Original Research. Robert Young, MD, 1 James Babb, PhD, 1 Meng Law, MD, 1,2 * Erica Pollack, BA, 1 and Glyn Johnson, PhD 1

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1 JOURNAL OF MAGNETIC RESONANCE IMAGING 26: (2007) Original Research Comparison of Region-of-Interest Analysis With Three Different Histogram Analysis Methods in the Determination of Perfusion Metrics in Patients With Brain Gliomas Robert Young, MD, 1 James Babb, PhD, 1 Meng Law, MD, 1,2 * Erica Pollack, BA, 1 and Glyn Johnson, PhD 1 Purpose: To compare routine ROI analysis and three different histogram analyses in the grading of glial neoplasms. The hypothesis is that histogram methods can provide a robust and objective technique for quantifying perfusion data in brain gliomas. Current region-of-interest (ROI)- based methods for the analysis of dynamic susceptibility contrast perfusion magnetic resonance imaging (DSC MRI) data are operator-dependent. Materials and Methods: A total of 92 patients underwent conventional and DSC MRI. Multiple histogram metrics were obtained for cerebral blood flow (CBF), cerebral blood volume (CBV), and relative CBV (rcbv) maps using tumoral (T), peritumoral (P), and total tumoral (TT) analysis. Results were compared to histopathologic grades. Statistical analysis included Mann-Whitney (MW) tests, Spearman rank correlation coefficients, logistic regression, and McNemar tests. Results: The maximum value of rcbv (rcbv max ) showed highly significant correlation with glioma grade (r 0.734, P 0.001). The strongest histogram correlations (P ) occurred with rcbv T SD (r 0.718), rcbv P SD 25 (r 0.724) and rcbv TT SD 50 (r 0.685). Multiple rcbv T, rcbv P, and rcbv TT histogram metrics showed significant correlations. CBF and CBV histogram metrics were less strongly correlated with glioma grade than rcbv histogram metrics. 1 Department of Radiology, NYU Medical Center, New York, New York, USA. 2 Department of Neurosurgery, NYU Medical Center, New York, New York, USA. Contract grant sponsor: National Cancer Institute/National Institute of Health; Contract grant numbers: ROI CA111996; ROI CA Presented at the 14th Annual Meeting of ISMRM, May 2006, Seattle, WA, USA. *Address reprint requests to: M.L., MD, Department of Radiology, NYU Medical Center, MRI Dept, Schwartz Building, Basement HCC, 530 First Avenue, New York, NY lawm01@med.nyu.edu Received July 11, 2006; Accepted May 30, DOI /jmri Publishedonline00Month2007inWileyInterScience( wiley.com). Conclusion: Histogram analysis of perfusion MR provides prediction of glioma grade, with peritumoral metrics outperforming tumoral and total tumoral metrics. Further refinement may lead to automated methods for perfusion data analysis. Key Words: MR perfusion; histogram analysis; brain tumors; cerebral gliomas; cerebral blood volume J. Magn. Reson. Imaging 2007;26: Wiley-Liss, Inc. HISTOGRAM ANALYSIS is a quantitative technique used in a number of neuroimaging studies but is most commonly used in magnetization transfer ratio studies of patients with diffuse cerebral disease such as multiple sclerosis (1 4). Dynamic susceptibility-weighted contrast-enhanced perfusion MR imaging (DSC MRI) is an established technique in the evaluation of cerebral glial neoplasms. Relative cerebral blood volume (rcbv) measurements show reliable correlation with tumor grade and histopathologic findings of tumor neovascularity (5 16). Perfusion data is most commonly analyzed using multiple small region-of-interest (ROI) measurements, an operator-dependent method. ROI measurement of tumor rcbv has shown good reproducibility, but nevertheless remains operator-dependent and somewhat subjective, with an unavoidable component of interobserver and intraobserver variability. Reliable, reproducible data may only be obtained by experienced operators. Therefore, developing a more objective method that simplifies the analysis may allow even inexperienced operators to obtain reproducible data. Importantly, as surrogate imaging markers for angiogenesis are being investigated to determine the efficacy of antiangiogenic therapies (17), intra- and interinstitutional reproducibility becomes crucial, particularly when performing multicenter clinical trials using DSC MRI. The hypothesis is that histogram methods are comparable to, if not superior to current ROI-based methods for calculating the maximum value of rcbv (rcbv max ) in the prediction of glioma grade. We compare three methods of histogram analysis using both ROI Wiley-Liss, Inc. 1053

2 1054 Young et al. and non-roi-based techniques with routine ROI analysis for the determination of glioma grade. MATERIALS AND METHODS Participants Approval for this study was obtained from the Institutional Board of Research Associates. This was a retrospective analysis of patients with a diagnosis of primary cerebral glioma who underwent MR examination at our institution between November 1999 and November A total of 92 patients had preoperative conventional MR and perfusion MR data suitable for evaluation. The patients had a mean age of 43 years (range, 4 85 years), with 61 males and 31 females. Histopathologic evaluation was performed on samples obtained by either volumetric resection (N 63) or stereotactic biopsy (N 29). Using a World Health Organization (WHO) classification system, tumor grades were segregated by experienced neuropathologists as low-grade glioma (LGG, Grade II), or high-grade glioma (HGG) consisting of anaplastic astrocytoma (AA, Grade III) and glioblastoma multiforme (GBM, Grade IV/IV). Gliomas with oligodendroglial components and juvenile pilocytic astrocytomas were excluded from this study. These tumors have been previously described to have elevated rcbv and may confound the utility of rcbv in predicting glioma grade (18,19). Conventional MR Imaging Imaging was performed on 1.5 Tesla systems (Siemens Vision, Avanto, or Symphony; Siemens AG, Erlangen, Germany). A localizing sagittal T1-weighted image was obtained followed by nonenhanced axial T1-weighted spin echo (repetition time [TR]/echo time [TE] 600 msec/14 msec), axial fluid-attenuated inversion recovery (FLAIR, TR/TE/inversion time [TI] 9000 msec/ 110 msec/2500 msec), and axial T2-weighted (TR/TE 3400 msec/119 msec) images. Postcontrast axial T1- weighted imaging was performed after the acquisition of the DSC MRI data. DSC MRI DSC MRI was performed with gradient-echo echo-planar perfusion images acquired during the first pass of a standard dose (0.1 mmol/kg) bolus of gadopentetate dimeglumine (Magnevist; Berlex Laboratories, Wayne, NJ, USA). From seven to 10 sections were selected for perfusion MR imaging through the tumor based on T2- weighted and FLAIR images. Imaging parameters were as follows: field of view mm, section thickness 5 mm, matrix size , in-plane voxel size mm, interslice gap 0% to 30%, flip angle 30, signal bandwidth 1470 Hz/pixel, slices Contrast was injected at a rate of 5 ml/second, except for four patients less than 10 years old, in whom the injection rate was reduced to 3 ml/ second. The contrast injection was followed by a 20-mL bolus of saline at 5 ml/second. A total of 60 images were acquired at one second intervals with the injection occurring at the tenth image. Standard algorithms were used to calculate cerebral blood flow (CBF), cerebral blood volume (CBV), and relative CBV (rcbv) from the DSC MR imaging data (6,20 23). Briefly, tissue concentration is found from the change in relaxation rate that occurs during bolus passage. The tissue concentration that results from an idealized, instantaneous bolus is then found by deconvolving the actual tissue concentration with an automated arterial input function (AIF) using singular value decomposition (24 26). During the first pass of the bolus of contrast agent, T* 2 is reduced and there is an accompanying signal decrease on T* 2 weighted images. The change in relaxation rate (R* 2 ) (i.e., the change in the reciprocal of T* 2 ) is calculated from the signal intensity change using the following equation: R* 2 (t) { ln[s(t)/ S 0 ]}/TE, where S(t) is the signal intensity at time t, S 0 is the precontrast signal intensity, and TE is the echo time. R* 2 is proportional to the concentration of contrast agent in the tissue, and CBV is proportional to the area under the curve of R* 2 (t), provided there is no recirculation or leakage of contrast agent. The effects of these imprecise assumptions are reduced by fitting a gammavariate function to the measured R* 2 curve, which approximates the curve that would have been obtained without recirculation or leakage. CBV can then be estimated from the area under the fitted curve rather than from the original data. Perfusion parameters are then found from the following equations: Cdt MTT, (1) C max Cdt CBV, (2) AIFdt CBF CBV MTT, (3) where C is the idealized tissue concentration found by deconvolution and C max is the maximum value of C. The minimum signal corresponding to the bolus peak is found in each pixel. The average signal drop and average bolus arrival time are then calculated for all pixels. Pixels where the bolus arrives early and where the signal drop is larger than average are assumed to be within arteries. The AIF is found by averaging the signals from all such pixels. Data processing was performed on a Unix workstation with programs developed in-house using C and IDL programming languages. Color overlay maps of CBF, CBV, and rcbv were calculated with the upper values set to 150 ml/100 g/minute, 10 ml/100 g, and five, respectively. These values were established in earlier work as providing the best thresholds to reduce the effect of very high values related to noise, blood vessels, and blood-brain barrier breakdown while providing an adequate scale for the visual color maps.

3 ROI vs. Three Histogram Analyses of DSC MRI 1055 Routine ROI Analysis ROIs were placed in the region of maximal abnormality as visually determined from the rcbv maps. Four separate ROI measurements were made, and the maximum value was recorded (as rcbv max ). It has been demonstrated that this method for the measurement of maximal abnormality provides the highest intra- and interobserver reproducibility in perfusion measurements (27). To minimize confounding factors in ROI analysis, the ROIs were targeted to the maximal abnormalities within the tumor and the size was kept constant (radius 1 image pixel 1.8 mm). For the rcb- V max measures, the tumor ROI was referenced with an ROI measure of the contralateral normal-appearing white matter, for a lesion in the white matter and the contralateral normal gray matter, and for a lesion in the gray matter. The method described for estimation of rcbv and gamma variate fit can be affected by noise. This is in part self-corrected by taking a relative measure of CBV from within the tumor to the contralateral normal brain. In this way, the estimation of rcbv will remove some of the effect of the noise in these estimations. Histogram Analysis The histogram was applied to the CBF, CBV, and rcbv color maps to display the pixel values from the magnitude image. The interval between the minimum and maximum pixel values was divided into 40 equallyspaced bins. Each pixel was assigned to the bin that surrounds its value. The number of pixels corresponding to each bin was counted and frequency counts were plotted as a function of the bin locations. The peak height (PH) was normalized by dividing each histogram frequency value by the total number of voxels in the sample. The PH was a measure of the frequency of appearance of the most common histogram value. A total of 14 different measures were obtained by histogram analysis: mean, median, standard deviation (SD), mean 50,SD 50, mean 25,SD 25, mean 10,SD 10, skewness, kurtosis, PH, peak position (PP), and area within 1 SD under the histogram curve (A1SD), where mean X and SD X denote the mean and SD computed over the top X% of the data (Fig. 1). The three methods applied to the color maps were: 1) tumoral (T), 2) peritumoral (P), and 3) total tumoral (TT). Method 1 (tumoral) was defined by an ROI drawn around the maximal tumor diameter on any single axial slice, regardless of lesion heterogeneity or radiologic evidence of necrosis. The tumoral ROI was drawn around the region of increased T2 signal abnormality on FLAIR or T2-weighted imaging. Method 2 (peritumoral) was defined by a semiautomated process as the area around and not including the manually drawn tumoral ROI. Based on previous work, a six-pixel width was used as the dilation factor for the peritumoral ROI. Method 3 (total tumoral), a non-roi technique, refers to analysis of all acquired perfusion images (7 10 images covering the tumor) without any segmentation of brain tissue. This means that every pixel on every single slice of the perfusion acquisition is included in the histogram analysis and no ROI is drawn. The three methods Figure 1. Sample histogram. Centile mean X and SD X measures are calculated from the top 50%, 25%, and 10% of the histogram curve. Also measured are kurtosis (how peaked the curve is) and skewness (how elongated the tails are). and three maps can be summarized as: rcbv T, rcbv P, rcbv TT ; CBF T, CBF P, CBF TT ; and CBV T, CBV P, CBV TT. Statistical Analysis The association between glioma grade and each measure from histogram and conventional ROI analysis was evaluated using Spearman rank correlations. The Mann-Whitney (MW) U test was used to compare LGGs and HGGs with respect to rcbv max and to each histogram measure. The Spearman correlations and MW tests were each based on a total of 127 measures (rcb- V max, 14 measures for each of CBF, CBV, and rcbv by the three histogram methods). Thus, to exert familywise control over the type I error rate and reduce the false discovery rate, the P values associated with the Spearman correlation and MW test were Bonferronicorrected (i.e., multiplied by 127, the number of P values generated) and were declared significant at the Bonferroni-corrected 5% family-wise significance level. Stepwise variable selection in the context of binary logistic regression was used to assess the relative utility of rcbv max and the histogram metrics in terms of their ability to detect HGGs and to identify subsets of histogram measures constituting significant independent predictors of HGG. The predictive utility of rcbv max was assessed relative to the CBF, CBV, and rcbv histogram measures generated by each individual method (i.e., only the histogram measures produced by a single method were allowed to compete with rcbv max and each other for selection into the model to predict HGG). The relative utility of models based on different subsets of metrics was summarized in terms of the percentage of times the prediction model correctly assigned the highest predicted probability to the observed tumor grade (denoted by %Concordant). Receiver operating characteristic (ROC) curve analyses were used to determine an optimal threshold for the diagnosis of HGGs on the basis of rcbv max and each histogram measure. For each measure, the optimal threshold was defined as the threshold associated with no less than 95% sensitivity

4 1056 Young et al. while maintaining the highest possible specificity. Mc- Nemar s test was used to compare rcbv max and histogram measures with respect to %Concordant, as determined by logistic regression, and the specificity associated with the optimal thresholds identified by ROC analysis. All statistical computations were carried out using SAS version 9.0 (SAS Institute, Cary, NC, USA). RESULTS The Spearman rank correlation of rcbv max with glioma grade was r This correlation was highly significant (P 0.001) and higher in magnitude than the correlation of glioma grade with any of the 126 histogram measures, although the correlation by rcbv max was not significantly different than the correlation by the best three histogram metrics produced by each of the three methods. Representative cases of LGGs and HGGs using the three histogram methods are illustrated in Figs The non-histogram-based method rcbv max and the top histogram-based Methods 1 3 derived from the rcbv maps showing Bonferroni-corrected significant correlation with glioma grade are summarized in Table 1; histogram-based methods derived from the CBF and CBV maps were not as useful, with the full results as follows: Method 1. Glioma grade was significantly correlated (P 0.001) with histogram-based rcbv T metrics: median, mean, SD, SD 50, mean 50, SD 25, mean 25, SD 10, mean 10, and PP. The highest three correlations were for rcbv T SD, SD 50, and mean 25 (r 0.718, 0.684, and 0.683, respectively). Histogrambased CBF T and CBV T were not useful. Method 2. Histogram-based rcbv P metrics significantly correlated with glioma grade (P 0.001) were: SD, SD 50,SD 25,SD 10, PH, skewness, kurtosis, and A1SD. Histogram-based CBV P PP was also significantly correlated with grade (r 0.427, P 0.001) while no CBF P measure was significant. The highest correlations were for rcbv P SD 25 (r 0.724), SD 50 (r 0.709), and PH (r 0.701). Method 3. All of the histogram-based rcbv TT metrics were significantly correlated with glioma grade (P 0.025) except PH. The highest correlations were for rcbv TT SD 50 (r 0.685), SD 25 (r 0.675), and PP (r 0.667). Histogram-based CBF T and CBV T were not useful. Predicting Glioma Grade Stepwise variable selection in the context of ordinal logistic regression was used to assess the relative utility of rcbv max and the histogram-based metrics produced by each individual method in terms of their ability to predict glioma grade. For each of the three methods, the %Concordant of the model to predict glioma grade (i.e., the percentage of times the model-predicted and observed glioma grades were concordant) based on the only histogram-based rcbv measures was significantly higher (P 0.01) than the %Concordant of the best model based on the entire set of CBF and CBV histogram measures. Furthermore, the %Concordant of the model based on the best histogram-based rcbv metrics was not significantly lower than the %Concordant of the model based on the best of all of the histogram metrics (i.e., CBF and CBV in addition to rcbv). Overall, the results indicate that among histogram measures, rcbv outperformed CBF and CBV in terms of predicting HGG, and the CBV and CBF metrics had no added value in the sense that their addition to a model based on rcbv alone did not lead to a significant improvement in diagnostic performance. For example, the 84% concordant achieved by Method 1 rcbv T SD achieved was not significantly different from the 90% concordant by Method 1 using the combination of CBF T (mean 25, PH) CBV T (PH) rcbv T (SD, mean 25 ). The %Concordant of the model to predict glioma grade using only rcbv max was significantly higher (P 0.01) than the %Concordant of the best model based on the CBF and CBV histogram measures produced by any of the three methods. Each of the three histogram-based rcbv methods produced an rcbv histogram statistic with a higher %Concordant than rcbv max, although the increase in %Concordant never achieved statistical significance. Overall, the results suggest that rcbv max outperformed the CBF and CBV histogram measures produced by each of the three methods in terms of predicting HGG and was statistically indistinguishable from the rcbv histogram measures in terms of diagnostic accuracy for HGG. Comparison of Low- and High-Grade Gliomas A MW U test was used to compare LGGs and HGGs with respect to rcbv max and each of the histogram measures. The LGGs and HGGs that exhibited Bonferronicorrected significant differences with respect to rcbv max (P 0.001) as well as each of the histogram measures are given in Table 2. Determination of Threshold Values We next identified the threshold that permitted the identification of HGGs with no less than 95% sensitivity while maintaining the highest possible specificity. For rcbv max, the threshold was estimated as Based on this, a diagnostic test to identify high grade tumors would declare a given tumor to be high grade if and only if the rcbv max value obtained for that tumor was This test achieved a sensitivity of 95.1% and a specificity of 80.65%. When a previously determined threshold of 1.75 was used (5), the test achieved a sensitivity of 98.4% and a specificity of 67.7%. For each of the three histogram methods, the three CBF, CBV, and rcbv metrics with the highest diagnostic utility for detecting high-grade tumors were selected for comparison to rcbv max. All nine of the selected measures were rcbv summary statistics. For each of these nine selected metrics, a threshold was identified that permitted the detection of high grade tumors with no less than 95% sensitivity while maintaining the highest possible specificity. McNemar s test was used to com-

5 ROI vs. Three Histogram Analyses of DSC MRI 1057 Figure 2. Low grade glioma (Grade II), histogram analysis. a,d: Method 1: Tumoral analysis is performed using an ROI drawn around the maximal tumor diameter. b,d: Method 2: Peritumoral analysis is performed using a semiautomated six pixel dilation factor around the user-defined tumor ROI. Top line in (d) is Method 1 and bottom line is Method 2. c,e: Method 3: Total tumoral analysis is performed utilizing all acquired perfusion images without any user input (in this case, 10 slices had been obtained through the tumor volume). pare the specificity of the diagnostic tests based on each of the rcbv histogram metrics to the specificity of the test based on the rcbv max thresholds of 2.15 (81% specificity) and 1.75 (68% specificity). As summarized in Table 3, each of the selected rcbv histogram metrics had a significantly higher specificity than was associated with rcbv max, with each rcbv histogram metric achieving no less than 93% to 100% specificity.

6 1058 Young et al. Figure 3. Anaplastic astrocytoma (Grade III). (a,d) tumoral; (b,d) peritumoral; and (c,e) total tumoral histogram analysis. [Color figure can be viewed in the online issue, which is available at The correlation with glioma grade by the best three histogram metrics produced by each of the three methods was not significantly different than the correlation between rcbv max and glioma grade as reported in earlier work (28). DISCUSSION Cerebral gliomas are markedly heterogeneous in terms of their biologic and genetic nature (29). DSC MRI provides estimations of the amount of tumor angiogenesis

7 ROI vs. Three Histogram Analyses of DSC MRI 1059 Figure 4. Glioblastoma multiforme (Grade IV). (a,d) tumoral; (b,d) peritumoral; and (c,e) total tumoral histogram analysis. Note user-defined ROI in (a) encompasses the entire tumor. [Color figure can be viewed in the online issue, which is available at and microvascularity, which can help predict their malignant potential. rcbv measures have shown excellent correlation with tumor grade. There is evidence that rcbv measurements may predict patient prognosis better than histopathologic features, particularly for low grade gliomas (30). Histopathologic evaluation is the current reference standard for establishing the diagnosis, determining tumor grade, guiding optimal management, and predicting the prognosis for these tumors. The limitations of histopathology, however, are

8 1060 Young et al. Table 1 Comparisons of Statistically Significant (P 0.001) Non-Histogram-Based rcbv max and Histogram-Based rcbv Methods 1-3 With Glioma Grade Non-histogram-based Histogram-based rcbv metrics 1 tumoral 2 peritumoral 3 total tumoral Metric (r value) rcbv max (0.734) SD (0.718) SD 25 (0.724) SD 50 (0.685) SD 50 (0.684) SD 50 (0.709) SD 25 (0.675) Mean 25 (0.683) Peak height (0.701) Peak position (0.667) *Only the three histogram-based rcbv metrics with the highest correlations are shown in the table with full results including the less useful histogram-based CBF and CBV metrics described in the text. SD X, mean X SD and mean computed over the top X% of the histogram. well known and include the following: 1) sampling error that may occur because only a few small samples of tissue are assessed, particularly from stereotactic biopsy, which may not include the most malignant or biologically active portion of the tumor; 2) it may be difficult to obtain a range of samples if the tumor is in a location that is inaccessible to the surgeon; 3) different institutions use different classification and grading systems; 4) variability in interpathologist and intrapathologist diagnoses; and 5) the dynamic nature of glial tumors results in heterogeneous tumor cell populations of different degrees of malignancy. Gross total resection (GTR) can provide a more complete sample for histopathologic assessment, as well as delaying tumor recurrence and progression while improving patient outcome (31,32). GTR may not include malignant tissue; however, that does not enhance or result in increased signal on T2-weighted images. Determination of perfusion metrics is currently undertaken in the research and clinical setting using software that relies upon accurate ROI analysis. Although the use of four small ROIs has demonstrated the most optimal reproducibility (27), there is an unavoidable component of interobserver and intraobserver variability. Reliable, reproducible data may only be able to be obtained by experienced operators. Therefore, developing a more objective method would allow even an inexperienced operator to obtain reliable and potentially more reproducible data. We used the entire data set of perfusion images without segmentation for total tumoral histogram analysis. The tumoral and peritumoral regions were specifically analyzed by ROI (Method 1) and semiautomated ROI schemes (Method 2), respectively. These latter two methods required some user dependence but were used to add spatial specificity to the histogram measures. The observed peritumoral hyperperfusion is consistent with the known infiltrative nature of gliomas with tumor extending beyond the margins of contrast enhancement to the perienhancing regions of T2 signal abnormality (33). There is very little literature regarding the utility of DSC MRI histogram analysis for cerebral gliomas. One group examined tumor heterogeneity in HGGs using histogram PH and percentage recovery (34). With Method 2, we found PH to be a valuable metric for peritumoral hyperperfusion, again in keeping with increased angiogenesis that occurs beyond the contrast enhancing portions of tumor. We were also able to detect statistically significant metrics from Method 3 using total tumoral analysis. While this may initially be unexpected, we believe that two major factors are responsible. First, the total tumoral analysis reflects the ability of the histogram technique to mathematically extract useful information despite its apparent lack of spatial specificity. Second, it is likely that the infiltrative nature of gliomas extends even further beyond the peritumoral signal abnormalities into normal appearing brain parenchyma on MRI. By including the normal-appearing brain parenchyma along with the tumoral and peritumoral regions, the total tumoral histogram includes contributions made by normal-appearing but microscopically tumor-infiltrated brain parenchyma. The total tumoral histogram, therefore, may provide the most complete assessment of tumor neovascularity and tumor burden upon the patient. By overcoming limitations of sampling error, this allows more comprehensive tumor evaluation than perhaps even histopathology performed after GTR. The utility of Method 3 postulates that operator-independent perfusion metrics that are fully reproducible can still provide an accurate assessment of tumor grade. We termed this method total tumoral because current first- Table 2 Histogram-Based Metrics With Bonferroni-Corrected Significant Differences Between Low and High Grade Tumors Perfusion Histogram-based metrics map 1 tumoral 2 peritumoral 3 total tumoral CBF Peak height None None CBV Peak height Median, mean, peak position None rcbv Median, mean, SD, SD 50, mean 50, SD 25, mean 25,SD 10, mean 10, peak position SD, SD 50,SD 25,SD 10, peak height, skewness, kurtosis, A1SD a SD, SD 50,SD 25, mean 25,SD 10, mean 10, peak height, peak position, skewness, kurtosis, A1SD a A1SD is area under 1 SD of the curve. SD X, mean X SD and mean computed over the top X% of the histogram.

9 ROI vs. Three Histogram Analyses of DSC MRI 1061 Table 3 Threshold Determined for Each rcbv Histogram Metric, Specificity Achieved by Each Threshold, and P Value From McNemar s Tests to Compare the Specificity to that Associated With rcbv ROI Thresholds of 1.75 and 2.15 Histogram-based rcbv metrics 1 tumoral 2 peritumoral 3 total tumoral High-grade if metric is: SD 1.7 SD SD SD 1.5 SD SD SD 2.2 SD Mean 2.3 Specificity (%) P value (vs. rcbvmax 1.75) P value (vs. rcbvmax 2.15) SDX, meanx the SD and mean computed over the top X% of the histogram. pass DSC MRI perfusion technology limits perfusion acquisition to a maximum of only 10 slices in order to maintain the necessary high temporal resolution of these dynamic studies. SD is a measure of the dispersion of data around the arithmetic mean. SD, or the square root of the variance, is defined as: N s Y i Y 2 / N 1, (4) i 1 where Y is the mean of the data. The SD was significantly greater in high grade tumors than in low grade tumors. The ability of SD to predict tumor grade reflects the biological nature of gliomas: absent to mild hyperperfusion in low grade tumors result in a homogeneous distribution of values with respect to the mean with relatively few high or low values, while marked hyperperfusion in high-grade tumors results in a heterogeneous distribution of values with relatively more high values. The main limitation of utilizing a SD measure is that precision and validity are compromised if the data are not distributed in a normal fashion. SD is sensitive to extreme values that can inflate its value and distort the apparent spread of data. We exerted some control over outliers by standardizing the upper limits used to determine the CBF, CBV, and rcbv color maps, from which the histogram metrics were derived. In addition, we segmented the data into centiles to measure the SD of the upper ranges of the histogram using SD 50,SD 25, and SD 10. For Methods 2 and 3, segmented SD had the highest correlations Method 2 SD 25 :r 0.724; and Method 3 SD 50 :r These peritumoral and total tumoral SD metrics likely benefited from the exclusion of relatively normal brain by restricting analysis to the upper centiles. Because of its inherent relationship with sample variability, SD may not be the best metric to use, despite its high correlation with glioma grade. We found the next best tumoral histogram metric to be mean 25, which results from mathematical segmentation of the histogram values. The mean is one of the most commonly applied measures for a series of values. Although it, too, may be distorted by a few extreme values, the mean is a robust metric whose utility is aided by segmentation. We may anticipate that changes in histogram skewness will accompany the observed changes in SD. Methods 2 and 3 reached Bonferroni-corrected significant changes in skewness (P and P , respectively), while Method 1 approached significance (P ). The strongest skewness correlation, found with Method 2 (r ), remains less than the best SD correlation. Skewness is a measure of the degree of asymmetry with respect to the center point defined as: N Y i Y 3 i 1 skewness N 1 s 3, (5) and is zero for a normal distribution. Skewness returns negative values if the tail is longer to the left and posi-

10 1062 Young et al. tive values if the tail is longer to the right. The possibility of both positive and negative values related to data heterogeneity in high grade tumors, as compared to SD that returns only positive values, may have weakened its correlation. In addition, positive skewness by highgrade tumors was limited by the predefined upper limits for the color maps. This had the effect of truncating elongated tails on the right side, with decreased shifting of the mean away from the median. A third potential confounder involves the shape of the histogram curve itself. The usual measure of skewness assumes a single unimodal curve with a net left or right shift. Heterogeneous tumors such as GBM, however, can result in bimodal or multimodal curves that reflect areas of avid hyperperfusion and frank necrosis. In these situations, the net result as measured by skewness may return an overly simplified representation of the actual data set. One limitation of this study pertains to the potential effect of glioma size on the histogram, which is merely a plot of pixel values. For the tumoral and peritumoral measures, lesion size presents a potential bias toward the use of SD metrics such that SD may be smaller in small HGGs and larger in larger LGGs. For the total tumoral measures, it is conceivable that larger tumors will have a more prominent impact on the total tumoral perfusion metrics than smaller tumors. In reality, however, the issue is much more complex as primary glial tumors are known to infiltrate adjacent normal appearing brain parenchyma. Although glioma size is often estimated in two-dimensional (2D) and 3D in both clinical and research practices, the exact dimensions of these infiltrative tumors often remains imprecise. Despite this unknown relationship with tumor size, we were still able to find significant correlations between rcbv TT metrics and tumor grade. We used 2D ROIs to represent the tumoral and peritumoral regions, rather than volumetric 3D assessments. Human gliomas are well recognized for their heterogeneity, with great variety in terms of the distribution and amount of more malignant vs. more indolent tumor cells. Tumoral and peritumoral histogram ROIs were manually drawn on the axial images with the greater tumor diameter, which we assumed represented the largest portion of the tumor. This is somewhat contrary to rcbv max technique in which we specifically target the foci with the greatest degrees of perfusion, no matter how small. Gliomas are as malignant as the most malignant focus, and thus rcbv max has been shown to be a very useful technique in predicting glioma grade. Although selection of the largest axial diameter is expected to decrease the correlation of the histogram methods with glioma grade, we are interrogating more of the tumor and this may become more valid in terms of monitoring tumors during and after therapy. Until sophisticated 3D volumetric rendering protocols attain greater availability and popularity, the standard axial image remains the mainstay of daily clinical practice. The histogram metrics were calculated from the CBF, CBV, and rcbv color maps. The histograms are therefore limited by predetermined minimum and maximum values used to calculate the color maps, which are necessary to maintain appropriate coloration scales. These restrictions also assisted the measurement of certain metrics, such as SD, although the contribution by tiny albeit very elongated tails is likely minimal. In contrast, routinely obtained rcbv max measures are determined by placing the ROI according to the rcbv color map and calculating the actual value from the raw perfusion data. Limiting the maximal values helps to minimize the influences of very elevated values, which may decrease contamination by hemorrhage or contrast leakage from blood-brain barrier disruption. Large ROIs do include large blood vessels, which may confound rcbv measurements. This is addressed in two ways. In applying the histogram, very high rcbv values obtained from large vessels are excluded from the histogram. Second, in the histogram analysis, we also investigate the top centiles of the histogram curves (mean X and SD X ). This allows us to evaluate the utility of high rcbv values (some of which have come from large vessels), in the prediction of tumor grade. 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