Parametric image reconstruction using spectral analysis of PET projection dataThis article has been downloaded from IOPscience. Please scroll down to see the full text article.1998 Phys. Med. Biol. 43 651(http://iopscience.iop.org/0031-9155/43/3/016)Download details:IP Address: 128.36.48.10The article was downloaded on 02/06/2011 at 16:34Please note that terms and conditions apply.View the table of contents for this issue, or go to the journal homepage for moreHome Search Collections Journals About Contact us My IOPsciencePhys. Med. Biol. 43 (1998) 651–666. Printed in the UK PII: S0031-9155(98)82927-8Parametric image reconstruction using spectral analysis ofPET projection dataSteven R Meikle†, Julian C Matthews, Vincent J Cunningham,Dale L Bailey, Lefteris Livieratos, Terry Jones and Pat PriceMRC Cyclotron Unit, Hammersmith Hospital, Royal Postgraduate Medical School, Du CaneRoad, London W12 0NN, UKReceived 26 March 1997, in final form 14 November 1997Abstract. Spectral analysis is a general modelling approach that enables calculationof parametric images from reconstructed tracer kinetic data independent of an assumedcompartmental structure. We investigated the validity of applying spectral analysis directlyto projection data motivated by the advantages that: (i) the number of reconstructions is reducedby an order of magnitude and (ii) iterative reconstruction becomes practical which may improvesignal-to-noise ratio (SNR). A dynamic software phantom with typical 2-[11C]thymidine kineticswas used to compare projection-based and image-based methods and to assess bias–variancetrade-offs using iterative expectation maximization (EM) reconstruction. We found that thetwo approaches are not exactly equivalent due to properties of the non-negative least-squaresalgorithm. However, the differences are small (<5%) and mainly affect parameters related toearly and late time points on the impulse response function (K1and, to a lesser extent, VD).The optimal number of EM iterations was 15–30 with up to a two-fold improvement in SNRover filtered back projection. We conclude that projection-based spectral analysis with EMreconstruction yields accurate parametric images with high SNR and has potential applicationto a wide range of positron emission tomography ligands.1. IntroductionQuantitative estimates of physiological parameters can be obtained from dynamic positronemission tomography (PET) studies by relating the time course of labelled compoundto the tracer concentration in plasma via an appropriate tracer kinetic model. If themodel is sufficiently insensitive to noise, parameters can be estimated at the pixel level,yielding so-called parametric or functional images. Conventionally, image reconstructionand kinetic modelling are treated as separate estimation tasks with reconstruction of the fulldynamic sequence of images being performed prior to physiological parameter estimation.Because of the large number of images to be reconstructed (typically 30 dynamic framesmultiplied by up to 50 axial slices), filtered back projection is usually preferred over iterativereconstruction algorithms and, as a result, parametric images are often characterized by poorsignal-to-noise.The tracer kinetic model can also be incorporated into the image reconstructionprocess, treating the two processes as a single parameter estimation task. The expectation† Present address: Department of PET and Nuclear Medicine, Royal Prince Alfred Hospital, Missenden Road,Camperdown NSW 2050, Australia. E-mail address: [email protected]/98/030651+16$19.50c! 1998 IOP Publishing Ltd 651652 S R Meikle et almaximization (EM) algorithm (Shepp and Vardi 1982, Lang and Carson 1984), for example,is easily extended to include a temporal component which may be described by a tracerkinetic model (Snyder 1984, Carson and Lange 1985, Matthews et al 1997). This approachhas the potential to improve the noise characteristics of parametric images and is theoreticallyappealing as it unifies the tracer model and the imaging model and allows for moreappropriate choice of weights in the optimization procedure. However, this approach has notbeen widely adopted as it remains computationally demanding. An alternative approach isto perform parameter estimation directly on the projection data prior to image reconstruction(Tsui and Budinger 1978, Huang et al 1982, Alpert et al 1984, Maguire et al 1996). Thisrequires that the model can be expressed as a linear function of the unknown parameters.The advantages of this approach are that: (i) the number of reconstructions is reduced by anorder of magnitude and (ii) as a consequence, iterative reconstruction of parametric imagesbecomes practical which may lead to an improved signal-to-noise ratio (Wilson and Tsui1993, Meikle et al 1994). However, the methods described to date are mainly restrictedto specific models which are based on a compartmental description of the tracer kinetics.For example, the weighted integration technique assumes that all tissues in the field ofview behave homogenously as a two-compartment system (Huang et al 1982, Alpert et al1984, Carson et al 1986), although the method can also be extended to three-compartmentmodels (Blomqvist 1984, Iida et al 1995). Further, the potential of iterative parametricimage reconstruction has not been fully explored.Our main interest is in the developmental tracers for oncology, particularly labelledanticancer drugs. In this important emerging application of PET (Price et al 1995,Wells et al 1996), as with other applications of new tracers, there is often insufficienta priori knowledge of the tracers’ fate in vivo to construct a compartmental model, andparameter estimation is prone to bias if the model assumptions are incorrect. Therefore,we have explored spectral analysis, a more general modelling approach, which enablesthe determination of pharmacokinetic parameters with relatively few model assumptions(Cunningham and Jones 1993). The technique can be applied at a pixel level enablingcalculation of parametric images independent of an assumed compartmental structure(Cunningham et al 1993). Therefore, it is applicable to a wide range of tracer studies.Furthermore, the model is linear and can, in theory, be applied equally well to projectiondata (Meikle et al 1996). If the validity of this approach can be demonstrated, spectralanalysis has the advantage over other projection-based methods of employing a more generalmodel