Gamma Distribution Model in the Evaluation of Breast Cancer Through Diffusion‐Weighted MRI: A Preliminary Study

Abstract

Background The gamma distribution (GD) model is based on the statistical distribution of the apparent diffusion coefficient (ADC) parameter. The GD model is expected to reflect the probability of the distribution of water molecule mobility in different regions of tissue, but also the intra‐ and extracellular diffusion and perfusion components (f1, f2, f3 fractions). Purpose To assess the GD model in the characterization and diagnostic performance of breast lesions. Study Type Prospective. Population In all, 48 females with 24 benign and 33 malignant breast lesions. Field Strength/Sequence A diffusion‐weighted sequence (b = 0–3000 s/mm2) with a 3 T scanner. Assessment For each group of benign, malignant, invasive, and in situ breast lesions, the ADC was obtained. Also, θ and k parameters (scale and shape of the statistic distribution, respectively), f1, f2, and f3 fractions were obtained from fitting the GD model to diffusion data. Statistical Tests Lesion types were compared regarding diffusion parameters using nonparametric statistics and receiver operating characteristic curve diagnostic performance. Results The majority of GD parameters (k, f1, f2, f3 fractions) showed significant differences between benign and malignant lesions, and between in situ and invasive lesions (f1, f2, f3 fractions) (P ≤ 0.001). The best diagnostic performances were obtained with ADC and f1 fraction in benign vs. malignant lesions (area under curve [AUC] = 0.923 and 0.913, sensitivity = 93.9% and 81.8%, specificity = 79.2% and 91.7%, accuracy = 87.7% and 86.0%, respectively). In invasive lesions vs. in situ lesions, the best diagnostic performance was obtained with f1 fraction, which outperformed ADC results (AUC = 0.978 and 0.941, and sensitivity = 91.3% for both parameters, specificity = 100.0% and 90.0%, accuracy = 93.9% and 90.9%, respectively). Data Conclusion This work shows that the GD model provides information in addition to the ADC parameter, suggesting its potential in the diagnosis of breast lesions. Level of Evidence 2: Technical Efficacy Stage 2 J. Magn. Reson. Imaging 2019;50:230–238.

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

“…were not significantly different between the different types [18]. The utility of this parameter should be further evaluated in larger populations.…”

“…Three different areas under the probability density function (PDF) curve were defined as follows: f1, the fraction of D <1.0×10 −3 mm 2 /sec; f2, the fraction of 1.0×10 −3 to 3.0×10 −3 mm 2 / sec; f3, the fraction of D >3.0×10 −3 mm 2 /sec. The f1 value is attributed to the intracellular component; the f2 is attributed to the extracellular extravascular component, and the f3 is attributed to the intravascular component [18,22,23].…”

“…The mono-exponential model may not precisely reflect the reality of diffusion behavior in heterogenous biological tissues, since this model assumes a Gaussian distribution. The bi-exponential model could be influenced by an uncertainty of the estimated perfusion, since signal measurements at low b-values are susceptible to measurement errors [15][16][17][18]. The DKI model is limited by the unclear biological interpretation of the kurtosis parameters [18][19][20][21].…”

“…The GD model is a twoparameter family of continuous probability distribution parametrized in terms of the shape parameters kappa (κ) and the scale parameter theta (θ), and this model assumes that the diffusion coefficient (D) is distributed continuously within a voxel. The GD model allows us to estimate fractions of a tissue type based on the concept that the area fractions for D <1.0 × 10 −3 mm 2 /sec, D = 1.0 × 10 −3 to 3.0 ×10 −3 mm 2 /sec, and D >3.0 ×10 −3 mm 2 /sec are attributed to intracellular, extracellular extravascular, and intravascular spaces, respectively [18,22,23]. Based on these fractions, we may be able to estimate histopathological conditions of neoplasms or organs.…”

“…The GD model has been used to assess prostate cancers [22][23][24], breast cancers [18], and renal function [25]. The GD model was also used to assess cerebral ischemic stroke in rat brains, and it was showed that this model exhibited a better performance than the conventional mono-exponential model and allowed for a significantly enhanced visualization of ischemic lesions [26].…”