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DeMonS--a new deconvolution method for estimating drug absorbed at different time intervals and/or drug disposition model parameters using a monotonic cubic spline.

DeMonS-a new numerical deconvolution method for estimating the amount of drug absorbed at different time intervals and/or drug disposition model parameters-is presented here. In DeMonS, the amount of drug absorbed at different time intervals and/or drug disposition model parameters are the unknown parameters to be calculated. The Fritsch-Butland non-decreasing cubic spline was constructed from the cumulative amount of drug absorbed-time data directly derived from the calculated amount of drug absorbed at different time intervals. The drug absorption rate, which is the derivative of this non-decreasing cubic spline, is therefore represented by a piecewise non-negative quadratic function. The drug concentrations were obtained by convoluting the drug absorption rate quadratic function with the drug disposition model function. The nonlinear optimization method with simple parameter bounds was used to estimate the optimal set of unknown parameters by minimizing the sum of squares of residuals between the observed and predicted drug concentrations. DeMonS has been applied to (i) the griseofulvin data for estimating drug absorbed at different time intervals when the drug disposition model parameters were determined separately from intravenous data, (ii) veralipride double-peak phenomenon data to estimate simultaneously the percentage of cumulative veralipride absorbed and the veralipride disposition model parameters without reference intravenous data, (iii) a comparative bioequivalence study of gastrointestinal therapeutic system (GITS) pseudoephedrine HCI (PeHCI) controlled-release oral dosage forms when the drug disposition model parameters were not available, and (iv) estimation of both drug disposition model parameters and the absorption rate of drug from Testoderm (testosterone transdermal system) in the presence of endogenous testosterone production. DeMonS was implemented using MATLAB and NAG MATLAB Toolbox, and is available for Windows 3.1.

Absorption

Stability of finite difference deconvolution I: theoretical analysis.

Analysis of the stability of finite difference deconvolution (FDD) shows that it is dependent on the characteristics of the unit impulse response function and the sampling schedule of the input response function, and that stability properties are improved when the cumulative amount function is directly estimated rather than the rate function. The estimated input rate for an intravenous (iv) unit impulse response function and the release rate for an oral solution unit impulse response function are unstable for any sampling schedule of the input response function. However, for an iv unit impulse response function, the estimated cumulative amount absorbed is stable for any sampling schedule of the response function. For an oral unit impulse response function, the estimated cumulative amount released is unstable for all the sampling points of the input response function located before the time of the maximum of the oral unit impulse response function, but it can be made stable if an appropriately designed sampling schedule of the input response function is used. In addition, the theoretical basis for choosing a sampling schedule to overcome the instability of FDD has been established.

Algorithms

Stability of finite difference deconvolution II: simulation studies.

Theoretical analysis of the stability of finite difference deconvolution (FDD) indicates that if the cumulative amount function is used to characterize the drug input the method is stable for any sampling schedule for an intravenous unit impulse response function. The analysis also indicates that the method is stable for an oral unit impulse response only for well designed sampling schedules. This article confirms these results through numerical simulation experiments. It is shown that the assumption that the unit impulse response is error-free has an influence on the performance of FDD which is generally of no practical significance, except possibly for the first few points estimated. It is also shown that there is no significant interaction between the statistical error due to data noise and the deterministic algorithm error. The major source of error in practice is likely to be the data noise in the input response function. The simulations confirm that, with the estimated cumulative amount function as the quantity estimated and, with a well designed sampling schedule for the case of an oral unit impulse response, FDD is in practice an accurate and stable method with acceptable precision under a typical error disturbance.

Algorithms

Drug absorption evaluation in the presence of changes in clearance: an algorithm and computer program for deconvolution with exact clearance correction.

Most commonly drug absorption is evaluated with a reference dosing given on separate occasions. The assumption that no change in drug disposition is taking place between the drug administrations is often violated resulting in errors in the calculations. A novel deconvolution method is presented which exactly compensates for a change in drug clearance. The method is based on a model independent disposition decomposition-recomposition technique. The distribution function is obtained from an i.v. administration by disposition decomposition. This distribution function is assembled together with the elimination kinetics containing the perturbed clearance to construct the perturbed disposition function in the subsequent disposition recomposition operation. The perturbed absorption response is finally deconvolved using the corresponding perturbed disposition function. It is shown that the perturbed clearance can be obtained from the log-linear terminal disposition phase once the distribution function has been obtained from an i.v. administration. The proposed method is implemented in an algorithm and computer program DCONB and demonstrated using human cimetidine drug level data from an i.v. and oral administration. The usage of DCONB is identical to DECONV previously published. It requires only regular sums of exponentials to be fitted to drug level data. Such fittings are routinely done in pharmacokinetics thereby enabling DCONB to be implemented very simply.

Algorithms

A computer program for the deconvolution of mass spectral peak abundance data from experiments using stable isotopes.

A computer program is described for deconvoluting the overlap which is often found in mass spectral peak abundance data from stable isotope experiments. Peak intensity data from calibration standards are corrected using parameters calculated from the analysis of separate external standard solutions of analytes and internal standard. If the calibration data are satisfactory, the same parameters and the slope and intercept values from the least squares analysis of the calibration data are used to correct and quantitate the mass spectral peak intensity data from the quality assurance and experimental samples. Reports and graphs appropriate to the process are produced. Applications are given for the analysis of plasma samples from stable isotope experiments with carprofen, cifenline, and midazolam.

Carbazoles

Baseline deconvolution, phase correction, and signal quantification in Fourier localized spectroscopic imaging.

Lineshapes of spectra obtained through chemical-shift imaging are often distorted due to the delay in sampling necessary for application of phase-encoding gradients. We have developed an automated fitting procedure which simultaneously performs signal quantification, phase correction, and baseline deconvolution of such spectra. The fit is based on the maximum likelihood method and can be implemented in either the time or the frequency domain.

Fourier Analysis

Maximum entropy deconvolution of heterogeneity in protein modification: protein adducts of 4-hydroxy-2-nonenal.

To explore the chemistry of the reactions of the cytotoxic aldehyde trans-4-hydroxy-2-nonenal (HNE) with proteins, we incubated this aldehyde in vitro with beta-lactoglobulin B, a model protein of molecular weight 18,277 Da. Direct characterization of reaction products using electrospray ionization mass spectrometry yielded spectra whose complexity suggested extensive product heterogeneity. Spectra were transformed to a true mass scale using both a conventional transform algorithm and a maximum entropy algorithm. Both transformations demonstrated the formation of aldehyde-protein adducts containing from three to nine aldehyde molecules per molecule of protein. Maximum entropy deconvolution resolved Schiff base adducts and/or dehydration products, differing from the Michael addition adducts by 18 Da. The dominant reaction pathway, however, was Michael addition of the aldehyde to nucleophilic functional groups on the protein. The large number of Michael adducts relative to the one available cysteine requires that other amino acids, such as histidine and lysine, also be modified. The data suggest that methods for analysis of HNE that involve displacement of Schiff base groups from proteins will only recover a small fraction of HNE.

Aldehydes

Deconvolution of gel filtration chromatographs of human plasma lipoproteins.

Gel filtration chromatographs of lipoproteins represent a superposition, or convolution, of the intrinsic polydispersity of the solute and the dispersion due to transport phenomena. We describe a deconvolution technique for improving the resolution of gel filtration chromatographs applicable to lipoproteins and other polydisperse solutes. A matrix of spreading functions, characterizing the dispersive properties of the column, was determined by fitting chromatographic data from a series of monodisperse standards with the solution to the transport equations and interpolating between the fit parameters. A successive approximation scheme was used in which a test distribution was incrementally corrected by an amount proportional to the error between the measured chromatograph and that derived from the test distribution. A nonlinear relaxing function was used to constrain the correction term such that the solution remained physically realizable (i.e., nonnegative absorbance) as it evolved. Deconvolved chromatographs of lipoproteins provided resolution of peaks that were obscured by spreading in the original data. The distribution of particle sizes within each fraction was calculated and verified experimentally by further separating the contents of fractions by gradient gel electrophoresis. Our technique, however, provided comparable resolution of the peaks without the additional experimental procedure.

Algorithms

Reference deconvolution, phase correction, and line listing of NMR spectra by the 1D filter diagonalization method.

We describe a new way to attack the problem of identifying and quantifying the number of NMR transitions in a given NMR spectrum. The goal is to reduce the spectrum to a tabular line list of peak positions, widths, amplitudes, and phases, and to have this line list be of high fidelity. In this context "high fidelity" means that each true NMR transition is represented by a single entry, with no spurious entries and no missed peaks. A high fidelity line list allows the measurement of chemical shifts and coupling constants with good accuracy and precision and is the ultimate in data compression. There are two parts to the problem. The first is to overcome common imperfections: the non-Lorentzian lineshapes that can arise whenever the magnetic field inhomogeneity is less than perfect, and nonzero time delays that cause frequency-dependent phase errors. The second is to fit the spectral features to a model of Lorentzian lines. We use the recently developed filter diagonalization method (FDM) to accomplish the reference deconvolution, the phase correction, and the fitting, and show good progress toward the goal of obtaining a high fidelity line list.

Fourier Analysis

Maximum-entropy three-dimensional reconstruction with deconvolution of the contrast transfer function: a test application with adenovirus.

We have developed an objective, quantitative, and general algorithm to improve the fidelity of three-dimensional reconstructions made from electron micrographs while at the same time filtering much of the noise present in the recorded data. The new technique is called constrained maximum entropy tomography (COMET). The essence of the method is that it will produce the most featureless reconstruction that fits the projection data within their observational accuracy. In particular, the COMET procedure will minimise the detrimental effects of errors in the measured data and deconvolute the effects of the contrast transfer function. An objective test has been performed using COMET on a conventional image reconstruction obtained from cryo-electron micrographs of adenovirus. The density for hexon, the major coat protein of the virus, which is known to high resolution from X-ray crystallography, provided a known high-resolution control. The COMET reconstruction is in considerably better agreement with the crystallographic electron density than the original reconstruction, throughout the entire resolution range.

Adenoviridae

Practical guidance for testing the accuracy of deconvolution results from quantal analysis.

A Monte Carlo study was carried out to test the reliability of the Maximum Likelihood Estimator (MLE) approach for quantal analysis. This widely used statistical method was applied to extract a finite mixture of Gaussian distributions from simulated data. The data were generated by convolving a distribution of discrete amplitude steps (multiples of a unitary step Q) with Gaussian noise of various standard deviations (sigma n). Our results offer practical guidance on when to use the MLE, taking into account the determining parameters: signal to noise ratio (Q/sigma n, the most important parameter), number of samples collected and the number of components (k). For a given set of parameters the algorithm always converged to the "true" values, never converged to the "true" values or converged in only a fraction of cases to the "true" values. The behavior of the fitting routine in the parameter space is displayed in contour plots. These contour plots can be used as a guide to test the accuracy of deconvolution results.

Computer Simulation

Estimation of drug absorption rates using a deconvolution method with nonequal sampling times.

A method affording direct estimation of the drug absorption rate from blood level data using arbitrary time intervals has been derived based on the staircase input principle. In the derivation, the drug was assumed to follow linear kinetics where the plasma concentration of the drug after an impulse input is expressed by a multiexponential function. Drug absorption was assumed to occur at a constant rate during each subsequent sampling interval. The absorption rate profiles obtained by the method using several numerical examples were expressed as a set of rectangular pulses. Divergence in the profiles reflected blood sampling measurement errors rather than errors due to the deconvolution. Smoothing of the rate profiles by calculating the mean of the absorption rates between adjacent time intervals gave realistic results. Absorption rate profiles for theophylline obtained by the method using published data gave information on the initiation and termination of the absorption as well as the extent of absorption from the dosage form.

Humans

Selection of a histidine-containing inhibitor of gelatinases through deconvolution of combinatorial tetrapeptide libraries.

A fully automated peptide synthesizer was used to generate tetrapeptide sublibraries from 24 natural and nonnatural amino acids, from which new inhibitors of gelatinases (matrix metalloproteinases MMP-2 and MMP-9) were selected as potential anticancer drugs. MMP-2 and MMP-9 from mouse Balbc/3T3 fibroblasts conditioned media were assayed in their linear range response by zymography to quantify inhibition at each step of the tetrapeptide library deconvolution. The histidine-epsilon-amino caproic acid-beta-alanine-histidine (His-epsilon Ahx-beta Ala-His) sequence was found to yield optimal inhibition of both MMP-2 and MMP-9. Inhibition by selected tetrapeptides was also evaluated with two other techniques, a native type IV collagen degradation assay and a fluorogenic enzymatic assay, confirming the tetrapeptide potency. The His-epsilon Ahx-beta Ala-His tetrapeptide also inhibited purified human MMP-2 and MMP-9 and the corresponding enzymes present in conditioned media from human tumour cells. Finally, the length of the spacer between the two terminal histidines was found to be crucial to the inhibitory potential. This approach may thus be considered as a-successful strategy to yield specific peptide or pseudopeptide inhibitors, although their potency remains moderate, since it was measured before any chemical optimization was undertaken.

3T3 Cells

A comparison of six deconvolution techniques.

We present results for the comparison of six deconvolution techniques. The methods we consider are based on Fourier transforms, system identification, constrained optimization, the use of cubic spline basis functions, maximum entropy, and a genetic algorithm. We compare the performance of these techniques by applying them to simulated noisy data, in order to extract an input function when the unit impulse response is known. The simulated data are generated by convolving the known impulse response with each of five different input functions, and then adding noise of constant coefficient of variation. Each algorithm was tested on 500 data sets, and we define error measures in order to compare the performance of the different methods.

Algorithms

A method for in situ characterization of b- and c-type cytochromes in Escherichia coli and in complex III from beef heart mitochondria by combined spectrum deconvolution and potentiometric analysis.

An analytical technique for the in situ characterization of b- and c-type cytochromes has been developed. From evaluation of the results of potentiometric measurements and spectrum deconvolutions, it was concluded that an integrated best-fit analysis of potentiometric and spectral data gave the most reliable results. In the total cytochrome b content of cytoplasmic membranes from aerobically grown Escherichia coli, four major components are distinguished with alpha-band maxima at 77 K of 555.7, 556.7, 558.6 and 563.5 nm, and midpoint potentials at pH 7.0 of 46, 174, -75 and 187 mV, respectively. In addition, two very small contributions to the alpha-band spectrum at 547.0 and 560.2 nm, with midpoint potentials of 71 and 169 mV, respectively, have been distinguished. On the basis of their spectral properties they should be designated as a cytochrome c and a cytochrome b, respectively. In Complex III, isolated from beef heart mitochondria, five cytochromes are distinguished: cytochrome c1 (lambda m (25 degrees C) = 553.5 nm; E'0 = 238 mV) and four cytochromes b (lambda m (25 degrees C) = 558.6, 561.2, 562.1, 566.1 nm and E'0 = -83, 26, 85, -60 mV).

Animals

Applications of a general method for deconvolution using compartmental analysis.

A method of deconvolution is illustrated using compartmental models. The approach can be used to determine an arbitrary unknown input function from a measured response and the impulse response of the system. Compartmental models are constructed to specify (a) the function fitting the response data and (b) the impulse response of the system. Simulation of these models is then used to construct the unknown input function.

Alanine

Model-free deconvolution techniques for estimating vascular transport functions.

In this paper we present two methods which can be used to numerically deconvolve indicator dilution curves to obtain vascular transport functions. In the first method, direct algebraic deconvolution is made stable and practical by the damped least squares method. The second method involves a time-shift of the output curve which is based on the first and second moments of the input and output curves. This method is stable, computationally simple and can provide reasonable estimates of the transport function.

Animals