- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Volume:71 Issue:4
- A study on modeling of rat tumours with the discrete-time Gompertz model
A study on modeling of rat tumours with the discrete-time Gompertz model
Authors : Levent ÖZBEK
Pages : 1169-1179
Doi:10.31801/cfsuasmas.914887
View : 41 | Download : 11
Publication Date : 2022-12-30
Article Type : Research Paper
Abstract :Cancer formation is one of the pathologies whose frequency has increased in the recent years. In the literature, the compartment models, which are non-linear, are used for such problems. In nonlinear compartment models, nonlinear state space models and the extended Kalman filter insert ignore into journalissuearticles values(EKF); are used to estimate the parameter and the state vector. This paper presents a discrete-time Gompertz model insert ignore into journalissuearticles values(DTGM); for the transfer of optical contrast agent, namely indocyanine green insert ignore into journalissuearticles values(ICG);, in the presence of tumors between the plasma and extracellular extravascular space insert ignore into journalissuearticles values(EES); compartments. The DTGM, which is proposed for ICG and the estimation of ICG densities used in the vascular invasion of tumor cells of the compartments and in the measurement of migration from the intravascular area to the tissues, is obtained from the experimental data of the study. The ICG values are estimated online insert ignore into journalissuearticles values(recursive); using the DTGM and the adaptive Kalman filter insert ignore into journalissuearticles values(AKF); based on the experimental data. By employing the data, the results show that the DTGM in conjunction with the AKF provides a good analysis tool for modeling the ICG in terms of mean square error insert ignore into journalissuearticles values(MSE);, mean absolute percentage error insert ignore into journalissuearticles values(MAPE);, and . When the results obtained from the compartment model used in the reference [9] are compared with the results obtained with the DTGM, the DTGM gives better results in terms of MSE, MAPE and $R^2$ criteria. The DTGM and the AKF compartment model require less numerical processing when compared to the EKF, which indicates that DTGM is a less complicated model. In the literature, EKF is used for such problems.Keywords : Indocyanine green, tumor cell, discrete time Gompertz models, adaptive Kalman filter, estimation
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