A Minimal PKPD Interaction Model for Evaluating Synergy Effects of Combined NSCLC Therapies

Abstract

This paper introduces a mathematical compartmental formulation of dose-effect synergy modelling for multiple therapies in non small cell lung cancer (NSCLC): antiangiogenic, immuno- and radiotherapy. The model formulates the dose-effect relationship in a unified context, with tumor proliferating rates and necrotic tissue volume progression as a function of therapy management profiles. The model accounts for inter- and intra-response variability by using surface model response terms. Slow acting peripheral compartments such as fat and muscle for drug distribution are not modelled. This minimal pharmacokinetic-pharmacodynamic (PKPD) model is evaluated with reported data in mice from literature. A systematic analysis is performed by varying only radiotherapy profiles, while antiangiogenesis and immunotherapy are fixed to their initial profiles. Three radiotherapy protocols are selected from literature: (1) a single dose 5 Gy once weekly; (2) a dose of 5 Gy × 3 days followed by a 2 Gy × 3 days after two weeks and (3) a dose of 5 Gy + 2 × 0.075 Gy followed after two weeks by a 2 Gy + 2 × 0.075 Gy dose. A reduction of 28% in tumor end-volume after 30 days was observed in Protocol 2 when compared to Protocol 1. No changes in end-volume were observed between Protocol 2 and Protocol 3, this in agreement with other literature studies. Additional analysis on drug interaction suggested that higher synergy among drugs affects up to three-fold the tumor volume (increased synergy leads to significantly lower growth ratio and lower total tumor volume). Similarly, changes in patient response indicated that increased drug resistance leads to lower reduction rates of tumor volumes, with end-volume increased up to 25–30%. In conclusion, the proposed minimal PKPD model has physiological value and can be used to study therapy management protocols and is an aiding tool in the clinical decision making process. Although developed with data from mice studies, the model is scalable to NSCLC patients.

Model Calibration of Pharmacokinetic-Pharmacodynamic Lung Tumour Dynamics for Anticancer Therapies

“…Pharmacokinetic and pharmacodynamic interactions were simulated based on our prior work [29] which contained relevant model coefficient values from the literature. This revision is proposed by employing the PKPD compartmental model to real clinical data from patients with NSCLC.…”

“…Given the GTV tumor volume provided by CT screening (from Table 2), this can be used to calibrate the PKPD model. The equivalent mass of the tumor from approximation formula 1 mm 3 = 10 −3 mg [29] was used to calibrate radiotherapy model parameters via a unit transformation from Gy −→ 1/mL. In order to set a reference value for the tumor value, we propose to quantify the volumetric difference between total tumor tissue and necrotic tissue, that is the effective volume still active in the tumor (in mm 3 ):…”

“…Quantitative analysis can be done in a variety of experimental settings, including in vitro and in vivo studies, involving animal or human data, for preclinical anticancer drug investigations in all existing therapies (i.e., radiotherapy, chemotherapy, immunotherapy, targeted drug therapy) [24][25][26][27][28]. Tumor growth kinetics follow the purely phenomenological approach from an initial exponential phase followed by a linear regimen, a mathematical formalism that can be characterized as pharmacokinetic and pharmacodynamic modeling [29][30][31].…”

“…In this work, a pharmacokinetic-pharmacodynamic (PKPD) model of radiotherapy is developed with a description of the following features: (i) the proliferation of the tumor, (ii) the necrosis of tumor cells, (iii) the clearance and inhibitory effect of the therapy, and (iv) the therapeutic effect of ablative radiation. The model is a revision of our previous work described in [29] and adjusted for integrating the rationale for dose fractionation, according to each patient RT schedule. For lung tumors, the computed dose distributions strongly depend on the accuracy of the predictions based on the model.…”

Probabilistically certified region of attraction of a tumor growth model with combined chemo‐ and immunotherapy

“…The pharmacodynamics effects have also been incorporated using a Hill function. The parameters values related to the pharmacokinetics and pharmacodynamics (PK/PD) of immunotherapy have been taken from Reference 27.…”