Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Elevated plasma membrane and sarcoplasmic reticulum Ca2+ pump mRNA levels in cultured aortic smooth muscle cells from spontaneously hypertensive rats

We have observed previously that Ca2+ pump-mediated Ca2+ efflux is elevated in cultured aortic smooth muscle cells from spontaneously hypertensive rats compared to those from Wistar-Kyoto rat controls. The objective of this work was to determine if these strains differ in mRNA levels for the PMCA1 isoform of the plasma membrane Ca2+-ATPase and the SERCA2 isoform of the sarcoplasmic reticulum Ca2+-ATPase. mRNA levels were compared in cultured aortic smooth muscle cells from 10-week-old male rats. PMCA1 and SERCA2 mRNA levels were elevated in SHR compared to WKY. Angiotensin II increased the level of PMCA1 and SERCA2 mRNA in both strains. These studies provide further evidence for alterered Ca2+ homeostasis in hypertension at the level of Ca2+ transporting ATPases in the spontaneously hypertensive rat model. These data are also consistent with the hypothesis that the expression of these two Ca2+ pumps may be linked. (C) 1997 Academic Press

The relationship between plasma potassium concentration and muscle torque during recovery following intense exercise

The present study investigated the relationship between plasma potassium ion concentration ([K+]) and skeletal muscle torque during three different 15-min recovery periods after fatigue induced by four 30-s sprints. Four males and one female completed the multiple sprint exercise on three separate days; recovery was passive, i.e. no cycling exercise (PRec), active cycling at 30% peak oxygen consumption (V) over dot(2peak) (30% Rec) and active cycling at 60% (V) over dot(2peak) (60% Rec). Plasma [K+] was measured from blood sampled from an antecubital vein of subjects at rest and at 0, 3, 5, 10 and 15 min into each recovery. Isokinetic leg strength was measured at rest and at 1, 6, 11 and 16 min during each recovery. Following the exhaustive sprints; [K+] increased significantly from an average mean (SEM) resting value of 3.81 (0.07) mmol.l(-1) to 4.48 (0.19) mmol.l(-1) (P < 0.01). In all recovery conditions, plasma [K+] returned to resting levels within 3 min following the fourth sprint. However, in the two active recovery conditions plasma [K+] increased over the remainder of the recovery periods to 4.36 (0.12) mmol.l(-1) in the 30% Rec condition and 4.62 (0.12) mmol.l(-1) in the 60% Rec condition, the latter being significantly higher than the former (P < 0.01). The maximum torque measured following the sprints decreased significantly, on average, to 61.1 (8.36)% of peak levels (P < 0.01). After 15 min of recovery, maximum torque was highest in the 30% Rec condition at 92.13 (3.06)% of peak levels (P < 0.01), compared to 85.23 (3.64)% and 85.71 (0.82)% for the PRec and 60% Rec conditions, respectively. In contrast to the significant differences in plasma [K+] across all three recovery conditions, muscle torque recovery was significantly different in only the 30% Rec condition. In summary, recovery of peak levels of muscle torque following fatiguing exercise does not appear to follow changes in plasma [K+].

The formal representation of process system modelling assumptions and their implications

In order to analyse the effect of modelling assumptions in a formal, rigorous way, a syntax of modelling assumptions has been defined. The syntax of modelling assumptions enables us to represent modelling assumptions as transformations acting on the set of model equations. The notion of syntactical correctness and semantical consistency of sets of modelling assumptions is defined and methods for checking them are described. It is shown on a simple example how different modelling assumptions act on the model equations and their effect on the differential index of the resulted model is also indicated.

Modeling of subcutaneous absorption kinetics of infusion solutions in the elderly using technetium

Absorption kinetics of solutes given with the subcutaneous administration of fluids is ill-defined. The gamma emitter, technitium pertechnetate, enabled estimates of absorption rate to be estimated independently using two approaches. In the first approach, the counts remaining at the site were estimated by imaging above the subcutaneous administration site, whereas in the second approach, the plasma technetium concentration-time profiles were monitored up to 8 hr after technetium administration. Boluses of technetium pertechnetate were given both intravenously and subcutaneously on separate occasions with a multiple dosing regimen using three doses on each occasion. The disposition of technetium after iv administration was best described by biexponential kinetics with a V-ss of 0.30 +/- 0.11 L/kg and a clearance of 30.0 +/- 13.1 ml/min. The subcutaneous absorption kinetics was best described as a single exponential process with a half-life of 18.16 +/- 3.97 min by image analysis and a half-life of 11.58 +/- 2.48 min using plasma technetium time data. The bioavailability of technetium by the subcutaneous route was estimated to be 0.96 +/- 0.12. The absorption half-life showed no consistent change with the duration of the subcutaneous infusion. The amount remaining at the absorption site with time was similar when analyzed using image analysis, and plasma concentrations assuming multiexponential disposition kinetics and a first-order absorption process. Profiles of fraction remaining at the absorption sire generated by deconvolution analysis, image analysis, and assumption of a constant first-order absorption process were similar. Slowing of absorption from the subcutaneous administration site is apparent after the last bolus dose in three of the subjects and can De associated with the stopping of the infusion. In a fourth subject, the retention of technetium at the subcutaneous site is more consistent with accumulation of technetium near the absorption site as a result of systemic recirculation.

Effects of process modification and heat pump drying on physical and sensory properties of Chinese style shredded beef

Chinese-style dried, shredded meat is traditionally prepared by sequential cooking, shredding, pre-drying, and final drying (roasting) of lean meat. In this study, shredded dried beef (a(w)<0.6) was prepared by omitting roasting but prolonging pre-drying. Sensory scores of the modified product were lower than those for the traditional product. When heat pump drying replaced traditional oven drying, drying time was shortened without significant difference in quality attributes. Desorption curves were established for shredded beef at several drying temperatures.