Angiogenesis and Invasion Organised By Mark Chaplain

An individual-based model approach to tumour growth in vitro

Dirk Drasdo
Max-Planck-Institute for Mathematics in the Sciences, Leipzig,
Germany
drasdo@mis.mpg.de

Coauthor(s): Stefan Hoehme

To what extent is tumour growth controlled by nutrients, biomechanical forces, and other factors? The main mechanisms that determine the growth kinetics of tumours at different stages and in different environments are still largely unknown. This question is usually addressed by examining in vitro model systems, which are experimentally well accessible and hence allow for systematic studies of parameter and growth condition dependencies. However even in vitro experiments are rarely free of unknown or uncontrolled influences. We present a mathematical model to study the spatio-temporal growth dynamics of two-dimensional tumour monolayers and three-dimensional tumour spheroids as a complementary tool to in-vitro experiments. Within our model each cell is represented individually and parameterized by experimentally completely measurable cell-biophysical and cell-kinetic parameters. Hence our modeling strategy allows us to study which mechanisms on the microscopic level of individual cells, determine the macroscopic properties of tumour growth. We quantitatively compare our in silico results to published experimental observations on avascular tumour spheroids and on monolayer cultures. Our findings stress the potential significance of a biomechanically-mediated inhibition during the experimentally observed transition from exponential to sub-exponential growth at sufficiently large tumour sizes. The good correspondence between our in silico results and the experimental data suggests that our model strategy may provide a starting point from which a quantitative modeling of in vivo tumour growth under normal and therapy conditions may also become feasible.

The possible role of post-operative azotemia in enhanced
survival of patients with metastatic renal cancer following
cytoreductive nephrectomy

Edward Gawlinski
Temple University, USA
ed@ba114.scitech.temple.edu

Coauthor(s): Robert Gatenby

Several recent clinical trials have found longer survival in patients with metastatic renal cancer if cytoreductive nephrectomy is performed prior to systemic therapy. Typically these studies show a modest but statistically significant increase in length of survival in patients undergoing cytoreductive nephrectomy compared to controls (non-nephrectomy) regardless of the subsequent systemic therapy employed. Spontaneous regressions of metastases following resection of the primary renal cancer, although rare, have also been reported in up to 6% of subjects. These effects are generally ascribed to systemic changes related to resection of the primary tumor including reduction of the total tumor burden, removal of a source for later metastases, and enhanced immune response.

We propose, as an alternative hypothesis, the observed clinical benefit from cytoreductive nephrectomy results from resection of the kidney rather than the cancer. This hypothesis is based on mathematical models of the tumour-host interface that demonstrate tumour-induced acidification of the microenvironment of peritumoral normal tissues is a necessary component of the invasive phenotype. These models indicate that the graded metabolic acidosis associated with mild chronic renal failure following resection of one kidney may be sufficient in some cancers to alter the dynamical interactions at the tumour-host interface reducing and even reversing the rate of invasion.

To test the modeling results we conducted a retrospective review of patients who underwent cytoreductive nephrectomy prior to systemic therapy with interferon alfa-2b in SWOG 8949. We find a significant correlation between postoperative decrease in renal function as measured by increased serum BUN and creatinine and improved patient survival and progression free survival.

We conclude that further investigation of this phenomenon is warranted to confirm our findings and determine if systemic acidification mediates the observed survival benefit of mild azotemia following cytoreductive nephrectomy in patients with metastatic renal cancer.

The Contribution of Net Proliferation and Invasion in the
Development of Successful Treatment for Gliomas

Kristin Swanson
University of Washington, USA
swanson@amath.washington.edu

Coauthor(s): E. C. Alvord, Jr

Gliomas are complex, heterogeneous brain tumors associated with a humbling prognosis. Despite several decades of continued bench and clinical work on these tumors, the effective treatment of gliomas remains elusive. We propose that part of this failure lies in the lack of understanding of the interaction of both net proliferation and migration of glioma cells in defining the actual extent of growth and invasion of the lesion beyond what medical imaging can show. Our studies of the relationship between these two basic components of glioma progression through mathematical modelling have already successfully predicted the behaviour of groups of patients, both low-grade and high-grade. We demonstrate how the extension of our mathematical modelling approach to individual patients permits much more rapid identification of successful new therapies.