Post-doctoral Scholar

Objectives: 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. One drawback of the standard Patlak method is that it requires the knowledge of full-time input function from the radiotracer injection time until the dynamic scan end time, which presents a challenge for use in the clinic. We propose a new relative Patlak plot method which does not need early-time input function and is therefore more convenient for practical use. The objective of this study is to examine the theoretical relationship between the standard Patlak plot and the new relative Patlak plot using mathematical analysis and validate the relationship using computer simulation and patient data.

Methods: The standard Patlak plot exploits the linearity between the normalized tissue concentration and normalized integral of input function C_P(t) after a steady-state time t^[asterisk]. The proposed relative Patlak plot model equation is very similar to the standard Patlak equation, except, the integral of input function C_P(t) in the new model is from t^[asterisk] to t, instead of being from 0 to t in the standard model. The integral of C_P(t) over early-time from 0 to t^[asterisk] is no longer needed in the new model. We used mathematical analysis to study the effect of early-time input function C_P(t) on the Patlak plot slope estimation and discovered the relation between the slope K_i’ of the new plot and the slope K_i of the standard Patlak plot. For validation, we simulated 10,000 noisy time activity curves with various FDG kinetics following a two-tissue compartmental model and the same Feng input function. A one-hour dynamic FDG-PET scan of a patient with breast cancer was used to compare the parametric images of K_i and K_i’ of the two plots. Results: Mathematical analysis proves that the relative Patlak slope K_i’ is equal to the standard Patlak slope K_i times a scaling factor. This factor only depends on the input function and is independent of tissue time activity. This linearity between K_i’ and K_i results in a global scaling factor in parametric imaging. While the absolute values of K_i’ and K_i were different, the two parametric images had the same appearance, indicating their equivalence in providing spatial distribution information. The theoretical relationship has been validated using both simulation and patient data. Conclusions: Parametric imaging by the relative Patlak plot determines the parametric image of the standard Patlak slope up to a scaling factor. The new plot only requires late-time input function data and is easier to use. It can replace the standard Patlak plot for certain applications where absolute K_i values are not necessary. Examples include, but not limited to, lesion detection and metabolic tumor volume segmentation using parametric map of tracer influx rate. Research Support: This work is supported in part by NIH R21 HL 131385 and AHA BGIA 25780046.