On a fractional order calculus model in diffusion weighted breast imaging to differentiate between malignant and benign breast lesions detected on X-ray screening mammography

<div><p>Objective</p><p>To evaluate a fractional order calculus (FROC) model in diffusion weighted imaging to differentiate between malignant and benign breast lesions in breast cancer screening work-up using recently introduced parameters (<i>β</i>_FROC, <i>D</i>_FROC and <i>μ</i>_FROC).</p><p>Materials and methods</p><p>This retrospective analysis within a prospective IRB-approved study included 51 participants (mean 58.4 years) after written informed consent. All patients had suspicious screening mammograms and indication for biopsy. Prior to biopsy, full diagnostic contrast-enhanced MRI examination was acquired including diffusion-weighted-imaging (DWI, b = 0,100,750,1500 s/mm²). Conventional apparent diffusion coefficient <i>D</i>_app and FROC parameters (<i>β</i>_FROC, <i>D</i>_FROC and <i>μ</i>_FROC) as suggested further indicators of diffusivity components were measured in benign and malignant lesions. Receiver operating characteristics (ROC) were calculated to evaluate the diagnostic performance of the parameters.</p><p>Results</p><p>29/51 patients histopathologically revealed malignant lesions. The analysis revealed an AUC for <i>D</i>_app of 0.89 (95% CI 0.80–0.98). For FROC derived parameters, AUC was 0.75 (0.60–0.89) for <i>D</i>_FROC, 0.59 (0.43–0.75) for <i>β</i>_FROC and 0.59 (0.42–0.77) for <i>μ</i>_FROC. Comparison of the AUC curves revealed a significantly higher AUC of <i>D</i>_app compared to the FROC parameters <i>D</i>_FROC (p = 0.009), <i>β</i>_FROC (p = 0.003) and <i>μ</i>_FROC (p = 0.001).</p><p>Conclusion</p><p>In contrast to recent description in brain tumors, the apparent diffusion coefficient <i>D</i>_app showed a significantly higher AUC than the recently proposed FROC parameters <i>β</i>_FROC, <i>D</i>_FROC and <i>μ</i>_FROC for differentiating between malignant and benign breast lesions. This might be related to the intrinsic high heterogeneity within breast tissue or to the lower maximal b-value used in our study.</p></div

Boxplots.

<p>Boxplots of the mean values for conventional apparent diffusion coefficient D_app (A) and fractional order calculus (FROC) model derived parameters D_FROC (B), β_FROC (C) and μ_FROC (D) for benign and malignant lesions. Vertical bars mark the range of the data excepting outliers, dots mark outliers, box marks 25^th– 75^th percentile, horizontal bar marks median.</p

Example of a breast cancer screening participant (66 years).

<p>Lesion with segmentation demonstrated as pink line. A) T2-weighted morphological sequence; B) diffusion weighted imaging (DWI, b = 1500 s/mm²); C) diffusion coefficient map D_app (scale given in μm²/ms); D) FROC diffusion coefficient map (scale given in μm²/ms); E) β_FROC-map demonstrating a more heterogeneous signal; F) μ_FROC-map demonstrating as well a relatively heterogeneous signal within the entire breast. Histopathology: invasive ductal carcinoma (IDC).</p

Sequence parameters.

<p>Sequence parameters.</p

Type and distribution of lesions within the study population.

<p>Type and distribution of lesions within the study population.</p

Receiving operator characteristics (ROC) curves.

<p>ROCs visualizing the diagnostic accuracy of the diffusion coefficient (D) and FROC derived parameters β_FROC, μ_FROC, and D_FROC.</p

Prediction of body compartments by anthropometric indices in multiple linear regression analyses (Women, n = 594).

<p>Total model R² for each body compartment and partial correlation coefficients (95% CI) for anthropometric indices. All variables were adjusted for age and height. TBV = Total body volume, TAT = total adipose tissue, SAT = subcutaneous adipose tissue, VAT = visceral adipose tissue, CAT = coronary adipose tissue, SMT = skeletal muscle tissue, BMI = body mass index, WC = waist circumference, HC = hip circumference. ¹<u>Predictors included</u>: BMI, WC, HC. All variables (predictors and outcome) adjusted by age and height with the residual method. ²Partial correlation coefficients (95% CI) are reported for predictor variables.</p

Anthropometric variables and body compartments as assessed by MRI by sex and age groups¹, all values are presented as mean (min, max).

<p>TBV = total body volume, TAT = total adipose tissue, VAT = visceral adipose tissue, SAT = subcutaneous adipose tissue, CAT = coronary adipose tissue, SMT = skeletal muscle tissue.</p>1<p>Sub-study participants were sampled by baseline age groups (35–44 y, 45–54 y, 55–64 y). Due to the 4-year baseline period (1994–1998), age groups at time of sub-study (2010–2012) may overlap.</p

a–f. Illustration of different MRI body compartments in the sub-study of the German EPIC cohorts.

<p>a–f. Illustration of different MRI body compartments in the sub-study of the German EPIC cohorts.</p

Prediction of body compartments by anthropometric indices in multiple linear regression analyses (Men, n = 598).

<p>Total model R² for each body compartment and partial correlation coefficients (95% CI) for anthropometric indices. All variables were adjusted for age and height. TBV = Total body volume, TAT = total adipose tissue, SAT = subcutaneous adipose tissue, VAT = visceral adipose tissue, CAT = coronary adipose tissue, SMT = skeletal muscle tissue, BMI = body mass index, WC = waist circumference, HC = hip circumference. ¹<u>Predictors included</u>: BMI, WC, HC. All variables (predictors and outcome) adjusted by age and height with the residual method. ²Partial correlation coefficients (95% CI) are reported for predictor variables.</p