Whole Blood and Plasma

The way how whole blood and plasma interpolation is performed in PKIN is governed by the configuration on the Blood tab. There are two selection items:

1. The left selection allows to choose among the different blood curves, namely Whole blood and Plasma (there are more choices if the model has multiple input curves). The selected blood curve is shown in the curve display (Plasma, or Whole blood).
2. The right selection defines the interpolation model for the selected blood curve. Default is Measured, which just represents linear interpolation between sample times. To replace linear interpolation by a smoother function select an appropriate definition from the list. The curve display shows the selected model Plasma model (or Whole blood model). Initially, the curve is calculated using default parameters.

The parameters of the blood model appear in the Standard pane and can be configured for fitting purposes. Activating the Fit plasma or Fit Whole Blood button starts a fitting process which adjusts the model parameters such that the interpolation curve comes into optimal agreement with the measurements. In the example below the model has not yet been fitted so that the distinction between the measurement and the model (sum of exponentials) is clearly visible. For more information about the fitting options please refer to the fitting of kinetic models.

Blood Models

In PKIN there are different choices of such blood models.

Measured:

This is the default model, whereby the input curve is linearly interpolated between measured values. Outside the measured values the interpolation rules are as follows: The input curve is

• set to zero for all times t<=0,
• linearly interpolated from t=0 until the first sample,
• remains at the value of the last measurement for times past the last sample. For short blood curves it is therefore recommended to interpolate the tail by using the sum-of-exponentials model.

3 Exponentials:

In this model the tail of the input curve from a starting point to be specified is replaced by a sum of up to three exponentials. The input curve before the start time is linearly interpolated as for the measured model.

Compartment Model, 3 Eigenvalues:

This model has been developed for the FDG tracer [14]. It is the result from modeling the distribution and delivery of FDG in the circulatory system by a compartment model, and is given by

Compartment Model, 2 Eigenvalues:

This is a reduced version of the above model given by

Metabolite correction (deprecated):

This model has been developed for correcting the buildup of the CO₂ metabolite in ¹¹C acetate studies [22]. The model assumes that the concentration of authentic ligand in plasma can be calculated from total blood activity by the following simple equation

where met denotes the metabolite level which is finally reached, and T represents the half-time of the exponential metabolite build-up. This model can be applied for other tracers with a similar behavior of metabolite buildup.

Note: the Metabolite correction model can not be fitted against the blood data. One way to use this metabolite correction is to determine the two parameters externally and enter them as constants in the model. An alternative is to estimate the metabolite parameters together with the kinetic parameters during a fit of the kinetic model (with the Fit blood parameters check enabled).

Bolus/Infusion optimization:

This model has been developed for the optimization of the activity ratio between an initial bolus and a subsequent infusion [23]. The aim is, that the activity level in plasma and in the tissue gets constant as soon as possible.

Multiinjection, HOT or COLD:

These models are used in combination with the model for multi-injection studies with ¹¹C-Flumazenil as described by Delforge et al. [26]. With the HOT model, there is an analytical correction for the buildup of metabolites included. The COLD model is entirely derived from the hot input curve based on the relative doses and includes similar metabolite correction.

The Blood Delay Parameter

All standard blood models have a Delay parameter to correct for a timing error between tissue and blood data. Positive delays represent delayed blood information and hence shift the blood curves to earlier times (to the left). This parameter is only relevant for fitting of the kinetic model. Therefore, when fitting the shape of the blood curve with Fit plasma or Fit whole blood, it is automatically disabled.

However, when fitting kinetic compartment models, it is possible to fit the blood delay as an additional parameter to the parameters of the kinetic model.

Blood delay fitting

1. On the Blood tab, select Plasma, and then check the fitting box of the Delay parameter.
2. On the KM tab, check the Fit blood param box.
3. Then activate Fit current region the KM tab.

To find out the fitted blood delay, select the Blood tab after fitting. The fit value is shown, and the input curve model appears shifted accordingly.

CAUTION: When Fit blood param is enabled, all checked parameters of the input curve model are fitted. So if other parameters than Delay are also enabled, the shape of the input curve will also change!

Default Values of Model Parameters

Each model has default values. Initially, they are factory settings, but they can be re-defined by the user if he wants to establish a default configurations which is more adequate from him. Note that the configurations are valid per PMOD login, so different logins could be prepared for processing types of data requiring different initial parameter values.