Group Analysis of Nonlinear Fin Equations

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of truly nonlinear equations for the class under consideration. Nonclassical symmetries of the fin equations are discussed. Adduced results amend and essentially generalize recent works on the subject [M. Pakdemirli and A.Z. Sahin, Appl. Math. Lett., 2006, V.19, 378-384; A.H. Bokhari, A.H. Kara and F.D. Zaman, Appl. Math. Lett., 2006, V.19, 1356-1340].Comment: 6 page

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

Optimized breath detection algorithm in electrical impedance tomography

This paper defines a method for optimizing the breath delineation algorithms used in Electrical Impedance Tomography (EIT). In lung EIT the identification of the breath phases is central for generating tidal impedance variation images, subsequent data analysis and clinical evaluation. The optimisation of these algorithms is particularly important in neonatal care since the existing breath detectors developed for adults may give insufficient reliability in neonates due to their very irregular breathing pattern. Our approach is generic in the sense that it relies on the definition of a gold standard and the associated definition of detector sensitivity and specificity, an optimisation criterion and a set of detector parameters to be investigated. The gold standard has been defined by 11 clinicians with previous experience with EIT and the performance of our approach is described and validated using a neonatal EIT dataset acquired within the EU-funded CRADL project. Three different algorithms are proposed that are improving the breath detector performance by adding conditions on 1) maximum tidal breath rate obtained from zero-crossings of the EIT breathing signal, 2) minimum tidal impedance amplitude and 3) minimum tidal breath rate obtained from Time-Frequency (TF) analysis. As a baseline the zero crossing algorithm has been used with some default parameters based on the Swisstom EIT device. Based on the gold standard, the most crucial parameters of the proposed algorithms are optimised by using a simple exhaustive search and a weighted metric defined in connection with the Receiver Operating Characterics (ROC). This provides a practical way to achieve any desirable trade-off between the sensitivity and the specificity of the detectors. [Abstract copyright: © 2018 Institute of Physics and Engineering in Medicine.

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

Clinical performance of a novel textile interface for neonatal chest electrical impedance tomography

Objective: Critically ill neonates and infants might particularly benefit from continuous chest electrical impedance tomography (EIT) monitoring at the bedside. In this study a textile 32-electrode interface for neonatal EIT examination has been developed and tested to validate its clinical performance. The objectives were to assess ease of use in a clinical setting, stability of contact impedance at the electrode–skin interface and possible adverse effects. Approach: Thirty preterm infants (gestational age: 30.3 ± 3.9 week (mean ± SD), postnatal age: 13.8 ± 28.2 d, body weight at inclusion: 1727 ± 869 g) were included in this multicentre study. The electrode–skin contact impedances were measured continuously for up to 3 d and analysed during the initial 20-min phase after fastening the belt and during a 10 h measurement interval without any clinical interventions. The skin condition was assessed by attending clinicians. Main results: Our findings imply that the textile electrode interface is suitable for long-term neonatal chest EIT imaging. It does not cause any distress for the preterm infants or discomfort. Stable contact impedance of about 300 Ohm was observed immediately after fastening the electrode belt and during the subsequent 20 min period. A slight increase in contact impedance was observed over time. Tidal variation of contact impedance was less than 5 Ohm. Significance: The availability of a textile 32-electrode belt for neonatal EIT imaging with simple, fast, accurate and reproducible placement on the chest strengthens the potential of EIT to be used for regional lung monitoring in critically ill neonates and infants

Model selection based algorithm in neonatal Chest EIT

This paper presents a new method for selecting a patient specific forward model to compensate for anatomical variations in electrical impedance tomography (EIT) monitoring of neonates. The method uses a combination of shape sensors and absolute reconstruction. It takes advantage of a probabilistic approach which automatically selects the best estimated forward model fit from pre-stored library models. Absolute/static image reconstruction is performed as the core of the posterior probability calculations. The validity and reliability of the algorithm in detecting a suitable model in the presence of measurement noise is studied with simulated and measured data from 11 patients. The paper also demonstrates the potential improvements on the clinical parameters extracted from EIT images by considering a unique case study with a neonate patient undergoing computed tomography imaging as clinical indication prior to EIT monitoring. Two well-known image reconstruction techniques, namely GREIT and tSVD, are implemented to create the final tidal images. The impacts of appropriate model selection on the clinical extracted parameters such as center of ventilation and silent spaces are investigated. The results show significant improvements to the final reconstructed images and more importantly to the clinical EIT parameters extracted from the images that are crucial for decision-making and further interventions

A parametric model for the changes in the complex valued conductivity of a lung during tidal breathing

Classical homogenization theory based on the Hashin-Shtrikman coated ellipsoids is used to model the changes in the complex valued conductivity (or admittivity) of a lung during tidal breathing. Here, the lung is modeled as a two-phase composite material where the alveolar air-filling corresponds to the inclusion phase. The theory predicts a linear relationship between the real and the imaginary parts of the change in the complex valued conductivity of a lung during tidal breathing, and where the loss cotangent of the change is approximately the same as of the effective background conductivity and hence easy to estimate. The theory is illustrated with numerical examples, as well as by using reconstructed Electrical Impedance Tomography (EIT) images based on clinical data from an ongoing study within the EU-funded CRADL project. The theory may be potentially useful for improving the imaging algorithms and clinical evaluations in connection with lung EIT for respiratory management and monitoring in neonatal intensive care units

Model Selection Based Algorithm in Neonatal Chest EIT

This paper presents a new method for selecting a patient specific forward model to compensate for anatomical variations in electrical impedance tomography (EIT) monitoring of neonates. The method uses a combination of shape sensors and absolute reconstruction. It takes advantage of a probabilistic approach which automatically selects the best estimated forward model fit from pre-stored library models. Absolute/static image reconstruction is performed as the core of the posterior probability calculations. The validity and reliability of the algorithm in detecting a suitable model in the presence of measurement noise is studied with simulated and measured data from 11 patients

Local conservation laws of second-order evolution equations

Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531-676], we completely describe local conservation laws of second-order (1+1)-dimensional evolution equations up to contact equivalence. The possible dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The canonical forms of equations with respect to contact equivalence are found for all nonzero dimensions of spaces of conservation laws.Comment: 11 pages, minor correction

Targeted Inactivation of Rin3 Increases Trabecular Bone Mass by Reducing Bone Resorption and Favouring Bone Formation

AbstractCommon genetic variants at the RIN3 locus on chromosome 14q32 predispose to Paget’s disease of bone (PDB) but the mechanisms by which they do so are unknown. Here, we analysed the skeletal phenotype of female mice with targeted inactivation of the mouse Rin3 gene (Rin3−/−) as compared with wild-type littermates. The Rin3−/− mice had higher trabecular bone volume (BV/TV%) compared with wild type. Mean ± standard deviation values at the distal femur at 8 weeks were 9.0 ± 2.5 vs. 7.0 ± 1.5 (p = 0.002) and at 52 weeks were 15.8 ± 9.5 vs. 8.5 ± 4.2 (p = 0.002). No differences were observed in femoral cortical bone parameters with the exception of marrow diameter which was significantly smaller in 52-week-old Rin3−/− mice compared to wild type: (0.43 mm ± 0.1 vs. 0.57 mm ± 0.2 (p = 0.001). Bone histomorphometry showed a lower osteoclast surface / bone surface (Oc.S/BS%) at 8 weeks in Rin3−/− mice compared to wild type (24.1 ± 4.7 vs. 29.7 ± 6.6; p = 0.025) but there were no significant differences in markers of bone formation at this time. At 52 weeks, Oc.S/BS did not differ between genotypes but single labelled perimeter (SL.Pm/B.Pm (%)) was significantly higher in Rin3−/− mice (24.4 ± 6.4 vs. 16.5 ± 3.8, p = 0.003). We conclude that Rin3 negatively regulates trabecular bone mass in mice by inhibiting osteoclastic bone resorption and favouring bone formation. Our observations also suggest that the variants that predispose to PDB in humans probably do so by causing a gain-in-function of RIN3.</jats:p