Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

Osamu Togao; Toru Chikui; Kenji Tokumori; Yukiko Kami; Kazufumi Kikuchi; Daichi Momosaka; Yoshitomo Kikuchi; Daisuke Kuga; Nobuhiro Hata; Masahiro Mizoguchi; Koji Iihara; Akio Hiwatashi

doi:10.1371/journal.pone.0243839

. 2020 Dec 14;15(12):e0243839. doi: 10.1371/journal.pone.0243839

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

Osamu Togao ^1,^*, Toru Chikui ², Kenji Tokumori ³, Yukiko Kami ², Kazufumi Kikuchi ⁴, Daichi Momosaka ⁴, Yoshitomo Kikuchi ⁴, Daisuke Kuga ⁵, Nobuhiro Hata ⁵, Masahiro Mizoguchi ⁵, Koji Iihara ⁵, Akio Hiwatashi ⁴

Editor: Niels Bergsland⁶

¹Department of Molecular Imaging & Diagnosis, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan

²Department of Oral and Maxillofacial Radiology, Faculty of Dental Science, Kyushu University, Fukuoka, Japan

³Department of Clinical Radiology, Faculty of Medical Technology, Teikyo University, Fukuoka, Japan

⁴Department of Clinical Radiology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan

⁵Department of Neurosurgery, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan

⁶University at Buffalo, UNITED STATES

Competing Interests: The authors have declared that no competing interests exist.

^✉

* E-mail: togao@radiol.med.kyushu-u.ac.jp

Roles

Osamu Togao: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing

Toru Chikui: Conceptualization, Methodology, Software, Supervision, Writing – original draft, Writing – review & editing

Kenji Tokumori: Methodology, Writing – original draft, Writing – review & editing

Yukiko Kami: Data curation, Methodology, Software, Writing – original draft, Writing – review & editing

Kazufumi Kikuchi: Data curation, Writing – original draft, Writing – review & editing

Daichi Momosaka: Data curation, Writing – original draft, Writing – review & editing

Yoshitomo Kikuchi: Data curation, Writing – original draft, Writing – review & editing

Daisuke Kuga: Data curation, Writing – original draft, Writing – review & editing

Nobuhiro Hata: Data curation, Writing – original draft, Writing – review & editing

Masahiro Mizoguchi: Data curation, Writing – original draft, Writing – review & editing

Koji Iihara: Data curation, Supervision, Writing – original draft, Writing – review & editing

Akio Hiwatashi: Conceptualization, Data curation, Supervision, Writing – original draft, Writing – review & editing

Niels Bergsland: Editor

PMCID: PMC7737570 PMID: 33315914

Abstract

The preoperative imaging-based differentiation of primary central nervous system lymphomas (PCNSLs) and glioblastomas (GBs) is of high importance since the therapeutic strategies differ substantially between these tumors. In this study, we investigate whether the gamma distribution (GD) model is useful in this differentiation of PNCSLs and GBs. Twenty-seven patients with PCNSLs and 57 patients with GBs were imaged with diffusion-weighted imaging using 13 b-values ranging from 0 to 1000 sec/mm². The shape parameter (κ) and scale parameter (θ) were obtained with the GD model. Fractions of three different areas under the probability density function curve (f1, f2, f3) were defined as follows: f1, diffusion coefficient (D) <1.0×10⁻³ mm²/sec; f2, D >1.0×10⁻³ and <3.0×10⁻³ mm²/sec; f3, D >3.0 × 10⁻³ mm²/sec. The GD model-derived parameters were compared between PCNSLs and GBs. Receiver operating characteristic (ROC) curve analyses were performed to assess diagnostic performance. The correlations with intravoxel incoherent motion (IVIM)-derived parameters were evaluated. The PCNSL group's κ (2.26 ± 1.00) was significantly smaller than the GB group's (3.62 ± 2.01, p = 0.0004). The PCNSL group's f1 (0.542 ± 0.107) was significantly larger than the GB group's (0.348 ± 0.132, p<0.0001). The PCNSL group's f2 (0.372 ± 0.098) was significantly smaller than the GB group's (0.508 ± 0.127, p<0.0001). The PCNSL group's f3 (0.086 ± 0.043) was significantly smaller than the GB group's (0.144 ± 0.062, p<0.0001). The combination of κ, f1, and f3 showed excellent diagnostic performance (area under the curve, 0.909). The f1 had an almost perfect inverse correlation with D. The f2 and f3 had very strong positive correlations with D and f, respectively. The GD model is useful for the differentiation of GBs and PCNSLs.

Introduction

The preoperative imaging-based differentiation of primary central nervous system lymphomas (PCNSLs) and glioblastomas (GBs) is of high importance since the therapeutic strategies differ substantially between these tumors [1, 2]. The treatment of GBs is based on the maximal possible safe surgical resection together with postoperative chemoradiation therapy [1] whereas PCNSLs require a biopsy for histological confirmation followed by chemoradiation therapy [2]. In typical cases, the differentiation of these tumors by conventional MRI is not always difficult since PCNSLs shows homogenous contrast enhancing lesions while GBs show irregular and heterogenous ring enhancing lesion with necrosis. However, it is frequently difficult to differentiate these tumors especially when they demonstrate atypical imaging features.

Several studies have indicated that advanced MRI techniques such as diffusion-weighted imaging (DWI) [3–6], dynamic susceptibility contrast perfusion-weighted imaging [6–8], and arterial spin labeling [9] are useful for distinguishing PCNSLs and GBs. According to those studies, PCNSLs are characterized by more restricted water diffusion and lower perfusion compared to GBs.

Many mathematical models have been proposed for the analysis of diffusion MRI. The mono-exponential model describes the Brownian motion of water molecules by calculating the apparent diffusion coefficient (ADC) based on the Gaussian distribution of diffusion displacement [3]. The bi-exponential intravoxel incoherent motion (IVIM) model aims to separate the true water diffusion and the capillary perfusion by using multiple low b-values [10, 11]. Diffusion kurtosis imaging (DKI) is an approach used to characterize non-Gaussian water diffusion, which estimates kurtosis metrics [12].

It has been reported that all of these approaches are useful in differentiating GBs and PCNSLs [3, 13, 14], but all have possible limitations. The mono-exponential model may not precisely reflect the reality of diffusion behavior in heterogenous biological tissues, since this model assumes a Gaussian distribution. The bi-exponential model could be influenced by an uncertainty of the estimated perfusion, since signal measurements at low b-values are susceptible to measurement errors [15–18]. The DKI model is limited by the unclear biological interpretation of the kurtosis parameters [18–21].

As one of the non-Gaussian distribution models, a statistical model based on the gamma distribution (GD) has been proposed for diffusion MRI analyses [22]. The GD model is a two-parameter family of continuous probability distribution parametrized in terms of the shape parameters kappa (κ) and the scale parameter theta (θ), and this model assumes that the diffusion coefficient (D) is distributed continuously within a voxel. The GD model allows us to estimate fractions of a tissue type based on the concept that the area fractions for D <1.0 × 10⁻³ mm²/sec, D = 1.0 × 10⁻³ to 3.0 ×10⁻³ mm²/sec, and D >3.0 ×10⁻³ mm²/sec are attributed to intracellular, extracellular extravascular, and intravascular spaces, respectively [18, 22, 23]. Based on these fractions, we may be able to estimate histopathological conditions of neoplasms or organs.

The GD model has been used to assess prostate cancers [22–24], breast cancers [18], and renal function [25]. The GD model was also used to assess cerebral ischemic stroke in rat brains, and it was showed that this model exhibited a better performance than the conventional mono-exponential model and allowed for a significantly enhanced visualization of ischemic lesions [26]. To the best of our knowledge, its application to brain tumors has never been reported. We conducted the present study to determine whether the GD model is useful in the differentiation of PCNSLs and GBs.

Materials and methods

This retrospective study was approved by the Institutional Review Board of Kyushu University Hospital (no. 2019–447), and the requirement for informed consent was waived.

Patients

The DWI protocol with multiple b-values has been a part of our routine preoperative MRI examination for patients with brain tumors since January 2013. The patient inclusion criteria for this study were: (1) The DWI with multiple b-values was conducted preoperatively for the patient during the period from January 2013 to August 2019; and (2) The patient subsequently underwent a surgical resection or biopsy within 1 month of the DWI with multiple b-values, and the histopathological diagnosis of PCNSL or GB was made. A total of 89 patients met these criteria. The exclusion criteria were as follows: (1) no distinct contrast enhancement observed in the lesion (n = 3); and (2) difficulty in the analysis of images due to severe artifacts (n = 2). Thus, a total of 84 patients including 27 with PCNSLs (age, 62.9 ± 15.5 years; Male, 17 patients; Female, 10 patients) and 57 with GBs (age, 66.0 ± 16.4 years; Male, 31 patients; Female, 26 patients) were included in this study. The difference between the number of patients with PCNSLs and GBs can be explained by the fact that the PCNSLs are less frequent compared to the GBs [27].

MRI

Multi-b-value DWI was performed on a 3T clinical scanner (Achieva 3.0TX or Ingenia 3.0T, Philips Healthcare, Best, The Netherlands) with an 8-channel or 15-channel head coil. The DWI was performed in axial planes by using a single-shot echo-planar imaging diffusion sequence, with 13 b-values (0, 10, 20, 30, 50, 80, 100, 200, 300, 400, 600, 800, 1000 sec/mm²) in three orthogonal directions. The other imaging parameters were: repetition time, 2,500 msec; echo time, 70 msec; matrix, 128×126 (reconstructed to 256×256); slice thickness, 5 mm, field of view, 230×230 mm; number of slices, 11; sensitivity encoding factor, 1.5; scan time, 2 min 7 sec. For reference, several standard MR images including contrast-enhanced T1-weighted images were acquired.

Image analysis

The mono-exponential model was computed using all of the above-listed b-values according to the following equation:

\frac{S_{b}}{S_{0}} = e^{- b \times A D C}

(1)

where Sb is the signal intensity for each b-value and S0 is the signal intensity at a b-value of zero.

In the bi-exponential model, the signal decay was estimated by the following the equation:

\frac{S_{b}}{S_{0}} = {(1 - f) ∙ e}^{- b D} + f ∙ e^{- b D *}

(2)

where D* is the pseudo-diffusion coefficient, and the f is the volume fraction within a voxel of water flowing in perfused capillaries.

The GD model is represented by ρ(D) and is given by:

ρ (D) = \frac{1}{Γ (κ) θ^{κ}} ・ D^{κ - 1} ∙ e x p (\frac{- D}{θ})

(3)

where κ describes the shape parameter and θ describes the scale parameter. When the distribution of D follows this equation, the signal intensity on DWI is given by:

S (b) = S 0 ∙ \frac{1}{{(1 + θ b)}^{κ}}

(4)

Three different areas under the probability density function (PDF) curve were defined as follows: f1, the fraction of D <1.0×10⁻³ mm²/sec; f2, the fraction of 1.0×10⁻³ to 3.0×10⁻³ mm²/sec; f3, the fraction of D >3.0×10⁻³ mm²/sec. The f1 value is attributed to the intracellular component; the f2 is attributed to the extracellular extravascular component, and the f3 is attributed to the intravascular component [18, 22, 23].

The DWI data in the digital imaging and communications in medicine (DICOM) format were transferred to a personal computer and fit to the GD model, and then the κ and θ values were estimated using the Image J software program (ver. 1.52p; U.S. National Institutes of Health, Bethesda, MD) and self-built plug-ins. After the export of the x- and y-coordinates and the κ and θ of each pixel within the region of interest (ROI), the f1, f2, and f3 values of each pixel were calculated using Microsoft Excel ver. 16.16.14.

ROI placement

The matrix sizes of the postcontrast T1-weighted images were adjusted to the same size as those of the DWI using the ImageJ function to match the geometric information of these images. ROIs were placed to delineate the enhancing lesion on the single slice that had the maximum area. On the size-adjusted postcontrast T1-weighted images, areas showing contrast enhancement were manually segmented by a neuroradiologist with 19 years of experience (O.T.) (Fig 1). The areas with necrosis, cystic lesion, hemorrhage, or obvious artifacts were carefully excluded from the ROI.

Fig 1A and 1B show a GB with ring enhancement, and Figures C and D show a PCNSL with solid enhancement. The ROIs were placed on postcontrast T1-weighted images to include contrast enhancing lesions (A, C, area #1). The ROIs were also placed on the non-contrast-enhancing T2-hyperintense areas surrounding the contrast-enhancing area (area #2) and the contralateral normal-appearing white matter (B, D, area #3).

The ROIs were copied from the postcontrast T1-weighted images and pasted to the DWI. Fine manual adjustments were made when there were locational mismatches due to image distortion or the patient's motion, etc. The ROIs were also placed on the peritumoral non-contrast-enhancing T2-hyperintense areas to evaluate whether there were differences in histological features including tumor infiltration or increased vascularity in the peritumoral areas between PCNSLs and GBs. In addition, the ROIs were placed on the contralateral normal-appearing white matter. The ROIs for the peritumoral non-contrast-enhancing T2-hyperintense areas and contralateral normal-appearing white matter were measured on the image obtained with the b-value of 0 sec/mm² image. The same ROIs were used for all DWI analyses.

Statistical analyses

The GD model-derived and IVIM-derived parameters were compared between the PCNSLs and GBs with the Mann-Whitney U-test. A receiver operating characteristic (ROC) curve analysis was performed to assess the diagnostic performance of the parameters in the differentiation of PCNSLs and GBs. The area under the curve (AUC) was calculated, and then the sensitivity and specificity were obtained. The optimal cutoff point was determined by Youden's method [28]. The diagnostic performance was considered excellent for AUC values between 0.9 and 1.0, good for AUC values between 0.8 and 0.9, fair for AUC values between 0.7 and 0.8, poor for AUC values between 0.6 and 0.7, and failed for AUC values between 0.5 and 0.6 [29].

To determine whether the combination of multiple parameters for both the GD model and the IVIM model increases the diagnostic performance, we first performed a stepwise analysis to select the explanatory variables for a multiple regression model from a group of candidate variables by going through a series of automated steps. A forward-selection rule was applied in which the analysis started with no explanatory variables and then added variables, one by one, based on which variable was the most statistically significant, until there were no remaining statistically significant variables [30, 31]. We then performed a binomial logistic regression analysis to examine the AUCs of the combinations of the selected parameters. Two independent AUCs were compared using the method of Delong et al. [32]. The correlations among the parameters were assessed with Pearson’ correlation. Statistical analyses were performed with Prism 5.0 (GraphPad Software, San Diego, CA), MedCalc 19.1 (Broekstraat, Mariakerke, Belgium), and JMP Pro 14.0 (SAS Institute, Cary, NC). P-values <0.05 were considered significant.

Results

Comparisons of the parameters between the PCNSL and GB groups

The detailed information for the parameters in the gadolinium enhancing lesion, peritumoral T2-hyperintense areas without contrast enhancement, and normal appearing white matter is summarized in Table 1.

Table 1. Gamma distribution model-derived parameters in PCNSLs and GBs.

		κ		θ (×10⁻⁶ mm²/s)		f1		f2		f3
Enhancing lesion	PCNSL	2.26±1.00	p = 0.0004	1.91±2.43	p = 0.6341	0.542±0.107	p<0.0001	0.372±0.098	p<0.0001	0.086±0.043	p<0.0001
Enhancing lesion	GB	3.62±2.01	p = 0.0004	1.72±1.63	p = 0.6341	0.348±0.132	p<0.0001	0.508±0.127	p<0.0001	0.144±0.062	p<0.0001
T2-hyperintense areas	PCNSL	8.23±2.42	p = 0.8528	0.39±0.19	p = 0.4747	0.140±0.066	p = 0.4014	0.775±0.074	p = 0.8882	0.085±0.045	p = 0.2570
T2-hyperintense areas	GB	8.36±3.18	p = 0.8528	0.40±0.25	p = 0.4747	0.188±0.150	p = 0.4014	0.752±0.128	p = 0.8882	0.073±0.040	p = 0.2570
NAWM	PCNSL	2.76±1.18	p = 0.6341	0.85±0.45	p = 0.1436	0.642±0.047	P<0.0001	0.316±0.036	p<0.0001	0.043±0.026	p = 0.0105
NAWM	GB	2.55±0.75	p = 0.6341	1.08±1.41	p = 0.1436	0.593±0.044	P<0.0001	0.354±0.038	p<0.0001	0.053±0.019	p = 0.0105

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PCNSL, primary central nerve system lymphoma; GB, glioblastoma; NAWM, normal appearing white matter.

The results of our comparisons of the GD model-derived parameters between the PCNSLs and GBs in the gadolinium-enhancing lesions are shown in Fig 2. In the gadolinium-enhancing lesions, the κ was significantly smaller in the PCNSL group (2.26 ± 1.00) than in the GB group (3.62 ± 2.01, p = 0.0004), the f1 was significantly larger in the PCNSL group (0.542 ± 0.107) than in the GB group (0.348 ± 0.132, p<0.0001), the f2 was significantly smaller in the PCNSL group (0.372 ± 0.098) than in the GB group (0.508 ± 0.127, p<0.0001), and the f3 was significantly smaller in the PCNSL group (0.086 ± 0.043) than in the GB group (0.144 ± 0.062, p<0.0001), while the θ was not significantly different between the groups.

Fig 2 — A: The κ was significantly smaller in the PCNSL group than in the GB group. B: The θ was not significantly different between the groups. **C–E:** The f1 was significantly larger and the f2 and f3 were significantly smaller in the PCNSL group than in the GB group.

In the peritumoral T2-hyperintense areas without contrast enhancement, no significant differences were found between the PCNSL and GB groups for any of the GD model derived parameters.

In the contralateral normal-appearing white matter, the f1 was significantly larger in the PCNSL group (0.642 ± 0.047) than in the GB group (0.593 ± 0.044, p<0.0001), the f2 was significantly smaller in the PCNSL group (0.316 ± 0.036) than in the GB group (0.354 ± 0.038, p<0.0001), and the f3 was significantly smaller in the PCNSL group (0.043 ± 0.026) than in the GB group (0.053 ± 0.019, p = 0.0105).

Fig 3 provides a PCNSL case that showed a ring-like enhancing mass lesion mimicking a GB. This lesion showed a low κ, a large f1, a small f2, and a small f3, suggesting PCNSL. Fig 4 demonstrates a GB case that showed a solid enhancing mass lesion. This lesion showed a small κ, a small f1, moderate f2 and large f3, which are consistent with GB.

Fig 4 — A: The post-contrast T1-weighted image shows a solid enhancing mass lesion in the right thalamus (arrow). The enhancing lesion shows partly high signal intensity on DWI (B) and a relatively high ADC (1.42×10⁻³ mm²/sec, C). This lesion shows a small κ (1.44, D), a large θ (3.15×10⁻⁶ mm²/sec, E), a small f1 (0.297, F), a moderate f2 (0.399, G), and a large f3 (0.304, H). The peritumoral T2-hyperintense area without contrast enhancement shows a large κ (3.94, D), a small θ (0.75×10⁻⁶ mm²/sec, E), a small f1 (0.308, F), a large f2 (0.597, G), and a small f3 (0.095, H).

The ADC values of the enhancing lesions were significantly smaller in the PCNSL group (0.883 ± 0.176 × 10⁻³ mm²/sec) compared to the GB group (1.246 ± 0.266 × 10⁻³ mm²/sec, p<0.0001). The PCNSL group's D values were significantly smaller (0.805 ± 0.167 × 10⁻³ mm²/sec) compared to the GB group's D values (1.146 ± 0.256 ×10⁻³ mm²/sec, p<0.0001). The D* was significantly smaller in the PCNSL group (34.0 ± 7.4 × 10⁻³ mm²/sec) versus the GB group (40.7 ± 5.6 × 10⁻³ mm²/sec, p<0.0001). The f was significantly smaller in the PCNSL group (0.082 ± 0.024) compared to the GB group (0.102 ± 0.023, p = 0.0005).

Diagnostic performance of the single and combined parameters

The ROC graphs and diagnostic performance parameters are shown in Fig 5 and Table 2. In the single-parameter analysis regarding the differential diagnosis of GBs and PCNSLs, the ADC, f1, D, and f2 all showed good performances. The ADC showed the highest AUC value at 0.879, and the f1 and D values showed comparable AUCs (f1, 0.877; D, 0.875). No significant differences were found in the comparisons of ROC curves for these three parameters: f1 vs. ADC, p = 0.6130, f1 vs. D, p = 0.8449; ADC vs. D, p = 0.3935. The κ, f3, D*, and f showed fair diagnostic performances, but the θ resulted in a failed performance.

Table 2. ROC analysis for diagnostic performance of the parameters in the differentiation between PCNSLs from GBs.

Parameters	Area Under Curve	Sensitivity (%)	Specificity (%)	Cutoff Value
κ	0.737	61.4	81.5	2.954
θ	0.533	68.4	48.1	0.971 ×10⁻³ mm²/sec
f1	0.877	82.5	81.5	0.474
f2	0.817	87.7	70.4	0.380
f3	0.778	71.9	70.4	0.104
κ+f1+f3	0.909	84.2	88.9	0.540	0.404		0.133
D	0.875	86.0	81.5	0.887×10⁻³ mm²/sec
D*	0.776	66.7	85.2	40.089×10⁻³ mm²/sec
f	0.731	78.9	63.0	0.087
D+f	0.884	82.5	81.5	0.998×10⁻³		0.072
ADC	0.879	87.7	77.8	0.972 ×10⁻³ mm²/sec

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ROC, receiver operating characteristics; PCNSL, primary central nerve system lymphoma; GB, glioblastoma; D, true diffusion coefficient; D*, pseudo-diffusion coefficient; f, perfusion fraction; ADC, apparent diffusion coefficient.

In the combined-parameters analysis, the stepwise procedure selected κ, f1, and f3 for the GD model, and the D and f for the IVIM model. The combination of κ, f1, and f3 revealed excellent diagnostic performance with the AUC of 0.909, sensitivity of 84.2%, and specificity of 88.9%. This combination increased the diagnostic performance of κ (p = 0.0016), and f3 (p = 0.0075), although it did not improve the performance of f1 (p = 0.1950). The AUC of this combination (0.909) was higher than that of ADC (0.879); however, there was no significant difference between them (p = 0.2152).

The combination of D and f showed good diagnostic performance with the AUC of 0.884, 82.5% sensitivity, and 81.5% specificity. This combination improved the diagnostic performance of f (p = 0.0077), although it did not improve the performance of D (p = 0.5276).

Among all of the single and combined parameters, the combination of κ, f1, and f3 showed the highest AUC; however, no significant differences were detected between this combination and the ADC (p = 0.2152) or the combination of D and f (p = 0.2207).

Correlations of the model parameters

Fig 6 shows the correlations among the GD model-derived and IVIM model-derived parameters in all tumors. The f1 had an almost perfect inverse correlation with D (all, r = −0.9756, p<0.0001; PCNSL, r = −0.9558, p<0.0001; GB, r = −0.9699, p<0.0001). The f2 had a very strong positive correlation with D (all, r = 0.8865, p<0.0001; PNCSL, r = 0.9619, p<0.0001; GB, r = 0.8273, p<0.0001). The f3 had a very strong positive correlation with the f (all, r = 0.8654, p<0.0001; PNCSL, r = 0.8317, p<0.0001; GB, r = 0.8611, p<0.0001). The f1 had an very strong negative correlation with the f2 (all, r = −0.9155, p<0.0001; PCNSL, r = −0.9150, p<0.0001; GB, r = −0.8874, p<0.0001).

Discussion

The results of our analyses revealed that in gadolinium-enhancing lesions, the κ was significantly smaller in the PCNSL group than in the GB group. The θ was not different between the groups. The f1 was larger, the f2 was smaller, and the f3 was lower in the PCNSLs than in the GBs. The low κ values observed in the PCNSLs indicated that the PDF curve had a right-skewed distribution, which meant that the PDF has its peak in the lower D area, and thus the fraction of lower D was larger. Since the θ values were not significantly different between the PCNSL and GB groups, it was likely that the lower κ values might result in the lower ADC and D values and the higher f1 values observed in the PCNSLs compared to the GBs. These findings are in accordance with studies that examined the mono-exponential model, in which PCNSLs showed lower ADC values relative to GBs [3–5].

The θ is a scale parameter and may thus reflect the heterogeneity of a biological tissue. We expected that the θ values would be larger in GBs than in PCNSLs since GBs are histologically characterized by intratumoral tissue heterogeneity whereas PCNSLs are characterized by the dense and homogenous distribution of tumor cells; however, no significant difference in the θ values was observed between the groups. The θ values showed large standard deviations in both the PCNSLs and the GBs, indicating that this value could vary widely even in the same type of tumor. The same trend was observed in a study of breast tumors in which the θ values were not significantly different between the different types [18]. The utility of this parameter should be further evaluated in larger populations.

It seems that the higher f1 and lower f2 in the PCNSLs and the lower f1 and higher f2 in the GBs well reflected the histological features of the respective tumors. Histologically, PCNSLs are characterized by high cell density at the expense of reduced available extracellular space, and necrosis is not a common feature of this tumor. GBs can show locally high cell density, but the overall cell density can be lowered depending on the fraction of microscopic necrosis or hemorrhage. Our present findings are consistent with a study that reported that the ADC was lower and the cell density was higher in PNCSLs than in high-grade gliomas [3].

The GB group showed larger f3 and f compared to the PCNSL group. This may be attributed to the difference in vascularity of these tumors. Pathologically, neovascularization is a key feature of GB while it is not prominent in PCNSL [33, 34]. Our results are consistent with those from previous studies using dynamic susceptibility contrast perfusion-weighted imaging and arterial spin labeling imaging [9, 35].

With respect to the diagnostic performance, the ADC, f1, and D showed comparable AUCs in the present study, indicating that all three of these parameters are useful in the differentiation of PNCSLs and GBs. The reason for the slightly higher AUC observed with the ADC could be the effect of perfusion on ADC measurements. In hyperperfused tissues, ADC will be affected by the perfusion effect and overestimated compared to D; however, since both f1 and D are parameters without a perfusion effect in theory, an overestimation caused by perfusion should not be observed in these values. Therefore, in hypervascular tumors such as GBs, the ADC should be larger than D. On the other hand, in hypovascular tumors such as PCNSLs, this difference between ADC and D should smaller. This means that the difference between ADC and D would be larger in GBs than in PCNSLs. Therefore, ADC could show higher diagnostic performance in the discrimination of these two tumors than D. In fact, the difference between the ADC and D values was greater in the GBs (0.100 × 10⁻³ mm²/sec) than in the PCNSLs (0.078 × 10⁻³ mm²/sec), which was most likely due to the higher perfusion effect on the ADC in GBs than in PCNSLs. Nevertheless, the combination of κ, f1, and f3 demonstrated the highest diagnostic performance among all of the single and combined parameters, with the AUC of 0.909. The AUC of this combination tended to be higher than that of ADC although there was no statistically significant difference. Whether the combination of parameters of the GD model has an additive value should be evaluated in a larger population, since we did not observe statistical significance in all of our comparisons.

We found the correlations between the GD model-derived and IVIM-derived parameters, particularly between the f1 and D, the f2 and D, and the f3 and f. The almost perfect negative correlation observed between the f1 and D may indicate that these two parameters contain virtually identical information. The positive correlation between f2 and D suggests that the increased extracellular space like that taken up by microscopic necrosis might result in the higher f2. The positive correlation between f3 and f indicates that both of these parameters well reflected tissue perfusion despite the different analysis methods used. The negative correlation between f1 and f2 was likely due to the complementary relationship between these two parameters. In general, intravascular space (≒ f3) is smaller compared to intracellular (≒ f1) and extracellular extravascular space (≒ f2). In fact, the f3-values were much smaller than the f1- and f2-values in both PCNSLs and GBs in the present study. Therefore, the increase in f1 would result in the decrease in f2, and vice versa. Although the GD-derived and IVIM-derived parameters provide similar information, the strength of the GD model-derived parameters is that all fraction values (f1, f2, f3) are expressed as fractions or percentages, which allows us to well characterize tumors from histological viewpoint. The IVIM-derived f-value is also expressed in a percentage or fraction; however, the IVIM analysis is not able to provide the fraction values for intracellular and extracellular-extravascular spaces. In this sense, the IVIM method is not a perfect method for the histological characterization of tumors.

In the T2-hyperintense lesions without contrast enhancement, no significant differences were observed between the PCNSL and GB groups for any parameters. There have been several studies that showed increased rCBV on DSC-perfusion imaging in peritumoral noncontrast-enhancing T2-hyperintense areas of GBs [36, 37]. The results of these studies indicated that the peritumoral areas of GB include not only vasogenic edema but also tumor cells infiltrating surrounding brain parenchyma; however, our study did not reveal any significant differences in the GD model-based parameters for peritumoral noncontrast-enhancing T2-hyperintense areas between PCNSLs and GBs. The f2 values in the noncontrast-enhancing T2-hyperintense areas were higher in both types of tumor compared to those in the contrast-enhancing areas and normal appearing white matter. We assume that the high f2 values in the noncontrast-enhancing T2-hyperintense areas are likely to reflect mostly perifocal vasogenic edema rather than tumor infiltration outside the enhancing lesion. Our result is consistent with the previous DWI study in which ADC could not be used to differentiate edema with infiltration of tumor cells from vasogenic edema in high-grade gliomas and PCNSLs [38].

In the normal-appearing white matter, the GB group showed larger f1, smaller f2, and larger f3 than the PCNSL group although these differences were small. This was unexpected, and the reasons for the differences remain unclear; however, since GBs frequently show extensive infiltration into the surrounding brain tissue, which is a fundamental feature of diffuse glioma, it is no wonder that the increased cell density and perfusion were observed in the normal-appearing white matter.

This study has several limitations. The number of patients was relatively small (n = 84) — especially the number of patients with PCNSL (n = 27). The only one person performed the ROI placements on a single slice, and not whole tumor volume was evaluated. The ROI placements on the gadolinium-enhancing lesions were occasionally difficult, particularly when the lesions showed irregular and thin ring-like enhancement. Although the best effort was made to include only enhancing lesions, it is possible that necrosis in tumors was included, and this could have affected the analyses. In addition, the selection of b-values has not yet been optimized. Prior studies of the GD model used the maximum b-values ranging from 1000 to 3000 sec/mm² [18, 22–24]. In a study of prostate cancers, Oshio et al. used the similar DWI parameters to ours and the highest b-value of 1000 s/mm², and reported that the good fitting accuracy was observed in both cancerous tissues (R² = 0.99226) and normal tissues (R² = 0.99842) [22]. Their result indicated that DWI with the highest b-value of 1000 s/mm² can be used for GD model analyses; however, since it was reported that the non-monoexponential diffusion-related signal decay generally becomes more obvious over more extended b-value ranges, the maximum b value of 1000 sec/mm² used in the present study might be lower than the optimal value. The optimal b-values and numbers should be elucidated in future studies.

Conclusions

The GD model well described the histological features of PCNSLs and GBs, and its use enabled the significant differentiation of these tumors. The κ, f2, and f3 values were significantly smaller and the f1 values were significantly larger in the PCNSLs than in the GBs. The combination of κ, f1, and f3 showed the highest AUC. The GD model-derived parameters correlated well with the IVIM-derived parameters. The GD model may therefore contribute to the characterization of various brain tumors from the histological viewpoint.

Supporting information

S1 Data. All measurements for gamma distribution model-derived and IVIM model-derived parameters.

(XLSX)

Click here for additional data file.^{(35.5KB, xlsx)}

Data Availability

All relevant data are within the manuscript and Supporting Information file.

Funding Statement

This work was supported by JSPS KAKENHI Grant Number JP17K10410 and JP20K08111. O.T. recieved these grants. https://www.jsps.go.jp/j-grantsinaid/ The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS One. doi: 10.1371/journal.pone.0243839.r001

Decision Letter 0

Niels Bergsland

10 Jul 2020

PONE-D-20-15410

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

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Reviewer #1: ----Summary

The manuscript reports the use of the diffusion MRI gamma distribution (GD) model in the differentiation of primary central nervous system lymphomas (PCNSLs) and glioblastomas (GBs).

The results indicate that the GD model is advantageous in terms of diagnostic performance when comparing these 2 lesions, namely when 3 specific parameters of this model are used in combination.

My overall impression is that the manuscript has quality and it is an interesting an innovative topic, but some aspects should be considered and better analysed.

----Comments to the Author

• Abstract:

Page 2 - “In this study, we investigate whether whether the gamma distribution (GD) model is useful in this differentiation of PNCSLs. and GBs” – The word “whether” is repeated and the full stop after PNCSLs should be removed.

Page 2 - “Receiver operating curve (ROC) analyses were performed to assess diagnostic performance.” – ROC stands for Receiver Operating Characteristic. This should appear as: Receiver Operating Characteristic (ROC) curve. Please check the rest of the document, as this is recurrent.

• Introduction:

Page 4 – Last paragraph – “The bi-exponential intravoxel incoherent motion (IVIM) model aims to separate the true water diffusion and the capillary perfusion by using multiple b-values [10, 11].” – multiple b-values but specifically multiple low b-values. Please add the word “low”

There are only a few articles in this topic, and the way the authors composed parts of the introduction is very similar to the reference number 22 (Shinmoto et al. 2014) and/or 24 (Borlinhas et al. 2019 ) of the document, and sometimes being exactly the same, but not being cited.

Example 1

“The IVIM model has an associated uncertainty to the estimated pseudodiffusion, and perfusion fraction, and a possible overparametrization of the model.7 The limitations of the DKI model are related to the unclear biological interpretation of the mean kurtosis parameter, and to the effects of the high b-values that the model requires.” – Reference 24 of the manuscript

“The bi-exponential model could be influenced by an uncertainty of the estimated perfusion, since signal measurements at low b-values are susceptible to measurement errors [15-17]. The DKI model is limited by the unclear biological interpretation of the kurtosis parameters [18-20].” – The actual text in the manuscript

Example 2

“The GD model allows us to estimate fractions of a tissue type based on the concept that the area fractions for D <1.0 × 10−3 mm2/sec, 1.0 × 10−3 to 3.0 ×10−3 mm2/sec, and D >3.0 ×10−3 mm2/sec are attributed to intracellular, extracellular extravascular, and intravascular spaces, respectively [21].” – The actual text in the manuscript

– “ADC values smaller than 1.0 mm2/scan be attributed to small tumor cells with restricted diffusion, and ADC values larger than 3.0 mm2/s can be attributed to perfusion, with ADC values between 1.0 mm2/sand 3.0 mm2/s attributed to water diffusion in the other components.” – Reference 21 of the manuscript

– “(…)extracellular fluid (ADCs between 1.0 and 3.0 mm2/s)" – Reference 22 of the manuscript

– “Through the PDF of ADC, three different areas under the function’s curve are defined as follows: the fraction of diffusion lower than 1.00 × 10-3 mm2/s is the f1 fraction and it reflects the small cell component; the fraction of diffusion higher than 3.00 × 10-3 mm2/s is the f3 fraction and it reflects the perfusion component; and the fraction of diffusion between 1.00 × 10-3 mm2/s and 3.00 × 10-3 mm2/s is the f2 fraction translating the extracellular component of the tissue.12,13” - Reference 24 of the manuscript

In this case, and as you can see, reference 21 is not specific when mentioning the meaning of f2. You have more specific references such as number 22 and 24 of your document.

Please add these references.

Page 5 - “The GD model allows us to estimate fractions of a tissue type based on the concept that the area fractions for D <1.0 × 10−3 mm2/sec, 1.0 × 10−3 to 3.0 ×10−3 mm2/sec, and D >3.0 ×10−3 mm2/sec are attributed to intracellular, extracellular extravascular, and intravascular spaces, respectively [21]” – This part “1.0 × 10−3 to 3.0 ×10−3 mm2/sec” must appear as “D=1.0 × 10−3 to 3.0 ×10−3 mm2/sec”

Page 5 – “The GD model is suitable for realistically interpreting diffusion data in a histological context.” - This sentence is very abrupt. If the reference you are using is the reference 21, Oshio et al. cautiously concluded the following: “(…) histological interpretation of the data appears possible.” In Oshio et al. work, the peripheral zone of the prostate and a prostate cancer were being compared, not different histological types of lesions for example. Your sentence can be misinterpreted.

Also, this sentence that you present should be connect to the information included in this paragraph.

Page 5 – “The GD model has been used to assess prostate cancers [21-23], breast cancers [24], and renal function [25]. To the best of our knowledge, its application to brain tumours has never been reported. We conducted the present study to determine whether the GD model is useful in the differentiation of PCNSLs and GBs.” – To the best of my knowledge that is true, but the GD model has been applied to brain studies. This is a relatively new application, and consequently, it would be worth mentioning this fact. Here is the a reference that you can use: Grinberg F, Farrher E, Ciobanu L, Geffroy F, Le Bihan D, et al. (2014) Non-Gaussian Diffusion Imaging for Enhanced Contrast of Brain Tissue Affected by Ischemic Stroke. PLoS ONE 9(2): e89225. doi:10.1371/journal.pone.0089225

• Material and Methods

- Patients

Page 6 - “Multi-b-value DWI” – It would be more adequate to read for example “The use of a DWI protocol with multiple b-values (…)”

Page 6 – The difference between the number of PCNSLs and GBs is relevant. Knowing that the PCNSLs are less frequent when compared to the GBs, this information could be added to justify the difference in the groups.

If available, the characteristics of the GB, like fraction of necrosis or haemorrhage should be reported. The addition of these characteristics would be enriching the study and could explain some outliers in the results.

- ROI placement

Page 9 – The legend of this figure 1 repeats the information that it is presented in the text: “The ROIs were also placed on the noncontrast-enhancing T2-hyperintense areas as well as on the contralateral normal-appearing white matter on the image obtained with the b-value of 0 sec/mm2 image.”

The reason why and the purpose of placing ROIs on the noncontrast-enhancing T2-hyperintense areas should be stated.

- Statistical Analysis

Page 9 – “The optimal cutoff point was determined by Youden's method.” – A literature reference should be provided to support the method.

Page 10 – “To determine whether the combination of multiple parameters for both the GD model and the IVIM model increases the diagnostic performance, we first performed a stepwise analysis to select appropriate parameters, and then we performed a binomial logistic regression analysis to examine the combinations of the selected parameters.” – Does “appropriate” means with the best diagnostic performances? “Examine” in what way? This should be presented in a clearer way.

• Results

- Comparisons of the parameters between the PCNSL and GB groups

Page 10 - 11 - “Figure 2 illustrates the results of our comparisons of the GD model-derived parameters between the PCNSLs and GBs in the gadolinium-enhancing lesions. The κ was significantly smaller in the PCNSL group (2.26 ± 1.00) than in the GB group (3.62 ± 2.01, p=0.0004). The θ was not significantly different between the groups. The f1 was significantly larger in the PCNSL group (0.542 ± 0.107) than in the GB group (0.348 ± 0.132, p<0.0001). The f2 was significantly smaller in the PCNSL group (0.372 ± 0.098) than in the GB group (0.508 ± 0.127, p<0.0001). The f3 was also significantly smaller in the PCNSL group (0.086 ± 0.043) than in the GB group (0.144 ± 0.062, p<0.0001). The detailed information for the parameters is summarized in Table 1. Figure 3 provides a PCNSL case that showed a ring-like enhancing mass lesion mimicking a GB. This lesion showed a low κ, a large f1, a small f2, and a small f3, suggesting PCNSL. Figure 4 demonstrates a GB case that showed a solid enhancing mass lesion. This lesion showed a small κ, a small f1, moderate f2 and large f3, which are consistent with GB. In the T2-hyperintense areas without contrast enhancement, no significant differences were found between the PCNSL and GB groups for any of the GD model derived parameters.” - This paragraph should be written in a more fluid way so the reader can better understand the ideas that the authors chose to highlight.

Page 14 – The results T2-hyperintense areas without contrast enhancement were mentioned but no analysis was made to the NAWM results. If the results were obtained these should be used to support the information shown about the GD model in the manuscript.

Page 14 – In the "all data" excel sheet for f parameter you use percentage and here you show a fraction. Please make it uniform to clearly inform the reader.

Page 18 – “(…) although the difference was not significantly different from the values for D (p=0.5276).” – This should be rephrased.

- Correlations of the model parameters

Page 18 – “The f1 had an almost perfect inverse correlation with D (all,

r = −0.976, p<0.0001; (…)” – According to figure 6, r = −0.9756, please confirm the information and change where necessary.

Page 18 – Considering that the correlation between f2 and D parameters is 0.88657, and it is mentioned because it is high compared to the other correlations, the correlation between f1 and f2 should also be mentioned. The correlation between f1 and f2 is above 0.9155 and the meaning of this result can be of interest to be discussed in the appropriate section of this work.

• Discussion

- The meaning of f3 and f parameters results and finding should be analysed in the discussion. Why f and f3 parameters are higher in the PCNSL when compared to the GB group of lesions?

- Another important result, which should be discussed, is that with the GD model parameters (κ, f1, and f3) it was possible to obtain a higher AUC when compared to ADC’s AUC. Can the author provide a justification or further analysis?

Page 20 – “The reason for the slightly higher AUC observed with the ADC could be the effect of perfusion on ADC measurements.” - Can the effect of perfusion on ADC explain the higher AUC observed? If that is the case, in what way can this be explained?

Page 21 – “We found the correlations between the GD model-derived and IVIM-derived parameters.” – This sentence is vague or incomplete please consider revising it.

Page 21 – “The almost perfect correlation observed between the f1 and D may indicate that these two parameters contain virtually identical information.” – It would be important to mention that it is a negative correlation.

Page 21 – “The positive correlation between f2 and D suggests the opposite, and the increased extracellular space like that taken up by microscopic necrosis might result in the higher f2.” – The “opposite” to what?

Page 21 – “Although the GD-derived and IVIM-derived parameters provide similar information, the strength of the GD model-derived parameters is that the values are expressed as a fraction or percentage, which allows us to characterize

tumors from histological viewpoint.” - “f “ is an IVIM-derived parameter and it is also expressed in percentage or fraction.

Page 21 – “The high f2 values in both types of tumor are likely to reflect mostly perifocal vasogenic edema rather than tumor infiltration outside the enhancing lesion” – “high f2 values” relative to what? The sentence would be more specific if it mentioned that it is referring to T2-hyperintense lesions. This idea would benefit from an addition of a literature reference.

Page 22 – Another limitation is the fact that only one person performed the ROI placement. The fact that the highest b-value in use was 1000s/mm2, should be better justified since in the brain higher b-values are usually used.

- Figures

Figure 1. It would be interesting to have the non-contrast-enhancing T2 image where the ROIs were also placed.

Figure 5 The y axis title is missing

Figure 6 Units should be included, when appropriate.

- Tables

Table 1 It would be easier to interpret the information shown in the table if p-values were also presented.

Table 2 In this table the reader is first exposed to the combination of parameters that were used to estimate diagnostic performances, additionally to the estimation of the diagnostic performances with the individual parameters. Why these specific combinations of parameters were considered? The justification should be clearly stated in the text.

In the legend “D, true diffusion coefficient; D*, ç; f, perfusion fraction” the meaning of D* is missing.

- Supporting information

Units should be added to the “all data” table where appropriate.

----Statement:

The topic is interesting but there are some parts of the study which the description should be improved so the reader can better understand it.

The major strengths of the article are: the application of a new diffusion model to brain tumours, which as far as I know it has not been done yet; the inclusion of an analysis of combined parameters and the evaluation of its performance; the inclusion of healthy tissue results, but these results were not compared to the results obtain for tumours which is a weakness. Consequently, the relevant weaknesses of the work are: the need for a deeper analysis of the obtained results; there are some methods and procedures that should be better described and justified; the use of b=1000 s/mm2 as the highest b-value is unusual in a brain diffusion studies, and this should be further justified.

Note: “Have the authors made all data underlying the findings in their manuscript fully available?” My answer was “no” because I only had access to the summary statistics, and not to the data points behind the statistics.

Reviewer #2: This study examined gamma distribution model of diffusion MRI and this model is useful to differentiate malignant lymphoma and glioblastoma.

This is well written paper and there are some minor points to revise.

In table 1, clarify the statistical significant differences between PCNSL and GB.

In figure 4, the k and f2 values at lateral peritumor area (lateral side) are high compared to contrast-enhanced tumor area.

Discussion

Limitation. The authors evaluate the only one slice of tumor, not whole tumor volume. Add this point in the limitation.

**********

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Reviewer #1: No

Reviewer #2: No

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PLoS One. 2020 Dec 14;15(12):e0243839. doi: 10.1371/journal.pone.0243839.r002

Author response to Decision Letter 0

7 Sep 2020

First of all, we would like to thank the two reviewers for their thorough reading and constructive criticism which greatly enhanced the quality of the paper. According to the comments, we have carefully revised the paper.

Reviewer #1:----Summary

The manuscript reports the use of the diffusion MRI gamma distribution (GD) model in the differentiation of primary central nervous system lymphomas (PCNSLs) and glioblastomas (GBs).

The results indicate that the GD model is advantageous in terms of diagnostic performance when comparing these 2 lesions, namely when 3 specific parameters of this model are used in combination.

My overall impression is that the manuscript has quality and it is an interesting an innovative topic, but some aspects should be considered and better analysed.

----Comments to the Author

• Abstract:

Response: Thank you for pointing out. These have been eliminated.

Response: Thank you very much. This has been corrected.

• Introduction:

Response: We agree with this point. The term “low” has been added here.

Example 1

Response: The reference #18 (previous #24, Borlinhas et al.) has been added and cited for these sentences as suggested.

Example 2

– “(…)extracellular fluid (ADCs between 1.0 and 3.0 mm2/s)" – Reference 22 of the manuscript

In this case, and as you can see, reference 21 is not specific when mentioning the meaning of f2. You have more specific references such as number 22 and 24 of your document.

Please add these references.

Response: We have added the two references (Borlinhas F, et al. and Shinmoto H, et al.) for the sentence “The GD model allows us to estimate fractions of a tissue type based on the concept that the area fractions for D <1.0 × 10−3 mm2/sec, 1.0 × 10−3 to 3.0 ×10−3 mm2/sec, and D >3.0 ×10−3 mm2/sec are attributed to intracellular, extracellular extravascular, and intravascular spaces, respectively [18, 22, 23]”

Response: This has been corrected to “D =1.0 × 10−3 to 3.0 ×10−3 mm2/sec” as suggested.

Also, this sentence that you present should be connect to the information included in this paragraph.

Response: We agree with this point. We want to state that these fractions (f1, f2, f3) allow us to estimate histological conditions of tumors and organs. For example, tumors with high f1, f2, and f3 should have high cell density, large interstitial space, and high vascularity, respectively. So, this sentence has been replaced by the following one. We think this sentence is now natural in the context.

Introduction (Page 5, line 17-18)

“Based on these fractions, we may be able to estimate histopathological conditions of neoplasms or organs.”

Response: Thank you very much for the reference. We have modified the paragraph as follows. We would like to keep the sentence “To the best of our knowledge...” since the application to brain “tumors” have never been reported yet.

Introduction (Page 5, Line 20 – Page 6, Line 2)

“The GD model has been used to assess prostate cancers [22-24], breast cancers [18], and renal function [25]. The GD model was also used to assess cerebral ischemic stroke in rat brains, and it was showed that this model exhibited a better performance than the conventional mono-exponential model and allowed for a significantly enhanced visualization of ischemic lesions [26]. To the best of our knowledge, its application to brain tumors has never been reported. We conducted the present study to determine whether the GD model is useful in the differentiation of PCNSLs and GBs.”

New reference

26. Grinberg F, Farrher E, Ciobanu L, Geffroy F, Le Bihan D, Shah NJ. Non-Gaussian diffusion imaging for enhanced contrast of brain tissue affected by ischemic stroke. PLoS One. 2014;9(2):e89225. Epub 2014/03/04. doi: 10.1371/journal.pone.0089225. PubMed PMID: 24586610; PubMed Central PMCID: PMCPMC3937347.

• Material and Methods

- Patients

Page 6 - “Multi-b-value DWI” – It would be more adequate to read for example “The use of a DWI protocol with multiple b-values (…)”

Response: Thank you for your suggestion. We have changed the wording as follows.

Materials and Methods (Page 6, Line 9, 11)

“The DWI protocol with multiple b-values has been a part of our routine preoperative MRI examination for patients with brain tumors since January 2013.”

“The DWI with multiple b-values was conducted preoperatively for the patient during the period from January 2013 to August 2019.”

Response: Yes, the MLs are less frequent compared to GBs. The following sentence and a new reference have been added.

Materials and Methods (Page 6, Line 20-21)

“The difference between the number of patients with PCNSLs and GBs can be explained by the fact that the PCNSLs are less frequent compared to the GBs [27].”

New reference

27. Ostrom QT, Cioffi G, Gittleman H, Patil N, Waite K, Kruchko C, et al. CBTRUS Statistical Report: Primary Brain and Other Central Nervous System Tumors Diagnosed in the United States in 2012-2016. Neuro Oncol. 2019;21(Suppl 5):v1-v100. Epub 2019/11/02. doi: 10.1093/neuonc/noz150. PubMed PMID: 31675094; PubMed Central PMCID: PMCPMC6823730.

Response: Thank you very much for your kind suggestion. But, in the present study, we excluded necrosis or hemorrhage in the ROI-based measurements since we would like to evaluate tumorous lesions. It is possible to report the fraction of necrosis or frequency of hemorrhage, but I am afraid it may be confusing for readers since we avoided the areas with necrosis or hemorrhage in the measurements.

- ROI placement

The reason why and the purpose of placing ROIs on the noncontrast-enhancing T2-hyperintense areas should be stated.

Response: The legend of Figure 1 has been summarized to avoid duplications with the text. The reason why we examined peritumoral noncontrast-enhancing T2-hyperintense areas was to evaluate if there were histological differences such as tumor infiltration or increased vascularity in peritumoral regions between PCNSLs and GBs. There have been several studies that showed increased rCBV on DSC-perfusion imaging in peritumoral noncontrast-enhancing T2-hyperintense areas of GBs. This means that such areas include not only vasogenic edema but also tumor cells infiltrating surrounding brain parenchyma; however, our study did not reveal any significant differences in GD model-based parameters for peritumoral noncontrast-enhancing T2-hyperintense areas between PCNSLs and GBs. We assume that the high f2 values observed in peritumoral noncontrast-enhancing T2-hyperintense areas compared to enhancing areas in both types of tumor are likely to reflect perifocal vasogenic edema rather than tumor infiltration outside the enhancing lesion. We have modified the sentence in Materials and Methods and Discussion as follows.

Fig. 1. Region-of-interest (ROI). The ROIs were placed on postcontrast T1-weighted images to include contrast enhancing lesions (A, C). The ROIs were also placed on the non-contrast-enhancing T2-hyperintense areas surrounding the contrast-enhancing area and the contralateral normal-appearing white matter (B, D).

Materials and Methods (Page 9, Line 14-21)

“The ROIs were also placed on the peritumoral non-contrast-enhancing T2-hyperintense areas to evaluate whether there were differences in histological features including tumor infiltration or increased vascularity in the peritumoral areas between PCNSLs and GBs. In addition, the ROIs were placed on the contralateral normal-appearing white matter. The ROIs for the peritumoral non-contrast-enhancing T2-hyperintense areas and contralateral normal-appearing white matter were measured on the image obtained with the b-value of 0 sec/mm2 image. The same ROIs were used for all DWI analyses.”

Discussion (Page 23, Line 11- Page 24, Line 3)

“In the T2-hyperintense lesions without contrast enhancement, no significant differences were observed between the PCNSL and GB groups for any parameters. There have been several studies that showed increased rCBV on DSC-perfusion imaging in peritumoral noncontrast-enhancing T2-hyperintense areas of GBs [36, 37]. The results of these studies indicated that the peritumoral areas of GB include not only vasogenic edema but also tumor cells infiltrating surrounding brain parenchyma; however, our study did not reveal any significant differences in the GD model-based parameters for peritumoral noncontrast-enhancing T2-hyperintense areas between PCNSLs and GBs. The f2 values in the noncontrast-enhancing T2-hyperintense areas were high in both types of tumor compared to those in the contrast-enhancing areas and normal appearing white matter. We assume that the high f2 values in the noncontrast-enhancing T2-hyperintense areas are likely to reflect mostly perifocal vasogenic edema rather than tumor infiltration outside the enhancing lesion. Our result is consistent with the previous DWI study in which ADC could not be used to differentiate edema with infiltration of tumor cells from vasogenic edema in high-grade gliomas and PCNSLs [38].”

New references

36. Law M, Cha S, Knopp EA, Johnson G, Arnett J, Litt AW. High-grade gliomas and solitary metastases: differentiation by using perfusion and proton spectroscopic MR imaging. Radiology. 2002;222(3):715-21. Epub 2002/02/28. doi: 10.1148/radiol.2223010558. PubMed PMID: 11867790.

37. Neska-Matuszewska M, Bladowska J, Sasiadek M, Zimny A. Differentiation of glioblastoma multiforme, metastases and primary central nervous system lymphomas using multiparametric perfusion and diffusion MR imaging of a tumor core and a peritumoral zone-Searching for a practical approach. PLoS One. 2018;13(1):e0191341. Epub 2018/01/18. doi: 10.1371/journal.pone.0191341. PubMed PMID: 29342201; PubMed Central PMCID: PMCPMC5771619.

- Statistical Analysis

Page 9 – “The optimal cutoff point was determined by Youden's method.” – A literature reference should be provided to support the method.

Response: The reference for Yuden’s method has been provided here.

28. Youden WJ. Index for rating diagnostic tests. Cancer. 1950;3(1):32-5. Epub 1950/01/01. doi: 10.1002/1097-0142(1950)3:1<32::aid-cncr2820030106>3.0.co;2-3. PubMed PMID: 15405679.

Response: We have provided more detailed explanations of the stepwise analysis in the paragraph as follows.

Materials and Methods (Page 10, Line 11-20)

“To determine whether the combination of multiple parameters for both the GD model and the IVIM model increases the diagnostic performance, we first performed a stepwise analysis to select the explanatory variables for a multiple regression model from a group of candidate variables by going through a series of automated steps. A forward-selection rule was applied in which the analysis started with no explanatory variables and then added variables, one by one, based on which variable was the most statistically significant, until there were no remaining statistically significant variables [30, 31]. We then performed a binomial logistic regression analysis to examine the AUCs of the combinations of the selected parameters. Two independent AUCs were compared using the method of Delong et al. [32].”

New references

30. Efroymson MA. Multiple regression analysis. In: Ralston A, Wilf HS, editors. Mathematical methods for digital computers. New York: Wiley; 1960.

31. Smith G. Step away from stepwise. J Big Data. 2018;5(32). doi: org/10.1186/s40537-018-0143-6.

• Results

- Comparisons of the parameters between the PCNSL and GB groups

Response: This paragraph has been rewritten and reorganized in a following order: 1) the results for the gadolinium enhancing lesions, 2) the results for peritumoral T2-hyperintense areas without contrast enhancement, 3) the results for normal appearing white matter, 4) representative figures for PCNLS and GB.

Results (Page 11, Line 6 – Page 12, Line 9)

“The detailed information for the parameters in the gadolinium enhancing lesion, peritumoral T2-hyperintense areas without contrast enhancement, and normal appearing white matter is summarized in Table 1.

The results of our comparisons of the GD model-derived parameters between the PCNSLs and GBs in the gadolinium-enhancing lesions are shown in Figure 2. In the gadolinium-enhancing lesions, the κ was significantly smaller in the PCNSL group (2.26 ± 1.00) than in the GB group (3.62 ± 2.01, p=0.0004), the f1 was significantly larger in the PCNSL group (0.542 ± 0.107) than in the GB group (0.348 ± 0.132, p<0.0001), the f2 was significantly smaller in the PCNSL group (0.372 ± 0.098) than in the GB group (0.508 ± 0.127, p<0.0001), and the f3 was significantly smaller in the PCNSL group (0.086 ± 0.043) than in the GB group (0.144 ± 0.062, p<0.0001), while the θ was not significantly different between the groups.

In the peritumoral T2-hyperintense areas without contrast enhancement, no significant differences were found between the PCNSL and GB groups for any of the GD model derived parameters.

Figure 3 provides a PCNSL case that showed a ring-like enhancing mass lesion mimicking a GB. This lesion showed a low κ, a large f1, a small f2, and a small f3, suggesting PCNSL. Figure 4 demonstrates a GB case that showed a solid enhancing mass lesion. This lesion showed a small κ, a small f1, moderate f2 and large f3, which are consistent with GB.”

Response: Thank you for pointing this out. We have added the statistical analyses on the NAWM. Unexpectedly, there were significant differences in the f1, f2, and f3 of NAWM between the PCNSLs and GB groups as follows. We have added the results and discussion on these differences as follows. I found some errors in the values for the NAWM in the GB group and have corrected them (the correction did not affect the statistical results).

Results (Page 11, Line 21- Page 12, Line 4)

“In the contralateral normal-appearing white matter, the f1 was significantly larger in the PCNSL group (0.642 ± 0.047) than in the GB group (0.593 ± 0.044, p<0.0001), the f2 was significantly smaller in the PCNSL group (0.316 ± 0.036) than in the GB group (0.354 ± 0.038, p<0.0001), and the f3 was significantly smaller in the PCNSL group (0.043 ± 0.026) than in the GB group (0.053 ± 0.019, p=0.0105).”

Discussion (Page 24, Line 4-9)

“In the normal-appearing white matter, the GB group showed larger f1, smaller f2, and larger f3 than the PCNSL group although these differences were small. This was unexpected, and the reasons for the differences remain unclear; however, since GBs frequently show extensive infiltration into the surrounding brain tissue, which is a fundamental feature of diffuse glioma, it is no wonder that the increased cell density and perfusion were observed in the normal-appearing white matter.”

Page 14 – In the "all data" excel sheet for f parameter you use percentage and here you show a fraction. Please make it uniform to clearly inform the reader.

Response: Thank you for pointing out. In the excel file named “all data”, the f-values have been expressed as a fraction.

Page 18 – “(…) although the difference was not significantly different from the values for D (p=0.5276).” – This should be rephrased.

Response: This has been rephrased as follows.

Results (Page 19, Line 11-12)

“..., although the AUC for this combination was not significantly different from that for D (p=0.5276).”

- Correlations of the model parameters

Page 18 – “The f1 had an almost perfect inverse correlation with D (all,

r = −0.976, p<0.0001; (…)” – According to figure 6, r = −0.9756, please confirm the information and change where necessary.

Response: We have rounded the r-values to four decimal places as follows.

Results (Page 19, Line 18 - Page 20, Line 3)

“Figure 6 shows the correlations among the GD model-derived and IVIM model-derived parameters in all tumors. The f1 had an almost perfect inverse correlation with D (all, r = −0.9756, p<0.0001; PCNSL, r = −0.9558, p<0.0001; GB, r = −0.9699, p<0.0001). The f2 had a very strong positive correlation with D (all, r=0.8865, p<0.0001; PNCSL, r=0.9619, p<0.0001; GB, r=0.8273, p<0.0001). The f3 had a very strong positive correlation with the f (all, r=0.8654, p<0.0001; PNCSL, r=0.8317, p<0.0001; GB, r=0.8611, p<0.0001).”

Response: Thank you for the suggestion. Yes, there was a very strong negative correlation between f1 and f2. The following results and discussion regarding the relationship between f1 and f2 have been added. The negative correlation between f1 and f2 was likely due to the complementary relationship between these two parameters. Since the f3-values (PCNSL group, 0.086±0.043; GB group, 0.144±0.062) were smaller compared to the f1- (PCNSL group, 0.542±0.107; GB group, 0.348±0.132) and f2-values (PCNSL group, 0.372±0.098; GB group, 0.508±0.127), the increased f1 would result in the decreased f2, and vice versa.

Results (Page 20, Line 1-3)

“The f1 had an very strong negative correlation with the f2 (all, r = −0.9155, p<0.0001; PCNSL, r = −0.9150, p<0.0001; GB, r = −0.8874, p<0.0001).”

Discussion (Page 23, Line 5-7)

“The negative correlation between f1 and f2 was likely due to the complementary relationship between these two parameters. Since the f3-values were smaller compared to the f1- and f2-values, the increase in f1 would result in the decrease in f2, and vice versa.”

• Discussion

- The meaning of f3 and f parameters results and finding should be analysed in the discussion. Why f and f3 parameters are higher in the PCNSL when compared to the GB group of lesions?

Response: Thank you for your suggestion. Yes, this is an important point and we should have mentioned this. The larger f3 and f values in the GB group compared to those in the PCNSL group can be attributed to the difference in vascularity of these tumors. Pathologically, neovascularization is a key feature of GB while it is not prominent in PCNSL. Our results for f3 and f are consistent with those from previous studies using dynamic susceptibility contrast perfusion-weighted MR imaging and arterial spin labeling imaging. We have added the discussions on the meaning of f3 and f as follows.

“The GB group showed larger f3 and f compared to the PCNSL group. This may be attributed to the difference in vascularity of these tumors. Pathologically, neovascularization is a key feature of GB while it is not prominent in PCNSL [33, 34]. Our results are consistent with those from previous studies using dynamic susceptibility contrast perfusion-weighted imaging and arterial spin labeling imaging [9, 35].”

New references

33. Hardee ME, Zagzag D. Mechanisms of glioma-associated neovascularization. Am J Pathol. 2012;181(4):1126-41. Epub 2012/08/04. doi: 10.1016/j.ajpath.2012.06.030. PubMed PMID: 22858156; PubMed Central PMCID: PMCPMC3463636.

34. Cha S, Knopp EA, Johnson G, Wetzel SG, Litt AW, Zagzag D. Intracranial mass lesions: dynamic contrast-enhanced susceptibility-weighted echo-planar perfusion MR imaging. Radiology. 2002;223(1):11-29. Epub 2002/04/04. doi: 10.1148/radiol.2231010594. PubMed PMID: 11930044.

35. Hartmann M, Heiland S, Harting I, Tronnier VM, Sommer C, Ludwig R, et al. Distinguishing of primary cerebral lymphoma from high-grade glioma with perfusion-weighted magnetic resonance imaging. Neurosci Lett. 2003;338(2):119-22. Epub 2003/02/05. doi: 10.1016/s0304-3940(02)01367-8. PubMed PMID: 12566167.

Response: Thank you very much. As pointed out, the AUC of this combination (0.909) was higher than that of ADC (0.879). Although there was no statistically significant difference between them (p=0.2152), this tendency could be meaningful and important. Whether the combination of parameters of the GD model has an additive value should be evaluated in a larger population. We have added the following sentences in Results and Discussion.

Results (Page 19, Line 6-8)

“The AUC of this combination (0.909) was higher than that of ADC (0.879); however, there was no statistically significant difference between them (p=0.2152).”

Discussion (Page 22, Line 16-19)

“The AUC of this combination tended to be higher than that of ADC although there was no significant difference. Whether the combination of parameters of the GD model has an additive value should be evaluated in a larger population, since we did not observe statistical significance in all of our comparisons.”

Response: I am sorry that our discussion lacked explanations for this result. The ADC is a diffusion coefficient but is influenced by tissue perfusion (that's why this is called “apparent” diffusion coefficient). In hyperperfused tissues, ADC will be affected by perfusion and overestimated compared to true diffusion coefficient D, while the perfusion effect will be excluded in the calculation of D. In hypervascular tumors such as GBs, the ADC would be larger than D. On the other hand, in hypovascular tumors such as PCNSLs, this difference between ADC and D should be smaller. This means that the difference between ADC and D would be larger in GBs than in PCNSLs. Therefore, ADC could show higher diagnostic performance in the discrimination of these two tumors than D. This paragraph has been modified and added more explanations as follows.

Discussion (Page 22, Line 3-14)

“The reason for the slightly higher AUC observed with the ADC could be the effect of perfusion on ADC measurements. In hyperperfused tissues, ADC will be affected by the perfusion effect and overestimated compared to D; however, since both f1 and D are parameters without a perfusion effect in theory, an overestimation caused by perfusion should not be observed in these values. Therefoere, in hypervascular tumors such as GBs, the ADC should be larger than D. On the other hand, in hypovascular tumors such as PCNSLs, this difference between ADC and D should smaller. This means that the difference between ADC and D would be larger in GBs than in PCNSLs. Therefore, ADC could show higher diagnostic performance in the discrimination of these two tumors than D. In fact, the difference between the ADC and D values was greater in the GBs (0.100 × 10−3 mm2/sec) than in the PCNSLs (0.078 × 10−3 mm2/sec), which was most likely due to the higher perfusion effect on the ADC in GBs than in PCNSLs.”

Page 21 – “We found the correlations between the GD model-derived and IVIM-derived parameters.” – This sentence is vague or incomplete please consider revising it.

Response: This sentence has been revised to be more specific as follows.

Results (Page 22, Line 21-22)

“We found the correlations between the GD model-derived and IVIM-derived parameters, particularly between the f1 and D, the f2 and D, and the f3 and f.”

Response: The term “negative” has been added as requested.

Discussion (Page 22, Line 1)

“The almost perfect negative correlation observed between the f1 and D may indicate that these two parameters contain virtually identical information.”

Response: This wording was not appropriate, and thus the term “opposite” has been deleted as follows.

Discussion (Page 23, Line 2-3)

“The positive correlation between f2 and D suggests that the increased extracellular space like that taken up by microscopic necrosis might result in the higher f2.”

tumors from histological viewpoint.” - “f “ is an IVIM-derived parameter and it is also expressed in percentage or fraction.

Response: Yes, as you pointed out, the IVIM-f is expressed in percentage or fraction. But the IVIM method cannot express the fractions or percentage of intracellular and extracellular-extravascular spaces. Therefore, we think IVIM is not a perfect method to characterize tumors from histological viewpoint.

Response: The f2 values in the noncontrast-enhancing T2-hyperintense areas were higher in both types of tumor compared to those in the contrast-enhancing areas and normal appearing white matter. The sentence has been revised as follows. This is a new finding and we could not find an appropriate reference related to this result. A new reference has been added.

Discussion (Page 23, Line 19 – Page 24, Line 4)

“The f2 values in the noncontrast-enhancing T2-hyperintense areas were higher in both types of tumor compared to those in the contrast-enhancing areas and normal appearing white matter. We assume that the high f2 values in the noncontrast-enhancing T2-hyperintense areas are likely to reflect mostly perifocal vasogenic edema rather than tumor infiltration outside the enhancing lesion. Our result is consistent with the previous DWI study in which ADC could not be used to differentiate edema with infiltration of tumor cells from vasogenic edema in high-grade gliomas and PCNSLs [38].

New refference

38. Server A, Kulle B, Maehlen J, Josefsen R, Schellhorn T, Kumar T, et al. Quantitative apparent diffusion coefficients in the characterization of brain tumors and associated peritumoral edema. Acta Radiol. 2009;50(6):682-9. Epub 2009/05/19. doi: 10.1080/02841850902933123. PubMed PMID: 19449234.

Response: The limitation for the ROI placement has been added. In a study of prostate cancers, Oshio et al. used the similar DWI parameters to ours and highest b-value of 1000s/mm2, and reported that the good fitting accuracy was observed in both cancer (R2=0.99226) and normal tissue (R2=0.99842). Their results indicated that DWI with the highest b-value of 1000 s/mm2 can be used for GD model analysis. We have modified the paragraph to justify the use of this b-value as follows.

Discussion (Page 24, Line 12-14)

“The only one person performed the ROI placements on a single slice, and not whole tumor volume was evaluated.”

Discussion (Page 24, Line 17- Page 25, Line 5)

“In addition, the selection of b-values has not yet been optimized. Prior studies of the GD model used the maximum b-values ranging from 1000 to 3000 sec/mm2 [18, 22-24]. In a study of prostate cancers, Oshio et al. used the similar DWI parameters to ours and the highest b-value of 1000 s/mm2, and reported that the good fitting accuracy was observed in both cancerous tissues (R2=0.99226) and normal tissues (R2=0.99842) [22]. Their result indicated that DWI with the highest b-value of 1000 s/mm2 can be used for GD model analyses; however, since it was reported that the non-monoexponential diffusion-related signal decay generally becomes more obvious over more extended b-value ranges, the maximum b value of 1000 sec/mm2 used in the present study might be lower than the optimal value. The optimal b-values and numbers should be elucidated in future studies.”

- Figures

Figure 1. It would be interesting to have the non-contrast-enhancing T2 image where the ROIs were also placed.

Response: Another case (new Figure 1 C, D) which well illustrates noncontrast-enhancing T2-hyperintense areas has been added.

Figure 5 The y axis title is missing

Response: Thank you very much! This has been corrected.

Figure 6 Units should be included, when appropriate.

Response: The units have been added for D and D*. The f1, f2, f3 and f are expressed as fractions and no units are necessary for them.

- Tables

Table 1 It would be easier to interpret the information shown in the table if p-values were also presented.

Response: The p-values have been added in Table 1 as suggested.

In the legend “D, true diffusion coefficient; D*, ç; f, perfusion fraction” the meaning of D* is missing.

Response: The stepwise analysis selected the combination of κ, f1, and f3. This is already stated in the text as follows. The meaning of D* (pseudo-diffusion coefficient) has been corrected.

Results (Page 19, Line 1-4)

“In the combined-parameters analysis, the stepwise procedure selected κ, f1, and f3 for the GD model, and the D and f for the IVIM model. The combination of κ, f1, and f3 revealed excellent diagnostic performance with the AUC of 0.909, sensitivity of 84.2%, and specificity of 88.9%.”

- Supporting information

Units should be added to the “all data” table where appropriate.

Response: The units have been added in all data table.

----Statement:

The topic is interesting but there are some parts of the study which the description should be improved so the reader can better understand it.

Response: We sincerely appreciate the reviewer’s positive comments. We believe that we have corrected all the weaknesses of the present study which the reviewer pointed out as seen above.

Response: In the supplementary data named “all data”, all raw data of measurements are available. We forgot to include raw data for T2-hyperintense areas and NAWM in the previous file and have added them in the new file.

Reviewer #2: This study examined gamma distribution model of diffusion MRI and this model is useful to differentiate malignant lymphoma and glioblastoma.

This is well written paper and there are some minor points to revise.

In table 1, clarify the statistical significant differences between PCNSL and GB.

Response: We have added all p-values in Table 1 as suggested.

In figure 4, the k and f2 values at lateral peritumor area (lateral side) are high compared to contrast-enhanced tumor area.

Response: Yes, the peritumoral T2-hyperintense area without contrast enhancement showed a large κ and a large f2 compared to the contrast-enhancing area. These findings are consistent with the results of the present study (Table 1). We have added the descriptions about the peritumoral T2-hyperintense areas in Fig. 3 and 4. Thank you very much for your suggestion.

Fig. 3. The peritumoral T2-hyperintense area without contrast enhancement shows a large κ (8.18, D), a small θ (0.46×10−6 mm2/sec, E), a small f1 (0.139, F), a large f2 (0.772, G), and a small f3 (0.090, H).

Fig. 4. The peritumoral T2-hyperintense area without contrast enhancement shows a large κ (3.94, D), a small θ (0.75×10−6 mm2/sec, E), a small f1 (0.308, F), a large f2 (0.597, G), and a small f3 (0.095, H).

Discussion

Limitation. The authors evaluate the only one slice of tumor, not whole tumor volume. Add this point in the limitation.

Response: We agree with this point. This has been added in the limitation as follows.

Discussion (Page 24, Line 12-14)

“The only one person performed the ROI placements on a single slice, and not whole tumor volume was evaluated.”

Attachment

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Click here for additional data file.^{(63.6KB, docx)}

PLoS One. doi: 10.1371/journal.pone.0243839.r003

Decision Letter 1

Niels Bergsland

5 Oct 2020

PONE-D-20-15410R1

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

PLOS ONE

Dear Dr. Togao,

There are just a few relatively minor issues to be addressed as pointed out by Reviewer 1.

Please submit your revised manuscript by Nov 19 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

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An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

We look forward to receiving your revised manuscript.

Kind regards,

Niels Bergsland

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: (No Response)

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: (No Response)

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: (No Response)

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: (No Response)

Reviewer #2: Yes

**********

6. Review Comments to the Author

Reviewer #1: The authors have addressed the topics indicated in the first revision and the manuscript has been significantly improved. Here, the authors can find some small details that still need to be considered.

• Results (Page 19, Line 11-12)

“..., although the AUC for this combination was not significantly different from that for D (p=0.5276).”

"This combination increased the diagnostic performance of f (p=0.0077), although the AUC for this combination was not significantly different from that for D (p=0.5276)."

- The language used in the phrases “(…) significantly different from that for (…)”through all the text should be rewritten in a clearer way in order to sound.

• Discussion (Page 23, Line 5-7)

- An explanation for this relation should be put forward taking into account the meaning of the parameters.

• “Page 21

“Although the GD-derived and IVIM-derived parameters provide similar information, the strength of the GD model-derived parameters is that the values are expressed as a fraction or percentage, which allows us to characterize tumours from histological viewpoint.” - “f “ is an IVIM-derived parameter and it is also expressed in percentage or fraction.

- In the way this sentence is presented, the reader may misunderstand the information that you are providing. You are stating that one strong point of the GD model parameters, when compared to IVIM parameters, is to be presented in percentage or fraction and that this is the reason why it allows the characterization of tumours. f is also expressed as fraction or percentage and it shows problems in this task. In the way that the sentence is constructed the reader may think that only GD parameters are expressed in fraction or percentage. Also, it is important to refer in what way can this characteristic contribute to the characterization of tumours' histology.

• Figure 1

- The name of the lesions should be included. Also, the lesions/ROIs in the images should be identified for example with numbers or letters, and that should be referenced and related in the legend of the figure.

Reviewer #2: The paper is revised as reviewer's comments and it is acceptable in this version.

This is very useful information for brain tumor imaging.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Yoshiyuki Watanabe

PLoS One. 2020 Dec 14;15(12):e0243839. doi: 10.1371/journal.pone.0243839.r004

Author response to Decision Letter 1

13 Nov 2020

• Results (Page 19, Line 11-12)

“..., although the AUC for this combination was not significantly different from that for D (p=0.5276).”

"This combination increased the diagnostic performance of f (p=0.0077), although the AUC for this combination was not significantly different from that for D (p=0.5276)."

- The language used in the phrases “(…) significantly different from that for (…)”through all the text should be rewritten in a clearer way in order to sound.

Response: First, we would like to thank you for your thorough reading and constructive criticism which greatly enhanced the quality of the paper. According to your comments, we have carefully revised the paper again. The sentences have been rewritten as follows.

“This combination increased the diagnostic performance of κ (p=0.0016), and f3 (p=0.0075), although it did not improve the performance of f1 (p=0.1950).” (Page 19, Line 4-6)

“This combination improved the diagnostic performance of f (p=0.0077), although it did not improve the performance of D (p=0.5276).” (Page 19, Line 9-10)

• Discussion (Page 23, Line 5-7)

- An explanation for this relation should be put forward taking into account the meaning of the parameters.

Response: The relationship between f1 and f2 has been explained considering the meaning of the parameters as follows.

“The negative correlation between f1 and f2 was likely due to the complementary relationship between these two parameters. In general, intravascular space (≒ f3) is smaller compared to intracellular (≒ f1) and extracellular extravascular space (≒ f2). In fact, the f3-values were much smaller than the f1- and f2-values in both PCNSLs and GBs in the present study. Therefore, the increase in f1 would result in the decrease in f2, and vice versa.” (Page 23, Line 4-9)

• “Page 21

Response: Thank you very much for the comments. We have modified the sentences as follows according to your suggestion. We think that obtaining all fraction values (f1, f2, f3) would help to characterize tumors from histological viewpoint since f1, f2, and f3 should reflect cell density, interstitial space, and vascularity, respectively.

“Although the GD-derived and IVIM-derived parameters provide similar information, the strength of the GD model-derived parameters is that all fraction values (f1, f2, f3) are expressed as fractions or percentages, which allows us to well characterize tumors from histological viewpoint. The IVIM-derived f-value is also expressed in a percentage or fraction; however, the IVIM analysis is not able to provide the fraction values for intracellular and extracellular-extravascular spaces. In this sense, the IVIM method is not a perfect method for the histological characterization of tumors.”(Page 23, Line 9-15)

• Figure 1

Response: Thank you for your suggestions. The names of the lesions have been included in the legend. The ROI numbers (#1, contrast enhancing areal; #2 T2-hyperintense area; #3, normal appearing white matter) have been added in the Figures and have been related in the legends as follows.

Fig. 1. Regions-of-interest (ROIs). Figures 1 A and B show a GB with ring enhancement, and Figures C and D show a PCNSL with solid enhancement. The ROIs were placed on postcontrast T1-weighted images to include contrast enhancing lesions (A, C, area #1). The ROIs were also placed on the non-contrast-enhancing T2-hyperintense areas surrounding the contrast-enhancing area (area #2) and the contralateral normal-appearing white matter (B, D, area #3).

Reviewer #2: The paper is revised as reviewer's comments and it is acceptable in this version.

This is very useful information for brain tumor imaging.

Response: We appreciate the reviewer’s comments.

Attachment

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PLoS One. doi: 10.1371/journal.pone.0243839.r005

Decision Letter 2

Niels Bergsland

30 Nov 2020

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

PONE-D-20-15410R2

Dear Dr. Togao,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Niels Bergsland

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: (No Response)

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: (No Response)

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

**********

6. Review Comments to the Author

Reviewer #1: The authors addressed the topics indicated in the previous review. The article provides an understanding of an important topic by applying a method that can bring more in-depth knowledge to this field of study.

Note that in Figure 1, the numbers that identify the ROIs are covering the relevant structures, which can raise doubts among readers. Please consider a solution, as for example the use of different colours to differentiate the ROIs instead, or a different positioning of the numbers.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: Yes: Filipa Borlinhas

PLoS One. doi: 10.1371/journal.pone.0243839.r006

Acceptance letter

Niels Bergsland

3 Dec 2020

PONE-D-20-15410R2

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

Dear Dr. Togao:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Niels Bergsland

Academic Editor

PLOS ONE

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

S1 Data. All measurements for gamma distribution model-derived and IVIM model-derived parameters.

(XLSX)

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Data Availability Statement

All relevant data are within the manuscript and Supporting Information file.

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PERMALINK

Gamma distribution model of diffusion MRI for the differentiation of primary central nerve system lymphomas and glioblastomas

Osamu Togao

Toru Chikui

Kenji Tokumori

Yukiko Kami

Kazufumi Kikuchi

Daichi Momosaka

Yoshitomo Kikuchi

Daisuke Kuga

Nobuhiro Hata

Masahiro Mizoguchi

Koji Iihara

Akio Hiwatashi

Roles

Abstract

Introduction

Materials and methods

Patients

MRI

Image analysis

ROI placement

Fig 1. Regions-of-interest (ROIs).

Statistical analyses

Results

Comparisons of the parameters between the PCNSL and GB groups

Table 1. Gamma distribution model-derived parameters in PCNSLs and GBs.

Fig 2. Comparisons of the GD model-derived parameters between the PCNSLs and GBs in the gadolinium-enhancing lesion.

Fig 3. A 62-year-old-male with a PCNSL.

Fig 4. A 66-year-old-male with a GB.

Diagnostic performance of the single and combined parameters

Fig 5. ROC graphs.

Table 2. ROC analysis for diagnostic performance of the parameters in the differentiation between PCNSLs from GBs.

Correlations of the model parameters

Fig 6. The correlations among the GD model-derived and IVIM model-derived parameters in all tumors.

Discussion

Conclusions

Supporting information

Data Availability

Funding Statement

References

Decision Letter 0

Niels Bergsland

Roles

Author response to Decision Letter 0

Decision Letter 1

Niels Bergsland

Roles

Author response to Decision Letter 1

Decision Letter 2

Niels Bergsland

Roles

Acceptance letter

Niels Bergsland

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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