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Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scales. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. We provide a unified view of ideas from data analysis, machine learning, and numerical analysis.

Journal Article↗

Time-fractional diffusion equation with time dependent diffusion coefficient.

We consider the time-fractional diffusion equation with time dependent diffusion coefficient given by (O)O(alpha)(C)(t) W (x,t) = D(alpha,gamma)(t)(gamma) [theta(2) W (x,t) /theta x(2)], where O is the Caputo operator. We investigate its solutions in the infinite and the finite domains. The mean squared displacement and the mean first passage time are also considered. In particular, for alpha = 0 , the mean squared displacement is given by approximately t(gamma) and we verify that the mean first passage time is finite for superdiffusive regimes.

Journal Article↗

Diffusion and thermal diffusion of semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition.

The approaching glass transition in polystyrene/toluene solutions leads to a sharp decay of both the collective diffusion coefficient D and the thermal diffusion coefficient D(T) at concentrations above 0.2 g/cm(3). The Soret coefficient S(T) = D(T)/D follows power-law scaling from semidilute to concentrated and is not influenced by the slowing down of the dynamics associated with the glass transition. Both D and D(T) are governed by the same friction coefficient. The scaling behavior of S(T) with concentration on approach of the glass transition is compared to the divergence of S(T) near a consolute critical point.

Journal Article↗

Does reversal of ischemia on diffusion-weighted imaging reflect higher apparent diffusion coefficient values?

This study investigated whether ischemia on diffusion-weighted imaging (DWI) that reverses has higher apparent diffusion coefficients (ADCs). A patient treated with thrombolytics was evaluated with serial magnetic resonance imaging studies before treatment, at 3 and 14 days and at 4 weeks. A 100.01-cm3 left frontoparietal stroke on baseline DWI was only 18.11 cm3 (18%) on 4-week fluid attenuated inversion recovery. The mean ADC was 7.43 x 10(-3) mm2/s in the 6 regions that reversed and 7.31 x 10(-3) mm2/s in the 6 regions that persisted (P < .036). With thrombolytic treatment, large ischemic lesions on DWI may reverse, and these areas display higher mean ADCs.

Brain Ischemia↗

Ofloxacin susceptibility testing quality control parameters for microdilution and disk diffusion, and confirmation of disk diffusion interpretive criteria.

The susceptibilities of 221 clinical isolates to ofloxacin were tested simultaneously by broth microdilution and disk diffusion methods with commercially prepared 5-micrograms ofloxacin disks. The acceptability of the following previously proposed zone diameter breakpoints was confirmed: greater than or equal to 16 mm, susceptible; 13 to 15 mm, intermediate; less than or equal to 12 mm, resistant. On the basis of a multilaboratory collaborative study, the following are proposed as acceptable ofloxacin MIC ranges for quality control organisms: Escherichia coli ATCC 25922, 0.03 to 0.06 micrograms/ml; Staphylococcus aureus ATCC 29213, 0.12 to 0.5 micrograms/ml; Pseudomonas aeruginosa ATCC 27853 and Enterococcus faecalis ATCC 29212, 1.0 to 4.0 micrograms/ml. Ofloxacin quality control zone diameter ranges for the disk diffusion test are tentatively proposed, but variations in the performance of different lots of Mueller-Hinton agar may prove to be a serious problem for users.

Bacteria↗

Salivary glands and lesions: evaluation of apparent diffusion coefficients with split-echo diffusion-weighted MR imaging--initial results.

The authors investigated the feasibility of performing diffusion-weighted (DW) magnetic resonance (MR) imaging with split acquisition of fast spin-echo signals (hereafter, split echo) for the assessment of salivary glands and salivary lesions. Eighteen patients without salivary disease and 10 patients with Sjögren syndrome, chronic parotitis, or focal salivary masses underwent split-echo and echo-planar DW MR imaging. DW MR images and apparent diffusion coefficient maps of the salivary gland had higher quality with split-echo rather than with echo-planar DW MR imaging.

Adult↗

Sensitivity of magnetic resonance diffusion-weighted imaging and regional relationship between the apparent diffusion coefficient and cerebral blood flow in rat focal cerebral ischemia.

BACKGROUND AND PURPOSE: Magnetic resonance (MR) diffusion-weighted imaging (DWI), a noninvasive procedure, may play an important role in detecting and accurately localizing the extent of evolving infarction within the period immediately following stroke. We evaluated the sensitivity and specificity of DWI in detecting ischemia and compared a quantitative measure derived from the DWI, the apparent diffusion coefficient (ADC), with autoradiographic cerebral blood flow (CBF) in an experimental model of focal cerebral ischemia in rats. METHODS: MR imaging data were obtained with a General Electric 4.7-T horizontal bore magnet CSI II system with self-shielded gradients. DWI was acquired within 41 +/- 6 minutes (mean +/- SD) after onset of ischemia and repeated at 169 +/- 14 minutes, followed by CBF determination at 237 +/- 21 minutes. DWI, ADC, and CBF images from each animal were then compared. RESULTS: The sensitivities for detecting an abnormality at 1 and 3 hours for DWI were significantly different, and the sensitivity of 3-hour DWI did not differ from the CBF sensitivity of 99%. A mean +/- SD ADC threshold of 460 +/- 95 microns 2/s was defined as 45% higher than the low ADC in the ischemic core compared with the contralateral ADC. Subthreshold ADC area and ischemic area were significantly correlated (r2 = .69, P < .05). In 19 of 48 regions of interest classified as ischemic (< 35 mL.100 g-1.min-1) from both the 3-hour ADC and CBF images, 3-hour ADC correlated significantly with CBF (r2 = .27, n = 19, P < .05), whereas in the nonischemic regions ADC was inversely correlated with CBF. Several ischemic regions showed a sharp drop in ADC to 37% (P < .001, n = 5) compared with all other regions (n = 43) from 1 to 3 hours. CONCLUSIONS: Because of the change in the sensitivity of detecting ischemia with DWI, the difference in correlation of CBF with ADC between ischemic and nonischemic cortex, and the presence of several regions in which ADC dropped to 37% from 1 to 3 hours, our data suggest that ADC values potentially can be used to monitor evolving infarction.

Animals↗

Treatment of diffuse histiocytic and diffuse mixed non-Hodgkin lymphomas with cyclophosphamide, doxorubicin, vincristine and prednisone (CHOP).

During 1977 to 1985 90 patients with large-cell non-Hodgkin lymphoma (diffuse histiocytic or diffuse mixed according to Rapport classification) were treated by the CHOP regimen (cyclophosphamide, doxorubicin, vincristine and prednisone) with a mean follow-up of 41 months. Thirty-four patients were treated with radiation therapy as well. The mean number of CHOP cycles to achieve complete response was 4.0 and the mean total number of cycles was 6.6. For 78 patients it was possible to calculate relative dose intensity (RDI) for each drug and the average RDI. Sixty-four patients (71%) achieved CR. The actuarial 5-year survival rate of all patients was 52%. The median RDI for cyclophosphamide was 0.72, for doxorubicin 0.70, for vincristine 0.69 and the median average RDI was 0.69. The following favorable prognostic factors were found to be of statistical significance: female sex and stages I-III as compared to stage IV. The 5-year survival rate for stage I & II patients treated by CHOP plus radiotherapy was 70% as compared to 55% for those treated by CHOP only; this difference was not statistically significant.

Adolescent↗

Diffuse parenchymal amyloidosis of lungs and breast. Its association with diffuse plasmacytosis and kappa-chain gammopathy.

A patient had systemic amyloidosis that extensively involved the lungs and breasts. Diffuse parenchymal pulmonary amyloidosis is rare but well described. Involvement of the breast in systemic amyloidosis is, however, most unusual. This patient's amyloidosis was associated with diffuse plasmacytosis and a kappa-chain gammopathy. The plasmacytosis was most prominent in the renal interstitium. Immunoperoxidase staining of the renal infiltrate and breast demonstrated IgG/kappa-staining plasma cells exclusively, suggesting that these cells were a monoclonal proliferation that contributed to the patient's M-protein and possibly to the patient's amyloid deposits.

Amyloidosis↗

Tumor extension in high-grade gliomas assessed with diffusion magnetic resonance imaging: values and lesion-to-brain ratios of apparent diffusion coefficient and fractional anisotropy.

PURPOSE: To determine whether the apparent diffusion coefficient (ADC) and fractional anisotropy (FA) can distinguish tumor-infiltrated edema in gliomas from pure edema in meningiomas and metastases. MATERIAL AND METHODS: Thirty patients were studied: 18 WHO grade III or IV gliomas, 7 meningiomas, and 5 metastatic lesions. ADC and FA were determined from ROIs placed in peritumoral areas with T2-signal changes, adjacent normal appearing white matter (NAWM), and corresponding areas in the contralateral healthy brain. Values and lesion-to-brain ratios from gliomas were compared to those from meningiomas and metastases. RESULTS: Values and lesion-to-brain ratios of ADC and FA in peritumoral areas with T2-signal changes did not differ between gliomas, meningiomas, and metastases (P = 0.40, P = 0.40, P = 0.61, P = 0.34). Values of ADC and FA and the lesion-to-brain ratio of FA in the adjacent NAWM did not differ between tumor types (P = 0.74, P = 0.25, and P = 0.31). The lesion-to-brain ratio of ADC in the adjacent NAWM was higher in gliomas than in meningiomas and metastases (P = 0.004), but overlapped between tumor types. CONCLUSION: Values and lesion-to-brain ratios of ADC and FA in areas with T2-signal changes surrounding intracranial tumors and adjacent NAWM were not helpful for distinguishing pure edema from tumor-infiltrated edema when data from gliomas, meningiomas, and metastases were compared.

Adult↗

Comparison of carbon monoxide (CO) single breath pulmonary diffusing capacity with non-rebreathing, open-circuit CO pulmonary diffusing capacity in healthy children.

INTRODUCTION: The standard technique for assessing pulmonary diffusing capacity of the lungs (DL) for carbon monoxide (CO) is the single breath (SB) technique. SB_DLco in children can be problematic because it requires a vital capacity >1.5 L. We have developed an open-circuit technique (OC), which uses the wash-in of CO over a series of 8-10 normal breaths that does not require rebreathing. In this study, we compared the SB_DLco against the OC_DLco. METHODS: Nineteen healthy children between 7 and 18 years performed SB_DLco and OC_DLco tests. The mean SB_DLco was significantly larger than the mean OC_DLco. The mean difference OC_DLco minus SB_ DLco was: -2.92 +/- 4.21 ml/min/mm Hg, though the difference was negatively correlated with the mean of the two (r = 0.73). The lower mean OC_DLco was in part due to lower lung volume (as measured by alveolar volume (VA)) during the maneuver. In both groups there was a positive correlation between VA and DLco, and the mean VA was -2.17 +/- 1.07 L lower using OC compared to SB. The difference was again negatively correlated with the mean (r = 0.82). The mean OC minus SB difference in DLco/VA was: 6.06 +/- 1.98 ml/min/mm Hg/L, though this difference was positively correlated with the mean, r = 0.76. CONCLUSIONS: We found a good correlation between both techniques for DLco, VA, and DLco/VA. The OC offers the advantage of minimal subject cooperation, and may be preferable to use in children.

Adolescent↗

When a diffusible axon guidance cue stops diffusing: roles for netrins in adhesion and morphogenesis.

Netrins are a small family of secreted proteins that are best known for their role as secreted long-range chemotropic guidance cues. Extracellular gradients of netrin protein, established by diffusion, are thought to direct cell and axon migration during neural development. In addition to this long-range role, recent findings provide increasing support for short-range functions, in which secreted netrin protein remains closely associated with its cellular source. Emerging evidence for short-range actions of netrins suggests that they contribute to tissue morphogenesis by regulating cell-cell and cell-matrix adhesion.

Animals↗

Evolution of regional changes in apparent diffusion coefficient during focal ischemia of rat brain: the relationship of quantitative diffusion NMR imaging to reduction in cerebral blood flow and metabolic disturbances.

Middle cerebral artery occlusion was performed in rats while the animals were inside the nuclear magnetic resonance (NMR) tomograph. Successful occlusion was confirmed by the collapse of amplitude on an electrocorticogram. The ultrafast NMR imaging technique UFLARE was used to measure the apparent diffusion coefficient (ADC) immediately after the induction of cerebral ischemia. ADC values of normal cortex and caudate-putamen were 726 +/- 22 x 10(-6) mm2/s and 659 +/- 17 x 10(-6) mm2/s, respectively. Within minutes of occlusion, a large territory with reduced ADC became visible in the ipsilateral hemisphere. Over the 2 h observation period, this area grew continuously. Quantitative analysis of the ADC reduction in this region showed a gradual ADC decrease from the periphery to the core, the lowest ADC value amounting to about 60% of control. Two hours after the onset of occlusion, the regional distribution of ATP and tissue pH were determined with bioluminescence and fluorescence techniques, respectively. There was a depletion of ATP in the core of the ischemic territory (32 +/- 20% of the hemisphere) and an area of tissue acidosis (57 +/- 19% of the hemisphere) spreading beyond that of ATP depletion. Regional CBF (rCBF) was measured autoradiographically with the iodo[14C]antipyrine method. CBF gradually decreased from the periphery to the ischemic core, where it declined to values as low as 5 ml 100 g-1. When reductions in CBF and in ADC were matched to the corresponding areas of energy breakdown and of tissue acidosis, the region of energy depletion corresponded to a threshold in rCBF of 18 +/- 14 ml 100 g-1 min-1 and to an ADC reduction to 77 +/- 3% of control. Tissue acidosis corresponded to a flow value below 31 +/- 11 ml 100 g-1 min-1 and to an ADC value below 90 +/- 4% of control. Thus, the quantification of ADC in the ischemic territory allows the distinction between a core region with total breakdown of energy metabolism and a corona with normal energy balance but severe tissue acidosis.

Adenosine Triphosphate↗

Diffuse-diffuse photon coupling via nonscattering void in the presence of refractive index mismatch on the void boundary.

It is well established that the diffusion approximation (DA) is valid for light propagation in highly scattering media, but it breaks down in nonscattering void regions. The methods that handle the void with refractive index matched boundary were previously developed. For the void with refractive index mismatched boundary, no theory is yet available. We derived the finite element method that can handle the void problem with refractive index mismatch on its boundary. The method uses the ray tracing to account for the multiple reflections of rays within the void due to refractive index mismatch on the void boundary. We applied the method to the four-layer adult head model and the good agreements with Monte Carlo simulation results were found in the mean time of flight data.

Algorithms↗

Effects of hemodialysis and anemia on pulmonary diffusing capacity, membrane diffusing capacity and capillary blood volume in uremic patients.

The study aimed at investigating pulmonary function in uremic patients, emphasizing the lung diffusing capacity for CO (DLCO) and its membrane and pulmonary capillary blood volume (Vc) components. The study sample comprised 25 uremic patients without clinical/radiological evidence of lung disease. They were enrolled in a chronic hemodialysis (HD) program and had anemia requiring transfusions. The subjects were tested for their lung function before and after both a first HD and a HD with blood transfusion (BT) that followed a few days later. After HD-induced removal of body fluid, and increase in pre-HD reduced forced vital capacity, alveolar volume and mid-expiratory flow rate (FEF25-75%) was observed. HD-induced DLCO decrease (p less than 0.005) was observed and was related to decreased Vc. The second HD with BT increased DLCO, due to partially normalized Hb. On average, a 7.2% DLCO increase corresponded to each 10-g/l Hb rise. In conclusion, (1) the beneficial effect of HD in uremic patients reverts the small-airway obstruction; (2) the lower values of DLCO in these patients are due to reduced Hb and HD causes further DLCO reduction via decrease of Vc, and (3) HD with BT still increases DLCO because improvement of Hb predominates.

Adult↗

CT and diffusion-weighted MR imaging in randomized order: diffusion-weighted imaging results in higher accuracy and lower interrater variability in the diagnosis of hyperacute ischemic stroke.

BACKGROUND AND PURPOSE: Diffusion-weighted MRI (DWI) has become a commonly used imaging modality in stroke centers. The value of this method as a routine procedure is still being discussed. In previous studies, CT was always performed before DWI. Therefore, infarct progression could be a reason for the better result in DWI. METHODS: All hyperacute (<6 hours) stroke patients admitted to our emergency department with a National Institutes of Health Stroke Scale (NIHSS) score >3 were prospectively randomized for the order in which CT and MRI were performed. Five stroke experts and 4 residents blinded to clinical data judged stroke signs and lesion size on the images. To determine the interrater variability, we calculated kappa values for both rating groups. RESULTS: A total of 50 patients with ischemic stroke and 4 patients with transient symptoms of acute stroke (median NIHSS score, 11; range, 3 to 27) were analyzed. Of the 50 patients, 55% were examined with DWI first. The mean delay from symptom onset until CT was 180 minutes; that from symptom onset until DWI was 189 minutes. The mean delay between DWI and CT was 30 minutes. The sensitivity of infarct detection by the experts was significantly better when based on DWI (CT/DWI, 61/91%). Accuracy was 91% when based on DWI (CT, 61%). Interrater variability of lesion detection was also significantly better for DWI (CT/DWI, kappa=0.51/0.84). The assessment of lesion extent was less homogeneous on CT (CT/DWI, kappa=0.38/0.62). The differences between the 2 modalities were stronger in the residents' ratings (CT/DWI: sensitivity, 46/81%; kappa=0.38/0.76). CONCLUSIONS: CT and DWI performed with the same delay after onset of ischemic stroke resulted in significant differences in diagnostic accuracy. DWI gives good interrater homogeneity and has a substantially better sensitivity and accuracy than CT even if the raters have limited experience.

Acute Disease↗

Incidence of diffuse large B-cell lymphoma of germinal center B-cell origin in whole diffuse large B-cell lymphoma: tissue fluorescence in situ hybridization using t(14;18) compared with immunohistochemistry.

Diffuse large B-cell lymphoma (DLBCL) can be divided into prognostically important categories such as germinal center B (GCB)-like and non-GCB-like groups. The t(14;18)(q32;q21) translocation defines a unique subset of DLBCL cases with a GCB gene expression profile. Two-color fluorescence in situ hybridization (FISH) analysis was applied to detect t(14;18) (q32;q21) in the nuclei of paraffin-embedded tissue sections from 61 patients with de novo DLBCL. Nine (15%) of 61 cases had a positive pattern. Fifty-seven cases were subclassified in an immunohistochemical study with anti-CD10, anti-bcl-6, and anti-MUM1 antibodies. In this classification, 21 cases (37%) were placed in the GCB group, and 36 (63%) were placed in the non-GCB group. There was a discrepancy between t(14;18) occurrence and bcl-2 protein expression. Bcl-2 protein expression was positive in 40 (67%) of 60 cases. The expression of bcl-2 protein in the GCB and non-GCB groups was not significantly different: 15 (71%) of 21 cases in the GCB group and 24 (67%) of 36 cases in the non-GCB group tested positive. We found no difference between the FISH-positive and FISH-negative groups in overall survival time (P = .6019, log-rank test). The overall survival rates of GCB and non-GCB groups did not differ significantly by immunohistochemical classification (P = .5399, log-rank test). Overall survival was significantly longer in the group with a low International Prognostic Index (IPI) score than in the group with a high IPI score (P = .0002, log-rank test). Our results suggest that immunohistochemical study and cytogenetic study with t(14;18) FISH cannot predict the clinical outcomes of DLBCL patients. A study with a larger number of patients may show a difference in clinical outcomes between FISH-positive and FISH-negative groups and between GCB and non-GCB groups.

Adult↗

Effect of hydrophilic components of the extracellular matrix on quantifiable diffusion-weighted imaging of human gliomas: preliminary results of correlating apparent diffusion coefficient values and hyaluronan expression level.

OBJECTIVE: The purpose of this study was to evaluate the relationship between apparent diffusion coefficient (ADC) measured by MR imaging and the level of immunohistochemical expression of hyaluronan or hyaluronic acid as one of the main hydrophilic components of the extracellular matrix in brain glial tumors. MATERIALS AND METHODS: Nineteen patients with primary glial brain tumors were included in the study. Mean ADC values were calculated in all tumors and were normalized with the ADC values of the contralateral normal-appearing brain ratios. All tumors underwent surgical resection, and the histologic diagnosis was based on the analysis of the surgical specimen. Mean values of the labeling index of hyaluronan (LI-HA) were calculated to determine quantifiably the histochemical expression of hyaluronan in the tumor. The mean ADC values and the mean ADC ratios (ADC(ratio)) of the tumors were then correlated to the mean values of the LI-HA. RESULTS: The mean ADC (93 x 10(-5) mm(2)/sec) and the mean ADC(ratio) (1.25) of the high-grade glial tumors were significantly lower than the mean ADC (123 x 10(-5) mm/sec) and the mean ADC(ratio) (1.64) of the low-grade glial tumors (p < 0.01). The mean LI-HA (72.8%) was also significantly lower in the high-grade gliomas than the mean LI-HA (93.4%) in the low-grade gliomas (p < 0.001). A positive correlation was found between mean ADC values and the mean LI-HA (tau = 0.35, p < 0.05) and also between the mean ADC(ratio) and the mean LI-HA (tau = 0.33, p < 0.05). CONCLUSION: Hyaluronan as one of the main hydrophilic components of the extracellular matrix in gliomas likely contributes to differences in the ADC values between high- and low-grade glial tumors.

Brain↗