Mathematical Modeling of Glioblastoma Wound Healing Assay (WHA) and Radiation Response in Non-Small Cell Lung Cancer (NSCLC)

Abstract

Glioblastoma is a brain tumor with a poor prognosis. This disease is characterized by its inherent heterogeneity and the migratory nature of its cancer cells. Understanding the mechanics of tumor cell infiltration into healthy tissue can potentially improve prognostic outcomes. To further investigate this effect, we used a wound healing assay on compliant collagen-I-coated polyacrylamide substrates and plating of U251 glioma cell lines. We then applied a Brownian dynamics-based tumor simulator (BDTS) to use minimal input parameters to assess and compare properties of a simple wound healing experiment, i.e. single cell random motility coefficients (D) and tissue culture doubling time (p). Interestingly, we found that without adjusting for a priori assumptions on how wound closure takes place, the ensemble behavior of the wound closure rate can be simulated with single cell input data. Our experiments confirmed that cells on substrates with higher Young’s moduli tend to close the gap more rapidly as an ensemble of individual cells. This finding validates the results of our simulated scenarios. Additionally, we demonstrated that heterogeneity in motility coefficients (D) or variations in doubling time (p) does not explain wound closure rate with any degree of significance compared to an assumption of uniform D and p values. These results demonstrate the ability of single cell data to accurately predict tumor level dynamics, and further demonstrate the relative robustness with respect to cell-to-cell heterogeneity. We demonstrate the importance of considering intratumoral heterogeneity and the development of resistance during fractionated radiotherapy when the same dose of radiation is delivered for all fractions (Fractional Equivalent Dosing, FED).A mathematical model was developed with the following parameters: a starting population of 1011 non-small cell lung cancer (NSCLC) tumor cells, 48-hour doubling time, and cell death per the linear-quadratic (LQ) model with α and β values derived from RSIα/β, in a previously described gene expression based model that estimates α and β. To incorporate both inter- and intratumor radiation sensitivity, RSIα/β output for each patient sample is assumed to represent an average value in a gamma distribution with the bounds set to -50% and +50% of RSIa/b. Therefore, we assume that within a given tumor there are subpopulations that have varying radiation sensitivity parameters that are distinct from other tumor samples with a different mean RSIα/β. A simulation cohort (SC) comprised of 100 lung cancer patients with available RSIα/β (patient specific α and β values) was used to investigate 60Gy in 30 fractions with fractionally equivalent dosing (FED). A separate validation cohort (VC) of 57 lung cancer patients treated with radiation with available local control (LC), overall survival (OS), and tumor gene expression was used to clinically validate the model. Cox regression was used to test for significance to predict clinical outcomes as a continuous variable in multivariate analysis (MVA). Finally, the VC was used to compare FED schedules with various altered fractionation schema utilizing a Kruskal-Wallis test. This was examined using the end points of end of treatment log cell count (LCC) and by a parameter described as mean log kill efficiency (LKE) defined as: LCC = log10(tumorcellcount) LKE=((log10(〖〖day〗_i〗_tumorcellcount )– log10(〖〖day〗_(i+1)〗_tumorcellcount )))/(〖day〗_i_dosage) Cox regression analysis on LCC for the VC demonstrates that, after incorporation of intratumoral heterogeneity, LCC has a linear correlation with local control (p = 0.002) and overall survival (p =< 0.001). Other suggested treatment schedules labeled as High Intensity Treatment (HIT) with a total 60Gy delivered over 6 weeks have a lower mean LCC and an increased LKE compared to standard of care 60Gy delivered in FED in the VC. We find that LCC is a clinically relevant metric that is correlated with local control and overall survival in NSCLC. We conclude that 60Gy delivered over 6 weeks with altered HIT fractionation leads to an enhancement in tumor control compared to FED when intratumoral heterogeneity is considered.