Abstract
In certain applications, e.g. during reconstruction of pulsatile hormone secretion, the traditional deterministic deconvolution techniques fail primarily due to ill conditioning. To overcome these problems, deconvolution was formulated using a stochastic approach within the Bayesian modelling framework. The stochastic deconvolution with a piece-wise constant definition of the signal (the input function) cannot be solved analytically but the solution was found by employing Markov chain Monte Carlo method. A computationally efficient sampling algorithm combined with a discrete deconvolution method was employed. An example analysis demonstrated the application of the stochastic deconvolution method to the estimation of hormone (insulin) secretion.
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References
W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, Chapman & Hall, London, 1996.
A. F. M. Smith, “Bayesian computational methods”, Phil. Trans. R. Soc. Lond. A, vol. 337, pp. 369–386, 1991.
A. F. M. Smith and G. O. Roberts, “Bayesian computation via the Gibbs sampler and related Markov-chain Monte-Carlo methods”, J.Roy.Statist.Soc.B., vol. 55, pp. 3–23, 1993.
D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind”, J. Assoc. Comput. Mach., vol. 9, pp. 97–101, 1962.
S. Twomey, “The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements”, J. Franklin Inst., vol. 279, pp. 95–109, 1965.
R. Hovorka, M. J. Chappell, K. R. Godfrey, F. N. Madden, M. K. Rouse, and P. A. Soons, “CODE: A deconvolution program implementing a regularisation method of deconvolution constrained to non-negative values. description and pilot evaluation”, Biopharm. Drug Dispos., vol. 19, pp. 39–53, 1998.
A. Jeffreys, The Theory of Probability, Cambridge University Press, Cambridge, 1961.
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machine”, J. Chem. Phys., vol. 21, pp. 1087–1091, 1953.
W. K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications”, Biometrika, vol. 57, pp. 97–109, 1970.
S. Chib and E. Greenberg, “Understanding the Metropolis-Hastings algorithm”, Amer. Statist., vol. 49, pp. 327–335, 1995.
W. R. Gilks, N. G. Best, and K. K. C. Tan, “Adaptive rejection Metropolis sampling within Gibbs sampling”, Appl. Statist., vol. 44, pp. 455–472, 1995.
D. R. Matthews, D. A. Lang, M. A. Burnett, and R. C. Turner, “Control of pulsatile insulin secretion in man”, Diabetologia, vol. 24, pp. 231–237, 1983.
B. Gumbiner, E. V. Van Cauter, W. F. Beltz, T. M. Ditzler, K. Griver, K. S. Polonsky, and R. R. Henry, “Abnormalities of insulin pulsatility and glucose oscillations during meals in obese noninsulin-dependent diabetic patients: effects of weight reduction”, J. Clin. Endocrinol. Metab., vol. 81, pp. 2061–2068, 1996.
N. M. O’Meara, J. Sturis, J. D. Blackman, D. C. Roland, E. Van Cauter, and K. S. Polonsky, “Analytical problems in detecting rapid insulin secretory pulses in normal humans”, Am. J. Physiol., vol. 264, pp. E231–E238, 1993.
R. Hovorka and R. H. Jones, “How to measure insulin secretion”, Diabetes/Metabolism Rev., vol. 10, pp. 91–117, 1994.
E. V. Van Cauter, F. Mestrez, J. Sturis, and K. S. Polonsky, “Estimation of insulin-secretion rates from C-peptide levels-comparison of individual and standard kinetic-parameters for C-peptide clearance”, Diabetes, vol. 41, pp. 368–377, 1992.
N. Best, M. K. Cowles, and S. K. Vines, CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output, Version 0.40, MRC Biostatistics Unit, Cambridge, 1997.
M. K. Charter and S. F. Gull, “Maximum entropy and its application to the calculation of drug absorption rates”, J. Pharmacokin. Biopharm., vol. 15, pp. 645–655, 1987.
D. Verotta, “Two constrained deconvolution methods using spline functions”, J. Pharmacokin. Biopharm., vol. 21, pp. 609–636, 1993.
D. J. Cutler, “Numerical deconvolution by least squares: Use of polynomials to represent the input function”, J. Pharmacokin. Biopharm., vol. 6, pp. 243–263, 1978.
D. J. Cutler, “Numerical deconvolution using least squares: Use of prescribed input functions”, J. Pharmacokin. Biopharm., vol. 6, pp. 227–241, 1978.
S. Vajda, K. R. Godfrey, and P. Valko, “Numerical deconvolution using system identification methods”, J. Pharmacokin. Biopharm., vol. 16, pp. 85–107, 1988.
P. Veng-Pedersen and N. B. Modi, “An algorithm for constrained deconvolution based on reparametrization”, J. Pharm. Sci., vol. 81, pp. 175–180, 1992.
R. Bellazzi, G. Magni, and G. De Nicolao, “Gibbs sampling for signal reconstruction”, in Proceedings of the 3rd IFAC International Symposium Modelling and Control in Biomedical Systems (Including Biological Systems), D. A. Linkens and E. R. Carson, Eds., Oxford, 1997, pp. 271–276, Elsevier.
P. Magni, R. Bellazzi, and G. De Nicolao, “Bayesian function learning using MCMC methods”, IEEE Trans. Pattn. Anal. Mach. Intell., vol. 20, pp. 1319–1331, 1999.
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Hovorka, R. (2000). Deconvolution and Credible Intervals using Markov Chain Monte Carlo Method. In: Brause, R.W., Hanisch, E. (eds) Medical Data Analysis. ISMDA 2000. Lecture Notes in Computer Science, vol 1933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39949-6_15
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DOI: https://doi.org/10.1007/3-540-39949-6_15
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