An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

How fluids bend: the elastic expansion for higher-dimensional black holes

Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.

Morphology–elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations

With improving clinical CT scanning technology, the accuracy of CT-based finite element (FE) models of the human skeleton may be ameliorated by an enhanced description of apparent level bone mechanical properties. Micro-finite element (μFE) modeling can be used to study the apparent elastic behavior of human cancellous bone. In this study, samples from the femur, radius and vertebral body were investigated to evaluate the predictive power of morphology–elasticity relationships and to compare them across different anatomical regions. μFE models of 701 trabecular bone cubes with a side length of 5.3 mm were analyzed using kinematic boundary conditions. Based on the FE results, four morphology–elasticity models using bone volume fraction as well as full, limited or no fabric information were calibrated for each anatomical region. The 5 parameter Zysset–Curnier model using full fabric information showed excellent predictive power with coefficients of determination ( r2adj ) of 0.98, 0.95 and 0.94 of the femur, radius and vertebra data, respectively, with mean total norm errors between 14 and 20%. A constant orthotropy model and a constant transverse isotropy model, where the elastic anisotropy is defined by the model parameters, yielded coefficients of determination between 0.90 and 0.98 with total norm errors between 16 and 25%. Neglecting fabric information and using an isotropic model led to r2adj between 0.73 and 0.92 with total norm errors between 38 and 49%. A comparison of the model regressions revealed minor but significant (p<0.01) differences for the fabric–elasticity model parameters calibrated for the different anatomical regions. The proposed models and identified parameters can be used in future studies to compute the apparent elastic properties of human cancellous bone for homogenized FE models.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Design and Test of a 0.5 THz Dipole Antenna With Integrated Schottky Diode Detector on a High Dielectric Constant Ceramic Electromagnetic Bandgap Substrate

This paper presents the first analysis of the input impedance and radiation properties of a dipole antenna, placed on top of Fan 's three-dimensional electromagnetic bandgap (EBG) structure, (Applied Physics Letters, 1994) constructed using a high dielectric constant ceramic. The best position of the dipole on the EBG surface is determined following impedance and radiation pattern analyses. Based on this optimum configuration an integrated Schottky heterodyne detector was designed, manufactured and tested from 0.48 to 0.52 THz. The main antenna features were not degraded by the high dielectric constant substrate due to the use of the EBG approach. Measured radiation patterns are in good agreement with the predicted ones.

Improved Localization of Implanted Subdural Electrode Contacts on MRI Using an Elastic Image Fusion Algorithm in Invasive EEG Recording

BACKGROUND: Accurate projection of implanted subdural electrode contacts in presurgical evaluation of pharmacoresistant epilepsy cases by invasive EEG is highly relevant. Linear fusion of CT and MRI images may display the contacts in the wrong position due to brain shift effects. OBJECTIVE: A retrospective study in five patients with pharmacoresistant epilepsy was performed to evaluate whether an elastic image fusion algorithm can provide a more accurate projection of the electrode contacts on the pre-implantation MRI as compared to linear fusion. METHODS: An automated elastic image fusion algorithm (AEF), a guided elastic image fusion algorithm (GEF), and a standard linear fusion algorithm (LF) were used on preoperative MRI and post-implantation CT scans. Vertical correction of virtual contact positions, total virtual contact shift, corrections of midline shift and brain shifts due to pneumencephalus were measured. RESULTS: Both AEF and GEF worked well with all 5 cases. An average midline shift of 1.7mm (SD 1.25) was corrected to 0.4mm (SD 0.8) after AEF and to 0.0mm (SD 0) after GEF. Median virtual distances between contacts and cortical surface were corrected by a significant amount, from 2.3mm after LF to 0.0mm after AEF and GEF (p<.001). Mean total relative corrections of 3.1 mm (SD 1.85) after AEF and 3.0mm (SD 1.77) after GEF were achieved. The tested version of GEF did not achieve a satisfying virtual correction of pneumencephalus. CONCLUSION: The technique provided a clear improvement in fusion of pre- and post-implantation scans, although the accuracy is difficult to evaluate.

Antinociceptive effects of three escalating dexmedetomidine and lignocaine constant rate infusions in conscious horses.

Dexmedetomidine and lignocaine IV are used clinically to provide analgesia in horses. The aims of this study were to investigate the antinociceptive effects, plasma concentrations and sedative effects of 2, 4 and 6 µg/kg/h dexmedetomidine IV, with a bolus of 0.96 µg/kg preceding each continuous rate infusion (CRI), and 20, 40 and 60 µg/kg/min lignocaine IV, with a bolus of 550 µg/kg preceding each CRI, in 10 Swiss Warmblood horses. Electrically elicited nociceptive withdrawal reflexes were evaluated by deltoid muscle electromyography. Nociceptive threshold and tolerance were determined by electromyography and behaviour following single and repeated stimulation. Plasma concentrations of drugs were determined by liquid chromatography and mass spectrometry. Sedation was scored on a visual analogue scale. Dexmedetomidine increased nociceptive threshold to single and repeated stimulation for all CRIs, except at 2 µg/kg/h, where no increase in single stimulation nociceptive threshold was observed. Dexmedetomidine increased nociceptive tolerance to single and repeated stimulation at all CRIs. There was large individual variability in dexmedetomidine plasma concentrations and levels of sedation; the median plasma concentration providing antinociceptive effects to all recorded parameters was 0.15 ng/mL, with a range from <0.02 ng/mL (below the lower limit of quantification) to 0.25 ng/mL. Lignocaine increased nociceptive threshold and tolerance to single and repeated stimulation at CRIs of 40 and 60 µg/kg/min, corresponding to plasma lignocaine concentrations >600 ng/mL. Only nociceptive tolerance to repeated stimulation increased at 20 µg/kg/min lignocaine. Lignocaine at 40 µg/kg/min and dexmedetomidine at 4 µg/kg/h were the lowest CRIs resulting in consistent antinociception. Lignocaine did not induce significant sedation.

The pharmacokinetics of dexmedetomidine administered as a constant rate infusion in horses.

Dexmedetomidine, the most selective α2 -adrenoceptor agonist in clinical use, is increasingly being used in both conscious and anaesthetized horses; however, the pharmacokinetics and sedative effects of this drug administered alone as an infusion are not previously described in horses. Seven horses received an infusion of 8 μg dexmedetomidine/kg/h for 150 min, venous blood samples were collected, and dexmedetomidine concentrations were assayed using liquid chromatography-mass spectrometry (LC/MS) and analyzed using noncompartmental pharmacokinetic analysis. Sedation was scored as the distance from the lower lip of the horse to the ground measured in centimetre. The harmonic mean (SD) plasma elimination half-life (Lambda z half-life) for dexmedetomidine was 20.9 (5.1) min, clearance (Cl) was 0.3 (0.20) L/min/kg, and volume of distribution at steady-state (Vdss ) was 13.7 (7.9) L/kg. There was a considerable individual variation in the concentration of dexmedetomidine vs. time profile. The level of sedation covaried with the plasma concentration of dexmedetomidine. This implies that for clinical use of dexmedetomidine constant rate infusion in conscious horses, infusion rates can be easily adjusted to effect, and this is preferable to an infusion at a predetermined value.

Accurate rotational constant and bond lengths of hexafluorobenzene by femtosecond rotational Raman coherence spectroscopy and ab initio calculations

The gas-phase rotational motion of hexafluorobenzene has been measured in real time using femtosecond (fs) time-resolved rotational Raman coherence spectroscopy (RR-RCS) at T = 100 and 295 K. This four-wave mixing method allows to probe the rotation of non-polar gas-phase molecules with fs time resolution over times up to ∼5 ns. The ground state rotational constant of hexafluorobenzene is determined as B 0 = 1029.740(28) MHz (2σ uncertainty) from RR-RCS transients measured in a pulsed seeded supersonic jet, where essentially only the v = 0 state is populated. Using this B 0 value, RR-RCS measurements in a room temperature gas cell give the rotational constants B v of the five lowest-lying thermally populated vibrationally excited states ν7/8, ν9, ν11/12, ν13, and ν14/15. Their B v constants differ from B 0 by between −1.02 MHz and +2.23 MHz. Combining the B 0 with the results of all-electron coupled-cluster CCSD(T) calculations of Demaison et al. [Mol. Phys.111, 1539 (2013)] and of our own allow to determine the C-C and C-F semi-experimental equilibrium bond lengths r e(C-C) = 1.3866(3) Å and r e(C-F) = 1.3244(4) Å. These agree with the CCSD(T)/wCVQZ r e bond lengths calculated by Demaison et al. within ±0.0005 Å. We also calculate the semi-experimental thermally averaged bond lengths r g(C-C)=1.3907(3) Å and r g(C-F)=1.3250(4) Å. These are at least ten times more accurate than two sets of experimental gas-phase electron diffraction r g bond lengths measured in the 1960s.

Feasible Dose Reduction in Routine Chest Computed Tomography Maintaining Constant Image Quality Using the Last Three Scanner Generations: From Filtered Back Projection to Sinogram-affirmed Iterative Reconstruction and Impact of the Novel Fully Integrated Detector Design Minimizing Electronic Noise

OBJECTIVE The aim of the present study was to evaluate a dose reduction in contrast-enhanced chest computed tomography (CT) by comparing the three latest generations of Siemens CT scanners used in clinical practice. We analyzed the amount of radiation used with filtered back projection (FBP) and an iterative reconstruction (IR) algorithm to yield the same image quality. Furthermore, the influence on the radiation dose of the most recent integrated circuit detector (ICD; Stellar detector, Siemens Healthcare, Erlangen, Germany) was investigated. MATERIALS AND METHODS 136 Patients were included. Scan parameters were set to a thorax routine: SOMATOM Sensation 64 (FBP), SOMATOM Definition Flash (IR), and SOMATOM Definition Edge (ICD and IR). Tube current was set constantly to the reference level of 100 mA automated tube current modulation using reference milliamperes. Care kV was used on the Flash and Edge scanner, while tube potential was individually selected between 100 and 140 kVp by the medical technologists at the SOMATOM Sensation. Quality assessment was performed on soft-tissue kernel reconstruction. Dose was represented by the dose length product. RESULTS Dose-length product (DLP) with FBP for the average chest CT was 308 mGy*cm ± 99.6. In contrast, the DLP for the chest CT with IR algorithm was 196.8 mGy*cm ± 68.8 (P = 0.0001). Further decline in dose can be noted with IR and the ICD: DLP: 166.4 mGy*cm ± 54.5 (P = 0.033). The dose reduction compared to FBP was 36.1% with IR and 45.6% with IR/ICD. Signal-to-noise ratio (SNR) was favorable in the aorta, bone, and soft tissue for IR/ICD in combination compared to FBP (the P values ranged from 0.003 to 0.048). Overall contrast-to-noise ratio (CNR) improved with declining DLP. CONCLUSION The most recent technical developments, namely IR in combination with integrated circuit detectors, can significantly lower radiation dose in chest CT examinations.