Optimization (DRAFT)

The parameters of plasma input TACs and compartmental models are estimated (fitted) using non-linear least-squares optimization algorithms, such as PSO and AIN. In times of very limited computing resources the traditional methods such as Newton-Gaussian or Levenberg-Marquardt algorithms were also used; being very fast, those methods are very dependent on the initial parameter guesses. These methods converge to the local optimum, but could be used as a part of global optimization routines. For example, the commonly used Nelder-Mead algorithm (Nelder & Mead, 1965; Price et al., 2002) forms the basis of globalized bounded nelder-Mead (GBNM) algorithm (Luersen et al., 2004a and 2004b). Topographical global optimization (TGO) is one of the methods that can be used to get good initial parameter estimates for local optimization routines (Sederholm, 2003; Henderson et al., 2017).

Alternatively, some models can be linearized to estimate the macroparameter of interest using linear regression, for example the multiple-time graphical analyses, or individual model parameters using for example GLSS (Feng et al., 1996) or NNLS.


See also:



References:

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Feng D, Huang S-C, Wang Z, Ho D. An unbiased parametric imaging algorithm for nonuniformly sampled biomedical system parameter estimation. IEEE Trans Med Imaging 1996; 15(4): 512-518.

Floudas CA, Pardalos PM (eds.): Encyclopedia of Optimization. 2nd ed., Springer, 2009.

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Liu L, Ding H, Huang HB. Improved simultaneous estimation of tracer kinetic models with artificial immune network based optimization method. Appl Radiat Isot. 2016; 107: 71-76.

Lu R, Liu L, Shen L. A distributed artificial immune network for optimizing tracer kinetic models with MATLAB distributed computing engine. J Algorithms Computational Technol. 2013; 7(2): 173-185. doi: 10.1260/1748-3018.7.2.173.

Motulsky HJ, Ransnas LA. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1987; 1: 365-374. doi: 10.1096/fasebj.1.5.3315805.

Murase K, Mochizuki T, Kikuchi T, Ikezoe J. Kinetic parameter estimation from compartment models using a genetic algorithm. Nucl Med Commun. 1999; 20(10): 925–932.

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Sederholm K. Globaali optimointi positroniemissiotomografia-kuvantamiseen liittyvässä mallintamisessa. Pro gradu, 2003.

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Yaqub M, Boellaard R, Kropholler MA, Lubberink M, Lammertsma AA. Simulated annealing in pharmacokinetic modeling of PET neuroreceptor studies: accuracy and precision compared with other optimization algorithms. Nuclear Science Symposium Conference Record, 2004 IEEE. 5: 3222-3225. doi: 10.1109/NSSMIC.2004.1466368.



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Created at: 2017-08-07
Updated at: 2018-04-22
Written by: Vesa Oikonen