Relative Patlak plot for dynamic PET parametric imaging without the need for early-time input function

Abstract

The Patlak graphical method is widely used in parametric imaging for modeling irreversible radiotracer kinetics in dynamic PET. The net influx rate of radiotracer can be determined from the slope of the Patlak plot. The implementation of the standard Patlak method requires the knowledge of full-time input function from the injection time until the scan end time, which presents a challenge for use in the clinic. This paper proposes a new relative Patlak plot method that does not require early-time input function and therefore can be more efficient for parametric imaging. Theoretical analysis proves that the effect of early-time input function is a constant scaling factor on the Patlak slope estimation. Thus, the parametric image of the slope of the relative Patlak plot is related to the parametric image of standard Patlak slope by a global scaling factor. This theoretical finding has been further demonstrated by computer simulation and real patient data. The study indicates that parametric imaging of the relative Patlak slope can be used as a substitute of parametric imaging of standard Patlak slope for tasks that do not require absolute quantification, such as lesion detection and tumor volume segmentation.

Figure 1.

Blood input functions in the simulation. (a) Full-time blood input function (circles) by the Feng model for the Standard Patlak and late time points (solid triangles) for the relative Patlak; (b) Linear relation between x and x′ with t* = 30 minutes.

Figure 2.

Comparison of the standard Patlak plot and relative Patlak plot in the simulation. (a) standard Patlak plot; (b) relative Patlak plot.

Figure 3.

Results of simulation. (a) Relation between ${K^{\prime }}_i$ and K_i; (b) Correlation coefficient of ${K^{\prime }}_i$ versus K_i for various t* values.

Figure 4.

Validation of the approximate linear relationship between x(t) and x′(t) for the bi-exponential input function C_P (t) = a₁e^−a2t + b₁e^−b2t. t* = 30 minutes. (a) Plot of the correlation coefficient of x(t) versus x′(t) for 1,000 realizations; (b) Correlation plot for a specific parameter set that corresponds to the sample point with the lowest correlation coefficient in (a).

Figure 5.

Blood input functions from dynamic FDG-PET scans of human patients. (a) breast cancer patient; (b) cardiac patient.

Figure 6.

Validation that late-time points of real patient blood input functions approximately follow a mono-exponential function model. (a) breast patient data, (b) cardiac patient data.

Figure 7.

Linear relation between x(t) and x′(t) for patient data with t ≥ t* = 30 minutes.(a) breast patient data, (b) cardiac patient data.

Figure 8.

Comparison of SUV images and parametric imaging using the standard Patlak plot and relative Patlak plot for the breast patient. (a) SUV images; (b) parametric image of the standard Patlak slope K_i; (c) parametric image of the relative Patlak slope ${K^{\prime }}_i$. The start time t* = 30 minutes. From the top to the bottom are the views from the planes of transverse, sagittal and coronal, respectively.

Figure 9.

Results of the breast patient scan. (a) Relation between ${K^{\prime }}_i$ and K_i (t* = 30 minutes); (b) Correlation coefficient between ${K^{\prime }}_i$ and K_i versus various start time t*.

Figure 10.

Comparison of SUV images and parametric imaging using the standard Patlak plot and relative Patlak plot for the cardiac patient. (a) SUV images; (b) parametric image of K_i; (c) parametric image of ${K^{\prime }}_i$. The start time t* = 30 minutes. From the top to the bottom are the views from the planes of transverse, sagittal and coronal, respectively.

Figure 11.

Results of the cardiac patient scan. (a) Relation between ${K^{\prime }}_i$ and K_i (t* = 30 minutes); (b) Correlation coefficient between K_i and ${K^{\prime }}_i$ versus various t* values.

Figure 12.

Parametric images of K_i and ${K^{\prime }}_i$ estimated with t* = 45 minutes for the cardiac patient data. (a) K_i by the standard Patlak plot; (b) ${K^{\prime }}_i$ by the relative Patlak plot.