Water diffusion heterogeneity index in the human brain is insensitive to the orientation of applied magnetic field gradients

The diagnostic accuracy of intravoxel incoherent motion and diffusion kurtosis imaging in the differentiation of malignant and benign soft-tissue masses: which is better?

BACKGROUND

It is difficult for conventional magnetic resonance imaging (MRI) to distinguish benign soft-tissue masses (STMs) from malignant masses.

PURPOSE

To quantitatively compare the diagnostic value of intravoxel incoherent motion (IVIM) and diffusion kurtosis imaging (DKI) in STMs.

MATERIAL AND METHODS

The data from 58 patients with STMs were retrospectively analyzed. The GE Discovery 3.0-T MRI scanner was used to acquire conventional MRI sequences, IVIM, and DKI images. The chi-square test, independent sample t-test, and Mann-Whitney U tests were used to compare the differences between conventional MRI features, IVIM, and DKI parameters (D_slow, D_fast, f, mean kurtosis [MK], and mean diffusivity [MD]) between the benign and malignant groups. Receiver-operating characteristic (ROC) curve analysis was also performed.

RESULTS

Tumor size and depth are statistically different in STTs. Ds_low, MK, and MD values in the malignant groups are significantly lower than the benign groups (P < 0.05). However, D_fast and f values are not statistically different between the two groups. The area under the curve (AUC) of D_slow value (0.859) is higher than MD (0.765) and MK (0.676) values for identifying benign and malignant STMs. The D_slow value showed the best specificity (82.93%). The sensitivity and specificity of IVIM and DKI parameters are higher than that of conventional MRI sequences.

CONCLUSION

IVIM and DKI can be used to distinguish between benign and malignant STMs, with D_slow as the most meaningful parameter.

Diffusion and quantification of diffusion of prostate cancer

For assessing a cancer treatment, and for detecting and characterizing cancer, Diffusion-weighted imaging (DWI) is commonly used. The key in DWI's use extracranially has been due to the emergence of of high-gradient amplitude and multichannel coils, parallelimaging, and echo-planar imaging. The benefit has been fewer motion artefacts and high-quality prostate images.Recently, new techniques have been developed to improve the signal-to-noise ratio of DWI with fewer artefacts, allowing an increase in spatial resolution. For apparent diffusion coefficient quantification, non-Gaussian diffusion models have been proposed as additional tools for prostate cancer detection and evaluation of its aggressiveness. More recently, radiomics and machine learning for prostate magnetic resonance imaging have emerged as novel techniques for the non-invasive characterisation of prostate cancer. This review presents recent developments in prostate DWI and discusses its potential use in clinical practice.

Symmetry Analysis and Conservation Laws for a Time-Fractional Generalized Porous Media Equation

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point symmetry groups and the corresponding optimal subgroups are determined. Then, the similarity reduction is performed to the given equation and some explicit solutions are derived. The asymptotic behaviours for the solutions are also discussed. Through the concept of nonlinear self-adjointness, the conservation laws arising from the admitted point symmetries are listed.

Utility of diffusion MRI characteristics of cervical lymph nodes as disease classifier between patients with head and neck squamous cell carcinoma and healthy volunteers

Diffusion MRI characteristics assessed by apparent diffusion coefficient (ADC) histogram analysis in head and neck squamous cell carcinoma (HNSCC) have been reported as helpful in classifying tumours based on diffusion characteristics. There is little reported on HNSCC lymph nodes classification by diffusion characteristics. The aim of this study was to determine whether pretreatment nodal microstructural diffusion MRI characteristics can classify diseased nodes of patients with HNSCC from normal nodes of healthy volunteers. Seventy-nine patients with histologically confirmed HNSCC prior to chemoradiotherapy, and eight healthy volunteers, underwent diffusion-weighted (DW) MRI at a 1.5-T MR scanner. Two radiologists contoured lymph nodes on DW (b = 300 s/m² ) images. ADC, distributed diffusion coefficient (DDC) and alpha (α) values were calculated by monoexponential and stretched exponential models. Histogram analysis metrics of drawn volume were compared between patients and volunteers using a Mann-Whitney test. The classification performance of each metric between the normal and diseased nodes was determined by receiver operating characteristic (ROC) analysis. Intraclass correlation coefficients determined interobserver reproducibility of each metric based on differently drawn ROIs by two radiologists. Sixty cancerous and 40 normal nodes were analysed. ADC histogram analysis revealed significant differences between patients and volunteers (p ≤0.0001 to 0.0046), presenting ADC distributions that were more skewed (1.49 for patients, 1.03 for volunteers; p = 0.0114) and 'peaked' (6.82 for patients, 4.20 for volunteers; p = 0.0021) in patients. Maximum ADC values exhibited the highest area under the curve ([AUC] 0.892). Significant differences were revealed between patients and volunteers for DDC and α value histogram metrics (p ≤0.0001 to 0.0044); the highest AUC were exhibited by maximum DDC (0.772) and the 25th percentile α value (0.761). Interobserver repeatability was excellent for mean ADC (ICC = 0.88) and the 25th percentile α value (ICC = 0.78), but poor for all other metrics. These results suggest that pretreatment microstructural diffusion MRI characteristics in lymph nodes, assessed by ADC and α value histogram analysis, can identify nodal disease.

Value of multiple models of diffusion-weighted imaging for improving the nodal staging of preoperatively node-negative rectal cancer

OBJECTIVE

To investigate the parameters of multiple diffusion-weighted imaging (DWI) models for improving nodal staging of preoperatively node-negative rectal cancer.

MATERIALS AND METHODS

A total of 74 rectal cancer patients without suspected metastatic lymph nodes on conventional MRI who underwent direct surgical resection between November 2018 and January 2020 were enrolled in this prospective study. DWI parameters of mono-exponential model (ADC), intravoxel incoherent motion (D, D* and f), stretched exponential model (DDC and α), and diffusion kurtosis imaging (MD and MK) within the whole tumor were measured to predict the nodal staging in rectal cancer patients.

RESULTS

The D*, DDC, and MK values were significantly different in patients with pN0 and pN1-2 (all P < 0.001). The D*, DDC, and MK showed good diagnostic performance with the area under the receiver operating characteristic (AUC) of 0.788, 0.827 and 0.799. Multivariate analysis indicated D* (odds ratio, OR = 1.163, P = 0.003) and DDC (OR = 0.007, P = 0.019) as significant predictors of nodal staging. The combination of DDC and D* demonstrated superior diagnostic performance with the AUC, sensitivity, specificity and accuracy of 0.872, 0.800, 0.932 and 0.878, respectively.

CONCLUSION

Multiple functional DWI parameters were potential to identify the rectal cancer patients with micro-nodal involvement for accurate treatment.

Non-gaussian models of 3-Tesla diffusion-weighted MRI for the differentiation of pancreatic ductal adenocarcinomas from neuroendocrine tumors and solid pseudopapillary neoplasms

PURPOSE

To assess the MRI performance in differentiating pancreatic ductal adenocarcinomas (PDACs), from solid pseudopapillary neoplasms (SPNs) and pancreatic neuroendocrine tumors (PNETs) using non-gaussian diffusion-weighted imaging models.

METHODS

This was a retrospective study of patients diagnosed with PDACs (01/2015-06/2019) or with PNETs or SPNs diagnosed (01/2011-12/2019) at our hospital. The lesions were randomized 1:1 to the primary and validation cohorts. The regions of interest (ROIs) were manually drawn on each slice at DWI (b = 1500 s/mm²) from 3 T MRI. D (diffusion coefficient), D* (pseudodiffusion coefficient), f (perfusion fraction), distributed diffusion coefficient (DDC), α (diffusion heterogeneity index), mean diffusivity (MD) and mean kurtosis (MK) were obtained. The parameters with largest performance for differentiation were used to establish a diagnostic model.

RESULTS

There were 148, 56, and 60 patients with PDAC, PNET, and SPN, respectively. For differentiating PDACs from SPNs, f and MK values were used to establish a diagnostic model with areas under the receiver operating characteristic curves (AUCs) of 0.92 and 0.89 in the primary and validation groups, respectively. For distinguishing PDACs from PNETs, α and MK values were used to establish a diagnostic model with AUCs of 0.87 and 0.86 in the primary and validation groups, respectively. The accuracy rate of the subjective evaluation with the assistance of non-gaussian DWI models for differentiating PDAC from SPNs and PNETs were higher than that of subjective diagnosis alone (P < 0.05).

CONCLUSIONS

The non-gaussian DWI models could assist radiologists in accurately differentiating PDACs from PNETs and SPNs.

Noninvasive DW-MRI metrics for staging hepatic fibrosis and grading inflammatory activity in patients with chronic hepatitis B

PURPOSE

To assess the value of various diffusion parameters obtained from monoexponential, biexponential, and stretched-exponential diffusion-weighted imaging (DWI) models for staging hepatic fibrosis (HF) and grading inflammatory activity in patients with chronic hepatitis B (CHB).

METHODS

82 patients with CHB and 30 healthy volunteers underwent DWI with 13 b-values on a 3T MRI unit. The standard apparent diffusion coefficient (ADC_st) was calculated using a monoexponential model. The true diffusion coefficient (D_t), pseudo-diffusion coefficient (D_p), and perfusion fraction (f) were calculated using a biexponential model. The distributed diffusion coefficient (DDC) and water-molecule diffusion heterogeneity index (α) were calculated using a stretched-exponential model. Receiver operating characteristic (ROC) curves were performed for diffusion parameters to compare the diagnosis performance.

RESULTS

The distributions of hepatic fibrosis stages and the inflammatory activity grades (METAVIR scoring system) were as follows: F0, n = 1; F1, n = 16; F2, n = 31; F3, n = 19; and F4, n = 15. A0, n = 1; A1, n = 14; A2, n = 46; and A3, n = 21. ADC_st, D_t and DDC values showed negative correlation with the fibrosis stage (r = - 0.418, - 0.717 and - 0.630, all P < 0.001) and the inflammatory activity grade (r = - 0.514, - 0.626 and - 0.550, all P < 0.001). The area under the ROC curve (AUC) of D_t (AUC = 0.854, 0.881) and DDC (AUC = 0.794, 0.834) were significantly higher than that of ADC_st (AUC = 0.637, 0.717) in discriminating significant fibrosis (≥ F2) and advanced fibrosis (≥ F3) (all P < 0.05). Although D_t (AUC = 0.867, 0.836) and DDC (AUC = 0.810, 0.808) showed higher AUCs than ADC_st (AUC = 0.767, 0.803), there was no significant difference in their ability in detecting inflammatory activity grade ≥ A2/A3 (P > 0.05).

CONCLUSIONS

D_t and DDC are promising indicators and outperform ADC_st for staging HF. While both D_t and DDC have similar diagnostic performance compared with ADC_st for grading inflammatory activity.

Prediction of false-negative extramural venous invasion in patients with rectal cancer using multiple mathematical models of diffusion-weighted imaging

PURPOSE

To investigate the parameters from mono-exponential, stretched-exponential, and intravoxel incoherent motion diffusion-weighted imaging (DWI) models for evaluating false-negative extramural venous invasion (EMVI) on conventional magnetic resonance imaging (MRI) in rectal cancer patients.

MATERIAL AND METHODS

Seventy-two rectal cancer patients with negative EMVI on conventional MRI who underwent direct surgical resection were enrolled in this prospective study. The apparent diffusion coefficient (ADC), true diffusion coefficient (D), pseudo-diffusion coefficient (D*), perfusion fraction (f), distributed diffusion coefficient (DDC), and water molecular diffusion heterogeneity index (α) values within the whole tumor were obtained to identify the patients with false-negative EMVI. Receiver operating characteristic (ROC) curves were applied to evaluate the diagnostic performance. Multivariate binary logistic regression analysis was conducted to determine the independent risk factors.

RESULTS

The DDC, D*, f, and α values were significantly different in the EMVI-positive and EMVI-negative groups (P =  0.018, and P <  0.001, respectively). The D*, f, and α values demonstrated good diagnostic performance with area under the ROC curve (AUC) of 0.861, 0.824, and 0.854, respectively. The combined model, including D*, α, and tumor location, proved superior diagnostic performance with the AUC, sensitivity, specificity, and accuracy of 0.971, 0.917, 0.967, and 0.931, respectively. The AUC of the combined model was significantly higher than that of the D*, f, and DDC (P = 0.004, 0.045, and 0.002, respectively).

CONCLUSION

Multi-b-value DWI may be a potential tool for identifying micro-EMVI in rectal cancer. The combination of DWI parameters and tumor location leads to superior diagnostic performance.

Comparing mono-exponential, bi-exponential, and stretched-exponential diffusion-weighted MR imaging for stratifying non-alcoholic fatty liver disease in a rabbit model

OBJECTIVES

To compare diffusion parameters obtained from mono-exponential, bi-exponential, and stretched-exponential diffusion-weighted imaging (DWI) in stratifying non-alcoholic fatty liver disease (NAFLD).

METHODS

Thirty-two New Zealand rabbits were fed a high-fat/cholesterol or standard diet to obtain different stages of NAFLD before 12 b-values (0-800 s/mm²) DWI. The apparent diffusion coefficient (ADC) from the mono-exponential model; pure water diffusion (D), pseudo-diffusion (D*), and perfusion fraction (f) from bi-exponential DWI; and distributed diffusion coefficient (DDC) and water molecular diffusion heterogeneity index (α) from stretched-exponential DWI were calculated for hepatic parenchyma. The goodness of fit of the three models was compared. NAFLD severity was pathologically graded as normal, simple steatosis, borderline, and non-alcoholic steatohepatitis (NASH). Spearman rank correlation analysis and receiver operating characteristic curves were used to assess NAFLD severity.

RESULTS

Upon comparison, the goodness of fit chi-square from stretched-exponential fitting (0.077 ± 0.012) was significantly lower than that for the bi-exponential (0.110 ± 0.090) and mono-exponential (0.181 ± 0.131) models (p < 0.05). Seven normal, 8 simple steatosis, 6 borderline, and 11 NASH livers were pathologically confirmed from 32 rabbits. Both α and D increased with increasing NAFLD severity (r = 0.811 and 0.373, respectively; p < 0.05). ADC, f, and DDC decreased as NAFLD severity increased (r = - 0.529, - 0.717, and - 0.541, respectively; p < 0.05). Both α (area under the curve [AUC] = 0.952) and f (AUC = 0.931) had significantly greater AUCs than ADC (AUC = 0.727) in the differentiation of NASH from borderline or less severe groups (p < 0.05).

CONCLUSIONS

Stretched-exponential DWI with higher fitting efficiency performed, as well as bi-exponential DWI, better than mono-exponential DWI in the stratification of NAFLD severity.

KEY POINTS

• Stretched-exponential diffusion model fitting was more reliable than the bi-exponential and mono-exponential diffusion models (p = 0.039 and p < 0.001, respectively). • As NAFLD severity increased, the diffusion heterogeneity index (α) increased, while the perfusion fraction (f) decreased (r = 0.811, - 0.717, p < 0.05). • Both α and f showed superior NASH diagnostic performance (AUC = 0.952, 0.931) compared with ADC (AUC = 0.727, p < 0.05).

Multiple mathematical models of diffusion-weighted imaging for endometrial cancer characterization: Correlation with prognosis-related risk factors

PURPOSE

To investigate mono-exponential, bi-exponential, and stretched-exponential models of diffusion-weighted imaging (DWI) for evaluation of prognosis-related risk factors of endometrial cancer (EC).

METHOD

Sixty-one consecutive patients with EC who preoperatively underwent pelvic MRI with multiple b value DWI between September 2016 and May 2018 were enrolled. The apparent-diffusion-coefficient (ADC), bi-exponential model parameters (D, D* and f) and stretched-exponential model parameters (DDC and α) were measured and compared to analyze the following prognosis-related risk factors confirmed by pathology: histological grade, depth of myometrial invasion, cervical stromal infiltration (CSI) and lymphovascular invasion (LVSI). A stepwise multilvariate logistic regression and the receiver operating characteristic (ROC) curves were performed for further statistical analysis.

RESULTS

Lower ADC, D, f, and DDC were observed in tumor with high grade compared with a low-grade group, and the largest area under curve (AUC) was obtained when combining f and DDC values. ADC, D, f, DDC, and α were significantly different in patients with deep myometrial invasion (DMI) compared to those without DMI; the combination of f, DDC and α showed the highest AUC. Significantly different ADC and f were found between patients' presence and absence CSI; the f values showed the highest diagnostic performance with an AUC of 0.825. Regarding the LVSI, ADC, D*, f, and DDC were significantly lower in tumors with LVSI compared to those without LVSI; the combination of f and DDC showed the largest AUC.

CONCLUSION

Multiple mathematical DWI models are a useful approach for the prediction of prognosis-related risk factors in EC.

Non-Gaussian Diffusion Models and T1 rho Quantification in the Assessment of Hepatic Sinusoidal Obstruction Syndrome in Rats

BACKGROUND

Non-Gaussian diffusion models and T₁ rho quantification may reflect the changes in tissue heterogeneity in hepatic sinusoidal obstruction syndrome (SOS).

PURPOSE

To investigate the feasibility of diffusion kurtosis imaging (DKI), stretched exponential model (SEM), and T₁ rho quantification in detecting and staging SOS in a monocrotaline (MCT)-induced rat model.

STUDY TYPE

Animal study.

POPULATION

Thirty male Sprague-Dawley rats gavaged with MCT to induce hepatic SOS and six male rats without any intervention.

FIELD STRENGTH/SEQUENCE

3.0T, DWI with five b-values (0-2000 s/mm² ) and T₁ rho with five spin lock times (1-60 msec).

ASSESSMENT

MRI was performed 1 day before and 1, 3, 5, 7, and 10 days after MCT administration. The corrected apparent diffusion coefficient (D_app ), kurtosis coefficient (K_app ), distributed diffusion coefficient (DDC), and intravoxel water molecular diffusion heterogeneity (α) were calculated from the corresponding non-Gaussian diffusion model. The T₁ rho value was calculated using a monoexponential model. Specimens obtained from the six timepoints were categorized into normal liver (n = 6), early-stage (n = 16), and late-stage (n = 14) SOS in accordance with the pathological score.

STATISTICAL TESTS

Parametric statistical methods and receiver operating characteristic (ROC) curves were employed to determine diagnostic accuracy.

RESULTS

The D_app , K_app , DDC, α, and T₁ rho values were correlated with pathological score with r values of -0.821, 0.726, -0.828, -0.739, and 0.714 (all P < 0.001), respectively. DKI (combined D_app and K_app ) and SEM (combined DDC and α) were better than T₁ rho for staging SOS. The areas under the ROC curve of DKI, SEM, and T₁ rho for differentiating normal liver and early-stage SOS were 0.97, 1.00, and 0.79, whereas those of DKI, SEM, and T₁ rho for differentiating early-stage and late-stage SOS were 1.00, 0.97, and 0.92, respectively.

DATA CONCLUSION

DKI, SEM, and T₁ rho may be helpful in staging SOS.

LEVEL OF EVIDENCE

2 TECHNICAL EFFICACY STAGE: 2 J. Magn. Reson. Imaging 2020;52:1110-1121.

Pulsed field gradient signal attenuation of restricted anomalous diffusions in plate, sphere, and cylinder with wall relaxation

The effect of boundary relaxation on pulsed field gradient (PFG) anomalous restricted diffusion is investigated in this paper. The PFG signal attenuation expressions of anomalous diffusion in plate, sphere, and cylinder are derived based on fractional calculus. In addition, approximate expressions for boundary relaxation induced short time signal attenuation under zero gradient field and boundary relaxation affected short time apparent diffusion coefficients are given in this paper. Unlike the exponential signal attenuation in normal diffusion, the PFG signal attenuation in anomalous diffusion with boundary relaxation is either a Mittag-Leffler-function-based attenuation or a stretched-exponential-function-based attenuation. The stretched exponential attenuations of all three structures clearly show the diffractive pattern. In contrast, only in the plate structure does the Mittag-Leffler-function-based attenuation display an obvious diffractive pattern. Additionally, anomalous diffusion with smaller time derivative order α has a weaker diffractive pattern and less signal attenuation. Moreover, the results demonstrate that boundary relaxation induced signal attenuation is significantly affected by the anomalous diffusion when no gradient field is applied. Meanwhile, the boundary relaxation significantly affects PFG signal attenuation of anomalous diffusion in the following ways: The boundary relaxation results in reduced radius from the minimum of the diffractive patterns, and it results in an increased apparent diffusion coefficient and decreased surfaces to volume ratio in varying the diffusion time experiment; the boundary relaxation also substantially affects the apparent diffusion coefficient of sphere structure in the variation of gradient experiment.

Histogram analysis from stretched exponential model on diffusion-weighted imaging: evaluation of clinically significant prostate cancer

OBJECTIVE

To evaluate the usefulness of histogram analysis of stretched exponential model (SEM) on diffusion-weighted imaging in evaluating clinically significant prostate cancer (CSC).

METHODS

A total of 85 patients with prostate cancer underwent 3 T multiparametric MRI, followed by radical prostatectomy. Histogram parameters of the tumor from the SEM [distributed diffusion coefficient (DDC) and α] and the monoexponential model [MEM; apparent diffusion coefficient (ADC)] were evaluated. The associations between parameters and Gleason score or Prostate Imaging Reporting and Data System v. 2 were evaluated. The area under the receiver operating characteristics curve was calculated to evaluate diagnostic performance of parameters in predicting CSC.

RESULTS

The values of histogram parameters of DDC and ADC were significantly lower in patients with CSC than in patients without CSC (p < 0.05), except for skewness and kurtosis. The value of the 25th percentile of α was significantly lower in patients with CSC than in patients without CSC (p = 0.014). Histogram parameters of ADC and DDC had significant weak to moderate negative associations with Gleason score or Prostate Imaging Reporting and Data System v. 2 (p < 0.001), except for skewness and kurtosis. For predicting CSC, the area under the curves of mean ADC (0.856), 50th percentile DDC (0.852), and 25th percentile α (0.707) yielded the highest values compared to other histogram parameters from each group.

CONCLUSION

Histogram analysis of the SEM on diffusion-weighted imaging may be a useful quantitative tool for evaluating CSC. However, the SEM did not outperform the MEM.

ADVANCES IN KNOWLEDGE

Histogram parameters of SEM may be useful for evaluating CSC.

Monoexponential, Biexponential, and stretched-exponential models using diffusion-weighted imaging: A quantitative differentiation of breast lesions at 3.0T

BACKGROUND

Diffusion-weighted imaging (DWI) plays an important role in the differentiation of malignant and benign breast lesions.

PURPOSE

To investigate the utility of various diffusion parameters obtained from monoexponential, biexponential, and stretched-exponential DWI models in the differential diagnosis of breast lesions.

STUDY TYPE

Prospective.

POPULATION

Sixty-one patients (age range: 25-68 years old; mean age: 46 years old) with 31 malignant lesions, 42 benign lesions, and 28 normal breast tissues diagnosed initially by clinical palpation, ultrasonography, or conventional mammography were enrolled in the study from January to September 2016.

FIELD STRENGTH

3.0T MR scanner, T₁ WI, T₂ WI, DWI (conventional and multi-b values), dynamic contrast-enhanced.

ASSESSMENT

The apparent diffusion coefficient (ADC) was calculated by monoexponential analysis. The diffusion coefficient (ADC_slow ), pseudodiffusion coefficient (ADC_fast ), and perfusion fraction (f) were calculated using the biexponential model. The distributed diffusion coefficient (DDC) and water molecular diffusion heterogeneity index (α) were obtained using a stretched-exponential model. All parameters were compared for malignant tumors, benign tumors, and normal breast tissues. A receiver operating characteristic curve was used to compare the ability of these parameters, in order to differentiate benign and malignant breast lesions.

STATISTICAL TESTS

All statistical analyses were performed using statistical software (SPSS).

RESULTS

ADC, ADC_slow , f, DDC, and α values were significantly lower in malignant tumors when compared with normal breast tissues and benign tumors (P < 0.05). However, ADC and f had higher area under the receiver operating characteristic curve (AUC) values (0.889 and 0.919, respectively).

DATA CONCLUSION

The parameters derived from the biexponential and stretched-exponential DWI could provide additional information for differentiating between benign and malignant breast tumors when compared with conventional diffusion parameters.

LEVEL OF EVIDENCE

4 Technical Efficacy: Stage 4 J. Magn. Reson. Imaging 2019;50:1461-1467.

Grading and proliferation assessment of diffuse astrocytic tumors with monoexponential, biexponential, and stretched-exponential diffusion-weighted imaging and diffusion kurtosis imaging

PURPOSE

To compare the main parameters derived from monoexponential, biexponential and stretched-exponential diffusion-weighted imaging (DWI) and diffusion kurtosis imaging (DKI) with respect to diagnostic performance for tumor grading and proliferation assessment in diffuse astrocytic tumors (DATs).

MATERIALS AND METHODS

Fifty-eight pathologically confirmed DAT patients who underwent DWI and DKI on a 3-T scanner were prospectively collected and retrospectively reviewed. Measurements including the apparent diffusion coefficient (ADC), true diffusion coefficient (D), pseudodiffusion coefficient (D^*), perfusion fraction (f), distributed diffusion coefficient (DDC), heterogeneity index (α), mean diffusivity (MD), fractional anisotropy (FA), and mean kurtosis (MK) were compared between tumor grades (Ⅱ, Ⅲ, and Ⅳ) by using a Jonckheere-Terpstra test. Receiver operating characteristic (ROC) curves were used to assess the diagnostic efficacy of these parameters. Spearman's rho with the Ki-67 labeling index (LI) was calculated for each parameter.

RESULTS

MK values differed significantly between all DAT subtypes and increased with grade. The ADC, D, f, DDC, α and MD values were significantly higher in grade Ⅱ tumors than in grade Ⅲ/Ⅳ tumors. D^* values were significantly lower in grade Ⅱ tumors than in grade Ⅳ tumors (all P < 0.05). In discriminating between grade Ⅱ and Ⅲ tumors, α, MK, MD, D and f had significantly greater area under the ROC curve (AUC) values than D^* and FA (0.927, 0.901, 0.896, 0.895, and 0.889, respectively vs 0.659 and 0.598, respectively, P < 0.05). In discriminating between grade Ⅲ and Ⅳ tumors, only MK demonstrated acceptable discrimination (AUC = 0.711). MK and D showed a strong correlation with the Ki-67 LI (ρ = 0.791 and -0.789, respectively, P < 0.001). D^*, f, MD, ADC, DDC and α showed a moderate correlation (|ρ| ranged from 0.415 to 0.698, P < 0.05).

CONCLUSION

MK and D have considerable potential to predict the degree of proliferation of DATs. MK could effectively characterize microstructural changes throughout the malignant transformation of DATs and provided useful complementary information for grading.

A comparative study of Gaussian and non-Gaussian diffusion models for differential diagnosis of prostate cancer with in-bore transrectal MR-guided biopsy as a pathological reference

Background Although several studies have been reported on evaluating the performance of Gaussian and different non-Gaussian diffusion models on prostate cancer, few studies have been reported on the comparison of different models on differential diagnosis for prostate cancer. Purpose To compare the utility of various metrics derived from monoexponential model (MEM), biexponential model (BEM), stretched-exponential model (SEM) based diffusion-weighted imaging (DWI) and diffusion kurtosis imaging (DKI) in the differential diagnosis of prostate cancer. Material and Methods Thirty-three patients underwent magnetic resonance imaging (MRI) examination. Multi-b value and multi-direction DWIs were performed. In-bore MR-guided biopsy was performed. Apparent diffusion coefficient (ADC), pure molecular diffusion (ADC_slow), pseudo-diffusion coefficient (ADC_fast), perfusion fraction (f), water molecular diffusion heterogeneity index (α), distributed diffusion coefficient (DDC), non-Gaussian diffusion coefficient (MD), and mean kurtosis (MK) values were calculated and compared between cancerous and non-cancerous groups. Receiver operating characteristic (ROC) analysis was performed for all parameters and models. Results ADC, ADC_slow, DDC, and MD values were significantly lower while MK value was significantly higher in prostate cancer than those of prostatitis and benign prostatic hyperplasia. ADC, ADC_slow, DDC, MD, and MK could discriminate between tumor and non-tumorous lesions (area under the curve, 0.856, 0.835, 0.866, 0.918, and 0.937, respectively). MK was superior to ADC in the discrimination of prostate cancer. DKI was superior to MEM in the discrimination of prostate cancer. Conclusions Parameters derived from both Gaussian and non-Gaussian models could characterize prostate cancer. DKI may be advantageous than DWI for detection of prostate cancer.

Assessment of different mathematical models for diffusion-weighted imaging as quantitative biomarkers for differentiating benign from malignant solid hepatic lesions

To quantitatively compare the monoexponential, biexponential, and stretched‐exponential diffusion‐weighted imaging (DWI) models in differentiating benign from malignant solid hepatic lesions. The institutional review board approved this retrospective study and waived the informed consent requirement. A total of 188 patients with 288 hepatic lesions included 202 malignant lesions and 86 benign lesions were assessed (confirmed by pathology or clinical follow‐up for 6 months). All patients underwent hepatic 3.0‐T MRI, including multi‐b DWI that used 12 b values. The ADC, D_p, D_t, perfusion fraction (f_p), α, and DDC values for normal liver, benign liver lesions, and malignant liver lesions were calculated. Independent sample t tests were used for comparisons. The diagnostic performance of the parameters was evaluated using ROC analysis. The AUC value for each model was also calculated. The value of D_p was significantly lower in benign lesions than in normal hepatic parenchyma while others were significantly higher (P < .001). Whereas Values of D_t and α in malignant hepatic lesions were significantly higher than in normal hepatic parenchyma (P < .001), and the D_p value was significantly lower (P < .001). Values of ADC, f_p, DDC, and α for malignant hepatic lesions were significantly lower than those for benign hepatic lesions (P < .001). ROC analysis showed that the diagnostic value of the biexponential model of normal hepatic parenchyma vs benign hepatic lesions and normal hepatic parenchyma vs malignant hepatic lesions was high (0.946 and 0.876, respectively). In the differential diagnosis of benign and malignant hepatic lesions, DDC had the highest AUC value (0.819). The biexponential and stretched‐exponential DWI may provide additional information and improve the differential diagnosis of benign and malignant hepatic lesions compared with the monoexponential DWI.

A Modified Tri-Exponential Model for Multi-b-value Diffusion-Weighted Imaging: A Method to Detect the Strictly Diffusion-Limited Compartment in Brain

Purpose: To present a new modified tri-exponential model for diffusion-weighted imaging (DWI) to detect the strictly diffusion-limited compartment, and to compare it with the conventional bi- and tri-exponential models.

Methods: Multi-b-value diffusion-weighted imaging (DWI) with 17 b-values up to 8,000 s/mm² were performed on six volunteers. The corrected Akaike information criterions (AICc) and squared predicted errors (SPE) were calculated to compare these three models.

Results: The mean f₀ values were ranging 11.9–18.7% in white matter ROIs and 1.2–2.7% in gray matter ROIs. In all white matter ROIs: the AICcs of the modified tri-exponential model were the lowest (p < 0.05 for five ROIs), indicating the new model has the best fit among these models; the SPEs of the bi-exponential model were the highest (p < 0.05), suggesting the bi-exponential model is unable to predict the signal intensity at ultra-high b-value. The mean ADC_very−slow values were extremely low in white matter (1–7 × 10⁻⁶ mm²/s), but not in gray matter (251–445 × 10⁻⁶ mm²/s), indicating that the conventional tri-exponential model fails to represent a special compartment.

Conclusions: The strictly diffusion-limited compartment may be an important component in white matter. The new model fits better than the other two models, and may provide additional information.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Autobiography of James S. Hyde

The papers, book chapters, reviews, and patents by James S. Hyde in the bibliography of this document have been separated into EPR and MRI sections, and within each section by topics. Within each topic, publications are listed chronologically. A brief summary is provided for each patent listed. A few publications and patents that do not fit this schema have been omitted. This list of publications is preceded by a scientific autobiography that focuses on selected topics that are judged to have been of most scientific importance. References to many of the publications and patents in the bibliography are made in the autobiography.

Assessment of early treatment response to neoadjuvant chemotherapy in breast cancer using non-mono-exponential diffusion models: a feasibility study comparing the baseline and mid-treatment MRI examinations

OBJECTIVES

To assess the feasibility of the mono-exponential, bi-exponential and stretched-exponential models in evaluating response of breast tumours to neoadjuvant chemotherapy (NACT) at 3 T.

METHODS

Thirty-six female patients (median age 53, range 32-75 years) with invasive breast cancer undergoing NACT were enrolled for diffusion-weighted MRI (DW-MRI) prior to the start of treatment. For assessment of early response, changes in parameters were evaluated on mid-treatment MRI in 22 patients. DW-MRI was performed using eight b values (0, 30, 60, 90, 120, 300, 600, 900 s/mm2). Apparent diffusion coefficient (ADC), tissue diffusion coefficient (D t), vascular fraction (ƒ), distributed diffusion coefficient (DDC) and alpha (α) parameters were derived. Then t tests compared the baseline and changes in parameters between response groups. Repeatability was assessed at inter- and intraobserver levels.

RESULTS

All patients underwent baseline MRI whereas 22 lesions were available at mid-treatment. At pretreatment, mean diffusion coefficients demonstrated significant differences between groups (p < 0.05). At mid-treatment, percentage increase in ADC and DDC showed significant differences between responders (49 % and 43 %) and non-responders (21 % and 32 %) (p = 0.03, p = 0.04). Overall, stretched-exponential parameters showed excellent repeatability.

CONCLUSION

DW-MRI is sensitive to baseline and early treatment changes in breast cancer using non-mono-exponential models, and the stretched-exponential model can potentially monitor such changes.

KEY POINTS

• Baseline diffusion coefficients demonstrated significant differences between complete pathological responders and non-responders. • Increase in ADC and DDC at mid-treatment can discriminate responders and non-responders. • The ƒ fraction at mid-treatment decreased in responders whereas increased in non-responders. • The mono- and stretched-exponential models showed excellent inter- and intrarater repeatability. • Treatment effects can potentially be assessed by non-mono-exponential diffusion models.

Comparison between types I and II epithelial ovarian cancer using histogram analysis of monoexponential, biexponential, and stretched-exponential diffusion models

PURPOSE

To evaluate the utility of histogram analysis of monoexponential, biexponential, and stretched-exponential models to a dualistic model of epithelial ovarian cancer (EOC).

MATERIALS AND METHODS

Fifty-two patients with histopathologically proven EOC underwent preoperative magnetic resonance imaging (MRI) (including diffusion-weighted imaging [DWI] with 11 b-values) using a 3.0T system and were divided into two groups: types I and II. Apparent diffusion coefficient (ADC), true diffusion coefficient (D), pseudodiffusion coefficient (D*), perfusion fraction (f), distributed diffusion coefficient (DDC), and intravoxel water diffusion heterogeneity (α) histograms were obtained based on solid components of the entire tumor. The following metrics of each histogram were compared between two types: 1) mean; 2) median; 3) 10th percentile and 90th percentile. Conventional MRI morphological features were also recorded.

RESULTS

Significant morphological features for predicting EOC type were maximum diameter (P = 0.007), texture of lesion (P = 0.001), and peritoneal implants (P = 0.001). For ADC, D, f, DDC, and α, all metrics were significantly lower in type II than type I (P < 0.05). Mean, median, 10th, and 90th percentile of D* were not significantly different (P = 0.336, 0.154, 0.779, and 0.203, respectively). Most histogram metrics of ADC, D, and DDC had significantly higher area under the receiver operating characteristic curve values than those of f and α (P < 0.05) CONCLUSION: It is feasible to grade EOC by morphological features and three models with histogram analysis. ADC, D, and DDC have better performance than f and α; f and α may provide additional information.

LEVEL OF EVIDENCE

4 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1797-1809.

Assessment of pathological complete response to preoperative chemoradiotherapy by means of multiple mathematical models of diffusion-weighted MRI in locally advanced rectal cancer: A prospective single-center study

PURPOSE

To assess stretched-exponential, mono-exponential and intravoxel incoherent motion (IVIM) models of diffusion-weighted MRI(DWI) in predicting pathological complete response (pCR) to neoadjuvant chemoradiotherapy (CRT) in rectal cancer patients.

MATERIALS AND METHODS

This prospective study recruited 98 consecutive patients with locally advanced rectal cancer who underwent 3 Tesla MR examination before, during and after CRT. The apparent diffusion coefficient (ADC), IVIM-derived parameters (D, f, and D*), and stretched-exponential model-derived parameters (DDC and α) were measured. The parameters and their corresponding changes during and after CRT were compared between pCR and non-pCR. Receiver-operating characteristic curve analysis was performed to evaluate the diagnostic performance. Coefficient of variations and intraclass correlation coefficient were calculated to assess reliability and agreement.

RESULTS

Nineteen patients achieved pCR while 79 did not. The pCR group had higher ADC and α (ADC₂ and α₂ ), and their changes (ΔADC₂ , and Δα₂ ) at the endpoint than non-pCR group. α₂ and ADC₂ yielded similar AUCs (P = 0.339), Δα₂ and ΔADC₂ yielded similar AUCs (P = 0.263) ADC and α presented substantial agreement, and α presented the minimum CV (5.0-7.0%).

CONCLUSION

ADC and α were useful for assessing pCR after CRT. α might be more useful because it demonstrated better diagnostic performance than IVIM-derived parameters and better reliability than ADC.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 2 J. MAGN. RESON. IMAGING 2017;46:175-183.

Diffusion-weighted imaging outside the brain: Consensus statement from an ISMRM-sponsored workshop

The significant advances in magnetic resonance imaging (MRI) hardware and software, sequence design, and postprocessing methods have made diffusion-weighted imaging (DWI) an important part of body MRI protocols and have fueled extensive research on quantitative diffusion outside the brain, particularly in the oncologic setting. In this review, we summarize the most up-to-date information on DWI acquisition and clinical applications outside the brain, as discussed in an ISMRM-sponsored symposium held in April 2015. We first introduce recent advances in acquisition, processing, and quality control; then review scientific evidence in major organ systems; and finally describe future directions. J. Magn. Reson. Imaging 2016;44:521-540.

Instantaneous signal attenuation method for analysis of PFG fractional diffusions

An instantaneous signal attenuation (ISA) method for analyzing pulsed field gradient (PFG) fractional diffusion (FD) has been developed, which is modified from the propagator approach developed in 2001 by Lin et al. for analyzing PFG normal diffusion. Both, the current ISA method and the propagator method have the same fundamental basis that the total signal attenuation (SA) is the accumulation of all the ISA, and the ISA is the average SA of the whole diffusion system at each moment. However, the manner of calculating ISA is different. Unlike the use of the instantaneous propagator in the propagator method, the current method directly calculates ISA as A(K(t'),t'+dt')/A(K(t'),t'), where A(K(t'),t'+dt') and A(K(t'),t') are the SA. This modification makes the current method applicable to PFG FD as the instantaneous propagator may not be obtainable in FD. The ISA method was applied to study PFG SA including the effect of finite gradient pulse widths (FGPW) for free FD, restricted FD and the FD affected by a non-homogeneous gradient field. The SA expressions were successfully obtained for all three types of free FDs while other current methods still have difficulty in obtaining all of them. The results from this method agree with reported results such as that obtained by the effective phase shift diffusion equation (EPSDE) method. The M-Wright phase distribution approximation was also used to derive an SA expression for time FD as a comparison, which agrees with ISA method. Additionally, the continuous-time random walk (CTRW) simulation was performed to simulate the SA of PFG FD, and the simulation results agree with the analytical results. Particularly, the CTRW simulation results give good support to the analytical results including FGPW effect for free FD and restricted time FD based on a fractional derivative model where there have been no corresponding theoretical reports to date. The theoretical SA expressions including FGPW obtained here such as [Formula: see text] may be applied to analyze PFG FD in polymer or biological systems with improved accuracy where SGP approximation cannot be satisfied. The method can perhaps provide new insight to FD MRI and hence benefit the development of diffusion biomarkers based on fractional derivative.

Application of brain multi-b-value diffusion-weighted imaging (DWI) in adolescent orphans from AIDS families

OBJECTIVE

To evaluate the application value of multi-b-value diffusion-weighted imaging (DWI) with mono-exponential model and stretched-exponential model in the diagnosis of HIV-positive patients.

METHODS

Multi-b-value (0, 50, 150, 200, 400, 600, 800 s mm(-2)) DWI was performed in 23 adolescent orphans from AIDS families, including 15 HIV-positive subjects and 8 HIV-negative healthy subjects. Apparent diffusion coefficient (ADC) values were fitted by mono-exponential model; distribution diffusion coefficient (DDC) values and heterogeneity index (α) values were fitted by stretched-exponential model in bilateral basal ganglia, then non-parametric tests were performed.

RESULTS

The signal intensity attenuation in multi-b-value DWI could be well described by both mono-exponential model and stretched-exponential model. In the left basal ganglia, mean α-values in HIV-positive subjects (α = 0.848 ± 0.068) were significantly lower than that in healthy subjects (α = 0.923 ± 0.050, p = 0.013). There was no statistical difference of α-values between HIV-positive subjects and healthy control subjects in the right basal ganglia. Apart from these, there were also no statistical differences of DDC values or ADC values between two groups in bilateral basal ganglia (all p > 0.05). In bilateral basal ganglia, DDC values were positively correlated with ADC values in HIV-positive patients (right basal ganglia: r = 0.832, p = 0.000; left basal ganglia: r = 0.770, p = 0.001) as well as in healthy cases (right basal ganglia: r = 0.927, p = 0.001; left basal ganglia: r = 0.878, p = 0.004). Receiver operating characteristic (ROC) curve analysis yielded area under the ROC curve (Az) values of 0.817 (p = 0.014 < 0.05) in the left basal ganglia. The sensitivity and specificity were 62.5% and 86.7%, respectively.

CONCLUSION

Through the study of asymptomatic HIV-positive subjects when b < 1000 s mm(-2), we can see stretched-exponential model DWI can provide more information than mono-exponential model DWI.

ADVANCES IN KNOWLEDGE

Multi-b-value DWI was performed in subjects with HIV. DWI measurements could be neuroimaging biomarkers of cerebral injury in the course of HIV infection.

Intravoxel incoherent motion diffusion-weighted imaging analysis of diffusion and microperfusion in grading gliomas and comparison with arterial spin labeling for evaluation of tumor perfusion

PURPOSE

To determine the utility of intravoxel incoherent motion (IVIM) imaging in grading gliomas and compare IVIM perfusion metrics with arterial spin labeling (ASL)-derived cerebral blood flow (CBF).

MATERIALS AND METHODS

Fifty-two patients with pathologically confirmed gliomas underwent IVIM and ASL imaging at 3.0T. IVIM perfusion-related diffusivity (D*), perfusion fraction (f), product of f and D*(f×D*), true diffusivity (D), and apparent diffusion coefficient (ADC) were obtained to distinguish glioma grades. The CBF derived from pseudocontinuous ASL within the solid tumor was compared and correlated with IVIM perfusion metrics for grading of gliomas. Values were also normalized to the contralateral normal-appearing white matter. Receiver-operating characteristic was performed to determine diagnostic efficiency. The reliability was estimated with intraclass coefficient, coefficient of variance, and Bland-Altman plots.

RESULTS

IVIM perfusion metrics and CBF were significantly higher in the high-grade than the low-grade gliomas (P < 0.001), ADC and D were significantly lower in the high-grade than the low-grade gliomas (P < 0.001). f×D* differed significantly between grades II through IV (P < 0.05 for all). The other metrics showed significant difference between grade II and grade III (P < 0.05 for all). Area under the curve (AUC) was largest for f×D* in distinguishing high-grade from low-grade gliomas (AUC = 0.979, P < 0.001) and between grade II and grade III (AUC = 0.957, P < 0.001). f×D* improved diagnostic performance of CBF in grading gliomas and showed strong correlation with CBF (r = 0.696, P < 0.001).

CONCLUSION

IVIM-derived metrics are promising biomarkers in preoperative grading gliomas. IVIM imaging may be an additive method to ASL and ADC for evaluating tumor perfusion and diffusion. J. Magn. Reson. Imaging 2016;44:620-632.

An effective phase shift diffusion equation method for analysis of PFG normal and fractional diffusions

Pulsed field gradient (PFG) diffusion measurement has a lot of applications in NMR and MRI. Its analysis relies on the ability to obtain the signal attenuation expressions, which can be obtained by averaging over the accumulating phase shift distribution (APSD). However, current theoretical models are not robust or require approximations to get the APSD. Here, a new formalism, an effective phase shift diffusion (EPSD) equation method is presented to calculate the APSD directly. This is based on the idea that the gradient pulse effect on the change of the APSD can be viewed as a diffusion process in the virtual phase space (VPS). The EPSD has a diffusion coefficient, K(β)(t)D rad(β)/s(α), where α is time derivative order and β is a space derivative order, respectively. The EPSD equations of VPS are built based on the diffusion equations of real space by replacing the diffusion coefficients and the coordinate system (from real space coordinate to virtual phase coordinate). Two different models, the fractal derivative model and the fractional derivative model from the literature were used to build the EPSD fractional diffusion equations. The APSD obtained from solving these EPSD equations were used to calculate the PFG signal attenuation. From the fractal derivative model the attenuation is exp(-γ(β)g(β)δ(β)Df1t(α)), a stretched exponential function (SEF) attenuation, while from the fractional derivative model the attenuation is Eα,1(-γ(β)g(β)δ(β)Df2t(α)), a Mittag-Leffler function (MLF) attenuation. The MLF attenuation can be reduced to SEF attenuation when α=1, and can be approximated as a SEF attenuation when the attenuation is small. Additionally, the effect of finite gradient pulse widths (FGPW) is calculated. From the fractal derivative model, the signal attenuation including FGPW effect is exp[ -Df1∫0(τ) K(β)(t)dt(α)]. The results obtained in this study are in good agreement with the results in literature. Several expressions that describe signal attenuation have not been reported and that can be of great importance for the PFG experiments. This EPSD equation method provides a new, simple path to calculate signal attenuation of PFG NMR experiments.

Grading of Gliomas by Using Monoexponential, Biexponential, and Stretched Exponential Diffusion-weighted MR Imaging and Diffusion Kurtosis MR Imaging

PURPOSE

To quantitatively compare the potential of various diffusion parameters obtained from monoexponential, biexponential, and stretched exponential diffusion-weighted imaging models and diffusion kurtosis imaging in the grading of gliomas.

MATERIALS AND METHODS

This study was approved by the local ethics committee, and written informed consent was obtained from all subjects. Both diffusion-weighted imaging and diffusion kurtosis imaging were performed in 69 patients with pathologically proven gliomas by using a 3-T magnetic resonance (MR) imaging unit. An isotropic apparent diffusion coefficient (ADC), true ADC, pseudo-ADC, and perfusion fraction were calculated from diffusion-weighted images by using a biexponential model. A water molecular diffusion heterogeneity index and distributed diffusion coefficient were calculated from diffusion-weighted images by using a stretched exponential model. Mean diffusivity, fractional anisotropy, and mean kurtosis were calculated from diffusion kurtosis images. All values were compared between high-grade and low-grade gliomas by using a Mann-Whitney U test. Receiver operating characteristic and Spearman rank correlation analysis were used for statistical evaluations.

RESULTS

ADC, true ADC, perfusion fraction, water molecular diffusion heterogeneity index, distributed diffusion coefficient, and mean diffusivity values were significantly lower in high-grade gliomas than in low-grade gliomas (U = 109, 56, 129, 6, 206, and 229, respectively; P < .05). Pseudo-ADC and mean kurtosis values were significantly higher in high-grade gliomas than in low-grade gliomas (U = 98 and 8, respectively; P < .05). Both water molecular diffusion heterogeneity index (area under the receiver operating characteristic curve [AUC] = 0.993) and mean kurtosis (AUC = 0.991) had significantly greater AUC values than ADC (AUC = 0.866), mean diffusivity (AUC = 0.722), and fractional anisotropy (AUC = 0.500) in the differentiation of low-grade and high-grade gliomas (P < .05).

CONCLUSION

Water molecular diffusion heterogeneity index and mean kurtosis values may provide additional information and improve the grading of gliomas compared with conventional diffusion parameters.

Accuracies and Contrasts of Models of the Diffusion-Weighted-Dependent Attenuation of the MRI Signal at Intermediate b-values

The diffusion-weighted-dependent attenuation of the MRI signal E(b) is extremely sensitive to microstructural features. The aim of this study was to determine which mathematical model of the E(b) signal most accurately describes it in the brain. The models compared were the monoexponential model, the stretched exponential model, the truncated cumulant expansion (TCE) model, the biexponential model, and the triexponential model. Acquisition was performed with nine b-values up to 2500 s/mm² in 12 healthy volunteers. The goodness-of-fit was studied with F-tests and with the Akaike information criterion. Tissue contrasts were differentiated with a multiple comparison corrected nonparametric analysis of variance. F-test showed that the TCE model was better than the biexponential model in gray and white matter. Corrected Akaike information criterion showed that the TCE model has the best accuracy and produced the most reliable contrasts in white matter among all models studied. In conclusion, the TCE model was found to be the best model to infer the microstructural properties of brain tissue.

Novel Magnetic Resonance Imaging Techniques in Brain Tumors

Magnetic resonance imaging is a powerful, noninvasive imaging technique with exquisite sensitivity to soft tissue composition. Magnetic resonance imaging is primary tool for brain tumor diagnosis, evaluation of drug response assessment, and clinical monitoring of the patient during the course of their disease. The flexibility of magnetic resonance imaging pulse sequence design allows for a variety of image contrasts to be acquired, including information about magnetic resonance-specific tissue characteristics, molecular dynamics, microstructural organization, vascular composition, and biochemical status. The current review highlights recent advancements and novel approaches in MR characterization of brain tumors.

Comparison of Intravoxel Incoherent Motion Diffusion-Weighted MR Imaging and Arterial Spin Labeling MR Imaging in Gliomas

Gliomas grading is important for treatment plan; we aimed to investigate the application of intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) in gliomas grading, by comparing with the three-dimensional pseudocontinuous arterial spin labeling (3D pCASL). 24 patients (13 high grade gliomas and 11 low grade gliomas) underwent IVIM DWI and 3D pCASL imaging before operation; maps of fast diffusion coefficient (D^∗), slow diffusion coefficient (D), fractional perfusion-related volume (f), and apparent diffusion coefficient (ADC) as well as cerebral blood flow (CBF) were calculated and then coregistered to generate the corresponding parameter values. We found CBF and D^∗ were higher in the high grade gliomas, whereas ADC, D, and f were lower (all P < 0.05). In differentiating the high from low grade gliomas, the maximum areas under the curves (AUC) of D^∗, CBF, and ADC were 0.857, 0.85, and 0.902, respectively. CBF was negatively correlated with f in tumor (r = −0.619, P = 0.001). ADC was positively correlated with D in both tumor and white matter (r = 0.887, P = 0.000 and r = 0.824, P = 0.000, resp.). There was no correlation between CBF and D^∗ in both tumor and white matter (P > 0.05). IVIM DWI showed more efficiency than 3D pCASL but less validity than conventional DWI in differentiating the high from low grade gliomas.

Comparison of stretched-Exponential and monoexponential model diffusion-Weighted imaging in prostate cancer and normal tissues

BACKGROUND

To compare stretched-exponential and monoexponential model diffusion-weighted imaging (DWI) in prostate cancer and normal tissues.

METHODS

Twenty-seven patients with prostate cancer underwent DWI exam using b-values of 0, 500, 1000, and 2000 s/mm(2) . The distributed diffusion coefficients (DDC) and α values of prostate cancer and normal tissues were obtained with stretched-exponential model and apparent diffusion coefficient (ADC) values using monoexponential model. The ADC, DDC (both in 10(-3) mm(2)/s), and α values (range, 0-1) were compared among different prostate tissues. The ADC and DDC were also compared and correlated in each tissue, and the standardized differences between DDC and ADC were compared among different tissues.

RESULTS

Data were obtained for 31 cancers, 36 normal peripheral zone (PZ) and 26 normal central gland (CG) tissues. The ADC (0.71 ± 0.12), DDC (0.60 ± 0.18), and α value (0.64 ± 0.05) of tumor were all significantly lower than those of the normal PZ (1.41 ± 0.22, 1.47 ± 0.20, and 0.85 ± 0.09) and CG (1.25 ± 0.14, 1.32 ± 0.13, and 0.82 ± 0.06) (all P < 0.05). ADC was significantly higher than DDC in cancer, but lower than DDC in the PZ and CG (all P < 0.05). The ADC and DDC were strongly correlated (R(2)  = 0.99, 0.98, 0.99, respectively, all P < 0.05) in all the tissue, and standardized difference between ADC and DDC of cancer was slight but significantly higher than that in normal tissue.

CONCLUSION

The stretched-exponential model DWI provides more parameters for distinguishing prostate cancer and normal tissue and reveals slight differences between DDC and ADC values.

Intravoxel incoherent motion diffusion-weighted MR imaging of gliomas: feasibility of the method and initial results

INTRODUCTION

The purpose of this study was to evaluate the feasibility of intravoxel incoherent motion (IVIM) imaging and its value in differentiating the histologic grade among human gliomas.

METHODS

The IVIM model generated parametric images for apparent diffusion coefficient ADC, slow diffusion coefficient D (or D slow), fast diffusion coefficient D* (or D fast), and fractional perfusion-related volume f in 22 patients with gliomas (WHO grade II-IV) using monopolar Stejskal-Tanner diffusion-weighted imaging (DWI) scheme and 14 b values ranging from 0 s/mm2 to a maximum of 1,300 s/mm2. A region-of-interest analysis on the tumor as well as in the white matter was conducted. The parameter values were tested for significant differences. The repeatability of the measurements was tested by coefficient of variation and Bland-Altman plots.

RESULTS

D, D*, and f in the high-grade gliomas demonstrated significant differences compared to the healthy white matter. D* and f showed a significant difference between low- and high-grade gliomas. D tended to be slightly lower in the WHO grade II compared to WHO grade III-IV tumors. f and D* demonstrated higher coefficients of variation than the ADC and D in tumor. The Bland-Altman plots demonstrated satisfactory results without any outliers outside the mean ± 1.96 standard deviation.

CONCLUSION

The IVIM-fitted post-processing of DWI-signal decay in human gliomas could show significantly different values of fractional perfusion-related volume and fast diffusion coefficient between low- and high-grade tumors, which might enable a noninvasive WHO grading in vivo.

Diffusion-weighted magnetic resonance imaging of the prostate: improved robustness with stretched exponential modeling

PURPOSE

This study aimed to compare the intraclass correlation coefficients of parameters estimated with stretched exponential and biexponential diffusion models of in vivo diffusion-weighted magnetic resonance imaging (MRI) of the prostate.

METHODS

After the institutional review board issued a waiver of informed consent for this Health Insurance Portability and Accountability Act-compliant study, 25 patients with biopsy-proven prostate cancer underwent 3T endorectal MRI and diffusion-weighted MRI of the prostate at 10 b values (0, 45, 75, 105, 150, 225, 300, 600, 900, and 1200 s/mm). The full set of b values was collected twice within a single acquisition. Intraclass correlation coefficients were calculated for intra-acquisition variability. From the biexponential model, the quantitative parameters diffusion coefficient (D), perfusion coefficient (D*), and perfusion fraction (f) were estimated. From the stretched exponential model, the quantitative parameters Kohlrausch decay constant (DK) and alpha (α) were estimated.

RESULTS

For the 25 patient data sets, the average intraclass correlation coefficients for DK and α were 95.8%, and 64.1%, respectively, whereas those for D, D*, and f were 84.4%, 25.3%, and 41.3%, respectively.

CONCLUSIONS

The stretched exponential diffusion model captures the nonlinear effects of intravoxel incoherent motion in the prostate. The parameters derived from this model are more reliable and reproducible than the parameters derived from the standard, widely used biexponential diffusion/perfusion model.

Two-step anomalous diffusion tensor imaging

We extend the formalism of anomalous diffusion imaging to include directional anisotropy of fitted parameters. The resulting technique is termed anomalous diffusion tensor imaging (aDTI), and allows the directional properties of the distributed diffusion coefficient (α) and the anomalous diffusion exponent, (γ) to be analysed using the same analytical techniques as regular diffusion tensor imaging (DTI). Together, these parameters quantify the rate of diffusion (α) and the complexity of the diffusion environment (γ). We generated tensor images for the anomalous exponent tensor (Γ) and distributed diffusivity tensor (A) from in vivo human brain data and present images of eigenvalues, eigenvectors, Trace/3 (Tr), fractional anisotropy (FA) and tensor shape measures. In white matter, A is found to have a median Tr = 0.56 × 10(- 3) mm(2) s(- 1), FA = 0.58 and Γ Tr = 0.69, FA = 0.13. We observed that white matter shows a similar anisotropic geometry for the distributed diffusion tensor as for the regular diffusion tensor, whereas the anomalous exponent tensor exhibits a different shape characteristic which may be informative of tissue microstructure.

Fractional Order Analysis of Sephadex Gel Structures: NMR Measurements Reflecting Anomalous Diffusion

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-(bD)(α)], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4,000 s-mm(-2)). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

Non-Gaussian diffusion imaging: a brief practical review

The departure from purely mono-exponential decay of the signal, as observed from brain tissue following a diffusion-sensitized sequence, has prompted the search for alternative models to characterize these unconventional water diffusion dynamics. Several approaches have been proposed in the last few years. While multi-exponential models have been applied to characterize brain tissue, several unresolved controversies about the interpretations of the results have motivated the search for alternative models that do not rely on the Gaussian diffusion hypothesis. In this brief review, diffusional kurtosis imaging (DKI) and anomalous diffusion imaging (ADI) techniques are addressed and compared with diffusion tensor imaging. Theoretical and experimental issues are briefly described to allow readers to understand similarities, differences and limitations of these two non-Gaussian models. However, since the ultimate goal is to improve specificity, sensitivity and spatial localization of diffusion MRI for the detection of brain diseases, special attention will be paid on the clinical feasibility of the proposed techniques as well as on the context of brain pathology investigations.

A simple method for rectified noise floor suppression: Phase-corrected real data reconstruction with application to diffusion-weighted imaging

Diffusion-weighted MRI is an intrinsically low signal-to-noise ratio application due to the application of diffusion-weighting gradients and the consequent longer echo times. The signal-to-noise ratio worsens with increasing image resolution and diffusion imaging methods that use multiple and higher b-values. At low signal-to-noise ratios, standard magnitude reconstructed diffusion-weighted images are confounded by the existence of a rectified noise floor, producing poor estimates of diffusion metrics. Herein, we present a simple method of rectified noise floor suppression that involves phase correction of the real data. This approach was evaluated for diffusion-weighted imaging data, obtained from ethanol and water phantoms and the brain of a healthy volunteer. The parameter fits from monoexponential, biexponential, and stretched-exponential diffusion models were computed using phase-corrected real data and magnitude data. The results demonstrate that this newly developed simple approach of using phase-corrected real images acts to reduce or even suppress the confounding effects of a rectified noise floor, thereby producing more accurate estimates of diffusion parameters.