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Reconstructing the rate of appearance of subcutaneous insulin by deconvolution.

In this paper a deconvolution scheme is presented to reconstruct the rate of appearance of subcutaneously injected insulin. Relevant aspects of experiment design are briefly described. Intravenous insulin kinetics are modeled to determine the impulse response of the system. The deconvolution problem is not ill conditioned and is solved using a least-squares method without imposing constraints on the input. An estimate of the error of the reconstructed input is provided. The reliability of the deconvolution scheme is tested by means of an independent validation study. Finally, the different sources of error that affect the method are discussed, and a figure of the global error is derived.

Humans

Hydrocortisone secretion: production rate and pulse characterization by numerical deconvolution.

Based on serial blood sampling over 24 h, hydrocortisone was shown to be secreted episodically in the horse. The purpose of the present experiment was to characterize peaks and troughs by analyzing the instantaneous secretion rate profile obtained by a deconvolution technique rather than from the plasma concentration time profile. Kinetic parameters of hydrocortisone were determined following intravenous bolus and intravenous perfusion of hydrocortisone. Stationary and nonlinearity of hydrocortisone disposition were demonstrated. With the use of clearance values calculated from constant perfusion administration, the 24-h hydrocortisone production rate was estimated at 0.46 +/- 0.08 mg.kg-1.24 h-1. The instantaneous secretory profile was reconstituted by deconvoluting the plasma concentration profile using structural parameters determined from the bolus hydrocortisone administration. When this secretory profile was subjected to a pulse analysis program, the number of detected peaks was found to be 17.25 +/- 1.26 and the mean peak duration 34.01 +/- 5.52 min. The total duration of secretory activity was estimated at 582.5 +/- 63.97 min. By comparison, when the plasma concentration profile was analyzed directly, the number of peaks was only 10.0 +/- 1.41 but their mean duration was much longer, i.e., 105.25 +/- 21.24 min. The origin of these differences and the advantages and limits of deconvolution analysis are discussed.

Animals

Porcine and human insulin absorption from subcutaneous tissues in normal and insulin-dependent diabetic subjects: a deconvolution-based approach.

The mechanisms of sc insulin absorption are not understood, and models for interpreting in vivo data cannot be developed without gross simplification. To overcome this difficulty we developed a new approach which makes use of deconvolution analysis and does not require any model of the sc tissue. In five normal subjects and seven insulin-dependent diabetic (IDDM) patients endogenous insulin secretion was suppressed by means of a hypoglycemic glucose clamp procedure (approximately 2.8 mmol/L) sustained by a continuous insulin infusion (approximately 4 pmol/min.kg). A bolus injection of insulin (5.4 nmol) was administered iv, and plasma insulin concentrations were measured frequently for 2 h to assess iv insulin kinetics. Insulin then was injected sc in the abdominal region, and plasma insulin concentrations were measured for 8 h. Each subject was studied twice, with porcine and semisynthetic human insulin (Actrapid, Novo). The rate of insulin absorption was reconstructed by deconvolution from the plasma concentrations and iv insulin kinetic data. Linearity of the iv insulin kinetics, essential for deconvolution analysis, was confirmed by a dose-response study in the range of the measured concentrations (150-1800 pmol/L). In most instances, a two-compartment model was adequate to describe the iv response. The mean plasma insulin clearance rates were 15.5 +/- 1.9 (+/- SD) mL/min.kg (porcine) and 17.2 +/- 6.0 (human) in normal subjects and 20.7 +/- 8.8 (porcine) and 20.9 +/- 9.1 (human) in the IDDM patients. The rate of appearance of human insulin from sc tissue was faster than that of porcine insulin in both normal and IDDM subjects, but no significant differences were found in bioavailability, which was 55 +/- 12% (+/- SD; porcine) and 61 +/- 34% (human) in the normal subjects, and 84 +/- 28% (porcine) and 86 +/- 23% (human) in the IDDM patients. The rate of absorption and bioavailability were higher in the IDDM patients than in the normal subjects, a difference possibly related to increased sc blood flow in the IDDM patients. No differences were found with regard to glucose requirement values, normalized to plasma insulin concentrations, in agreement with the finding that the bioavailability of the two insulin species was similar.

Adolescent

Deconvolution of emission tomographic data: a clinical evaluation.

A method of improving the quality of images in single photon emission computed tomography (SPECT) is demonstrated using transaxial images of the liver and brain. Deconvolution of the nuclear medicine data by a point source response function (PSRF) acquired previously in a scattering medium attempts to compensate for scattered radiation within the patient. The average geometric response of the collimator of the gamma camera is also compensated for with this technique. Three patients with known metastatic lesions in the liver and three with primary lesions in the brain were imaged. Clinical assessment of reconstructed slices both before and after deconvolution demonstrates that compensating for the effects of scatter and of collimator blurring leads to enhanced detail of pathological lesions. In all cases, cold lesions seen prior to deconvolution were enhanced in detail and, in addition, new lesions were seen with this technique.

Adult

Deconvolution study of the absorption rate and disposition kinetic values of lindane in sheep.

Absorption rate and plasma and fat disposition of lindane after various lindane percutaneous treatments in shorn and unshorn sheep were investigated. To analyze data with a deconvolution method, IV administration was performed to determine the basic pharmacokinetic values of lindane in sheep. After IV administration, the steady state volume of distribution was very high (8.07 +/- 3.60 L/kg of body weight), and the mean residence time was long (28.1 +/- 11.7 hours). Deconvolution analysis indicated that lindane absorption was continuous until 33 to 41 days after spraying with a 0.025% lindane solution. Total amount of absorbed lindane in shorn (15,171 +/- 4,463 micrograms/kg) sheep was about twice that in unshorn (7,615 +/- 3,128 micrograms/kg) sheep; from deconvolution analysis, it was calculated that the time required for 50% of the available dose to be absorbed was between 115 and 179 hours. After percutaneous lindane administration, the fat concentration was compared with the available lindane dose. The apparent half-life of lindane elimination in fat was 225 +/- 47.4 hours, which is similar to the value calculated for the absorption rate constant. By comparing fat and plasma concentrations, it was calculated that for a mean plasma concentration of 5 ng/ml, the fat lindane concentration was 1.65 +/- 0.87 micrograms/g (ie, lower than the generally accepted tolerance level of 2 micrograms/g).

Adipose Tissue

An overview of computer algorithms for deconvolution-based assessment of in vivo neuroendocrine secretory events.

The availability of increasingly efficient computational systems has made feasible the otherwise burdensome analysis of complex neurobiological data, such as in vivo neuroendocrine glandular secretory activity. Neuroendocrine data sets are typically sparse, noisy and generated by combined processes (such as secretion and metabolic clearance) operating simultaneously over both short and long time spans. The concept of a convolution integral to describe the impact of two or more processes acting jointly has offered an informative mathematical construct with which to dissect (deconvolve) specific quantitative features of in vivo neuroendocrine phenomena. Appropriate computer-based deconvolution algorithms are capable of solving families of 100-300 simultaneous integral equations for a large number of secretion and/or clearance parameters of interest. For example, one application of computer technology allows investigators to deconvolve the number, amplitude and duration of statistically significant underlying secretory episodes of algebraically specifiable waveform and simultaneously estimate subject- and condition-specific neurohormone metabolic clearance rates using all observed data and their experimental variances considered simultaneously. Here, we will provide a definition of selected deconvolution techniques, review their conceptual basis, illustrate their applicability to biological data and discuss new perspectives in the arena of computer-based deconvolution methodologies for evaluating complex biological events.

Algorithms

Deconvolution of Compton scatter in SPECT.

A deconvolution algorithm has been developed which compensates for Compton scattering in SPECT images. Compton scatter is modeled as a convolution of the nonscattered projection data with an exponential function. Deconvolution of the total (scatter + nonscatter) projection data yields compensated true projection. Using Monte Carlo methods, the scattered and nonscattered components of a SPECT image are simulated thus allowing a comparison of scatter compensated results with direct nonscatter results. The quality of the compensation is evaluated by comparing the ratio of total to direct counts with the ratio of compensated to direct counts. This deconvolution technique has been developed and evaluated for experimentally acquired SPECT data as well as for simulated data.

Filtration

Continuous DNA Methylation Deconvolution-Based Surrogate for B-Cell Differentiation State in CLL.

Chronic Lymphocytic Leukemia (CLL) is clinically divided into IGHV mutated (M-CLL) and IGHV unmutated (U-CLL) subtypes, which are thought to arise from distinct cells of origin along the B-cell differentiation pathway. We measured genome-scale DNA methylation in purified CLL samples ( n = 89) and utilized reference-based cell deconvolution techniques to develop a continuous metric of epigenetic similarity across a B-naive-like to B-memory-like scale (B-Index). B-Index accurately classifies CLL into clinical subtypes (98.8%), has a stronger epigenetic signal than IGHV gene percent identity, and demonstrates additional epigenetic signal within the M-CLL subgroup. We demonstrate that U-CLL is epigenetically more similar to B-memory than B-naive cells and reconcile previous reports of a B-naive-like epigenetic signal. The B-memory-like program of U-CLL is enriched for binding sites of transcription factors related to the germinal center activation pathway. Our findings provide epigenetic evidence for discerning CLL mechanisms of initiation and cell of origin. We also identified an epigenetic signal associated with tumor burden, which may have some relation to viral infections such as Epstein-Barr-Virus. Our cell-type deconvolution-based approach to developing a continuous metric for CLL epigenetic differentiation state can be applied to other tumors with multiple subtypes across differentiation stages.

B-memory-like

Evaluation of in vivo drug release by numerical deconvolution using oral solution data as weighting function.

Determination of in vivo drug release using compartmental model analysis is hampered by problems such as flip-flop phenomena and vanishing exponential terms. The usefulness of numerical deconvolution to estimate in vivo drug release was evaluated in this study by means of simulated data comparing solid dosage forms with a solution as a reference standard. Concentration-time data were generated using the standard linear two-compartment body model with various first-order release and absorption rate constants. Random errors of 5 and 10% were added to data sets for further analysis. The results of the study using error-free data afforded excellent agreement with the theoretical values except in one case where the release rate constant was overestimated by 6%. When random error was added to the data, the resulting in vivo release profile showed considerable fluctuation and no single rate constant could be assigned. However, further analysis showed that the method does not create additional error during the calculating process, as previously suggested, but merely reflects the inherent error added to the raw data. If the raw data are poor, no useful information can be obtained without using an arbitrary technique such as smoothing or fitting. In this regard, the time course of drug release obtained after numerical deconvolution merits investigation.

Absorption

Numerical stability of pharmacokinetic deconvolution algorithms.

The sensitivity of pharmacokinetic deconvolution algorithms with respect to simulated experimental error has been studied. Approximations of cumulative absorption profiles reconstructed from simulated data sets with normally distributed random error were compared with corresponding known input functions. The coincidence of both functions was assessed in 600 numerical experiments by the nonparametric Kolmogorov-Smirnov test. A constrained iterative nonlinear regression procedure based on the analytical convolution of multiphasic zero-order input functions with linear disposition models was found to perform well under conditions where the results of direct numerical deconvolution and model-based mass balance methods were unsatisfactory.

Absorption

Adaptive computer program for determination of absorption profiles by numerical deconvolution: application to amoxicillin absorption.

We have developed a specific numerical deconvolution program for the Apple Macintosh microcomputer. After comparison with other methods, we used the program to evaluate the influence of nifedipine on the absorption and bioavailability of amoxicillin. The technique provided a model-independent approach. This study shows that the simultaneous administration of nifedipine with amoxicillin leads to a significant increase in both the total quantity of amoxicillin absorbed (+22%) and the rate of absorption. Parameters of clearance, volume of distribution, and elimination were unaffected. Numerical deconvolution analysis showed that nifedipine did not modify the absorption kinetics of amoxicillin, which are characterized by a lag time followed by a constant rate of absorption, suggesting zero-order kinetics with first-order kinetics at the end of the process. The results suggest the existence of a specialized, saturable transport molecule for this antibiotic.

Adult

Differentiation between transmembrane helices and peripheral helices by the deconvolution of circular dichroism spectra of membrane proteins.

The interpretation of the circular dichroism (CD) spectra of proteins to date requires additional secondary structural information of the proteins to be analyzed, such as X-ray or NMR data. Therefore, these methods are inappropriate for a CD database whose secondary structures are unknown, as in the case of the membrane proteins. The convex constraint analysis algorithm (Perczel, A., Hollósi, M., Tusnády, G., & Fasman, G. D., 1991, Protein Eng. 4, 669-679), on the other hand, operates only on a collection of spectral data to extract the common spectral components with their spectral weights. The linear combinations of these derived "pure" CD curves can reconstruct the original data set with great accuracy. For a membrane protein data set, the five-component spectra so obtained from the deconvolution consisted of two different types of alpha helices (the alpha helix in the soluble domain and the alpha T helix, for the transmembrane alpha helix), a beta-pleated sheet, a class C-like spectrum related to beta turns, and a spectrum correlated with the unordered conformation. The deconvoluted CD spectrum for the alpha T helix was characterized by a positive red-shifted band in the range 195-200 nm (+95,000 deg cm2 dmol-1), with the intensity of the negative band at 208 nm being slightly less negative than that of the 222-nm band (-50,000 and -60,000 deg cm2 dmol-1, respectively) in comparison with the regular alpha helix, with a positive band at 190 nm and two negative bands at 208 and 222 nm with magnitudes of +70,000, -30,000, and -30,000 deg cm2 dmol-1, respectively.

Adenosine Triphosphatases

Deconvolution analysis of 99mTc-methylene diphosphonate kinetics in metabolic bone disease.

The kinetics of 99mTc-methylene diphosphonate (MDP) and 47Ca were studied in three patients with osteoporosis, three patients with hyperparathyroidism, and two patients with osteomalacia. The activities of 99mTc-MDP were recorded in the lumbar spine, paravertebral soft tissues, and in venous blood samples for 1 h after injection. The results were submitted to deconvolution analysis to determine regional bone accumulation rates. 47Ca kinetics were analysed by a linear two-compartment model quantitating short-term mineral exchange, exchangeable bone calcium, and calcium accretion. The 99mTc-MDP accumulation rates were small in osteoporosis, greater in hyperparathyroidism, and greatest in osteomalacia. No correlations were obtained between 99mTc-MDP bone accumulation rates and the results of 47Ca kinetics. However, there was a significant relationship between the level of serum alkaline phosphatase and bone accumulation rates (R = 0.71, P less than 0.025). As a result deconvolution analysis of regional 99mTc-MDP kinetics in dynamic bone scans might be useful to quantitate osseous tracer accumulation in metabolic bone disease. The lack of correlation between the results of 99mTc-MDP kinetics and 47Ca kinetics might suggest a preferential binding of 99mTc-MDP to the organic matrix of the bone, as has been suggested by other authors on the basis of experimental and clinical investigations.

Adult

The appended curve technique for deconvolutional analysis--method and validation.

Deconvolutional analysis (DCA) is useful in correction of organ time activity curves (response function) for variations in blood activity (input function). Despite enthusiastic reports of applications of DCA in renal and cardiac scintigraphy, routine use has awaited an easily implemented algorithm which is insensitive to statistical noise. The matrix method suffers from the propagation of errors in early data points through the entire curve. Curve fitting or constraint methods require prior knowledge of the expected form of the results. DCA by Fourier transforms (FT) is less influenced by single data points but often suffers from high frequency artifacts which result from the abrupt termination of data acquisition at a nonzero value. To reduce this artifact, we extend the input (i) and response curves to three to five times the initial period of data acquisition (P) by appending a smooth low frequency curve with a gradual taper to zero. Satisfactory results have been obtained using a half cosine curve of length 2-3P. The FTs of the input and response I and R, are computed and R/I determined. The inverse FT is performed and the curve segment corresponding to the initial period of acquisition (P) is retained. We have validated this technique in a dog model by comparing the mean renal transit times of 131I-iodohippuran by direct renal artery injection to that calculated by deconvolution of an intravenous injection. The correlation was excellent (r = 0.97, P less than 0.005). The extension of the data curves by appending a low frequency "tail" before DCA reduces the data termination artifact. This method is rapid, simple, and easily implemented on a microcomputer.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals

Deconvolution applied to the kinetics of extracorporal drug removal. Haemodialysis of cefsulodin.

A novel approach to the evaluation of the kinetics of drug removal by an extracorporal device (ECD), e.g., haemodialysis, haemofiltration, and haemoperfusion, is presented. The rate and extent of extracorporal drug removal (ECR) are determined by deconvolution. The proposed method is model independent in the sense that no specific models of corporal or extracorporal disposition are required. The estimation of various derived functions and parameters useful for describing ECR such as clearance and fractional drug removal are facilitated by the technique. The kinetics of cefsulodin elimination by haemodialysis in 3 patients were evaluated using the deconvolution approach. The results indicated that cefsulodin was dialyzable with approximately 50% of the drug in the body removed by haemodialysis over 3-4 h.

Cefsulodin

A note on appropriate constraints on the initial input response when applying deconvolution.

When deconvolution is employed to estimate cumulative input profiles, nonzero initial values may result unless certain constraints are imposed on the function used to approximate the input response c(t). It is shown that the initial value of the response to a nonimpulse input is zero, i.e., c(t0) = 0, where t0 is the input lag time. If, in addition, the initial value of the impulse response is zero, i.e., c delta (0) = 0, then c'(t0) = 0. Therefore, it is appropriate to impose the constraint c(t0) = 0 in general and c'(t0) = 0 when c delta (0) = 0 if c(t) is the response to a nonimpulse input. The use of such constraints is demonstrated in an example where the cumulative in vivo dissolution profile is estimated by deconvolution.

Animals

Comments on two recent deconvolution methods.

In a recent paper Vajda et al. presented a deconvolution method based on the assumptions that the response of a system and the input function to a system are described by first-order linear processes. The method is similar to one proposed by Veng-Pedersen, and obtains similar results. In this article a simpler, not new, and now generally available method for this special use is considered to point out potential risks associated with all three deconvolution methods.

Cimetidine