ORIGINAL ARTICLE
A Histogram-Based Similarity Measure for Quantitative Magnetic Resonance Imaging: Application in Acute Mild Traumatic Brain Injury Benjamin S. Aribisala, PhD,*† Christopher J.A. Cowie, PhD,* Jiabao He, PhD,* Joshua Wood, BSc,* David A. Mendelow, PhD,‡§ Patrick Mitchell, PhD,§ and Andrew M. Blamire, PhD*
Objectives: The most commonly used summary metric in neuroimaging is the mean value, but this pays little attention to the shape of the data distribution and can therefore be insensitive to subtle changes that alter the data distribution. Methods: We propose a distributional-based metric called the normalized histogram similarity measure (HSM) for characterization of quantitative images. We applied HSM to quantitative magnetic resonance imaging T1 relaxation data of 44 patients with mild traumatic brain injury and compared with data of 43 age-matched controls. Results: Significant differences were found between the patients and the controls in 8 gray matter regions using the HSM whereas in only 1 gray matter region based on the mean values. Conclusions: Our results show that HSM is more sensitive than the standard mean values in detecting brain tissue changes. Future studies on brain tissue properties using quantitative magnetic resonance imaging should consider the use of HSM to properly capture any tissue changes. Key Words: magnetic resonance imaging, histogram, similarity measure, traumatic brain injury, image relaxometry (J Comput Assist Tomogr 2014;38: 915–923)
Q
uantitative analysis of brain magnetic resonance imaging (MRI) scans is an important focus for image postprocessing because evaluation of small signal changes may be useful as biomarkers for disease detection, assessment of injury, or disease severity and for monitoring disease progression. Quantitation often uses either regions of interest (ROIs)1 or pixel-wise analysis (eg, voxel-based morphometry2 and statistical parametric mapping).3 Pixel-wise methods allow for data exploration with no a priori anatomical hypothesis; however, because the analysis is conducted on a single-pixel basis, the intrinsic sensitivity is low. Alternatively, ROI analysis is used to sum pixel values over a wider region, giving higher sensitivity, although a priori anatomical knowledge is required to define the target analysis region. In most clinical research applications, ROI analysis is widely used with manual definition of each ROI on the image to be analyzed4 or on an accompanying high-resolution image and subsequently applied to the data to be quantified5 before extraction of the specific feature of interest, most commonly the
arithmetic or geometric mean of pixel values.6–8 Other measures of central tendency such as median have equally been used in clinical investigations.9,10 This approach condenses the available information contained within the discrete pixels of the ROI into a single value, which may be simple to interpret but may equally overcompress the data, missing vital features and making it difficult to detect subtle changes. An alternative approach is to use distributional analysis of the ROI to capture local tissue changes and allow ROI description using parametric modeling,11 the prime example being histogram analysis.12 Previous work in neuroimaging studies has demonstrated that histogram analysis reveals a significant difference between patient groups and control groups using MRI biomarkers such as magnetization transfer ratio,10 cerebral blood flow,13 diffusion tensor imaging9 and relaxometry.11 Histogram analysis offers a number of metrics such as skewness, kurtosis, peak height and position, histogram area, as well as percentiles, which have been identified to be sensitive to the extent and severity of clinical conditions such as multiple sclerosis,9 cerebra glioma,10 and cognitive impairment with no dementia.14 Here, we propose a histogram similarity measure (HSM) as an objective tool for analyzing quantitative MRI data sets, and we consider the application of this histogram analysis measure to detect diffuse injury after blunt head trauma. This metric was inspired by Yang and Mueller's15 work on remote sensing. They developed a ratio-based HSM as an unbiased histogram matching quality measure for optimal radiometric normalization in optical imaging (applied to detect changes in forest coverage from satellite images). Yang and Mueller's original HSM produces values that scale with the number of histogram bins, which makes its interpretation and application to clinical data difficult. Here, we introduce a modified normalized HSM, which we hypothesize will provide improved discrimination between patient and control group data over the commonly used mean or histogram skewness as well as provide objective data on changes in individual subjects.
HISTOGRAM-BASED FEATURE EXTRACTION Histogram Similarity Measure
From the *Institute of Cellular Medicine & Newcastle Magnetic Resonance Centre, Newcastle University, Newcastle upon Tyne; †Brain Research Imaging Centre, University of Edinburgh, Edinburgh; ‡Institute of Neuroscience, Newcastle University, Newcastle upon Tyne; and §Department of Neurosurgery, Newcastle upon Tyne NHS Foundation Trust, Newcastle upon Tyne, UK. Received for publication April 26, 2014; accepted July 17, 2014. Reprints: Andrew M. Blamire, PhD, Newcastle Magnetic Resonance Centre, Campus for Ageing and Vitality, Newcastle University, Newcastle upon Tyne, NE4 5PL, UK (e‐mail: [email protected]). Funded by Sir Jules Thorn Charitable Trust. The authors declare no conflict of interest. Copyright © 2014 by Lippincott Williams & Wilkins
The HSM developed here for MRI analysis compares the data histogram extracted from the individual patient ROI with a reference histogram taken to be representative of the normal state and computes the extent to which one histogram is similar to the other. The proposed metric is based on simple histogram ratios rather than distance metrics such as Euclidean distance, root mean error, or Manhattan distance because these are scale variant and difficult to interpret.16 Yang and Mueller15 proposed the symmetric metric described below, where we define Ha and Hb to be 1-dimensional
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(1D) histograms. The symmetric histogram ratio Rab is then defined as follows: 8 Ha ðiÞ > > ; if Ha ðiÞ Hb ðiÞ > > < Hb ðiÞ Rab ðiÞ ¼ Hb ðiÞ (1) > ; if Ha ðiÞ > Hb ðiÞ > > ð i Þ H > : a 0; if Ha ðiÞ ¼ Hb ðiÞ ¼ 0 where i = 1, 2… N, and N is the number of bins for which Ha (i) ≠ 0 and Hb (i) ≠ 0. Rab gives the ratio of a pair of histogram frequency counts and takes the multiplicative inverse of any ratio that is larger than 1, such that Rab is always less than or equal to 1 for every pair of bins. The overall similarity Sab of the pair of histograms is computed by summing all Rab over the number of bins in the histograms (Eq. 2). N
Sab ¼ ∑ Rab ðiÞ
(2)
i¼1
Sab is an unbiased ratio-based similarity metric that does not suffer from the limitations of distance-based similarity measures.15 In the original form,15 and when applied to MRI data, this measure suffers from several limitations as follows: (1) it can take any positive value without any form of normalization, which makes it difficult to interpret results; (2) it is sensitive to the number of bin points in the histogram (N) because Sab scales with the number of bins; and (3) it does not fully take into account a situation where Ha (i) ≠ 0 and Hb (i) = 0 (or vice versa), that is, where the histograms are not fully overlapping. Here, we propose a normalized variation of the HSM that does not suffer from these limitations.
Normalized HSM We define the normalized histogram measure Sabn such that Sabn ¼ H8 ab ðiÞ > Ha ðiÞ ; > > > Hb ðiÞ > > > > < Hb ðiÞ ; ¼ Ha ðiÞ > > Hb ðiÞ > > > ; > > > Ha ðiÞ : 0;
1 M ∑ Rab ðiÞ M i¼1
(3)
if Ha ðiÞ Hb ðiÞ if Ha ðiÞ > Hb ðiÞ
(4)
if Hb ðiÞ ¼ 0 and Ha ðiÞ ≠ 0 if Ha ðiÞ ¼ Hb ðiÞ ¼ 0
where M is the total number of bin points for which at least one of Ha (i) or Hb (i) is nonzero. Basically, Sabn is calculated by first computing the pairwise ratio of the histogram frequencies using Eq. 4, then summing the ratios across all the bin locations in the histograms and finally normalizing the sum by the number of bin points in the histograms. Sabn is an unbiased similarity measure that considers all the bin points in the pair of histograms, allowing for complete shifts in the histogram. In addition, it is easy to interpret because its value ranges from 0 to 1, with 0 representing not similar and 1 representing perfectly similar.
MATERIALS AND METHODS The algorithm was implemented and evaluated as part of a large quantitative MRI-based study in patients after mild
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traumatic brain injury (TBI). The method was incorporated into an automated image ROI analysis pipeline17 and compared against use of geometric mean, which has been demonstrated to be the most appropriate measure of central tendency for representing ROI in quantitative MRI scans.18 We also compared the proposed metric with skewness, being a standard and wellused histogram measure that takes into account aspects of the distribution shape. Specifically, this was evaluated by determining the ability of the 3 methods (HSM, geometric mean, and skewness) to detect hypothesized shifts in quantitative T1 (qT1) measurements between patients and controls, indicative of diffuse brain injury.
Subjects and MRI Data Scan data were used from a total of 87 subjects who were recruited for a study of the use of quantitative MRI to detect blunt TBI. This group comprised 44 mild TBI patients (Glasgow Coma Scale score, 14–15; mean [SD] age, 34[15]years) and 43 healthy adults (mean [SD] age, 42[15]years) with no history of neurological disease or prior TBI. Scanning in the patient group was performed within 10 days of injury (mean, 4.9 days; range, 1–10 days). The protocol for human investigation was approved by the local ethical committee, and all subjects provided written consent. To test the discriminating power of the proposed normalized HSM, we extracted the feature from qT1 mapping data acquired on a 3-T Philips Achieva System (Philips Medical Systems, Best, the Netherlands) using an 8-channel sensitivity encoding head coil. The full imaging protocol consisted of 3 scans with identical slice angulations acquired from each subject: (a) High-resolution 3-dimensional (3D) T1-weighted anatomical scan (magnetization-prepared rapid acquisition with gradient echo; repetition time [TR], 8.1 milliseconds; echo time [TE], 4.6 milliseconds; matrix size, 150 240 240; isotropic 1-mm resolution) (b) A fast, qT1 measurement using a custom inversion recovery– prepared echo planar imaging sequence (TR, 15 seconds; TE, 24 milliseconds; turbo inversion recovery, 0.25–2.5 seconds in 12 uniform steps; matrix, 128 128; 72 axial slices; isotropic 2-mm resolution) (c) Low-resolution B0 field map using a dual echo 3D gradient echo (TR, 27 milliseconds; TE, 2.6/6.1 milliseconds; matrix, 128 128 72; 2-mm resolution)
Quantitative T1 maps were calculated on a pixel-by-pixel basis by fitting the acquired data to the T1 inversion recovery curve using the standard 3-parameter monoexponential model (M0, flip angle, and T1). Spatial distortion of the echo planar imaging-based T1 maps was corrected using the B0 field map with the phase region expanding labeller for unwrapping discrete estimates and functional magnetic resonance imaging of the brain (FMRIB) utility for geometrically unwarping EPIs19 algorithms.
Image Analysis To prepare the imaging data for analysis, any visible lesions were manually removed from all patient data sets before analysis, allowing us to investigate only the normal-appearing tissues. This was done by a neurosurgeon (CJAC) who manually masked out any region of contusion, hematoma, or visible edema with reference to the conventional anatomical scan. The masks generated from this process were applied to the qT1 maps to restrict the analysis to normal-appearing tissue alone. Masked data were then subjected to an image analysis method whereby the whole brain was automatically divided into 14 ROIs for gray and © 2014 Lippincott Williams & Wilkins
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white matter.17 These regions were pairs of right and left inferior frontallobe, superior frontal lobe, temporal lobe, temporaloccipital lobe, occipital lobe, temporal-parietal lobe, as well as parietal lobe. This analysis method operated by transforming a standard space parcellated brain template into individual subject space. The subject's anatomical scan was then segmented into gray matter (GM), white matter, and cerebrospinal fluid masks20 and combined with the brain region template to generate tissuespecific anatomical ROI (this method has been demonstrated to significantly reduce partial volume errors compared with the same analysis performed in standard space).17 The algorithm was then used to extract regional gray and white matter qT1 histograms in each of the 14 target ROIs using a bin width of 20 milliseconds. The resulting histograms were normalized by dividing each histogram frequency value by the subject's total intracranial volume in pixels (total number of pixels in segmented white matter, GM, and cerebrospinal fluid) to correct for differences in the brain sizes between subjects. The algorithm was implemented in MATLAB (R2009b; The MathWorks Inc, Natick, Mass) running on a Linux platform using in-house–developed routines but incorporated existing processing methods from the FMRIB’s software library19 package when appropriate. All segmentation steps were performed using FMRIB’s software library Segmentation Tool (FMRIB’s automated segmentation tool).20 For each ROI and tissue class, the reference histogram (Hb [i], Eq. 1) was taken as the mean histogram over the control group. The normalized HSM (Eq. 3) was computed for each subject in both the control and TBI groups. Hence, each subject was represented by Sabn. In addition, for comparison, the more usual tissue-specific regional geometric mean and histogram skewness were computed for each subject. As part of the validation procedure of the proposed metric, a separate analysis was performed using subgroup analysis of the control data alone, in which no differences would be expected between the subgroups. The entire control population was divided into 2 groups comprising 28 and 15 subjects each (denoted CON28 and CON15). Histograms were averaged across the larger CON28 group for use as the reference histogram (Hb [i]), and the normalized HSM was then computed for each member of both the CON28 and CON15 groups. Group HSM values were then compared.
Statistical Analysis The association between the normalized HSM and mean values was evaluated using Pearson rank correlation coefficients. The Kolmogorov-Smirnov test was used to compare the regional
Histogram-Based Feature for Quantitative MRI
normalized HSMs for the TBI and the control group. The normalized HSM computed from the 2 subgroups of the control cohort was also compared using the Kolmogorov-Smirnov test. The Student t test was used to compare the regional mean values of the TBI group and the control group. The skewness computed for the TBI group and the control group was compared using the Kolmogorov-Smirnov test. Because 14 target regions were compared between the control and the TBI group, there is a need to correct type I error rate and reduce the false discovery rate. To this extent, the P values associated with the Pearson correlations, the Kolmogorov-Smirnov test, and the t test were Bonferroni corrected. Statistical significance between the groups was set to P < 0.05. Receiver operating characteristic (ROC) curves were also calculated to compare the discriminating power of the various measures. All statistical computations and analysis were done using SPSS 17 software (SPSS Inc, Chicago, Ill).
RESULTS Image selections showing a single slice from the 3D qT1 map and corresponding T1-weighted anatomical scan in a TBI patient are shown in Figure 1. Illustrative group mean histograms for the control and TBI groups in white matter and GM for selected right hemisphere ROIs are shown in Figure 2. Table 1 presents the group regional mean relaxation times for both gray and white matter in each ROI. Values in the healthy control subjects are consistent with previous studies at 3 T.21,22 The histograms are clearly not clean Gaussian distributions but show some apparent bimodal characteristics that most likely represent heterogeneity in tissue relaxation times across these relatively large brain regions. Patient data show a slightly different overall histogram shape with a general shift toward higher T1 values, which is also seen in the mean values in Table 1 and in the skewness in Table 3. Significant differences in tissue T1 were seen in 3 white matter regions and 7 GM regions (P < 0.05, Table 1). When multiple comparisons were taken into account, no white matter regions remained significant, whereas the number of significant GM regions reduced to 2. Similar observations were seen in the skewness values, as shown in Table 3. Significant differences in skewness were seen in 1 white matter region and 10 GM regions (P < 0.05, Table 3), but when multiple comparisons were taken into account, no white matter regions remained significant, whereas the number of significant GM regions reduced to 1. Characterization of the data using the regional normalized HSM is presented in Table 2 for each ROI in both gray and white matter. These values have no physical significance (unlike the relaxation times themselves) but range
FIGURE 1. Representative images from a 47-year-old male subject who sustained a mild TBI as a result of a fall. Left, Anatomical T1-weighted scan showing significant bilateral swelling of the soft tissue (scalp) but absence of any focal signal change within the brain parenchyma. Middle, qT1 map of the same slice. Right, T1 map with overlay of the right frontal white matter ROI. © 2014 Lippincott Williams & Wilkins
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FIGURE 2. Regional group mean histograms of the qT1 data in the controls (solid line) and the subjects with mild TBI (dotted line) for ROIs in the right hemisphere. White matter: inferior frontal lobe (WM1), superior frontal lobe (WM2), and temporal-parietal lobe (WM6). GM: inferior frontal lobe (GM1), superior frontal lobe (GM2), and temporal-parietal lobe (GM6).
between 0 and 1, representing the degree of overlap between histograms, with lower values indicating less similarity to the control group mean histogram. Even in the control subjects, the HSM is numerically relatively modest (particularly in the white matter); however, values in the patient group are proportionally more different from those in the controls, which is the case for
T1 values themselves. A greater number of individual regions were therefore significantly different when using the HSM (3 white matter and 12 GM regions), and 7 of the GM areas remained significant after Bonferroni correction. An alternative view of the data that indicates the data range is seen in the box plots shown in Figures 3 and 4 (Figs. 4A, B, and C for the geometric mean values,
TABLE 1. Quantitative T1 values (Mean and SD, Milliseconds) in 43 Control Subjects and 44 Mild TBI Subjects White Matter
GM
Region
Control
TBI
AUC
Control
TBI
AUC
Right frontal inferior Left frontal inferior Right frontal superior Left frontal superior Right temporal lobe Left temporal lobe Right temporal occipital Left temporal occipital Right occipital Left occipital Right temporal parietal Left temporal parietal Right parietal Left parietal
791 (29) 788 (27) 815 (31) 809 (30) 804 (29) 800 (31) 785 (29) 775 (28) 812 (47) 802 (33) 795 (28) 801 (35) 814 (29) 815 (30)
801 (42) 802 (43) 820 (44) 814 (39) 819 (35)* 818 (38)* 797 (37) 791 (36)* 819 (44) 817 (41) 799 (35) 806 (41) 822 (38) 821 (42)
0.570 0.599 0.533 0.528 0.654 0.656 0.613 0.640 0.571 0.615 0.560 0.543 0.560 0.564
1227 (36) 1232 (42) 1159 (52) 1166 (50) 1246 (83) 1225 (84) 1226 (113) 1211 (52) 1068 (112) 1084 (97) 1251 (35) 1259 (29) 1186 (42) 1190 (41)
1251 (75) 1262 (85)* 1177 (98) 1183 (89) 1296 (112)* 1269 (104)* 1274 (149) 1277 (123)* 1181 (175)*† 1157 (159)*† 1261 (57) 1269 (45) 1217 (103) 1215 (64)*
0.591 0.598 0.577 0.551 0.669 0.685 0.588 0.651 0.676 0.632 0.564 0.585 0.564 0.612
Values in boldface are statistically significant at P < 0.05. *TBI significantly different from control (P < 0.05), not corrected for multiple comparison. †TBI significantly different from control (P < 0.05), corrected for multiple comparison.
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TABLE 2. Histogram Similarity Values (Group Mean and SD) in 43 Control Subjects and 44 Mild TBI Subjects Normalized HSM White Matter Region Right frontal inferior Left frontal inferior Right frontal superior Left frontal superior Right temporal lobe Left temporal lobe Right temporal occipital Left temporal occipital Right occipital Left occipital Right temporal parietal Left temporal parietal Right parietal Left parietal
GM
Control
TBI
AUC
Control
TBI
AUC
0.43 (0.07)*† 0.31 (0.05)*‡ 0.37 (0.08) 0.42 (0.07)*† 0.31 (0.05) 0.25 (0.04) 0.34 (0.07)*† 0.29 (0.05)*† 0.21 (0.06) 0.33 (0.07) 0.31 (0.06) 0.23 (0.05) 0.29 (0.05) 0.31 (0.05)*
0.38 (0.11)§ 0.27 (0.08)§ 0.34 (0.09) 0.40 (0.09) 0.29 (0.06) 0.24 (0.05) 0.34 (0.06) 0.28 (0.05) 0.20 (0.04)§ 0.32 (0.07) 0.31 (0.05) 0.23 (0.04) 0.28 (0.06) 0.29 (0.06)
0.646 0.647 0.583 0.580 0.601 0.563 0.504 0.506 0.603 0.543 0.505 0.510 0.554 0.579
0.66 (0.05)*‡ 0.64 (0.06)*‡ 0.48 (0.07)*‡ 0.51 (0.07)*‡ 0.50 (0.11)*‡ 0.45 (0.10)*‡ 0.30 (0.09)*‡ 0.50 (0.10)*‡ 0.32 (0.08)*‡ 0.32 (0.07)*‡ 0.46 (0.05) 0.45 (0.05) 0.47 (0.06)* 0.48 (0.06)
0.55 (0.13)§∥∥ 0.51 (0.14)§∥ 0.41 (0.1)§∥ 0.45 (0.09)§ 0.43 (0.17)§ 0.42 (0.12)§ 0.25 (0.1)§∥ 0.36 (0.18)§∥ 0.24 (0.11)§∥ 0.28 (0.11) 0.41 (0.08)§∥ 0.42 (0.07) 0.39 (0.12)§∥ 0.44 (0.08)§
0.797 0.814 0.730 0.721 0.588 0.596 0.657 0.749 0.691 0.592 0.709 0.621 0.701 0.655
Values in boldface are statistically significant at P < 0.05 *Combined TBI and control regional similarity metrics significantly correlate with regional mean values, Pearson correlation (P < 0.001). †Combined TBI and control regional similarity metrics significantly correlate with regional mean values, Pearson correlation (P < 0.05), corrected for multiple comparison. ‡Combined TBI and control regional similarity metrics significantly correlate with regional mean values, Pearson correlation (P < 0.001), corrected for multiple comparison. §TBI significantly different from control (P < 0.05), not corrected for multiple comparison. ∥TBI significantly different from control (P < 0.05), corrected for multiple comparison.
HSM, and skewness, respectively). The ROIs depicted in these figures match the histograms in Figure 2. It is clear from these data that there is a significant overlap in mean T1 values and skewness between the patients and the controls, such that there
is no significant difference between the groups in either gray or white matter regions. However, although some patients have HSM within the control range, a large number of patients have considerably lower HSM beyond the values seen in the control
FIGURE 3. Box plot showing the distributions of the TBI group versus the control group using the regional mean values and HSM of the qT1 data. Top, Regional mean values, from left to right: right inferior frontal lobe, right superior frontal lobe, and right temporal-parietal lobe. Bottom, HSM, from left to right: right inferior frontal lobe, right superior frontal lobe, and right temporal-parietal lobe. Open boxes, white matter; filled boxes, GM. Boxes indicate the interquartile range with whiskers, showing total data range, and outliers, marked by triangles. © 2014 Lippincott Williams & Wilkins
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FIGURE 4. Top, Box plot showing the distributions of the TBI group versus the control group using the regional skewness of the qT1 data within the right inferior frontal lobe (A), right superior frontal lobe (B), and right temporal-parietal lobe (C). Bottom, Box plot showing the distributions of the HSM values in the analysis of the control group as 2 subgroups (D). Data are from the right inferior frontal lobe ROI. Open boxes, white matter; filled boxes, GM. Boxes indicate the interquartile range with whiskers, showing total data range, and outliers, marked by triangles.
group (particularly in GM regions), suggesting a potential diagnostic value for detecting diffuse injury in these patients. On the other hand, when comparing the control data treated as 2 subgroups (CON28 and CON15), HSM showed that there was no significant difference, with complete overlap in data range between the groups (Fig. 4D). This suggests that HSM has not only the potential to discriminate between the patient and the control group but also the potential to correctly classify the control group. To determine the ability of the HSM to discriminate between TBI patients and controls, ROC curves were constructed and
the area under the ROC curve (AUC) was calculated. Illustrative ROC curves from the left and right inferior frontal lobe GM ROIs are shown in Figure 5. The AUC is approximately 0.8 for the HSM in both hemispheres (where values > 0.8 are taken as showing good discrimination between groups), whereas for the mean T1 data, AUCs are approximately 0.6. The AUC values for each region and tissue class comparing the TBI group against the control are given in Tables 1 to 3. It is worth noting that this analysis based only upon the relaxation characteristics of brain tissue that appears normal on conventional MRI and excludes obvious
FIGURE 5. ROC curves for the GM ROI in the left and right frontal inferior lobe ROIs. Solid line ROC curve for HSM; dashed line ROC curve for the mean ROI qT1 value.
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TABLE 3. Skewness Values (Group Mean and SD) in 43 Control Subjects and 44 Mild TBI Subjects Group Mean Skewness Values White Matter Region Right frontal inferior Left frontal inferior Right frontal superior Left frontal superior Right temporal lobe Left temporal lobe Right temporal occipital Left temporal occipital Right occipital Left occipital Right temporal parietal Left temporal parietal Right parietal Left parietal
GM
Control
TBI
AUC
Control
TBI
AUC
2.43 (0.49) 2.73 (0.50) 2.53 (0.46) 2.15 (0.5) 1.82 (0.39) 2.82 (0.52) 2.83 (0.53) 2.43 (0.55) 2.60 (0.46) 2.12 (0.41) 2.03 (0.45) 2.68 (0.54) 1.76 (0.37) 2.08 (0.36)
2.37 (0.51) 2.53 (0.52) 2.51 (0.55) 2.01 (0.51) 1.7 (0.47) 2.59 (0.57)* 2.74 (0.51) 2.28 (0.55) 2.53 (0.62) 2.02 (0.51) 1.99 (0.47) 2.6 (0.6) r1.76 (0.43) 2 (0.43)
0.532 0.614 0.511 0.565 0.621 0.635 0.558 0.577 0.584 0.572 0.530 0.544 0.518 0.548
1.62 (0.2) 1.62 (0.2) 1.34 (0.26) 1.8 (0.26) 2.18 (0.33) 2.5 (0.34) 2.43 (0.46) 2.11 (0.38) 1.9 (0.34) 2.14 (0.34) 1.32 (0.17) 1.78 (0.15) 1.04 (0.15) 1.82 (0.17)
1.84 (0.5) 1.82 (0.47)* 1.47 (0.39) 1.9 (0.36)* 2.37 (0.47) 2.63 (0.46) 2.76 (0.63)* 2.4 (0.63)* 2.25 (0.54)* 2.42 (0.54)* 1.51 (0.41)* 1.92 (0.33)* 1.36 (0.45)*† 2.07 (0.4)*
0.624 0.622 0.584 0.595 0.603 0.591 0.658 0.625 0.687 0.652 0.657 0.640 0.743 0.677
Values in boldface are statistically significant at P < 0.05 *TBI significantly different from control (P < 0.05), not corrected for multiple comparison. †TBI significantly different from control (P < 0.05), corrected for multiple comparison.
lesions. These data therefore suggest that mild TBI does lead to subtle changes in qT1 values, which alter the overall shape of the histogram, but causes only slight changes in mean ROI value.
DISCUSSION The most commonly used statistic in neuroimaging research is the mean value computed from some specific ROIs. Geometric mean, like other measures of central tendency (such as arithmetic mean and median), can suffer from effects of pixel averaging, making it difficult to detect subtle tissue changes during analysis of neuroimaging data. We have proposed a distributional statistic that quantifies the similarity of regional histograms. When applied to quantitative relaxation imaging data in patients after mild TBI, this measure demonstrated significant group differences relative to the control group and was considerably more sensitive than the arithmetic mean alone. After head injury, a proportion of patients will appear entirely normal on conventional imaging assessment, whether by the routine clinical standard computed tomography or by MRI. However, a large proportion of these same patients will have ongoing cognitive deficits indicative of brain injury. These observed sequelae apply equally across the range of injury severity.23 The apparent mismatch between normal neuroimaging results and abnormal scores on clinical or cognitive measures suggests that diffuse injury may have taken place at a level that is not detectable by qualitative imaging techniques.24 We therefore hypothesized that quantitative relaxometry methods, coupled with a histogram analysis, would reveal greater differences between patients and controls than were visible on conventional MRI or by simple mean-based ROI analysis. This hypothesis was strongly supported by our observations. The range of HSM values observed in GM ROIs in a number of patients fell outside the normal limits observed in the control subjects, indicating a potential use for this metric in detecting damage in the individual patient. To substantiate this hypothesis, subsequent studies will examine the diagnostic and prognostic value of the HSM in the light of clinical © 2014 Lippincott Williams & Wilkins
observations and assessment of long-term outcome in these individual subjects. Further, the observation that the GM measures offer a better discrimination between groups than the white matter measures suggests that both tissue classes should be investigated to identify any subtle tissue changes that may provide diagnostic information. Recent MRI research in TBI has focused predominantly on white matter regions such as the corpus callosum, the brain stem, and long white matter tracts. These areas are known from postmortem examinations to be highly susceptible to the shearing forces involved in TBI25 that cause pathological axonal damage, termed diffuse axonal injury (DAI).26 Magnetic resonance imaging studies using diffusion tensor imaging have reported chronic differences in these white matter structures that are hypothesized to indicate DAI,27,28 and this hypothesis has been substantiated experimentally in a mouse model.29 However, DAI not only is limited to brain areas containing long axonal tracts but also occurs at junctions between areas of differing density, such as at the gray-white matter interface.30 Here, the acceleration/deceleration forces have the greatest impact because the less dense GM moves more rapidly than the denser white matter underlying it. This movement causes focal alteration, leading to delayed disconnection of axons connecting the gray and white matter. Progressive structural and subcellular consequences of the mechanical deformation include altered axolemmal permeability, calcium-induced proteolysis, and mitochondrial damage.31 Despite this evidence for GM injury, relatively few quantitative MRI studies have examined the cortical GM, in part because of difficulties during data processing; the intervolutions of gray and white matter within the gyri and the sulci of the cortex make the MRI data more susceptible to partial volume effects. However, those studies that have analyzed cortical GM have shown significant differences in quantitative diffusion values (which indicate structural damage) between patients with brain injury and matched controls, both in the acute and the chronic phase of injury.30,32,33 Our finding of an increase in qT1 mean values in the patient group and extensive areas of altered HSM may therefore represent the consequences of DAI within the gray-white interface. www.jcat.org
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The HSM was designed to discriminate between study groups and requires definition of reference histograms, which can be computed by averaging the control group histograms. This is simple to compute and easy to interpret. The proposed measure is not restricted to comparison of the control and the patient group only; it can be used in studies focusing on assessing disease severity and studies focusing on monitoring disease progression. Although a typical histogram from the control group can be used as a reference histogram, we used the group mean histogram to correct for intragroup variations. An important issue in histogram construction is the choice of the bin size, which must be carefully chosen to ensure accurate representation of the data. In this application, we applied a cost-based method34 to compute a data-driven optimal bin size of 20 milliseconds. This approach allowed us to investigate various bin sizes and to choose the optimum size. In the current analysis, we applied the metric to a 1D histogram. Multiparametric imaging protocols are becoming increasingly common,35,36 and these can be used for multispectral analysis37,38 (n-dimensional scatterplots). Although we defined the HSM in terms of a 1D data set, the methods can be simply extended to n-dimensions, requiring only calculation of the histogram in the relevant space.
CONCLUSIONS We have proposed a distributional feature called the normalized HSM. We implemented the proposed feature on qT1 neuroimaging data and used it to differentiate between patients with mild TBI and a matched control group. Our results show that the proposed measure performs better than the commonly used mean values at discriminating the control group from the patient group. ACKNOWLEDGMENTS The authors thank Carol Smith, Louise Morris, and Tim Hodgson for assisting with the scanning, as well as all of our volunteers. REFERENCES 1. Maillard P, Delcroix N, Crivello F, et al. An automated procedure for the assessment of white matter hyperintensities by multispectral (T1, T2, PD) MRI and an evaluation of its between-centre reproducibility based on two large community databases. Neuroradiology. 2008;50:31–42. 2. Mechelli A, Price CJ, Friston KJ, et al. Voxel-based morphometry of the human brain: methods and applications. Curr Med Imaging Rev. 2005;1:105–113. 3. Ashburner J. Computational anatomy with the SPM software. Magn Reson Imaging. 2009;27:1163–1174. 4. Kumar R, Gupta RK, Rao SB, et al. Magnetization transfer and T2 quantitation in normal appearing cortical gray matter and white matter adjacent to focal abnormality in patients with traumatic brain injury. Magn Reson Imaging. 2003;21:893–899. 5. Schmierer K, Wheeler-Kingshott CAM, Tozer DJ, et al. Quantitative magnetic resonance of postmortem multiple sclerosis brain before and after fixation. Magn Reson Med. 2008;59:268–277. 6. Keller J, Vymazal J, Ridzon P, et al. Quantitative brain MR imaging in amyotrophic lateral sclerosis. MAGMA. 2011;24:67–76. 7. Laule C, Kolind S, Bjarnason T, et al. In vivo multiecho T-2 relaxation measurements using variable TR to decrease scan time. Magn Reson Imaging. 2007;25:834–839. 8. McCreary C, Bjarnason T, Skihare V, et al. Multiexponential T2 and magnetization transfer MRI of demyelination and remyelination in murine spinal cord. Neuroimage. 2009;45:1173–1182. 9. Ge Y, Law M, Grossman R. Applications of diffusion tensor MR imaging in multiple sclerosis. In: Ulmer JL, Parsons L, Moseley M, et al, eds. White
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Matter in Cognitive Neuroscience: Advances in Diffusion Tensor Imaging and Its Applications. New York, NY: New York Acad Sciences; 2005: 202–219. 10. Law M, Young R, Babb J, et al. Histogram analysis versus region of interest analysis of dynamic susceptibility contrast perfusion MR imaging data in the grading of cerebral gliomas. Am J Neuroradiol. 2007;28:761–766. 11. Muskulus M, Lunel S. Mathematical modelling and feature extraction for probing crucial changes associated with Alzheimer's disease. Curr Med Imaging Rev. 2011;7:43–50. 12. Tofts P, Davies G, Dehmeshki J. Quantitative MRI of the Brain: Measuring Changes Caused by Disease. Chichester, West Sussex: J Wiley & Sons; 2004. 13. Young R, Babb J, Law M, et al. Comparison of region-of-interest analysis with three different histogram analysis methods in the determination of perfusion metrics in patients with brain gliomas. J Magn Reson Imaging. 2007;26:1053–1063. 14. Zhou Y, Qun X, Qin LD, et al. A primary study of diffusion tensor imaging-based histogram analysis in vascular cognitive impairment with no dementia. Clin Neurol Neurosurg. 2011;113:92–97. 15. Yang Z, Mueller R. Unbiased histogram matching quality measure for optimal radiometric normalisation. Paper presented at: American Society for Photogrammetry and Remote Sensing Annual Meeting; 2008; Portland, OR. 16. Yang Z, Mueller R. Heterogeneously sensed imagery radiometric response normalization for citrus grove change detection. In: Chen YR, Meyer GE, eds. Optics for Natural Resources, Agriculture, and Foods II. Bellingham, WA: Spie-Int Soc Optical Engineering; 2007:N7610–N7610. 17. Aribisala B, He J, Blamire A. Comparative study of standard space and real space analysis of quantitative MR brain data. J Magn Reson Imaging. 2011; 33:1503–1509. 18. Bjarnason T. Proof that gmT(2) is the Reciprocal of gmR(2). Concepts Magn Reson Part A Bridg Educ Res. 2011;38A:128–131. 19. Members of the Analysis Group, FMRIB, Oxford, UK. FMRIB Software Library. A Comprehensive Library of Analysis Tools for FMRI, MRI and DTI Brain Imaging Data. Release 3.1. Oxford, England: Oxford University; 2007. 20. Zhang Y, Brady M, Smith S. Segmentation of brain MR images through a HMRF model and the expectation-maximization algorithm. IEEE Trans Med Imaging. 2001;20:45–57. 21. Wansapura JP, Holland SK, Dunn RS, et al. NMR relaxation times in the human brain at 3.0 tesla. J Magn Reson Imaging. 1999;9: 531–538. 22. Wright PJ, Mougin OE, Totman JJ, et al. Water proton T-1 measurements in brain tissue at 7, 3, and 1.5 T using IR-EPI, IR-TSE, and MPRAGE: results and optimization. MAGMA. 2008;21:121–130. 23. Thornhill S, Teasdale G, Murray GD, et al. Disability in young people and adults one year after head injury: prospective cohort study. Br Med J. 2000;320:1631–1635. 24. Lee H, Wintermark M, Gean A, et al. Focal lesions in acute mild traumatic brain injury and neurocognitive outcome: CT versus 3 T MRI. J Neurotrauma. 2008;25:1049. 25. Smith DH, Meaney DF, Shull WH. Diffuse axonal injury in head trauma. J Head Trauma Rehabil. 2003;18:307–316. 26. Adams JH, Doyle D, Ford I, et al. Diffuse axonal injury in head injury—definition, diagnosis and grading. Histopathology. 1989; 15:49–59. 27. Kumar R, Husain M, Gupta RK, et al. Serial changes in the white matter diffusion tensor imaging metrics in moderate traumatic brain injury and correlation with neuro-cognitive function. J Neurotrauma. 2009;26:481–495.
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28. Sidaros A, Engberg A, Sidaros K, et al. Diffusion tensor imaging during recovery from severe traumatic brain injury and relation to clinical outcome: a longitudinal study. Brain. 2008;131:559–572.
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29. Mac Donald CL, Dikranian K, Song SK, et al. Detection of traumatic axonal injury with diffusion tensor imaging in a mouse model of traumatic brain injury. Exp Neurol. 2007;205:116–131.
35. Chang C, Lui C, Wang J, et al. Multi-parametric neuroimaging evaluation of cerebrotendinous xanthomatosis and its correlation with neuropsychological presentations. BMC Neurol. 2010;10:59.
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36. Garteiser P, Doblas S, Watanabe Y, et al. Multiparametric assessment of the anti-glioma properties of OKN007 by magnetic resonance imaging. J Magn Reson Imaging. 2010;31:796–806.
31. Buki A, Povlishock JT. All roads lead to disconnection? Traumatic axonal injury revisited. Acta Neurochir. 2006;148:181–194.
37. Aribisala B, Cowie C, He J, et al. Multi-parametric classification of traumatic brain injury patients using automatic analysis of quantitative MRI scans. In: Liao HG, Edwards PJ, Pan XC, et al, eds. Medical Imaging and Augmented Reality. Berlin, Germany: Springer-Verlag Berlin; 2010:51–59.
32. Kim E, Sohn CH, Chang KH, et al. Patterns of accentuated grey-white differentiation on diffusion-weighted imaging or the apparent diffusion coefficient maps in comatose survivors after global brain injury. Clin Radiol. 2011;66:440–448. 33. Newcombe V, Chatfield D, Outtrim J, et al. Mapping traumatic axonal injury using diffusion tensor imaging: correlations with functional outcome. Plos One. 2011;6:e19214.
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38. Hu X, Wong K, Young G. Support vector machine multiparametric MRI identification of pseudoprogression from tumor recurrence in patients with resected glioblastoma. J Magn Reson Imaging. 2011;33:296–305.
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A Histogram-Based Similarity Measure for Quantitative Magnetic Resonance Imaging: Application in Acute Mild Traumatic Brain Injury Benjamin S. Aribisala, PhD,*† Christopher J.A. Cowie, PhD,* Jiabao He, PhD,* Joshua Wood, BSc,* David A. Mendelow, PhD,‡§ Patrick Mitchell, PhD,§ and Andrew M. Blamire, PhD*
Objectives: The most commonly used summary metric in neuroimaging is the mean value, but this pays little attention to the shape of the data distribution and can therefore be insensitive to subtle changes that alter the data distribution. Methods: We propose a distributional-based metric called the normalized histogram similarity measure (HSM) for characterization of quantitative images. We applied HSM to quantitative magnetic resonance imaging T1 relaxation data of 44 patients with mild traumatic brain injury and compared with data of 43 age-matched controls. Results: Significant differences were found between the patients and the controls in 8 gray matter regions using the HSM whereas in only 1 gray matter region based on the mean values. Conclusions: Our results show that HSM is more sensitive than the standard mean values in detecting brain tissue changes. Future studies on brain tissue properties using quantitative magnetic resonance imaging should consider the use of HSM to properly capture any tissue changes. Key Words: magnetic resonance imaging, histogram, similarity measure, traumatic brain injury, image relaxometry (J Comput Assist Tomogr 2014;38: 915–923)
Q
uantitative analysis of brain magnetic resonance imaging (MRI) scans is an important focus for image postprocessing because evaluation of small signal changes may be useful as biomarkers for disease detection, assessment of injury, or disease severity and for monitoring disease progression. Quantitation often uses either regions of interest (ROIs)1 or pixel-wise analysis (eg, voxel-based morphometry2 and statistical parametric mapping).3 Pixel-wise methods allow for data exploration with no a priori anatomical hypothesis; however, because the analysis is conducted on a single-pixel basis, the intrinsic sensitivity is low. Alternatively, ROI analysis is used to sum pixel values over a wider region, giving higher sensitivity, although a priori anatomical knowledge is required to define the target analysis region. In most clinical research applications, ROI analysis is widely used with manual definition of each ROI on the image to be analyzed4 or on an accompanying high-resolution image and subsequently applied to the data to be quantified5 before extraction of the specific feature of interest, most commonly the
arithmetic or geometric mean of pixel values.6–8 Other measures of central tendency such as median have equally been used in clinical investigations.9,10 This approach condenses the available information contained within the discrete pixels of the ROI into a single value, which may be simple to interpret but may equally overcompress the data, missing vital features and making it difficult to detect subtle changes. An alternative approach is to use distributional analysis of the ROI to capture local tissue changes and allow ROI description using parametric modeling,11 the prime example being histogram analysis.12 Previous work in neuroimaging studies has demonstrated that histogram analysis reveals a significant difference between patient groups and control groups using MRI biomarkers such as magnetization transfer ratio,10 cerebral blood flow,13 diffusion tensor imaging9 and relaxometry.11 Histogram analysis offers a number of metrics such as skewness, kurtosis, peak height and position, histogram area, as well as percentiles, which have been identified to be sensitive to the extent and severity of clinical conditions such as multiple sclerosis,9 cerebra glioma,10 and cognitive impairment with no dementia.14 Here, we propose a histogram similarity measure (HSM) as an objective tool for analyzing quantitative MRI data sets, and we consider the application of this histogram analysis measure to detect diffuse injury after blunt head trauma. This metric was inspired by Yang and Mueller's15 work on remote sensing. They developed a ratio-based HSM as an unbiased histogram matching quality measure for optimal radiometric normalization in optical imaging (applied to detect changes in forest coverage from satellite images). Yang and Mueller's original HSM produces values that scale with the number of histogram bins, which makes its interpretation and application to clinical data difficult. Here, we introduce a modified normalized HSM, which we hypothesize will provide improved discrimination between patient and control group data over the commonly used mean or histogram skewness as well as provide objective data on changes in individual subjects.
HISTOGRAM-BASED FEATURE EXTRACTION Histogram Similarity Measure
From the *Institute of Cellular Medicine & Newcastle Magnetic Resonance Centre, Newcastle University, Newcastle upon Tyne; †Brain Research Imaging Centre, University of Edinburgh, Edinburgh; ‡Institute of Neuroscience, Newcastle University, Newcastle upon Tyne; and §Department of Neurosurgery, Newcastle upon Tyne NHS Foundation Trust, Newcastle upon Tyne, UK. Received for publication April 26, 2014; accepted July 17, 2014. Reprints: Andrew M. Blamire, PhD, Newcastle Magnetic Resonance Centre, Campus for Ageing and Vitality, Newcastle University, Newcastle upon Tyne, NE4 5PL, UK (e‐mail: [email protected]). Funded by Sir Jules Thorn Charitable Trust. The authors declare no conflict of interest. Copyright © 2014 by Lippincott Williams & Wilkins
The HSM developed here for MRI analysis compares the data histogram extracted from the individual patient ROI with a reference histogram taken to be representative of the normal state and computes the extent to which one histogram is similar to the other. The proposed metric is based on simple histogram ratios rather than distance metrics such as Euclidean distance, root mean error, or Manhattan distance because these are scale variant and difficult to interpret.16 Yang and Mueller15 proposed the symmetric metric described below, where we define Ha and Hb to be 1-dimensional
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(1D) histograms. The symmetric histogram ratio Rab is then defined as follows: 8 Ha ðiÞ > > ; if Ha ðiÞ Hb ðiÞ > > < Hb ðiÞ Rab ðiÞ ¼ Hb ðiÞ (1) > ; if Ha ðiÞ > Hb ðiÞ > > ð i Þ H > : a 0; if Ha ðiÞ ¼ Hb ðiÞ ¼ 0 where i = 1, 2… N, and N is the number of bins for which Ha (i) ≠ 0 and Hb (i) ≠ 0. Rab gives the ratio of a pair of histogram frequency counts and takes the multiplicative inverse of any ratio that is larger than 1, such that Rab is always less than or equal to 1 for every pair of bins. The overall similarity Sab of the pair of histograms is computed by summing all Rab over the number of bins in the histograms (Eq. 2). N
Sab ¼ ∑ Rab ðiÞ
(2)
i¼1
Sab is an unbiased ratio-based similarity metric that does not suffer from the limitations of distance-based similarity measures.15 In the original form,15 and when applied to MRI data, this measure suffers from several limitations as follows: (1) it can take any positive value without any form of normalization, which makes it difficult to interpret results; (2) it is sensitive to the number of bin points in the histogram (N) because Sab scales with the number of bins; and (3) it does not fully take into account a situation where Ha (i) ≠ 0 and Hb (i) = 0 (or vice versa), that is, where the histograms are not fully overlapping. Here, we propose a normalized variation of the HSM that does not suffer from these limitations.
Normalized HSM We define the normalized histogram measure Sabn such that Sabn ¼ H8 ab ðiÞ > Ha ðiÞ ; > > > Hb ðiÞ > > > > < Hb ðiÞ ; ¼ Ha ðiÞ > > Hb ðiÞ > > > ; > > > Ha ðiÞ : 0;
1 M ∑ Rab ðiÞ M i¼1
(3)
if Ha ðiÞ Hb ðiÞ if Ha ðiÞ > Hb ðiÞ
(4)
if Hb ðiÞ ¼ 0 and Ha ðiÞ ≠ 0 if Ha ðiÞ ¼ Hb ðiÞ ¼ 0
where M is the total number of bin points for which at least one of Ha (i) or Hb (i) is nonzero. Basically, Sabn is calculated by first computing the pairwise ratio of the histogram frequencies using Eq. 4, then summing the ratios across all the bin locations in the histograms and finally normalizing the sum by the number of bin points in the histograms. Sabn is an unbiased similarity measure that considers all the bin points in the pair of histograms, allowing for complete shifts in the histogram. In addition, it is easy to interpret because its value ranges from 0 to 1, with 0 representing not similar and 1 representing perfectly similar.
MATERIALS AND METHODS The algorithm was implemented and evaluated as part of a large quantitative MRI-based study in patients after mild
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traumatic brain injury (TBI). The method was incorporated into an automated image ROI analysis pipeline17 and compared against use of geometric mean, which has been demonstrated to be the most appropriate measure of central tendency for representing ROI in quantitative MRI scans.18 We also compared the proposed metric with skewness, being a standard and wellused histogram measure that takes into account aspects of the distribution shape. Specifically, this was evaluated by determining the ability of the 3 methods (HSM, geometric mean, and skewness) to detect hypothesized shifts in quantitative T1 (qT1) measurements between patients and controls, indicative of diffuse brain injury.
Subjects and MRI Data Scan data were used from a total of 87 subjects who were recruited for a study of the use of quantitative MRI to detect blunt TBI. This group comprised 44 mild TBI patients (Glasgow Coma Scale score, 14–15; mean [SD] age, 34[15]years) and 43 healthy adults (mean [SD] age, 42[15]years) with no history of neurological disease or prior TBI. Scanning in the patient group was performed within 10 days of injury (mean, 4.9 days; range, 1–10 days). The protocol for human investigation was approved by the local ethical committee, and all subjects provided written consent. To test the discriminating power of the proposed normalized HSM, we extracted the feature from qT1 mapping data acquired on a 3-T Philips Achieva System (Philips Medical Systems, Best, the Netherlands) using an 8-channel sensitivity encoding head coil. The full imaging protocol consisted of 3 scans with identical slice angulations acquired from each subject: (a) High-resolution 3-dimensional (3D) T1-weighted anatomical scan (magnetization-prepared rapid acquisition with gradient echo; repetition time [TR], 8.1 milliseconds; echo time [TE], 4.6 milliseconds; matrix size, 150 240 240; isotropic 1-mm resolution) (b) A fast, qT1 measurement using a custom inversion recovery– prepared echo planar imaging sequence (TR, 15 seconds; TE, 24 milliseconds; turbo inversion recovery, 0.25–2.5 seconds in 12 uniform steps; matrix, 128 128; 72 axial slices; isotropic 2-mm resolution) (c) Low-resolution B0 field map using a dual echo 3D gradient echo (TR, 27 milliseconds; TE, 2.6/6.1 milliseconds; matrix, 128 128 72; 2-mm resolution)
Quantitative T1 maps were calculated on a pixel-by-pixel basis by fitting the acquired data to the T1 inversion recovery curve using the standard 3-parameter monoexponential model (M0, flip angle, and T1). Spatial distortion of the echo planar imaging-based T1 maps was corrected using the B0 field map with the phase region expanding labeller for unwrapping discrete estimates and functional magnetic resonance imaging of the brain (FMRIB) utility for geometrically unwarping EPIs19 algorithms.
Image Analysis To prepare the imaging data for analysis, any visible lesions were manually removed from all patient data sets before analysis, allowing us to investigate only the normal-appearing tissues. This was done by a neurosurgeon (CJAC) who manually masked out any region of contusion, hematoma, or visible edema with reference to the conventional anatomical scan. The masks generated from this process were applied to the qT1 maps to restrict the analysis to normal-appearing tissue alone. Masked data were then subjected to an image analysis method whereby the whole brain was automatically divided into 14 ROIs for gray and © 2014 Lippincott Williams & Wilkins
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white matter.17 These regions were pairs of right and left inferior frontallobe, superior frontal lobe, temporal lobe, temporaloccipital lobe, occipital lobe, temporal-parietal lobe, as well as parietal lobe. This analysis method operated by transforming a standard space parcellated brain template into individual subject space. The subject's anatomical scan was then segmented into gray matter (GM), white matter, and cerebrospinal fluid masks20 and combined with the brain region template to generate tissuespecific anatomical ROI (this method has been demonstrated to significantly reduce partial volume errors compared with the same analysis performed in standard space).17 The algorithm was then used to extract regional gray and white matter qT1 histograms in each of the 14 target ROIs using a bin width of 20 milliseconds. The resulting histograms were normalized by dividing each histogram frequency value by the subject's total intracranial volume in pixels (total number of pixels in segmented white matter, GM, and cerebrospinal fluid) to correct for differences in the brain sizes between subjects. The algorithm was implemented in MATLAB (R2009b; The MathWorks Inc, Natick, Mass) running on a Linux platform using in-house–developed routines but incorporated existing processing methods from the FMRIB’s software library19 package when appropriate. All segmentation steps were performed using FMRIB’s software library Segmentation Tool (FMRIB’s automated segmentation tool).20 For each ROI and tissue class, the reference histogram (Hb [i], Eq. 1) was taken as the mean histogram over the control group. The normalized HSM (Eq. 3) was computed for each subject in both the control and TBI groups. Hence, each subject was represented by Sabn. In addition, for comparison, the more usual tissue-specific regional geometric mean and histogram skewness were computed for each subject. As part of the validation procedure of the proposed metric, a separate analysis was performed using subgroup analysis of the control data alone, in which no differences would be expected between the subgroups. The entire control population was divided into 2 groups comprising 28 and 15 subjects each (denoted CON28 and CON15). Histograms were averaged across the larger CON28 group for use as the reference histogram (Hb [i]), and the normalized HSM was then computed for each member of both the CON28 and CON15 groups. Group HSM values were then compared.
Statistical Analysis The association between the normalized HSM and mean values was evaluated using Pearson rank correlation coefficients. The Kolmogorov-Smirnov test was used to compare the regional
Histogram-Based Feature for Quantitative MRI
normalized HSMs for the TBI and the control group. The normalized HSM computed from the 2 subgroups of the control cohort was also compared using the Kolmogorov-Smirnov test. The Student t test was used to compare the regional mean values of the TBI group and the control group. The skewness computed for the TBI group and the control group was compared using the Kolmogorov-Smirnov test. Because 14 target regions were compared between the control and the TBI group, there is a need to correct type I error rate and reduce the false discovery rate. To this extent, the P values associated with the Pearson correlations, the Kolmogorov-Smirnov test, and the t test were Bonferroni corrected. Statistical significance between the groups was set to P < 0.05. Receiver operating characteristic (ROC) curves were also calculated to compare the discriminating power of the various measures. All statistical computations and analysis were done using SPSS 17 software (SPSS Inc, Chicago, Ill).
RESULTS Image selections showing a single slice from the 3D qT1 map and corresponding T1-weighted anatomical scan in a TBI patient are shown in Figure 1. Illustrative group mean histograms for the control and TBI groups in white matter and GM for selected right hemisphere ROIs are shown in Figure 2. Table 1 presents the group regional mean relaxation times for both gray and white matter in each ROI. Values in the healthy control subjects are consistent with previous studies at 3 T.21,22 The histograms are clearly not clean Gaussian distributions but show some apparent bimodal characteristics that most likely represent heterogeneity in tissue relaxation times across these relatively large brain regions. Patient data show a slightly different overall histogram shape with a general shift toward higher T1 values, which is also seen in the mean values in Table 1 and in the skewness in Table 3. Significant differences in tissue T1 were seen in 3 white matter regions and 7 GM regions (P < 0.05, Table 1). When multiple comparisons were taken into account, no white matter regions remained significant, whereas the number of significant GM regions reduced to 2. Similar observations were seen in the skewness values, as shown in Table 3. Significant differences in skewness were seen in 1 white matter region and 10 GM regions (P < 0.05, Table 3), but when multiple comparisons were taken into account, no white matter regions remained significant, whereas the number of significant GM regions reduced to 1. Characterization of the data using the regional normalized HSM is presented in Table 2 for each ROI in both gray and white matter. These values have no physical significance (unlike the relaxation times themselves) but range
FIGURE 1. Representative images from a 47-year-old male subject who sustained a mild TBI as a result of a fall. Left, Anatomical T1-weighted scan showing significant bilateral swelling of the soft tissue (scalp) but absence of any focal signal change within the brain parenchyma. Middle, qT1 map of the same slice. Right, T1 map with overlay of the right frontal white matter ROI. © 2014 Lippincott Williams & Wilkins
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FIGURE 2. Regional group mean histograms of the qT1 data in the controls (solid line) and the subjects with mild TBI (dotted line) for ROIs in the right hemisphere. White matter: inferior frontal lobe (WM1), superior frontal lobe (WM2), and temporal-parietal lobe (WM6). GM: inferior frontal lobe (GM1), superior frontal lobe (GM2), and temporal-parietal lobe (GM6).
between 0 and 1, representing the degree of overlap between histograms, with lower values indicating less similarity to the control group mean histogram. Even in the control subjects, the HSM is numerically relatively modest (particularly in the white matter); however, values in the patient group are proportionally more different from those in the controls, which is the case for
T1 values themselves. A greater number of individual regions were therefore significantly different when using the HSM (3 white matter and 12 GM regions), and 7 of the GM areas remained significant after Bonferroni correction. An alternative view of the data that indicates the data range is seen in the box plots shown in Figures 3 and 4 (Figs. 4A, B, and C for the geometric mean values,
TABLE 1. Quantitative T1 values (Mean and SD, Milliseconds) in 43 Control Subjects and 44 Mild TBI Subjects White Matter
GM
Region
Control
TBI
AUC
Control
TBI
AUC
Right frontal inferior Left frontal inferior Right frontal superior Left frontal superior Right temporal lobe Left temporal lobe Right temporal occipital Left temporal occipital Right occipital Left occipital Right temporal parietal Left temporal parietal Right parietal Left parietal
791 (29) 788 (27) 815 (31) 809 (30) 804 (29) 800 (31) 785 (29) 775 (28) 812 (47) 802 (33) 795 (28) 801 (35) 814 (29) 815 (30)
801 (42) 802 (43) 820 (44) 814 (39) 819 (35)* 818 (38)* 797 (37) 791 (36)* 819 (44) 817 (41) 799 (35) 806 (41) 822 (38) 821 (42)
0.570 0.599 0.533 0.528 0.654 0.656 0.613 0.640 0.571 0.615 0.560 0.543 0.560 0.564
1227 (36) 1232 (42) 1159 (52) 1166 (50) 1246 (83) 1225 (84) 1226 (113) 1211 (52) 1068 (112) 1084 (97) 1251 (35) 1259 (29) 1186 (42) 1190 (41)
1251 (75) 1262 (85)* 1177 (98) 1183 (89) 1296 (112)* 1269 (104)* 1274 (149) 1277 (123)* 1181 (175)*† 1157 (159)*† 1261 (57) 1269 (45) 1217 (103) 1215 (64)*
0.591 0.598 0.577 0.551 0.669 0.685 0.588 0.651 0.676 0.632 0.564 0.585 0.564 0.612
Values in boldface are statistically significant at P < 0.05. *TBI significantly different from control (P < 0.05), not corrected for multiple comparison. †TBI significantly different from control (P < 0.05), corrected for multiple comparison.
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TABLE 2. Histogram Similarity Values (Group Mean and SD) in 43 Control Subjects and 44 Mild TBI Subjects Normalized HSM White Matter Region Right frontal inferior Left frontal inferior Right frontal superior Left frontal superior Right temporal lobe Left temporal lobe Right temporal occipital Left temporal occipital Right occipital Left occipital Right temporal parietal Left temporal parietal Right parietal Left parietal
GM
Control
TBI
AUC
Control
TBI
AUC
0.43 (0.07)*† 0.31 (0.05)*‡ 0.37 (0.08) 0.42 (0.07)*† 0.31 (0.05) 0.25 (0.04) 0.34 (0.07)*† 0.29 (0.05)*† 0.21 (0.06) 0.33 (0.07) 0.31 (0.06) 0.23 (0.05) 0.29 (0.05) 0.31 (0.05)*
0.38 (0.11)§ 0.27 (0.08)§ 0.34 (0.09) 0.40 (0.09) 0.29 (0.06) 0.24 (0.05) 0.34 (0.06) 0.28 (0.05) 0.20 (0.04)§ 0.32 (0.07) 0.31 (0.05) 0.23 (0.04) 0.28 (0.06) 0.29 (0.06)
0.646 0.647 0.583 0.580 0.601 0.563 0.504 0.506 0.603 0.543 0.505 0.510 0.554 0.579
0.66 (0.05)*‡ 0.64 (0.06)*‡ 0.48 (0.07)*‡ 0.51 (0.07)*‡ 0.50 (0.11)*‡ 0.45 (0.10)*‡ 0.30 (0.09)*‡ 0.50 (0.10)*‡ 0.32 (0.08)*‡ 0.32 (0.07)*‡ 0.46 (0.05) 0.45 (0.05) 0.47 (0.06)* 0.48 (0.06)
0.55 (0.13)§∥∥ 0.51 (0.14)§∥ 0.41 (0.1)§∥ 0.45 (0.09)§ 0.43 (0.17)§ 0.42 (0.12)§ 0.25 (0.1)§∥ 0.36 (0.18)§∥ 0.24 (0.11)§∥ 0.28 (0.11) 0.41 (0.08)§∥ 0.42 (0.07) 0.39 (0.12)§∥ 0.44 (0.08)§
0.797 0.814 0.730 0.721 0.588 0.596 0.657 0.749 0.691 0.592 0.709 0.621 0.701 0.655
Values in boldface are statistically significant at P < 0.05 *Combined TBI and control regional similarity metrics significantly correlate with regional mean values, Pearson correlation (P < 0.001). †Combined TBI and control regional similarity metrics significantly correlate with regional mean values, Pearson correlation (P < 0.05), corrected for multiple comparison. ‡Combined TBI and control regional similarity metrics significantly correlate with regional mean values, Pearson correlation (P < 0.001), corrected for multiple comparison. §TBI significantly different from control (P < 0.05), not corrected for multiple comparison. ∥TBI significantly different from control (P < 0.05), corrected for multiple comparison.
HSM, and skewness, respectively). The ROIs depicted in these figures match the histograms in Figure 2. It is clear from these data that there is a significant overlap in mean T1 values and skewness between the patients and the controls, such that there
is no significant difference between the groups in either gray or white matter regions. However, although some patients have HSM within the control range, a large number of patients have considerably lower HSM beyond the values seen in the control
FIGURE 3. Box plot showing the distributions of the TBI group versus the control group using the regional mean values and HSM of the qT1 data. Top, Regional mean values, from left to right: right inferior frontal lobe, right superior frontal lobe, and right temporal-parietal lobe. Bottom, HSM, from left to right: right inferior frontal lobe, right superior frontal lobe, and right temporal-parietal lobe. Open boxes, white matter; filled boxes, GM. Boxes indicate the interquartile range with whiskers, showing total data range, and outliers, marked by triangles. © 2014 Lippincott Williams & Wilkins
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FIGURE 4. Top, Box plot showing the distributions of the TBI group versus the control group using the regional skewness of the qT1 data within the right inferior frontal lobe (A), right superior frontal lobe (B), and right temporal-parietal lobe (C). Bottom, Box plot showing the distributions of the HSM values in the analysis of the control group as 2 subgroups (D). Data are from the right inferior frontal lobe ROI. Open boxes, white matter; filled boxes, GM. Boxes indicate the interquartile range with whiskers, showing total data range, and outliers, marked by triangles.
group (particularly in GM regions), suggesting a potential diagnostic value for detecting diffuse injury in these patients. On the other hand, when comparing the control data treated as 2 subgroups (CON28 and CON15), HSM showed that there was no significant difference, with complete overlap in data range between the groups (Fig. 4D). This suggests that HSM has not only the potential to discriminate between the patient and the control group but also the potential to correctly classify the control group. To determine the ability of the HSM to discriminate between TBI patients and controls, ROC curves were constructed and
the area under the ROC curve (AUC) was calculated. Illustrative ROC curves from the left and right inferior frontal lobe GM ROIs are shown in Figure 5. The AUC is approximately 0.8 for the HSM in both hemispheres (where values > 0.8 are taken as showing good discrimination between groups), whereas for the mean T1 data, AUCs are approximately 0.6. The AUC values for each region and tissue class comparing the TBI group against the control are given in Tables 1 to 3. It is worth noting that this analysis based only upon the relaxation characteristics of brain tissue that appears normal on conventional MRI and excludes obvious
FIGURE 5. ROC curves for the GM ROI in the left and right frontal inferior lobe ROIs. Solid line ROC curve for HSM; dashed line ROC curve for the mean ROI qT1 value.
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Histogram-Based Feature for Quantitative MRI
TABLE 3. Skewness Values (Group Mean and SD) in 43 Control Subjects and 44 Mild TBI Subjects Group Mean Skewness Values White Matter Region Right frontal inferior Left frontal inferior Right frontal superior Left frontal superior Right temporal lobe Left temporal lobe Right temporal occipital Left temporal occipital Right occipital Left occipital Right temporal parietal Left temporal parietal Right parietal Left parietal
GM
Control
TBI
AUC
Control
TBI
AUC
2.43 (0.49) 2.73 (0.50) 2.53 (0.46) 2.15 (0.5) 1.82 (0.39) 2.82 (0.52) 2.83 (0.53) 2.43 (0.55) 2.60 (0.46) 2.12 (0.41) 2.03 (0.45) 2.68 (0.54) 1.76 (0.37) 2.08 (0.36)
2.37 (0.51) 2.53 (0.52) 2.51 (0.55) 2.01 (0.51) 1.7 (0.47) 2.59 (0.57)* 2.74 (0.51) 2.28 (0.55) 2.53 (0.62) 2.02 (0.51) 1.99 (0.47) 2.6 (0.6) r1.76 (0.43) 2 (0.43)
0.532 0.614 0.511 0.565 0.621 0.635 0.558 0.577 0.584 0.572 0.530 0.544 0.518 0.548
1.62 (0.2) 1.62 (0.2) 1.34 (0.26) 1.8 (0.26) 2.18 (0.33) 2.5 (0.34) 2.43 (0.46) 2.11 (0.38) 1.9 (0.34) 2.14 (0.34) 1.32 (0.17) 1.78 (0.15) 1.04 (0.15) 1.82 (0.17)
1.84 (0.5) 1.82 (0.47)* 1.47 (0.39) 1.9 (0.36)* 2.37 (0.47) 2.63 (0.46) 2.76 (0.63)* 2.4 (0.63)* 2.25 (0.54)* 2.42 (0.54)* 1.51 (0.41)* 1.92 (0.33)* 1.36 (0.45)*† 2.07 (0.4)*
0.624 0.622 0.584 0.595 0.603 0.591 0.658 0.625 0.687 0.652 0.657 0.640 0.743 0.677
Values in boldface are statistically significant at P < 0.05 *TBI significantly different from control (P < 0.05), not corrected for multiple comparison. †TBI significantly different from control (P < 0.05), corrected for multiple comparison.
lesions. These data therefore suggest that mild TBI does lead to subtle changes in qT1 values, which alter the overall shape of the histogram, but causes only slight changes in mean ROI value.
DISCUSSION The most commonly used statistic in neuroimaging research is the mean value computed from some specific ROIs. Geometric mean, like other measures of central tendency (such as arithmetic mean and median), can suffer from effects of pixel averaging, making it difficult to detect subtle tissue changes during analysis of neuroimaging data. We have proposed a distributional statistic that quantifies the similarity of regional histograms. When applied to quantitative relaxation imaging data in patients after mild TBI, this measure demonstrated significant group differences relative to the control group and was considerably more sensitive than the arithmetic mean alone. After head injury, a proportion of patients will appear entirely normal on conventional imaging assessment, whether by the routine clinical standard computed tomography or by MRI. However, a large proportion of these same patients will have ongoing cognitive deficits indicative of brain injury. These observed sequelae apply equally across the range of injury severity.23 The apparent mismatch between normal neuroimaging results and abnormal scores on clinical or cognitive measures suggests that diffuse injury may have taken place at a level that is not detectable by qualitative imaging techniques.24 We therefore hypothesized that quantitative relaxometry methods, coupled with a histogram analysis, would reveal greater differences between patients and controls than were visible on conventional MRI or by simple mean-based ROI analysis. This hypothesis was strongly supported by our observations. The range of HSM values observed in GM ROIs in a number of patients fell outside the normal limits observed in the control subjects, indicating a potential use for this metric in detecting damage in the individual patient. To substantiate this hypothesis, subsequent studies will examine the diagnostic and prognostic value of the HSM in the light of clinical © 2014 Lippincott Williams & Wilkins
observations and assessment of long-term outcome in these individual subjects. Further, the observation that the GM measures offer a better discrimination between groups than the white matter measures suggests that both tissue classes should be investigated to identify any subtle tissue changes that may provide diagnostic information. Recent MRI research in TBI has focused predominantly on white matter regions such as the corpus callosum, the brain stem, and long white matter tracts. These areas are known from postmortem examinations to be highly susceptible to the shearing forces involved in TBI25 that cause pathological axonal damage, termed diffuse axonal injury (DAI).26 Magnetic resonance imaging studies using diffusion tensor imaging have reported chronic differences in these white matter structures that are hypothesized to indicate DAI,27,28 and this hypothesis has been substantiated experimentally in a mouse model.29 However, DAI not only is limited to brain areas containing long axonal tracts but also occurs at junctions between areas of differing density, such as at the gray-white matter interface.30 Here, the acceleration/deceleration forces have the greatest impact because the less dense GM moves more rapidly than the denser white matter underlying it. This movement causes focal alteration, leading to delayed disconnection of axons connecting the gray and white matter. Progressive structural and subcellular consequences of the mechanical deformation include altered axolemmal permeability, calcium-induced proteolysis, and mitochondrial damage.31 Despite this evidence for GM injury, relatively few quantitative MRI studies have examined the cortical GM, in part because of difficulties during data processing; the intervolutions of gray and white matter within the gyri and the sulci of the cortex make the MRI data more susceptible to partial volume effects. However, those studies that have analyzed cortical GM have shown significant differences in quantitative diffusion values (which indicate structural damage) between patients with brain injury and matched controls, both in the acute and the chronic phase of injury.30,32,33 Our finding of an increase in qT1 mean values in the patient group and extensive areas of altered HSM may therefore represent the consequences of DAI within the gray-white interface. www.jcat.org
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The HSM was designed to discriminate between study groups and requires definition of reference histograms, which can be computed by averaging the control group histograms. This is simple to compute and easy to interpret. The proposed measure is not restricted to comparison of the control and the patient group only; it can be used in studies focusing on assessing disease severity and studies focusing on monitoring disease progression. Although a typical histogram from the control group can be used as a reference histogram, we used the group mean histogram to correct for intragroup variations. An important issue in histogram construction is the choice of the bin size, which must be carefully chosen to ensure accurate representation of the data. In this application, we applied a cost-based method34 to compute a data-driven optimal bin size of 20 milliseconds. This approach allowed us to investigate various bin sizes and to choose the optimum size. In the current analysis, we applied the metric to a 1D histogram. Multiparametric imaging protocols are becoming increasingly common,35,36 and these can be used for multispectral analysis37,38 (n-dimensional scatterplots). Although we defined the HSM in terms of a 1D data set, the methods can be simply extended to n-dimensions, requiring only calculation of the histogram in the relevant space.
CONCLUSIONS We have proposed a distributional feature called the normalized HSM. We implemented the proposed feature on qT1 neuroimaging data and used it to differentiate between patients with mild TBI and a matched control group. Our results show that the proposed measure performs better than the commonly used mean values at discriminating the control group from the patient group. ACKNOWLEDGMENTS The authors thank Carol Smith, Louise Morris, and Tim Hodgson for assisting with the scanning, as well as all of our volunteers. REFERENCES 1. Maillard P, Delcroix N, Crivello F, et al. An automated procedure for the assessment of white matter hyperintensities by multispectral (T1, T2, PD) MRI and an evaluation of its between-centre reproducibility based on two large community databases. Neuroradiology. 2008;50:31–42. 2. Mechelli A, Price CJ, Friston KJ, et al. Voxel-based morphometry of the human brain: methods and applications. Curr Med Imaging Rev. 2005;1:105–113. 3. Ashburner J. Computational anatomy with the SPM software. Magn Reson Imaging. 2009;27:1163–1174. 4. Kumar R, Gupta RK, Rao SB, et al. Magnetization transfer and T2 quantitation in normal appearing cortical gray matter and white matter adjacent to focal abnormality in patients with traumatic brain injury. Magn Reson Imaging. 2003;21:893–899. 5. Schmierer K, Wheeler-Kingshott CAM, Tozer DJ, et al. Quantitative magnetic resonance of postmortem multiple sclerosis brain before and after fixation. Magn Reson Med. 2008;59:268–277. 6. Keller J, Vymazal J, Ridzon P, et al. Quantitative brain MR imaging in amyotrophic lateral sclerosis. MAGMA. 2011;24:67–76. 7. Laule C, Kolind S, Bjarnason T, et al. In vivo multiecho T-2 relaxation measurements using variable TR to decrease scan time. Magn Reson Imaging. 2007;25:834–839. 8. McCreary C, Bjarnason T, Skihare V, et al. Multiexponential T2 and magnetization transfer MRI of demyelination and remyelination in murine spinal cord. Neuroimage. 2009;45:1173–1182. 9. Ge Y, Law M, Grossman R. Applications of diffusion tensor MR imaging in multiple sclerosis. In: Ulmer JL, Parsons L, Moseley M, et al, eds. White
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