Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Batchelor's theory extended to elongated cylindrical or ellipsoidal particles

Extensions to Batchelor's theory have been derived to take into account different shaped particles while relating extensional viscosity enhancement to three parameters - shape, volume fraction and particle aspect ratio. The extended theory now allows calculation of the extensional viscosity enhancement, at a given volume fraction of particles, for either ellipsoidal or cylindrical particles. The formula improves the predictive capability of Batchelor's theory when compared with measurements found in the literature for different rod-like polymer solutions. (c) 2005 Elsevier B.V. All rights reserved.

Investigation of the antinociceptive efficacy and relative potency of extended duration injectable 3-acylmorphine-6-sulfate prodrugs in rats

This investigation was designed to examine the antinociceptive activity in rats of 3-O-acyl prodrugs of M6S relative to the parent drug, after intravenous and intramuscular injection, using the tail flick latency test of antinociception. M6S, 3-acetylmorphine-6-sulfate (3AcM6S), 3-propionylmorphine-6-sulfate (3PrM6S), 3-butanoylmorphine-6-sulfate (3BuM6S) and 3-heptanoylmorphine-6-sulfate (3HpM6S) were administered by the IV route in a dose of 4.10 mu mol/kg. Relatively high levels of antinociception (>40% Maximum Possible Effect) were achieved following administration of M6S, 3AcM6S and 3PrM6S, whereas insignificant antinociception (<20%MPE) was achieved following administration of 3BuM6S or 3HpM6S. Although the mean duration of action for 3AcM6S (6 h) was longer than for M6S or 3PrM6S (4 h), the mean area (+/- S.E.M.) under the degree of antinociception versus time curve (AUG) for 3AcM6S (151.6 +/- 6.9%MPE h) was not significantly different (p <0.05) from that for M6S (120.8 +/- 32.7%MPE h) or for 3PrM6S (106.0 +/- 21.3%MPE h). The mean ED50 (range) doses for M6S, 3AcM6S and 3PrM6S were calculated to be 4.16 (3.61-4.48), 4.32 (3.55-5.09) and 4.54 (4.21-4.79) mu mol/kg, respectively. Preliminary studies were conducted on potential long-acting formulations containing 8 x ED50 doses of M6S and the 3-acetyl and 3-propionyl esters suspended in soybean oil. These showed that 3PrM6S gave a greater AUC (mean + S.E.M.) (1087.4 +/- 97.4%MPE h) and longer duration of action (20 h) than did M6S (613.1 +/- 155.9%MPE h; 10 h duration) or 3AcM6S (379.3 + 114.2%MPE h: 8 h duration). Further studies are needed to more fully investigate these findings. (C) 1998 Elsevier Science B.V. All rights reserved.

Extended delayed recall of AVLT word lists: Effects of age and sex on adult performance

An extension of a previous study of age and sex effects on verbal recall (Geffen, Moar, O'Hanlon, lark, & Geffen, 1990) examined forgetting of words over extended delays. The AVLT was administered to 201 normal adults (99 males, 102 females) ranging in age between 20 and 59 years. Recall was tested at intervals of 30 minutes, 24 hours, and 7 days after acquisition. Testing of the latter two intervals was conducted by telephone (Experiment 1, N = 177). After 30 minutes there was no significant loss of the 10 to 11 words retained from five acquisition trials. However, an overall mean of about one word was forgotten after 1 day and a further word after 7 days. The oldest age group (50-59 years) acquired fewer words and forgot more words than the younger groups. Females of all age groups performed slightly better than males at acquisition, at retention, and at recall after longer delays. A second experiment showed that telephone testing at the longer delay intervals was equivalent to testing face to face. These results extend the use of the AVLT by assessing memory decay beyond the immediate testing period. Telephone follow-up is a convenient and economical method of testing delayed recall.

Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

Integrable Kondo impurities in the one-dimensional supersymmetric extended Hubbard model

An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local moments of the impurities are presented as a non-trivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

Integrable Kondo impurities in one-dimensional extended Hubbard models

Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a (2s alpha + 1)-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

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.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

A new algorithm and refined bounds for extended gcd computation

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipliers obtained.