Bayesian MS Lesion Classification Modeling ... - Semantic Scholar

Bayesian MS Lesion Classification Modeling Regional and Local Spatial Information Rola Harmouche* Louis Collins** Douglas Arnold** Simon Francis** Tal Arbel* *Centre for Intelligent Machines **Montreal Neurological Institute rharmo,arbel
@cim.mcgill.ca [email protected], doug,simon
@mrs.mni.mcgill.ca McGill University, Montreal, Quebec, Canada Abstract A fully automatic Bayesian framework for multiple sclerosis (MS) lesion classification is presented, using posterior probability distributions and entropy values to classify normal and lesion tissue. Spatial variability in intensities of multimodal MR images over the brain is explicitly modeled by building region-specific multivariate likelihood distributions. Local smoothness is ensured by incorporating neighboring voxel tissue information using Markov Random fields. A probabilistic measure of confidence for the classification is then presented, which can also be used to assess disease burden. The method was tested on 10 patients with MS by comparing automatically classified lesions, with and without regional information, to manual classifications by five expert raters using volume count and overlap. Results improve with the incorporation of spatial information, and are comparable to manual classifications. This method also enables a more accurate classification in the posterior fossa, where no other method reports success.

1. Introduction Multiple sclerosis is an inflammatory demyelinating disease of the central nervous system (CNS). The quantification of MS lesions seen in magnetic resonance imaging (MRI) data serves as an objective indicator of the burden of focal inflammatory disease in the white matter. Manual identification of lesions by experts is time consuming and subjective. This is particularly true in the posterior fossa, where the variability between manual classifications is greater than in the cerebrum, and where important structures are densely packed. Furthermore, tissue and lesion intensities vary depending on spatial location in the brain, rendering both manual and automatic classification difficult. This paper presents an automated Bayesian approach to MS lesion classification, which addresses the problem of tissue intensity variations. Previous work has addressed this

issue by including spatial information as classifier features [2, 16]. Probabilistic and Bayesian methods previously explored [15, 3, 1] mainly incorporated spatial information in the prior probability, while tissue class variations were not explicitly modeled in the likelihood functions. Our approach incorporates voxel spatial location in a standardized anatomical coordinate system and neighborhood information using Markov random fields. The likelihood is modeled using a distinct multivariate gaussian for different regions in the brain. The a priori information is modeled using a location-specific statistical atlas, along with Markov random fields to smooth the final result. Our approach uses the posterior probability distribution to provide measures of confidence in the solution, and to reduce false classifications. This method is the first to successfully classify lesions in the posterior fossa (cerebellum and brain stem), in addition to providing results that are comparable to manual classifications in the cerebrum. The paper is outlined as follows: The method is described in more detail (Section 2), followed by the experimental setup (Section 3) and a brief discussion of the results (Section 4).

2. Bayesian MS Lesion Classification In this paper, we develop a Bayesian framework whereby MRI voxels are classified as one of the following tissue classes: Background (Bkg), Grey matter (GM), white matter (WM), Cerebro-Spinal fluid (CSF), T1-hypointense lesions or black holes (T1-les), and T2-hyperintense lesions excluding black holes (T2-les). Intensity information  at the   voxel located at position    is represented by a 3D vector consisting of intensities from T1-weighted (T1w), T2-weighted (T2w) and Proton Density (PD) MR images. We represent the confidence in competing tissue classes  by the conditional posterior probability density function        , estimated according to Bayes’

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Theory:       

!    "   #    $

(1)

where ! % "    is the conditional likelihood function, and !     is the location-specific prior probability density function. &('*)',+.-/1023*465879:0?    " @A

(2)

    " @A is a 3-dimensional gaussian distribution, and @ is the region to which the voxel at location B   belongs.

The posterior probability distribution can be used to assess the level of confidence in the classification. The maximum a posteriori probability depicts the degree of confidence in the winning class. Shannon’s entropy, a measure of uncertainty of a random variable, provides extra information about the uncertainty of the overall posterior distribution. The probability ratio between the second most probable class and the maximum a posteriori probability, is also used to indicate whether 2 tissue classes are competing for the winning position. After classification, voxels that have

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been classified as lesions with less than a 0.5 posterior probability, an entropy above 0.5, or a probability ratio below 0.4 are eliminated. These thresholds were set empirically.

3. Experiments

T1w-MRI

Testing was performed on 10 patients with multiple sclerosis. Prior to classification, the MR volumes undergo preprocessing, which includes bias field correction using N3 [13], intra-subject registration of the multimodal volumes [6], extraction of brain parenchyma [14], and intensity range normalization. This renders the volumes comparable in both intensity and anatomy in standard space. For each patient, lesions were manually classified by 5 expert raters. A silver standard (SS) was produced, in which any voxel classified as lesion by 3 of the 5 raters was assumed to be a valid lesion. Our method was compared to the silver standard as well as a similar Bayesian approach having spatial information only in the prior term, without region-specific likelihood distributions. Inter-rater variability was compared to the variability between the automatic methods and the silver standard by means of lesion volume and spatial overlap. The latter was assessed on the basis of a modified bdcXPc statistic [7]: cXc_>gfJh

ikjmlJ ionkl

entropy

PD-MRI

classifier

T1w-MRI

T2w-MRI

entropy

regions

lesions classified

PD-MRI

classifier

MAP

lesions SS

regions

lesions classified

MAP

lesions SS

(3)

where A is the volume of the true lesions and B is the volume of the automatically classified lesions.

4. Results and discussion Classifications of a patient volume in the cerebrum and the posterior fossa are shown (figure 3). All lesions were successfully classified in both regions, resulting in a consistent and accurate classifier in all locations required for disease assessment. Table 1 displays T2-hyperintense lesion bdcXPc values for all test cases, in addition to the average posterior fossa bdcXPc . The average manual interrater bdcEPc is similar to that obtained using our proposed method. Thus, our classifier performs as well as manual labeling, with the advantage of providing consistent results. The bpcqEPc value increases significantly when including spatial information in the likelihood, especially in the posterior fossa (PF). Figure 4 shows volume comparisons between automatic and silver standard T2-hyperintense lesion classifications for all cases studied. A line of best fit with a slope of 1.12 was calculated, indicating a slight overestimate of the overall lesion volume. Low lesion volumes are observed in cases 5 and 8, due to the presence of false negatives. The Pearson correlation coefficient, a measure of correlation or predictability between two variables, was found to

Figure 3. Automatic and SS classification results in the cerebrum (top 2 rows) and posterior fossa (bottom 2 rows) are shown for case 5. The entropy and posterior probability spectral maps range from purple (0.01) to red (1). The classified labels are Bkg (dark blue), CSF (light blue), GM (green), WM (yellow), T2-les (red) and T1-les (white). The extracted lesions are shown in green.

automatic overall lesion volume (cc log scale)

e

T2w-MRI

100

y=x

10

1 10

5

7 8

2 49 1

1

6 3 10

manual overall lesion volume (cc log scale)

100

Figure 4. Manual vs Automatic hyperintense lesion volumes

T2-

be 0.967 when comparing lesion volumes of the classifier results with the silver standard (srDtpu tXt`v ). This indicates that the volumes found by our proposed method correlate

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Table 1. T2-hyperintense lesion bdcXPc values for experts and different classification methods for the entire brain and the PF Case 01 02 03 04 05 06 07 08 09 10 mean PF (mean)

average inter-rater 0.781 0.621 0.550 0.546 0.769 0.483 0.660 0.625 0.585 0.826 0.644 0.440

automatic no regions 0.700 0.370 0.351 0.186 0.473 0.570 0.444 0.639 0.197 0.656 0.440 0.260

automatic with regions 0.673 0.662 0.523 0.387 0.593 0.666 0.691 0.669 0.433 0.788 0.609 0.390

well with the manually classified volumes. Entropy values for lesions are generally higher than those of other tissue classes, as the lesion prior probability is generally lower than priors of other classes. Most discrepancies between the classifier results and the silver standard are due to false positives. The false positives are mostly located in the periventricular area, which is an area of high lesion probability, and are classified with high confidence. Even though these voxels are not classified as lesions by the silver standard, they lie in bright T2w-MRI and PD-MRI areas, and appear to be dirty white matter, thus unhealthy tissue. The posterior probability is thus an indicator of tissue health and can be used to asses disease burden. For most of the cases examined, any false negatives were due to lesions misclassified as GM because of intensity similarities between these tissues. The Markov random field eliminates noise and strengthens the cohesiveness of the classification. The bdcXc values presented are comparable to most recently reported results [5, 15, 17, 8]. However, these were obtained by either using a only a few select (sometimes central) slices [17, 5], or brain volumes from a few patients [8]. Our bdcXPc values are obtained using all slices from 10 patient volumes, including slices in the posterior fossa, where higher inter-rater variability tends to result in lower bdcXcw .

5. Conclusions A method that successfully classifies brain tissues including MS lesions is presented. The method uses a Bayesian approach to find a posterior probability distribution for tissue classes. Likelihood intensity distributions are modeled using region-specific multivariate Gaussian dis-

tributions, in order to best represent the spatial variability in tissue class intensities. The location-specific a priori information also includes neighborhood information using Markov random fields. The a posteriori probability distribution is used to establish a measure of confidence in the classification using the maximum a posteriori probability, e the probability ratio and Shannon’s entropy. cqEPc results are similar to manual classifications and are comparable to previously reported values, however using a larger validation set and including classifications in the posterior fossa, where no other method reports results.

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