Image Fitting - Introduction

The Image Fitting tool is very powerful and flexible - it can fit virtually any function to a set on images representing different independent variable ("x") values. On the other hand, the tool comes with a set of "preset" formulas, so that you can set up for some of the more common fitting tasks, such as inversion-recovery or saturation recovery T₁ estimation, diffusion coefficient or T₂ estimation. In addition, there is a "roaming fit" facility, where the fit parameters are estimated for pixels within a region of interest. The fit is illustrated on a graph showing the pixel intensity values and the fitted function, so that you can interactively investigate your data, and assess the quality of the fits.

The Fitting Tool produces a set of new images - one image for every fit variable. The new images contain the estimates of the fit variables in every pixel.

Start the Image Fitting tool from the Toolkits menu:

The Image Fitting frame will now appear as shown below:

The procedure for performing image fitting can be summarised as follows:

• Decide on the name of the independent variable. This can simply be "x" (the default), or can be chosen to reflect the physical parameter that varies in your set of images. For example, if you are fitting to multiple echo time data to estimate T₂, then you could change the independent variable name to "TE".
• Choose the number of fit variables, and the fit variable names, their physically-meaningful limits, and an initial guess at the fitted value. The names should be chosen to reflect the physical parameters that are to be estimated. For example, for T₂ fitting you would choose:
  • "M0" the initial transverse magnetisation.
  • "T2" the transverse relaxation time.
• Enter your formula. The formula can use:
  • The operators *, /, +, - and ^ that can be seen in the Operators menu. You can also use parentheses (..).
  • Any of the built in functions that can be seen in Functions menu.
  • The constants pi and e that can be seen in the Constants menu.
  • The independent variable name that you set ("x" by default).
  • The fit variable names.
  You can either type in the formula, or use the Operators, Functions and Constants menu to insert text into the formula. For example, for T₂ fitting you would enter:

  "M0*exp(-TE/T2)"

• Decide how many input images you want to work with. There are basically two options:
  • You have one input image for each value of the independent variable. For example, you have ten echo times, and therefore ten input images each containing all the image slices for a given echo time.
  • All the independent variable values are in one image.
  You set up the Image Fitting tool so that it understands the structure of your data.
• Set the "base name" for the output images. Each output image will have a name composed of the base name, and the fit variable name.