Niels Rode Kristensen
Pharmacometrics, Experimental Medicine, Novo Nordisk A/S
Objectives: The objective of this contribution is to demonstrate the performance of a new deconvolution method based on stochastic differential equations (SDEs). The new method is equivalent to an existing impulse-response based stochastic deconvolution method for linear time-invariant systems, but, unlike the existing method, the new method can easily be extended to handle nonlinear, time-varying systems. Being based on SDEs, the new method facilitates reconstruction of unknown input signals (with confidence intervals) based on arbitrarily irregularly sampled data using arbitrarily fine discretization.
Methods: A stochastic state space model structure is used to describe the relationship between the unknown input and the observed output of the system, and the reconstruction of the unknown input signal is performed by means of a smoothing algorithm based on state filtering. Different assumptions may be applied for the evolution of the unknown input signal, e.g. a random walk or an integrated random walk, which corresponds to applying a penalty on the first or second derivative, respectively. This penalty may be adjusted manually or determined automatically using a maximum likelihood criterion.
Results: Simulated as well as real data was used to demonstrate the performance of the new deconvolution method. Using data from a simulated glucose clamp study, the new method provided a reconstruction of the unknown glucose disposal rate (with confidence intervals), which was identical to the one provided by the existing impulse-response based stochastic deconvolution method. Results obtained with the two methods where also similar when reconstructing C-peptide and LH secretion profiles using real data. The ability of the new method to handle nonlinear, time-varying systems was demonstrated using simulated data by showing that the unknown rate of appearance, following extravascular administration, of a drug with nonlinear elimination kinetics could be reconstructed.
Conclusion: The performance of a new deconvolution method based on SDEs, which may be applied to linear as well as nonlinear systems, was investigated. The new method was demonstrated to be equivalent to an existing method for linear time-invariant systems, while facilitating extension to nonlinear, time-varying systems, which was also demonstrated. Furthermore, the use of SDEs within the new method was shown to provide flexibility in terms of allowing arbitrarily irregular sampling and arbitrarily fine discretization.
Reference: PAGE 13 (2004) Abstr 531 [www.page-meeting.org/?abstract=531]
Poster: poster