title: The use of the Levenberg-Marquardt curve-fitting algorithm in pharmacokinetic modelling of DCE-MRI data.
abstract: The use of curve-fitting and compartmental modelling for calculating physiological parameters from measured data has increased in popularity in recent years. Finding the 'best fit' of a model to data involves the minimization of a merit function. An example of a merit function is the sum of the squares of the differences between the data points and the model estimated points. This is facilitated by curve-fitting algorithms. Two curve-fitting methods, Levenberg-Marquardt and MINPACK-1, are investigated with respect to the search start points that they require and the accuracy of the returned fits. We have simulated one million dynamic contrast enhanced MRI curves using a range of parameters and investigated the use of single and multiple search starting points. We found that both algorithms, when used with a single starting point, return unreliable fits. When multiple start points are used, we found that both algorithms returned reliable parameters. However the MINPACK-1 method generally outperformed the Levenberg-Marquardt method. We conclude that the use of a single starting point when fitting compartmental modelling data such as this produces unsafe results and we recommend the use of multiple start points in order to find the global minima.
authors.affiliation: Department of Bio-Medical Physics, University of Aberdeen and Grampian University Hospitals NHS Trust, Foresterhill, Aberdeen AB25 2ZD, UK. t.ahearn@biomed.abdn.ac.uk
authors.forename: T S
authors.initials: TS
authors.lastname: Ahearn
authors.forename: R T
authors.initials: RT
authors.lastname: Staff
authors.forename: T W
authors.initials: TW
authors.lastname: Redpath
authors.forename: S I K
authors.initials: SI
authors.lastname: Semple
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D003287:Contrast Media / Q000493:pharmacokinetics*; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008657:Metabolic Clearance Rate; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D019047:Phantoms, Imaging
chemical_list: D003287:Contrast Media