Multivariate Optimization Method Research Articles

A Biomathematical Model of Particle Clearance and Retention in the Lungs of Coal Miners: II. Evaluation of Variability and Uncertainty

The objective of this study is to investigate the sources of variability and uncertainty in a previously developed human lung dosimetry model. That three-compartment model describes the retention and clearance kinetics of respirable particles in the gas-exchange region of the lungs. It was calibrated using exposure histories and lung dust burden data in U.S. coal miners. A multivariate parameter estimation and optimization method was developed for fitting the dosimetry model to these human data. Models with various assumptions about overloading of alveolar clearance and interstitialization (sequestration) of particles were evaluated. Variability in the estimated clearance rate coefficients was assessed empirically by fitting the model to groups' and to each miner's data. Distributions of lung and lymph node particle burdens were computed at working lifetime exposures, using the variability in the estimated individual clearance rate coefficients. These findings confirm those of the earlier analysis; i.e., the best-fitting exposure–dose model to these data has substantial interstitialization/sequestration of particles and no dose-dependent decline in alveolar clearance. Among miners with different characteristics for smoking, disease, and race, the group median estimated alveolar clearance rate coefficients varied by a factor of approximately 4. Adjustment for these group differences provided some improvement in the dosimetry model fit to all miners (up to 25% reduction in MSE), although unexplained interindividual differences made up the largest source of variability. The predicted mean lung and lymph node particle burdens at age 75 after exposure to respirable coal mine dust at 2 mg/m2 for a 45-year working lifetime were 12 g (5th and 95th percentiles, 3.0–26 g) and 1.9 g (0.26–5.3), respectively. This study provides quantitative information on variability in particle retention and clearance kinetics in humans. It is useful for risk assessment by providing estimated lung dust burdens associated with occupational exposure to respirable particles.

Identification of Fuzzy Relational Models from Unevenly Distributed Data Using Optimization Methods

A wide range of algorithms for Fuzzy Relational Model (FRM) identification from process data have been developed over the last decade. It has been shown that the use of multi-variable optimization methods to establish the strengths of fuzzy relationships results in accurate models. Accuracy means here, however, the fit between training data and model predictions. If the available training data is unevenly distributed then optimization results in good model fit in regions where training data is clustered, but the regions where training data is sparse are less well modelled. The problem is frequently encountered as little influence is often possible on how training data is acquired. In this paper identification methods are proposed which take into account the distribution of training data. To enhance the model quality over the entire model range the input space is divided into regions in which the model error is considered separately during optimization. It is shown that the division of the input space by fuzzy partitioning is not sufficient. Problems which can occur due to unevenly distributed data are discussed and, based on the fuzzy partitioning, a new division of the input space is derived. These new input regions are described using rectangular or triangular fuzzy sets. It is shown that both shapes of fuzzy regions result in FRM with better predictive capabilities on unseen process data. An example for the application of the FRM in a Model Predictive Controller (MPC) is also given.

Evolution from univariate to multivariate optimization methods in liquid chromatography

The rational evolution of optimization methods, from univariate to multivariate, is described together with selected examples of their application. A novel approach, parametric modulation, is then proposed which overcomes many limitations of the present methods. In this approach, each mobile phase, stationary phase, temperature, etc. to be optimized is maintained in discrete and separate zones along the column. The overall retention is a rigorously predictable function of the retention time in each individual environment. Hence, complete multivariate optimization can be achieved with good accuracy using a minimum number of preliminary experiments. © 1996 John Wiley & Sons, Inc.

Chiral separations in supercritical fluid chromatography: a multivariate optimization method*

A multivariate optimization method, based on the method of steepest ascent, is proposed for the separation of two enantiomers on a chiral stationary phase in open-tubular column supercritical fluid chromatography. The objective of the method is to optimize start density, density gradient and temperature in order to locate a desired resolution in a first step and, if desired, minimize the retention time in a second step without decrease in resolution.

Algorithmic efficiency of simulated annealing for heat exchanger network design

Heat exchanger network synthesis by simulated annealing, a new multivariable optimization method based on the mathematical theory of Markov chains, has recently been reported by Dolan et al. ( Foundations of Computer- Aided Process Operations, CACHE, Elsevier, New York, 1987; AIChE Jl 35, 725, 1989). Two aspects of the algorithm strongly affect computation time: the evaluation of the change in cost between different randomly generated states and the annealing temperature schedule. This paper describes a new implementation of the simulated annealing algorithm that efficiently treats the first aspect through the use of a linked-list data structure to calculate changes in cost directly, resulting in a speed increase of two orders of magnitude over earlier implementations of the algorithm. The second aspect is addressed through the use of the annealing schedule of Aarts and van Laarhoven ( Philips J. Res. 40, 193, 1985). This new implementation of the algorithm is used to generate a new low-cost solution to the 7SP4 problem (Papoulias and Grossmann, Comput. Chem. Engng 7, 707, 1983; Floudas et al., AIChE Jl 32, 276, 1986).

Preparation of 11C-labelled SCH 23390 for the in vivo study of dopamine D-1 receptors using positron emission tomography

The dopamine D-1 receptor antagonist, SCH 23390 ((R)-(+)-8-chloro-2,3,4,5-tetrahydro-3-methyl-5- phenyl-1H-3-benzazepin-7-ol), was labelled by alkylation of the desmethyl compound SCH 24518 ((R)-(+)-8-chloro-2,3,4,5-tetrahydro-5-phenyl-1H-3-benzazepin-7-ol) with [ 11C]methyl iodide. A multivariate optimization method, Simplex, was employed to obtain the optimal radiochemical yield. Both straight-phase and reversed-phase preparative HPLC were investigated in the purification of [ 11C]SCH 23390. Reaction in acetone with subsequent straight-phase LC separation resulted in 80% radiochemical yield, based on [ 11C]methyl iodide, with a total synthesis time of 35–40 min and a radiochemical purity >99%. The average specific activity was on the order of 11.1 GBq/mmol. The 11C-labelled SCH 23390 was used to visualize the dopamine D-1 receptor-rich areas of a monkey brain by positron emission tomography. The data obtained showed a rapid distribution of radioactivity into the brain and a conspicious accumulation of [ 11C]SCH 23390 in the striatum.