Predictive modeling of in vivo response to gemcitabine in pancreatic cancer

Abstract

A clear contradiction exists between cytotoxic in-vitro studies demonstrating effectiveness of Gemcitabine to curtail pancreatic cancer and in-vivo studies failing to show Gemcitabine as an effective treatment. The outcome of chemotherapy in metastatic stages, where surgery is no longer viable, shows a 5-year survival <5%. It is apparent that in-vitro experiments, no matter how well designed, may fail to adequately represent the complex in-vivo microenvironmental and phenotypic characteristics of the cancer, including cell proliferation and apoptosis. We evaluate in-vitro cytotoxic data as an indicator of in-vivo treatment success using a mathematical model of tumor growth based on a dimensionless formulation describing tumor biology. Inputs to the model are obtained under optimal drug exposure conditions in-vitro. The model incorporates heterogeneous cell proliferation and death caused by spatial diffusion gradients of oxygen/nutrients due to inefficient vascularization and abundant stroma, and thus is able to simulate the effect of the microenvironment as a barrier to effective nutrient and drug delivery. Analysis of the mathematical model indicates the pancreatic tumors to be mostly resistant to Gemcitabine treatment in-vivo. The model results are confirmed with experiments in live mice, which indicate uninhibited tumor proliferation and metastasis with Gemcitabine treatment. By extracting mathematical model parameter values for proliferation and death from monolayer in-vitro cytotoxicity experiments with pancreatic cancer cells, and simulating the effects of spatial diffusion, we use the model to predict the drug response in-vivo, beyond what would have been expected from sole consideration of the cancer intrinsic resistance. We conclude that this integrated experimental/computational approach may enhance understanding of pancreatic cancer behavior and its response to various chemotherapies, and, further, that such an approach could predict resistance based on pharmacokinetic measurements with the goal to maximize effective treatment strategies.

Figure 1. Gemcitabine toxicity in-vitro for MiaPaCa-2 and S2-VP10 pancreatic cell lines.

Viability for cells treated with varying concentrations of Gemcitabine was determined after 24 hours of drug exposure.

Figure 2. Calculation of MVD and Parameter A.

(A) Sample S2-VP10 histology slide stained for Factor VIII (40×). (B) Parameter A (non-dimensional) describing the relative strength of apoptosis calculated from in-vitro measurements as a function of gemcitabine concentration (and with extent of vascularization parameter B = 0.43).

Figure 3. Tumor growth (V/G) predicted by the mathematical model.

Simulated tumor growth ( Eq. 7 ) for radially symmetric (A) MiaPaCa-2 and (B) S2-VP10 in-vivo tumors after treatment beginning when radius R = 1.5 mm, taking into consideration diffusion gradients in 3D and a moderate extent of vascularization.

Figure 4. Measurement of tumor radii from bioluminescent imaging of untreated and gemcitabine-treated SCID mice.

Gompertz growth curves were fitted to these data to illustrate the tumor growth. (A) MiaPaCa-2 radii and fitting to Gompertz equations (untreated) and (treated). (B) Bioluminescence signal shown for representative mice with S2-VP20 tumors. (C) S2-VP10 radii and fitting to Gompertz equations (untreated) and (treated). (D) Bioluminescence signal shown for representative mice with S2-VP20 tumors. Error bars in (A) and (C) correspond to standard error of the mean.