Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum

Robust, fast and accurate mapping of diffusional mean kurtosis

Diffusional kurtosis imaging (DKI) is a methodology for measuring the extent of non-Gaussian diffusion in biological tissue, which has shown great promise in clinical diagnosis, treatment planning, and monitoring of many neurological diseases and disorders. However, robust, fast, and accurate estimation of kurtosis from clinically feasible data acquisitions remains a challenge. In this study, we first outline a new accurate approach of estimating mean kurtosis via the sub-diffusion mathematical framework. Crucially, this extension of the conventional DKI overcomes the limitation on the maximum b-value of the latter. Kurtosis and diffusivity can now be simply computed as functions of the sub-diffusion model parameters. Second, we propose a new fast and robust fitting procedure to estimate the sub-diffusion model parameters using two diffusion times without increasing acquisition time as for the conventional DKI. Third, our sub-diffusion-based kurtosis mapping method is evaluated using both simulations and the Connectome 1.0 human brain data. Exquisite tissue contrast is achieved even when the diffusion encoded data is collected in only minutes. In summary, our findings suggest robust, fast, and accurate estimation of mean kurtosis can be realised within a clinically feasible diffusion-weighted magnetic resonance imaging data acquisition time.

Fractal relaxation model with a nonlinear diffusion coefficient for fitting anomalous diffusion data in magnetic resonance imaging

In this paper a relaxation model of signal attenuation in diffusion-weighted magnetic resonance imaging (dMRI) with varying diffusion coefficient in terms of fractal derivative is proposed, in which the diffusion coefficient is a power law of the effective diffusion time. The relaxation model provides measures of diffusion constant, fractal dimension of diffusive trajectory of water molecule and the time power-law behavior of the diffusion coefficient. The proposed model was used to describe the magnetic resonance attenuation signal of the bullfrog sciatic nerve, and the corresponding spectral entropy was calculated to detect the environmental complexity in bullfrog sciatic nerve for water molecular diffusion. The results showed that the fractal derivative relaxation model (the VDC model) can accurately depict the diffusion pattern of water molecules in complex heterogeneous biological media at large b values. The VDC model provides an alternative theoretical reference for biological tissue detection based on time-dependent diffusion of water molecules.

Evaluation of breast cancer malignancy, prognostic factors and molecular subtypes using a continuous-time random-walk MR diffusion model

PURPOSE

To assess the continuous-time random-walk (CTRW) model's diagnostic value in breast lesions and to explore the associations between the CTRW parameters and breast cancer pathologic factors.

METHOD

This retrospective study included 85 patients (70 malignant and 18 benign lesions) who underwent 3.0T MRI examinations. Diffusion-weighted images (DWI) were acquired with 16b-values to fit the CTRW model. Three parameters (Dm, α, and β) derived from CTRW and apparent diffusion coefficient (ADC) from DWI were compared among the benign/malignant lesions, molecular prognostic factors, and molecular subtypes by Mann-Whitney U test. Spearman correlation was used to evaluate the associations between the parameters and prognostic factors. The diagnostic performance was assessed by the area under the receiver operating characteristic curve (AUC) based on the diffusion parameters.

RESULTS

All parameters, ADC, Dm, α, and β were significantly lower in the malignant than benign lesions (P < 0.05). The combination of all the CTRW parameters (Dm, α, and β) provided the highest AUC (0.833) and the best sensitivity (94.3%) in differentiating malignant status. And the positive status of estrogen receptor (ER) and progesterone receptor (PR) showed significantly lower β compared with the negative counterparts (P < 0.05). The high Ki-67 expression produced significantly lower Dm and ADC values (P < 0.05). Additionally, combining multiple CTRW parameters improved the performance of diagnosing molecular subtypes of breast cancer. Moreover, Spearman correlations analysis showed that β produced significant correlations with ER, PR and Ki-67 expression (P < 0.05).

CONCLUSIONS

The CTRW parameters could be used as non-invasive quantitative imaging markers to evaluate breast lesions.

Optimization of quasi-diffusion magnetic resonance imaging for quantitative accuracy and time-efficient acquisition

PURPOSE

Quasi-diffusion MRI (QDI) is a novel quantitative technique based on the continuous time random walk model of diffusion dynamics. QDI provides estimates of the diffusion coefficient, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace/> <mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> in mm²  s^-1 and a fractional exponent, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> , defining the non-Gaussianity of the diffusion signal decay. Here, the b-value selection for rapid clinical acquisition of QDI tensor imaging (QDTI) data is optimized.

METHODS

Clinically appropriate QDTI acquisitions were optimized in healthy volunteers with respect to a multi-b-value reference (MbR) dataset comprising 29 diffusion-sensitized images arrayed between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:mrow> <mml:annotation>$$ b=0 $$</mml:annotation></mml:semantics> </mml:math> and 5000 s mm^-2 . The effects of varying maximum b-value ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> ), number of b-value shells, and the effects of Rician noise were investigated.

RESULTS

QDTI measures showed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> dependence, most significantly for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> in white matter, which monotonically decreased with higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> leading to improved tissue contrast. Optimized 2 b-value shell acquisitions showed small systematic differences in QDTI measures relative to MbR values, with overestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace/> <mml:mspace/> <mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ \kern0.50em {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and underestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> in white matter, and overestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> anisotropies in gray and white matter. Additional shells improved the accuracy, precision, and reliability of QDTI estimates with 3 and 4 shells at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>5000</mml:mn></mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}}=5000 $$</mml:annotation></mml:semantics> </mml:math>  s mm^-2 , and 4 b-value shells at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>3960</mml:mn></mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}}=3960 $$</mml:annotation></mml:semantics> </mml:math>  s mm^-2 , providing minimal bias in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> compared to the MbR.

CONCLUSION

A highly detailed optimization of non-Gaussian dMRI for in vivo brain imaging was performed. QDI provided robust parameterization of non-Gaussian diffusion signal decay in clinically feasible imaging times with high reliability, accuracy, and precision of QDTI measures.