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

Gamma distribution model of diffusion MRI for evaluating the isocitrate dehydrogenase mutation status of glioblastomas

OBJECTIVE

To determine whether the γ distribution (GD) model of diffusion MRI is useful in the evaluation of the isocitrate dehydrogenase (IDH) mutation status of glioblastomas.

METHODS

12 patients with IDH-mutant glioblastomas and 54 patients with IDH-wildtype glioblastomas were imaged with diffusion-weighted imaging using 13 b-values from 0 to 1000 s/mm2. The shape parameter (κ) and scale parameter (θ) were obtained with the GD model. Fractions of three different areas under the probability density function curve (f1, f2, f3) were defined as follows: f1, diffusion coefficient (D) < 1.0×10-3 mm2/s; f2, D > 1.0×10-3 and <3.0×10-3 mm2/s; f3, D > 3.0 × 10-3 mm2/s. The GD model-derived parameters measured in gadolinium-enhancing lesions were compared between the IDH-mutant and IDH-wildtype groups. Receiver operating curve analyses were performed to assess the parameters' diagnostic performances.

RESULTS

The IDH-mutant group's f1 (0.474  ±  0.143) was significantly larger than the IDH-wildtype group's (0.347  ±  0.122, p = 0.0024). The IDH-mutant group's f2 (0.417  ±  0.131) was significantly smaller than the IDH-wildtype group's (0.504  ±  0.126, p = 0.036). The IDH-mutant group's f3 (0.109  ±  0.060) was significantly smaller than the IDH-wildtype group's (0.149  ±  0.063, p = 0.0466). The f1 showed the best diagnostic performance among the GD model-derived parameters with the area under the curve value of 0.753.

CONCLUSION

The GD model could well describe the pathological features of IDH-mutant and IDH-wildtype glioblastomas, and was useful in the differentiation of these tumors.

ADVANCES IN KNOWLEDGE

Diffusion MRI based on the γ distribution model could well describe the pathological features of IDH-mutant and IDH-wildtype glioblastomas, and its use enabled the significant differentiation of these tumors. The γ distribution model may contribute to the non-invasive identification of the IDH mutation status based on histological viewpoint.

A comparison among gamma distribution, intravoxel incoherent motion, and mono-exponential models with turbo spin-echo diffusion-weighted MR imaging in the differential diagnosis of orofacial lesions

OBJECTIVES

To compare the gamma distribution (GD), intravoxel incoherent motion (IVIM), and monoexponential (ME) models in terms of their goodness-of-fit, correlations among the parameters, and the effectiveness in the differential diagnosis of various orofacial lesions.

METHODS

A total of 85 patients underwent turbo spin-echo diffusion-weighted imaging with six b-values. The goodness-of-fit of three models was assessed using Akaike Information Criterion. We analysed the correlations and compared the effectiveness in the differential diagnosis among the parameters of GD model (κ, shape parameter; θ, scale parameter; fractions of diffusion: ƒ₁, cellular component; ƒ₂, extracellular diffusion; ƒ₃, perfusion component), IVIM model (D, true diffusion coefficient; D*, pseudodiffusion coefficient; f, perfusion fraction), and ME model (apparent diffusion coefficient, ADC).

RESULTS

The GD and IVIM models showed a better goodness-of-fit than the ME model (p < 0.05). ƒ₁ had strong negative correlations with D and ADC (ρ = -0.901 and -0.937, respectively), while ƒ₃ had a moderate positive correlation with f (ρ = 0.661). Malignant entity presented significantly higher ƒ₁ and lower D and ADC than benign entity (p < 0.0001). Malignant lymphoma had significantly higher ƒ₁ in comparison to squamous cell carcinoma (p = 0.0007) and granulation (p = 0.0075). The trend in ƒ₁ was opposite to the trend in D. Malignant lymphoma had significant lower ƒ₃ than squamous cell carcinoma (p = 0.005) or granulation (p = 0.0075).

CONCLUSIONS

The strong correlations were found between the GD- and IVIM-derived parameters. Furthermore, the GD model's parameters were useful for characterising the pathological structure in orofacial lesions.

The Mathematics of Quasi-Diffusion Magnetic Resonance Imaging

Quasi-diffusion imaging (QDI) is a novel quantitative diffusion magnetic resonance imaging (dMRI) technique that enables high quality tissue microstructural imaging in a clinically feasible acquisition time. QDI is derived from a special case of the continuous time random walk (CTRW) model of diffusion dynamics and assumes water diffusion is locally Gaussian within tissue microstructure. By assuming a Gaussian scaling relationship between temporal (α) and spatial (β) fractional exponents, the dMRI signal attenuation is expressed according to a diffusion coefficient, D (in mm2 s−1), and a fractional exponent, α. Here we investigate the mathematical properties of the QDI signal and its interpretation within the quasi-diffusion model. Firstly, the QDI equation is derived and its power law behaviour described. Secondly, we derive a probability distribution of underlying Fickian diffusion coefficients via the inverse Laplace transform. We then describe the functional form of the quasi-diffusion propagator, and apply this to dMRI of the human brain to perform mean apparent propagator imaging. QDI is currently unique in tissue microstructural imaging as it provides a simple form for the inverse Laplace transform and diffusion propagator directly from its representation of the dMRI signal. This study shows the potential of QDI as a promising new model-based dMRI technique with significant scope for further development.

Volumetric tumor delineation and assessment of its early response to radiotherapy with optical coherence tomography

Texture analyses of optical coherence tomography (OCT) images have shown initial promise for differentiation of normal and tumor tissues. This work develops a fully automatic volumetric tumor delineation technique employing quantitative OCT image speckle analysis based on Gamma distribution fits. We test its performance in-vivo using immunodeficient mice with dorsal skin window chambers and subcutaneously grown tumor models. Tumor boundaries detection is confirmed using epi-fluorescence microscopy, combined photoacoustic-ultrasound imaging, and histology. Pilot animal study of tumor response to radiotherapy demonstrates high accuracy, objective nature, novelty of the proposed method in the volumetric separation of tumor and normal tissues, and the sensitivity of the fitting parameters to radiation-induced tissue changes. Overall, the developed methodology enables hitherto impossible longitudinal studies for detecting subtle tissue alterations stemming from therapeutic insult.

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

The preoperative imaging-based differentiation of primary central nervous system lymphomas (PCNSLs) and glioblastomas (GBs) is of high importance since the therapeutic strategies differ substantially between these tumors. In this study, we investigate whether the gamma distribution (GD) model is useful in this differentiation of PNCSLs and GBs. Twenty-seven patients with PCNSLs and 57 patients with GBs were imaged with diffusion-weighted imaging using 13 b-values ranging from 0 to 1000 sec/mm2. The shape parameter (κ) and scale parameter (θ) were obtained with the GD model. Fractions of three different areas under the probability density function curve (f1, f2, f3) were defined as follows: f1, diffusion coefficient (D) <1.0×10-3 mm2/sec; f2, D >1.0×10-3 and <3.0×10-3 mm2/sec; f3, D >3.0 × 10-3 mm2/sec. The GD model-derived parameters were compared between PCNSLs and GBs. Receiver operating characteristic (ROC) curve analyses were performed to assess diagnostic performance. The correlations with intravoxel incoherent motion (IVIM)-derived parameters were evaluated. The PCNSL group's κ (2.26 ± 1.00) was significantly smaller than the GB group's (3.62 ± 2.01, p = 0.0004). The PCNSL group's f1 (0.542 ± 0.107) was significantly larger than the GB group's (0.348 ± 0.132, p<0.0001). The PCNSL group's f2 (0.372 ± 0.098) was significantly smaller than the GB group's (0.508 ± 0.127, p<0.0001). The PCNSL group's f3 (0.086 ± 0.043) was significantly smaller than the GB group's (0.144 ± 0.062, p<0.0001). The combination of κ, f1, and f3 showed excellent diagnostic performance (area under the curve, 0.909). The f1 had an almost perfect inverse correlation with D. The f2 and f3 had very strong positive correlations with D and f, respectively. The GD model is useful for the differentiation of GBs and PCNSLs.

The application of a gamma distribution model to diffusion-weighted images of the orofacial region

OBJECTIVES

This study evaluated the correlation among the diffusion-derived parameters obtained by monoexponential (ME), intravoxel incoherent motion (IVIM) and γ distribution (GD) models and compared these parameters among representative orofacial tumours.

METHODS

Ninety-two patients who underwent 1.5 T MRI including diffusion-weighted imaging were included. The shape parameter (κ), scale parameter (θ), ratio of the intracellular diffusion (ƒ₁), extracellular diffusion (ƒ₂) and perfusion (ƒ₃) were obtained by the GD model; the true diffusion coefficient (D) and perfusion fraction (f) were obtained by the IVIM model; and the apparent diffusion coefficient (ADC) was obtained by the ME model.

RESULTS

ƒ₁ had a strongly negative correlation with the ADC (ρ = -0.993) and D (ρ = -0.926). A strong positive correlation between f and ƒ₃ (ρ = 0.709) was found. Malignant lymphoma (ML) had the highest ƒ₁, followed by squamous cell carcinoma (SCC), malignant salivary gland tumours, pleomorphic adenoma (Pleo) and angioma. Both the IVIM and GD models suggested the highest perfusion in angioma and the lowest perfusion in ML. The GD model demonstrated a high extracellular component in Pleo and revealed that the T_4a+T_4b SCC group had a lower ƒ₂ than the T₂+T₃ SCC group, and poor to moderately differentiated SCC had a higher ƒ₁ than highly differentiated SCC.

CONCLUSIONS

Given the correlation among the diffusion-derived parameters, the GD model might be a good alternative to the IVIM model. Furthermore, the GD model's parameters were useful for characterizing the pathological structure.