Application of separable parameter space techniques to multi-tracer PET compartment modeling

Jeff L Zhang,A Michael Morey,Dan J Kadrmas

doi:10.1088/0031-9155/61/3/1238

Abstract

Multi-tracer positron emission tomography (PET) can image two or more tracers in a single scan, characterizing multiple aspects of biological functions to provide new insights into many diseases. The technique uses dynamic imaging, resulting in time-activity curves that contain contributions from each tracer present. The process of separating and recovering separate images and/or imaging measures for each tracer requires the application of kinetic constraints, which are most commonly applied by fitting parallel compartment models for all tracers. Such multi-tracer compartment modeling presents challenging nonlinear fits in multiple dimensions. This work extends separable parameter space kinetic modeling techniques, previously developed for fitting single-tracer compartment models, to fitting multi-tracer compartment models. The multi-tracer compartment model solution equations were reformulated to maximally separate the linear and nonlinear aspects of the fitting problem, and separable least-squares techniques were applied to effectively reduce the dimensionality of the nonlinear fit. The benefits of the approach are then explored through a number of illustrative examples, including characterization of separable parameter space multi-tracer objective functions and demonstration of exhaustive search fits which guarantee the true global minimum to within arbitrary search precision. Iterative gradient-descent algorithms using Levenberg–Marquardt were also tested, demonstrating improved fitting speed and robustness as compared to corresponding fits using conventional model formulations. The proposed technique overcomes many of the challenges in fitting simultaneous multi-tracer PET compartment models.

Highlights

Rapid multi-tracer positron emission tomography (PET) is a technique where multiple PET tracers are imaged in a single scan
Three sets of representative multi-tracer PET data were retrospectively selected from ongoing investigator-initiated trials at the University of Utah performed with Informed Consent under protocols approved by the university Institutional Review Board
It should be noted that multi-tracer PET fits depend upon tracer combinations, injection order and timing, and noise properties of the images; the results found here are representative of typical imaging cases, but cannot be guaranteed to apply for all multi-tracer PET imaging scenarios

Summary

Introduction

Rapid multi-tracer PET is a technique where multiple PET tracers are imaged in a single scan. Perhaps the most robust multitracer PET signal-separation algorithms rely upon parallel compartment modeling of all tracers present in order to apply the kinetic constraints and recover imaging estimates from each individual tracer. The conventional compartment model is comprised of a series of homogenous compartments driven by an input function, and where temporal exchange between compartments is governed by rate parameters and simple linear differential equations. The solutions to these equations are nonlinear and present a complex fitting environment which becomes further compounded in the presence of multiple tracers. The imaging signal, R(t), typically cannot measure each compartment individually; rather, the imaging signal comprises the sum over all compartments, C(t; b(t), {ki}), often with the addition of a vascular term due to imaging signal from whole-blood, B(t):

Methods

Results

Conclusion