scholarly journals State and Parameter Estimation of a Mathematical Carcinoma Model under Chemotherapeutic Treatment

2020 ◽  
Vol 10 (24) ◽  
pp. 9046
Author(s):  
Máté Siket ◽  
György Eigner ◽  
Dániel András Drexler ◽  
Imre Rudas ◽  
Levente Kovács
Keyword(s):  
Parameter Estimation ◽  
Tumor Growth ◽  
Nonlinear Problems ◽  
Model Parameters ◽  
State Variables ◽  
State Estimator ◽  
Third Order ◽  
Tumor Growth Model ◽  
Chemotherapeutic Treatment ◽  
Tumor Growth Modeling

One challenging aspect of therapy optimization and application of control algorithms in the field of tumor growth modeling is the limited number of measurable physiological signals—state variables—and the knowledge of model parameters. A possible solution to provide such information is the application of observer or state estimator. One of the most widely applied estimators for nonlinear problems is the extended Kalman filter (EKF). In this study, a moving horizon estimation (MHE)-based observer is developed and compared to an optimized EKF. The observers utilize a third-order tumor growth model. The performance of the observers is tested on measurements gathered from a laboratory mice trial using chemotherapeutic drug. The proposed MHE is designed to be suitable for closed-loop applications and yields simultaneous state and parameter estimation.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

SYSTEM IDENTIFICATION IN TUMOR GROWTH MODELING USING SEMI-EMPIRICAL EIGENFUNCTIONS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250003 ◽  
Author(s):  
THIERRY COLIN ◽  
ANGELO IOLLO ◽  
DAMIANO LOMBARDI ◽  
OLIVIER SAUT
Keyword(s):  
System Identification ◽  
Tumor Growth ◽  
Solution Space ◽  
Cellular Division ◽  
Volume Increase ◽  
Tumor Growth Model ◽  
Species Population ◽  
Tumor Growth Modeling ◽  
Low Dimensional ◽  
Semi Empirical

A tumor growth model based on a parametric system of partial differential equations is considered. The system corresponds to a phenomenological description of a multi-species population evolution. A velocity field taking into account the volume increase due to cellular division is introduced and the mechanical closure is provided by a Darcy-type law. The complexity of the biological phenomenon is taken into account through a set of parameters included in the model that need to be calibrated. To this end, a system identification method based on a low-dimensional representation of the solution space is introduced. We solve several idealized identification cases corresponding to typical situations where the information is scarce in time and in terms of observable fields. Finally, applications to actual clinical data are presented.

Combined state-parameter estimation with the LETKF for convective-scale weather forecasting

2020 ◽  
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjic
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Roughness Length ◽  
Surface Wind ◽  
Model Error ◽  
Surface Fluxes ◽  
Model Parameters ◽  
State Variables ◽  
Augmented State ◽  
The Impact

<p>We investigate the feasibility of addressing model error by perturbing and  estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly-operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to six hours of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.</p>

A mathematical method for parameter estimation in a tumor growth model

2015 ◽  
Vol 36 (1) ◽  
pp. 733-748 ◽  
Author(s):  
D. Knopoff ◽  
D. Fernández ◽  
G. Torres ◽  
C. Turner
Keyword(s):  
Mathematical Method ◽  
Parameter Estimation ◽  
Tumor Growth ◽  
Growth Model ◽  
Tumor Growth Model

scholarly journals Using an Observer in a Sliding Mode for Modeling Antiangiogenic Therapy

2019 ◽  
pp. 52-71
Author(s):  
M. S. Vinogradova ◽  
S. B. Tkachev ◽  
O. S. Tkacheva
Keyword(s):  
Tumor Growth ◽  
Sliding Mode ◽  
Biological Systems ◽  
Antiangiogenic Therapy ◽  
Nonlinear Dynamic System ◽  
State Observer ◽  
Sliding Modes ◽  
State Variables ◽  
Tumor Growth Model ◽  
Biomedical System

Currently, a slew of biomedical system models have been proposed, but in certain cases their real-world application is a challenge.This is because in these models not all state variables can be measured. The task of restoring the state vector, which is to obtain estimates for its non-measurable components, can be solved by control theory methods, in which it is formulated as the task of constructing a state observer.The article analyses Russian and foreign publications available in the field concerned to consider the problem of observer applications to biological systems. One of the types of state observers, an observer operating in a sliding mode in particular, is under consideration. The procedure to construct it for biological systems is shown by an example of a tumor growth model in which treatment is based on blocking the processes of angiogenesis.For a nonlinear dynamic system describing the tumor growth in the process of antiangiogenic therapy, its normal form is shown and a nonlinear state observer in sliding modes is constructed. As the measurable system output, a variable appropriate to the tumor volume was selected. The estimate of the total vector of the system state, obtained by the observer, is used to build state feedback that stabilises the program trajectory. Mathematical modelling, which shows that, in principle, in sliding modes an observer can be used for control of biological systems, proves the theoretical principles.

Parameter Estimation of Nonlinear Biomedical Systems Using Extended Kalman Filter Algorithm

2017 ◽  
pp. 76-99 ◽  
Author(s):  
Kamalanand Krishnamurthy
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Computational Models ◽  
Three Dimensional ◽  
Model Parameters ◽  
State Variables ◽  
Three Dimensional Model ◽  
Biomedical Systems ◽  
Estimation Of Model Parameters

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.

scholarly journals Joint State-Parameter Estimation for Tumor Growth Model

2021 ◽  
Vol 81 (2) ◽  
pp. 355-377
Author(s):  
Annabelle Collin ◽  
Thibaut Kritter ◽  
Clair Poignard ◽  
Olivier Saut
Keyword(s):  
Parameter Estimation ◽  
Tumor Growth ◽  
Growth Model ◽  
State Parameter ◽  
Tumor Growth Model ◽  
Joint State

Parameter Estimation of Nonlinear Biomedical Systems Using Extended Kalman Filter Algorithm

2018 ◽  
pp. 690-713
Author(s):  
Kamalanand Krishnamurthy
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Computational Models ◽  
Three Dimensional ◽  
Model Parameters ◽  
State Variables ◽  
Three Dimensional Model ◽  
Biomedical Systems ◽  
Estimation Of Model Parameters

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

2015 ◽  
Vol 25 (04) ◽  
pp. 1530012 ◽  
Author(s):  
Kristina Mallory ◽  
Robert A. Van Gorder
Keyword(s):  
Coupled Oscillators ◽  
Chaotic Behavior ◽  
Bilinear System ◽  
Model Parameters ◽  
State Variables ◽  
Third Order ◽  
Lorenz Equation ◽  
Competitive Modes ◽  
Chaotic Parameter ◽  
Special Case

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky–Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky–Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

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