1. ANALYZING TUMOR GROWTH
The Gompertz Model

2. The Gompertz Function
Special case of the generalized logistic function
Asymmetrical: right-hand asymptote is approached more slowly than left
Originally created to describe human mortality
Common model to predict growth of cancerous tumors

3. F(t)=ae-be The General Equation -ct b, c are positive numbers
a: asymptote
b: displacement along the x- axis (translates the graph to the left or right)
c: growth rate

4. The Recursive Formula In S(t + r)= a+b*InS(t)
Recursive formula + linear regression analysis gets the most accurate fit for breast, lung cancer
S(t+r): remaining population
r : the constant age increment between two consecutive measurements
b: initial growth rate, 0<b<1
a: survival fraction after one iteration

5. Standard Tumor Growth

6. Significance Able to find carrying capacity and key turning points
Optimize treatment
Varying constants allows model to work across many types of tumors
Cyan: uninhibited growth
Magenta: early stage treatment
Black: medium stage treatment
Yellow: late stage treatment

7. References
Bassukas, Ioannis D. “Use of the Recursion Formula of the Gompertz Survival Function to Evaluate Life-Table Data.” Mechanisms of Ageing and Development, vol. 89, no. 3, 24 July 1996, pp. 155–163., doi: / (96)
Benzekry, Sébastien, et al. “Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth.” PLoS Computational Biology, vol. 10, no. 8, 2014, doi: /journal.pcbi
Tjørve, Kathleen M. C., and Even Tjørve. “The Use of Gompertz Models in Growth Analyses, and New Gompertz-Model Approach: An Addition to the Unified-Richards Family.” Plos One, vol. 12, no. 6, 5 June 2017, doi: /journal.pone