A study of non-invasive Patlak quantification for whole-body dynamic FDG-PET studies of mice

Abstract

Physiological changes in dynamic PET images can be quantitatively estimated by kinetic modeling technique. The process of PET quantification usually requires an input function in the form of a plasma-time activity curve (PTAC), which is generally obtained by invasive arterial blood sampling. However, invasive arterial blood sampling poses many challenges especially for small animal studies, due to the subjects’ limited blood volume and small blood vessels. A simple non-invasive quantification method based on Patlak graphical analysis (PGA) has been recently proposed to use a reference region to derive the relative influx rate for a target region without invasive blood sampling, and evaluated by using the simulation data of human brain FDG-PET studies. In this study, the non-invasive Patlak (nPGA) method was extended to whole-body dynamic small animal FDG-PET studies. The performance of nPGA was systematically investigated by using experimental mouse studies and computer simulations. The mouse studies showed high linearity of relative influx rates between the nPGA and PGA for most pairs of reference and target regions, when an appropriate underlying kinetic model was used. The simulation results demonstrated that the accuracy of the nPGA method was comparable to that of the PGA method, with a higher reliability for most pairs of reference and target regions. The results proved that the nPGA method could provide a non-invasive and indirect way for quantifying the FDG kinetics of tumor in small animal studies.

Introduction

Positron emission tomography (PET) is a popular functional imaging technology that visualizes physiological changes through the administration of radiopharmaceutical molecular tracers into living systems. ¹⁸F-fluorodeoxyglucose (FDG) is the most widely used tracer in PET studies, and it is mainly used for the in vivo measurement of glucose metabolism. The visualization of subtle metabolic changes is especially attractive for the early detection of malignant tumors, which usually have elevated glucose metabolism. Thus PET imaging with FDG (FDG-PET) has become an important tool in clinical oncology for cancer diagnosis, staging, treatment planning and response assessment [1]. One unique benefit of functional imaging is that quantitative functional parameters can be derived by using tracer kinetic modeling techniques. This delivers a simple way for the quantitative description and objective comparison of complex physiological processes. The process of parameter estimation for deriving physiological parameters is usually based on an underlying kinetic model, which is specific to the used tracer. A plasma time–activity curve (PTAC) is usually used as an input function for a given kinetic model while a tissue time–activity curve (TTAC) derived from the dynamic PET images is used as an output function [2], [3].

There are a number of different approaches for estimating the parameters of a kinetic model. The nonlinear least squares (NLS) method can provide statistically optimal estimates of the kinetic parameters through iteratively adjusting estimated parameters nonlinearly to achieve the minimum least squares difference between the measured and estimated TTACs [2]. Usually a weighted NLS method, referred to as WNLS, is used to address the comparable low signal to noise ratio in the early frames with shorter imaging durations. However, the NLS/WNLS methods with iterative processes have two drawbacks: the outcomes are highly sensitive to the choice of appropriate initial parameters, and the computation cost is high due to the slow converging speed [2]. The graphical analysis method was introduced to transform the nonlinear iterative parameter estimation process to a computationally efficient linear plot, whose slope or intercept reflects the parameters of interest [4], [5]. For example, the slope of the Patlak graphical analysis (PGA) is equal to the influx rate, which is directly proportional to metabolic rate of glucose (MRGlc) in a FDG-PET study [4].

The process of obtaining a PTAC generally relies on frequent invasive arterial blood sampling. This process is relatively inconvenient and may expose operators to extra radiation. In particular, such invasive approaches are much more challenging for small animal studies because of the subjects’ limited blood volume and small blood vessels. The image-derived methods [6], [7], [8], [9] and population-based methods [10], [11] have been presented to reduce or eliminate invasive blood sampling in kinetic modeling. Given multiple regions of interest (ROIs) with distinct TTACs, complex biological systems can be modeled as a single-input-multi-output (SIMO) system. The kinetic parameters and the input function can be estimated simultaneously when multiple distinct TTACs are available for different ROIs [12]. If a reference region is available to reflect the non-specific binding in a neuroreceptor study, the non-invasive Logan method can be used to avoid the problems associated with the traditional invasive Logan approach [13]. The slope of the linear regression of the non-invasive Logan method represents the ratio of the distribution volume between the target and the reference regions. Thus, it is potential for the Patlak method to be extended to derive the non-invasive estimation of the influx rate in FDG-PET studies with an appropriate reference region.

A non-invasive PGA (nPGA) method has been recently introduced for deriving a set of relative influx rates for FDG-PET studies by using reference regions. The method was evaluated using the simulated TTACs of different regions in the human brain [14]. However, it is unclear whether the nPGA method could be extended to whole-body small animal studies for multiple organs and regions. In this study, we aimed to systematically investigate the performance of the nPGA method in the quantification of glucose metabolism for small animal studies as compared with the traditional PGA method. The experimental FDG-PET studies of fifteen mice and computer simulations were used in the evaluation.