Predictive Modeling of Drug Response in Non-Hodgkin's Lymphoma

Abstract

We combine mathematical modeling with experiments in living mice to quantify the relative roles of intrinsic cellular vs. tissue-scale physiological contributors to chemotherapy drug resistance, which are difficult to understand solely through experimentation. Experiments in cell culture and in mice with drug-sensitive (Eµ-myc/Arf-/-) and drug-resistant (Eµ-myc/p53-/-) lymphoma cell lines were conducted to calibrate and validate a mechanistic mathematical model. Inputs to inform the model include tumor drug transport characteristics, such as blood volume fraction, average geometric mean blood vessel radius, drug diffusion penetration distance, and drug response in cell culture. Model results show that the drug response in mice, represented by the fraction of dead tumor volume, can be reliably predicted from these inputs. Hence, a proof-of-principle for predictive quantification of lymphoma drug therapy was established based on both cellular and tissue-scale physiological contributions. We further demonstrate that, if the in vitro cytotoxic response of a specific cancer cell line under chemotherapy is known, the model is then able to predict the treatment efficacy in vivo. Lastly, tissue blood volume fraction was determined to be the most sensitive model parameter and a primary contributor to drug resistance.

Fig 1. Strategy for model calibration and validation.

Values for mathematical model input parameters are initially calibrated from experimental data obtained from untreated subjects and cell culture, yielding blood volume fraction, diffusion penetration distance, radius of blood sources, and fraction of cells killed in culture. Based on these parameter values, the model then calculates the fraction of tumor volume that would be killed in vivo, which can be compared to experimental data obtained from treated subjects.

Fig 2. Drug response experiments in vitro.

(Left) Measurement of in vitro cell kill in cell culture for Eμ-myc/Arf-/- and Eμ-myc/p53-/- cells after 48 hours at 50 nM Dox concentration (N.S.: not statistically significant). (Right) Results from a flow cytometry study were used to measure apoptotic cells. Eμ-myc/p53-/- cells are displayed along the top row with Eμ-myc/Arf-/- cells along the bottom; controls (no drug) are in the left column, and drug-treated cells (Dox) are in the right column. For each block, lower left quadrant represents live (proliferating) cells; lower right quadrant shows apoptotic cells; upper right quadrant shows dead cells.

Fig 3. Necrotic cell fraction in murine lymphoma tumors after treatment with Dox.

Data are shown for tumor slices S1 through S5. Most of the necrosis is a result of the drug treatment since necrosis measured in untreated tumors was negligible (Table 2). Note that the drug-sensitive tumors shrank in size after treatment and thus had one less histological slice than the drug-resistant tumors (to account for this, two slices of the drug-resistant tumor are included in the central region S3, i.e., five total slices for Eμ-myc/Arf-/- and six for Eμ-myc/p53-/-). All error bars represent standard deviation from at least n = 3 measurements in each section. Asterisks show level of statistical significance determined by student’s t-test with α = 0.05 (asterisk, P < 0.05).

Fig 4. Whole-tumor measurement of lymphoma characteristics.

Measurements from the IHC data after treatment with Dox shows cell fractions for: (A) apoptosis, (B) endothelium, (C) hypoxia, (D) proliferation. Note that the drug-sensitive tumors shrank in size after treatment and thus had one less histological slice than the drug-resistant tumors in the middle Set (S3). Error bars represent standard deviation (n = 3 regions of interest per slice).

Fig 5. Mathematical model predicts lymphoma tumor death due to chemotherapy drug treatment.

Comparison of histopathology measurements with mathematical model predictions (Eq 2, solid lines) based on estimates of two parameters r _b / L and $f_{\text{kill}}^{\text{M}}$. Data points for drug-resistant cells (blue) were scaled by 3.5 (see Fig 2A) to be comparable with data for drug-sensitive cells (green). Obtained R ² = 0.86; estimated $f_{\text{kill}}^{\text{M}}$ = 0.25, and r _b / L = 0.068. Diffusion distance of drug from the vessels (40 ± 20 μm) was assumed in the best case not to exceed half that of O₂. Each point represents measurements from one tumor Set; 5 data points for the drug-sensitive cell line (green) and 6 data points for the drug-resistant cell line (blue).

Fig 6. Sensitivity analysis results.

Plots of absolute values of sensitivity coefficients for the three parameters for (A) the drug-sensitive cell line, Eμ-myc/Arf-/- and (B) the drug-resistant cell line, Eμ-myc/p53-/-. The range of variation for each parameter is listed in S1 Table. S represents sensitivity coefficient.