Tri-Compartmental Restriction Spectrum Imaging Breast Model Distinguishes Malignant Lesions from Benign Lesions and Healthy Tissue on Diffusion-Weighted Imaging

Simple Summary Women at high risk for breast cancer are regularly screened using contrast-enhanced magnetic resonance imaging (MRI) to identify potential malignancy. Diffusion-weighted MRI (DW-MRI) is a non-contrast technique that measures the differential movement of water molecules in tissues and is sensitive to cancer cells. In this study, we use a multi-exponential advanced DW-MRI model called restriction spectrum imaging (RSI) to characterize the diffusion characteristics of malignant lesions, benign lesions, and healthy breast tissue to help differentiate benign from malignant disease. In a cohort of patients, we show that cancer exhibits more restricted diffusion compared to benign breast lesions and healthy tissue, whereas benign and healthy tissue are not different from each other. Abstract Diffusion-weighted MRI (DW-MRI) offers a potential adjunct to dynamic contrast-enhanced MRI to discriminate benign from malignant breast lesions by yielding quantitative information about tissue microstructure. Multi-component modeling of the DW-MRI signal over an extended b-value range (up to 3000 s/mm2) theoretically isolates the slowly diffusing (restricted) water component in tissues. Previously, a three-component restriction spectrum imaging (RSI) model demonstrated the ability to distinguish malignant lesions from healthy breast tissue. We further evaluated the utility of this three-component model to differentiate malignant from benign lesions and healthy tissue in 12 patients with known malignancy and synchronous pathology-proven benign lesions. The signal contributions from three distinct diffusion compartments were measured to generate parametric maps corresponding to diffusivity on a voxel-wise basis. The three-component model discriminated malignant from benign and healthy tissue, particularly using the restricted diffusion C1 compartment and product of the restricted and intermediate diffusion compartments (C1 and C2). However, benign lesions and healthy tissue did not significantly differ in diffusion characteristics. Quantitative discrimination of these three tissue types (malignant, benign, and healthy) in non-pre-defined lesions may enhance the clinical utility of DW-MRI in reducing excessive biopsies and aiding in surveillance and surgical evaluation without repeated exposure to gadolinium contrast.


Introduction
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) demonstrates the highest sensitivity (71-94%) to detect breast cancer compared to conventional imaging (ultrasound, mammography, and tomography). DCE breast MRI evaluation is based on morphology, distribution, and kinetics; these features are incorporated in the assessment of malignancy potential by the Breast Imaging Reporting and Data System (BI-RADS) [1][2][3][4][5]. The American College of Radiology Commission on Breast Imaging appropriateness criteria recommend that women at high risk for breast cancer begin annual screening with DCE-MRI as early as 25 years old [6]. However, DCE-MRI is associated with limitations including variable specificity rate (61-97%), which leads to excessive biopsies and increases patient anxiety [1][2][3]7].
Diffusion-weighted MRI (DW-MRI) has emerged as a method with the potential to differentiate benign from malignant breast lesions and yields quantitative information about tissue microstructure without the use of exogenous contrast [8,9]. Information about tissue structure can be provided by measuring an apparent diffusion coefficient (ADC) in varying degrees of diffusion weighting (b-values), due to the differential Brownian diffusion of water molecules [8]. Although DW-MRI is part of the standard of care for many body applications and included in the final assessment for detection of malignancies in the liver, prostate, and ovaries, there continue to be limitations and no lexicon descriptors or quantification of DW-MRI and ADC in BI-RADS at this time. These include limitations due to significant geometric distortions which can impair the evaluation of small lesions [9], variations in ADC values related to acquisition parameters across sites [10][11][12], and substantial overlap in ADC values for malignant and benign lesions [13,14]. Therefore, the clinical utility of using ADC as a robust imaging biomarker of the probability of malignancy of lesions is limited and mostly recommended as an adjunct measurement with DCE-MRI [15,16]. To advance DW-MRI as a reliable non-contrast adjunct to DCE-MRI in evaluating breast lesions, a more comprehensive diffusion model is needed that more accurately describes the complex microenvironment of the breast, consisting of healthy fat and fibroglandular tissues, benign lesions, and malignant lesions.
Multi-component modeling of the DW-MRI signal over extended ranges of b-values (typically up to 2000-3000 s/mm 2 ) theoretically isolates the slowly diffusing (restricted) water component in tissues [8]. The magnitude of this restricted diffusion component is hypothesized to be modulated by both cellularity and nuclear volume fraction of individual cells [17]. In the restriction spectrum imaging (RSI) model, each component is defined by a constant apparent diffusion coefficient representing a distinct pool of water diffusion signal [18]. The main outputs of this technique are maps of the relative size of each component. In brain [19], prostate [20,21], and breast [22][23][24], RSI has demonstrated potential to distinguish cancer tissues from non-cancer tissues by isolating this slowly diffusing water signal, and corresponding magnitude. Vidić et al. demonstrated that the normalized magnitude of the slowest element in a two-component model performed well in discriminating signal intensity within pre-defined benign and malignant breast lesion regions of interest (ROIs) [22].
A further optimized three-component RSI model to fit the DW-MRI signal in the breast demonstrated the ability to differentiate malignant from healthy fibroglandular tissue [23], with comparable contrast-to-noise ratio and area-under-the-curve to conventional DCE-MRI [23,24]. This three-component model was used to generate a classification algorithm for non-predefined lesions which demonstrated the clinical utility of RSI in breast cancer diagnosis [24]. However, the study did not investigate the model's ability to discriminate malignant and benign breast lesions. Further refining this model to include discrimination of benign lesions from both malignant lesions and healthy tissue would increase the clinical Cancers 2022, 14, 3200 3 of 12 robustness of the model and increase the radiologist's confidence in ascribing a lesion as malignant or benign. Therefore, the aim of this study was to evaluate the utility of the three-component RSI model to distinguish between malignant, benign, and healthy tissue in a small patient population with biopsy-proven malignant and benign breast lesions.

Subjects
A retrospective study of the RSI characteristics of benign and malignant breast lesions was conducted. This study was approved by the Institutional Review Board of the authors' institution. All patients were females, 20-78 years old. Patients with known breast malignancy and who were imaged with DCE-MRI and the relevant diffusion protocol at our single institution between July 2015 and December 2019 were identified (208 total patients) ( Figure 1). algorithm for non-predefined lesions which demonstrated the clinical utility of RSI in breast cancer diagnosis [24]. However, the study did not investigate the model's ability to discriminate malignant and benign breast lesions. Further refining this model to include discrimination of benign lesions from both malignant lesions and healthy tissue would increase the clinical robustness of the model and increase the radiologist's confidence in ascribing a lesion as malignant or benign. Therefore, the aim of this study was to evaluate the utility of the three-component RSI model to distinguish between malignant, benign, and healthy tissue in a small patient population with biopsy-proven malignant and benign breast lesions.

Subjects
A retrospective study of the RSI characteristics of benign and malignant breast lesions was conducted. This study was approved by the Institutional Review Board of the authors' institution. All patients were females, 20-78 years old. Patients with known breast malignancy and who were imaged with DCE-MRI and the relevant diffusion protocol at our single institution between July 2015 and December 2019 were identified (208 total patients) ( Figure 1). Patients with both pathology-proven malignancy and one or more synchronous pathology-proven benign lesion(s) in either the contralateral or ipsilateral breast were included (122 patients) to control for interpatient variability. Therefore, 79 patients without synchronous benign lesions were excluded. Patients previously treated with a cytotoxic regimen, chemotherapy, or ipsilateral radiation therapy prior to MRI scanning were excluded from analysis (86 patients). Additionally, patients with simple cysts that are readily identified with standard imaging (11 patients), non-pathology-proven benign lesions (8 patients), and incomplete or alternative MRI protocol (12 patients) were excluded from the analysis. Therefore, our final patient population consisted of 12 patients with concurrent pathology-proven malignant and benign lesions in either breast. Patients with both pathology-proven malignancy and one or more synchronous pathology-proven benign lesion(s) in either the contralateral or ipsilateral breast were included (122 patients) to control for interpatient variability. Therefore, 79 patients without synchronous benign lesions were excluded. Patients previously treated with a cytotoxic regimen, chemotherapy, or ipsilateral radiation therapy prior to MRI scanning were excluded from analysis (86 patients). Additionally, patients with simple cysts that are readily identified with standard imaging (11 patients), non-pathology-proven benign lesions (8 patients), and incomplete or alternative MRI protocol (12 patients) were excluded from the analysis. Therefore, our final patient population consisted of 12 patients with concurrent pathology-proven malignant and benign lesions in either breast.

Histopathology
Lesions were pathologically assessed via core needle or excisional biopsy. All 12 patients had only one malignant lesion and at least one benign lesion, with 2 of these patients having an additional ipsilateral benign lesion for a total of 14 benign lesions ( Table 1). All of the 14 total benign lesions were pathology-proven benign and included stromal fibrosis, fibroadenomas, focal ductal hyperplasia, benign sclerosing adenosis, radial scar, and benign  Malignant lesions included invasive ductal carcinoma (IDC), invasive mammary carcinoma (IMC), invasive lobular carcinoma (ILC), ductal carcinoma in situ (DCIS), IDC + DCIS, and IMC + DCIS. Lesions ranged from 2.1 × 1.9 cm to 6.2 × 5.8 cm based on the radiologists' reports and represented masses, non-mass enhancement (NME), and mass + NME (Table 1).

Data Processing
Data were processed and analyzed using MATLAB R2016b (The MathWorks Inc., Natick, MA, USA), as previously described in Rodríguez-Soto et al. [23]. Briefly, after distortion correction with RPG, datasets were noise corrected by estimating the noise floor as the average of the background signal determined from a histogram of the DW-MRI data. The noise floor value was then subtracted from all voxels. Following noise correction, data were corrected for eddy current artifacts, then all diffusion directions at a given b-value were averaged. Averaged DW-MRI datasets were normalized by the 98th percentile of the b = 0 s/mm 2 volume to preserve T 2 information while mitigating the chance of using an arbitrarily high noise value for normalization, as done previously [23].
Previously, Rodríguez-Soto et al. established that the diffusion signal, S diff , in breast cancer is best modeled as a linear combination of three exponential decays as described by the RSI framework [18,23]: where C i is the signal contribution of each exponential component (i = 1, 2, and 3 for the three-component breast model) and b represents the b-values. In brief, Rodríguez-Soto et al. first estimated diffusion coefficients of each exponential component (D 1 = 0 mm 2 /s (restricted diffusion), D 2 = 1.5 × 10 −3 mm 2 /s (hindered diffusion), and D 3 = 10.8 × 10 −3 mm 2 /s (pseudo-diffusion)) through global fitting of the tri-exponential model to cancer and control tissue. To estimate the parametric C i maps, these diffusion coefficients are fixed to enable comparison of signal contributions across different voxels and patients, and a non-negative least squares fitting of the model to the signal versus b-value curve from each voxel is performed [23]. The resulting C 1 , C 2 , and C 3 maps were directly estimated from the model. Additionally, C 1 C 2 , the product of the C 1 and C 2 components, was demonstrated by Andreassen et al. to discriminate between cancer and healthy breast tissue in a clinically helpful manner and was thus included in our analysis [24]. In the present work, the square root of the product, √ C 1 C 2 , was also estimated to provide the information of C 1 C 2 at the same scale as the RSI C i map outputs. Additionally, conventional mono-exponential ADC maps were computed using averaged DW-MRI datasets without noise correction, using b-values up to 1500 s/mm 2 . Negative and undefined ADC values were excluded.
Using all available data in the exam protocol (including DCE-MRI and anatomical T 2 -weighted images), full volume regions of interest (ROIs) were manually drawn on DW-MRI images for all malignant and benign lesions, as shown in Figure 2.
as the average of the background signal determined from a histogram of the DW-MRI data. The noise floor value was then subtracted from all voxels. Following noise correction, data were corrected for eddy current artifacts, then all diffusion directions at a given b-value were averaged. Averaged DW-MRI datasets were normalized by the 98th percentile of the b = 0 s/mm 2 volume to preserve T2 information while mitigating the chance of using an arbitrarily high noise value for normalization, as done previously [23].
Previously, Rodríguez-Soto et al. established that the diffusion signal, Sdiff, in breast cancer is best modeled as a linear combination of three exponential decays as described by the RSI framework [18,23]: where Ci is the signal contribution of each exponential component (i = 1, 2, and 3 for the three-component breast model) and b represents the b-values. In brief, Rodríguez-Soto et al. first estimated diffusion coefficients of each exponential component (D1 = 0 mm 2 /s (restricted diffusion), D2 = 1.5 × 10 −3 mm 2 /s (hindered diffusion), and D3 = 10.8 × 10 −3 mm 2 /s (pseudo-diffusion)) through global fitting of the tri-exponential model to cancer and control tissue. To estimate the parametric Ci maps, these diffusion coefficients are fixed to enable comparison of signal contributions across different voxels and patients, and a nonnegative least squares fitting of the model to the signal versus b-value curve from each voxel is performed [23]. The resulting C1, C2, and C3 maps were directly estimated from the model. Additionally, C1C2, the product of the C1 and C2 components, was demonstrated by Andreassen et al. to discriminate between cancer and healthy breast tissue in a clinically helpful manner and was thus included in our analysis [24]. In the present work, the square root of the product, , was also estimated to provide the information of C1C2 at the same scale as the RSI Ci map outputs. Additionally, conventional mono-exponential ADC maps were computed using averaged DW-MRI datasets without noise correction, using b-values up to 1500 s/mm 2 . Negative and undefined ADC values were excluded.
Using all available data in the exam protocol (including DCE-MRI and anatomical T2-weighted images), full volume regions of interest (ROIs) were manually drawn on DW-MRI images for all malignant and benign lesions, as shown in Figure 2.  Malignant ROIs were drawn for the lesions corresponding to pathology-proven cancer, and benign ROIs were drawn for those corresponding to pathology-proven benign lesions. Healthy control ROIs containing healthy fat and fibroglandular tissue were defined as boxes of 33,600 voxels placed in the contralateral breast relative to the malignancy being evaluated, drawn on DCE-MRI images. Healthy control ROIs were then resampled to the DW-MRI resolution to cover 500 voxels. Any benign lesion voxels contained within healthy control ROIs were excluded. Additionally, the axillary region, large cysts (>2.5 cm), and Cancers 2022, 14, 3200 6 of 12 susceptibility artifacts (e.g., from surgical clips) were excluded. ROIs were reviewed and approved by a breast radiologist (RRP). After assessing data normality, the median of each ROI was computed, resulting in a single data point per tissue type per patient.

Statistical Analysis
Statistical analyses were performed using R statistical programming (R Foundation for Statistical Computing, Vienna, Austria). Shapiro-Wilk test for normality was used to evaluate the normality of data within each ROI. Levene's test for homogeneity of variance was used to examine the normality of data across patients, followed by ranked two-way repeated-measures analysis of variance (ANOVA) to evaluate the effects of tissue type and diffusion components. Individual differences were evaluated by post hoc Wilcoxon signedrank test with Bonferroni correction to preserve rigor. The threshold for significance (α) was set at 0.05 for all analyses. Results are reported as median and interquartile range values.

Contrast Enhancement Kinetics of Benign Lesions Suggest Suspicious Pathology
Pre-biopsy MRI reports were reviewed for all benign lesions in the study group. All benign lesions were interpreted as suspicious and required biopsy ( Figure 3). These lesions displayed either Type II or Type III contrast enhancement pattern, thus increasing suspicion for malignancy per BI-RADS criteria. [1][2][3][4][5] (Figure 3).
lesions. Healthy control ROIs containing healthy fat and fibroglandular tissue were defined as boxes of 33,600 voxels placed in the contralateral breast relative to the malignancy being evaluated, drawn on DCE-MRI images. Healthy control ROIs were then resampled to the DW-MRI resolution to cover 500 voxels. Any benign lesion voxels contained within healthy control ROIs were excluded. Additionally, the axillary region, large cysts (>2.5 cm), and susceptibility artifacts (e.g., from surgical clips) were excluded. ROIs were reviewed and approved by a breast radiologist (RRP). After assessing data normality, the median of each ROI was computed, resulting in a single data point per tissue type per patient.

Statistical Analysis
Statistical analyses were performed using R statistical programming (R Foundation for Statistical Computing, Vienna, Austria). Shapiro-Wilk test for normality was used to evaluate the normality of data within each ROI. Levene's test for homogeneity of variance was used to examine the normality of data across patients, followed by ranked two-way repeated-measures analysis of variance (ANOVA) to evaluate the effects of tissue type and diffusion components. Individual differences were evaluated by post hoc Wilcoxon signed-rank test with Bonferroni correction to preserve rigor. The threshold for significance (α) was set at 0.05 for all analyses. Results are reported as median and interquartile range values.

Contrast Enhancement Kinetics of Benign Lesions Suggest Suspicious Pathology
Pre-biopsy MRI reports were reviewed for all benign lesions in the study group. All benign lesions were interpreted as suspicious and required biopsy ( Figure 3). These lesions displayed either Type II or Type III contrast enhancement pattern, thus increasing suspicion for malignancy per BI-RADS criteria. [1][2][3][4][5] (Figure 3). (a) Enhancement patters are defined as: "Fast/washout" (fast initial enhancement with washout on delayed sequences); "Fast/plateau" (fast initial enhancement with plateau on delayed sequences); "Medium/washout" (medium initial enhancement with washout on delayed sequences); "Medium/plateau" (medium initial enhancement with washout on delayed sequences); "None provided" (no kinetic assessment was provided in the report). (b) Representative graph of a benign lesion showing fast initial enhancement with plateau on delayed sequences.

Malignant Lesions Display Higher C1 and C2 Compartment Values Compared to Benign Lesions and Healthy Tissue
On average, malignant lesion ROIs contained approximately 20-fold the number of voxels compared to benign lesion ROIs (Table 2). A representative example of malignant, Figure 3. Enhancement pattern of benign and malignant lesions. (a) Enhancement patters are defined as: "Fast/washout" (fast initial enhancement with washout on delayed sequences); "Fast/plateau" (fast initial enhancement with plateau on delayed sequences); "Medium/washout" (medium initial enhancement with washout on delayed sequences); "Medium/plateau" (medium initial enhancement with washout on delayed sequences); "None provided" (no kinetic assessment was provided in the report). (b) Representative graph of a benign lesion showing fast initial enhancement with plateau on delayed sequences.

Malignant Lesions Display Higher C 1 and C 2 Compartment Values Compared to Benign Lesions and Healthy Tissue
On average, malignant lesion ROIs contained approximately 20-fold the number of voxels compared to benign lesion ROIs (Table 2). A representative example of malignant, benign, and healthy tissue ROIs on both DW-MRI b = 0 s/mm 2 images and peak intensity post-contrast images in a single patient are shown in Figure 3.
Visually, the malignant, benign, and healthy tissue displayed different signal intensities across compartment maps (Figure 4). For example, malignant lesions (Figure 4b,c,e,f) display the highest signal in C 1 , C 2 , C 1 C 2 , and √ C 1 C 2 compared to benign lesions (Figure 4h,i,k,l) and healthy tissue (Figure 4n,o,q,r).  benign, and healthy tissue ROIs on both DW-MRI b = 0 s/mm 2 images and peak intensity post-contrast images in a single patient are shown in Figure 3. Visually, the malignant, benign, and healthy tissue displayed different signal intensities across compartment maps (Figure 4). For example, malignant lesions ( Figure  4b,c,e,f) display the highest signal in C1, C2, C1C2, and compared to benign lesions (Figure 4h,i,k,l) and healthy tissue (Figure 4n,o,q,r).  Tables 2 and 3). In the C2 compartment, benign lesions were not different from malignant lesions (p = 0.30) or healthy tissue (p = 0.90), but malignant lesions had higher (p < 0.01) C2 values compared to healthy tissue. The C2 values were 2.6 (1.7) for malignant lesions, 1.7 (1.5) for benign lesions, and 0.90 (0.73) for healthy tissue. The C3 signal was comparable (p = 1) for all tissue types: 0.13 (0.40) for malignancy, 0.34 (0.70) for benign tissue, and 0.34 (0.43) for healthy tissue. Benign lesions were not significantly different from healthy tissue in any of the compartments ( Figure 5, Table 3). Additionally, mono-exponential ADC did not significantly differ between the three tissue types ( Table 2).  Tables 2 and 3). In the C 2 compartment, benign lesions were not different from malignant lesions (p = 0.30) or healthy tissue (p = 0.90), but malignant lesions had higher (p < 0.01) C 2 values compared to healthy tissue. The C 2 values were 2.6 (1.7) for malignant lesions, 1.7 (1.5) for benign lesions, and 0.90 (0.73) for healthy tissue. The C 3 signal was comparable (p = 1) for all tissue types: 0.13 (0.40) for malignancy, 0.34 (0.70) for benign tissue, and 0.34 (0.43) for healthy tissue. Benign lesions were not significantly different from healthy tissue in any of the compartments ( Figure 5, Table 3). Additionally, mono-exponential ADC did not significantly differ between the three tissue types ( Table 2).

Combinations of C 1 and C 2 Also Discriminate Malignant and Benign Lesions
Overall, C 1 C 2 and √ C 1 C 2 combination maps resulted in significantly higher (p < 0.05) values for malignant lesions compared to benign lesions and healthy tissue (Table 2, Figure 5). The C 1 C 2 median values were 0.7 (1.0), 0.08 (0.29), and 0.03 (0.05) for malignant lesions, benign lesions, and healthy tissue, respectively. The product C 1 C 2 discriminated malignant lesions from benign (p < 0.01) and healthy (p < 0.001) tissues (Table 3). Additionally, the square root of the product √ C 1 C 2 separated malignant from benign (p < 0.01) and healthy (p < 0.01) tissues (Table 3). The values for √ C 1 C 2 were 0.81 (0.58), 0.29 (0.46), and 0.16 (0.16) for malignant, benign, and healthy tissue, respectively. However, neither C 1 C 2 nor √ C 1 C 2 significantly distinguished between benign lesions and healthy tissue.    Figure 5. Comparison of tissue types per compartment C 1 , C 2 , C 3 , C 1 C 2 , and Magenta, cyan, and yellow boxes indicate malignant, benign, and healthy breast tissues, respectively. Significance from ranked two-way repeated measures ANOVA are indicated by the black bars and asterisks (** p < 0.001).

Discussion
The main objective of this study was to evaluate how the breast-optimized threecomponent RSI model can discriminate malignant lesions, benign lesions, and healthy breast tissue. We sought to understand the limitations of this technique and assess the degree of overlap between malignant, benign, and healthy breast tissue to evaluate the potential clinical utility of the model in decreasing the number of excessive biopsies.
Our results show that a three-component advanced DW-MRI model can discriminate malignant tissue from benign lesions and healthy breast tissue in a small group of patients. Additionally, the product and the square root of the product of two of the compartments (C 1 and C 2 ) perform similarly to C 1 alone in discriminating malignant lesions from benign Cancers 2022, 14, 3200 9 of 12 lesions and healthy tissue. Importantly, we found that benign lesions were not significantly different from healthy breast tissue in any compartment or compartment combination.
Understanding what differences comprise these three groups may increase our understanding of the diffusion metric results. The three compartments theoretically represent different degrees of diffusion, where C 1 is hypothesized to represent the most restricted diffusion derived from cancer cells or the restricted water component within adipocytes in fatty tissue [28], C 2 is hypothesized to represent intermediate or hindered diffusion predominantly from fibroglandular tissue, and C 3 is hypothesized to represent the least restricted diffusion such as pools of fluid or flow through blood vessels [23,24]. Our data suggest that malignant lesions display high conspicuity in the C 1 compartment, both in the individual C 1 map and in the context of a derived C 1 C 2 or √ C 1 C 2 parameter. In other words, C 1 can be used to distinguish the malignancy of a lesion due to increased restricted diffusion compared to benign lesions and healthy tissue. Though benign lesions had a generally higher C 2 compartment than healthy tissue, there was considerable variability between samples in this compartment, resulting in nonsignificant differences between malignant and benign tissues and benign and healthy tissues. Further, all three tissue types demonstrated comparable degrees of unhindered diffusion, represented by the C 3 compartment, suggesting that vascular flow was similar across tissue types. Overall, the compartment demonstrating the most restricted diffusion separated malignant from benign lesions, regardless of lesion subtype and size.
Interestingly, we found no significant differences between benign lesions and healthy breast tissue in any of the compartments. The three-compartment RSI model used in this study follows that used in Andreassen et al. and Rodríguez-Soto et al., where control ROIs comprised the entire contralateral breast, including any benign lesions, were used to establish the model [23,24]. Our findings support their assumption that benign lesions generally display similar diffusion properties as healthy breast tissue in a model where the diffusion signal is decomposed into three distinct compartments. Only a few studies have evaluated the ability of DW-MRI in discriminating healthy and benign breast tissues, with mixed results: Sharma et al. [29] found significantly higher ADC values for healthy tissues compared to benign lesions, while Woodhams et al. [14] demonstrated no significant differences between the tissue types. Since the ADC of healthy breast tissue has been found to vary with breast density [30], our study was limited to subjects with concurrent benign and malignant lesions, with the healthy control also derived from the same patient. This allowed us to perform a paired analysis to mediate the potential effects of breast density on diffusion metrics. DW-MRI is a potential complement to DCE-MRI that may reduce the number of excessive biopsies from false-positive interpretations. In our cohort, all benign lesions were classified as suspicious from contrast enhancement kinetics and thus required tissue biopsy. Several groups have already demonstrated the ability of the mono-exponential ADC diffusion estimate in discriminating between benign and malignant lesions in the breast [22,31,32]. However, the translation of DW-MRI into clinical practice has been limited by a lack of consensus in cut-off values from variation due to geometric distortions [9], chosen sequence parameters [12], and vendor-and system-specific bias [10]. Additionally, in the literature, reported absolute ADC threshold values are in the range 0.55 × 10 −3 -1.88 × 10 −3 mm 2 /s for malignant lesions and 1.10 × 10 −3 -2.06 × 10 −3 mm 2 /s for benign lesions [33]. In our small cohort, we found that malignant lesions, benign lesions, and healthy breast tissue had ADC values that overlapped considerably. The wide overlap between ADC measurements for benign and malignant lesions makes ADC less robust of an imaging biomarker on a per-patient basis, and only a handful of studies have been conducted regarding separating benign lesions from healthy breast tissue [14,29]. This study extends the work by Andreassen et al. in demonstrating the potential clinical utility of an advanced DW-MRI framework that compartmentalizes diffusion on a voxel-level and is specific to the breast [24]. In a small sample of patients, the three-component RSI model was able to discriminate malignant lesions from benign lesions and healthy breast tissue. Small sample size is the primary limitation of our study. We limited our sample subset to patients who had both concurrent biopsy-proven malignancies and biopsy-proven benign lesions from a single institution. While this aided in reducing interpatient variability, this significantly limited the number of patients eligible for evaluation. Additionally, malignant lesions were enriched in our population given that our study group consisted of women with known malignancy. Future work will also focus on prospectively analyzing women at high risk and average risk of breast cancer to further evaluate the robustness of this model as it pertains to the general population. While our data is statistically significant in this small patient sample, continued evaluation in a larger population across several institutions may lead to further optimization of the model, and this may include evaluation of even higher b-values (over 4000 s/mm 2 ) to better discriminate the restricted diffusion compartment from intermediate and free diffusion, at the cost of increased scan time. Large components of fat in breast tissue may also require further optimization in this model, which was initially developed in less fatty tissues (e.g., brain and prostate) [8,18]. Though DW-MRI data was fat-suppressed using SPAIR, incomplete suppression may affect the derived coefficients in our small sample set. Additionally, water trapped within adipocytes and lipids may produce artificially restricted signal within fat. It is also possible that our ROIs may contain more than one tissue type (e.g., small benign lesions containing some fatty tissue, or healthy tissue ROIs containing occult malignancy). Lastly, an assumption of the RSI model is that diffusion within each voxel is isotropic, which is a gross approximation of the diffusion process. Future iterations of the model will consider anisotropic diffusion such as fractional anisotropy to address the diffusion directionality within breast tissue.

Conclusions
This three-component RSI model, along with T 2 -weighted information, provides a promising supplement to DCE-MRI for improved specificity and may play a role in the development of future non-contrast breast MRI protocols. Institution-standardized DW-MRI sequences are already included in breast imaging MRI protocols and their limitations have been briefly described in this paper. Our findings indicate that malignant lesions demonstrate high conspicuity on compartment maps indicating the most restricted diffusion compared to benign lesions and healthy breast tissue, which showed no significant differences. The model may increase radiologists' confidence in ascribing a lesion as malignant versus benign. Future directions include applying this technique to a larger subset of patients, evaluating early high-risk atypical benign lesions and DCIS, and investigating the model's ability to differentiate lesions of various molecular subtypes.