Computational reactive-diffusive modeling for stratification and prognosis determination of patients with breast cancer receiving Olaparib

Abstract

Mathematical models based on partial differential equations (PDEs) can be exploited to handle clinical data with space/time dimensions, e.g. tumor growth challenged by neoadjuvant therapy. A model based on simplified assessment of tumor malignancy and pharmacodynamics efficiency was exercised to discover new metrics of patient prognosis in the OLTRE trial. We tested in a 17-patients cohort affected by early-stage triple negative breast cancer (TNBC) treated with 3 weeks of olaparib, the capability of a PDEs-based reactive-diffusive model of tumor growth to efficiently predict the response to olaparib in terms of SUV_max detected at ¹⁸FDG-PET/CT scan, by using specific terms to characterize tumor diffusion and proliferation. Computations were performed with COMSOL Multiphysics. Driving parameters governing the mathematical model were selected with Pearson's correlations. Discrepancies between actual and computed SUV_max values were assessed with Student's t test and Wilcoxon rank sum test. The correlation between post-olaparib true and computed SUV_max was assessed with Pearson's r and Spearman's rho. After defining the proper mathematical assumptions, the nominal drug efficiency (ε_PD) and tumor malignancy (r_c) were computationally evaluated. The former parameter reflected the activity of olaparib on the tumor, while the latter represented the growth rate of metabolic activity as detected by SUV_max. ε_PD was found to be directly dependent on basal tumor-infiltrating lymphocytes (TILs) and Ki67% and was detectable through proper linear regression functions according to TILs values, while r_c was represented by the baseline Ki67-to-TILs ratio. Predicted post-olaparib SUV*_max did not significantly differ from original post-olaparib SUV_max in the overall, gBRCA-mutant and gBRCA-wild-type subpopulations (p > 0.05 in all cases), showing strong positive correlation (r = 0.9 and rho = 0.9, p < 0.0001 both). A model of simplified tumor dynamics was exercised to effectively produce an upfront prediction of efficacy of 3-week neoadjuvant olaparib in terms of SUV_max. Prospective evaluation in independent cohorts and correlation of these outcomes with more recognized efficacy endpoints is now warranted for model confirmation and tailoring of escalated/de-escalated therapeutic strategies for early-TNBC patients.

Figure 1

Key methodological steps of the mathematical model. (A): Gompertzian curve representing tumor metabolic activity in terms of SUV_max in different cancer growth phases; (B): Pearson’s correlations among SUV_max modifications under olaparib and baseline clinicopathological parameters of interest. (C): Nominal personalized olaparib efficiency ε_PD versus nominal personalized breast cancer malignancy r_c; t, time; delta, variation; i, initial; FP, free tumor proliferation phase (Phase I); CP, challenged tumor proliferation phase (Phase II); T, primary tumor size; TPS, tumor proportion score; IC, immune cells; TILs, tumor-infiltrating lymphocytes; SUV, standard uptake value. In panel B grey numbers are Pearsons’ coefficients. The more positive the correlations, the darker the blue circles, while the more negative the correlations, the darker the red circles. The peripheral red circles identify non-significant correlations.

Figure 2

Virtual scenario of different pharmacodynamic efficiency and olaparib duration. Computed SUV*_max progressing with time for a real and a fictious case, having a different nominal personalized olaparib efficiency ε_PD and a different NAT duration. The progress is reported limited to Phase II of challenged proliferation. Case A: results from patient n.13 of our cohort; Case B: virtual case of patient n.13 with 20% decrement of ε_PD and a total NAT duration of 27 days instead of 21; t, time; d, days.