FrP1B4.6 I. INTRODUCTION

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1 Proceedings of the 9th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 3-6, 007. Optimal Clustering of Kinetic Patterns on Malignant Breast Lesions: Comparison between K-means Clustering and Three-time-points Method in Dynamic Contrast-enhanced MRI FrPB4.6 S. H. Lee,3, J. H. Kim,,3,*, K. G. Kim,3, J. S. Par, S. J. Par,3, W. K. Moon Interdisciplinary Program in Radiation Applied Life Science, Seoul National University College of Medicne, Korea Department of Radiology, Seoul National University Hospital, Korea 3 Intitute of Radiation Medicine, Seoul National University Medical Research Center, Korea Abstract Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is useful for breast cancer diagnosis and treatment planning. Nevertheless, due to the multi-temporal nature of DCE-MRI data, the assessment of early stage breast cancer is a challenging tas. In this study, we applied an unsupervised clustering approach and cluster validation technique to the analysis of malignant intral-tumoral inetic curves in DCE-MRI. K-means cluster analysis was performed from real world malignant tumor cases and the data were transformed into an optimal number of reference patterns representative each cluster. The optimal number of clusters was estimated by a cluster validation index, which was calculated with the ratio of inter-class scatter to intra-class scatter. This technique then classifies tumor specific patterns from a given MRI data by measuring the vector distances from the reference pattern set, and compared the result from the - means clustering with that from three-time-points (3TP) method, which represents a clinical standard protocol for analysis of tumor inetics. The evaluation of twenty five cases indicates that optimal -means clustering reflects partitioning intra-tumoral inetic patterns better than the 3TP technique. This method will greatly enhance the capability of radiologists to identify and characterize internal inetic heterogeneity and vascular change of a tumor in breast DCE-MRI. Keywords DCE-MRI, breast cancer, inetics, -means clustering, 3TP method, visualization I. INTRODUCTION Dynamic contrast-enhanced MRI (DCE-MRI) has been successfully applied for detection and staging of breast cancer as well as differentiation between malignant and benign lesions [-4]. DCE-MRI is useful for determining the biological properties of a tumor because contrast enhancement features are representative of histologic features of the tumor [5-7]. One of the roles of DCE-MRI is in optimizing treatment of candidates for breast conservation surgery. In order to optimize the results of breast-conserving therapy, accurate assessment of tumor extent prior to surgery and monitoring of preoperative chemotherapy to achieve downstaging of malignancy are required. Especially, in case of only partial response, to reliably visualize the size and location of the residual tumor is necessary in order to better plan the subsequent surgical therapy. The cancerous intra-tumoral inetic patterns can be used as surrogate information for early measures of response in clinical trials of molecularly targeted anti-angiogenic therapies and for the local recurrence in invasive cancer. This method has not only the potential to provide information on microvascular physiology, but is also non-invasive and spares the potential morbidities of biopsy, lending itself to serial measurements through a course of therapy. The importance of defining the physiological characteristics of tumors and their microvessels is central to imaging evaluations of therapeutic interventions. Angiogenic microvessels, important for the growth and survival of cancer cells, are characterized in part by larger endothelial cell gaps resulting in greater permeability to small molecules [8]. Thus, spatial heterogeneity in the inetics of contrast transit is thought to reflect variations in tissue perfusion and microvascular permeability [9]. American college of radiology (ACR) breast imaging and reporting data system (BI-RADS) describes the initial slope from pre-contrast phase to the initial enhancement phase, and the delayed slope in the later phases for inetic curve assessment [0]. To interpret breast MR studies using the BI-RADS criteria, enhancing regions need to be visually identified and delayed enhancement is typically assessed using signal intensity (SI) time curves. Degani et al. and Furman-Haran et al used the contrast enhancement patterns obtained at three-time-points (3TP) during contrast uptae to produce a color-coded parametric map [-3]. The enhancement rate defined by the intensity difference in the first two time points (the wash-in phase) was coded by color intensity, and the change in enhancement between the second and third time points (the wash-out phase) was coded by color hue. Kuhl et al showed that the use of curve shape (washout, plateau, or persistent enhancement) based on three-time-points (3TP) method could distinguish malignant lesions from benign [4]. Curves that exhibited a washout type behavior after initial enhancement had an 87% probability of being malignant, whereas curves that exhibited persistent only showed a 6 % lielihood of being malignant. Washout behavior of lesions has also been shown to be correlated with tumor angiogenesis and vascular permeability [5]. However, other many investigators have found that there was a considerable overlap in the range of enhancement rates of malignant and benign lesions [6] /07/$ IEEE 089

2 The 3TP method does not consider enhancement patterns at full time points. In addition, the enhancement pattern varies according the imaging protocol and all of the first post contrast series of malignant tumors with wash-out behavior in late phase do not show the pea contrast enhancement. Thus, our hypothesis is that the model-free approach to use full time points will suitable to classifying the various inetic patterns of real-world tumors and to better reflecting their therapeutic changes of tissue perfusion and microvascular permeability in terms of classification accuracy and details. In this study, we attempted to classify the intra-tumoral inetic patterns in breast DCE-MRI into the optimal number of reference patterns acquired from -means clustering and cluster validation technique, and to compare with the results from 3TP method. The -means clustering was additionally applied by six clusters in order to agree with the number of class representatives in the 3TP method. The color-coded maps were visualized by assigning the intra-tumoral inetic patterns to class representatives from -means clustering and 3TP method, respectively. Finally, the classification accuracy was estimated by the validation of classification scatters for each method. A. Materials II. METHODOLOGY The study population consisted of 5 total patients with histological proven carcinoma. All lesions were infiltrating ductal carcinoma. All patients were scanned on a.5 T Sonata (Siemens, Erlangen, Germany). First, the precontrast T weighted three dimensional fast low angle shot (3D FLASH) sagittal image (field of view 00 mm, matrix , slice thicness mm ) was obtained with fat suppression, and four consecutive post-contrast images using the same condition after an injection of 0. mmol/ g Gd-DTPA (Magnevist, Schering, Berlin, Germany) (Table ). The contrast medium was administered manually at a flow rate of ml /s for 5 sec and the imaging was performed within 5 sec after injecting the contrast agent. Imaging Time TABLE I PROTOCOL FOR DCE-MR IMAGING Magnet Srength (T) TR/TE (ms) Flip Angle Pre-contrast /.83 Post-contrast B. Data Acquisition Scan Time (sec) Before selection of time curves, all series were aligned using a 3D rigid registration algorithm based on open source Insight Toolit (ITK). After that, the maximum intensity 84 image among every time series was made in order to use as the reference image for segmentation of tumor volume. The segmentation was performed semi-automatically by combination of 3D connected threshold region growing method and 3D erosion and dilation. The segmentation volume was not significantly different from the radiologist s tumor VOI. The enhancement patterns were collected voxel by voxel from the entire segmented tumor VOIs. The total number of the enhancement patterns was 3,67,60 and these patterns were used as input data for clustering. C. 3TP Method The enhancement curves in each tumor volume were classified based on the contrast enhancement criteria of the 3TP method. The inetic properties of the tumor were quantified by computing percentage enhancement (PE) and signal enhancement ratio (SER) defined as followings expressions (Figure ). s pre PE = pre () s pre SER = s pre () where S 0, S and S are the pre-contrast (baseline), the initial post-contrast and the last post-contrast signal intensities. Fig.. Voxel classification scheme based on PE and SER values D. K-means Clustering The -means clustering algorithm was used to divide all enhancement curves from tumor volumes into clusters. The result was a set of centers, each of which was located at the centroid of the partitioned dataset. This algorithm was performed in the following steps (Figure ) and notations used in this algorithm are given at Table. ) The numbers of cluster and iteration were chosen and the inetic dataset was inputted. The initial candidates 090

3 for the cluster centers were randomly selected from the dataset. for ( j) ( r j) Sb Pj x = Sw= Pj xi vj j= j= xi Cj (5) TABLE II NOTATIONS USED IN K-MEANS ALGORITHM Fig.. Steps of -means clustering algorithm The number of clusters m(c j x i) N N j x i v j C j S w S b P j The total number of patterns The number of patterns from class v j The ith pattern The centroid of the jth cluster The jth cluster Inter-class scatter index Intra-class scatter index The probability of class v j (N j/n) E ( r j) ( j ) x Membership function {0. } Error function The nearest neighbor pattern within the nearest centroid outside of class v j The nearest neighbor pattern within class v j ( r j) from ) Each pattern was assigned to the nearest cluster using a vector distance measure. For each pattern, the membership function was calculated in each cluster. The membership function defined the proportion of a pattern that belongs to a cluster. The -means algorithm used a hard membership function which assigns each inetic signal to a single cluster. 3) The centroids (centers) of these clusters were recalculated to find new cluster centers and the sum of the square errors between a centroid and its membership inetic patterns in each cluster was calculated. vj n mc ( j xi) xi i= for j=,, (3) n mc ( j xi) i i j for i=,, n; j=,,. (4) j= xi Cj = = E = x v 4) If a centroid had no membership pattern, the candidate of the center from the dataset until all centroids included more than a single membership pattern. Step ) and 3) were repeated until it converged. In this study, the convergence criterion was where there was no more reassignment of patterns to new clusters when the change of the sum of square errors (E) fell below a threshold. 5) Cluster validation index (CVI) was calculated in order to obtain optimal partitions of clusters as the ratio of inter-class scatter to intra-class scatter from = to 0 by the following our proposed formulas. S CVI = S b w E. Evaluation of Classification Accuracy The centroids of the enhancement curves calculated from the -means clustering algorithm were used to classify the inetic patterns within the segmented tumor volume in DCE-MRI. The classification criterion was to assign each inetic curve to the nearest reference centroid using distance measure. The 3TP method also assigned each inetic curve to the relevant class using PE and SER values. Classification scatter index (CSI) was proposed as the method for evaluation of classification accuracy. The CSI was given by the probability and the standard deviation (SD) of each class as the following expression. F. Image Visualization Pj SDj j= CSI =. (6) The voxels corresponding to the position of inetic curves assigned by each classification criterion were highlighted with different colors, which were raned by the magnitude of the initial enhancement of the -means cluster centroids or by the classification scheme of the 3TP method. III. RESULTS The classification results were represented within a tumor volume by different colors reflecting each reference pattern. The homogeneity or heterogeneity of the enhancement patterns within the tumor volume was able to be visually identified (Figure 3). The optimal number of the -means clustering obtained from our dataset was 8 based on 09

4 (a) (b) (c) Fig. 3. Volume rendering by cropping a tumor volume and classification results from each reference patterns; (a) 3TP method, (b) -means clustering (=6), (c) optimal -means clustering (=8) the CVI from = to 0. The classification accuracy of - means clustering with the optimal number of clusters (=8) was not only better than that of the 3TP method based on CSI in all patients except two patients, but also that of - means clustering with six clusters. A part of the inetic curves extracted from our dataset and the -means reference centroids of =6 and 8 are shown in Figure 4. Figure 5 shows the CVIs from = to 0 and the CSIs for each classification method in all patients. When the classification of intra-tumoral inetic patterns was performed by the reference patterns with the optimal number of clusters, it was able to be represented by the reference patterns with the relatively lowest overall SD. IV. DISCUSSION This study presents the comparative results on classification of inetic patterns between the -means clustering and the 3TP methods. The -means clustering can classify more effectively the inetic patterns within a malignant lesion with better classification accuracy than the 3TP method. In addition, we determined the optimal number of clusters with the cluster validation index in order to prevent over or under-partitioned clustering. This can reflect computationally more reliable clustering results by considering the compactness of intra-clusters and the distance between nearby inter-clusters. The optimal clustering is important to diagnose tumor stages because the classification result of the contrast enhancement patterns by it is related to accuracy in predicting the chemotherapeutic change of tumor volume or the tumor recurrence. On the other hand, -means clustering uses an unsupervised classification without any user-defined training classes and a model-free approach which does not require a prior nowledge about the physiological process lie the 3TP method. Thus, the strategy of this study is advantageous in assuming no prior nowledge of class patterns, in generating distinct and spectral classes, and in grouping non-typical inetic curves of malignant lesions. (a) (b) (c) Fig. 4. (a) A part of inetic curves extracted from our dataset, (b) centroid curves of =6 and (c) centroid curves of =8 (optimum number of clusters) 09

5 (a) (b) Fig. 5. (a) CVI calculated from each number of clusters from = to 0 and (b) CSI calculated from classification results using three different methods (red=3tp method; green=-means clustering (=6); blue=optimal -means clustering (=8)) in tumor volume for each patient. Note the CVI is maximum at the number of clusters, =8 (optimal cluster) and the CSI value is smaller at the -means clustering both with =6 and 8 than at the 3TP method in all patients except two patients. V. CONCLUSION This study provides new insight to explore various enhancement patterns of malignant lesions, which can be classified as the reference patterns having classification accuracy and details as well as optimal partitions. As we can obtain more accurate inetic information of a malignant lesion, more reasonable interpretation in tumor diagnosis and therapy will be achieved. REFERENCES [] S. H. Heywang, D. Hahn, H. Schmidt, I. Krische, W. Eiermann, R. Bassermann, J. Lissner, MR imaging of the breast using Gadolinium-DTPA, J. Comput. Assist. Tomogr., vol. 0, no., pp , 986. [] W. A. Kaiser, E. Zeitler, MR imaging of the breast: fast imaging sequences with and without Gd-DTPA, Radiology, vol. 70, no. 3 Pt, pp , 989. [3] S. G. Orel, M. D. Schnall, MR imaging of the breast for the detection, diagnosis and staging of breast cancer, Radiology, vol. 0, no., pp. 3 30, 00. [4] K. Kinel, N. M. Hylton, Challenges to interpretation of breast MRI, J. Magn. Reson. Imaging, vol. 3, no. 6, pp. 8-89, 00. [5] B. Solomon, S. Orel, C. Reynolds, M. Schnall, Delayed development of enhancement in fat necrosis after breast conservation therapy: a potential pitfall of MR imaging of the breast, Am. J. Roentgenol., vol. 70, no. 4, pp , 998. [6] K. Turetsche, S. Huber, E. Floyd, T. Helbich, T. P. Roberts, D. M. Shames, K. S. Tarlo, M. F. Wendland, R. C. Brash, MR imaging characterization of microvessels in experimental breast tumors by using a particulate contrast agent with histopathologic correlation, Radiology, vol. 8, no., pp , 00. [7] H. Neubauer, M. Li, R. Kuehne-Heid, A. Shneider, W. A. Kaiser, High grade and non-high grade ductal carcinoma in situ on dynamic MR mammography: characteristic findings for signal increase and morphological pattern of enhancement, Br. J. Radiol., vol. 76, no. 90, pp. 3-, 003. [8] H. F. Dvora, J. A. Nagy, D. Feng, L. F. Brown, A. M. Dvora, Vascular permeability factor/vascular endothelial growth factor and the significance of microvascular hyperpermeability in angiogenesis, Curr. Top. Microbiol. Immunol., vol. 37, pp. 97-3, 999. [9] A. R. Padhani, A. Dzi-Jurasz, Perfusion MR imaging of extracranial tumor angiogenesis, Top. Magn. Reson. Imaging, vol. 5, no., pp. 4-57, 004. [0] Breast Imaging Reporting and Data System (BI-RADS) MRI st edn., American College of Radiology, 003. [] H. Degani, V. Gusis, D. Weinstein, S. Fields, S. Strano, Mapping pathophysiological features of breast tumors by MRI at high spatial resolution, Natl. Med., vol. 3, no. 7, pp , 997. [] E. Furman-Haran, D. Grobgeld, R. Margalit, H. Degani, Response of MCF7 human breast cancer to tamoxifen: evaluation by the three-time-point, contrast-enhanced magnetic resonance imaging method, Clin. Cancer Res., vol. 4, no. 0, pp , 998. [3] E. Furman-Haran, H. Degani, Parametric analysis of breast MRI, J. Comput. Assist. Tomogr., vol. 6, no. 3, pp , 00. [4] C. uhl, Dynamic breast MR imaging: are signal intensity time course data useful for differential diagnosis of enhancing lesions?, Radiology, vol., pp. 0-0, 999. [5] L. Esserman, N. Hilton, T. George, N. Weidner, Contrastenhanced magnetic resonance imaging to access tumor histopathology and angiogenesis in breast carcinoma, The Breast Journal, vol. 5, no., pp. 3-, 999. [6] E. S. Fobben, C. Z. Rubin, L. Kalisher, A. G. Dembner, M. H. Seltzer, E. J. Santoro, Breast MR imaging with commercially available techniques: radiologic-pathologic correlation, Radiology, vol. 96, pp. 43-5,