Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

The mathematical modelling of the environmental performance of buildings as an aid in the design process

This thesis is a theoretical study of the accuracy and usability of models that attempt to represent the environmental control system of buildings in order to improve environmental design. These models have evolved from crude representations of a building and its environment through to an accurate representation of the dynamic characteristics of the environmental stimuli on buildings. Each generation of models has had its own particular influence on built form. This thesis analyses the theory, structure and data of such models in terms of their accuracy of simulation and therefore their validity in influencing built form. The models are also analysed in terms of their compatability with the design process and hence their ability to aid designers. The conclusions are that such models are unlikely to improve environmental performance since: a the models can only be applied to a limited number of building types, b they can only be applied to a restricted number of the characteristics of a design, c they can only be employed after many major environmental decisions have been made, d the data used in models is inadequate and unrepresentative, e models do not account for occupant interaction in environmental control. It is argued that further improvements in the accuracy of simulation of environmental control will not significantly improve environmental design. This is based on the premise that strategic environmental decisions are made at the conceptual stages of design whereas models influence the detailed stages of design. It is hypothesised that if models are to improve environmental design it must be through the analysis of building typologies which provides a method of feedback between models and the conceptual stages of design. Field studies are presented to describe a method by which typologies can be analysed and a theoretical framework is described which provides a basis for further research into the implications of the morphology of buildings on environmental design.

Spray dried combinations of lactoferrin with antibiotics appear superior to monotherapy for reducing biofilm formation by pseudomonas aeruginosa

SD Apo Lactoferrin-Tobramycin/Gentamicin Combinations are superior to monotherapy in the eradication of Pseudomonas aeruginosa Biofilm in the lungs Wilson Oguejiofor1, Lindsay J. Marshall1, Andrew J. Ingham1, Robert Price2, Jag. Shur2 1School of Life and Health Sciences, Aston University, Birmingham, UK. 2School of Pharmacy and Pharmacology, University of Bath, Bath, UK. KEYWORDS: lactoferrin, apo lactoferrin, spray drying, biofilm, cystic fibrosis Introduction Chronic lung infections from the opportunistic pathogeen Pseudomonas aeruginosa has been recognised as a major contributor to the incidences of high morbidity and mortality amongst cystic fibrosis (CF) patients (1,2). Currently, strategies for managing lung infections in CF patients involves the aggressive use of aerosolised antibiotics (3), however, increasing evidence suggests that the biofilm component of P. aeruginosa in the lower airway remains unperturbed and is associated with the development of antibiotic resistance. If this is so then, there is an urgent need to suitably adjust the current treatment strategy so that it includes compounds that prevent biofilm formation or disrupt established biofilms. It is well understood that biofilm formation is strongly dependent on iron (Fe3+) availability (4), therefore aerosolised anti-infective formulations which has the ability to chelate iron may essentially be a well suited therapy for eliminating P. aeruginosa biofilms on CF airway epithelial cells (5). In this study, we report the use of combination therapy; an aminoglycosides (tobramycin and gentamicin) and an antimicrobial peptide (lactoferrin) to significantly deplete P. aeruginosa biofilms. We demonstrate that lactoferrin-tobramycin and lactoferrin-gentamicin combinations are superior to the single antibiotic regime currently being employed to combat P. aeruginosa biofilms. MATERIALS AND METHOD Antibiotics: The antibiotics used in this study included gentamicin and tobramycin supplied by Fagron, UK. Bacterial strain and growth conditions: Pseudomonas aeruginosa strain PAO1 was provided by Prof. Peter Lambert of Aston University, Birmingham UK. The Strains were routinely grown from storage in a medium supplemented with magnesium chloride, glucose and casamino acids. Dialysis of lactoferrin: Apo lactoferrin was prepared by dialyzing a suspension of lactoferrin for 24 hrs at 4 °C against 20 mmol/L sodium dihydrogen phosphate, 20 mmol/L sodium acetate and 40 mmol/L EDTA (pH 3.5). Ferric ion (Fe3+) removal was verified by atomic absorption spectroscopy measurements. Spray drying of combinations of lactoferrin and apo lactoferrin with the different aminoglycosides: Combinations of tobramycin and gentamicin with the different preparations of lactoferrin were spray dried (SD) as a 2% (w/v) aqueous suspension. The spray drying parameters utilized for the production of suitable micron-sized particles includes: Inlet temperature, 180°C, spray flow rate, 606 L/hr; pump setting, 10%; aspirator setting, 85% (34m3/hr) to produce various outlet temperatures ranging from 99 - 106°C. Viability assay: To test the bactericidal activity of the various combinations, a viability assay was performed as previously described by Xu, Xiong et al. (6) with some modifications. Briefly, 10µL of ~ c. 6.6 x 107 CFU mL-1 P. aeruginosa strain PAO1 suspension were incubated (37°C, 60 mins) with 90 µL of a 2 µg/mL concentration of the various combinations and sampled every 10 mins. After incubation, the cells were diluted in deionised water and plated in Mueller hinton agar plates. Following 24 h incubation of the plates at 37°C, the percentage of viable cells was determined relative to incubation without added antibiotics. Biofilm assay: To test the susceptibility of the P. aeruginosa strain to various antibiotics in the biofilms mode of growth, overnight cultures of P. aeruginosa were diluted 1:100 into fresh medium supplemented with magnesium chloride, glucose and casamino acids. Aliquots of the dilution were dispensed into a 96 well dish and incubated (37°C, 24 h). Excess broth was removed and the number of colony forming units per milliliter (CFU/mL) of the planktonic bacteria was quantified. The biofilms were then washed and stained with 0.1% (w/v) crystal violet for 15 mins at room temperature. Following vigorous washing with water, the stained biofilms were solubilized in 30% acetic acid and the absorbance at 550nm of a 125 µL aliquot was determined in a microplate reader (Multiskan spectrum, Thermo Scientific) using 30% acetic acid in water as the blank. Aliquots of the broth prior to staining were used as an indicator of the level of planktonic growth. RESULTS AND DISCUSSION Following spray drying, the mean yield, volume weighted mean diameter and moisture content of lactoferrin powder were measured and were as follows (Table 1 and table 2); Table 1: Spray drying parameters FormulationInlet temp (°C)Outlet temp (°C)Airflow rate (L/hr)Mean yield (%)Moisture content (%) SD Lactoferrin18099 - 10060645.2 ±2.75.9 ±0.4 SD Apo Lactoferrin180100 - 10260657.8 ±1.85.7 ±0.2 Tobramycin180102 - 10460682.1 ±2.23.2 ±0.4 Lactoferrin + Tobramycin180104 - 10660687.5 ±1.43.7 ±0.2 Apo Lactoferrin + Tobramycin180103 - 10460676.3 ±2.43.3 ±0.5 Gentamicin18099 - 10260685.4 ±1.34.0 ±0.2 Lactoferrin + Gentamicin180102 - 10460687.3 ±2.13.9 ±0.3 Apo Lactoferrin + Gentamicin18099 -10360680.1±1.93.4 ±0.4 Table 2: Particle size distribution d10 d50d90 SD Lactoferrin1.384.9111.08 SD Apo Lactoferrin1.284.7911.04 SD Tobramycin1.254.9011.29 SD Lactoferrin + Tobramycin1.175.2715.23 SD Apo Lactoferrin + Tobramycin1.115.0614.31 SD Gentamicin1.406.0614.38 SD Lactoferrin + Gentamicin1.476.2314.41 SD Apo Lactoferrin + Gentamicin1.465.1511.53 The bactericidal activity of the various combinations were tested against P. aeruginosa PAO1 following a 60 minute incubation period (Figure 1 and Figure 2). While 2 µg/mL of a 1:1 combination of spray dried apo lactoferrin and Gentamicin was able to completely kill all bacterial cells within 40 mins, the same concentration was not as effective for the other antibiotic combinations. However, there was an overall reduction of bacterial cells by over 3 log units by the other combinations within 60 mins. Figure 1: Logarithmic plot of bacterial cell viability of various combinations of tobramycin and lactoferrin preparations at 2µg/mL (n = 3). Figure 2: Logarithmic plot of bacterial cell viability of various combinations of gentamicin and lactoferrin preparations at 2µg/mL (n = 3). Crystal violet staining showed that biofilm formation by P. aeruginosa PAO1 was significantly (ANOVA, p < 0.05) inhibited in the presence of the different lactoferrin preparations. Interestingly, apo lactoferrin and spray dried lactoferrin exhibited greater inhibition of both biofilm formation and biofilm persistence (Figure 2). Figure 2: Crystal violet staining of residual biofilms of P. aeruginosa following a 24hr incubation with the various combinations of antibiotics and an exposure to 48 hr formed biofilms. CONCLUSION In conclusion, combination therapy comprising of an antimicrobial peptide (lactoferrin) and an aminoglycosides (tobramycin or gentamicin) provides a feasible and alternative approach to monotherapy since the various combinations are more efficient than the respective monotherapy in the eradication of both planktonic and biofilms of P. aeruginosa. ACKNOWLEDGEMENT The authors would like to thank Mr. John Swarbrick and Friesland Campina for their generous donation of the Lactoferrin. REFERENCES 1.Hassett, D.J., Sutton, M.D., Schurr, M.J., Herr, A.B., Caldwell, C.C. and Matu, J.O. (2009), "Pseudomonas aeruginosa hypoxic or anaerobic biofilm infections within cystic fibrosis airways". Trends in Microbiology, 17, 130-138. 2.Trust, C.F. (2009), "Antibiotic treatment for cystic fibrosis". Report of the UK Cystic Fibrosis Trust Antibiotic Working Group. Consensus document. London: Cystic Fibrosis Trust. 3.Garcia-Contreras, L. and Hickey, A.J. (2002), "Pharmaceutical and biotechnological aerosols for cystic fibrosis therapy". Advanced Drug Delivery Reviews, 54, 1491-1504. 4.O'May, C.Y., Sanderson, K., Roddam, L.F., Kirov, S.M. and Reid, D.W. (2009), "Iron-binding compounds impair Pseudomonas aeruginosa biofilm formation, especially under anaerobic conditions". J Med Microbiol, 58, 765-773. 5.Reid, D.W., Carroll, V., O'May, C., Champion, A. and Kirov, S.M. (2007), "Increased airway iron as a potential factor in the persistence of Pseudomonas aeruginosa infection in cystic fibrosis". European Respiratory Journal, 30, 286-292. 6.Xu, G., Xiong, W., Hu, Q., Zuo, P., Shao, B., Lan, F., Lu, X., Xu, Y. and Xiong, S. (2010), "Lactoferrin-derived peptides and Lactoferricin chimera inhibit virulence factor production and biofilm formation in Pseudomonas aeruginosa". 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