Accounting for quiescent cells in tumour growth and cancer treatment

A four-state cell-cycle model with explicit G1-phase representation, termed the quiescent-cell model (QCM), has been proposed to represent biologically the G1-phase specific effect of the chemotherapeutic tamoxifen. The QCM was used to model untreated and tamoxifen-treated tumour xenograft data from the literature with equivalent accuracy to previously developed tumour growth models. Open-loop analysis demonstrated that perturbations to the two newly introduced parameters, kG01 and kG10, significantly altered untreated tumour growth predictions. However, the sensitivity did not carry over to closed-loop simulations, where alterations to kD and kGS proved most significant in determining overall controller performance. Additional mismatch studies comparing controllers designed using the QCM to controllers designed with the Gompertz model and saturating-rate, cell-cycle model returned similar performance for a step-wise tumour reduction case study, but the quiescent-cell controller delivered a more aggressive treatment regimen. More importantly, the Gompertz and saturating-rate, cell-cycle controllers were unable to follow a reference trajectory when measurement updates were made biweekly, with both controllers returning tamoxifen dose schedules alternating between the maximum and minimum allowable dose.