1. Fitting functions to measured data

Four-dimensional data can be modeled by analytical functions.

Model (as implemented in GUI)

Function name

Equation

Remarks

ExpDec, T2, ADC

Fit_exp

 

Exp3P

Fit_exp3

 

 

Fit_exp4

 

ExpEnh

Fit_expenh

This function should be used for exponential enhancement e.g. after injection of contrast media. A1 is negative in that case and F is set to zero before CM is arrives in the tissue.

 

Fit_gauss

 

GaussIntS

Fit_gaussints

A1 is associated to the center of the sigmoid function and A2 is the slope. This function can be used to model the rate of CM enhancement and therefore something which is related to blood flow.

 

For function fitting the fit tool shown in the figure shown below (Analysis/Function fit) has to be used. It allows entering the model, the weighting vector used for performing the fit and the destination for the calculated maps (window or file). The maximum c 2 value is important for calculation of the maps. The result of those pixels is set to zero for which the fit reveals larger c 2 than the given maximum. This allows to control the accuracy of the fit and discard those points, for which the model might not be appropriate or the signal to noise ration to low. If the fit tool is active, it is possible to click into the data window in order to check if the fit leads to accurate result. If the data cannot be described be the model function correctly or if the data is partly corrupted, the weighting vector (also shown as a green line in the graph) can be changed in order to select the interval, in which the fit should be optimal. High values in the weighting vector have to be selected for important data points. The values can be entered manually or weighting models can be selected by the specific button:

TE: Equal weighting for all points

TD: Temporally decreasing weighting, as defined by an exponential decay function.

How this can affect the result of the fit is shown in the figure below. On the left side, the values of the weighting vector were selected equally for all data points. This results in a lower estimate of the initial slope of the curve. If the initial slope is important for the interpretation of the data, this might be an undesired effect. On the right side, the first elements of the weighting vector were increased. This improved the fit in the first part of the data curve, while it might reduce the accuracy for the whole measurement.