P O S I T R O NE M I S S I O N

T O M O G R A P H Y

PET Clin 2 (2007) 235–249

235

Partial Volume CorrectionStrategies in PETOlivier Rousset, PhDa,*, Arman Rahmim, PhDa,Abass Alavi, MDb, Habib Zaidi, PhD, PDc

- Postreconstruction-based partial volumecorrection methods

Postreconstructionregion-of-interest–based partialvolume correction methods

Postreconstruction voxel-based methodsof partial volume correction

- Reconstruction-based partial volumecorrection methods

Voxel-based methodsRegion-of-interest–based methods

- Clinical and research applicationsof partial volume correction

- Potential pitfallsImage registrationAnatomic image segmentationTissue inhomogeneity

- Summary- References

In PET imaging, the resolution obtained in the used, but this text assumes the use of three-dimen-

reconstructed images is limited by a combinationof various physical and instrumentation-relatedfactors, namely (1) positron range, (2) photonnoncollinearity, (3) crystal size and decoding ofinteracting crystals, (4) the acquisition mode (eg,two-dimensional versus three-dimensional) andthe reconstruction algorithm and associated filter-ing [1]. Because of the limited resolution, the sizesof voxels used in functional imaging are set to belarger than those used in higher-resolutionstructural modalities such as MR imaging or CT,to avoid excessive noise or sampling artifacts. (Intwo-dimensional imaging, the term ‘‘pixel’’ is

This work was supported by Grant No. SNSF 3100A0-1Grants RO1AA12839 (NIAAA), K24DA00412-01A1 (NIDAa Division of Nuclear Medicine, Russell H. Morgan DeparHopkins University, Johns Hopkins Outpatient Centre, RoUSAb Division of Nuclear Medicine, Department of RadioloSpruce Street, Philadelphia, PA 19104, USAc Division of Nuclear Medicine, Geneva University Hosp* Corresponding author.E-mail address: olivier@jhu.edu (O. Rousset).

1556-8598/07/$ – see front matter ª 2007 Elsevier Inc. All rightspet.theclinics.com

sional imaging, the more usual case.) Therefore anexisting problem is the tissue-fraction effect, inwhich contributions from different tissues, withpossibly different tracer uptake and metabolism,may be combined within a single voxel. This prob-lem is not specific to functional imaging but also isof concern in higher-resolution structural imagingmodalities such as CT [2] and MR imaging [3].This effect often is stated as scanner blurring, orpoint spread, an effect in which activities withina region spill to nearby regions. Both effects origi-nate from the finite resolution capabilities in PETimaging and in reality are two faces of a single

16547 from the Swiss National Foundation, and by), NS38927 (NIH), and P01HD24448-10 (NIH).tment of Radiology and Radiological Sciences, Johnsom 3245, 601 N. Caroline St., Baltimore, MD 21287,

gy, Hospital of the University of Pennsylvania, 3400

ital, CH-1211 Geneva, Switzerland

reserved. doi:10.1016/j.cpet.2007.10.005

Rousset et al236

phenomenon. This unified aspect of partial volumeeffects (PVE) is reflected in the authors’ system ofnotations, listed in Table 1.

The following discussion assumes a perfectly reg-istered high-resolution image (eg, MR imaging) ofthe object and a lower-resolution PET image ofthat same object. The partial volume operator P isdenoted as the n � m matrix modeling the com-bined tissue-fraction effect as well as the PETpoint-spread blurring effect (n is the number ofPET image voxels, m the number of high-resolutionvoxels) from the space of the high-resolution imageto the PET image space. This notation/model issomewhat different from the common notation inwhich the tissue-fraction effect is modeled beforethe point-spread effect and P then is taken asa square matrix modeling the blurring effect onthe PET image. In fact, to compute the overallPVE, it is more accurate to perform forward projec-tion of the high-resolution image of the objectwhile incorporating the various finite-resolutioneffects in PET, followed by application of the recon-struction algorithm used, thus determining theoverall PVE (Table 1).

Table 1: Notations

Symbol Definition

b vector of observed PETimage voxels

s # of tissue segmentsx vector of segment

valuesm # of high-resolution

(MR imaging) voxelsR segment to MR imaging

mappingn # of PET voxelsP MR imaging to PET

partial volume operatorh voxel noise in PET imageA region averaging

operatorr PET image voxel

covariance matrixB vector of measured PET

region valuesG Geometric Transfer

Matrix (GTM)h’ PET region noiser’ PET region covariance

matrixy vector of partial

volume–correctedimage voxels

For many reasons, the first medical applicationsof positron radiation focused on the brain, andmost of the first human PET prototypes were devel-oped specifically for functional brain imaging [4].Likewise, the first partial volume correction (PVC)techniques focused on neurologic PET proceduresin which the enhancement of the quantitative capa-bilities of PET was driven by brain research [5,6].The most sophisticated PVC strategies rely on anadjunct coregistered structural image in which MRimaging plays a pivotal role because of the bettercontrast between the gray and white mattercompared with CT [7–10]. Now, however, the useof correlated anatomic information provided bythe CT component of dual-modality imagingsystems (eg, PET/CT) makes it possible to performaccurate PVC in other organs and tissues includingcardiovascular [11], atherosclerotic [12], andwhole-body oncologic imaging [13,14].

PVC methods can be categorized broadly as (1)postreconstruction-based and (2) reconstruction-based methods; which are discussed separately inlater sections. Within each of these categories,region-of-interest (ROI)–based and voxel-basedapproaches are discussed. Clinical and researchapplications of various PVC strategies used in PETare addressed also.

Postreconstruction-based partial volumecorrection methods

Postreconstruction region-of-interest–basedpartial volume correction methods

Recovery coefficient methodThe first attempts to compensate for PVE usingrecovery coefficients were made by Hoffman andcolleagues [5], who computed a set of recoverycoefficients based on known size, shape, and loca-tion (within the PET scanner) of the objects beingimaged. The same group later extended thisapproach to predict the recovery coefficients fordifferent brain structures that were approximatedusing a series of non-overlapping spheres [6]. Atthis time, the PVE was tackled in the context ofhot objects against a cold background and thusdealt with only one aspect of the problem, referredto as ‘‘spill-out’’ (the loss of activity because of thesmall size of the object relative to the PET scanner’sspatial resolution). It soon was realized that,depending on the background’s activity concentra-tion, spill-in from the surrounding warm tissuesmight be as important as spill-out and should becompensated. The concept of contrast recoverycoefficient, introduced by Kessler and colleagues[15], reflects the rate of recovery that lies abovethe surrounding medium. This quantity is justifiedonly when the background itself is not subject to

Partial Volume Correction Strategies in PET 237

PVE and is of known concentration and uniformactivity.

For simplicity, several investigators adopted thisconcept and applied formulations derived by Hoff-man and Kessler to clinical data to achieve moreaccurate assessment of relevant parameters (eg, tocorrect for brain atrophy) [16]. The technique isused commonly in clinical oncology when a prioriinformation about the tumor (ie, a spherical shapeof known size) is available [13,17–20]. The ap-proach is limited, however, by the crude approxi-mations involved, and more sophisticatedtechniques were sought.

Fleming and colleagues [21] have proposedanother simple method to account for the PVE bymeasuring the total uptake rather than the activityconcentration in the ROI using a new index, thespecific uptake size index. The technique consistsin defining volumes of interest for the structure ofinterest (eg, striatum), large enough to guaranteethe inclusion of all the partial volume counts de-tected outside the physical volume of the structures.The technique was validated further and proved tobe useful for accurate quantification of specificbinding ratio in Iodine-123 fluoropropyl-2-ß-car-bomethoxy-3-ß-(4-iodophenyl)nortropane singleproton emission tomography ([123I]FP-CIT SPECT)brain images [22].

Geometric transfer matrix methodThe geometric transfer matrix (GTM) method isbased on considering as many ROIs as the numberof tissue segments considered in the analysis, result-ing in as many equations to be solved as the numberof unknown true segment values. RSFi is the regionalspread function of tissue i (ie, the response of thescanner to the activity within each tissue segment,which is assumed to be uniform). RSFi is computedfor each segment i by creating an image Ui of the ithsegment with unit activity (the other segments being

Fig. 1. A PET image is considered as the blur

set to 0), followed by the forward projection (Fproj)and reconstruction (Recon) steps [23–25]:

RSFi 5 Recon�

Fproj ðUiÞ�

ð1Þ

The resulting blurred images then define the RSFfor each segment within which the activity isassumed to be homogeneous, as shown in Fig. 1.Consideration of the issue of noise is elaboratedlater.

The next step consists in computing what fractionof each segment i contributes to each ROIj, asshown in Fig. 2; these contributions define the gij

elements of the GTM, denoted here by G.Next, referring to the vector containing the un-

known true tissue segment values as x (size s � 1where s is the number of tissue segments withinwhich activity is assumed homogeneous) and thevector containing the average measured valueswithin the ROIs drawn on the PET images as B(size s � 1), one arrives at the model:

Gx 5 B ð2Þ

In practice, the matrix G is always invertible. Oneshould note that individual ROIs are drawn to cor-respond closely to each tissue segment, so that thematrix G has most of its largest values along itsdiagonals. Therefore, the rows or columns of Gare not linear combinations of one another, andG can be seen to be invertible. Solving for the vectorof unknown segment values x, one then arrives at:

x 5 G�1B ð3Þ

wherein the values for vector B are measured re-gional activity concentrations, and the matrix Ghas been estimated.

Perturbation-based geometric transfer matrixmethodA refinement to this approach, proposed by Du andcolleagues [26], is based on the observation that

red superposition of tissues of homogeneous activity.

Fig. 2. In this example, four segments of homogeneous activity are assumed: cortical gray matter plus thalamus(VOI1), putamen (VOI2), caudate nucleus (VOI3), and white matter plus scalp (VOI4). The RSF corresponding toeach segment is then calculated, and its intersection fraction with each of the ROIs (j 5 1.4) is computed,thus defining the elements of the 4 � 4 GTM in this example.

Rousset et al238

statistical iterative reconstruction algorithms (eg,ordered subset expectation maximization, OSEM)are nonlinear, suggesting that the response of thescanner to a particular segment can depend onthe activities in the other segments. The approachproposed by the authors is to perturb the initiallyestimated image ~f for the contribution of eachsegment to arrive at a better estimate of the RSFdistributions. This approach can be written in ournotation as:

RSFi 51

di

nRecon

�Fproj

�~f 1di Ui

��

� Recon�

Fproj�~f��o ð4Þ

where di is set to be a certain percentage (eg, 10% inRef. [26]) of the average counts in each segment i.(The notation used by Du and colleagues doesnot consider the tissue-fraction effect, because it de-notes high-resolution segments and PET ROIs inthe same space, thus modeling only the point-spread function (PSF) effect. The authors of thisarticle thus extend the notation to the more generalcase).

The method was tested using phantoms andsimulations in the context of brain SPECT imagingand showed noticeable reductions of bias in PVCcompared with the conventional method basedon the linear assumption [27].

Methods using voxel-based noise modelsAlternatives to this approach also have been sug-gested by Labbe and colleagues [28] and by Astonand colleagues [29]. These alternatives are stillROI based in that they perform PVC for measuredROI values, but they attempt to model the noiseat the voxel level. A novel analytic comparison ofthese methods with the one derived by Roussetand colleagues [25] is presented here.

Approximately following the notations of Astonand colleagues [29], let R be a matrix mappingthe true segment values x to the high-resolution(eg, MR) image voxels (thus m � s, where m is thenumber of high-resolution voxels). As such, ele-ments of R are strictly 0 or 1 for hard segmentationor can take values in the range [0,1] for soft/fuzzysegmentation of MR images. Also, denoting b to

Partial Volume Correction Strategies in PET 239

store the reconstructed PET image values at the voxellevel (with size n � 1), this model can be writtenas:

PRx1h 5 b ð5Þ

where P, as previously defined, maps the MR imageto the PET image incorporating the overall PVE (ie,tissue fraction as well as the PSF effect), and h

models the noise in the reconstructed PET imagethat can be generalized to model the contributionof different types of noise. In the present frame-work, the approach of Rousset and colleagues [25]can be derived by considering the s � n averagingoperator A, which essentially considers s regions(ie, as many regions as the original segments) andcalculates the average image values within each re-gion; thus:

APRx 1 Ah 5 Ab ð6Þ

Which, defining h’ 5 Ah, G 5 APR and B 5 Ab, canbe written as

Gx 1 h0 5 B ð7Þ

Note that B is thus simply the measured average re-gion values, and G (which is a square s � s matrix)models the PVE on the original segments as mea-sured by the defined regions and is thus the stan-dard GTM.

Now modeling the noise vector h’ using a generalregion noise covariance matrix r’ (size s � s), theweighted least-squares solution to Equation 7 (ie,weighted by r’�1) is:

x 5 ðGTr0 �1GÞ�1GTr0 �1B ð8Þ

Next, recalling as explained before, that the GTM Gis in practice always invertible, one arrives at manycancellations in Equation 8 resulting in:

x 5 G�1B ð9Þ

That is, according to this method, the PVC segmentvalues are independent of the noise properties. Thisimportant observation shows that the presentframework is not biased in the sense that it doesnot make any assumptions or approximationsabout the noise distribution in the reconstructedPET images. It also suggests that, in ongoing ad-vanced PVC research, this framework should beused for benchmark comparisons because it makesa minimal number of assumptions. Aston and col-leagues [29] are able to reduce their derivation tothat of Rousset and colleagues [25] by making anassumption regarding the noise model, but it isnot necessary to make that assumption to arrive atthe GTM approach. In fact, as argued previously,given the ROI-averaging framework set by Equation6, one may arrive at Rousset and colleagues’ [25]

formulation without making specific assumptionsabout the noise model.

The approach instead can be implemented bydirectly solving Equation 5, as described by Astonand colleagues [29], at the voxel level. Thus, model-ing the voxel noise h using a general image voxelcovariance matrix r (size n � n), the least-squaressolution of Equation 5 weighted by r�1 yields:

x 5 ðRTPTr�1PRÞ�1RTPTr�1b ð10Þ

Here, unlike the previous solution, a cancellation ofterms does not occur, because the matrix PR isa non-square matrix (n � x) mapping the true seg-ment values to blurred PET images and as such isnot invertible. Labbe and colleagues [28] proposedthe nonweighted least-squares approach (ie, withan assumption of uncorrelated, identically distrib-uted voxel noise, thus r f I) arriving at:

x 5 ðRTPTPRÞ�1RTPTb ð11Þ

Nevertheless, the aforementioned assumption isgenerally not valid in PET reconstructions, and thevoxels tend to reveal unequal variances, especiallywith iterative reconstructions in which voxel vari-ances are very nonuniform and typically are highlycorrelated with true voxel intensities [30,31]. Assuch, a better approximation worthy of further in-vestigation for OSEM-type algorithms is to set:

rwdiag�

b2�

ð12Þ

where b2 is the vector of squared imaged intensities,which can be arrived at roughly by using approxi-mate noise analysis for iterative algorithms (seeEquation 41 in Ref. [30]). Nevertheless, Equation12 is still a rough approximation, and the variancesdepend on the object in a more complicated way, asderived extensively by Barrett and colleagues [30]and more precisely by Qi [31]. Furthermore, it isnot accurate to assume that image voxels are uncor-related, and the amount of correlation is highly de-pendent on a number of factors (eg, the number ofiterations of the reconstruction algorithm andwhether resolution recovery methods are used [32]).

The authors believe that the accurate modeling ofnoise using Equation 10 has considerable potentialfor obtaining more precise (ie, less variant) PVCestimates. At the same time, the task of estimatingthe covariance matrix r is quite intense [31] andwould be compounded further in practice becauseit would be estimated based on the measured dataset, which is only a single, noisy projection of thetrue object [33]. The degree of valid approximationsin the estimation of the covariance matrix r thatwould be acceptable for the task of estimatingPVC segment values x remains an open question.Therefore it is useful to compare such derivations

Rousset et al240

with that of Equation 9, which, as was shown, isindependent of the noise model.

Postreconstruction voxel-based methodsof partial volume correction

Potential advantages of PVE-corrected images, asopposed to PVE-corrected ROI-measured concen-trations, include the ability to delineate functionalvolumes accurately and to improve the tumor-to-background ratio, which could improve consider-ably the analysis of response-to-therapy studiesand diagnostic examinations as well as treatmentplanning for PET-based radiation therapy. In thiscontext, however, the problem is more complexand has been attempted frequently, based ona number of often strong assumptions andapproximations.

Partition-based methodsTo perceive the complexity of the problem, oneshould note that the true segment distribution f(r)at any voxel r being estimated can be written as:

f�r�

5XN

i 5 1

xiUi

�r�

ð13Þ

assuming N homogeneous segments each with ac-tivity xi. As such, each voxel can have the contribu-tions of up to N segments (thus one equation withN unknowns for each voxel). The strategy in theROI-based PVC methods was to set up as manyROIs as there are unknown segments, to arrive at es-timated concentrations for the ROIs given theknowledge of the RSFs. Within the present contextof voxel-based PVC, a simple approach has beento set N 5 1 [34]. This approach aims to compen-sate for signal dilution in nonactive tissues suchas cerebrospinal fluid (CSF). This compensation isimportant in the case of tissue atrophy to avoid mis-interpreting the decrease of metabolism as beingcaused by the PVE. Setting N 5 1 in this equation,while applying the partial volume operator toboth sides, gives:

bðrÞ5 Pf ðrÞ5 x1PU1ðrÞ ð14Þ

Assuming entirely consistent reconstructions (ie, nonoise) and very accurate modeling of the operator P,solving Equation 14 at any non-zero measured PETvoxel would yield the value of xi. Realistically, how-ever, within segment 1 one may instead define x1(r)and compute it as:

x1

�r�

5bðrÞ

PU1ðrÞð15Þ

A more realistic approach proposed by Muller-Gartner and colleagues [35] has been to modelpresence of three distinct regions: (1) gray matter,

(2) white matter, and (3) background and CSF ac-tivity. (It is worth paying close attention towhether the detected activity in this third regionis not simply the result of spillover from adjacenttissue plus noise.) The relevant equation in thiscase is:

bðrÞ5 Pf ðrÞ5 x1PU1ðrÞ1x2PU2ðrÞ1x3PU3ðrÞ ð16Þ

The approach is based on assuming the presence ofROIs within regions 2 and 3 such that they are notcontaminated by PVEs (thus extracting values of x2

and x3). Similar to the N 5 1 case, x1(r) now can beestimated as:

x1

�r�

5bðrÞ � x2PU2ðrÞ � x3PU3ðrÞ

PU1ðrÞð17Þ

This approach, for the simplified N 5 2 case (activityonly in gray and white matter) is depicted in Fig. 3.

Another method proposed by Rousset and col-leagues [36], and later incorporated in the softwaredescribed by Quarantelli and colleagues [37], hasbeen to extract the white matter activity usingROI-based PVC methods, followed by applicationof this calculation. The Muller-Gartner methodwas extended by Meltzer and colleagues [38] forthe case N 5 4 wherein a voxel of interest with dis-tinct activity (amygdala) is considered within graymatter. The same group also reported on the com-parative analysis of two- and three-compartmentmethods and concluded that the two-compartmentapproach is better suited for comparative PETstudies, whereas the three-compartment approachprovides better accuracy for absolute quantitativemeasures [39].

In comparison with the ROI-based PVC methods,the aforementioned (N > 1) approaches are (1)based on the assumption of possibility of extractingnon–partial volume–contaminated activities fromsome remote ROIs (particularly for white matterand CSF), and additionally (2) tend to limit N toa very few regions to provide solutions to the multi-unknown problem. By contrast, the ROI-basedmethods are based on a collective modeling of theROIs’ partial volume contributions to one another,rather than focusing on individual voxels at eachcomputation. A quantitative comparison of themethods is provided in [36]. Nevertheless, thesearch for voxel-based PVC remains appealing,and deconvolution methods have seemed naturalfor this problem, as discussed in the followingsection.

Iterative deconvolution methodsOne intuitive approach to this problem, whichdoes not require the use of a high-resolutionmodality or assumptions regarding surroundingstructures, is to employ analytic deconvolution

Fig. 3. A simplified depiction of the Muller-Gartner approach for the N 5 2 case (gray matter, white matter). Theterm x2½activity� � PU2½RSF� for white matter is subtracted from the original image b(r), followed by division,within the ROI for the gray matter, by its regional spread function, which is typically thresholded (eg, 20%)to avoid amplification of noise.

Partial Volume Correction Strategies in PET 241

methods, because the PVE typically is presented asa convolution of the original image with the systemPSF (which may well be space-variant). Neverthe-less, because of the presence of noise in the images,and because simple deconvolution methods am-plify the high-frequency content of images, thusmaking the resulting images unsuitable for visualinterpretation, more advanced approaches areneeded. Many alternatives have been described inthe literature. (Readers are encouraged to consultSchafer and colleagues [40] and especially Carasso[41].) In the Richardson-Lucy algorithm derivedfrom Bayes’s theorem (and not necessarily basedon additional noise assumptions, although Pois-son’s assumption also arrives at same solution),one uses [41]:

yi11 5 yi � PT b

Pyið18Þ

where the partial volume–corrected image, vector y,is iteratively estimated (from iteration i to i11)from the partial volume–contaminated image, vec-tor b, and the estimated blurring matrix, P. The algo-rithm, however, gives the inverse filtering solutionwhen iterated until convergence [41], thus needingto be terminated early or regularized.

Another notable alternative has been the applica-tion of the reblurred VanCittert method [41]:

yi11 5 yi 1 l PT�b� Pyi

�ð19Þ

where l˛ð0; 2Þis a constant that controls conver-gence. The method can be derived by applicationof the steepest descent scheme to the minimizationof jjPy-bjj2 (ie, least-squares criterion based on theGaussian model). Like the Richardson-Lucy

algorithm, however, this method iteratively resultsin increasingly noisy image estimates, suggestingthe need for early termination or use of regulariza-tion (eg, see Ref. [42]). For a review of these and al-ternative methods (eg, the Poisson maximuma priori maximum entropy, Tikhonov-Miller restora-tion, and linear slow evolution from the continua-tion boundary [slow evolution from thecontinuation boundary] methods), the reader is re-ferred to Carasso [41].

One such approach was implemented recently inthe context of oncologic PET imaging. The authorsused an iterative three-dimensional deconvolutionalgorithm and a local model of the PET scanner’sPSF followed by application of a PVE correctionto the mean voxel value within a voxel of interest[43]. The authors report more accurate quantitativeassessments of uptake in lesions greater than 1.5 �full-width at half-maximum (FWHM) of the imag-ing system’s PSF.

Multi-resolution approachA newer approach makes use of the multi-resolutionmethod [44]: the algorithm extracts details of a high-resolution image (eg, MR imaging) and transformsthese details to integrate them into a low-resolutionimage (eg, PET). The method proposes using waveletanalysis to decompose the images into layers of dif-ferent resolution/frequency content. The high-reso-lution (eg, MR) image therefore will result inadditional levels of resolution images, from which,it is proposed, the details lost in the low-resolutionimage can be constructed. The study used a purelylinear model of scaling the wavelet-transformed

Rousset et al242

images between the two modalities studied; this lin-ear model does not seem to be justified, except that itresults in ROI quantitation comparable with thatobtained by standard PVC methods. This methodseems to be quite promising and remains to be ex-tended by more accurately relating the transformedresolution levels of high-resolution and low-resolu-tion modalities.

Combined noise and partial volumecorrection modelAnother promising method proposed by Chiver-ton and colleagues [45] is the use of an elaboratestatistical framework for combining image noisereduction and partial volume estimation. Theapproach works by considering the relationshipbetween true voxel concentrations and the com-posite (ie, partial volume–contaminated) voxelconcentrations, as well as the statistical relationsbetween composite values and the noisy realiza-tions. The latter component, however, is assumedto obey Gaussian statistics, an assumption thatmay be inadequate, especially for low-statisticsdata. This distribution can be highly dependenton the type of reconstruction method used[30,31]. This approach still needs to be validatedmore thoroughly.

Reconstruction-based partial volumecorrection methods

PVC commonly is presented in the context of com-pensating for the spill-in/spill-out effects present inreconstruction images, resulting from the limitedresolution capabilities of the imaging system. Onetherefore would think that, for a structure of a givensize, the higher the resolution of a modality, the lessthe PVE will be. Another way of thinking about thisproblem, however, is to note that improving the res-olution of reconstructions performed on a givenscanner would, in effect, be a move in the directionof PVC. Reconstruction methods that improve theeffective resolution of the scanner (at a given noiselevel) can be considered as PVC methods. In thissense, there are numerous approaches to reconstruc-tion that attempt to achieve the aforementionedgoals [46,47]; the use of statistical iterative recon-structions has been an important step in this direc-tion both for voxel-based [11,48] and ROI-based[49–52] reconstructions. Within the context of thesealgorithms (and building on them), a number of re-cent methods deserve to be highlighted.

Voxel-based methods

Resolution recovery methodsIn resolution recovery methods, the system matrixis modeled more accurately to incorporate the

blurring effects in PET (positron range, noncolli-nearity, intercrystal scattering and/or crystal pene-tration effects). A number of such methods existand have been reviewed elsewhere [53]. Thesemethods have been shown to result in considerablyimproved contrast-versus-noise plots for extendedobjects, because of better modeling of blurringeffects in PET (ie, higher effective resolution, andthus less PVE, at a given noise level) [54,55].

Bayesian methodsBayesian methods were developed originally tosuppress noise in PET reconstructed images bypenalizing voxel variations between neighboringvoxels [56]. More sophisticated methods involvedthe use of anatomic information from MR imagingor CT to avoid blurring effects at the boundaries ofregions, as reviewed extensively by Rousset andZaidi [53]. As such, these methods obtain improvednoise levels at nearly similar contrast and effectiveresolutions. Alternatively, Bayesian methods canbe thought of as obtaining improved contrast andeffective resolution at a given level of noise, thusreducing the PVE.

The main problem with these methods, however,has been the introduction of bias in the reconstruc-tion images because of strong assumptions ofuniformity correlations between anatomic andfunctional regions. By contrast, Zhang and col-leagues [57] and Bowsher and colleagues [58]have proposed elaborate and involved methodsthat are able to account for exceptions to theassumed anatomy–function correlation and thusallow for the possibility that intensity regions inthe emission reconstruction may not correspondto regions in the anatomic image. These methods,however, require some user interactions and theestimation of several hyperparameters. A jointmixture framework proposed by Rangarajan andcolleagues [59] offers the aforementioned advan-tage but does not involve user interactions or theneed to determine complicated hyperparameters.

Region-of-interest–based methods

A different, novel approach to this problem hasbeen to quantify ROIs directly from projectiondata, taking into account the effect of PVE (amongother effects, such as scatter). Derived from the earlywork of Huesman [49], this approach has been de-veloped and investigated by Muzic and colleagues[60] in cardiac imaging, by Chen and colleagues[61] and Schoenahl and Zaidi [62] in tumor imag-ing, and by Vanzi and colleagues [52] in dopaminetransporter imaging. This method has the particularadvantage of being able to estimate region variancefor subsequent use in model analysis to obtain

Partial Volume Correction Strategies in PET 243

parameter estimates; however, these methods re-main to be extended to three-dimensional imaging.

Clinical and research applications of partialvolume correction

Quantitative PET measurements of physiologic andbiologic processes in vivo are influenced by variousphysical degrading factors including partial volumeaveraging among neighboring tissues with differingtracer concentrations resulting from the limitedspatial resolution of state-of-the-art PET scanners.PVC is important for describing the true functionalcontribution of PET in providing clinicians andscientists with relevant functional information invarious pathologies. This information might allowaccurate quantification of physiologic processesincluding cerebral blood flow, glucose metabolism,neuroreceptor binding, tumor metabolism, andmyocardial perfusion.

It has been shown in brain PET imaging that,despite substantial improvements in PET scanners’spatial resolution, the loss of cerebral volumeresulting from healthy aging processes can causeunderestimation of PET physiologic measurements.Thus, the failure to account for the effect of partialvolume averaging of brains with expanded sulcihas contributed to the confounding results infunctional imaging studies of aging. After PVC, nocerebral blood flow decline with age in healthyindividuals is described [63–65]. Likewise, it hasbeen demonstrated that reduced glucose metabo-lism measured by PET in dementia of the Alzheimertype is not simply an artifact caused by an increasein CSF space induced by atrophy but reflects a truemetabolic reduction per gram of tissue [66]. In ep-ileptic foci, also, hypometabolism is larger thana mere atrophy effect [67]. Assessment of the dopa-minergic system with PET has shown thatdopamine transporters are noticeably reduced inLesh-Nyhan disease; PVC highlights this finding[68]. Dopa-decarboxylase activity has been shownto be reduced greatly in patients who have Parkin-son disease, compared with normal controls [69].

In myocardial imaging, the use of recoverycoefficients and spillover factors derived either the-oretically or using experimental measurements waspopular in the 1980s [70,71]. The same approachwas used for the quantification of myocardial bloodflow using Nitrogen-13–labeled (13NH3) ammonia[72] where the spillover from the blood pool intothe myocardial wall was significant. Partial volumelosses in the myocardium also can be estimated us-ing an extravascular density image, created by thesubtraction of a blood pool from a transmissionimage [73]. The authors have shown that theextravascular density image can correct for partial

volume averaging over a range of myocardial thick-nesses applicable to patient studies. Nevertheless,the method was found to be sensitive to errors inboth the blood pool and transmission images inthe thinnest regions.

A more appealing approach taking advantage ofthe availability of correlated structural imaging(CT) was proposed to derive count recovery mapsin SPECT myocardial perfusion imaging that wasvalidated experimentally in an elegant study usinga porcine heart model [11]. This method could beextended easily for use in cardiovascular PET imag-ing but would be challenging to apply in tumorimaging because of the difficulties in delineatingaccurately the metabolically active parts of a tumor(eg, in lesions with wholly or partially necroticcenters) using structural imaging [14].

In tumor imaging, several studies reported thatPVE is a serious issue that affects both image qualityand the quantitative accuracy of estimated indicescharacterizing lesion uptake, such as the standard-ized uptake value (SUV). The most straightforwardapproach uses a set of precalculated recoverycoefficients for more reliable estimates of the SUVin pulmonary lesions [20,74,75] and breast cancer[76]. The bias affecting estimates of tumor-to-back-ground ratio resulting from the PVE is dependenton lesion size. The generally accepted criterion isthat PVC is required if the lesion size is less thantwo to three times the spatial resolution (FWHM)of the imaging system when the parameter of inter-est is the maximum voxel value within a particularvoxel of interest. In fact, it has been demonstratedthat when the parameter of interest is the averagecount density, the bias introduced by the PVE couldexceed 10%, even for lesions 0w6 times the FWHM,depending on the true tumor-to-background ratio[77].

As mentioned previously for cardiac imaging,the lesion size determined by structural imaging(CT or MR imaging) also can be used to compen-sate for PVE, thus allowing a more accurate esti-mate of the SUV. Hickeson and colleagues [13]reported an increase in accuracy from 58% to89% by using this technique for assessing the met-abolic activity of lung nodules measuring less than2 cm when a SUV threshold of 2.5 was adopted todistinguish between benign and malignant lesions(Fig. 4). Similar techniques also were used for pre-clinical imaging using a clinical PET/CT scanner.High-resolution CT is used for more precise local-ization of PET findings in addition to PVCthrough size-dependent recovery coefficient correc-tion [78].

The use of global metabolic activity (obtained bymultiplying segmented MR imaging volumes by themeasured mean cerebral metabolic rates for glucose

Fig. 4. Images of a 72-year-old woman with small cell lung carcinoma. (A) Transaxial and (B) coronal images ofFDG-PET scan demonstrate focus of mildly increased uptake in right middle lobe. The maximum standardizeduptake value (SUVmax) was 1.39, which is less than threshold for malignancy. (C) Transaxial chest CT image dem-onstrates that nodule measures 1.0 � 0.8 cm. Corrected SUV was obtained by drawing ellipsoid or circular ROI (inblack) with diameter of 0.8 cm (two voxels) larger than that of the area of perceived increase in activity at planeof maximal FDG uptake, and drawing another ROI (in gray) with diameter of 0.8 cm larger than first ROI to de-termine background activity (activity per volume outside smaller ROI and inside larger ROI). Corrected SUV thenwas obtained by determining activity in first smaller ROI corrected for background activity, dividing by lesion’ssize on CT and ratio of injected dose to body mass, and correcting for decay of 18F. Corrected SUV of this lesionwas 3.54, which exceeds threshold for malignancy. (From Hickeson M, Yun M, Matthies A, et al. Use of a cor-rected standardized uptake value based on the lesion size on CT permits accurate characterization of lung nod-ules on FDG-PET. Eur J Nucl Med Mol Imaging 2002;29:1639–47; with kind permission from Springer Science andBusiness Media.)

Rousset et al244

using PET), introduced by Alavi and colleagues [10]in assessment of the brain in patients who had Alz-heimer disease and in age-matched controls, hasmade possible the accurate measurement of theglobal metabolic activity of the red marrow usingsegmented MR imaging for PVC of PET data [79].This strategy may have potential research and clini-cal applications in the study of the global metabolicactivity of the individual component and in thediagnosis of benign and malignant bone marrowdisorders.

Potential pitfalls

Despite the remarkable advances and achievementsto date, PVC still is limited by the inaccuracies of thevarious procedures involved in the implementationof sophisticated methods, particularly those relying

on an adjunct structural modality image (CT or MRimaging). These limitations, which include thespatial realignment of functional and anatomicimages, segmentation of the high-resolution ana-tomic image, and tissue inhomogeneities, are dis-cussed briefly.

Image registration

Dual-modality imaging systems provide a hardwareapproach to spatial alignment of functional and an-atomic images that is of particular value when nu-meric algorithms fail. Software approaches remainvital to the solution of many registration problemsin clinical practice, however, and might even com-plement hardware approaches in many cases [80].The accuracy of the PVC techniques will dependin part on the accuracy of the realignment of the an-atomic and functional images. The impact of

Partial Volume Correction Strategies in PET 245

misalignment has been investigated in the contextof brain imaging for the region-based approach[25,37,81,82] and for the pixel-based approaches[35,37,38,83]. For the GTM approach, the errorsresulting from misregistration affect only theobserved estimates and do not modify thecoefficients of the GTM matrix. Therefore, the effectof the registration error on the corrected estimates isof the same magnitude as the effect of misregistra-tion on the observed estimates because of inaccu-rate placement of the ROIs [82]. It has beenshown that these errors have a relatively modest im-pact on the final accuracy of the corrected estimates(< 2% of true value for typical 1- to 2-mm misregis-tration errors) [81,82]. Some authors, however, sug-gested recently that misregistration errors have thestrongest impact on data accuracy and precision[37].

Anatomic image segmentation

Medical image segmentation has been identified asthe key problem of medical image analysis andremains a popular and challenging area of research[84]. In brain MR imaging, a wide variety of brainMR imaging segmentation techniques, includinga number of promising approaches, have beendevised and are described in the literature [85].Similar to image registration, the accuracy of algo-rithms for PVC depends in part on the degree ofaccuracy in the segmentation of the anatomicimages. Errors in the segmentation procedurehave greater impact but are relatively limited tothe mis-segmented region [81]. Overall, the accu-racy of the corrected estimates seems to be impactedmore by the success of the segmentation of thestructural information provided by MR imaging

Fig. 5. Representative slices of clinical T1-weighted MR imapatient’s original MR images coregistered to correspondinrithm bundled in the Statistical Parametric Mapping packaalgorithm [88]; and a histogram-based segmentation algorigray areas to gray matter, and dark gray areas to cerebrospitation results. Because of brain extraction, atrophic region

than by the influence of image co-registration. Zai-di and colleagues [86] investigated the impact ofbrain MR image segmentation on PVC. Three algo-rithms were compared: the first, bundled in theStatistical Parametric Mapping package [87], andthe second, the Expectation Maximization Seg-mentation algorithm [88], incorporate a prioriprobability images derived from MR images ofa large number of subjects. The third, referred toas the ‘‘histogram-based segmentation algorithm(HSBA) algorithm,’’ is a histogram-based segmen-tation algorithm incorporating an ExpectationMaximization approach to model a four-Gaussianmixture for both global and local histograms [89].Fig. 5 illustrates an example in which brains wereextracted inappropriately using the brain extrac-tion tool for the HBSA segmentation. Regionswhere some degree of atrophy was present wereextracted as nonbrain matter by the brain extrac-tion tool. It was concluded that the PVC activitiesin some regions of the brain show large relativedifferences when performing paired analysis ontwo algorithms, indicating that the segmentationalgorithm for ROI-based PVC must be chosencarefully.

It was suggested that, in the absence of majorsources of registration or segmentation errors,recovered activity concentration estimates were typ-ically within 5% to 10% of the true tracer concentra-tion with an SD of a few percent in both phantomand simulation studies [25,29,37,81]. Potentialinnovative developments for future simultaneousPET/MR imaging technology dedicated for brainresearch [90] would be combining various MRimaging segmentation methods to compensate forboth PVC and attenuation [91].

ges segmentation. Images from left to right show theg PET image; the segmentation result using the algo-ge [87]; the Expectation Maximization Segmentation

thm [89]. White areas correspond to white matter, lightnal fluid. Arrows show discrepancies between segmen-s were removed. Arrows indicate possible errors.

Rousset et al246

Tissue inhomogeneity

Inaccuracies resulting from mis-segmentation canbe considered in the context of a more generalproblem of tissue heterogeneity. In fact, the key lim-iting factor of these techniques is the hypothesismade regarding the homogeneity of tracer distribu-tion in each region or tissue component. Someinvestigators gave suggested performing tests ofinhomogeneity based on Krylov subspace iterationto assess the suitability of assuming a homogeneoustracer distribution [29]. This test, however, is validonly when an accurate noise model is available,which is still a challenging task. If known a priori,the tissue mixture of each identified componentcan serve as a basis for computing the requiredRSFs. This computation can be performed usingstatistical probabilistic anatomic maps that can bedefined as the probability of each tissue class (eg,gray matter, white matter, CSF) being present ina given location of a standardized, or stereotaxicspace [92].

Summary

It is gratifying to see the progress that PVC has madein PET. Recent developments have been enormous,particularly in the last decade. The focus has beenon improving accuracy, precision, and computa-tional speed through efficient implementation inconjunction with decreasing the amount of opera-tor interaction. PVC of PET data is well establishedin research environments, but its use in clinicalsettings is still limited to institutions with advancedtechnical support. As the challenges discussed inthis article are met, and experience is gained, imple-mentation of validated techniques in commercialsoftware packages will be useful to attract theinterest of the clinical community and increasethe popularity of these tools.

References

[1] Zaidi H, Alavi A. Current trends in PET and com-bined (PET/CT and PET/MR) systems design.PET Clinics, in press.

[2] Hsieh J. Nonlinear partial volume artifact correc-tion in helical CT. IEEE Trans Nucl Sci 1999;46:743–7.

[3] Van Leemput K, Maes F, Vandermeulen D, et al.A unifying framework for partial volume seg-mentation of brain MR images. IEEE Trans MedImaging 2003;22:105–19.

[4] Zaidi H, Montandon M-L. The new challenges ofbrain PET imaging technology. Curr Med ImagRev 2006;2:3–13.

[5] Hoffman EJ, Huang SC, Phelps ME. Quantitationin positron emission computed tomography: 1.

Effect of object size. J Comput Assist Tomogr1979;3:299–308.

[6] Mazziotta JC, Phelps ME, Plummer D, et al.Quantitation in positron emission computed to-mography: 5. Physical-anatomical effects. J Com-put Assist Tomogr 1981;5:734–43.

[7] Chawluk JB, Alavi A, Dann R, et al. Positron emis-sion tomography in aging and dementia: effect ofcerebral atrophy. J Nucl Med 1987;28:431–7.

[8] Tanna NK, Kohn MI, Horwich DN, et al. Analysisof brain and cerebrospinal fluid volumes withMR imaging: impact on PET data correction foratrophy. Part II. Aging and Alzheimer dementia.Radiology 1991;178:123–30.

[9] Kohn MI, Tanna NK, Herman GT, et al. Analysisof brain and cerebrospinal fluid volumes withMR imaging. Part I. Methods, reliability, and val-idation. Radiology 1991;178:115–22.

[10] Alavi A, Newberg AB, Souder E, et al. Quantita-tive analysis of PET and MRI data in normalaging and Alzheimer’s disease: atrophy weightedtotal brain metabolism and absolute whole brainmetabolism as reliable discriminators. J NuclMed 1993;34:1681–7.

[11] Da Silva AJ, Tang HR, Wong KH, et al. Absolutequantification of regional myocardial uptake of99mTc-sestamibi with SPECT: experimental vali-dation in a porcine model. J Nucl Med 2001;42:772–9.

[12] Bural GG, Torigian DA, Chamroonrat W, et al.Quantitative assessment of the atheroscleroticburden of the aorta by combined FDG-PET andCT image analysis: a new concept. Nucl MedBiol 2006;33:1037–43.

[13] Hickeson M, Yun M, Matthies A, et al. Use ofa corrected standardized uptake value basedon the lesion size on CT permits accuratecharacterization of lung nodules on FDG-PET.Eur J Nucl Med Mol Imaging 2002;29:1639–47.

[14] Soret M, Bacharach SL, Buvat I. Partial-volumeeffect in PET tumor imaging. J Nucl Med 2007;48:932–45.

[15] Kessler RM, Ellis JR, Eden M. Analysis of emis-sion tomographic scan data: limitationsimposed by resolution and background. J Com-put Assist Tomogr 1984;8:514–22.

[16] Herscovitch P, Auchus AP, Gado M, et al. Correc-tion of positron emission tomography data forcerebral atrophy. J Cereb Blood Flow Metab1986;6:120–4.

[17] Avril N, Bense S, Ziegler SI, et al. Breast imagingwith fluorine-18-FDG PET: quantitative imageanalysis. J Nucl Med 1997;38:1186–91.

[18] Wahl LM, Asselin MC, Nahmias C. Regions of in-terest in the venous sinuses as input functionsfor quantitative PET. J Nucl Med 1999;40:1666–75.

[19] Geworski L, Knoop BO, de Cabrejas ML, et al.Recovery correction for quantitation in emissiontomography: a feasibility study. Eur J Nucl Med2000;27:161–9.

Partial Volume Correction Strategies in PET 247

[20] Menda Y, Bushnell DL, Madsen MT, et al. Eval-uation of various corrections to the standard-ized uptake value for diagnosis of pulmonarymalignancy. Nucl Med Commun 2001;22:1077–81.

[21] Fleming JS, Bolt L, Stratford JS, et al. The specificuptake size index for quantifying radiopharma-ceutical uptake. Phys Med Biol 2004;49:N227–34.

[22] Tossici-Bolt L, Hoffmann SMA, Kemp PM, et al.Quantification of [123I]FP-CIT SPECT brainimages: an accurate technique for measurementof the specific binding ratio. Eur J Nucl MedMol Imaging 2006;33:1491–9.

[23] Rousset O, Ma Y, Kamber M, et al. 3D simula-tions of radiotracer uptake in deep nuclei of hu-man brain. Comput Med Imaging Graph 1993;17:373–9.

[24] Rousset OG, Ma Y, Marenco S, et al. In vivocorrection for partial volume effects in PET: accu-racy and precision. In: Myers R, Cunningham V,Bailey DL, editors. Quantification of brain func-tion using PET, vol. 1. San Diego (CA): AcademicPress; 1996. p. 158–65.

[25] Rousset OG, Ma Y, Evans AC. Correction for par-tial volume effects in PET: principle and valida-tion. J Nucl Med 1998;39:904–11.

[26] Du Y, Tsui BMW, Frey EC. Partial volume effectcompensation for quantitative brain SPECTimaging. IEEE Trans Med Imaging 2005;24:969–76.

[27] Du Y, Tsui BMW, Frey EC. Model-based compen-sation for quantitative 123I brain SPECT imag-ing. Phys Med Biol 2006;51:1269–82.

[28] Labbe C, Froment JC, Kennedy A, et al. Positronemission tomography metabolic data correctedfor cortical atrophy using magnetic resonanceimaging. Alzheimer Dis Assoc Disord 1996;10:141–70.

[29] Aston JA, Cunningham VJ, Asselin MC, et al.Positron emission tomography partial volumecorrection: estimation and algorithms. J CerebBlood Flow Metab 2002;22:1019–34.

[30] Barrett H, Wilson D, Tsui B. Noise properties ofthe EM algorithm: I. Theory. Phys Med Biol1994;39:833–46.

[31] Qi J. A unified noise analysis for iterative imageestimation. Phys Med Biol 2003;48:3505–19.

[32] Rahmim A, Cheng J-C, Sossi V. Improved noisepropagation in statistical image reconstructionwith resolution modeling. IEEE Nuclear ScienceSymposium Conference Record 2005;5:2576–8.

[33] Li Q, Asma E, Qi J, et al. Accurate estimation ofthe Fisher information matrix for the PET imagereconstruction problem. IEEE Trans Med Imag-ing 2004;23:1057–64.

[34] Videen TO, Perlmutter JS, Mintun MA, et al.Regional correction of positron emission tomog-raphy data for the effects of cerebral atrophy.J Cereb Blood Flow Metab 1988;8:662–70.

[35] Muller-Gartner HW, Links JM, Prince JL, et al.Measurement of radiotracer concentration in

brain gray matter using positron emission to-mography: MRI-based correction for partial vol-ume effects. J Cereb Blood Flow Metab 1992;12:571–83.

[36] Rousset OG, Ma Y, Wong DF, et al. Pixel- versusregion-based partial volume correction inPET. In: Carson R, Daube-Witherspoon ME,Herscovitch P, editors. Quantitative functionalimaging with positron emission tomography.vol. 1. San Diego (CA): Academic Press; 1998.p. 67–75.

[37] Quarantelli M, Berkouk K, Prinster A, et al. Inte-grated software for the analysis of brain PET/SPECT studies with partial-volume-effect correc-tion. J Nucl Med 2004;45:192–201.

[38] Meltzer CC, Zubieta JK, Links JM, et al. MR-basedcorrection of brain PET measurements for hetero-geneous gray matter radioactivity distribution.J Cereb Blood Flow Metab 1996;16:650–8.

[39] Meltzer CC, Kinahan PE, Greer PJ, et al. Compar-ative evaluation of MR-based partial-volume cor-rection schemes for PET. J Nucl Med 1999;40:2053–65.

[40] Schafer RW, Mersereau RM, Richards MA. Con-strained iterative restoration algorithms. ProcIEEE 1981;69:432–50.

[41] Carasso A. Linear and nonlinear image deblur-ring: a documented study. SIAM Journal onNumerical Analysis 1999;36:1659–89.

[42] Rudin L, Osher S, Fatemi E. Nonlinear total var-iation based noise removal algorithms. PhysicaD 1992;60:259–68.

[43] Teo B-K, Seo Y, Bacharach SL, et al. Partial-vol-ume correction in PET: validation of an iterativepostreconstruction method with phantom andpatient data. J Nucl Med 2007;48:802–10.

[44] Boussion N, Hatt M, Lamare F, et al. A multireso-lution image based approach for correction ofpartial volume effects in emission tomography.Phys Med Biol 2006;51:1857–76.

[45] Chiverton J, Wells K, Partridge M. A combinednoise reduction and partial volume estimationmethod for image quantitation. Proceedings ofthe IEEE Nuclear Science Symposium and Medi-cal Imaging Conference 2006;6:322–8.

[46] Qi J, Leahy RM. Iterative reconstruction tech-niques in emission computed tomography.Phys Med Biol 2006;51:R541–78.

[47] Reader A, Zaidi H. Advances in PET image recon-struction. PET Clinics 2007;2:173–90.

[48] Baete K, Nuyts J, Van Paesschen W, et al. Ana-tomical-based FDG-PET reconstruction for thedetection of hypo-metabolic regions in epilepsy.IEEE Trans Med Imaging 2004;23:510–9.

[49] Huesman RH. A new fast algorithm for the eval-uation of regions of interest and statistical uncer-tainty in computed tomography. Phys Med Biol1984;29:543–52.

[50] Carson RE. A maximum likelihood method forregion-of-interest evaluation in emission to-mography. J Comput Assist Tomogr 1986;10:654–63.

Rousset et al248

[51] Formiconi AR. Least squares algorithm for regionof interest evaluation in emission tomography.IEEE Trans Med Imaging 1993;12:90–100.

[52] Vanzi E, De Cristofaro M, Ramat S, et al. A directROI quantification method for inherent PVE cor-rection: accuracy assessment in striatal SPECTmeasurements. Eur J Nucl Med Mol Imaging2007;34:1480–9.

[53] Rousset O, Zaidi H. Correction of partial volumeeffects in emission tomography. In: Zaidi H, ed-itor. Quantitative analysis of nuclear medicineimages. New York: Springer; 2006. p. 236–71.

[54] Reader AJ, Julyan PJ, Williams H, et al. EM algo-rithm system modeling by image-space tech-niques for PET reconstruction. IEEE Trans NuclSci 2003;50:1392–7.

[55] Panin VY, Kehren F, Michel C, et al. Fully 3-DPET reconstruction with system matrix derivedfrom point source measurements. IEEE TransMed Imaging 2006;25:907–21.

[56] Green PJ. Bayesian reconstructions from emis-sion tomography data using a modified EMalgorithm. IEEE Trans Med Imaging 1990;9:84–93.

[57] Zhang Y, Fessler J, Clinthorne N, et al. Joint esti-mation for incorporating MRI anatomic imagesinto SPECT reconstruction. In: Proceedings ofthe IEEE Nuclear Science Symposium and Medi-cal Imaging Conference October 30–November5, 1994, Norfolk, VA.

[58] Bowsher JE, Johnson VA, Turkington TG, et al.Bayesian reconstruction and use of anatomicala priori information for emission tomography.IEEE Trans Med Imaging 1996;15:673–86.

[59] Rangarajan A, Hsiao I-T, Gindi G. A Bayesianjoint mixture framework for the integration ofanatomical information in functional imagereconstruction. J Mat Imag Vision 2000;12:119–217.

[60] Muzic RF, Chen CH, Nelson AD. A method tocorrect for scatter, spillover, and partial volumeeffects in region of interest analysis in PET.IEEE Trans Med Imaging 1998;17:202–13.

[61] Chen CH, Muzic RF, Nelson AD, et al. Simulta-neous recovery of size and radioactivity concen-tration of small spheroids with PET data.J Nucl Med 1999;40:118–30.

[62] Schoenahl F, Zaidi H. Towards optimal model-based partial volume effect correction in onco-logical PET imaging. Proceedings of the IEEENuclear Science Symposium and Medical Imag-ing Conference 2004;5:3177–81.

[63] Meltzer CC, Cantwell MN, Greer PJ, et al. Doescerebral blood flow decline in healthy aging?A PET study with partial-volume correction.J Nucl Med 2000;41:1842–8.

[64] Van Laere KJ, Dierckx RA. Brain perfusionSPECT: age- and sex-related effects correlatedwith voxel-based morphometric findings inhealthy adults. Radiology 2001;221:810–7.

[65] Yanase D, Matsunari I, Yajima K, et al. Brain FDGPET study of normal aging in Japanese: effect of

atrophy correction. Eur J Nucl Med Mol Imaging2005;32:794–805.

[66] Ibanez V, Pietrini P, Alexander GE, et al. Regionalglucose metabolic abnormalities are not the re-sult of atrophy in Alzheimer’s disease. Neurology1998;50:1585–93.

[67] Knowlton RC, Laxer KD, Klein G, et al. In vivohippocampal glucose metabolism in mesialtemporal lobe epilepsy. Neurology 2001;57:1184–90.

[68] Wong DF, Harris JC, Naidu S, et al. Dopaminetransporters are markedly reduced in Lesch-Nyhan disease in vivo. Proc Natl Acad Sci U S A1996;93:5539–43.

[69] Rousset OG, Deep P, Kuwabara H, et al. Effect ofpartial volume correction on estimates of the in-flux and cerebral metabolism of 6-[(18)F]fluoro-L-dopa studied with PET in normal control andParkinson’s disease subjects. Synapse 2000;37:81–9.

[70] Henze E, Huang SC, Ratib O, et al. Measure-ments of regional tissue and blood-pool radio-tracer concentrations from serial tomographicimages of the heart. J Nucl Med 1983;24:987–96.

[71] Herrero P, Markham J, Bergmann SR. Quantita-tion of myocardial blood flow with H2 15Oand positron emission tomography: assessmentand error analysis of a mathematical approach.J Comput Assist Tomogr 1989;13:862–73.

[72] Nuyts H, Maes A, Vrolix M, et al. Three-dimen-sional correction for spillover and recovery ofmyocardial PET images. J Nucl Med 1996;37:767–74.

[73] Wassenaar RW, deKemp RA. Characterization ofPET partial volume corrections for variable myo-cardial wall thicknesses. IEEE Trans Nucl Sci2006;53:175–80.

[74] Vesselle H, Schmidt RA, Pugsley JM, et al.Lung cancer proliferation correlates with[F-18]Fluorodeoxyglucose uptake by positronemission tomography. Clin Cancer Res 2000;6:3837–44.

[75] Vesselle H, Turcotte E, Wiens L, et al. Relation-ship between non-small cell lung cancer fluoro-deoxyglucose uptake at positron emissiontomography and surgical stage with relevanceto patient prognosis. Clin Cancer Res 2004;10:4709–16.

[76] Mankoff D, Dunnwald L, Gralow J, et al. Changesin blood flow and metabolism in locally advancedbreast cancer treated with neoadjuvant chemo-therapy. J Nucl Med 2003;44:1806–14.

[77] Soret M, Riddell C, Hapdey S, et al. Biases affectingthe measurements of tumor-to-background activityratio in PET. IEEE Trans Nucl Sci 2002;49:2112–8.

[78] Tatsumi M, Nakamoto Y, Traughber B, et al. Initialexperience in small animal tumor imaging witha clinical positron emission tomography/com-puted tomography scanner using 2-[F-18]fluoro-2-deoxy-D-glucose. Cancer Res 2003;63:6252–7.

Partial Volume Correction Strategies in PET 249

[79] Basu S, Houseni M, Bural G, et al. Magnetic res-onance imaging based bone marrow segmenta-tion for quantitative calculation of pure redmarrow metabolism using 2-deoxy-2-[F-18]fluoro-D: -glucose- positron emission tomogra-phy: a novel application with significant implica-tions for combined structure-function approach.Mol Imaging Biol 2007;9:361–5.

[80] Pietrzyk U. Does PET/CT render software fusionobsolete? Nuklearmedizin 2005;44:S13–7.

[81] Frouin V, Comtat C, Reilhac A, et al. Correctionof partial volume effect for PET striatal imaging:fast implementation and study of robustness.J Nucl Med 2002;43:1715–26.

[82] Slifstein M, Mawlawi O, Laruelle M. Partialvolume effect correction: methodological con-sideration. In: Gjedde A, Hansen SB,Knudsen GM, et al, editors. Physiological imag-ing of the brain with PET. Volume 1. San Diego(CA): Academic Press; 2001. p. 67–75.

[83] Strul D, Bendriem B. Robustness of anatomicallyguided pixel-by-pixel algorithms for partialvolume effect correction in positron emission to-mography. J Cereb Blood Flow Metab 1999;19:547–59.

[84] Zaidi H. Medical image segmentation: quo vadis.Comput Methods Programs Biomed 2006;84:63–7.

[85] Suri JS, Singh S, Reden L. Computer vision and pat-tern recognition techniques for 2-D and 3-D MR

cerebral cortical segmentation (part I): a state-of-the-art review. Pattern Anal Applicat 2002;5:46–76.

[86] Zaidi H, Ruest T, Schoenahl F, et al. Comparativeevaluation of statistical brain MR image segmen-tation algorithms and their impact on partialvolume effect correction in PET. Neuroimage2006;32:1591–607.

[87] Ashburner J, Friston KJ. Unified segmentation.Neuroimage 2005;26:839–51.

[88] Van Leemput K, Maes F, Vandermeulen D, et al.Automated model-based tissue classification ofMR images of the brain. IEEE Trans Med Imaging1999;18:897–908.

[89] Kovacevic N, Lobaugh NJ, Bronskill MJ, et al.A robust method for extraction and automaticsegmentation of brain images. Neuroimage2002;17:1087–100.

[90] Schlemmer H, Pichler BJ, Wienhard K, et al.Simultaneous MR/PET for brain imaging: firstpatient scans [abstract]. J Nucl Med 2007;48:45.

[91] Zaidi H, Montandon M-L, Slosman DO. Magneticresonance imaging-guided attenuation and scattercorrections in three-dimensional brain positronemission tomography. Med Phys 2003;30:937–48.

[92] Evans A, Marrett S, Neelin P, et al. Anatomicalmapping of functional activation in stereotacticcoordinate space. Neuroimage 1992;1:43–53.