried to shew the mathematician a field for his labour—a field…

Introduction to the Calculus of Variations

- Mathematics
- 1999

This is a self-contained paper which introduces a fundamental problem in the calculus of variations, the problem of finding extreme values of functionals. The reader should have a solid background in…

Calculus, Early Transcendentals

- Mathematics
- 2002

Chapter 0 Before Calculus 0.1 Functions 0.2 New Functions from Old 0.4 Families of Functions 0.5 Inverse Functions Inverse Trigonometric Functions 0.6 Exponential and Logarithmic Functions Chapter 1…

Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin

- Education
- 2008

Guesstimation is a book that unlocks the power of approximation--it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and…

Mathematical Biophysics, Vol

- 2, Chapter XXVII, Dover, New York,
- 1960

On growth and form i

- Economics
- 1917

THIS book, at once substantial and stately, is to the credit of British science and an achievement for its distinguished author to be proud of. It is like one of Darwin's books, well-considered,…

Segment analysis of human coronary arteries.

- MedicineBlood vessels
- 1987

The new concept of vessel segment and the method of analysis are proposed as a means for an accurate description of the branching characteristics of the coronary network, comparing the network with others in the cardiovascular system and comparing the vasculature in the normal versus that in the diseased heart.