Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

Ground-State Entanglement of the BCS Model

The concept of local concurrence is used to quantify the entanglement between a single qubit and the remainder of a multiqubit system. For the ground state of the BCS model in the thermodynamic limit the set of local concurrences completely describes the entanglement. As a measure for the entanglement of the full system we investigate the average local concurrence (ALC). We find that the ALC satisfies a simple relation with the order parameter. We then show that for finite systems with a fixed particle number, a relation between the ALC and the condensation energy exposes a threshold coupling. Below the threshold, entanglement measures besides the ALC are significant.

Impact of Stent-Graft Oversizing on the Thoracic Aorta: Experimental Study in a Porcine Model

Purpose: To analyze in an experimental animal model the effect of 4 different levels of stents-graft oversizing on non-atherosclerotic aortas such as those found in young individuals who undergo stent-graft repair for traumatic aortic injuries. Methods: The diameter of the porcine thoracic aorta is similar to the aorta of young adults (18-20 mm), so 25 pigs were randomized into 5 groups: 1 control (without stent-graft) and 4 oversizing groups (A: 10%-19%, B: 20%-29%, C: 30%-39%, and D: >40%). Two types of biomechanical tests were performed on all aortas 4 weeks after endoprosthesis deployment. Results: The results of the detachment test, which analyzed the strength necessary to remove the stent-graft from the aorta, were similar in the 4 groups (A: 42 N, B: 41 N, C: 46 N, and D: 46 N). However, 2 aortas ruptured during the tests (groups C and D). The second test was performed in 3 aortic segments. Maximum shear strength, maximum stress, and maximum tension supported by the aortic wall had a negative and linear correlation with oversizing. There were significant differences in all 4 groups when compared with the control group. Strain, which reflects the elastic properties of the aortic wall, was very similar in all 4 groups, but a great difference was found when compared with the control group (p<0.0001). Conclusion: The study showed an important subacute change in the biomechanical properties of the aortic wall after implantation of an oversized endoprosthesis. This weakness of the aortic wall was confirmed by 2 ruptures during the detachment test. These results partially explain the interaction of stent-grafts with non-atherosclerotic thoracic aortas and may serve as a basis for further studies and the development of specific material to be used in vascular trauma and young patients. J Endovasc Ther. 2011; 18: 576-584

Modelling of cold-formed purlin-sheeting systems .1. Full model

Purlin-sheeting systems used for roofs and walls commonly take the form of cold-formed channel or zed section purlins, screw-connected to corrugated sheeting. These purlin-sheeting systems have been the subject of numerous theoretical and experimental investigations over the past three decades, but the complexity of the systems has led to great difficulty in developing a sound and general model. This paper presents a non-linear elasto-plastic finite element model, capable of predicting the behaviour of purlin-sheeting systems without the need for either experimental input or over simplifying assumptions. The model incorporates both the sheeting and the purlin, and is able to account for cross-sectional distortion of the purlin, the flexural and membrane restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The validity of the model is shown by its good correlation with experimental results. A simplified version of this model, which is more suitable for use in a design environment, is presented in a companion paper. (C) 1997 Elsevier Science Ltd.

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Risk Factors for Visual Field Progression in Treated Glaucoma

Objective: To determine intraocular pressure (IOP)-dependent and IOP-independent variables associated with visual field (VF) progression in treated glaucoma. Design: Retrospective cohort of the Glaucoma Progression Study. Methods: Consecutive, treated glaucoma patients with repeatable VF loss who had 8 or more VF examinations of either eye, using the Swedish Interactive Threshold Algorithm (24-2 SITA-Standard, Humphrey Field Analyzer II; Carl Zeiss Meditec, Inc, Dublin, California), during the period between January 1999 and September 2009 were included. Visual field progression was evaluated using automated pointwise linear regression. Evaluated data included age, sex, race, central corneal thickness, baseline VF mean deviation, mean follow-up IOP, peak IOP, IOP fluctuation, a detected disc hemorrhage, and presence of beta-zone parapapillary atrophy. Results: We selected 587 eyes of 587 patients (mean [SD] age, 64.9 [13.0] years). The mean (SD) number of VFs was 11.1 (3.0), spanning a mean (SD) of 6.4 (1.7) years. In the univariable model, older age (odds ratio [OR], 1.19 per decade; P = .01), baseline diagnosis of exfoliation syndrome (OR, 1.79; P = .01), decreased central corneal thickness (OR, 1.38 per 40 mu m thinner; P < .01), a detected disc hemorrhage (OR, 2.31; P < .01), presence of beta-zone parapapillary atrophy (OR, 2.17; P < .01), and all IOP parameters (mean follow-up, peak, and fluctuation; P < .01) were associated with increased risk of VF progression. In the multivariable model, peak IOP (OR, 1.13; P < .01), thinner central corneal thickness (OR, 1.45 per 40 mu m thinner; P < .01), a detected disc hemorrhage (OR, 2.59; P < .01), and presence of beta-zone parapapillary atrophy (OR, 2.38; P < .01) were associated with VF progression. Conclusions: IOP-dependent and IOP-independent risk factors affect disease progression in treated glaucoma. Peak IOP is a better predictor of progression than is IOP mean or fluctuation.

Gamma ventral capsulotomy for treatment of resistant obsessive-compulsive disorder: A structural MRI pilot prospective study

Objective: The purpose of this study was to investigate regional structural abnormalities in the brains of five patients with refractory obsessive-compulsive disorder (OCD) submitted to gamma ventral capsulotomy. Methods: We acquired morphometric magnetic resonance imaging (MRI) data before and after 1 year of radiosurgery using a 1.5-T MRI scanner. Images were spatially normalized and segmented using optimized voxel-based morphometry (VBM) methods. Voxelwise statistical comparisons between pre- and post-surgery MRI scans were performed using a general linear model. Findings in regions predicted a priori to show volumetric changes (orbitofrontal cortex, anterior cingulate gyrus, basal ganglia and thalamus) were reported as significant if surpassing a statistical threshold of p<0.001 (uncorrected for multiple comparisons). Results: We detected a significant regional postoperative increase in gray matter volume in the right inferior frontal gyri (Brodmann area 47, BA47) when comparing all patients pre and postoperatively. Conclusions: Our results support the current theory of frontal-striatal-thalamic-cortical (FSTC) circuitry involvement in OCD pathogenesis. Gamma ventral capsulotomy is associated with neurobiological changes in the inferior orbitofrontal cortex in refractory OCD patients. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

POISSON DISTRIBUTION TO ANALYZE NEAR-THRESHOLD MOTOR EVOKED POTENTIALS

Motor unit action potentials (MUAPs) evoked by repetitive, low-intensity transcranial magnetic stimulation can be modeled as a Poisson process. A mathematical consequence of such a model is that the ratio of the variance to the mean of the amplitudes of motor evoked potentials (MEPs) should provide an estimate of the mean size of the individual MUAPs that summate to generate each MEP. We found that this is, in fact, the case. Our finding thus supports the use of the Poisson distribution to model MEP generation and indicates that this model enables characterization of the motor unit population that contributes to near-threshold MEPs. Muscle Nerve 42: 825-828, 2010

Focal and linear endocardial and epicardial catheter-based cryoablation of normal and infarcted ventricular tissue

Background: This study of a chronic porcine postinfarction model examined whether linear epicardial cryoablation was capable of creating large, homogenous lesions in regions of the myocardium including scarred ventricle. Endocardial and epicardial focal cryolesions were also compared to determine if there were significant differences in lesion characteristics. Methods: Eighty focal endocardial and 28 focal epicardial cryoapplications were delivered to eight normal caprine and four normal porcine ventricular myocardium, and 21 linear cryolesions were applied along the border of infarcted epicardial tissue in a chronic porcine infarct model in six swines. Results: Focal endocardial cryolesions in normal animals measured 9.7 +/- 0.4 mm (length) by 7.3 +/- 1.4 mm (width) by 4.8 +/- 0.2 mm (depth), while epicardial lesions measured 10.2 +/- 1.4 mm (length) by 7.7 +/- 2 mm (width) by 4.6 +/- 0.9 mm (depth); P > 0.05. Linear epicardial cryolesions in the chronic porcine infarct model measured 36.5 +/- 7.8 mm (length) by 8.2 +/- 1.3 mm (width) by 6.0 +/- 1.2 mm (depth). The mean depth of linear cryolesions applied to the border of the infarct scar was 7 +/- 0.7 mm, as measured by magnetic resonance imaging. Conclusions:Cryoablation can create deep lesions when delivered to the ventricular epicardium. Endocardial and epicardial cryolesions created by a focal cryoablation catheter are similar in size and depth. The ability to rapidly create deep linear cryolesions may prove to be beneficial in substrate-based catheter ablation of ventricular arrhythmias.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

An identifiability analysis of a parent-metabolite pharmacokinetic model for ivabradine.

The paper considers the structural identifiability of a parent–metabolite pharmacokinetic model for ivabradine and one of its metabolites. The model, which is linear, is considered initially for intravenous administration of ivabradine, and then for a combined intravenous and oral administration. In both cases, the model is shown to be unidentifiable. Simplification of the model (for both forms of administration) to that proposed by Duffull et al. (1) results in a globally structurally identifiable model. The analysis could be applied to the modeling of any drug undergoing first-pass metabolism, with plasma concentrations available from drug and metabolite.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.