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Multi-exponential model of diffusion signal in healthy and cancerous breast tissue with fixed ADCs

Ana Elvira Rodríguez-Soto¹, Maren M. Sjaastad Andreassen², Christopher Charles Conlin¹, Helen Park³, Igor Vidic⁴, Neil Peter Jerome^4,5, Agnes Østlie⁵, Tone Frost Bathen^2,5, Pål Erik Goa^4,5, Tyler Seibert⁶, Michael Hahn¹, Anders Martin Dale⁷, and Rebecca Rakow-Penner¹
¹Department of Radiology, University of California, San Diego, La Jolla, CA, United States, ²Department of Circulation and Medical Imaging, Norwegian University of Science and Technology, Trondheim, Norway, ³School of Medicine, University of California, San Diego, La Jolla, CA, United States, ⁴Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway, ⁵Department of Radiology and Nuclear Medicine, St. Olav's University Hospital, Trondheim, Norway, ⁶Radiation Medicine and Applied Sciences, University of California, San Diego, La Jolla, CA, United States, ⁷Department of Neurosciences, University of California, San Diego, La Jolla, CA, United States

Synopsis

Breast DWI has shown great potential to become a contrast-free diagnostic tool for breast cancer. The purpose of this work was to determine a unified model to describe the diffusion signal of cancer and healthy breast tissues, and compare tumor conspicuity of model components to DCE-MRI and DWI estimates. Multi-exponential models with fixed ADCs were determined and the weights of each component estimated. Tumor conspicuity, defined as contrast-to-noise ratio, was found to be ~3 times higher in DCE-MRI than in the weights of multi-exponential components. This model may increase the sensitivity and specificity of DWI for breast cancer diagnosis.

Introduction

Diffusion-weighted imaging (DWI) has shown great potential to become a contrast-free diagnostic tool for breast cancer screening and surveillance. In order for this to occur, DWI must be at least as sensitive and specific as the standard of care dynamic contrast-enhanced (DCE)-MRI. The diffusion signal behavior of certain breast cancer types has been described as bi-exponential [1,2]. This phenomenon is attributed to a shift in the relative size between slow and fast diffusion components due to increased cellularity in cancer [3]. To date, studies characterizing the diffusion properties of breast tissues typically compare DWI estimates between fibroglandular and tumor tissues in small regions of interest (ROIs)[1,4,5]. However, to increase the sensitivity and specificity of breast DWI for diagnostic purposes, it would be advantageous to discriminate cancer from all other healthy breast tissues. Towards this goal, the purpose of this work was to determine a unified multi-exponential model to describe both cancerous and healthy breast tissues, and to evaluate tumor conspicuity compared to DCE-MRI and DWI estimates.

Methods

Diagnostic or surveillance MRI at 3T was performed in a group of 49 and 25 pathology proven breast cancer patients from two sites, respectively. None of the participants received treatment previous to MRI scan. The DWI and DCE-MRI pulse sequence parameters are shown in the Table. Differences in data across sites were used to determine an initial robust joint model that could be used in DWI data collected at different scanners and with pulse sequence parameters.

All analyses were performed in MATLAB. Diffusion directions for a determined b-value were averaged before processing (assuming isotropic diffusion). The following ROIs were drawn on DWI images informed by DCE and anatomical images: (i) control regions including either cancer-free contralateral side or regions without cancer, (ii) cancer lesions (Figure 1), and (iii) background regions. Averaged DWI data were noise corrected [6] and normalized by the maximum signal intensity value in b=0 s/mm² volume to preserve T₂ information. The diffusion signal was modeled as the linear combination of multiple exponential decays:
$$ S_{diff}(b,N)=\sum_{i}^{N}f_{i,N} e^{-b\cdot D_{i,N}} $$
where N is the total number of exponential decays (here 1, 2, or 3), f_i,N are the weights of each exponential component, b are the b-values in s/mm², and D_i,N are the ADCs of each exponential component (D₁<D₂<D₃).

First, global ADCs were estimated across all voxels from control and cancer ROIs, patients and sites for mono-, bi- and tri-exponential models. To account for the different sites and imaging protocols, the fitting procedure minimized the global negative log likelihood of ADCs across all data. Once ADCs were determined, the f_i,N for all voxels was estimated using these fixed ADC values. For comparison, conventional ADC and apparent diffusional kurtosis (K_app) were computed [7]. Tumor conspicuity of DWI estimates (i.e. ADC, K_app, and f_i,N), DWI b_max, and DCE-MRI was measured as the contrast-to-noise ratio (CNR):
$$ CNR = \frac{\mu_{cancer} - \mu_{control}}{\sigma_{background}} $$
The CNR for all DWI estimates were compared using repeated-measures analyses of variance (RM-ANOVA) with Sidak post hoc tests.

Results

Estimated ADC for mono-exponential model was D_1,1=4.7×10^-4mm²/s, D_1,2=2.4×10^-5 and D_2,2=2.2×10^-3mm²/s for bi-exponential model, and D_1,3=1.6×10^-9, D_2,3=1.4×10^-3 and D_3,3=8.9×10^-3mm²/s for tri-exponential model; with normalized mean squared errors (MSE) of 12.5%, 1.3%, and 0.8%, respectively. The average decay weights (f_i,N) for the three models are shown in Figure 2. As expected, tumor conspicuity was highest (p<0.01) in DCE-MRI compared to the weights of the components of multi-exponential models (f_i,N), DWI b_max, K_app and ADC, in descending order (Figure 3). The CNR of weights f_i,N was on average 3 times lower (p<0.01) than that of DCE-MRI, and one and two orders of magnitude higher (p<0.01) than that of DWI b_max, and ADC and K_app. Resulting maps for all estimates are shown in Figure 4 for both sites. Compared to DCE-MRI and weight maps, tumors were difficult to discern from surrounding tissues in conventional ADC or K_app.

Tumors were visible in the f_1,1 map of the mono-exponential decay, but indiscernible from healthy fibroglandular tissue. When bi- or tri-exponential models were used, the magnitude of the slower component (f_1,N) was larger in tumor lesions and to some extent in suppressed fat tissues. The magnitude of faster components (f_2,N and f_3,3) enhanced tumors, cysts, fibroglandular tissue and vessels. Altogether, these data may be used as differential features between healthy, benign, and malignant breast tissues. Although the use of a tri-exponential model may suggest data overfitting, we observed that the magnitude of f_i,N of all tissues were dominated by two components perhaps due to the difference in orders of magnitude of the estimated ADCs. In other words, no tissue was bright in all three f_i,3 maps of the tri-exponential model.

Discussion and Conclusions

Results suggest that DWI methods based on multi-exponential models and fixed ADCs may be useful in increasing tumor conspicuity without the use of contrast agents. We attributed this to: the use of high b-values, retainment of T₂ weighting in DWI data, and isolation of slow diffusion component in tumor tissues. Future work includes combining information of the different multi-exponential components to further increase tumor conspicuity in breast DWI, and evaluating the diagnostic value of multi-exponential models in an independent cohort compared to DCE-MRI.

Acknowledgements

California Breast Cancer Research Program Early Career Award and GE Healthcare.

References

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Figures

Table. Pulse sequence parameters. Note the differences in scanner, acquisition plane and matrix size across sites. Data from both protocols were used to determine a robust diffusion model that can be generalized to data collected in different scanners and with pulse sequence parameters.

Figure 1. Example images of DCE phase 2 (A, I), DCE subtraction (B, J), T₂-weighted (C, K), and DWI b=0 s/mm² volumes (E, M) from both U.S. (left panel) and European (right panel) sites. Spatial agreement between anatomical and DW images (blue overlay in G, H, O, and P) and examples of control (green) and cancer (red) regions of interest (ROI) are also shown.

Figure 2. Apparent diffusion coefficients (D_i,N) of multi-exponential models were determined by simultaneously fitting both control (green) and cancer (red) ROIs of both sites. Values of D_i,N were then fixed to estimate the magnitude of exponential decays f_i,N for A) mono-, B) bi-, and C) tri-exponential models for these ROIs. 2D plots of the magnitude of exponential decays f_i,3 of tri-exponential model are shown in panel D.

Figure 3. Tumor conspicuity was measured as contrast-to-noise ratio (CNR) for ADC (black), apparent diffusional kurtosis (K_app, blue), DWI b_max, decay weights (f_i,N) of multi-exponential models, and DCE-MRI. Plot shows average CNR per patient (squares), and average (solid lines) and standard deviation (dotted lines) across all patients. Tumor conspicuity was significantly higher (×45) when using decay weights (f_i,N) maps compared to conventional DWI estimates, but lower (×3) than DCE-MRI.

Figure 4. Images from both U.S. (top panel) and European (bottom panel) sites including: T₂-weighted, DWI b_max (b_max=4000 and 3000 s/mm² for each site), and maps of ADC, apparent diffusional kurtosis (K_app), and the decay weights (f_i,N) of mono-, bi-, and tri-exponential models. Arrowheads indicate tumor location. Note the increased tumor conspicuity in f_1,N compared to ADC and K_app, and somewhat reduced conspicuity compared to DCE-MRI in the bottom panel.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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