Estimating the growth kinetics of experimental tumours from as few as two determinations of tumour size: implications for clinical oncology

Clinical information on tumor growth is often limited to a few determinations of the size of the tumor burden taken at variable time. As a consequence, fitting of growth equations to clin- ical data is hampered by the small number of available data. On the other hand, characterising the tumor growth kinetics in terms of clinically relevant parameters, such as the doubling time of the tumors, is increasingly required to optimize and personalise treat- ments. A computational method is presented which can estimate the growth kinetics of tumors from as few as two determinations of its size taken at two successive time points, provided the size at which tumor growth saturates is known. The method is studied by using experimental data obtained in vitro with multicell tumor spheroids and in vivo with tumors grown in mice, and its outputs are compared to those obtained by fitting of experimental data with the Gompertz growth equation. Under certain assumptions and limitations the method provides comparable estimates of the doubling time of tumors with respect to the classical nonlinear fit- ting approach. The method is then tested against simulated tumor growth trajectories spanning the range of tumor sizes observed in the clinics. The simulations show that a relative classification of tu- mors on the basis of their growth kinetics can be obtained even if the size at which tumor growth saturates is not known. This re- sult opens the possibility to classify patients bearing fast or slow growing tumors and, hence, to adapt therapeutic regimens under a more rationale basis.