Characterization of the Diffusion Signal of Breast Tissues using Multi-exponential Models

Abstract

Purpose:

Restriction spectrum imaging (RSI) decomposes the diffusion-weighted (DW) MRI signal into separate diffusion components of known apparent diffusion coefficients (ADCs). The number of diffusion components and optimal ADCs for RSI are organ-specific and determined empirically. The purpose of this work was to determine the RSI model for breast tissues.

Methods:

The DW-MRI signal was described using a linear combination of multiple exponential components. A set of ADC values was estimated to fit voxel in cancer and control regions of interest (ROIs). Later, the signal contributions of each diffusion component were estimated using these fixed ADC values. Relative fitting residual and Bayesian information criterion (BIC) were assessed. Contrast-to-noise ratio (CNR) between cancer and fibroglandular tissue in RSI-derived signal contribution maps was compared to dynamic contrast enhanced (DCE) imaging.

Results:

A total of 74 women with breast cancer were scanned at 3.0T MRI. The fitting residuals of conventional ADC and BIC suggest that a three-component model improves the characterization of the diffusion signal over a bi-exponential model. Estimated ADCs of tri-exponential model were D_1,3=0, D_2,3=1.5×10⁻³ and D_3,3=10.8×10⁻³ mm²/s. The RSI-derived signal contributions of the slower diffusion components were larger in tumors than in fibroglandular tissues. Further, the CNR and specificity at 80% sensitivity of DCE and a subset of RSI-derived maps were equivalent.

Conclusion:

Breast DW-MRI signal was best described using a tri-exponential model. Tumor conspicuity in breast RSI model is comparable to that of DCE without the use of exogenous contrast. These data may be used as differential features between healthy and malignant breast tissues.

Introduction

The American Cancer Society recommends that women at high risk for breast cancer receive both mammography and magnetic resonance imaging (MRI) exams yearly starting at age 30.¹ Breast MRI is also currently used for evaluating new breast cancer diagnosis² and response to neoadjuvant chemotherapy.³ Clinical breast MRI protocols include dynamic contrast-enhanced (DCE)-MRI, which requires intravenous administration of gadolinium-based contrast agents to visualize vascular patterns (i.e. tumor angiogenesis).⁴ Despite high sensitivity for breast cancer detection, DCE-MRI faces a number of challenges such as lengthy acquisition protocols, dependency on expert radiologist readers, and conflicting results regarding detection specificity.^5–9 Further, such contrast agents have been linked to brain deposition with unknown sequelae¹⁰, and some are contraindicated in patients with renal failure and pregnant women.¹¹ Hence, there is a need to develop highly specific and sensitive methods to improve breast cancer detection.

MRI has higher diagnostic accuracy compared to mammography and ultrasound in women at high risk for breast cancer or with dense breasts.¹² Breast MRI protocols typically consist of fat suppressed T₂-weighted imaging, pre- and multi-phased dynamic post-contrast T₁-weighted imaging, and diffusion-weighted (DW) imaging.¹³ DW-MRI has been more recently introduced into breast MRI protocols as a promising screening tool for breast cancer. Conventional DW-MRI has demonstrated potential for discriminating pre-defined benign and malignant breast lesions.^14–16 The combined use of DCE- and DW-MRI improves sensitivity and specificity in cancer detection compared to either technique individually.⁴

DW-MRI probes the diffusion of water in tissues, allowing for the characterization of tissue microstructure across different histologies.¹⁷ In fact, evidence suggests that cancers diagnosed with MRI are more likely to be invasive than those detected with mammography.¹⁸ Despite the quantitative nature of DW-MRI, resulting images are sometimes used to qualitatively inform clinical MRI exam interpretation.^14,19 Cancer lesions are conspicuous on these images due to the combined effect of lengthened T₂ and the shift in the relative size between slow and fast water diffusion components in neoplasms compared to fibroglandular tissue.^19,20 This effect is enhanced by the fact that breast DW-MRI data are typically fat suppressed,¹³ thereby further increasing tumor-to-background contrast. However, inadequate fat suppression and the presence of additional ongoing biological processes (e.g. edema or lactation) may affect the extracted diffusion estimates and image interpretation.^21,22 Thus, there is a need for DW-MRI models that fully capture and allow for the differentiation of breasts complex tissue microstructure.

Restriction spectrum imaging (RSI) is an advanced DW-MRI technique that has previously demonstrated potential in improving tumor conspicuity when evaluating disease severity and response to treatment in brain^23,24 and prostate^25,26. In RSI, an advanced linear mixture model is used to decompose the DW-MRI signal into separate water diffusion components such as restricted, hindered and free water pools. Changes in the signal intensity between voxels is considered to result from changes in the relative size of these intravoxel water compartments. Further, the RSI model does not normalize by signal at b=0 s/mm² as it is done in conventional DW-MRI estimates. As a result, RSI outputs display the joint effect of changes in diffusion properties and T₂ due to the presence of cancer in tissues microenvironment. For different organs, the number of discernable diffusion components and their corresponding diffusion coefficients have been determined empirically and theoretically.²⁷

Previously, Vidić et al. demonstrated that a normalized bi-exponential model was able to discriminate between pre-defined ROIs of benign and malignant breast lesions but did not explore additional diffusion components or assess optimal diffusion coefficients for both cancer and healthy breast tissues.²⁸ Considering the complex tissue microenvironment in the breast, we hypothesized that the RSI framework will be helpful in improving tumor conspicuity. Thus, the purpose of this work was to determine the optimal number of RSI diffusion components and their corresponding apparent diffusion coefficients (ADCs) for breast tissues.

Methods

Subjects

Patients from two different institutions (sites) with known breast lesions were invited to participate in this study before receiving treatment and underwent a breast MRI at 3.0T before receiving treatment. Only patients with malignant lesions confirmed by histopathologic analysis were included in this study. This study was approved by the institutional review boards from both sites. All participants provided both oral and written consent.

Patients were from two sites, 57 women from site 1 and 25 women from site 2 were enrolled in this study. From site 1, eight participants were excluded from the study; six women had contralateral cancer or mastectomy and in two cases DW-MRI data were of low quality.

MRI Data Collection

Data from two sites were used to increase the applicability of the model across acquisition protocols and vendors. Data at site 1 were collected using a 3T MR750 scanner (DV25–26, GE Healthcare, Milwaukee, Wisconsin, USA) and an 8-channel breast array coil. Pulse sequence parameters: axial DCE-MRI 3D fast spoiler gradient-recalled (SPGR) acquisition— echo time (TE)=2.6 ms, repetition time (TR)=5.4 ms, flip angle (FA)=10°, field of view (FOV)=320×320 mm², acquisition matrix 512×406, reconstruction matrix 512×512, voxel size 0.625×0.625×2.4 mm³; axial T₂ fat suppressed fast spin echo (FSE)— TE/TR=107/4520 ms, FA=111°, FOV=320×320 mm², acquisition matrix 512×320, voxel size=0.625×0.625×5mm³; axial reduced-FOV echo-planar imaging (EPI) DW-MRI— TE/TR=82/9000 ms, b-values (number of diffusion directions)=0, 500 (6), 1500 (6), and 4000 (15) s/mm², FOV=160×320 mm², acquisition matrix 48×96, voxel size=2.5×2.5×5 mm³, spectral attenuated inversion recovery (SPAIR) fat suppression, phase-encoding (PE) direction A/P, and no parallel imaging.

Data at site 2 were collected using a 3T Skyra scanner (VD13-VE11, Siemens, Erlangen, Germany) and 16-channel breast array coil. Pulse sequence parameters: sagittal DCE-MRI 3D fast low angle shot (FLASH) acquisition— unilateral sagittal plane; TE/TR=2.2/5.8 ms, FA=15°, FOV=180×180 mm², acquisition matrix 256×256, reconstruction matrix 256×256, voxel size 0.7×0.7×2.5 mm³, generalized auto-calibrating partially parallel acquisition (GRAPPA) with acceleration factor of 2 and 36 reference lines; sagittal T₂ FSE— unilateral sagittal plane, TE/TR=118/5500ms, FA=120°, FOV=180×180 mm², acquisition matrix 256×256, voxel size=0.7×0.7×2.5 mm³; sagittal EPI DW-MRI— unilateral sagittal plane; TE=88 ms, TR=10,600 ms for 15 participants and TR=11,800 ms for 10 participants, b-values=0, 200 (6), 600 (6), 1200 (6), 1800 (6), 2400 (6), and 3000 (6) s/mm², FOV=180×180 mm², acquisition matrix 90×90, voxel size=2.0×2.0×2.5 mm³, spectral fat saturation in strong mode was used on 15 participants and SPAIR fat suppression was used on 10 participants, PE direction A/P, GRAPPA with acceleration factor of 2 and 24 reference lines.

The b=0 s/mm² volumes at both sites were collected in the A/P and P/A PE directions to correct DW-MRI data for geometric and intensity distortions due to B₀ inhomogeneities using the reverse polarity gradient (RPG) method.²⁹

DW-MRI Data Preprocessing

Analyses were performed using MATLAB R2016b (The MathWorks Inc., Natick, Massachusetts, USA). The noise probability density function of MRI data when using multiple-receiver coils and sum of squares reconstruction is a non-central chi distribution.³⁰ Thus, the noise floor was estimated by first masking out all voxels within the body and the average of the peak corresponding to the background signal was found as determined from the histogram of the DW-MRI data at the maximum b-value. Diffusion-weighted data were noise corrected by subtracting the noise floor value from all voxels. In order to evaluate data quality before fitting, the signal to noise ratio (SNR) was estimated as average signal within cancer or fibroglandular ROIs divided by the standard deviation of a background ROI at each b-value.

All diffusion directions for a determined b-value were averaged. Data were then normalized by the 98^th percentile signal intensity value in b=0 s/mm² volume. In contrast to conventional ADC estimation, in RSI the DW-MRI signal is not divided by b=0 s/mm² thus preserving T₂ information. The following volumetric ROIs were manually drawn on the resulting images, informed by all available data in the exam protocol (including DCE and T₂-weighted images): (i) control regions including either the cancer-free contralateral breast (site 1) or regions without cancer in the ipsilateral breast at least 10 mm away from the cancer lesion (site 2), (ii) whole-volume cancer lesions, and (iii) background regions. Control ROIs excluded the axillary region, large cysts (>2.5cm), and susceptibility artifacts (e.g. from surgical clips). Control ROIs were initially drawn as boxes and were masked using binarized T₂-weighted images, resampled to DW-MRI space, to remove the background from the ROI. Volumetric cancer ROIs were manually drawn on the averaged DW images. All cancer ROIs were validated by a breast radiologist at each site (R.R.P. and A.Ø.). Examples of these ROIs are shown in Supporting Information Figures S1 and S2. In order to investigate the differences in RSI estimates between cancer and non-cancerous tissues in breast, fibroglandular tissue and fatty tissue ROIs were generated by thresholding the b=0 s/mm² volume. The threshold was determined (using Matlab graythresh function) within the initial control ROI in the b=0 s/mm² volume.

RSI Modeling

In RSI, the diffusion signal was modeled as the linear combination of multiple exponential decays:

$$S_{diff}(b,N)={\sum }_{i=1}^N{C}_{i,N}{e}^{-b{D}_{i,N}}=S_0{\sum }_{i=1}^N{e}^{-b{D}_{i,N}}$$ [1]

where N is the total number of exponential decays (here 2 and 3), C_i,N are the signal contributions of each exponential component, b are the b-values, and D_i,N are the apparent diffusion coefficients of each exponential component, and D_1,N<D_2,N <D_3,N. Note that in RSI, D_i,N are fixed to allow for comparison of signal contributions C_i,N across different tissues. The signal contributions C_i,N include information on the proton density and T₂ properties of each voxel, which are contained in the b=0 s/mm² volume, S₀. The fractional contributions, f_i,N, of each signal component C_i,N were also estimated as:

$$S_{diff}(b,N)=S_0{\sum }_{i=1}^N{f}_{i,N}\text{and}{f}_{i,N}=\frac{C_{i,N}}{{\sum }_i^N{C}_{i,N}}$$ [2]

In order to determine the apparent diffusion coefficients (D_i,N) to describe breast tissues, global fittings of bi- and tri-exponential models to DW-MRI data from cancer and control ROIs were performed. A simplex search was performed using the built-in MATLAB function fminsearch to minimize the sum-of-squared difference between the observed and fitted signal values across all voxels. A non-negative least squares fit of the current estimates for D_i,N were used to estimate the fitted C_i,N values at each iteration of the minimization. To enforce non-negativity on D_i,N for each compartment, this optimization procedure was performed on the log(D_i,N) values which were then exponentiated afterwards. No upper bounds were imposed on the possible values for D_i,N.²⁷ After D_i,N were determined, maps of the signal contributions of each exponential component C_i,N were estimated via nonnegative least-squares fitting of the model to the signal-vs-b-value curve from each voxel.²⁷

The relative fitting residual and relative Bayesian information criterion (BIC) were calculated for both bi- and tri-exponential models. Relative fitting residual was calculated as the difference between observed and predicted diffusion-weighted signal divided by the observed signal in all ROIs, as well as for conventional apparent diffusion coefficient (ADC) maps of b-values ≤1,500 s/mm². The BIC was used because it penalizes the model’s likelihood for increasing the number of estimated parameters.³¹ Lower BIC values denote improved model fitting. However, absolute BIC values are arbitrary, therefore, we report the difference in BIC (ΔBIC = BIC_bi – BIC_tri).

In order to compare tumor conspicuity on RSI outputs (C_i,N) to the gold standard and other conventional DW-MRI methods, the contrast-to-noise (CNR) ratio was approximated as the average signal of tumor divided by the average signal of fibroglandular tissue. The CNR was estimated for C_i,N, conventional ADC and DCE.

Statistical Analysis

Statistical analyses were performed using SPSS statistics software (version 26 for Mac OS X, IBM Corporation, Armonk, NY, USA). All signal contributions are reported as median, interquartile range and range values. Kolmogorov-Smirnov test was used to examine data normality and related-samples Friedman’s one-way analysis of variance by ranks tests were used to identify differences in C_i,N and f_i,N signal contributions and CNR across diffusion components and tissues (cancer vs fibroglandular tissue). The threshold for significance (α) was set at 0.05 for all analyses. In order to investigate the robustness of RSI to SNR, we performed our fitting analysis using only data of b-values ≤1,500 s/mm² and found that the estimated D_i,N values were the same as those in the original analysis. The area under the curve (AUC) of receiver operating characteristic (ROC) curves were used to evaluate the diagnostic value of normalized and non-normalized RSI outputs, DCE and ADC. The specificity of each parameter at 80% specificity is also reported.

Results

Demographic information can be found in Table 1. Representative images of both sites are shown in Figure 1. The diffusion signals of control and tumor ROIs were then fitted by bi- and tri-exponential models to estimate fixed ADCs.

Table 1.

Demographic information of participants.

Characteristics	Site 1	Site 2
Number of lesions	50	25
Average patient age, years (range)	47.6±11.5 (27–73)	52.8±11.2 (29–75)
Histological type
Carcinoma with medullary features		3
Ductal carcinoma in situ (DCIS)	1	1
Invasive ductal carcinoma (IDC)	42	17
Invasive lobular carcinoma (ILC)	4	1
Metaplastic carcinoma	2
Mixed IDC and ILC	1
Mucinous carcinoma		1
Papillary carcinoma		1
Tubular carcinoma		1

Figure 1.

Images from diffusion-weighted magnetic resonance imaging (DW-MRI) were averaged over all diffusion directions for each b-value, and noise corrected. Representative images at different b-values and for both sites (top and bottom rows) are shown.

SNR in Cancer and Fibroglandular Tissue ROIs

The SNR of data from site 2 was lower than that from site 1. In general, SNR was higher at low non-zero b-values than at b=0 s/mm² for both cancer and fibroglandular tissue ROIs (Table 2). This was due to the averaging of diffusion directions at non-zero b-values. As expected, the SNR became progressively lower at higher b-values. The lowest median SNR was 19.1 (interquartile range 6.3) and 8.2 (interquartile range 3.2) for cancer and fibroglandular tissue, respectively.

Table 2.

SNR for cancer and fibroglandular (FBG) ROIs after noise correction and averaging over diffusion directions of the same b-value for each site.

Site	b-value (s/mm2)	Median Cancer SNR (IQR)	Median Fibroglandular Tissue SNR (IQR)	Median Fat SNR (IQR)
1	0	88.7 (82.6)	51.5 (48.5)	9.8 (7.0)
	500	119.6 (111.0)	52.7 (47.3)	15.2 (7.7)
	1500	65.6 (61.8)	18.5 (13.0)	11.1 (4.7)
	4000	39.8 (46.3)	13.6 (11.3)	13.5 (8.5)
2	0	57.1 (18.8)	10.6 (10.5)	8.6 (5.7)
	200	84.8 (49.3)	15.7 (13.0)	13.0 (6.6)
	600	59.2 (24.5)	11.6 (6.5)	10.3 (5.5)
	1200	39.6 (18.7)	9.7 (4.7)	9.1 (4.2)
	1800	29.5 (12.3)	8.8 (4.1)	8.7 (3.0)
	2400	22.6 (8.5)	8.5 (4.5)	8.0 (3.1)
	3000	19.1 (6.3)	8.2 (3.2)	7.6 (3.7)

RSI Model for Breast

The relative fitting residuals of conventional ADC, and bi-, and tri-exponential models in control ROIs were 2.1%, 1.6%, and 1.0% of the overall signal value, while the residuals for the cancer ROIs were 3.3%, 1.0%, and 0.3%, respectively. Residuals were considerably smaller for the tri-exponential model. Similarly, a ΔBIC of 74 was estimated between the bi- and tri-exponential models, indicating that a tri-exponential model further improves the fitting of breast DW-MRI data.

Estimated diffusion coefficients using the bi-exponential model were D_1,2=2.8×10⁻⁵ and D_2,2=2.4×10⁻³ mm²/s, and D_1,3=1.6×10⁻¹⁷, D_2,3=1.5×10⁻³ and D_3,3=10.8×10⁻³ mm²/s for tri-exponential model (Table 3). The determined diffusion coefficients for each site were D_1,2=4.8×10⁻⁵ and D_2,2=2.2×10⁻³ mm²/s and D_1,2=8.6×10⁻⁷ and D_2,2=2.9×10⁻³ mm²/s for site 1 and site 2, respectively. Similarly, when using three exponentials we calculated the diffusion coefficients to be D_1,3=6.5×10⁻⁶, D_2,3=1.2×10⁻³ and D_3,3=4.6×10⁻³ mm²/s for site 1 and D_1,3=2.1×10⁻¹⁸, D_2,3=1.9×10⁻³ and D_3,3=16.5×10⁻³ mm²/s for site 2. In all cases, for the tri-exponential model, the slowest diffusion coefficients D_1,3 is far smaller than can be quantified accurately. Thus, in this RSI model for breast D_1,3 was set to 0 mm²/s, replacing the slowest diffusion component with a constant offset term (C_1,3).

Table 3.

Diffusion coefficients of RSI bi- and tri-exponential breast model estimated for each site and together.

Model	Parameter	Site 1 (mm2/s)	Site 2 (mm2/s)	Joint Model (mm2/s)	Joint Model excluding fat (mm2/s)
Bi-exponential	D1,2	4.8×10−5	8.6×10−7	2.8×10−5	5.8×10−5
	D2,2	2.2×10−3	2.9×10−3	2.4×10−3	2.3×10−3
Three-component	D1,3	6.5×10−6	2.1×10−18	1.6×10−17	9.8×10−7
	D2,3	1.2×10−3	1.9×10−3	1.5×10−3	1.4×10−3
	D3,3	4.6×10−3	16.5×10−3	10.8×10−3	7.2×10−3

The signal contributions C_i,N for cancer and fibroglandular tissue ROIs were not significantly different (p>0.05) when estimated using D_1,3=1.6×10⁻¹⁷ mm²/s and D_1,3=0 mm²/s for the tri-exponential model. The diffusion signal of all tissues was then described with the following three-component model:

$$S_{diff}(b)=C_{1,3}+C_{2,3}{e}^{-b\cdot 1.5\times {10}^{-3}}+C_{3,3}{e}^{-b\cdot 10.8\times {10}^{-3}}$$

Because the magnitudes of D_1,N were so small we investigated if the source of this restricted diffusion was the fatty tissue voxels in control ROIs. Thus, we performed the same RSI model fitting excluding fatty tissue voxels and found that D_1,N were very similar to those from the original analysis including fatty tissue in control ROI (Table 3, last column).

RSI Estimates in Breast Cancer and Fibroglandular Tissue

The signal contributions of RSI C_i,N and f_i,N and estimated conventional ADC values within cancer and fibroglandular ROIs are shown in Table 4. The ADC values between tumor and fibroglandular tissue were not statistically different from each other; however, displayed a trend towards statistical difference (p=0.065, Figure 2A).

Table 4.

Average signal contribution of the fibroglandular tissue and cancer regions of interest (ROIs) for bi- exponential and three-component models. Signal contributions C_i,N are in arbitrary units and f_i,N are normalized.

Model	Parameter	Cancer		Fibroglandular tissue
		Median (range)	IQ Range	Median (range)	IQ Range	p-value
Conventional ADC (mm2/s)	ADC (×10-3)	0.93	0.30	1.1	1.1	p>0.05
Bi-exponential	C1,2	1.43	1.76	0.51	0.30	p<0.05*
	C2,2	5.25	6.16	3.11	3.70	p>0.05
	f1,2	0.31	0.21	0.14	0.18	p<0.05*
	f2,2	0.69	0.21	0.86	0.17	p<0.05*
Three-component	C1,3	1.02	1.15	0.37	0.19	p<0.05*
	C2,3	5.17	6.89	2.52	3.42	p<0.05*
	C3,3	0.31	0.52	1.01	1.10	p<0.05
	f1,3	0.22	0.20	0.10	0.17	p<0.05*
	f2,3	0.72	0.27	0.62	0.26	p>0.05
	f3,3	0.09	0.11	0.25	0.17	p<0.05*

Figure 2.

Boxplot of A) conventional ADC, B) median signal contributions of the components of the bi-exponential and three-component model, and C) median fractional signal contributions within cancer (red) and control (blue) regions of interest (ROIs). In both models, the magnitude of the components of cancer and control ROIs were statistically different (p<0.05, horizontal bars).

Median cancer and fibroglandular tissue signal contributions (C_i,N) for bi-exponential and three-component models are shown in Figure 2B. The signal contribution attributed to the slowest diffusion compartments from the bi-exponential model (C_1,2) was different (p<0.05) between cancer and fibroglandular tissues. Similarly, the signal contribution of the two slowest components derived from the three-component model (C_1,3 and C_2,3) were also different between tumor and fibroglandular tissue ROIs (p<0.05). In terms of the normalized signal contributions, the bi-exponential model f_1,2 and f_2,2, and f_1,3 were higher (p<0.05) in cancer ROIs than in fibroglandular tissue (Figure 2C and Table 4). In contrast, f_3,3, the compartments attributed to the fastest diffusion was higher (p<0.05) in fibroglandular tissue than in cancer tissues.

In order to understand the relationship of the multiple signal contributions in the three-component model, the average values for each subject were plotted between tissues (Figure 3). These plots showed that tumor ROIs present larger signal in both C_1,3 and C_2,3 compared to fibroglandular tissue. Further, given that data were collected with fat suppression, the signal contributions in fatty tissue were minimal.

Figure 3.

Apparent diffusion coefficients (D_i,N) of a three-component model ($S_{diff}\left(b\right)=C_{\mathrm{1,3}}+C_{\mathrm{2,3}}{e}^{-b·D_{\mathrm{2,3}}}+C_{\mathrm{3,3}}{e}^{-b·D_{\mathrm{3,3}}}$) were determined by simultaneously fitting both control and cancer ROIs of both sites. Values of D_i,N were then fixed (D_2,3=1.4×10⁻³ mm²/s, and D_3,3=10.2×10⁻³ mm²/s) and used to estimate the signal contribution of each component C_i,N. Two-dimensional plots of the magnitude of A) C_1,3 vs C_2,3, B) C_1,3 vs C_3,3, and C) C_2,3 and C_3,3 are shown for fibroglandular tissue (blue circles), fat (yellow squares) and cancer (red squares) ROIs. Circles and bar represent the C_i,N ROI median and 25^th and 75^th percentiles for each subject.

To test the generality of the three-component model, we compared the signal contributions in cancer ROIs across models determined with data from each site and together (Supporting Information Table S1). We found that in cancer tissues, the signal contribution C_3,3 and f_3,3 generated from the individual site models were different (p<0.05) from each other. Similarly, in fibroglandular tissue, the fractional signal contribution f_3,3 was different (p<0.05) across individual site models.

CNR between cancer lesions and fibroglandular tissue

Results of CNR between tumor and fibroglandular tissue are shown in Table 5 (and Supporting Information Figure S3). Compared to DCE, the CNR of all DW-MRI estimates was lower (p<0.05), with the exception of signal contributions of the slowest compartments in RSI models C_1,3 and C_2,3, and f_1,3. Further, the CNR of conventional ADC was lower (p<0.05) than that of DCE, and C_1,2, C_1,3, and f_1,3 RSI signal contributions. In contrast, the CNR of C_3,3 and f_3,3 was higher (p<0.05) than that of ADC. This means that RSI signal contributions C_2,2, C_2,3, f_1,2, and f_2,2 yielded similar CNR to that of conventional ADC (Figure 4).

Table 5.

Median contrast-to-noise ratio (CNR), area under the curve (AUC) and specificity at 80% sensitivity between cancer and fibroglandular tissues extracted from RSI-derived maps and compared to dynamic contrast-enhanced (DCE) MRI and conventional apparent diffusion coefficient (ADC).

Parameter	Median CNR	CNR Interquartile range (range)	AUC	Specificity at 80% Sensitivity (%)
DCE	5.1	4.5 (0.7–17.8) †	0.79	81.0
ADC	0.8	1.0 (0.3 – 11.4) ‡	0.46	34.3
C1,2	2.8	3.1 (0.6 – 11.9) ‡†	0.94	90.8
C2,2	1.3	2.0 (0 – 22.0) ‡	0.77	61.6
C1,3	2.9	3.2 (0.5 – 48.5) †	0.90	82.2
C2,3	1.6	3.0 (0.1 – 39.0)	0.84	73.5
C3,3	0.5	0.7 (0 – 3.1) ‡†	0.36	*
f1,2	2.2	2.1 (0.3 – 41.3) ‡	0.54	44.2
f2,2	0.8	0.2 (0.2 – 2.6) ‡	0.46	35.2
f1,3	2.2	3.5 (0.3 – 45.2) †	0.51	40.4
f2,3	1.1	0.4 (0.2 – 5.9) ‡	0.78	66.4
F3,3	0.3	0.5 (0 – 1.2) ‡†	0.26	*

^‡= statistical difference compared to DCE.

^†= statistical difference compared to ADC.

^*= maximum sensitivity of 44% and corresponding specificity of 25%.

Figure 4.

Processed images from patient from site 1 in Figure 1 including A) T2-weighted and B) dynamic contrast-enhanced (DCE) images, C) conventional apparent diffusion coefficient map, and the signal contributions (C_i,N) of bi-exponential (D-E) and three-component (F-H) models. The fractional signal contributions are also shown for bi-exponential (I-J) and three-component (K-M) models. Arrowheads indicate tumor location. Signal contribution in tumors was higher than surrounding tissues in both C_1,N and C_2,N in both models. The compartment C_3,3 displays vascular flow information.

Performance of DCE, ADC and RSI to differentiate cancer lesions from fibroglandular tissue

The AUC of DCE and ADC were 0.79 and 0.46, respectively (Table 5). The AUC of the two slowest compartments of the non-normalized RSI outputs C_1,2, C_2,2, C_1,3, and C_2,3 were comparable or higher than those of DCE (0.94, 0.77, 0.90 and 0.84, resp.). The AUC of C_3,3 was 0.36. Of the normalized RSI outputs, f_2,3 had the highest AUC (0.78), while the rest were much lower (f_1,2=0.54, f_2,2=0.46, f_1,3=0.51, and f_3,3=0.26). The specificity of DCE at 80% sensitivity was of 81% in this cohort, while that of conventional ADC was only 34.3%. The three RSI outputs with the highest specificity were C_1,2 (90.8%), C_1,3 (82.2%), and C_2,3 (73.5%).

Discussion

In the RSI framework, the diffusion-weighted MR signal is fit to an organ-specific multi-exponential model containing fixed ADCs. By doing so, direct comparison of the signal from each model component (attributed to different water pools) can be performed across tissues. The RSI framework is also characterized by the inclusion of signal from all relevant tissues, including cancer lesions, into an organ-specific model. This strategy has been shown to improve tumor conspicuity in prostate and brain applications.^27,32 Here, we determined the RSI model parameters for breast and compared lesion conspicuity across RSI-derived maps, conventional ADC and the clinical standard DCE.

DW-MRI data at high b-values are strongly affected by the presence of noise, which has a distribution that depends on the utilized coils and reconstruction methods.³³ In RSI, data are inherently noisy due to the use of high b-values. We found that the median SNR within cancer lesions and fibroglandular tissue ROIs was ≥20 and ≥8, respectively. Although no consensus has been reached as to the necessary SNR to accurately estimate conventional DW-MRI estimates for breast applications³⁴, an SNR >20 has been suggested to be adequate.³⁵ However, these SNR guidelines were made for voxel-wise quantitative DW-MRI, while in RSI all voxels are fit simultaneously. Our results suggests that that the SNR requirements for RSI modeling are more lenient than those for conventional DWI estimates.

In the present work, we used two and three diffusion components to describe the diffusion signal of breast tissues and determine the corresponding diffusion coefficients of each exponential component. The ΔBIC (BIC_bi – BIC_tri) results suggest that a three-component model improves the characterization of the diffusion signal over a bi-exponential model. Further, the relative fitting residuals when using a three-component model are two and ten times smaller in control and cancer ROIs, respectively, compared to conventional ADC.

In the present study, DW-MRI data acquisition differed between sites. The rationale to include data from different protocols, MRI scanners, and vendors was to increase the generalizability of the models determined here. A limitation of this setup may be the difference in TEs of DW-MRI data between sites (82 and 88 msec). However, given the TEs used and T₂ values of fibroglandular and cancer tissues (46 and 68 msec, respectively) at 3T,²⁰ the expected signal decay due to T₂ effects is somewhat similar (~70–85%) across sites for both tissues. The RSI model parameters estimated from each site revealed that the estimated ADCs of the faster compartments (for both bi- and tr-exponential models) are larger in data from site 2. This is attributed to both the differences in TE between sites and the inclusion of more b-values, which improve the characterization of the diffusion-weighted signal curve between zero and 500 s/mm². Similarly, the estimated diffusion coefficient of the slowest component of the RSI three-component model appears to be driven by the data from site 2. However, the diffusion coefficients of both sites are smaller than what can be accurately quantified in studies using clinical scanners. Importantly, the signal contributions within tumor ROIs were overall not different when estimated using the models determined from each site independently. Thus, suggesting that the joint RSI breast model established here may be applied to data acquired with different parameters within a certain range. Future work will focus on testing the validity and limitations of this model on an independent sample.

Control ROIs included fatty tissue voxels because in breast RSI, tissues that are not cancer are considered background and are included in the model fitting process. The definition of the control ROI used to determine the RSI model directly impacts the estimated ADC values. Thus, we excluded fatty tissue from the RSI breast model fitting process and found that the main difference between RSI models was in D_3,3 (excluding fatty tissue D_3,3=7.2×10⁻³ mm²/s vs including fatty tissue D_3,3=10.8×10⁻³ mm²/s). These results indicate that by removing fatty tissue from the analysis, the component attributed to pseudo-diffusion evolves at a slower rate due to the exclusion of low signal in fatty tissue. Finally, these data suggest that water in both cancer and fibroglandular tissue also experiences restricted diffusion. The amount of water molecules experiencing restricted diffusion appears to be higher in tumor tissues (Figure 3A).

Representative DW-MRI derived maps for each site are shown in Figures 4 and 5 together with T₂-weighted and DCE images, and conventional ADC (b-values ≤1,500 s/mm²) maps (Figures 4A–C and 5A–C). Tumor signal contributions in RSI outputs C_1,2 and C_1,3 (Figures 4D,F and 5D,F) displayed higher intensities than in fibroglandular tissues, while signal of both tumors and fibroglandular tissues were similar in C_2,2 and C_2,3 (Figures 4E,G and 5E,G). Thus, C_1,3 and C_2,3 signals were attributed to hindered and restricted diffusion. High signal intensities observed in C_3,3, correspond to the location of vessels, therefore we hypothesized that this compartment contains information pertaining to vascular flow (Figures 4H and 5H). In the bi-exponential model, flow information appears to be contained in the fast signal contributions C_2,2 (Figures 4C and 5C).

Figure 5.

Processed images from patient from site 2 in Figure 1 including A) T2-weighted and B) dynamic contrast-enhanced (DCE) images, C) conventional apparent diffusion coefficient map, and the signal contributions (C_i,N) of bi-exponential (D-E) and three-component (F-H) models. The fractional signal contributions are also shown for bi-exponential (I-J) and three-component (K-M) models. Arrowheads indicate tumor location.

The bottom rows of Figures 5 and 6 show maps of the normalized RSI signal contributions. It can be observed that the CNR between tumor and fibroglandular tissue is similar to that of ADC. Even though we found that the CNR of f_1,3 (Figures 4L and 4L) was statistically higher, the contrast between cancer and fibroglandular tissues are visually very similar. In contrast, in non-normalized three-component RSI model outputs, the CNR between tumor and fibroglandular tissues is similar to that of DCE (Table 5 and Supporting Information Figure S3). More importantly, the specificity of RSI C_1,2 and C_1,3 at 80% is sensitivity is comparable or higher (90.8% and 82.2%) than that of DCE (81.0%), without the use of exogenous contrast. In the RSI outputs, T₂ information is preserved, which increases tumor conspicuity with respect to healthy breast tissues and background. In our data, the differences magnitude in signal intensity between fibroglandular and cancer tissues due to T₂ effects is approximately 13% (assuming T₂ values of 47 and 68 msec, respectively²⁰) with the TEs used here. In contrast, the signal difference due to diffusion (assuming ADC values of 0.93×10⁻³ and 1.1×10⁻³ mm²/s, from our results) is about 5% for b-values of 500 and 1,500 s/mm² and 1–2% for b-value of 4,000 s/mm² between these tissues. The effect of TEs and T₂ values of tissues on RSI outputs will be evaluated in future work.

Several studies have used multi-compartment models to characterize the diffusion properties of cancer and healthy breast tissues.^19,36–40 The most commonly used multi-compartment model in breast is intravoxel incoherent motion imaging (IVIM), which uses a bi-exponential decay with two different ADCs.⁴¹ The slow ADC (D) describes water diffusion in the tissue, while the fast ADC (D_p) is associated with perfusion in capillaries. The percent of voxel-wise signal in the capillaries is described via the perfusion fraction f. The values of D_p in breast tumors (mostly ductal) estimated at 3T range between 10.0±10.1×10⁻³ mm²/s⁴⁰ and 21.7±11.0 ×10⁻³ mm²/s,³⁸ while the values of f range between 16.5 ±13.2%⁴⁰ and 6.4 ± 3.1%³⁸. The magnitude of the fast diffusion compartment (D_3,3=10.8×10⁻³ mm²/s) of the RSI breast model determined here is in good agreement with the values reported for breast tumors. However, the fractional signal contribution of this compartment (f_3,3=22%, IQR=20%) is somewhat higher than those extracted using the IVIM model. A source of this discrepancy may be the different number of exponential components. Finally, the IVIM perfusion fraction and RSI fractional signal contribution (f_3,3) of fibroglandular tissue are both lower than that of tumor tissues.³⁸

As described above, IVIM aims to separate water diffusion in the tissue from that in the capillaries (pseudo-diffusion). Moreover, multi-compartmental models have been developed to further characterize water diffusion within tissues. The breast RSI model presented here appears to isolate the signal from pseudo-diffusion (D_3,3) and to decompose the diffusion-weighted signal from within breast tissues into hindered (D_2,3) and restricted (D_1,3) components. The persistent signal at high b-values in cancerous tissue and the fact that D_1,3 was set to 0 mm²/s, suggests that the diffusion in this compartment was too slow to be accurately measured with our experimental setup (i.e. long diffusion time⁴²). Thus, we hypothesize that the biophysical origin of the slowest compartment is restricted diffusion of intracellular water, wherein the water molecules reflect off relatively impermeable cellular membranes,⁴³ whereas less confined water molecules in the extracellular space experience hindered diffusion.⁴⁴ Histological analysis will be used to test this hypothesis in future work.

The diffusion-weighted MR signal of breast lesions collected at high b-values (up to 2,500 s/mm²) was previously fit to bi- and tri-exponential models by Nakagawa et al. to simultaneously characterize perfusion and diffusion properties of cancer lesions.⁴⁵ The authors reported a correlation between the tri-exponential model-derived fast diffusion coefficient (D_p, attributed to perfusion) and tumor enhancement derived from DCE-MR. In addition, the slowest (D_s) and fastest (D_p) diffusion coefficients (attributed to restricted diffusion and perfusion, respectively) were statistically different between malignant and benign breast lesions. Direct comparison between the results of the present study and that by Nakagawa et al. is not possible due to the differences in diffusion models and lesions examined. However, results from both studies demonstrate the relevance of multi-component models in breast DW-MRI and indicate their potential in clinical applications.

Other multi-compartmental models have been developed to probe properties of tissue-specific microstructure. For example, in prostate, Panagiotaki et al developed the vascular, extra-cellular and restricted diffusion for cytometry in tumors (VERDICT) model.⁴⁶ Similarly, Gilani et al developed a model which distinguishes between the vascular, ductal, and cellular compartments.⁴⁷ In both cases, the researchers demonstrated an association between estimates from multi-compartmental models and physiological parameters such as intra- and extra-cellular volumes, lumen radius, and vascular fraction.^46,47 These two models and RSI are different multicompartmental approaches for describing DW-MRI signal that vary mainly in whether the compartmental diffusion coefficients are fixed between voxels. In practice however, the diffusion coefficients are fixed in VERDICT, as well as in RSI.⁴⁸ Fixed diffusion coefficients enable meaningful comparisons of the volume parameters (C or f) between voxels. If the diffusion coefficients are voxel-wise independent, the volume parameters of each voxel would likely be derived using different diffusion coefficients, which would confound comparisons across voxels.

Similarly, in rat brain tissue, White et al. demonstrated an association between volume fractions and orientation distribution of neurites and RSI outputs.²⁴ In its current form, the RSI breast model does not utilize orientation information, which may be helpful in determining the different constituents of cancerous or fibroglandular tissues. In the present work, notably, most of the cancer lesions were IDC; therefore, the resulting model may be biased towards identification of such cancers. Future work will focus on increasing the number of other breast cancer types and incorporating orientation information to evaluate the ability of RSI to identify aggressive tumors and evaluate response to treatment.

Conclusions

The overarching goal of this work was to generate quantitative maps in which tumor conspicuity is maximized without the use of exogenous contrast agents. Signal contributions C_1,3 and C_2,3 (Figure 4) generated from the three-component RSI model have similar CNR between cancer and fibroglandular tissues to the clinical standard DCE. However, visual inspection (Figures 4 and 5) reveals that this may not be in fact the case. Based on the plots from bi-exponential and three-component models in Figure 2B, it becomes evident that C_1,3 has a higher tumor conspicuity compared to C_2,3. Combination of multiple RSI outputs is ongoing work in our laboratory and has shown potential for accurate automatic classification of breast lesions.⁴⁹ Future work includes the use of RSI-derived signal contributions and advanced computer algorithms to evaluate the diagnostic value of multi-exponential models in an independent cohort. Altogether, these data may be used to aid in radiological differentiation between benign tissues and malignant breast lesions without the use of intravenous contrast agents.

Supplementary Material

1

Supporting Information Figure S1. Example images of A) dynamic contrast-enhanced (DCE) MRI, B) DCE pre/post contrast subtraction, C) T₂-weighted, and D) DW-MRI b=0 s/mm² volumes from site 1. Overlaid regions of interest (ROIs) are control (blue), cancer (red), and noise (grey), respectively.

Supporting Information Figure S2. Example images of A) dynamic contrast-enhanced (DCE) MRI, B) DCE pre/post contrast subtraction, C) and E) T₂-weighted, and F) and D) DW-MRI b=0 s/mm² volumes from site 2. Overlaid regions of interest (ROIs) are control (blue), cancer (red), and noise (grey), respectively. Note that control ROIs were placed on a different image to avoid inclusion of tumor tissue/peritumor infiltration in the control ROI.

Supporting Information Figure S3. Median contrast-to-noise ratio (CNR), area under the curve (AUC) and specificity at 80% sensitivity between cancer and fibroglandular tissues extracted from RSI-derived maps and compared to dynamic contrast-enhanced (DCE) MRI and conventional apparent diffusion coefficient (ADC).

Supporting Information Table S1. Signal contributions of cancer for data from both sites estimated using individual site models.