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Use of a simulated annealing algorithm to fit compartmental models with an application to fractal pharmacokinetics
Rebeccah E Marsh1, Terence A Riauka, Steve A McQuarrie
1Department of Physics, Faculty of Science, University of Alberta, Edmonton, Alberta, Canada. rmarsh@ualberta.ca <rmarsh@ualberta.ca>
Abstract:
Increasingly, fractals are being incorporated into pharmacokinetic models to describe transport and chemical kinetic processes occurring in confined and heterogeneous spaces. However, fractal compartmental models lead to differential equations with power-law time-dependent kinetic rate coefficients that currently are not accommodated by common commercial software programs. This paper describes a parameter optimization method for fitting individual pharmacokinetic curves based on a simulated annealing (SA) algorithm, which always converged towards the global minimum and was independent of the initial parameter values and parameter bounds. In a comparison using a classical compartmental model, similar fits by the Gauss-Newton and Nelder-Mead simplex algorithms required stringent initial estimates and ranges for the model parameters. The SA algorithm is ideal for fitting a wide variety of pharmacokinetic models to clinical data, especially those for which there is weak prior knowledge of the parameter values, such as the fractal models.
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