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

Diffusion-weighted MR image analysis based on gamma distribution model for differentiating benign and malignant brain tumors

BACKGROUND

Considering the invasiveness of the biopsy method, we attempted to evaluate the ability of the gamma distribution model using magnetic resonance imaging images to stage and grade benign and malignant brain tumors.

METHODS

A total of 42 patients with malignant brain tumors (including glioma, lymphoma, and choroid plexus papilloma) and 24 patients with benign brain tumors (meningioma) underwent diffusion-weighted imaging using five b-values ranging from 0 to 2000 s/mm2 with a 1.5 T scanner. The gamma distribution model is expected to demonstrate the probability of water molecule distribution based on the apparent diffusion coefficient. For all tumors, the apparent diffusion coefficient, shape parameter (κ), and scale parameter (θ) were calculated for each b-value. In the staging step, the fractions (ƒ1, ƒ2, ƒ3) expected to reflect the intracellular, and extracellular diffusion and perfusion were investigated. Diffusion <1 × 10-4 mm2/s (ƒ1), 1 × 10-4 mm2/s < Diffusion > 3 × 10-4 mm2/s (ƒ2), and Diffusion >3 × 10-4 mm2/s (ƒ3); in the grading step, fractions were determined to check heavily restricted diffusion. Diffusion lower than 0.3 × 10-4 mm2/s (ƒ11). Diffusion lower than 0.5 × 10-4 mm2/s (ƒ12). Diffusion lower than 0.8 × 10-4 mm2/s (ƒ13).

RESULTS

The findings were analyzed using nonparametric statistics and receiver operating characteristic curve diagnostic performance. Gamma model parameters (κ, ƒ1, ƒ2, ƒ3) showed a satisfactory difference in differentiating meningioma from glioma. For b value = 2000 s/mm2, ƒ1 had a better diagnostic performance than κ and apparent diffusion coefficient (sensitivity, 88%; specificity, 68%; P < .001). The best diagnostic performance was related to ƒ3 in b = 2000 s/mm2 (area under the curve = 0.891, sensitivity = 83%, specificity = 80%, P < .001). In the grading step, ƒ12 (area under the curve = 0.870, sensitivity = 92%, specificity = 72%, P < .001) had the best diagnostic performance in differentiating high-grade from low-grade gliomas with b = 2000 s/mm2.

CONCLUSION

The findings of our study highlight the potential of using a gamma distribution model with diffusion-weighted imaging based on multiple b-values for grading and staging brain tumors. Its potential integration into routine clinical practice could advance neurooncology and improve patient outcomes through more accurate diagnosis and treatment planning.

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.

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.