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Lesion identification using unified segmentation-normalisation models and fuzzy clustering

In this paper, we propose a new automated procedure for lesion identification from single images based on the detection of outlier voxels. We demonstrate the utility of this procedure using artificial and real lesions. The scheme rests on two innovations: First, we augment the generative model used for combined segmentation and normalization of images, with an empirical prior for an atypical tissue class, which can be optimised iteratively. Second, we adopt a fuzzy clustering procedure to identify outlier voxels in normalised gray and white matter segments. These two advances suppress misclassification of voxels and restrict lesion identification to gray/white matter lesions respectively. Our analyses show a high sensitivity for detecting and delineating brain lesions with different sizes, locations, and textures. Our approach has important implications for the generation of lesion overlap maps of a given population and the assessment of lesion-deficit mappings. From a clinical perspective, our method should help to compute the total volume of lesion or to trace precisely lesion boundaries that might be pertinent for surgical or diagnostic purposes.


1-Influence of the number of iterations
illustrates the evolution of the priors for the extra class when repeating the segmentation routine several times. One observation is the increase of abnormal tissue extent in the priors (as shown for simulated case 06). However, because it was not possible to define morphological constraints on the extent of the abnormal tissue at higher iterations, the priors of the abnormal tissue wrongly included some normal GM voxels (principally due to closer T1 signal between the abnormal voxels in the extra class and the normal voxels in the GM). Critically, the probability that healthy GM in the vicinity of the lesion is classified in the extra class (i.e., as damaged tissue) increased with the number of iterations (for more details see Figure S1C). This also demonstrated the increased False Positive Rate (FPR; i.e. 1specificity) as a function of the number of iterations ( Figure S1B). The FPR is defined as: where FP and TN represent the number of false positives and true negatives respectively. To avoid this artefact, a small number of iterations (<5 iterations; e.g. FPR<2% for simulated case 06) appeared to be a reasonable compromise for a better definition of the extra class, without altering classification of normal tissue.
In principle, one could use the evidence of the unified model, at each iteration, as an objective function to optimise the empirical priors. This is possible because we are using an explicit generative model for the segmentation and it is possible (in principle) to integrate out dependencies on the model parameters to provide the evidence of likelihood of the data under each empirical prior. We will pursue this elsewhere and assume that two iterations is near-optimal for our purposes.

2-Segmentation of the healthy tissue
We also investigated whether adding this extra class altered the segmented healthy tissue when the brain is normal. On a subgroup of 8 normal brains, we segmented the T1 images with the standard unified segmentation routine in 3 classes (as implemented in SPM5) and with the modified segmentation routine in 4 classes.
The segmented classes are almost identical for the two methods, as illustrated in the scatter-plots for GM (or WM) tissue with the standard segmentation and the new segmentation ( Figure S2). In addition, we computed the absolute differences between the GM and WM obtained from both segmentations and calculated their mean (±SD) over all voxels for each subject. From this analysis, the maximum mean differences over the 8 subjects in GM and WM probabilities were negligible (maximum = 0.007±0.01 and 0.003±0.008 respectively). This supported a high specificity of this new segmentation (i.e. the extra class was empty when the brain was normal).

3-Influence of the spatial smoothing
We tested the effects of spatial smoothing in all simulated lesions. We compared different full-width-at-half-maximum (FWHM) values of the Gaussian kernel (0mm, 4mm, 8mm, 12mm, 16mm and 20mm). Lesion identification (i.e., outlier identification) was performed on GM and WM images with several FWHM values.
For each FWHM value, we assessed Dice's similarity index between each binary lesion map (i.e. thresholded LES F ) and the "real" lesion (i.e. the manually defined lesion considered as true positives) using the following formula: where TP, FP, and FN represent the number of true positives, false positives, and false negatives respectively. Because the lesion is a fuzzy set (i.e. LES F contained values between 0 and 1), the Dice index was generated at several U thresholds.
We found a direct influence of spatial smoothing on the sensitivity of the method, as illustrated by the Dice similarity index plots (see Figure S3A).

4-Influence of the U thresholds
As shown in the manuscript, the identified lesion is represented by the fuzzy set The binarisation effect is illustrated in Figure S4 for two simulated lesions. Low threshold values sometimes led to the identification of regions outside the lesion (e.g., false positives in simulated case 01). Intermediate thresholds of 0.3 or 0.5 provided better results with these simulated lesions. Note that the definition of "exact" lesion boundaries in a mono-spectral mode is difficult even with manual segmentation, because of partial volume effects in T1 images with limited spatial resolution.