Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Comparison of physiological triggering schemes for diffusion-weighted magnetic resonance imaging in kidneys

To determine the potential benefit of combined respiratory-cardiac triggering for diffusion-weighted imaging (DWI) of kidneys compared to respiratory triggering alone (RT).

Evaluation of renal allograft function early after transplantation with diffusion-weighted MR imaging

To determine the inter-patient variability of apparent diffusion coefficients (ADC) and concurrent micro-circulation contributions from diffusion-weighted MR imaging (DW-MRI) in renal allografts early after transplantation, and to obtain initial information on whether these measures are altered in histologically proven acute allograft rejection (AR).

Predicting and monitoring cancer treatment response with diffusion-weighted MRI

An imaging biomarker that would provide for an early quantitative metric of clinical treatment response in cancer patients would provide for a paradigm shift in cancer care. Currently, nonimage based clinical outcome metrics include morphology, clinical, and laboratory parameters, however, these are obtained relatively late following treatment. Diffusion-weighted MRI (DW-MRI) holds promise for use as a cancer treatment response biomarker as it is sensitive to macromolecular and microstructural changes which can occur at the cellular level earlier than anatomical changes during therapy. Studies have shown that successful treatment of many tumor types can be detected using DW-MRI as an early increase in the apparent diffusion coefficient (ADC) values. Additionally, low pretreatment ADC values of various tumors are often predictive of better outcome. These capabilities, once validated, could provide for an important opportunity to individualize therapy thereby minimizing unnecessary systemic toxicity associated with ineffective therapies with the additional advantage of improving overall patient health care and associated costs. In this report, we provide a brief technical overview of DW-MRI acquisition protocols, quantitative image analysis approaches and review studies which have implemented DW-MRI for the purpose of early prediction of cancer treatment response.

Synthetic-echo time postprocessing technique for generating images with variable T2-weighted contrast: diagnosis of meniscal and cartilage abnormalities of the knee

To assess the feasibility and accuracy of a synthetic-echo time (TE) magnetic resonance (MR) postprocessing technique for the diagnostic evaluation of abnormalities of menisci and articular cartilage in the knee.

Diffusion-weighted imaging for the follow-up of patients after matrix-associated autologous chondrocyte transplantation

To evaluate the use of diffusion-weighted imaging (DWI) for the assessment of cartilage maturation in patients after matrix-associated autologous chondrocyte transplantation (MACT).

EPITHET: Positive Result After Reanalysis Using Baseline Diffusion-Weighted Imaging/Perfusion-Weighted Imaging Co-Registration

the Echoplanar Imaging Thrombolytic Evaluation Trial (EPITHET) was a prospective, randomized, double-blinded, placebo-controlled, phase II trial of alteplase between 3 and 6 hours after stroke onset. The primary outcome of infarct growth attenuation on MRI with alteplase in mismatch patients was negative when mismatch volumes were assessed volumetrically, without coregistration, which underestimates mismatch volumes. We hypothesized that assessing the extent of mismatch by coregistration of perfusion and diffusion MRI maps may more accurately allow the effects of alteplase vs placebo to be evaluated.

Susceptibility-weighted imaging of the brain: Does gadolinium administration matter?

Susceptibility-weighted MR imaging (SWI) is usually obtained without administration of intravenous gadolinium (Gd). However, it is occasionally necessary to perform SWI after Gd is injected. The effects of Gd on SWI have not been systematically examined. The aim of this prospective study was to investigate whether performing SWI after Gd would influence the diagnostic image quality, parenchymal signal and vascular enhancement. An additional aim is to suggest potential future applications for Gd-enhanced SWI.

Diffusion-weighted MR imaging of the placenta in fetuses with placental insufficiency

PURPOSE: To evaluate diffusion-weighted magnetic resonance (MR) imaging of the human placenta in fetuses with and fetuses without intrauterine growth restriction (IUGR) who were suspected of having placental insufficiency. MATERIALS AND METHODS: The study was approved by the local ethics committee, and written informed consent was obtained. The authors retrospectively evaluated 1.5-T fetal MR images from 102 singleton pregnancies (mean gestation ± standard deviation, 29 weeks ± 5; range, 21-41 weeks). Morphologic and diffusion-weighted MR imaging were performed. A region of interest analysis of the apparent diffusion coefficient (ADC) of the placenta was independently performed by two observers who were blinded to clinical data and outcome. Placental insufficiency was diagnosed if flattening of the growth curve was detected at obstetric ultrasonography (US), if the birth weight was in the 10th percentile or less, or if fetal weight estimated with US was below the 10th percentile. Abnormal findings at Doppler US of the umbilical artery and histopathologic examination of specimens from the placenta were recorded. The ADCs in fetuses with placental insufficiency were compared with those in fetuses of the same gestational age without placental insufficiency and tested for normal distribution. The t tests and Pearson correlation coefficients were used to compare these results at 5% levels of significance. RESULTS: Thirty-three of the 102 pregnancies were ultimately categorized as having an insufficient placenta. MR imaging depicted morphologic changes (eg, infarction or bleeding) in 27 fetuses. Placental dysfunction was suspected in 33 fetuses at diffusion-weighted imaging (mean ADC, 146.4 sec/mm(2) ± 10.63 for fetuses with placental insufficiency vs 177.1 sec/mm(2) ± 18.90 for fetuses without placental insufficiency; P < .01, with one false-positive case). The use of diffusion-weighted imaging in addition to US increased sensitivity for the detection of placental insufficiency from 73% to 100%, increased accuracy from 91% to 99%, and preserved specificity at 99%. CONCLUSION: Placental dysfunction associated with growth restriction is associated with restricted diffusion and reduced ADC. A decreased ADC used as an early marker of placental damage might be indicative of pregnancy complications such as IUGR.

Diffusion-weighted MR imaging of native and transplanted kidneys

Applications of diffusion-weighted (DW) magnetic resonance (MR) imaging outside the brain have gained increasing importance in recent years. Owing to technical improvements in MR imaging units and faster sequences, the need for noninvasive imaging without contrast medium administration, mainly in patients with renal insufficiency, can be met successfully by applying this technique. DW MR imaging is quantified by the apparent diffusion coefficient (ADC), which provides information on diffusion and perfusion simultaneously. By using a biexponential fitting process of the DW MR imaging data, these two entities can be separated, because this type of fitting process can serve as an estimate of both the perfusion fraction and the true diffusion coefficient. DW MR imaging can be applied for functional evaluation of the kidneys in patients with acute or chronic renal failure. Impairment of renal function is accompanied by a decreased ADC. Acute ureteral obstruction leads to perfusion and diffusion changes in the affected kidney, and renal artery stenosis results in a decreased ADC. In patients with pyelonephritis, diffuse or focal changes in signal intensity are seen on the high-b-value images, with increased signal intensity corresponding to low signal intensity on the ADC map. The feasibility and reproducibility of DW MR imaging in patients with transplanted kidneys have already been demonstrated, and initial results seem to be promising for the assessment of allograft deterioration. Overall, performance of renal DW MR imaging, presuming that measurements are of high quality, will further boost this modality, particularly for early detection of diffuse renal conditions, as well as more accurate characterization of focal renal lesions.

Diffusion-weighted MRI in head and neck radiology: applications in oncology

Extracranial application of diffusion-weighted magnetic resonance imaging (MRI) has gained increasing importance in recent years. As a result of technical advances, this new non-invasive functional technique has also been applied in head and neck radiology for several clinical indications. In cancer imaging, diffusion-weighted MRI can be performed for tumour detection and characterization, monitoring of treatment response as well as the differentiation of recurrence and post-therapeutic changes after radiotherapy. Even for lymph node staging promising results have been reported recently. This review article provides overview of potential applications of diffusion-weighted MRI in head and neck with the main focus on its applications in oncology.

Science to practice: Can diffusion-weighted MR imaging findings be used as biomarkers to monitor the progression of renal fibrosis?

In an experimental murine model of unilateral ureteral obstruction, Togao et al demonstrated that diffusion-weighted (DW) magnetic resonance (MR) imaging can depict and enable monitoring of abnormal changes in the progression of renal fibrosis; because these microstructural changes are complex and multifactorial, future studies focused on their specificity should be performed before they are applied in clinical trials.