A physiological approach to renal clearance : from premature neonates to adults

Aims We propose using glomerular filtration rate (GFR) as the physiological basis for distinguishing components of renal clearance. Methods Gentamicin, amikacin and vancomycin are thought to be predominantly excreted by the kidneys. A mixed-effects joint model of the pharmacokinetics of these drugs was developed, with a wide dispersion of weight, age and serum creatinine. A dataset created from 18 sources resulted in 27,338 drug concentrations from 9,901 patients. Body size and composition, maturation and renal function were used to describe differences in drug clearance and volume of distribution. Results This study demonstrates that GFR is a predictor of two distinct components of renal elimination clearance: (1) GFR clearance associated with normal GFR and (2) non-GFR clearance not associated with normal GFR. All three drugs had GFR clearance estimated as a drug-specific percentage of normal GFR (gentamicin 39%, amikacin 90% and vancomycin 57%). The total clearance (sum of GFR and non-GFR clearance), standardized to 70 kg total body mass, 176 cm, male, renal function 1, was 5.58 L/h (95% confidence interval [CI] 5.50-5.69) (gentamicin), 7.77 L/h (95% CI 7.26-8.19) (amikacin) and 4.70 L/h (95% CI 4.61-4.80) (vancomycin). Conclusions GFR provides a physiological basis for renal drug elimination. It has been used to distinguish two elimination components. This physiological approach has been applied to describe clearance and volume of distribution from premature neonates to elderly adults with a wide dispersion of size, body composition and renal function. Dose individualization has been implemented using target concentration intervention

Nonuniform time discretization approach to batch and continuous process scheduling

The scheduling of batch and continuous operations has received considerable attention in the recent process systems engineering literature. Two basic conceptual models have been investigated: the cyclic, campaigned operations type and the non-cyclic type. The former has been used for multipurpose operations in which cross-contamination is a major concern while the latter is found in many types of specialty chemicals settings. From a modeling point of view, the campaigned operations offer a more convenient representation of time via campaign lengths and cycle times, while the noncyclic operation requires that time be treated as a continuum. The by now classical approach to resource constrained scheduling problems is to introduce a discretization of time and a set of assignment variables which identify whether or not a particular task is to be executed in a particular equipment item in given time interval. In general to adequately represent the processing times and other event times of the plant, the time quantum required for the discretization can be quite small compared to the planning horizon length, thus leading to very large 0-1 variable dimensionality and often excessively large computation times. In this thesis a general framework for accommodating a wide range of scheduling scenarios arising in multi product/multipurpose batch/continuous chemical processes is developed. The scheduling problem is formulated as a mixed integer nonlinear program based on a continuous time representation. Flexible equipment assignment and variable batch sizes are taken into account. To solve the resulting MINLP model an algorithm based on the Bayesian Heuristic Approach (BHA) to discrete optimization was developed. Test results suggest that the BHA combined with the continuous time representation shows promise for the solution of batch/continuous scheduling problems

A decomposition strategy for the variational inference of complex systems

<div><p>Markov chain Monte Carlo approaches have been widely used for Bayesian inference. The drawback of these methods is that they can be computationally prohibitive especially when complex models are analyzed. In such cases, variational methods may provide an efficient and attractive alternative. However, the variational methods reported to date are applicable to relatively simple models and most are based on a factorized approximation to the posterior distribution. Here, we propose a variational approach that is capable of handling models that consist of a system of differential-algebraic equations and whose posterior approximation can be represented by a multivariate distribution. Under the proposed approach, the solution of the variational inference problem is decomposed into three steps: a Maximum A Posteriori optimization which is facilitated by using an orthogonal collocation approach, a Preprocessing step which is based on the estimation of the eigenvectors of the posterior covariance matrix, and an Expected Propagation optimization problem. To tackle multivariate integration, we employ quadratures derived from the Smolyak rule (sparse grids). Examples are reported to elucidate the advantages and limitations of the proposed methodology. The results are compared to the solutions obtained from a Markov chain Monte Carlo approach. It is demonstrated that significant computational savings can be gained using the proposed approach. This paper has supplementary material online.</p></div