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Calculus and Medicine

Medicine uses Calculus quite often and in many ways. However, due to time constraints, this will only delve into the most effectatious of the uses: the use of calculus to solve for the volume of blood flow through a length of blood at a point in time.

By Hay Longhurst

Vascular Blood Flow

Calculus is commonly used to determine the blood flow through a specific section of a vein.

We can model the vein as a cylindrical tube with a pressure differential of ΔP, length of Δx, and radius of R. The viscocity of blood is η and has a velocity v. We can find v at a radius r < R by the equation:

Bibliography

Use In Medicine

Example

http://www.bloodflowonline.com/learn-about-blood-viscosity/blood-viscosity-basics

http://www.cvphysiology.com/Hemodynamics/H011.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/pfric.html#veff

http://circ.ahajournals.org/content/102/19/2371.full

https://prezi.com/z56alvfoyncf/calculus-applications-to-biology-and-medicine/

https://prezi.com/udtqzwlpuxl_/calculus-in-medicine/

http://en.wikipedia.org/wiki/Anterior_interosseous_artery

http://en.wikipedia.org/wiki/Radial_artery

http://www.cvphysiology.com/Blood%20Flow/BF001.htm

http://circ.ahajournals.org/content/86/1/232.abstract

Doctors can use this to find the flux (volume per unit time) by multiplying the velocity by the area and taking the Integral of the ensuing expression with respect to the radius r < R.

In an artery of radius 1.4 mm and a difference in pressure that is 9 mmHg, what is the blood flow across a length of 40mm of the artery, if the viscocity of blood is .015 Poise?

22.6 cubic mm per sec

Thank You!

Uses

This can warn Doctors of the potential of heart attacks, clots, strokes, and other cardiac and vascular problems. The information can even be shared between doctors to allow for the prevention of many problems including epidermic, sleeping, gastric, and even psychological.

ECG

62

bpm

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