Fast Inverse Laplace Transform Research Articles

Computational Method for Specific Energy Loss by Fast Inverse Laplace Transform

This study proposes a novel computational technique for specific energy loss for pulse incidence. Our method is based on a fast inverse Laplace transform (FILT) with an electromagnetic field solver in the complex frequency domain. Using the FILT algorithm, the specific energy loss in the complex frequency domain can be computed and transformed into the time domain. In our method, the specific energy loss can be computed until the desired observation time without solving the electromagnetic field at the previous observation time. The finite-difference complex-frequency domain (FDCFD) was used for the complex frequency domain solver. The results demonstrated that our proposed method could compute the dissipated energy of inhomogeneous, non-dispersive lossy dielectrics.

Enhanced Resolution Analysis for Water Molecules in MCM-41 and SBA-15 in Low-Field T2 Relaxometric Spectra.

Mesoporous silica materials are the subjects for relaxometric NMR studies in which we obtain information on the properties of molecules in confined geometries. The signal analysis in such investigations is generally carried out with the help of the Inverse Laplace Transform (ILT), which is accompanied by a regularization procedure. The appropriate selection of the regularization method may positively affect the resolution of the spectrum and the essence of the final conclusions. In this work, we examined the MCM-41 and SBA-15 model systems in various saturation states, using L-Curve regularization for relaxation spectra based on our own version of the fast fast ILT implementation. In a single relaxometric spectrum, the water contributions from the internal volume in the pores and between the silica particles were identified, which allowed us to trace the dynamics of the corresponding drying trends during the removal of water from the sample as a function of total water saturation.

Optimal Parallel Algorithm of Fast Inverse Laplace Transform for Electromagnetic Analysis

Fast inverse Laplace transform (FILT) is a simple and concise technique for performing inverse Laplace transforms. This letter develops an efficient parallel algorithm for FILT for solving various electromagnetic problems. This algorithm can be easily combined with existing computational methods used in electromagnetics to realize efficient time- and frequency-domain analyses.

Novel FDTD Scheme for Analysis of Frequency- Dependent Medium Using Fast Inverse Laplace Transform and Prony’s Method

A novel finite-difference time-domain (FDTD) approach is proposed for the analysis of wave propagation in a general frequency-dependent medium. In the proposed method, formulation of the fractional derivatives in the time-domain representation is circumvented by using the fast inverse Laplace transform (FILT) and Prony’s method. The FILT is used to transform the dispersion expressed in a frequency-domain response into a time-domain response, and Prony’s method is utilized to extract the parameters and transform the time-domain responses into those in the z -domain so that they can be incorporated into the FDTD method directly. The update equation of the electric field in the FDTD method is then formulated by using the z -transformation. Stability analysis of the proposed scheme is also investigated by means of the root-locus method. Reflection coefficients of dispersive media, such as Debye, Cole–Cole, Davidson–Cole, and Havriliak–Negami media simulated in a 1-D domain and a three-layered biological medium of skin, fat, and muscle tissues inside a waveguide with a TE10 fundamental mode in a 2-D domain, are found to be in good agreement with those obtained by an analytical method over a broad frequency range, demonstrating the validity of the proposed FDTD scheme.

Evaluation of Protein Binding Effect on Local Disposition of Oxacillin in Rat Liver by a Two-compartment Dispersion Model

The effect of protein binding upon the hepatic uptake of oxacillin was evaluated in the rat isolated perfused liver, based on the two-compartment dispersion model by means of the fast inverse Laplace transform (FILT). The perfusion experiment was carried out using the perfusates without and with bovine serum albumin (BSA, 40 g L-1). Oxacillin was injected as a pulse through the portal vein, and the outflow concentration-time course of oxacillin was fitted to the dispersion model using the non-linear least squares program MULTI(FILT). The partition ratio (k'), which is the measure of the extent of the reversible distribution into the hepatic tissue, was 0.163 +/- 0.041 (s.d.) in the presence of BSA, and 0.095 +/- 0.018 in the absence of BSA, which suggests interaction of the albumin-bound drug with the hepatic tissue. The elimination rate constant (ke) from the perfusate in the absence of BSA was 8.0 +/- 0.55 min-1 and that in the presence of BSA was 3.3 +/- 1.4 min-1 while the unbound fraction of the drug in the presence of 40 g L-1 BSA was 0.282. The hepatic elimination rate of oxacillin was not proportional to the unbound concentration of drug suggesting hepatic uptake of the bound fraction.

A hybrid method for transient wave propagation in a multilayered solid

We present a hybrid method for the evaluation of transient elastic-wave propagation in a multilayered solid, integrating reverberation matrix method with the theory of generalized rays. Adopting reverberation matrix formulation, Laplace–Fourier domain solutions of elastic waves in the multilayered solid are expanded into the sum of a series of generalized-ray group integrals. Each generalized-ray group integral containing Kth power of reverberation matrix R represents the set of K-times reflections and refractions of source waves arriving at receivers in the multilayered solid, which was computed by fast inverse Laplace transform (FILT) and fast Fourier transform (FFT) algorithms. However, the calculation burden and low precision of FILT–FFT algorithm limit the application of reverberation matrix method. In this paper, we expand each of generalized-ray group integrals into the sum of a series of generalized-ray integrals, each of which is accurately evaluated by Cagniard–De Hoop method in the theory of generalized ray. The numerical examples demonstrate that the proposed method makes it possible to calculate the early-time transient response in the complex multilayered-solid configuration efficiently.

S-Domain analysis of lightning surges in three-phase systems using nonuniform single-phase line model

Surge response of the transmission tower in a three-phase transmission system is computed using s-domain nonuniform single-phase transmission line modelling. First, tower top voltage is obtained considering the tower and the ground wire by excluding the effect of the phase conductors, and then the induced voltages on the phase conductors as a result of the current flowing through the ground wire are computed using the magnetic coupling between the ground wire and the phase conductors. The first step of the analysis is the formulation of the system response in the s-domain, and the second step is the frequency to time domain conversion, which is carried out using fast inverse Laplace transform (FILT). The voltages on the phase conductors and the voltages across the tower insulators are computed, and some of the results obtained using s-domain analysis are compared with those obtaining using electromagnetic transients program (EMTP). The effect of frequency dependence of the line parameters is investigated.

Development of Evaluation Methods and Computer Softwares for Pharmacokinetic Analysis.

Some evaluation methods and computer analysis programs on personal computers have been developed for pharmacokinetic analysis. Akaike's Information Criterion (AIC) was introduced to statistically select an optimum model for drug disposition. The moment analysis which has bee been used in chromatography and chemical engineer was applied to the evaluation of absorption, distribution, metabolism and excretion (ADME) of drugs. A pharmacokinetic analysis program based on nonlinear least squares, MULTI, was developed on a personal computer in the early age. We have made other analysis program MULTI (RUNGE) where a pharmacokinetic model is defined as ordinal differential equations, MULTI (FILT) based on a Fast Inverse Laplace Transform (FILT) and MULTI (FEM) based on the Finite Element Method (FEM). MULTI2 (BAYES) based on Bayesian least squares and MULTI (ELS) based on extended least squares were developed for the population pharmacokinetics (PPK).

Computation of Transmission Line Transients by Using Fast Inverse Laplace Transform

In this paper. transients appearing power transmission systems due to line energization are computed by using Fast inverse Laplace Transform (FILT). s-domain transfer function of the system is calculated by using distributed parameter representation of transmission line. For the frequency to time domain transformation of transfer function, Fast Inverse Laplace Transform is applied. Comparisons are made between the results obtained by FILT and conventional methods such as conventional Laplace transform and Electromagnetic Transients Program (EMTP).

New hepatocellular diffusion model for analysis of hepatobiliary transport processes of drugs

A new hepatocellular diffusion model was developed to kinetically evaluate the hepatobiliary transport processes of drugs in the perfusion system, based on the physiological structure of the liver. Since the equations describing the hepatocellular diffusion phenomena were derived as image forms in the Laplace domain, the fast inverse Laplace transform (FILT) was adopted to manipulate the image equations. Cefixime and cefpiramide were selected as model drugs. The concentrations in the perfusate and the excreted amounts into the bile were simultaneously measured at appropriate intervals after the rapid administration of each drug into the portal vein. The hepatocellular diffusion model was fitted to the biliary excretion profiles from rat livers, by means of a nonlinear least squares program, MULTI(FILT). According to this model, the hepatobiliary transport process of drug is kinetically separated into three steps, that is, the diffusion into and through the hepatocytes, the transfer from the hepatocytes into the bile canaliculi, and the movement through the bile canaliculi to the outlet of bile duct. These steps are characterized by the diffusion rate constant through hepatocytes (kdif), the permeability rate constant into the bile canaliculi (kbmc) and the transit time through the bile canaliculi to the outlet of bile duct (tcan), respectively. It was demonstrated that kdif of cefixime (0.023 min-1) was significantly smaller than that of cefpiramide (0.044 min-1), while the differences in kbmc and tcan were not obvious between cefixime and cefpiramide. kbmc and tcan of both drugs were about 1.2 min-1 and about 1.0 min, respectively. These parameters were correlated to the excretion ratio into the bile (Fbile) and the mean transit time from the sinusoid through the hepatocytes to the outlet of bile duct (tbile).

Estimation of a concentration profile of acyclovir in the skin after topical administration

The Laplace transformed equations for the time courses of drug concentration in the skin and net absorption were derived from Fick's diffusion law assuming a two-layer skin model. Based on these equations, a new method for estimating drug concentration in the skin directly from the absorption profile was developed by the use of a fast inverse Laplace transform (FILT) algorithm. The absorption profiles of topically administered acyclovir in rats obtained through deconvolution of urinary excretion time courses against i.v. injection data were analyzed according to this method. The amount of acyclovir excreted into urine was only 0.42% of the applied dose at 8 h after topical application with polyethylene glycol ointment, suggesting low skin permeability, while most of acyclovir injected intravenously was excreted within 4 h. However, the analysis revealed that a considerable level (57 jug/cm3) higher than the minimum inhibitory concentration (MIC) was maintained in the viable tissue under the steady-state conditions.

Analysis of skin penetration enhancement based on a two-layer skin diffusion model with polar and nonpolar routes in the stratum corneum: dose-dependent effect of 1-geranylazacycloheptan-2-one on drugs with different lipophilicities.

The effects of 1-geranylazacycloheptan-2-one (GACH) on the in vitro skin penetration of seven drugs with various lipophilicities were studied. The penetration of drugs from aqueous vehicle through the guinea pig skin was increased depending on the pretreatment dose of GACH. The largest enhancement was observed for 5-fluorouracil (5-FU) and a bell-shaped relationship was obtained between enhancement ratio and the octanol/water partition coefficients of drugs. Further, Laplace transformed equations for percutaneous absorption of drug were derived from Fick's second law based on a two-layer skin diffusion model with polar and nonpolar routes in the stratum corneum. Through curve-fitting of their equations to penetration profiles using a nonlinear regression program MULTI(FILT) combined with a fast inverse Laplace transform (FILT) algorithm, the action mechanism of GACH was discussed in terms of its effect on the partitioning and diffusivity of drugs in each domain. With an increase in pretreatment dose of GACH, the estimated partition parameters of drugs into the nonpolar route increased but their diffusivities were little affected. The analysis based on a linear free-energy relationship suggested that the increase in partitioning of drugs into the nonpolar route was explained by its increasing polarity with GACH pretreatment.

Analysis of arterial–venous blood concentration difference of drugs based on recirculatory theory with fast inverse laplace transform (FILT)

An arterial and venous blood (or plasma) concentration difference of drugs across the lung of rats was evaluated based on the recirculatory concept. The recirculatory system is given by the combination of the transfer functions for the pulmonary and the systemic circulations and is described by a Laplace-transformed equation, i.e., an image equation. For the manipulation of the image equations, the fast inverse Laplace transform (FILT) was adopted and MULTI(FILT) was used for the simultaneous curve fitting to estimate the pharmacokinetic parameters in the recirculatory model. Metoprolol as a test drug and cephalexin as a control drug were infused respectively into the femoral vein for 30 min, and arterial and venous blood samples were collected simultaneously through the cannula at the femoral artery and at right atrium during and after the infusion. Exponential functions were assumed for the weight functions through both the pulmonary and systemic circulations. Results of the curve fitting showed that the single-pass extraction ratio through the pulmonary circulation (Ep) of metoprolol was about 0.2, whereas that of cephalexin was negligible. The mean transit times through the pulmonary circulation (tp) of metoprolol and cephalexin were both about 0.5 min, which is small. The single-pass extraction ratios through the systemic circulation (Es) of metoprolol and cephalexin were both about 0.1, and the mean transit times through the systemic circulation (ts) were 11.5 min and 8.2 min, respectively.

Analysis of enterohepatic circulation of cefixime in rat by fast inverse Laplace transform (FILT)

The enterohepatic circulation of cefixime in rat was evaluated by a nonlinear least square analysis program, MULTI(FILT), into which the fast inverse Laplace transform (FILT) was incorporated. The plasma time course in the bile duct-cannulated rat exhibited a biexponential curve after the rapid iv administration of cefixime. Several pharmacokinetic models for the enterohepatic circulation were constructed based on the recirculatory concept and the Laplace-transformed equations corresponding to these models were derived by means of the method of transfer function. The transformed equations were simultaneously fitted to the time courses of plasma concentration in rats with laparotomy and with bile duct cannula. The optimum model was selected based on the Akaike's information criterion (AIC). The local moment characteristics for a single pass through enterohepatic circulation were further calculated from the time courses of both the plasma concentration and the amount excreted into the bile. The recovery ratio (Fc) and the mean circulatory time (-tc) through a single pass of enterohepatic circulation were estimated 27.9% and 1.07 hr, respectively. The recovery ratio (Fa) and the mean absorption time (-tc) for the absorption process from the intestinal tract into the systemic circulation were 68.3% and 0.0234 hr, respectively. The recovery ratio (Fb) and the mean transit time (-tb) for the disposition process through the systemic circulation into the bile were 40.8% and 1.05 hr, respectively.

Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse Laplace transform (FILT).

A dispersion model developed in chromatographic theory is applied to the analysis of the elution profile in the liver perfusion system of experimental animals. The equation for the dispersion model with the linear nonequilibrium partition between the perfusate and an organ tissue is derived in the Laplace-transformed form, and the fast inverse Laplace transform (FILT) is introduced to the pharmacokinetic field for the manipulation of the transformed equation. By the analysis of the nonlinear least squares method associated with FILT, this model (two-compartment dispersion model) is compared to the model with equilibrium partition between the perfusate and the liver tissue (one-compartment dispersion model) for the outflow curves of ampicillin and oxacillin from the rat liver. The model estimation by Akaike's information criterion (AIC) suggests that the two-compartment dispersion model is more proper than the one-compartment dispersion model to mathematically describe the local disposition of these drugs in the perfusion system. The blood space in the liver, VB, and the dispersion number DN are estimated at 1.30 ml (+/- 0.23 SD) and 0.051 (+/- 0.023 SD), respectively, both of which are independent of the drugs. The efficiency number, RN, of ampicillin is 0.044 (+/- 0.049 SD) which is significantly smaller than 0.704 (+/- 0.101 SD) of oxacillin. The parameters in the two-compartment dispersion model are correlated to the recovery ratio, FH, mean transit time, tH, and the relative variance, sigma 2/t-2H, of the elution profile of drugs from the rat liver.