Experimental design methodologies for the identification of Michaelis-Menten type kinetics

The main objective of this work was to investigate the application of experimental design techniques for the identification of Michaelis-Menten kinetic parameters. More specifically, this study attempts to elucidate the relative advantages/disadvantages of employing complex experimental design techniques in relation to equidistant sampling when applied to different reactor operation modes. All studies were supported by simulation data of a generic enzymatic process that obeys to the Michaelis-Menten kinetic equation. Different aspects were investigated, such as the influence of the reactor operation mode (batch, fed-batch with pulse wise feeding and fed-batch with continuous feeding) and the experimental design optimality criteria on the effectiveness of kinetic parameters identification. The following experimental design optimality criteria were investigated: 1) minimization of the sum of the diagonal of the Fisher information matrix (FIM) inverse (A-criterion), 2) maximization of the determinant of the FIM (D-criterion), 3) maximization of the smallest eigenvalue of the FIM (E-criterion) and 4) minimization of the quotient between the largest and the smallest eigenvalue (modified E-criterion). The comparison and assessment of the different methodologies was made on the basis of the Cramér-Rao lower bounds (CRLB) error in respect to the parameters vmax and Km of the Michaelis-Menten kinetic equation. In what concerns the reactor operation mode, it was concluded that fed-batch (pulses) is better than batch operation for parameter identification. When the former operation mode is adopted, the vmax CRLB error is lowered by 18.6 % while the Km CRLB error is lowered by 26.4 % when compared to the batch operation mode. Regarding the optimality criteria, the best method was the A-criterion, with an average vmax CRLB of 6.34 % and 5.27 %, for batch and fed-batch (pulses), respectively, while presenting a Km’s CRLB of 25.1 % and 18.1 %, for batch and fed-batch (pulses), respectively. As a general conclusion of the present study, it can be stated that experimental design is justified if the starting parameters CRLB errors are inferior to 19.5 % (vmax) and 45% (Km), for batch processes, and inferior to 42 % and to 50% for fed-batch (pulses) process. Otherwise equidistant sampling is a more rational decision. This conclusion clearly supports that, for fed-batch operation, the use of experimental design is likely to largely improve the identification of Michaelis-Menten kinetic parameters.

Famílias estruturadas de modelos com modelo base ortogonal: Teoria e aplicações

Dissertação apresentada para obtenção do Grau de Doutor em Matemática com especialização em Estatística pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia.

Ultrasound velocity profile (UVP) measurements in shallow open-channel flows

1st European IAHR Congress, 6-4 May, Edinburgh, Scotland

The friction force mouse-pad and the forearm muscles efforts (preliminary results)

The objective of the article is to evaluate the impact of the friction force mouse-pad in the contraction level of the forearm muscles M. extensor carpi ulnaris, M. extensor digitorum and M. extensor carpi radialis longus. A standard protocol of mouse movements was performed involving horizontal, vertical and diagonal mouse displacements drag-and-drop type. The operators were instructed to execute the protocol with their normal working speed. The movements protocol were performed by each subject (n=17) with three selected pairs mouse-pad, classified as low, medium and high friction force pairs. The mean time to execute the protocol with each mouse was ~138s. Mean values of ~13%MVE and ~17%MVE were found in the M. extensor carpi ulnaris and in the M. extensor digitorum respectively when performing the movements’ protocol. A 8.1% increase in %MVE was observed in the M. extensor digitorum and a 9.4% increase in %MVE was observed in the M. extensor carpi ulnaris when the high friction force pair was operated, relatively to the low friction force pair (p<0.05). The main preliminary conclusions of this study is that operating a high friction force mouse-pad may increase the risk to symptoms or disorders in the wrist due to an increase in the forearm muscles contraction levels, particularly during work with drawing application

Flexible multivariate GARCH modeling with an application to international stock markets

This paper offers a new approach to estimating time-varying covariance matrices in the framework of the diagonal-vech version of the multivariate GARCH(1,1) model. Our method is numerically feasible for large-scale problems, produces positive semidefinite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the nev^ estimator with a number of existing ones.

Optimisation and design of post-tensioning anchorage corner blisters in concrete box girder bidges

The design of anchorage blisters of internal continuity post-tensioning tendons of bridges built by the cantilever method, presents some peculiarities, not only because they are intermediate anchorages but also because these anchorages are located in blisters, so the prestressing force has to be transferred from the blister the bottom slab and web of the girder. The high density of steel reinforcement in anchorage blisters is the most common reason for problems with concrete cast in situ, resulting in zones with low concrete compacity, leading to concrete crushing failures under the anchor plates. A solution may involve improving the concrete compression and tensile strength. To meet these requirements a high-performance fibre reinforced self-compacting mix- ture (HPFRC) was used in anchorage corner blisters of post-tensioning tendons, reducing the concrete cross-section and decreasing the reinforcement needed. To assess the ultimate capacity and the adequate serviceability of the local anchorage zone after reducing the minimum concrete cross-section and the confining reinforcement, specified by the anchorage device supplier for the particular tendon, load transfer tests were performed. To investigate the behaviour of anchorage blisters regarding the transmission of stresses to the web and the bottom slab of the girder, and the feasibility of using high performance concrete only in the blister, two half scale models of the inferior corner of a box girder existing bridge were studied: a reference specimen of ordinary reinforced concrete and a HPFRC blister specimen. The design of the reinforcement was based in the tensile forces obtained on strut-and-tie models. An experimental program was carried out to assess the models used in design and to study the feasibility of using high performance concrete only in the blister, either with casting in situ, or with precast solutions. A non-linear finite element analysis of the tested specimens was also performed and the results compared.

Análise experimental da resistência ao corte do núcleo interior de alvenarias de pano múltiplo consolidadas com injecção de grouts

A quantidade de edifícios em degradação em Portugal que necessita de reabilitação é bastante elevada. As alvenarias antigas e históricas por vezes apresentam um estado avançado de degradação por ineficiente concepção ou por falta de manutenção. Desta forma as alvenarias necessitam de acções de reforço e consolidação com o intuito de fortalecer as suas resistências a diversos tipos de carregamentos. A presente dissertação está relacionada com uma técnica de consolidação das mais utilizadas e actuais, a injecção de grouts em alvenarias. O reforço por injecção de grouts é bastante utilizado em alvenarias de pano múltiplo, onde permite uma maior coesão entre materiais, uniformidade de tensões e continuidade de panos. Os principais objectivos de consolidação de uma alvenaria através da técnica de injecção de grouts são: a ocupação de espaços vazios de forma a aumentar a sua rigidez e a sua resistência; e o restabelecimento das ligações entre panos que ao longo do tempo deixou de existir, ou seja, um comportamento monolítico quando aplicado um carregamento vertical ou horizontal como um sismo. Daí a importância da análise de resistência ao corte numa da alvenaria de pano múltiplo. O presente trabalho teve uma componente laboratorial muito extensa, onde se efectuou injecções em modelos paralelipipédicos simulando o núcleo interior de uma parede de alvenaria antiga. O grout constituído por cal hidraúlica, superplastificante e água foi injectado no molde com um dos meios porosos de um dos dois materiais, calcário ou cerâmico. Após a cura cortaram-se em fatias os provetes e analisou-se a velocidade de propagação de ultra-sons com dois tipos de trandutores (cilíndricos e cónicos). Os ensaios mecânicos utilizados foram o diagonal test e o ensaio de corte directo de modo a determinar a resistência ao corte e finalmente comparou-se os valores dos ensaios para determinação das propriedades. Ainda com o intuito de avaliar as ligações grout-partícula do meio poroso foram avaliadas algumas fotografias tiradas a partir da lupa binocular. A técnica de injecção de grouts demonstrou-se uma técnica muito interessante e eficiente na análise de corte, no entanto esta técnica apresenta melhores resultados quando é utilizada em consonância com outras técnicas.