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.

Generation of parametric Ki images for FDG PET using two 5‐min scans

“…Based on the existing dual‐time‐point protocol already used in clinical practice, we successfully developed and validated a new approach of generating K i images from the dual‐time‐point imaging data alone. Other approaches using a 30‐min temporally continuous dynamic scan have been reported previously for K i estimation 14–17 . A vendor product of FlowMotion TM multiparametric PET has also been released commercially by Siemens for direct Patlak reconstruction 17,48,49 .…”

“…This seriously limits its clinical application. Efforts have been made to simplify the dynamic imaging protocol by acquiring a single dynamic scan, [14][15][16][17] usually starting 10-30 min post injection and ending to 55-60 min post injection, and calculating its Patlak plot 18 from which it is possible to derive K i quantification of FDG PET. To avoid sequential arterial blood sampling, studies have been reported to combine a single dynamic scan (~60-80min post injection) with a population-based input function to facilitate their subjects for each ROI is smaller than 10%.…”

Mathematical Models for FDG Kinetics in Cancer: A Review

“…Then, in the plane referred to Cartesian coordinates , define the functions and by . The points give the parametric representation of a curve which is known as the standard Patlak plot [ 38 ]. Comparison with Equation ( 34 ) and the condition on show that the curve is asymptotically linear.…”

“…Comparison with Equation ( 34 ) and the condition on show that the curve is asymptotically linear. Thus the slope and the adimensional constant intercept are estimated in terms of the data by linear regression [ 38 ]. The procedure may be applied pixel-wise.…”

“…The slope coefficient , which is related to the rate of tracer uptake, comes from application of linear regression to the whole Patlak curve, with t varying from 0 to ∞. The coefficient is different from the slope of the line asymptotically approximating the Patlak curve [ 38 ]. This remark holds independently of the number of compartments.…”