Integral Approximation Method Research Articles

Population Pharmacokinetic Model of ADVATE in Pediatric and Adult Patients with Hemophilia A.

Abstract 3492Poster Board III-429 IntroductionThe objective of this analysis was to characterize the population pharmacokinetic (PK) model of ADVATE® (Antihemophilic Factor (Recombinant), Plasma/Albumin-Free Method) in hemophilia A patients. This included estimation of typical population pharmacokinetic parameters and inter-individual and residual variability and identification of covariates that are significant predictors of variability in a pooled population of children and adults. Patients and MethodsPlasma FVIII activity PK data were collected for 3 ADVATE® clinical trials in previously treated patients: 184 full PK data sets for 100 adults/adolescents, aged 10 to 65 years, and from 52 reduced sample PK data sets for 52 children, aged 1 to 6 years. Population PK analysis was conducted using non-linear mixed effects modeling with the first-order integral approximation method in SAS® software (NLMIXED procedure). A two-compartment model was used as the base model and the influence of age and weight were explored. ResultsTwo-compartment PK models with additive plus proportional residual variability model and exponential inter-individual variability model adequately described the data. Clearance (CL) is significantly correlated with age and body weight and central volume of distribution (V1) is also related with body weight. The estimated population PK parameters were (mean parameter, (inter-individual variability %)): CL (2.92 mL/kg·h, 22%), V1 (0.46 dL/kg, 5.2%), peripheral volume V2 (0.09 dL/kg) and inter-compartmental clearance Q (2.07 mL/ kg·h). ConclusionsA population PK model that describes the combined PK data from adults and pediatric studies has been constructed. A significant portion of inter-individual variability in both volume and clearance can be explained by subject weight. An additional smaller effect of age on clearance but not volume was observed. A population PK model for Factor VIII could provide the clinician with advantages in designing a patient specific treatment regimen. It could provide more relevant guidance in individual patient pharmacokinetics than just incremental recovery without the burden of a full PK assessment of the patient. Disclosures:Oh:Baxter: Employment. Off Label Use: Prophylaxis is not indicated in the US. Björkman:Baxter: Consultancy; Octapharma: Consultancy. Schroth:Baxter: Employment. Fritsch:Baxter: Employment. Collins:Bayer: Consultancy; Novo Nordisk: Consultancy; Baxter: Consultancy. Fischer:Bayer: Consultancy; Wyeth: Consultancy; Baxter: Consultancy. Blanchette:Bayer: Consultancy; Baxter: Consultancy. Casey:Baxter: Employment. Spotts:Baxter: Employment. Ewenstein:Baxter: Employment.

Extraction of Via-Plate Capacitance of an Eccentric Via by an Integral Approximation Method

An integral approximation method is proposed to extract the via-plate capacitance of an eccentric via in the via hole (anti-pad). An analytical formula is derived for the coaxial capacitance part, which is used as a benchmark to validate the integral approximation method. Furthermore, numerical simulations are also used to validate the method. It is shown that small eccentricity results in only a few percentage increase of the via-plate capacitance, which is helpful in specifying the manufacturing tolerance of via designs.

Unsteady heat conduction involving phase changes for an irregular bubble/particle entrapped in a solid during freezing – An extension of the heat-balance integral method

Temperature distributions in the molten layer and solid with distinct properties around a bubble or particle entrapped in the solid during unidirectional solidification are determined by applying a heat-balance integral approximation method. The present model can be used to simulate growth, entrapment or departure of a bubble or particle inclusion in solids encountered in manufacturing and materials processing, MEMS, contact melting processes, drilling, etc. In this work, the proposed heat-balance equations are derived by integrating unsteady elliptic heat diffusion equations and introducing the Stefan boundary condition. Due to the time-dependent irregular shapes of phases, coefficients of assumed quadratic temperature profiles are considered to be functions of longitudinal coordinate and time. Temperature coefficients in distinct regions therefore are determined by solving equations governing temperature coefficients derived from heat-balance equations, imposing boundary conditions, and introducing a fictitious boundary condition. The computed temperature fields show agreement with predictions from the finite-difference method. Since the number of independent variables is reduced by one, this work provides an effective method to solve unsteady elliptic diffusion problems experiencing solid–liquid phase changes in irregular shapes.

Decomposition kinetics of alkaline earth carbonates by integral approximation method

The decomposition kinetics of four synthetic alkaline earth metal carbonates (MgCO3, CaCO3, SrCO3 and BaCO3) was studied under non-isothermal conditions from thermo-gravimetric measurements as compared to. The integral approximation method of Coats and Redfern was used to determine the kinetic parameters for the decomposition processes. The decomposition reactions followed mostly first order kinetics and the activation energy of the decomposition reactions increased with the increase in the molecular mass of the carbonates. The change in enthalpy for the decomposition processes was also calculated and compared with the activation energies for the decomposition processes. The activation energy of the decomposition process for all the carbonates was higher than the enthalpy of the reaction excepting SrCO3.

Non-isothermal decomposition kinetics of magnesite

Kinetics of thermal decomposition of Indian magnesite was studied by thermo-gravimetric analysis under non-isothermal condition. Coats and Redfern Integral approximation method was used to determine the kinetic parameters. Using the kinetic parameters different kinetic functions were analyzed with the experimental data to ascertain the decomposition mechanism of magnesium carbonate and it was observed that the decomposition reaction followed a contracting sphere kinetic mechanism.

Scale analysis and integral approximation applied to heat and mass transfer in packed beds

In this paper, we apply two mathematical tools for the analysis of models describing heat and mass transfer in dispersed systems, namely scale analysis and integral approximation. The particular model investigated is a 1-D model describing the cooling of packed beds of fresh agricultural produce using the porous media approach. With scale analysis, one can determine relevant terms in the model and subsequently one can make justified approximations. Traditionally, in the porous media approach one assumes that temperature gradients in individual products are negligible, as expressed by the Biot number Bi < 0.1. By means of the integral approximation method, we have shown that the porous medium approach can be extended to the range Bi < 10 via the definition of an internal heat resistance. Via the integral approximation method, we have calculated the internal resistance for a variety of products having simple geometries. Scale analysis shows that for the problem investigated, there are two regimes, depending on whether solid and fluid phase are in so-called local thermal equilibrium.

Non‐Isothermal Decomposition Kinetics of Alkaline Earth Metal Carbonates

The kinetics of thermal decomposition of four synthetic alkaline earth metal carbonates (MgCO3, CaCO3, SrCO3, and BaCO3) was studied under non‐isothermal conditions using thermo‐gravimetry. The activation energy and the pre‐exponential factor for the decomposition reactions were determined using the Agarwal and Sivasubramanium integral approximation method. A new method was developed using a Turbo‐C‐based computer program to evaluate the integral of the kinetic equation. It was observed that the decomposition reaction of MgCO3 and CaCO3 followed two‐dimensional diffusion‐controlled kinetics and the decomposition reaction of SrCO3 and BaCO3 followed a Ginstling–Brounshtein model‐based diffusion‐controlled kinetics.

Analysis of melting of alloy powder bed with constant heat flux

Melting of an alloy powder bed with constant heat flux for application in selective laser sintering (SLS) is analyzed in this paper. Since melting of an alloy occurs in a range of temperatures, instead of at a single melting point, there will be a mushy zone – containing partially melted powders – between the unmelted region and the completely melted region. The mushy zone can be further divided into two sub-regions: (1) a lower part with constant porosity (shrinkage takes place), and (2) an upper part with constant volume (no shrinkage). Temperature distributions in different regions and locations of melting interfaces are obtained using an integral approximation method. The results show that increasing initial porosity and temperature of the powder bed accelerate the melting process. The melting slows down with increasing thermal conductivity of the interstitial gas.

Analysis of electromagnetic wave propagation with resonance effect in collision-free magnetized plasma

In an inhomogeneous collision-free (lossless) magnetized plasma, there is resonance where the refractive index becomes infinite. Previously, the multilayered method by matrix multiplication has been used for the analysis of electromagnetic wave propagation in an aniso-tropic inhomogeneous medium. In the case of collision-free magnetized plasma, solution of the wave equation is unstable at the resonance point because the wave equation exhibits singularity. In order to rectify this problem, the inhomogeneous medium containing resonance is divided into thin layered media. At each layer, the analytical solution of the electromagnetic field is derived by an integral equation. The solutions are connected by way of the boundary condition in this integral approximation method. In the present paper, the effectiveness of the integral approximation method in an anisotropic inhomogeneous medium is discussed. Also, this computational method is applied to the problem of mode conversion from the Z mode to the L-O mode in regard to the electromagnetic wave generated in space and to resolution of the mechanism of the electromagnetic energy absorption at resonance. New knowledge is therefore obtained. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 88(10): 55–66, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10198

Dynamic simulation on the preparation process of thin films by pulsed laser

An ablation model of targets irradiated by pulsed laser is established. By using the simple energy balance conditions, the relationship between ablation surface location and time is derived. By an adiabatic approximation, the continuous-temperature condition, energy conservation and all boundary conditions can be established. By applying the analytical method and integral-approximation method, the solid and liquid phase temperature distributions are obtained and found to be a function of time and location. The interface of solid and liquid phase is also derived. The results are compared with the other published data. In addition, the dynamics process of pulsed laser deposition of KTN (Kta0.65Nb0.35O3) thin film is simulated in detail by using fluid dynamics theory. By combining the expression of the target ablation ratio and the dynamic equation and by using the experimental data, the effects of laser action parameters on the thickness distribution of thin film and on the thin film component characteristics are discussed. The results are in good agreement with the experimental data.

Integral approximation method for calculating ultrasonic beam propagation in anisotropic materials

Plane-wave solutions to the acoustic wave equations in a generally anisotropic solid are reviewed, along with their connection to geometric ray theory. A Fourier-transform formulation of the field of a focused beam (coherent point source) passed from a liquid couplant to an anisotropic specimen through a plane surface is derived. The integral is approximated asymptotically using the stationary-phase method. The result for isotropic media is derived analytically to facilitate a direct comparison to the ray theory. The application of this method to the anisotropic case is illustrated, using the real-world example of the austenitic stainless-steel weld.

An integral approximate solution of heat transfer in the grinding process

An integral approximation solution of heat transfer in the grinding process is presented in this paper. Heat transfer models for the abrasive grain, fluid and workpiece were developed by using the integral approximation method. For the case in which film boiling does not occur in the grinding zone during the grinding process, the workpiece background temperature rise calculated by the present model agreed very well with previous theoretical analysis. The present model can also correctly simulate the grinding process when film boiling occurs in the grinding zone. Furthermore, a simplified model, which is applied only for cases where film boiling does not occur in the grinding zone, has also been developed.

Upper and lower bounds for the rate constant of bimolecular reactions: integral approximation method

A method for the calculation of rate constants of bimolecular reactions for an arbitrary type of spherically isotropic transfer probabilities and the interaction potentials between reagents has been developed. On the basis of this method, an integral representation of upper and lower bounds for quenching radius is proposed. It has been shown that a relative deviation of the upper from the lower estimate cannot exceed 20%. Comparison with the available analytical results shows good accuracy of the approximations in the description of the viscosity dependence of quenching radius.

Theoretical models for diffusion in glassy polymers. II

AbstractThe author refines and generalizes a model for diffusion in glassy polymers which he previously introduced. The model unifies many diverse observations by explicity formulating the common property of a glassy polymer in all its various modes, namely the finite relaxation time due to its slow response to changing conditions. An integral approximation method is used to study the motion of the penetrant front and the glass‐gel interface and a useful polynomial approximation method is introduced for use in special simple situations.

Use of partial löwdin (PLA) and limited expansion of diatomic overlap (LEDO) integral approximation methods in molecular orbital calculations of the isomer pairs HCN, CNH and FCN, CNF

Molecular orbital calculations, using a free atom double zeta basis set and embodying the PLA and LEDO integral approximation methods, are performed on the isomer pairs HCN, CNH and FCN, CNF in their respective linear configurations. For each integral approximation method, the C—N separation is fixed at the experimental value for FCN and, for variable X—C and X—N separations, the calculated total energies, orbital energies, one-electron density functions and natural hybrid populations are compared for each pair of isomers. One ab initio calculation is also performed for each isomer at a selected molecular geometry. Additional calculations are performed on the related model ionic systems H+CN– and CN–H+ to provide further insight into the bonding in the two hydrocyano species.

Use of partial (and full) Löwdin integral approximations in molecular orbital calculations on HCN and FCN

Tests and applications of the PLA and FLA integral approximation methods are made by calculating a wide range of molecular properties for HCN using a basis of single-zeta atomic orbitals. A comparison of the results with those obtained from an ab initio calculation establishes the PLA method as the better of the two approximation methods. The molecular orbitals for HCN and FCN are then determined for five different X–C separations (using a double-zeta basis set), and the changes in the electron distribution of each molecule are discussed with the aid of appropriate electron density maps, as well as population analyses related to a basis of natural hybrids.

Solutions of Boltzmann Equation and Transport Processes

An integral approximation (IA) method is proposed for the solution of certain integro-differential equations of which the linearized Boltzmann equation is one example. The lowest-order solution in this method consists of replacing the integral operator of the equation by a known function such that the solution has the correct initial value, correct initial slope in time, and correct behavior at large times. The deviation of the integral operator from the function is treated as a perturbation in higher orders. The method is applied as an example to the calculation of time correlation functions and thermal transport coefficients. Deviations from the exponential behavior of the correlation functions are explicitly evaluated. Another method of solution which involves a cumulant expansion (CU) is also used for the evaluation of these quantities. Both methods are then compared with the Chapman–Enskog (CE) method. The IA method provides a better physical approximation and better numerical estimates for the thermal transport coefficients than the CU or CE methods.