Senior author David Odde, from the University of Minnesota, said: "Ideally, a tumour progression model would be consistent across a wide range of spatial-temporal scales to predict how molecular-level perturbations, resulting from either cell mutation or therapeutic intervention, would affect tumour-level progression and, ultimately, patient outcome."

He continued: "In this respect, the existing simulation methods, such as continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumour spreading behaviour, and discrete agent-based approaches that capture individual cell events such as proliferation or migration, are not as accurate as we would like."

To develop a model that could address this problem, the team looked at the progression and spread of the brain cancer glioblastoma. "Glioblastoma is well suited to proliferation-migration modelling approaches, because the tumour cells rarely spread to other sites outside of the central nervous system, and the cells are both highly proliferative and migratory," Odde explained.

"In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from CT or MRI," he said. "However, these estimates of glioblastoma cell migration rates, modelled via a diffusion-like process, are approximately one to two times larger than single-cell measurements in animal models of the disease. We wanted to identify possible sources for this discrepancy."

The researchers re-evaluated the underlying assumptions of the RD framework and found a possible origin of the discrepancy, in that the RD framework assumes individual particles do not occupy volume and therefore are permitted to overlap. Real cells clearly do occupy volume, meaning overlapping configurations are physically unattainable.

"When we implemented the adjustment to the RD framework, the non-overlapping model helps to explain the apparent discrepancy between measured and estimated diffusion coefficients, and provides a more realistic in silico tumour simulator based on measurable parameters," Odde said. "As a result, experimentally measured tumour growth rates can now be explained by experimentally-measured single cell migration rates. Importantly from a clinical perspective, the simulations demonstrate that a fast-progressing tumour can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates."

Odde said: "This type of tumour progression modelling offers the potential to predict tumour-spreading behaviour to improve prognostic accuracy and guide therapy development."