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Calculus Applications to Tumor Growth

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Marlow Schulz

on 28 May 2014

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Transcript of Calculus Applications to Tumor Growth

Calculus Connection
There are over 200 types of cancer
No one model for all types.
Use “direct curve fitting”
Different growth model equations are fitted to the volume of each individual tumor and the model with the best fitting is selected.

Tumor Growth
Tumors grow based on the nutrient supply available
Tumor angiogenesis is the proliferation of blood vessels that penetrate into the tumor to supply nutrients and oxygen and to remove waste products
The center of the tumor largely consists of dead cells, called the necrotic center of the tumor
The tumor grows outward in roughly a spherical shell shape

Exponential Growth Method
Volume continuously increases exponentially over time

Gompertzian Model
growth rate declines over time
How tumor will react to treatment
Most effective when growing the fastest
Second derivative
First derivative test to find maximum
When growth rate is 0
critical numbers
Models of Tumor Growth
Other Applications
Calculus Applications to Tumor Growth
volume at time t
volume when time is zero
exponential growth constant
Growth Rate?
Rate of change= Derivative
Derive volume equation to find the growth rate of the tumor!
differential equation
volume at a certain time
growth constant
constant for growth retardation
Can calculus cure cancer?
By Marlow Schulz
By using the principles of calculus, we can find out how fast a tumor is shrinking/growing, the size when the tumor will stop growing, when certain treatments should be given and finding the volume of a tumor.

Gompertzian Method takes into account the fact that a tumor does not grow exponentially forever.
size is limited
horizontal asymptote as time approaches infinity
Full transcript