Differential Models of Time-Variant Tumor Growth Trajectories with Sensitive, Persister, Resistant Cell Population in Lung Tumors During Tyrosine Kinase Inhibitor Therapy

Abstract

Modeling the dynamics of three tumor cell populations, i.e., sensitive, persister, and resistant tumor cells, during molecularly targeted therapy with tyrosine kinase inhibitors (TKIs) would be valuable for adjusting treatment plans for patients with epidermal growth factor receptor-mutated non-small cell lung cancer (EGFR-mt NSCLC). We hypothesized the time-variant tumor growth trajectories (TGTs) of patients with stage IV EGFR-mt NSCLC for the three tumor cell populations could be expressed using differential models after several follow-up computed tomography examinations. We aimed to propose differential models for TGTs in three cell populations from patients with EGFR-mt NSCLC treated with an EGFR-TKI (osimertinib). We selected two differential equations—Bertalanffy–Pütter (BP) and Gompertz—to develop TGT models. The parameters of the models were optimized based on a dual annealing method within parameter ranges determined using synthetic patient data. Using CT examinations that were not employed for model fitting, the mean absolute percentage errors (MAPEs) for BP-based and Gompertz-based models were 36.1 ± 40.2% and 43.9 ± 60.1%, respectively, for three follow-up computed tomography (FCT) examinations, which indicated no statistically significant difference (p = 0.61). This study suggests that the proposed BP-based and Gompertz-based differential models could have the potential to express TGTs in patients with stage IV EGFR-mt NSCLC treated with EGFR-TKIs after three follow-up CT examinations, although MAPEs should be mitigated in future works.