Here's how tumour growth can be explained by maths

Washington: There is indeed some magic in numbers!

Universidad Carlos III de Madrid (UC3M) has carried out a study that now mathematically explains how tumours induce the growth of blood vessels.

The study maintains that the tips of the blood vessels expand like a soliton, a solitary wave similar to a tsunami. "If we know how blood vessels move towards a tumor and know they take the form of a soliton, we can slow down their growth or prevent them from reaching and feeding the tumor by controlling the movement of this wave," said researcher Luis L. Bonilla.

In the study, the UC3M scientists have made a mathematical description of the density of blood vessels associated with the growth of tumours through differential equations. Moreover, they confirmed this model through numerical simulations.

"We saw that in the first stages, the density of the tips of the capillaries that move toward the tumor take the form of a soliton, similar to the waves of a tsunami or those that form in an irrigation canal when you stop the water with a brick and suddenly remove it," explained Bonilla.

This line of research began at UC3M in 2014. "It was then that we identified some problems about angiogenesis and we were able to deduce the equation for the density of the capillary tips, something that eluded researchers for years," Bonilla continued.

"A soliton is a wave that can spread for a long time without changing much," explained co-researcher Bjorn Birnir. And what that means within the context of this study is that "the tips of the veins take on a shape that does not change, lasting from the time the soliton forms until it reaches the tumour," he said.

The study has been published in Scientific Reports.