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Calculus and Medicine
9
Overview
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.