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PubMed1981

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↗

PubMed1988

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↗

PubMed1985

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↗

PubMed1986

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↗

PubMed1990

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↗

PubMed1988

Numerical deconvolution using system identification methods.

A deconvolution method is presented for use in pharmacokinetic applications involving continuous models and small samples of discrete observations. The method is based on the continuous-time counterpart of discrete-time least squares system identification, well established in control engineering. The same technique, requiring only the solution of a linear regression problem, is used both in system identification and input identification steps. The deconvolution requires no a priori information, since the proposed procedure performs system identification (including optimal selection of model order), selects the form of the input function and calculates its parametric representation and its values at specified time points.

Models, Biological↗

PubMed1995

A nonparametric subject-specific population method for deconvolution: II. External validation.

A lot of attention has been given in the past to deconvolution and in particular to its nonparametric variants. In a companion paper (1), we present a fully nonparametric deconvolution method in which subject specificity is explicitly taken into account. To do so we use so-called "longitudinal splines." A longitudinal spline is a nonparametric function composed of a template spline, in common to all subjects, and of a distortion spline representing the difference of the subject's function from the template. In this paper we concentrate on testing and documenting the performance of this nonparametric methodology in terms of the approximation of unknown functions. We simulate population data using parametric functions, and use longitudinal splines to recover the unknown functions. We consider different estimation methods including (1) parametric nonlinear mixed effect, (2) least squares, and (3) two-stage. Methods 2-3 are more robust than Method 1, and obtain reliable estimates of the unknown functions. The lack of robustness of Method 1 appears to be due to the misspecifications of the distribution of the subjects' parameters. Results also suggest that in a data-rich situation nonparametric nonlinear mixed-effect models should be preferred.

Models, Theoretical↗

PubMed1999

Linear spectral deconvolution of catabolic plasma concentration decay in dialysis.

Deconvolution can be a useful step in the process of modelling biological data, as it produces an overview of the information content of the data, as well as directions about the structure of the mathematical model able to describe the generating system. This paper concerns the application of a deconvolution technique, spectral analysis, to the modelling process of the concentrations of metabolites sampled in plasma during dialysis: the spectral analysis consists in linearly identifying the whole spectrum of multi-exponential decays, describing the compartmental nature of the process. The application to urea and creatinin time series provides a careful determination of the spectra of the exponential decays, thus giving interesting insight into the system kinetics: a sharp, slow decay (about 0.23 h-1 for urea and 0.17 h-1 for creatinin) affects all the subjects, whereas a variable set of smaller and faster components accounts for interpatient variability as well as for the multicompartmental nature of the process. The power ratio of the components is an index of the relative amount of volume in the related compartments. The identified spectra provide a description of the data that, although computed in a very simple way, is consistent with the results of the classical identification techniques previously applied in building compartmental models of dialysis.

Computational Biology↗

PubMed1997

Removal of catheter distortion in multiple indicator dilution studies: a deconvolution-based method and case studies on glucose blood-tissue exchange.

The study of blood-tissue exchange by the multiple indicator dilution technique often needs frequent sampling in the blood of the indicator dilution curves (IDC). Usually, this requires the use of a catheter supported by a pump. This causes a distortion in the IDC, which must be removed for proper interpretation of the data. A deconvolution-based methodology to remove IDC distortion is presented. First, the catheter impulse response is modelled by means of data obtained from a suitable experiment. Then the reconstruction of the blood IDC is tackled by a new nonparametric deconvolution algorithm, which provides (quasi) time-continuous signals and exploits statistically based criteria for the choice of the regularisation parameter. The methodology is applied to the removal of catheter distortion in studies of glucose blood-tissue exchange in the human forearm and myocardium.

Blood Glucose↗

PubMed2001

Practical injection-rate CT perfusion imaging: deconvolution-derived hemodynamics in a case of stroke.

Previously reported methods of dynamic, contrast-enhanced, CT perfusion imaging in acute stroke have been promising but substantially limited by their dependence on very rapid rates of injection (typically 10-20 ml/s in an arm vein). Newly available deconvolution software permits the use of lower rates of injection (e. g., 3-4 ml/s), and rapidly provides maps of cerebral blood flow, cerebral blood volume and mean transit time. We report the potential of CT perfusion imaging performed with an injection rate of 4 ml/s to provide information on the extent of hemodynamic abnormality, and to help distinguish viable from nonviable ischemic tissue. The slower injection rates permitted by deconvolution analysis substantially enhance the practicality of CT perfusion imaging for studying stroke.

Brain↗

PubMed1999

A deconvolution technique for processing small intestinal transit data.

The deconvolution technique can be used to compute small intestinal impulse response curves from scintigraphic data. Previously suggested approaches, however, are sensitive to noise from the data. We investigated whether deconvolution based on a new simple iterative convolving technique can be recommended. Eight healthy volunteers ingested a meal that contained indium-111 diethylene triamine penta-acetic acid labelled water and technetium-99m stannous colloid labelled omelette. Imaging was performed at 30-min intervals until all radioactivity was located in the colon. A Fermi function=(1+e-alphabeta)/(1+e(t-alpha)beta) was chosen to characterize the small intestinal impulse response function. By changing only two parameters, alpha and beta, it is possible to obtain configurations from nearly a square function to nearly a monoexponential function. Small intestinal input function was obtained from the gastric emptying curve and convolved with the Fermi function. The sum of least squares was used to find alpha and beta yielding the best fit of the convolved curve to the observed small intestinal time-activity curve. Finally, a small intestinal mean transit time was calculated from the Fermi function referred to. In all cases, we found an excellent fit of the convolved curve to the observed small intestinal time-activity curve, that is the Fermi function reflected the small intestinal impulse response curve. Small intestinal mean transit time of liquid marker (median 2.02 h) was significantly shorter than that of solid marker (median 2.99 h; P<0.02). The iterative convolving technique seems to be an attractive alternative to ordinary approaches for the processing of small intestinal transit data.

Adult↗

PubMed1984

F/F deconvolution of fluorescence decay data.

An approach for the deconvolution of multiexponential fluorescence decay data in which a single exponential decay is used in place of the usual excitation profile is described. For analysis by the method of moments, the resulting decay lifetimes are identical to those in the multiexponential decay, while the pre-exponential factors are a simple function of the true values and the parameters of the single exponential decay. This approach, which we call the F/F deconvolution method, is capable of eliminating the errors in decay analyses which arise from the wavelength dependence of the instrument response function.

Computers↗

PubMed1982

A deconvolution program for processing radiotracer dilution curves.

We present a computer program for deconvolution of noisy signals. The unknown signal is modelled as a stochastic process and the solution is given by the 'maximum a posteriori estimator'. This is computed by two algorithms: the first uses and the Kalman filter; the second the conjugate gradient technique which permits introduction of a positivity constraint. The program has proved to give accurate results in stimulation studies. It has been applied to the deconvolution analysis of radionuclide angiocardiography time-activity curves. This improves the reliability of the results in left-to-right cardiac shunt quantitation.

Angiocardiography↗

PubMed1982

Computer simulation for deconvolution of a heat conduction batch microcalorimeter by the D-B Finite Element Technique.

The method described here is a general numerical analysis procedure which has been applied to a heat conduction Batch calorimeter for the deconvolution of its thermograms, and is based on a computer simulation of the heat conduction behavior of the instrument with time. We show by means of test signals that the method can deconvolute the signal with a resolving time that is about two orders of magnitude smaller than the time constant of the calorimeter itself. The method can be applied to time signals generally, provided that the instrument producing them can be simulated.

Calorimetry↗

PubMed1994

Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners.

Singular value decomposition (SVD) is deeply rooted in the theory of linear algebra, and because of this is not readily understood by a large group of researchers who could profit from its application. In this paper, we discuss the subject on a level that should be understandable to scientists who are not well versed in linear algebra. However, because it is necessary that certain key concepts in linear algebra be appreciated in order to comprehend what is accomplished by SVD, we present the section, 'Bare basics of linear algebra'. This is followed by a discussion of the theory of SVD. Next we present step-by-step examples to illustrate how SVD is applied to deconvolute a titration involving a mixture of three pH indicators. One noiseless case is presented as well as two cases where either a fixed or varying noise level is present. Finally, we discuss additional deconvolutions of mixed spectra based on the use of the pseudoinverse.

Mathematical Computing↗

PubMed1992

Quantal analysis using maximum entropy noise deconvolution.

When applying quantal analysis to synaptic transmission it is often unclear how much of the measured postsynaptic signal fluctuation arises from random sampling and noise rather than from the probabilistic transmitter release process. Unconstrained noise deconvolution methods do not overcome this because they tend to overfit the data, often giving a misleading picture of the underlying process. Instead, maximum entropy deconvolution provides a solution which is the smoothest, or most featureless, distribution that is still compatible with the data, taking noise and sample size into account. A simple way of achieving this is described, together with results of Monte Carlo simulations which show that the features present in the maximum entropy solution usually reflect the process underlying the data and not random sampling or noise.

Algorithms↗

PubMed1987

A FORTRAN program for deconvolution analysis using the matrix algorithm method with special reference to renography.

A FORTRAN IV program is presented for deconvolution analysis using the matrix algorithm method. With the deconvolution technique retention functions are calculated from time-activity curve data representing both kidneys and blood background. The program computes for each kidney the minimum and maximum time of the retention function. It also calculates the initial amplitudes, absolute as well as relative, and the mean transit time of the retention functions. The design of the program allows for optional reviews of intermediate outputs at important stages. It also allows for the plotting of conventional time-activity curves of both kidneys corrected for blood background. Finally, the program plots the retention functions and some of their characteristics.

Algorithms↗

PubMed1986

Simultaneous analysis of multiple fluorescence decay curves by Laplace transforms. Deconvolution with reference or excitation profiles.

The properties and potentials of the noniterative Laplace deconvolution (LAP2) (M. Ameloot and H. Hendrickx, Biophys. J. 44 (1983) 27) are further investigated. It is shown that LAP2 is exact and that no extrapolations have to be calculated or assumed for the data measured in the actual time window if the impulse response function of the investigated system can be described by a sum of exponentials. The formulas for the LAP2 deconvolution against the measured decay of a reference compound instead of the recorded excitation profile are derived. The procedure for the simultaneous analysis of multiple fluorescence decay curves by LAP2 is described in detail. This global analysis allows one to link any decay parameter, is fast and compares favorably with the nonlinear least-squares iterative reconvolution methods. Because of its short computation time the global analysis by LAP2 provides an efficient way to analyze the fluorescence decay surface in terms of decay associated spectra.

Anthracenes↗