Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Diffusion-weighted magnetic resonance imaging in metastatic gastrointestinal stromal tumor (GIST): a pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT.

BACKGROUND: Diffusion-weighted magnetic resonance imaging (MRI) is increasingly being used for assessing the treatment succes in oncology, but the real clinical value needs to evaluated by comparison with other, already established, metabolic imaging techniques. PURPOSE: To prospectively evaluate the clinical potential of diffusion-weighted MRI with apparent diffusion coefficient (ADC) mapping for gastrointestinal stromal tumor (GIST) response to targeted therapy compared with 18F-fluorodeoxyglucose positron emission tomography/computed tomography (18F-FDG PET/CT). MATERIAL AND METHODS: Eight patients (mean age, 56 ± 11 years) known to have metastatic GIST underwent 18F-FDG PET/CT and MRI (T1Gd, DWI [b = 50,300,600], ADC mapping) simultaneously, before and after change in targeted therapy. MR and PET/CT examinations were first analyzed blindly. Second, PET/CT images were co-registered with T1Gd-MR images for lesion detection. Only 18F-FDG avid lesions were considered. Maximum standardized uptake value (SUVmax) and the corresponding minimum ADCmin were measured for the six largest lesions per patient, if any, on baseline and follow-up examinations. The relationship between changes in SUVmax and ADCmin was analyzed (Spearman's correlation). RESULTS: Twenty-four metastases (12 hepatic, 12 extra-hepatic) were compared on PET/CT and MR images. SUVmax decreased from 7.7 ± 8.1 g/mL to 5.5 ± 5.4 g/mL (P = 0.20), while ADCmin increased from 1.2 ± 0.3 × 10(-3)mm(2)/s to 1.5 ± 0.3 × 10(-3)mm(2)/s (P = 0.0002). There was a significant association between changes in SUVmax and ADCmin (rho = - 0.62, P = 0.0014), but not between changes in lesions size (P = 0.40). CONCLUSION: Changes in ADCmin correlated with the response of 18F-FDG avid GIST to targeted therapy. Thus, diffusion-weighted MRI may represent a radiation-free alternative for follow-up treatment for metastatic GIST patients.

Assessment of liver tumor response by high-field (3T) MRI after radiofrequency ablation: Short- and mid-term evolution of diffusion parameters within the ablation zone.

PURPOSE: To compare the apparent diffusion coefficient (ADC) values of malignant liver lesions on diffusion-weighted MRI (DWI) before and after successful radiofrequency ablation (RF ablation). MATERIALS AND METHODS: Thirty-two patients with 43 malignant liver lesions (23/20: metastases/hepatocellular carcinomas (HCC)) underwent liver MRI (3.0T) before (<1month) and after RF ablation (at 1, 3 and 6months) using T2-, gadolinium-enhanced T1- and DWI-weighted MR sequences. Jointly, two radiologists prospectively measured ADCs for each lesion by means of two different regions of interest (ROIs), first including the whole lesion and secondly the area with the visibly most restricted diffusion (MRDA) on ADC map. Changes of ADCs were evaluated with ANOVA and Dunnett tests. RESULTS: Thirty-one patients were successfully treated, while one patient was excluded due to focal recurrence. In metastases (n=22), the ADC in the whole lesion and in MRDA showed an up-and-down evolution. In HCC (n=20), the evolution of ADC was more complex, but with significantly higher values (p=0.013) at 1 and 6months after RF ablation. CONCLUSION: The ADC values of malignant liver lesions successfully treated by RF ablation show a predictable evolution and may help radiologists to monitor tumor response after treatment.

Diffusion-weighted MRI in metastatic gastrointestinal tumors (GIST): A pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT

Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumor (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT. Methods and materials: Five patients (3W/2M, aged 56 ± 13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analyzed blindly, then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analyzed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analyzed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2 ± 7.7 g/mL to 5.9 ± 5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

Diffusion-weighted MRI in metastatic gastrointestinal tumours (GIST): a pilot study on the assessment of treatment response in comparison with 18 F-FDG PET/CT

Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumour (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT Methods and Materials: Five patients (3 W/2M, aged 56±13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analysed blindly and then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analysed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analysed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2±7.7 g/mL to 5.9±5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

Functional MRI evaluation of liver tumour response after radiofrequency: short- and mid-term evolution of diffusion parameters

Purpose: To evaluate the short- and mid-term evolutions of the apparent diffusion coefficient of lesions treated with RF, in order to determine if the ADC can be used as a marker of tumour response. Methods and Materials: Twenty patients were treated for a liver malignancy with RF and were examined on a 1.5 T/3.0 T machine with T2, gadolinium-enhanced T1 and diffusion sequences: before treatment (< 1 month), just after treatment (< 1 month) and midterm (3-6 months). The ADC was measured in the whole lesion and in the area with the most restricted diffusion (MRDA). The ROI size was also measured on the diffusion map. The Pearson/ANOVA tests were used. Results: All patients were successfully treated with complete disappearance of CE. The lesional size on T2 showed a negative evolution in time (p < 0.002). The ADC in the whole lesion showed a bell-shaped evolution (increasing just after RF, then decreasing, p = 0.02). The ROI size on the diffusion map followed a similar course (p = 0.01). For the MRDA, such evolutions were also found, but they were not significant. There was a negative correlation between CE and the ADC (p < 0.02) and between the lesional size on T2 and ADC (p = 0.03) in the whole lesion. There were also positive correlations between the ROI size and ADC (p = 0.0008) and between CE and the size on T2 (p = 0.0002). The ADC in MRDA showed some non-significant correlations with other variables. Conclusion: The lesions successfully treated with RF have a clear and predictable evolution in terms of T2 size, CE and ADC.

High b-value diffusion-weighted imaging: A sensitive method to reveal white matter differences in schizophrenia.

Over the last 10 years, diffusion-weighted imaging (DWI) has become an important tool to investigate white matter (WM) anomalies in schizophrenia. Despite technological improvement and the exponential use of this technique, discrepancies remain and little is known about optimal parameters to apply for diffusion weighting during image acquisition. Specifically, high b-value diffusion-weighted imaging known to be more sensitive to slow diffusion is not widely used, even though subtle myelin alterations as thought to happen in schizophrenia are likely to affect slow-diffusing protons. Schizophrenia patients and healthy controls were scanned with a high b-value (4000s/mm(2)) protocol. Apparent diffusion coefficient (ADC) measures turned out to be very sensitive in detecting differences between schizophrenia patients and healthy volunteers even in a relatively small sample. We speculate that this is related to the sensitivity of high b-value imaging to the slow-diffusing compartment believed to reflect mainly the intra-axonal and myelin bound water pool. We also compared these results to a low b-value imaging experiment performed on the same population in the same scanning session. Even though the acquisition protocols are not strictly comparable, we noticed important differences in sensitivities in the favor of high b-value imaging, warranting further exploration.

Diffusion tensor imaging shows structural remodeling of stroke mirror region: results from a pilot study.

Background: The role of the non-injured hemisphere in stroke recovery is poorly understood. In this pilot study, we sought to explore the presence of structural changes detectable by diffusion tensor imaging (DTI) in the contralesional hemispheres of patients who recovered well from ischemic stroke. Methods: We analyzed serial DTI data from 16 stroke patients who had moderate initial neurological deficits (NIHSS scores 3-12) and good functional outcome at 3-6 months (NIHSS score 0 or modified Rankin Score ≤1). We segmented the brain tissue in gray and white matter (GM and WM) and measured the apparent diffusion coefficient (ADC) and fractional anisotropy in the infarct, in the contralesional infarct mirror region as well as in concentrically expanding regions around them. Results: We found that GM and WM ADC significantly increased in the infarct region (p < 0.01) from acute to chronic time points, whereas in the infarct mirror region, GM and WM ADC increased (p < 0.01) and WM fractional anisotropy decreased (p < 0.05). No significant changes were detected in other regions. Conclusion: DTI-based metrics are sensitive to regional structural changes in the contralesional hemisphere during stroke recovery. Prospective studies in larger cohorts with varying levels of recovery are needed to confirm our findings.

Hepatic hemangiomas: Factors associated with T2 shine-through effect on diffusion-weighted MR sequences.

PURPOSE: To determine the frequency and factors associated with the presence of T2 shine-through effect in hepatic hemangiomas on diffusion-weighted (DW) magnetic resonance (MR) sequences. MATERIALS AND METHODS: This retrospective study was approved by institutional review board with waiver of informed consent. One hundred forty-nine consecutive patients with 388 hepatic hemangiomas who underwent a liver MR between January 2010 and November 2011 were included. MR analysis evaluated the lesion characteristics (signal intensities and enhancement patterns (classical, rapidly filling, delayed filling)), the presence of T2 shine-through effect on DW sequences (b values of 0, 150, and 600s/mm(2)), and apparent diffusion coefficient (ADC) values. Multivariate analysis was performed to study the factors associated with the T2 shine-through effect. RESULTS: T2 shine-through effect was observed in 204/388 (52.6%) of hepatic hemangiomas and in 100 (67.1%) patients. Mean ADC value of hemangiomas with T2 shine-through effect was significantly lower than hemangiomas without (2.0±0.48 vs 2.38±0.45, P<.0001). On multivariate analysis, high signal intensity on fat-suppressed T2-weighted fast spin-echo images, hemangiomas with classical or delayed enhancement, and the ADC of the liver were the only significant factors associated with T2 shine-through effect. CONCLUSION: T2 shine-through effect is commonly observed in hepatic hemangiomas and is related to hemangiomas characteristics. Radiologists should be aware of this phenomenon which could lead to misdiagnosis. Its presence should not question the diagnosis of hemangiomas when typical MR findings are found.

High b-value Diffusion-weighted Imaging: A Sensitive Method to Reveal White Matter Changes in Schizophrenia

Background: b-value is the parameter characterizing the intensity of the diffusion weighting during image acquisition. Data acquisition is usually performed with low b value (b~1000 s/mm2). Evidence shows that high b-values (b>2000 s/mm2) are more sensitive to the slow diffusion compartment (SDC) and maybe more sensitive in detecting white matter (WM) anomalies in schizophrenia.Methods: 12 male patients with schizophrenia (mean age 35 +/-3 years) and 16 healthy male controls matched for age were scanned with a low b-value (1000 s/mm2) and a high b-value (4000 s/mm2) protocol. Apparent diffusion coefficient (ADC) is a measure of the average diffusion distance of water molecules per time unit (mm2/s). ADC maps were generated for all individuals. 8 region of interests (frontal and parietal region bilaterally, centrum semi-ovale bilaterally and anterior and posterior corpus callosum) were manually traced blind to diagnosis.Results: ADC measures acquired with high b-value imaging were more sensitive in detecting differences between schizophrenia patients and healthy controls than low b-value imaging with a gain in significance by a factor of 20- 100 times despite the lower image Signal-to-noise ratio (SNR). Increased ADC was identified in patient's WM (p=0.00015) with major contributions from left and right centrum semi-ovale and to a lesser extent right parietal region.Conclusions: Our results may be related to the sensitivity of high b-value imaging to the SDC believed to reflect mainly the intra-axonal and myelin bound water pool. High b-value imaging might be more sensitive and specific to WM anomalies in schizophrenia than low b-value imaging

Characterizing the connectome in schizophrenia with diffusion spectrum imaging.

Schizophrenia is a complex psychiatric disorder characterized by disabling symptoms and cognitive deficit. Recent neuroimaging findings suggest that large parts of the brain are affected by the disease, and that the capacity of functional integration between brain areas is decreased. In this study we questioned (i) which brain areas underlie the loss of network integration properties observed in the pathology, (ii) what is the topological role of the affected regions within the overall brain network and how this topological status might be altered in patients, and (iii) how white matter properties of tracts connecting affected regions may be disrupted. We acquired diffusion spectrum imaging (a technique sensitive to fiber crossing and slow diffusion compartment) data from 16 schizophrenia patients and 15 healthy controls, and investigated their weighted brain networks. The global connectivity analysis confirmed that patients present disrupted integration and segregation properties. The nodal analysis allowed identifying a distributed set of brain nodes affected in the pathology, including hubs and peripheral areas. To characterize the topological role of this affected core, we investigated the brain network shortest paths layout, and quantified the network damage after targeted attack toward the affected core. The centrality of the affected core was compromised in patients. Moreover the connectivity strength within the affected core, quantified with generalized fractional anisotropy and apparent diffusion coefficient, was altered in patients. Taken together, these findings suggest that the structural alterations and topological decentralization of the affected core might be major mechanisms underlying the schizophrenia dysconnectivity disorder. Hum Brain Mapp, 36:354-366, 2015. © 2014 Wiley Periodicals, Inc.

Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond.

The complex structural organization of the white matter of the brain can be depicted in vivo in great detail with advanced diffusion magnetic resonance (MR) imaging schemes. Diffusion MR imaging techniques are increasingly varied, from the simplest and most commonly used technique-the mapping of apparent diffusion coefficient values-to the more complex, such as diffusion tensor imaging, q-ball imaging, diffusion spectrum imaging, and tractography. The type of structural information obtained differs according to the technique used. To fully understand how diffusion MR imaging works, it is helpful to be familiar with the physical principles of water diffusion in the brain and the conceptual basis of each imaging technique. Knowledge of the technique-specific requirements with regard to hardware and acquisition time, as well as the advantages, limitations, and potential interpretation pitfalls of each technique, is especially useful.

Long-term monitoring of post-stroke plasticity after transient cerebral ischemia in mice using in vivo and ex vivo diffusion tensor MRI.

WE USED A MURINE MODEL OF TRANSIENT FOCAL CEREBRAL ISCHEMIA TO STUDY: 1) in vivo DTI long-term temporal evolution of the apparent diffusion coefficient (ADC) and diffusion fractional anisotropy (FA) at days 4, 10, 15 and 21 after stroke 2) ex vivo distribution of a plasticity-related protein (GAP-43) and its relationship with the ex vivo DTI characteristics of the striato-thalamic pathway (21 days). All animals recovered motor function. In vivo ADC within the infarct was significantly increased after stroke. In the stroke group, GAP-43 expression and FA values were significantly higher in the ipsilateral (IL) striatum and contralateral (CL) hippocampus compared to the shams. DTI tractography showed fiber trajectories connecting the CL striatum to the stroke region, where increased GAP43 and FA were observed and fiber tracts from the CL striatum terminating in the IL hippocampus.Our data demonstrate that DTI changes parallel histological remodeling and recovery of function.

Diffusion-weighted MR imaging in musculoskeletal diseases: Current concepts.

MR imaging is currently regarded as a pivotal technique for the assessment of a variety of musculoskeletal conditions. Diffusion-weighted MR imaging (DWI) is a relatively recent sequence that provides information on the degree of cellularity of lesions. Apparent diffusion coefficient (ADC) value provides information on the movement of water molecules outside the cells. The literature contains many studies that have evaluated the role of DWI in musculoskeletal diseases. However, to date they yielded conflicting results on the use and the diagnostic capabilities of DWI in the area of musculoskeletal diseases. However, many of them have showed that DWI is a useful technique for the evaluation of the extent of the disease in a subset of musculoskeletal cancers. In terms of tissue characterization, DWI may be an adjunct to the more conventional MR imaging techniques but should be interpreted along with the signal of the lesion as observed on conventional sequences, especially in musculoskeletal cancers. Regarding the monitoring of response to therapy in cancer or inflammatory disease, the use of ADC value may represent a more reliable additional tool but must be compared to the initial ADC value of the lesions along with the knowledge of the actual therapy.

Diffusion-weighted magnetic resonance imaging: biomarker for treatment response in oncology

The authors report a case where a quantitative assessment of the apparent diffusion coefficient (ADC) of liver metastasis in a patient undergoing chemotherapy has shown to be an effective early marker for predicting therapeutic response, anticipating changes in tumor size. A lesion with lower initial ADC value and early increase in such value in the course of the treatment tends to present a better therapeutic response.