A Statistical Model-Based Approach for the Automatic Quantitative Analysis of Perfusion Gated SPECT Studies Sebastian Ordas1 , Santiago Aguad´e2 , Joan Castell2 and Alejandro Frangi1 1 Computational
Imaging Laboratory, Universitat Pompeu Fabra Pg Circumvallacio 8 - E08003, Barcelona, Spain 2 Hospital Universitat Vall d’ Hebron, Barcelona, Spain ABSTRACT
In this paper we present a statistical model-based approach to three-dimensional (3D) analysis of gated SPECT perfusion studies. By means of a 3D Active Shape Model (3D-ASM) segmentation algorithm, delineations of the endo- and epicardial borders of the left ventricle are obtained, in all temporal phases and image slices of the study. Prior knowledge was captured from a training set of cardiac MRI and SPECT studies, from which geometrical (shape) and grey-level (appearance) statistical models were built. From the fitted shape, a truly 3D representation of the left ventricle, a series of global and regional functional parameters can be assessed. A myocardial center surface representation is built on top of which scalar maps of perfusion, thickness or motion can be depicted. Preliminary results were quite encouraging, suggesting that statistical model-based segmentation may serve as a robust technique for routine use. Keywords: model-based segmentation, active shape model, myocardial perfusion imaging, SPECT quantitative analysis
1. INTRODUCTION Despite advances that have been made in the generation of new SPECT acquisition protocols and hardware technology, the automatic analysis of these studies still constitutes an open issue. In particular, clinicians seek for an improved robustness and accuracy in the segmentation task, in combination with better visualization and analysis capabilities, all within practical computation times compatible with clinical use. Any effort towards improving current software analysis packages, is thus highly valuable. In the last few years, the quantification of images using model-based approaches has gained very much attention in the medical image analysis community.1 The rationale behind these approaches is to use a generic template model of the structure of interest, which is subsequently instantiated or deformed to accommodate to the information provided by the image data. From the very many alternatives, a growing interest has been given to statistical model-based approaches since they allow learning shape statistics from a given population of training samples and therefore, are able to construct a compact and specific anatomical model. Moreover, they provide principled means to efficiently parameterize shape variability, thus allowing for dimensionality reduction. Statistical models of shape (ASM)2 and appearance (AAM)3 variability are two model-driven segmentation schemes initially put forward by Cootes et al. and subsequently further extended and applied by several groups to a variety of medical applications. 3D extensions of these methods are starting to appear,4–7 with an encouraging performance in segmenting the left ventricle in cardiac MRI, US, and CT; but were not yet applied to SPECT. The most exploited approaches for the automatic identification and segmentation of the left ventricle (LV) in clinical practise are the methods of Germano8 and Faber9 et al. These techniques start by identifying the LV region and long axis in the transaxial images, either manually or using a threshold-based approach.10, 11 The approach in8 continues by applying dilation and eroding operations in order to isolate the myocardium from the other organs. The center of mass of this mask (should be located inside the LV blood-pool, otherwise further refinement is required) constitutes the origin of a sampling coordinate system composed of radial count profiles. An ellipsoid is iteratively fit to a maximal count myocardial surface, which is considered to be located at the center For correspondence contact:
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Figure 1.
Examples of patients with perfusion defect areas.
of the myocardium. To determine the valve plane, once again, a threshold-based criteria is followed, using the geometry of the end-diastolic surface, onto which is mapped the count distribution averaged over all intervals.. Finally, an asymmetric Gaussian profile is adapted to every profile and the locations of plus and minus one standard deviations define the inner and outer myocardial surfaces. The commercially available analysis package QPS, developed at Cedars-Sinai Medical Center (Los Angeles, USA), uses this algorithm. The approach in9 employs a geometric modeling approach in which maximal count circumferential profiles are obtained as the center of the myocardium. The algorithm assumes that the myocardial thickness at end diastole (ED) is 1 cm, and it calculates myocardial thickening along the cardiac cycle by using Fourier analysis, assuming that the change in count is proportional to the change in thickness owing to the partial-volume effect. By determining the center and absolute thickness of the left ventricle myocardium at ED, the center of the myocardium and the percent thickening along the cardiac cycle are determined. The commercially available EC Toolbox, developed at Emory University (Atlanta, USA), uses this algorithm. In pathologic perfusion SPECT studies, situations with substantial sparse or missing information due to perfusion defects are quite common (see Fig. 1). In order to cope with them, the aforementioned algorithms use a large amount of parameters, rules and criteria that are empirically determined. Extracardiac uptake (liver and intestine) is a regular source of complication for these algorithms, as they tend to get attracted onto those stronger edges. This fact is specially harmful when the external uptake focus is close to the myocardium. We believe that the main drawback of these approaches is that their geometrical models are not appropriate for those circumstances. For instance, in our experience, when processing images of small hearts they tend to underestimate the LV volume at end systole (ES), giving an exaggerated ejection fraction (EF). In e.g.12 this fact was also evidenced. Because of the typical low resolution in SPECT, the cross-talk of perfusion data of opposite walls at ES, and the papillary muscle and blood background in the LV cavity, it is impossible to detect a non-existent endocardial border. Nevertheless, a priori information of the organ and confident information from other parts of the image (epicardium), should help determine a valid LV shape. Deformable models13 and levelset-based14, 15 algorithms are other more sophisticated approaches that were recently applied to SPECT segmentation, giving promising results on simulated data. However, further validation on real clinical cases, where artifacts and severe perfusion defects are very common, is needed. The correct determination of the mitral valve plane is very important for not inducing wrong volume estimates. A first attempt would be to manually set its location, with the consequent user dependency.16 One of the previously described segmentation methods9 approximate the mitral valve by two connected planes: one perpendicular to the LV long axis in the lateral half of the LV, and the other angled in the septal half of the LV. Their location and orientation are empirically fixed using thresholds of image maximum values found in the mid-ventricular portion of the LV. In another approach called the membrane algorithm,15 a deformable surface is initialized from the result of the myocardium segmentation. The drawback of this method is to rely on not having confounding image appearance in the basal region, a critical issue in non model-based algorithms like level sets.
Segmentation strategies based on statistical models learnt from heart examples can provide anatomical constraints to LV shape recovery, without entrusting on other ad hoc or simpler geometrical approximations like ellipsoids, constant thickness heart models, central myocardium positioned at the maximum intensity location of count profiles, myocardial borders given by inflexion points in radial count profiles, etc. Thanks to statistical constraints, these models are capable of efficiently handling situations with substantial sparse or missing information and providing shapes with valid heart anatomies, learnt from the training set. In synthesis, the applicability of a statistical model-based methodology in nuclear cardiac imaging constitutes our main hypothesis. To this aim, we have assessed the performance of a 3D-ASM algorithm in segmenting the left ventricle in perfusion SPECT studies. To our knowledge, this work constitutes the first application of such a technique in segmenting perfusion tomographic images. The employed methodology can work either on the acquired transaxial slices or the commonly used reformatted short axis images. This is a nice and important property of the method: it can work with arbitrarily oriented and sparse image data.7 The use of the transaxial slices is preferably because automatic techniques for reformatting the image data10, 17 sometimes fail, and time consuming operator assistance is required to define the LV long axis. Automatic reformatting procedures may also erroneously restrict the operating region of subsequently applied segmentation algorithms. If used directly on the transaxial images, our approach would not rely on the determination of the volume of interest, LV long axis, and basal plane, as a separate and critical preprocessing procedure. From the fitted shape, the long axis can be easily and automatically determined, and the reformatting performed. No operator manipulation would therefore be needed, other than for a rough model initialization. We have compared our segmentation results with respect to those obtained with Germano’s approach, in a preliminary test aimed as a proof-of-concept of our method. The evaluation data set comprised 25 studies (10 healthy and 15 pathologic). Global functional parameters like left ventricle ejection fraction (EF), chamber volume at end systole (ESV), and end diastole (EDV), were computed and compared. Other (regional) parameters like wall thickness, motion, and perfusion were only visually compared by the collaborating physicians. A software package coined QCIA (Quantitative Cardiac Image Analysis) for quantitative functional analysis and visualization of SPECT studies is currently under development. The application is written in C++ and is based on the Statistical Modeling Library (SMoLib) developed in our group, and the open source libraries VTK (Visualization Tool Kit), ITK (Insight Segmentation and Registration Tool Kit) and DCMTK (DICOM Tool Kit) for visualization, processing and DICOM interfacing, respectively. Already available features include wall thickness, myocardial perfusion and captation defect area assessment, polar maps, 3D animation tools, etc. An insight on these tools will also be provided. The paper proceeds by describing the 3D-ASM segmentation algorithm in the next section, the experimental setup in Sec. 3, and the results in Sec. 4. In Sec. 5 we present preliminary results on the development of automatic quantitative analysis and visualization tools for regional functional assessment. We conclude the article with a discussion and with some comments on future research in the topic.
2. THREE-DIMENSIONAL ACTIVE SHAPE MODEL (3D-ASM) An ASM comprises a shape (geometric) and an appearance (grey-level) model. The former primarily holds information about the shape and its allowed variations in a Point Distribution Model (PDM), determined by a Principal Component Analysis (PCA). The latter is responsible of learning grey-level patterns from the training set image data, that are to be compared against those identified in a new (unseen) image during the fitting stage. The algorithm therefore consists of an iterative process in which the appearance model looks into the image for new candidate positions to deform the shape model, under geometric constraints that keep the deformation process always within legal statistical limits. Our current research goes in the line of building statistical models capable of keeping separately the shape from the appearance models. This paper constitutes an example of such an approach, as the 3D-ASM was trained on image data sets of different modalities: the shape model was built from MRI studies, which have an excellent temporal and spatial resolution, and the appearance model from a training set of SPECT studies. Both models are described below.
2.1. Shape Model In a cardiac shape model, a set of landmarks is positioned in the endo- and epicardial boundaries of the ventricles. In order to guarantee that the final model will gather representative statistics of the underlying population, these landmarks should be placed in a consistent way over a large database of training shapes. A key step in building a shape model involves establishing these correspondences correctly; otherwise an inefficient parametrization of the object class will result. As there is no generally accepted definition of anatomically meaningful correspondence, it is difficult to judge its correctness. Even if a dense set of anatomical landmarks would exist in the object class and could be easily identified, manually specifying uniquely corresponding boundary points along the training set turns into an impractical, error-prone and subjective task. This is particularly evident in 3D, where the number of landmarks necessary to build a shape model increases dramatically. The statistical shape model used in this research was constructed with the autolandmarking method proposed by Frangi et al.18 In Ordas et al.,19 the behavior of this algorithm was assessed in a large database comprising 90 MRI studies of healthy and diseased hearts. These same shape models were used in this work, but we only considered a single ventricle representation, with a total of 2848 points (1777 in the epicardium and 1071 in the endocardium). Consider a set X = {xi ; i = 1 · · · n} with n of such autolandmarked shapes. Each shape is described by the concatenation of m 3–D landmarks pj = (p1j , p2j , p3j ); j = 1 · · · m. X is thus a distribution in a 3m-dimensional space. The goal is to obtain a general and compact representation of the population, learnt from the training set. This representation allows to approximate any shape by using the following linear model n
x=x ˆ + Φb
(1)
the model, and Φ is a where x ˆ = n1 i=1 xi is the average landmark vector, b is the shape parameter vector of n 1 x)(xi −ˆ x)T . The matrix whose columns are the principal components of the covariance matrix S = n−1 i=1 (xi −ˆ principal components of S are the eigenvectors, φi , with corresponding eigenvalues, λi (sorted so that λi ≥ λi+1 ). If Φ contains only the first t < min{m, n} eigenvectors corresponding to the largest non-zero eigenvalues, we can approximate any shape of the training set, x, using Eq. (1) where Φ = (φ1 |φ2 | · · · |φt ) and b is a t-dimensional ˆ). Assuming that the cloud of landmark vectors follows a multi-dimensional vector given by b = ΦT (x − x Gaussian distribution, the variance of the i-th parameter, bi , across the training set is given by λi . As a prerequisite for a correct shape description, the samples have to be normalized with respect to a reference coordinate frame. Normalization is needed in order to eliminate differences across objects due to rotation, translation and size. Once the shape samples are aligned, the remaining differences are solely shape-related and thus, the effect of trivial variations in pose and scale is eliminated.
2.2. Appearance Model The procedure that we adopted for building the appearance model can be interpreted as a 3D extension of the basic 2D-ASM scheme.2 In a 3D application, the model mesh intersects the image planes in a set of intersection points that do not necessarily belong to the model’s mesh. If the model is divided into regions, the intersection points can be assigned to one of these labeled regions and therefore, instead of building an appearance model for every point (2D case), we can build one for every region. In our implementation, a total of 18 appearance models were built from the training set (described below) (fig. 2(a)). Each one is composed of a mean and a covariance matrix of normalized grey-level profiles. The partial volume effect is responsible for myocardium intensity variations during the cardiac cycle (the myocardium appears brighter at end systole and darker at end of diastole). Normalization is therefore needed to be independent of global intensity variations. We decided not to use a multi-resolution framework as it is usual in ASM-like methods. The reason was two-fold. On the one hand, in SPECT images the LV borders present a smooth transition, and further smoothness was not desired. On the other hand, we did not experience problems with convergence, being this fact the principal reason for using those schemes. To construct the appearance model, expert segmentations where manually drawn in the rest and stress stages of 10 normal perfusion studies from Vall d’ Hebron University Hospital (Barcelona, Spain). Patients were imaged 1 hour after administration of 99mTc-tetrofosmin using an Elscint SP4 (Elscint, Ltd., Haifa, Israel) scintillation camera with a high resolution collimator. The acquisition matrix size was 64 x 64 pixels with an isotropic voxel of 5.293 mm3 . Reconstructions were reformatted into short axis slices using the software provided by the acquisition system.
Figure 2.
3D-ASM matching procedure. (a) Region definition in the shape model (shown surface corresponds to the epicardium of the mean shape), (b) intersection of the model with the image planes, (c) points originated from the intersection of the model with a single image slice, and (d) forces propagation from a single intersection point to the rest of the nodes in the mesh using a weighting function (Gaussian kernel) decaying with the geodesic distance to the origin of the update. The extent of propagation is indicated with the shaded region around the point.
(a) Figure 3.
(b)
(c)
Linear regression analysis to correlate EF (a), EDV (b), and ESV (c) measurements obtained by the QPS and QCIA methods.
2.3. Matching Procedure The 3D-ASM matching procedure that we followed has been described in detail in the work of van Assen et al.7 ; it is therefore only summarized here. The algorithm starts by roughly positioning the mean shape at the center of the heart. It is important to scale the initial shape so that it spans through all image slices and to (roughly) orient it perpendicular to the stack of short axis slices. For every iteration of the algorithm, the image planes intersect the model’s mesh yielding stacks of 2D contours (Fig. 2(b)). These contours are composed of the intersections of the image planes with individual mesh triangles. Candidate displacements are searched in every image slice, by evaluating the Mahalanobis distance between the actual grey-level profiles and the mean profile stored for each region. The resulting candidate points act as forces that deform the mesh, but are only available at the intersections with the image planes (Fig. 2(c)). Forces propagation to the rest of the nodes in the mesh is performed by a weighting function (Gaussian kernel) decaying with the geodesic distance to the origin of the update (Fig. 2(d)). To facilitate through-plane motion, force vectors are projected on the model surface normals, which also have a component perpendicular to the image planes. The resulting propagated mesh is projected on the model’s subspace, yielding a model parameter vector and a new model instance by using Eq. 1. The steps above are repeated either for a fixed number of iterations or until convergence is achieved, given some decision rule. In our experiments, the algorithm was set to run for a fixed number of iterations (60) using 95% of the total shape model variability. The entire process, from LV segmentation to global and regional functional parameters calculation, takes approximately 1.5 minutes for each gated phase of the study, on a dual Xeon 2.8 GHz CPU, 2 GHz RAM under Linux Fedora 2. In order to be compatible with daily clinical practise, further speed-up of the process is necessary.
Figure 4.
Statistical model-based segmentation. A priori knowledge learnt from examples provides anatomical constraints to LV shape recovery, producing valid LV shapes even in cases with severe perfusion defects. Shown examples are the same of Fig.1.
Figure 5.
Apical perfusion defect artifact. A case illustrating the differences in LV shape recovery. The EDV measured with QPS (a) was 81ml and with QCIA (c), 98ml. LVEF with QPS was 40% and with QCIA, 32%. In (c) and (d), a 3D display of the endocardial surface excursion from the end diastolic gated phase (grid) with the QPS and QCIA algorithms, respectively. There is a clear difference in the LV shape recovered with the two methods.
3. EXPERIMENTS We have compared our segmentation results with those assessed with Germano’s QPS package by means of a linear regression analysis, to correlate EF, EDV, and ESV measurements obtained with the two methods. None operator corrections were made in any case. The data set used for the segmentation tests comprised 25 gated perfusion SPECT studies, all covering eight temporal phases. 10 were normal studies and 15 were patients with coronary artery disease. Patients were imaged 1 hour after administration of 99mTc-tetrofosmin using a Siemens ECAM SPECT (Siemens Medical Systems, Illinois, USA) system with a double-detector at 90 with high resolution collimators. Image data with a voxel dimension of 5.763 mm3 was reformatted into standard short axis slices using the software provided by the acquisition system.
4. RESULTS Automated processing was successful in 100% of analyzed studies using our QCIA platform. A reasonable linear agreement with the QPS method was observed for EF (y = 6.76 + 0.76 x, r2 = 0.88), EDV (y = -31 + 1.43 x, r2 = 0.93), and ESV (y = -2.39 + 1.24 x, r2 = 0.96) measurements. Fig. 3 displays these quantitative results. We have identified the determination of the mitral valve plane as the main cause of LV volume estimation discrepancies. Our shape model was built from a training set of MRI studies, thereby providing high resolution anatomical constraints to LV shape recovery. Because expert segmentations spanned from the base to the apex, the deformation process itself made the shape deform and grow towards an acceptable position of the basal plane and apex. In this way, the method does not need the detection of the mitral valve plane as a separate procedure; but the current approach can be extended with some (automatic) methodology that can provide an “anchor” plane to the fitting process.
Figure 6.
Segmentation on the transaxial image slices of the non-gated (time-compressed) images of the same previous study of Fig.5. None delimitation of the volume of interest around the LV was used as a preprocessing step. This example illustrates the independence of the method to the reformatting of the images.
Figure 7.
External uptake artifact. The endocardial border estimated by the QPS method lies erroneously proximal to the external focus uptake (a). This artifact is clear from the 3D display of endocardial LV excursion (b). QCIA results in the same slice (c), endocardial LV excursion (d) and 3D rendering of the retrieved LV shape (e), are visually satisfactory.
Two cases gave an erroneous LV delineation with QPS. They are described below as they serve as examples of the benefits implied by the use of anatomically-based shape modeling. In Fig. 4 the segmentation results on the same examples with perfusion defects of Fig. 1 are shown. Very low but still existing levels of counts are frequently seen in many severely hypoperfused areas. Nevertheless, when there is not perfusion data (counts) at all, it is not possible to find edges that do not exist. This is particular problematic when the scarring is apical20 and the most apical boundary of the LV cannot be seen. Fig. 5 shows an example for which the (automatic) reformatting software failed to circumscribe the correct volume of interest due to this problem. Fig. 5 (a, c) show how QPS could not overcome this situation. Our method provided a correct anatomical interpolation in the apex with a smooth connection between non-infarcted portions of the wall, based on reliable information from other parts of the image. Figs. 5 (b, d) show this case. The EDV (phase shown) measured with QPS was 81 ml and with QCIA, 94.84 ml. LVEF with QPS was 40% and with QCIA, 32%. There is a clear difference in the LV shape recovered with the two methods. Consequently, regional functional parameters like wall thickness and perfusion may also differ, but this issue was not compared in this work. In Fig. 6 it is shown the segmentation result on the non-gated (time-compressed) images of the same study, but directly on the transaxial (non reformatted) images; without any previous delimitation of the volume of interest around the LV. The volume measured in this case was 102 ml. In the second case, a healthy study with an external uptake focus (intestine) close to the myocardium led to an erroneous LV delineation with the QPS approach: the brighter spot attracted the estimated border towards its vicinity. From Figs. 7 (a-b) it is clear that the LV shape retrieved by the QPS method was not anatomically plausible. Figs. 7 (c-e) show the segmentations with QCIA. The local bump was not seen in any of the MRI training examples and therefore, the shape model retrieved a similar (without the bump) but still valid LV shape.
Figure 8.
Myocardial central surface. For every point in the endocardial surface, the shortest distance to the epicardial surface is assessed (a). The middle points in all these segments are collected and based on the same mesh connectivity of the endocardial surface, a new mesh is built. For regional wall thickness assessment, each node in the central surface is assigned a scalar value proportional to the length of its correspondent segment (b). In (c) an example is illustrated showing the center surface surrounded by the endocardial and epicardial intersections with the image planes.
Figure 9.
Perfusion map. Having achieved an accurate LV segmentation, a center surface representation is constructed with a perfusion map on its surface (a). The perfusion defect extension (b) is assessed based on normal limits calculated from a (selectable) reference database or by comparing the rest/stress states of the same patient.
5. QUANTIFICATION AND VISUALIZATION TOOLS FOR LV FUNCTION ASSESSMENT In this section we provide an insight on automatic quantitative analysis and visualization tools for regional functional assessment, still under development in the QCIA platform. Myocardial Central Surface From the fitted shape, for every point in the endocardial surface, the shortest distance to the epicardial surface is assessed. A myocardial center surface is built by collecting the middle points in all these segments and using the same mesh connectivity of the endocardial surface (see Figs. 8 (a-b)). Wall Thickness A wall thickness map is constructed by simply defining a scalar for every point in the middle surface with a value proportional to the longitude of the corresponding segment (Fig. 8 (c)). Perfusion Map A scalar is defined for every intersection point between the myocardial center surface and the image planes, with a value proportional to the average of counts along the corresponding profile. The rest of the points in the mesh are assigned an interpolated value resulting from averaging the nearest intersection points, weighted by the geodesic distance to them (Fig. 9 (a)).
Figure 10.
Preliminary results of the developed quantification and visualization tools. In the first row, the endocardial surface excursion from the end diastolic gated phase. In the 3D animation tool, it is possible to fix the shape centroid or the long axis. None of them were fixed in this example. The second and third rows illustrate the myocardial central surface with perfusion and wall thickness maps.
Perfusion Defect Area Assessment A surface representation is built only considering those portions of the perfusion map which are outside the normal captation range defined from a population of normal studies or with respect to rest/stress states of the same patient (Fig. 9 (b)). Endocardial Excursion In our approach it is possible to fix the position either of the shape model centroid, the LV long axis, or none of them. Any combination of the previous maps can easily be rendered in the 3D animation tool. Fig. 10 may serve as an example. The minimum and maximum values for the scalar ranges of the previously described tools can be calculated from a selectable population of normal studies or from rest/stress states of the same patient.
6. CONCLUSIONS A 3D statistical model-based algorithm was used for the segmentation of the left ventricle in dynamic perfusion SPECT studies. The method was applied successfully to 25 clinical studies, and runs fully automatic; providing segmentation results perfectly reproducible. Once the automatic segmentation of every phase is obtained, global
and regional functional parameters can be calculated. The availability of an accurate endo- and epicardial surface segmentation allowed for the construction of a myocardial center surface representation on top of which scalar maps of perfusion and wall thickness can be depicted in a per time frame and/or per stage (rest/stress) fashion. Such a representation of radio tracer captation difference between stress and rest changes can be visualized and localized directly on raw patient data. The developed statistical model can keep separately the geometric (shape) from the grey-level (appearance) models. In this way, it is possible to train the algorithm on image data sets of different modalities. The high resolution of functional MRI studies allowed for using an anatomically well-described LV shape representation. Our method does not use any additional a priori hints like manual or automatic mitral valve plane location or region of interest definition. While the former would be valuable in future versions of the algorithm, the latter is not necessary.
7. ACKNOWLEDGEMENTS This work was partially funded by Red IM3: Imagen M´edica Molecular y Multimodalidad (ISCIII G03/185), Redes Tem´aticas Colaborativas, Ministerio de Sanidad y Consumo de Espa˜ na (http://im3.rediris.es) and TIC200204495-C02 grants. GridSystems S.A., Palma de Mallorca, Spain (http://www.gridsystems.com) is also acknowledged for providing the InnerGrid Nitya Middleware for grid computing and technical support. The work of S. Ordas is supported by the Spanish Ministry of Education under a FPU Grant AP2002-3955. The work of A.F. Frangi is supported by the Spanish Ministry of Science and Technology under a Ram´ on y Cajal Research Fellowship.
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