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.
Keywords: anomalous diffusion; antiangiogenic therapy; fractal kinetics; immunotherapy; lung cancer; mathematical modelling; mouse data; multiple therapy; radiotherapy; synergy; variability.