Quantifying Glioblastoma Drug Response Dynamics Incorporating Treatment Sensitivity and Blood Brain Barrier Penetrance From Experimental Data

Abstract

Many drugs investigated for the treatment of glioblastoma (GBM) have had disappointing clinical trial results. Efficacy of these agents is dependent on adequate delivery to sensitive tumor cell populations, which is limited by the blood-brain barrier (BBB). Additionally, tumor heterogeneity can lead to subpopulations of cells with different sensitivities to anti-cancer drugs, further impacting therapeutic efficacy. Thus, it may be important to evaluate the extent to which BBB limitations and heterogeneous sensitivity each contribute to a drug's failure. To address this challenge, 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 as a guide for parameter ranges, we ran model simulations and performed a parameter sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients. Results from this analysis combined with simulations suggest that BBB permeability may play a slightly greater role in therapeutic efficacy than relative drug sensitivity. Additionally, we discuss recommendations for future experiments based on insights gained from this model. Further research in this area will be vital for improving the development of effective new therapies for glioblastoma patients.

Complementary role of mathematical modeling in preclinical glioblastoma: differentiating poor drug delivery from drug insensitivity

“…In this paper, we demonstrate that our model, using relatively minimal experimental data, arrives at similar conclusions to the highly sophisticated experiments conducted in Marin et al for a subset of the cell lines [6]. First, we describe the mathematical model as presented in Massey et al [7]. Then, we provide a brief description of the cell lines and experiments that were used.…”

“…Distinct from Massey et al, a Bayesian approach was employed for fitting parameters in an attempt to capture the generic behavior of the cell line while acknowledging the varying behavior in individual mice [7]. Similar to Massey et al though, parameters were calibrated in a sequential process enabled by the experimental design [7].…”

“…Recently, in Massey et al ., we detailed our approach of how a mathematical model could utilize only a subset of the data collected in Marin et al . to identify the driving factor of drug failure: limited drug delivery or the presence of a population insensitive to treatment [6, 7]. This is significant because it enables researchers to quickly assess cell lines and determine which deserve deeper experimentation.…”

“…First, we describe the mathematical model as presented in Massey et al . [7]. Then, we provide a brief description of the cell lines and experiments that were used.…”

“…Model Parameter Definitions and Values. Adapted from Massey et al[7]. *Note: ADC dose was given according to animal weights, but variation was unremarkable so we modeled the dose as a constant.…”