What Is a Tumour Growth Model?

For decades, scientists have been using computational models to understand more about various types of cancer and how they behave in the human body. In particular, these models have been utilised to monitor the growth of the tumour over time, both in patients who are undergoing chemotherapy and in those who are not.

As well as providing actionable evidence of how well a certain treatment is working for the individual in question, these types of models also provide quantitative data on tumour behaviour over a much larger dataset. This allows for greater understanding of the cancer’s behaviour and, in time, the development of more personalised treatment plans for individual sufferers of the disease.

The different types of tumour growth model

While scientists have long agreed on the merits of using computational models to monitor and predict tumour growth, the exact methods of doing so have been a subject of some debate. There are a number of different techniques used to create a tumour growth model, each of which is summarised below:

• Exponential

Since cancer cells multiply regularly in the early stages of growth, the exponential model is quite effective at predicting how the tumour will behave at this point. However, its efficacy drops away as nutrient depletion and angiogenesis inhibit the tumour’s activity later on.

• Mendelsohn

Developed by ML Mendelsohn in the 1960s, this model is a generalisation of the exponential model and, like its counterpart, is only effective in describing unlimited growth. It ties the growth rate to some specified power of the cancerous cell population.

• Logistic

Created by Pierre Francois Verhulst in 1838, the logistic model assumes that growth has a ceiling, as defined by its carrying capacity. It predicts that the growth rate will decrease as the growth population increases, until it reaches zero when the carrying capacity is met.

• Linear

The linear model is one of the first that was used to examine the growth of colonies of cancerous cells. It assumes that while growth is exponential initially, it will later reach a plateau and continue to grow but at a constant rate.

• Surface

At its heart, the surface model operates on the assumption that only surface cells in a solid growth are capable of dividing, while those beneath remain constant. This explains the early exponential growth as the surface cells reproduce, but later slow when the tumour is composed of more inner cells.

• Bertalanffy

Pioneered by Ludwig Bertalanffy, this model operates on the assumption that tumour growth is intrinsically linked to surface area, but also accounts for the incidence of death rates among cells. It has been lauded as one of the most accurate models of tumour growth in humans.

• Gompertz

Originally devised by Benjamin Gompertz in 1825 to describe mortality rates, the Gompertz model is a generalisation of the logistical model and contains a curve asymmetrical to the inflection point. It has been found to be most effective when applied to breast and lung cancer.