Linearized
initialization

This configuration is only related to the compartment models and determines which initial values are used for the iterative fitting:

▪Disabled: the user-defined parameters are used.

▪Enabled: an automatic procedure determines initial parameters which should be reasonably close to the solution. This is done by the linear least squares method. Note that the initial values are not shown to the user. However, to see the values, please switch to the linear least squares method and fit.

Parameter
conversion

Behavior of the parameters when switching between models.

Float blood parameters

If this box it is checked on, all parameters of the Input curves which have the fit box checked are also included into the set of fitted parameters. This feature has two uses:

▪Fitting the relative time delay between the tissue and the blood data simultaneously with the kinetic rate constants. However, it is easier to directly use the dedicated button.

▪(Rarely) Fitting a shape parameter such as the half-time of a metabolite build-up together with the rate constants as explained below.

Note: When using Fit All, the blood parameters will not be fitted, even if Fit blood is enabled.

Single fitting

Default mode of performing one single fit.

Random fitting

This configuration is only related to models which require iterative fitting:  

▪Multiple fits are performed, and the result parameters of the fit with minimal chi squared returned. The fits are started with randomized sets of initial parameters using a uniform distribution with ±100% range.
Note: If Parameters initialization is enabled, randomization uses the automatically determined parameters for the random number generation.

▪

▪In case randomized fitting is enabled, the labels of the fitting buttons are adjusted correspondingly.

Note: The purpose of randomized fitting is to avoid local minima, but there is still a chance that the returned solution may contain unphysiological parameter combinations.

Grid fitting

This configuration is only related to models which require iterative fitting:

▪Multiple fits are performed, and the result parameters of the fit with minimal chi squared returned. Initial parameter sets are generated by by stepping each parameter in increments between a lower value and an upper value.

▪The number (n) specified equals the number of distinct values used, so the number of increments is n-1.

▪The interval of the parameter range to be covered is defined on the Restrictions panel. It is necessary to adjust these ranges to physiologically reasonable values, because the default ranges are very wide.

▪In case grid fitting is enabled, the labels of the fitting buttons are adjusted correspondingly.

Data shortening to

Enables a sequence of fits with a successively shorter data segment to study the parameter sensitivity to acquisition duration.

Fitting method

Selection of the numerical optimization method applied for iterative fitting:

▪Marquardt: Marquardt-Levenberg algorithm [59]. Usually works faster and has the additional advantage that it accumulates information about the covariance matrix. Therefore, an estimate of the standard error can be calculated for the fitted parameters. They are shown as %SE (coefficient of variation), ie. as a percentage of the parameter value.

▪Powell: Conjugate direction set method [59].

The iterative optimizations terminate, when no substantial improvement can be found any more, or when the Max iterations restriction is hit.

Note: Several models (linear and multi-linear regression) are not fitted iteratively because they have closed form solutions. In these cases the Fitting method settings are not relevant.

Max. iterations

Maximal number of iterations which are allowed in the iterative Marquardt and Powell fitting.