Comparing Methods for Parameter Estimation of the Gompertz Tumor Growth Model

Spyridon Patmanidis (1) , Alexandros C. Charalampidis (2) , Ioannis Kordonis (3) , Georgios D. Mitsis (4) , George P. Papavassilopoulos (1)

1 NTUA - National Technical University of Athens [Athens]
2 IETR - Institut d'Électronique et des Technologies du numéRique
3 USC - University of Southern California
4 McGill University = Université McGill [Montréal, Canada]

Cancer, also known as malignant tumor or malignant neoplasm, is the name given to a collection of related diseases. In all types of cancer, some of the body's cells begin to divide abnormally without stopping and have the potential to invade surrounding tissues. In this work, we focus on estimating the parameters of a model which tries to describe the growth of a cancer tumor based on the available measurements of the tumor volume and on comparing the effectiveness with respect to the accuracy of the estimation of the various methods we have tested. The Gompertz function is used as the model basis, and our analysis aims to compute the growth rate and the plateau size of the tumor. The methods used to estimate these parameters are based on least squares, maximum likelihood and the Extended Kalman Filter (EKF). In this work, we present five different methods. The results show that, when the process and measurement noise characteristics are known, maximizing the joint probability density function of the observations using numerical integration to compute the probability density functions yields most times the best results. The methods based on the EKF also yield satisfactory results.

Mots clés: Tumor Growth Modeling; Biomedical Systems; Nonlinear Systems; Parameter Estimation; Maximum Likelihood; Extended Kalman Filter; Least Squares

Domaines: Mathématiques [math]; Systèmes et contrôle [cs.SY]; Cancer; Machine Learning [stat.ML]; Traitement du signal et de l'image [eess.SP]; Biologie animale

Spyridon Patmanidis, Alexandros C. Charalampidis, Ioannis Kordonis, Georgios D. Mitsis, George P. Papavassilopoulos. Comparing Methods for Parameter Estimation of the Gompertz Tumor Growth Model. 20th IFAC World Congress, Jul 2017, Toulouse, France. pp.12203 - 12209, ⟨10.1016/j.ifacol.2017.08.2289⟩. ⟨hal-01707693⟩