MRGlu (FDG BFM, Slice-dependent Times)

The 2-Tissue (BFM) model implements fitting a two-tissue compartment model in each image pixel. It is based on an analytic solution of the system of differential equations which results in the calculation of two eigenvalues a₁ and a₂.

The expected tissue activity is obtained by the convolution of the input function with a sum of two decaying exponentials plus a contribution from whole blood.

For FDG, irreversible binding can be assumed and k₄ set to zero, whereby a₁ becomes zero. Hereby the number of fitted parameters is reduced and the operational equation simplifies to

Overview of the BFM Processing in PXMOD

In the MRGlu (FDG BFM, Slice-dependent Times) model, sonly the irreversible configuration is supported. It uses the simplified basis function solution with fits 4 parameters: q₁, q₂, a₂, v_B. The operational equation is linear in the parameters q₁, q₂, v_B, and nonlinear in a₂ . The q₁ and q₂ parameters are a combination of the rate constants.

Basis function method according to Hong and Fryer [1] in the irreversible case:

For a certain tracer the physiological range of the rate constants can be determined. These ranges are translated into a range of a₂ values which can be expected in the data. With FDG, for instance, a₂ Î[0.06,0.6]min^-1 was proposed in [1]. The range [0.06,2.4] is used as a default.
The basis functions are pre-calculated for tabulated a₂ values which span the prescribed range.
When fitting data, each value of a₂ is examined: the operational equation using the corresponding basis function is fitted with respect to the remaining parameters q₁, q₂, v_B using the singular value decomposition method without weighting. Since all of them enter linearly, the solution is unique and can be quickly calculated. For each of the calculations the chi-square criterion is recorded.
Finally the combination q₁, q₂, v_B, a₂ with minimal chi square is considered as the solution.

It is possible to allow fitting of the blood volume fraction v_B, or to fix it at a specific value. The configuration whether v_B is fitted or fixed is specified in the preprocessing setup.

When setting up the processing it is recommended to enable calculation of the a₂ map and inspect it regarding the prescribed range. If the prescribed maximum or minimum value is very frequently encountered this indicates that the range should be expanded.

Acquisition and Data Requirements

Image Data

A dynamic FDG PET data set representing the measurements covering a sufficient time range after injecting of a ¹⁸F-Deoxy-Glucose (FDG) bolus. If the scanner FOV was not at a fixed location during the scan, the slice-times need to be contained in the image attributes. The model has been tested with the data of Siemens equipment (DICOM Conformance statement, see Frame Reference Time) capable of continuous table movement.

Blood Data

Blood activity from the time of injection until the end of the scan. It is important, that the blood and the image data have the same time base and decay correction is relative to the same time.

Blood Preprocessing

The only necessary configuration is specification of the blood activity curve, either as a file, or as a VOI placed over a vessel such as the descending aorta or the left ventricle. Note, however, that the blood information must be available from the time of injection, whereas later measurements are sufficient for the tissue.

Model Preprocessing

The model processing panel includes two classes of options.

The check boxes at the top are related to the data:

Data with slice-wise timing

Enabling the check instructs PXMOD to extract a dedicated time for each slice.

Zero time at administration

The slice reference times are relative to the time when the acquisition was started. If there is a delay between the tracer injection and scan start, this offset has to be added to the slice reference times. This operation is enabled by checking the box. Note, that if available an appropriated time is extracted from the Radiopharmaceutical Start DateTime (0018,1078) information. For GE data, the private field (0009,103B) is used.

The indicated button opens a dialog window for inspecting the times of the slices during the acquisitions.

The actual model parameters are listed in the lower part.

vB	Blood volume fraction. Can be fitted or fixed. If checked, the blood fraction is fitted during map calculation. Otherwise, the specified value will be used for spillover correction.
alpha2	Second eigenvalue. For defining its basis function range first enable the alpha2 parameter and then adjust the Lower and Upper values.
#Basis Functions	Number of intermediate a₂ values generated between Lower and Upper. The increments are logarithmically spaced.
Resampling	Sampling increment applied during the basis function calculation.
Threshold	Discrimination threshold for background masking. All pixels with energy below Threshold[%] of the maximal energy will be masked to zero.

Model Configuration

MRGlu	Metabolic Rate of Glucose in [mmol/min/100ml], the actual result of the model. It is calculated as: MRGlu = K_i*Plasma_Glucose/Lumped_Constant
Ki	Influx K_i=(K₁*k₃)/(k₂+k₃) of the irreversible 2-tissue compartment model; is directly proportional to MRGlu.
DV	Distribution volume of FDG in tissue.
vB	Blood volume fraction defining the pixel-wise blood spillover correction. To fit, please activate in the Preprocessing tab. Note, however, that the noise will be increased.
K1,k2,k3	Rate constants of the irreversible 2-tissue compartment model.
alpha2	Shows the a₂ values corresponding to the basis function of the solution. Can be used to check whether the defined range was adequate.

Reference

1. Hong YT, Fryer TD: Kinetic modelling using basis functions derived from two-tissue compartmental models with a plasma input function: general principle and application to [18F]fluorodeoxyglucose positron emission tomography. Neuroimage 2010, 51(1):164-172. DOI