The use of the Levenberg-Marquardt curve-fitting algorithm in pharmacokinetic modelling of DCE-MRI data

T S Ahearn, R T Staff, T W Redpath, S I K Semple

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)N85-92
JournalPhysics in Medicine and Biology
Issue number9
Publication statusPublished - 7 May 2005


  • Algorithms
  • Animals
  • Computer Simulation
  • Contrast Media
  • Humans
  • Image Interpretation, Computer-Assisted
  • Magnetic Resonance Imaging
  • Metabolic Clearance Rate
  • Models, Biological
  • Numerical Analysis, Computer-Assisted
  • Phantoms, Imaging

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