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.

Transvascular and interstitial transport in rat hepatocellular carcinomas: Dynamic contrast‐enhanced MRI assessment with low‐ and high‐molecular weight agents

“…Our results suggest, as previously reported (27,30), that the more physiological St Lawrence and Lee model gives more accurate results, but is also less precise because of the interdependency of the parameters and their sensitivity to initial values. At first sight, the simplest model (Kety) should be chosen to explain the R 1 curves because the three models generate similar errors.…”

“…The optimization of the fit was achieved with the function lsqcurvefit based on the LevenbergMarquardt algorithm. When using one starting point, this approach is prone to estimating erroneous values when localized best-fit combination of parameters is found (30). Therefore, multiple starts values for the parameters were explored to find the solution corresponding to the true global minimum of the error function.…”

Fitting the two‐compartment model in DCE‐MRI by linear inversion

“…[7]). A literature-based arterial input function c a (t) was used (22), prepadded with zeroes to create a 20s baseline.…”

“…X = (A T A) −1 A T C. The NLLS was implemented by fitting the analytical solution (Eq. [7]) using the Levenberg- For each reconstruction P i of a parameter P = F p , P S, T p , T e , the error E i (P ) was determined as a percentage of the exact value:…”

A fast generalizable solution method for glucose control algorithms

“…Fast and efficient computational methods are important for real-time therapy guidance and are a growing trend in Bio-Engineering [1][2][3][4][5][6][7][8][9][10][11]. More recently, significant clinical outcomes have been achieved by table-based glucose control protocols [12][13][14] that mimic and are developed from computer-based protocols [15][16][17][18], but are much simpler to implement and more likely to be accepted by clinical staff [19].…”