Teichm\"uller's problem in space

Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a spatial analogue of a classical result due to Teichm\"uller. Unlike Teichm\"uller's result, our bounds are explicit. Explicit bounds are based on two sharp well-known distortion results: the quasiconformal Schwarz lemma and the bound for linear dilatation. Moreover, Bernoulli type inequalities and asymptotically sharp bounds for special functions involving complete elliptic integrals are applied to simplify the computations. Finally, we discuss the behavior of the quasihyperbolic metric under quasiconformal maps and prove a sharp result for quasiconformal maps of R^n \ {0} onto itself.Comment: 25 pages, 2 figure

Estimation of optimal number of gates in dual gated ¹⁸F-FDG cardiac PET

Gating of positron emission tomography images has been shown to reduce the motion effects, especially when imaging small targets, such as coronary plaques. However, the selection of optimal number of gates for gating remains a challenge. Selecting too high number of gates results in a loss of signal-to-noise ratio, while too low number of gates does remove only part of the motion. Here, we introduce a respiratory-cardiac motion model to determine the optimal number of respiratory and cardiac gates. We evaluate the model using a realistic heart phantom and data from 12 cardiac patients (47–77 years, 64.5 on average). To demonstrate the benefits of our model, we compared it with an existing respiratory model. Based on our study, the optimal number of gates was determined to be five respiratory and four cardiac gates in the phantom and patient studies. In the phantom study, the diameter of the most active hot spot was reduced by 24% in the dual gated images compared to non-gated images. In the patient study, the thickness of myocardium wall was reduced on average by 21%. In conclusion, the motion model can be used for estimating the optimal number of respiratory and cardiac gates for dual gating

Magnetic Resonance-Based Attenuation Correction and Scatter Correction in Neurological Positron Emission Tomography/Magnetic Resonance Imaging—Current Status With Emerging Applications

In this review, we will summarize the past and current state-of-the-art developments in attenuation and scatter correction approaches for hybrid positron emission tomography (PET) and magnetic resonance (MR) imaging. The current status of the methodological advances for producing accurate attenuation and scatter corrections on PET/MR systems are described, in addition to emerging clinical and research applications. Future prospects and potential applications that benefit from accurate data corrections to improve the quantitative accuracy and clinical applicability of PET/MR are also discussed. Novel clinical and research applications where improved attenuation and scatter correction methods are beneficial are highlighted

A Respiratory Motion Estimation Method Based on Inertial Measurement Units for Gated Positron Emission Tomography

We present a novel method for estimating respiratory motion using inertial measurement units (IMUs) based on microelectromechanical systems (MEMS) technology. As an application of the method we consider the amplitude gating of positron emission tomography (PET) imaging, and compare the method against a clinically used respiration motion estimation technique. The presented method can be used to detect respiratory cycles and estimate their lengths with state-of-the-art accuracy when compared to other IMU-based methods, and is the first based on commercial MEMS devices, which can estimate quantitatively both the magnitude and the phase of respiratory motion from the abdomen and chest regions. For the considered test group consisting of eight subjects with acute myocardial infarction, our method achieved the absolute breathing rate error per minute of 0.44 +/- 0.23 1/min, and the absolute amplitude error of 0.24 +/- 0.09 cm, when compared to the clinically used respiratory motion estimation technique. The presented method could be used to simplify the logistics related to respiratory motion estimation in PET imaging studies, and also to enable multi-position motion measurements for advanced organ motion estimation.</p

Predicting Skeletal Muscle and Whole-Body Insulin Sensitivity Using NMR-Metabolomic Profiling

Purpose: Abnormal lipoprotein and amino acid profiles are associated with insulin resistance and may help to identify this condition. The aim of this study was to create models estimating skeletal muscle and whole-body insulin sensitivity using fasting metabolite profiles and common clinical and laboratory measures.Material and Methods: The cross-sectional study population included 259 subjects with normal or impaired fasting glucose or type 2 diabetes in whom skeletal muscle and whole-body insulin sensitivity (M-value) were measured during euglycemic hyperinsulinemic clamp. Muscle glucose uptake (GU) was measured directly using [F-18]FDG-PET. Serum metabolites were measured using nuclear magnetic resonance (NMR) spectroscopy. We used linear regression to build the models for the muscle GU (Muscle-insulin sensitivity index [ISI]) and M-value (whole-body [WB]-ISI). The models were created and tested using randomly selected training (n = 173) and test groups (n = 86). The models were compared to common fasting indices of insulin sensitivity, homeostatic model assessment-insulin resistance (HOMA-IR) and the revised quantitative insulin sensitivity check index (QUICKI).Results: WB-ISI had higher correlation with actual M-value than HOMA-IR or revised QUICKI (rho = 0.83 vs -0.67 and 0.66; P < 0.05 for both comparisons), whereas the correlation of Muscle-ISI with the actual skeletal muscle GU was not significantly stronger than HOMA-IR's or revised QUICKI's (rho = 0.67 vs -0.58 and 0.59; both nonsignificant) in the test dataset.Conclusion: Muscle-ISI and WB-ISI based on NMR-metabolomics and common laboratory measurements from fasting serum samples and basic anthropometrics are promising rapid and inexpensive tools for determining insulin sensitivity in at-risk individuals. (C) Endocrine Society 2020

Periodic solutions for some phi-Laplacian and reflection equations

This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular initial and boundary value problems with reflection, which allows us to prove existence of solutions of the latter using the existence of the formerThe work was partially supported by FEDER and Ministerio de Economía y Competitividad, Spain, project MTM2013-43014-P. The second author was supported by FPU scholarship, Ministerio de Educación, Cultura y Deporte, Spain and Xunta de Galicia (Spain), project EM2014/032S