Brian F. Hutton

Image registration: an essential tool for nuclear medicine

Abstract. There is increasing interest in being able to automatically register medical images from either the same or different modalities. Registered images are proving useful in a range of applications, not only providing more correlative information to aid in diagnosis, but also assisting with the planning and monitoring of therapy, both surgery and radiotherapy. The practising nuclear medicine specialist is faced with a dilemma in choosing an appropriate method since the literature in the field is extensive, with conflicting evidence as to what methods are optimal. Although most barriers to implementing registration in routine practice have been removed, there remains a lack of commercial, validated software. The alternative is to install a dual-modality instrument. The objective of this review is to present a general overview of medical image registration with emphasis on the application and issues relevant to nuclear medicine.

A clinical perspective of accelerated statistical reconstruction

Although the potential benefits of maximum likelihood reconstruction have been recognised for many years, the technique has only recently found widespread popularity in clinical practice. Factors which have contributed to the wider acceptance include improved models for the emission process, better understanding of the properties of the algorithm and, not least, the practicality of application with the development of acceleration schemes and the improved speed of computers. The objective in this article is to present a framework for applying maximum likelihood reconstruction for a wide range of clinically based problems. The article draws particularly on the experience of the three authors in applying an acceleration scheme involving use of ordered subsets to a range of applications. The potential advantages of statistical reconstruction techniques include: (a) the ability to better model the emission and detection process, in order to make the reconstruction converge to a quantitative image, (b) the inclusion of a statistical noise model which results in better noise characteristics, and (c) the possibility to incorporate prior knowledge about the distribution being imaged. The great flexibility in adapting the reconstruction for a specific model results in these techniques having wide applicability to problems in clinical nuclear medicine.

Monte Carlo and experimental evaluation of accuracy and noise properties of two scatter correction methods for SPECT

Scatter correction is a prerequisite for quantitative SPECT, but potentially increases noise. Monte Carlo simulations (EGS4) and physical phantom measurements were used to compare accuracy and noise properties of two scatter correction techniques: the triple-energy window (TEW), and the transmission dependent convolution subtraction (TDCS) techniques. Two scatter functions were investigated for TDCS: (i) the originally proposed mono-exponential function (TDCSmono) and (ii) an exponential plus Gaussian scatter function (TDCSGauss) demonstrated to be superior from our Monte Carlo simulations. Signal to noise ratio (S/N) and accuracy were investigated in cylindrical phantoms and a chest phantom. Results from each method were compared to the true primary counts (simulations), or known activity concentrations (phantom studies). 99mTc was used in all cases. The optimized TDCS(Gauss) method overall performed best, with an accuracy of better than 4% for all simulations and physical phantom studies. Maximum errors for TEW and TDCS(mono) of -30 and -22%, respectively, were observed in the heart chamber of the simulated chest phantom. TEW had the worst S/N ratio of the three techniques. The S/N ratios of the two TDCS methods were similar and only slightly lower than those of simulated true primary data. Thus, accurate quantitation can be obtained with TDCS(Gauss), with a relatively small reduction in S/N ratio.

Minimum cross-entropy reconstruction of PET images using prior anatomical information

An algorithm is presented for the reconstruction of PET images using prior anatomical information derived from MR images of the same subject. The cross-entropy or Kullback-Leiber distance is a measure of dissimilarity between two images. We propose to reconstruct PET images by minimizing a weighted sum of two cross-entropy terms. The first is the cross-entropy between the measured emission data and the forward projection of the current estimate of the PET image. Minimizing this term alone is equivalent to the ML-EM reconstruction. The second term is the cross-entropy between the current estimate of the PET image and a prior image model which incorporates anatomical information derived from registered MR images. A weighting parameter determines the relative emphasis given to the emission data and the prior model in the reconstruction. Details of this algorithm are presented as well as test reconstructions for real and simulated data. The performance of the algorithm was evaluated with respect to errors in prior anatomical information. The algorithm provided significant improvement in the quality of reconstructed images as compared with the ML-EM reconstruction technique. The reconstructed images had higher resolution as compared with the images obtained from MAP-like reconstructions which do not utilize anatomical information. The algorithm displayed robustness with respect to errors in prior anatomical information.

Application of distance-dependent resolution compensation and post-reconstruction filtering for myocardial SPECT

Compensation for distance-dependent resolution can be directly incorporated in maximum likelihood reconstruction. Our objective was to examine the effectiveness of this compensation using either the standard expectation maximization (EM) algorithm or an accelerated algorithm based on use of ordered subsets (OSEM). We also investigated the application of post-reconstruction filtering in combination with resolution compensation. Using the MCAT phantom, projections were simulated for 360 degrees data, including attenuation and distance-dependent resolution. Projection data were reconstructed using conventional EM and OSEM with subset size 2 and 4, with/without 3D compensation for detector response (CDR). Also post-reconstruction filtering (PRF) was performed using a 3D Butterworth filter of order 5 with various cutoff frequencies (0.2-1.2 cycles cm(-1)). Image quality and reconstruction accuracy were improved when CDR was included. Image noise was lower with CDR for a given iteration number. PRF with cutoff frequency greater than 0.6 cycles cm(-1) improved noise with no reduction in recovery coefficient for myocardium but the effect was less when CDR was incorporated in the reconstruction. CDR alone provided better results than use of PRF without CDR. Results suggest that using CDR without PRF, and stopping at a small number of iterations, may provide sufficiently good results for myocardial SPECT. Similar behaviour was demonstrated for OSEM.

Improved efficiency for MRI-SPET registration based on mutual information

Abstract.Mutual information has been proposed as a criterion for image registration. The criterion is calculated from a two-dimensional grey-scale histogram of the image pair being registered. In this paper we study how sparse sampling can be used to increase speed performance using the registration algorithm of Maes et al. (IEEE Trans Med Imaging 1997; 16: 187–198) with a focus on registration of MRI-SPET brain images. In particular we investigate how sparse sampling and parameters such as the number of bins used for the grey-scale histograms and smoothing of the data prior to registration affect accuracy and robustness of the registration. The method was validated using both simulated and human data. Our results show that sparse sampling introduced local maxima into the mutual information similarity function when the number of bins used for the histograms was large. To speed up registration while retaining robustness, smoothing of the data prior to registration was used and a coarse to fine subsampling protocol, where the number of bins in the histograms were dependent on the subsampling factor, was employed. For the simulated data, the method was able to recover known transformations with an accuracy of about 1 mm. Using the human data, there were no significant differences in the recovered transformation parameters when the suggested subsampling scheme was used compared with when no subsampling was used, but there was a more than tenfold increase in speed. Our results show that, with the appropriate choice of parameters, the method can accurately register MRI-SPET brain images even when very efficient sampling protocols are used.

Validation of fully automatic brain SPET to MR co-registration

Abstract.Fully automatic co-registration of functional to anatomical brain images using information intrinsic to the scans has been validated in a clinical setting for positron emission tomography (PET), but not for single-photon emission tomography (SPET). In this paper we evaluate technetium-99m hexamethylpropylene amine oxime to magnetic resonance (MR) co-registration for five fully automatic methods. We attached six small fiducial markers, visible in both SPET and MR, to the skin of 13 subjects. No increase in the radius of SPET acquisition was necessary. Distortion of the fiducial marker distribution observed in the SPET and MR studies was characterised by a measure independent of registration and three subjects were excluded on the basis of excessive distortion. The location of each fiducial marker was determined in each modality to sub-pixel precision and the inter-modality distance was averaged over all markers to give a fiducial registration error (FRE). The component of FRE excluding the variability inherent in the validation method was estimated by computing the error transformation between the arrays of MR marker locations and registered SPET marker locations. When applied to the fiducial marker locations this yielded the surface registration error (SRE), and when applied to a representative set of locations within the brain it yielded the intrinsic registration error (IRE). For the best method, mean IRE was 1.2 mm, SRE 1.5 mm and FRE 2.4 mm (with corresponding maxima of 3.3, 4.3 and 5.0 mm). All methods yielded a mean IRE <3 mm. The accuracy of the most accurate fully automatic SPET to MR co-registration was comparable with that published for PET to MR. With high standards of calibration and instrumentation, intra-subject cerebral SPET to MR registration accuracy of <2 mm is attainable.

Non-rigid image registration using a median-filtered coarse-to-fine displacement field and a symmetric correlation ratio

Conventional approaches to image registration are generally limited to image-wide rigid transformations. However, the body and its internal organs are non-rigid structures that change shape due to changes in the bodys posture during image acquisition, and due to normal, pathological and treatment-related variations. Inter-subject matching also constitutes a non-rigid registration problem. In this paper, we present a fully automated non-rigid image registration method that maximizes a local voxel-based similarity metric. Overlapping image blocks are defined on a 3D grid. The transformation vector field representing image deformation is found by translating each block so as to maximize the local similarity measure. The resulting sparsely sampled vector field is median filtered and interpolated by a Gaussian function to ensure a locally smooth transformation. A hierarchical strategy is adopted to progressively establish local registration associated with image structures at diminishing scale. Simulation studies were carried out to evaluate the proposed algorithm and to determine the robustness of various voxel-based cost functions. Mutual information, normalized mutual information, correlation ratio (CR) and a new symmetric version of CR were evaluated and compared. A T1-weighted magnetic resonance (MR) image was used to test intra-modality registration. Proton density and T2-weighted MR images of the same subject were used to evaluate inter-modality registration. The proposed algorithm was tested on the 2D MR images distorted by known deformations and 3D images simulating inter-subject distortions. We studied the robustness of cost functions with respect to image sampling. Results indicate that the symmetric CR gives comparable registration to mutual information in intra- and inter-modality tasks at full sampling and is superior to mutual information in registering sparsely sampled images.

Transmission-based scatter correction of 180° myocardial single-photon emission tomographic studies

Meaningful comparison of single-photon emission tomographic (SPET) reconstructions for data acquired over 180° or 360° can only be performed if both attenuation and scatter correction are applied. Convolution subtraction has appeal as a practical method for scatter correction; however, it is limited to data acquired over 360°. A new algorithm is proposed which can be applied equally well to data acquired over 180° or 360°. The method involves estimating scatter based on knowl edge of reconstructed transmission data in combination with a reconstructed estimate of the activity distribution, obtained using attenuation correction with broad beam attenuation coefficients. Processing is implemented for planes of activity parallel to the projection images for which a simplified model for the scatter distribution may be applied, based on the measured attenuation. The appropriate broad beam (effective) attenuation coefficients were determined by considering the scatter buildup equation. It was demonstrated that narrow beam attenuation coefficients should be scaled by 0.75 and 0.65 to provide broad beam attenuation coefficients for technetium-99m and thallium-201 respectively. Using a thorax phantom, quantitative accuracy of the new algorithm was compared with conventional transmission-based convolution subtraction (TDCS) for 360° data. Similar heart to lung contrasts were achieved and correction of 180° data yielded a 10.4% error for cardiac activity compared to 5.2% for TDCS. Contrast for myocardium to ventricular cavity was similarly good for scatter-corrected 180° and 360° data, in contrast to attenuation-corrected data, where contrast was significantly reduced. The new algorithm provides a practical method for correction of scatter applicable to 180° myocardial SPET.

Correction of partial volume effects in myocardial SPECT

BackgroundMarked partial volume effects occur in myocardial single photon emission computed tomographic (SPECT) studies because of limited resolution in imaging the myocardial wall and contractile motion of the heart. Little work has been undertaken to develop correction techniques for SPECT except for efforts to improve the reconstructed resolution. Our purpose was to examine the extent of the problem and propose a correction method.Methods and ResultsA potential correction method, developed initially for positron emission tomography, involved estimation of extravascular density by means of subtracting vascular density derived in a blood pool study from total density derived from a transmission study. Provided partial volume errors are the same for transmission and emission data, activity per gram of extravascular tissue can be obtained by means of dividing the perfusion regional data by extravascular density for the same region. Simulations were designed to assess the importance of partial volume errors and the use of extravascular density to correct the errors. Recovery coefficients for the myocardium were estimated by means of simulation of the beating heart on the basis of published values for ventricular dimensions. Resolution for transmission with a scanning line source system was compared with emission resolution. The effect of spillover on measured partial volume losses was assessed, and a method for matching spillover for emission and extravascular density was demonstrated. Correction for partial volume effects was demonstrated for a phantom with variable wall thickness.Significant variation in recovery coefficient was demonstrated between posterior and septal walls for individual patients independent of heart size. Filtering was necessary to account for the difference in transmission resolution measured in the axial direction. Spillover effects has a significant influence on the measured recovery for small objects; however, for a specific reconstruction algorithm and defined region size, correction was implemented to match the spillover effects for emission and extravascular density. Use of extravascular density for correction of partial volume loss, for ordered subsets expectation maximization reconstruction with compensation for resolution, was demonstrated to be accurate to within 10%.ConclusionsThe feasibility of correcting partial volume effects with extravascular density was demonstrated. Correction is effective provided care is taken to match both resolution and spillover for emission and extravascular density.