# Gompertzian tumour growth

Source: https://onco.cc/technologies/gompertzian-growth-model/  
OnCo record `gompertzian-growth-model` (Technology). Data CC BY-NC 4.0, attribute "Data from OnCo (onco.cc)"; commercial use needs a licence.

## TL;DR

Tumours do not grow exponentially forever: growth slows as they enlarge, following a curve Benjamin Gompertz devised for human mortality in 1825 and Anna Kane Laird fitted to tumours in 1964. It explains why small tumours are the most chemosensitive and why doubling times lengthen.

## Summary

The Gompertz function describes growth whose rate falls exponentially with size, so a tumour grows fastest when small and approaches a plateau as it outstrips its blood supply. Laird showed in 1964 that it fitted animal and human tumours far better than exponential growth, and it became the basis of Norton and Simon's reasoning about dose density, of models of micrometastatic disease after surgery, and of estimates of how long a tumour has been present at diagnosis. Its parameters are hard to measure in a single patient, and other sigmoidal laws (logistic, von Bertalanffy) fit many series equally well.

## Fields

- Kind: Technology
- Status: established
- Last checked: 2026-09-17
- Tags: mathematical-model
- Principle: dV/dt = a·V·ln(K/V): the growth rate is proportional to size times the logarithm of the distance from the carrying capacity K, giving a sigmoid curve with a decelerating phase.
- Since: 1964
- Strengths: Fits most tumour growth series; Explains higher chemosensitivity of small tumours; Underpins dose-density and adjuvant timing arguments
- Limitations: Parameters rarely measurable in one patient; Competing sigmoid laws fit as well; Says nothing about mechanism

## Sources

- Wikipedia: https://en.wikipedia.org/wiki/Gompertz_function
- Laird 1964, British Journal of Cancer: https://doi.org/10.1038/bjc.1964.55

## Connected records

- fronts: [AI & Computation](https://onco.cc/fronts/ai-computation/), [Drug Discovery Platforms](https://onco.cc/fronts/drug-discovery/)
- technologies: [Cytotoxic chemotherapy](https://onco.cc/technologies/cytotoxic-chemotherapy/), [Log-kill hypothesis (Skipper)](https://onco.cc/technologies/log-kill-hypothesis/), [Norton-Simon hypothesis and dose-dense chemotherapy](https://onco.cc/technologies/norton-simon-hypothesis/)

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