Quantifying glioblastoma drug response dynamics incorporating resistance and blood brain barrier penetrance from experimental data

Abstract

Many drugs investigated for the treatment of glioblastoma (GBM) have had poor clinical outcomes, as their efficacy is dependent on adequate delivery to sensitive tumor cell populations, which is limited by the blood-brain barrier (BBB). Further complicating evaluation of therapeutic efficacy, tumors can become resistant to anti-cancer drugs, and it can be difficult to gauge the extent to which BBB limitations and resistance each contribute to a drugs failure. To address this question, we developed a minimal mathematical model to characterize these elements of overall drug response, informed by time-series bioluminescence imaging data from a treated patient-derived xenograft (PDX) experimental model. By fitting this mathematical model to a preliminary dataset in a series of nonlinear regression steps, we estimated parameter values for individual PDX subjects that correspond to the dynamics seen in experimental data. Using these estimates, we performed a parameter sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients. Results from this analysis combined with simulation results suggest that BBB permeability may play a slightly larger role in therapeutic efficacy than drug resistance. Our model and fitting technique to estimate parameters from data may be a useful tool in aiding further exploration of these challenges in future studies of drug efficacy with larger datasets.