Análise da biorremediação de compostos monoaromáticos em água através da pseudomonas aeruginosa

The monoaromatic compounds are toxic substances present in petroleum derivades and used broadly in the chemical and petrochemical industries. Those compounds are continuously released into the environment, contaminating the soil and water sources, leading to the possible unfeasibility of those hydrous resources due to their highly carcinogenic and mutagenic potentiality, since even in low concentrations, the BTEX may cause serious health issues. Therefore, it is extremely important to develop and search for new methodologies that assist and enable the treatment of BTEX-contaminated matrix. The bioremediation consists on the utilization of microbial groups capable of degrading hydrocarbons, promoting mineralization, or in other words, the permanent destruction of residues, eliminating the risks of future contaminations. This work investigated the biodegradation kinetics of water-soluble monoaromatic compounds (benzene, toluene and ethylbenzene), based on the evaluation of its consummation by the Pseudomonas aeruginosa bacteria, for concentrations varying from 40 to 200 mg/L. To do so, the performances of Monod kinetic model for microbial growth were evaluated and the material balance equations for a batch operation were discretized and numerically solved by the fourth order Runge-Kutta method. The kinetic parameters obtained using the method of least squares as statistical criteria were coherent when compared to those obtained from the literature. They also showed that, the microorganism has greater affinity for ethylbenzene. That way, it was possible to observe that Monod model can predict the experimental data for the individual biodegradation of the BTEX substrates and it can be applied to the optimization of the biodegradation processes of toxic compounds for different types of bioreactors and for different operational conditions.

Análise da biorremediação de compostos monoaromáticos em água através da pseudomonas aeruginosa

The monoaromatic compounds are toxic substances present in petroleum derivades and used broadly in the chemical and petrochemical industries. Those compounds are continuously released into the environment, contaminating the soil and water sources, leading to the possible unfeasibility of those hydrous resources due to their highly carcinogenic and mutagenic potentiality, since even in low concentrations, the BTEX may cause serious health issues. Therefore, it is extremely important to develop and search for new methodologies that assist and enable the treatment of BTEX-contaminated matrix. The bioremediation consists on the utilization of microbial groups capable of degrading hydrocarbons, promoting mineralization, or in other words, the permanent destruction of residues, eliminating the risks of future contaminations. This work investigated the biodegradation kinetics of water-soluble monoaromatic compounds (benzene, toluene and ethylbenzene), based on the evaluation of its consummation by the Pseudomonas aeruginosa bacteria, for concentrations varying from 40 to 200 mg/L. To do so, the performances of Monod kinetic model for microbial growth were evaluated and the material balance equations for a batch operation were discretized and numerically solved by the fourth order Runge-Kutta method. The kinetic parameters obtained using the method of least squares as statistical criteria were coherent when compared to those obtained from the literature. They also showed that, the microorganism has greater affinity for ethylbenzene. That way, it was possible to observe that Monod model can predict the experimental data for the individual biodegradation of the BTEX substrates and it can be applied to the optimization of the biodegradation processes of toxic compounds for different types of bioreactors and for different operational conditions.

X-Ray Diffraction of Highway Materials, HR-128, 1969

X-ray diffraction data during adsorption of water vapor on Na- and Ca-montmorillonites show that interlayer expansion is continuous but nonuniform. X-ray and adsorption isotherm data indicate an ice-like configuration of water molecules is completed with the fourth layer of interlayer water for the Ca-clay; a fifth layer intrudes to give a less ordered structure. Data for the Na-clay indicate a laminar stacking arrangement for up to three layers of interlayer water. The Na-clay adsorbs more than twice as much water and undergoes four times as large a volume change than the Ca-clay. The free energy change during adsorption of water vapor on the Ca-clay is nearly twice that for the Na-clay. Free energy changes with increasing relative pressure reflect interlayer expansion increments.

Computational approaches and tools for modeling biomass pyrolysis

Thesis (Ph.D.)--University of Washington, 2016-08

Three-dimensional kinetic simulations of active suspensions: effect of chemotaxis and steric interaction

In this work, the effects of chemotaxis and steric interactions in active suspensions are analyzed by extending the kinetic model proposed by Saintillan and Shelley [1, 2]. In this model, a conservation equation for the active particle configuration is coupled to the Stokes equation for the flow arising from the force dipole exerted by the particles on the fluid. The fluid flow equations are solved spectrally and the conservation equation is solved by second-order finite differencing in space and second-order Adams-Bashforth time marching. First, the dynamics in suspensions of oxytactic run-and-tumble bacteria confined in thin liquid films surrounded by air is investigated. These bacteria modify their tumbling behavior by making temporal comparisons of the oxygen concentration, and, on average, swim towards high concentrations of oxygen. The kinetic model proposed by Saintillan and Shelley [1, 2] is modified to include run-and-tumble effects and oxygentaxis. The spatio-temporal dynamics of the oxygen and bacterial concentration are analyzed. For small film thicknesses, there is a weak migration of bacteria to the boundaries, and the oxygen concentration is high inside the film as a result of diffusion; both bacterial and oxygen concentrations quickly reach steady states. Above a critical film thickness (approximately 200 micron), a transition to chaotic dynamics is observed and is characterized by turbulent-like 3D motion, the formation of bacterial plumes, enhanced oxygen mixing and transport into the film, and hydrodynamic velocities of magnitudes up to 7 times the single bacterial swimming speed. The simulations demonstrate that the combined effects of hydrodynamic interactions and oxygentaxis create collective three-dimensional instabilities which enhances oxygen availability for the bacteria. Our simulation results are consistent with the experimental findings of Sokolov et al. [3], who also observed a similar transition with increasing film thickness. Next, the dynamics in concentrated suspensions of active self-propelled particles in a 3D periodic domain are analyzed. We modify the kinetic model of Saintillan and Shelley [1, 2] by including an additional nematic alignment torque proportional to the local concentration in the equation for the rotational velocity of the particles, causing them to align locally with their neighbors (Doi and Edwards [4]). Large-scale three- dimensional simulations show that, in the presence of such a torque both pusher and puller suspensions are unstable to random fluctuations and are characterized by highly nematic structures. Detailed measures are defined to quantify the degree and direction of alignment, and the effects of steric interactions on pattern formation will be presented. Our analysis shows that steric interactions have a destabilizing effect in active suspensions.

Changes in physical and chemical parameters of the traditional portuguese product água-mel during the production process

Changes in physical and chemical parameters (viscosity, total soluble solids and Hunter color parameters L*, a*, b*, chroma and hue angle) of água-mel were investigated throughout processing. Kinetic parameters for color change of heatprocessed água-mel were monitored. A zero-order kinetic model was applied to changes in L* and b*, while a* and C* were described using a first-order kinetic model. The heating process changed all three color parameters (L*, a*, b*), causing a shift toward the darker colors. Parameters L* decreased, while a*, b*, C* and hue angle (°h) increased during heating. Regarding changes in total soluble solids and in apparent viscosity, both fitted first-order kinetics. A direct relationship was found between the changes in these two parameters. The increase in both total soluble solids and viscosity affected a*, b* and C*. In addition, a flow diagram for the Portuguese água-mel production process has been established.

In vitro study of interaction between quinine and Garcinia kola

Purpose: To investigate the interaction between quinine and Garcinia kola using an in vitro adsorption study. Methods: In vitro interaction between quinine and G. kola was conducted at 37 ± 0.1 °C. Adsorption of quinine (2.5 - 40 μg/ml) to 2.5 % w/v G. kola suspension was studied. Thereafter, quinine desorption process was investigated. The amount of quinine adsorbed and desorbed was quantified using HPLC. A Freundlich isotherm was constructed to describe the resulting data and percentage of quinine desorbed was determined from the desorption data. Results: An adsorption isotherm of the data gave a Freundlich constant (K) of 52.66 μg/g, with a slope of 0.69 indicating a high capacity and affinity of G. kola to adsorb quinine at a concentration smaller than 2.41 μg/g of G. kola. However the adsorptive capacity of G. kola for quinine at 37 ± 0.1 °C appears to be a saturable process as observed from the isotherm. Quinine desorption from G. kola peaked at 1 hour (37.51 %) and decreased to a constant amount (about 35 %) over the remaining sampling time. Conclusion: Quinine is adsorbed on G. kola in vitro. This suggests that concurrent administration of quinine and G. kola should be avoided, to prevent potential drug interaction and decreased drug bioavailability.

Electrochemical Oxidation Of Landfill Leachate In A Flow Reactor: Optimization Using Response Surface Methodology.

Response surface methodology based on Box-Behnken (BBD) design was successfully applied to the optimization in the operating conditions of the electrochemical oxidation of sanitary landfill leachate aimed for making this method feasible for scale up. Landfill leachate was treated in continuous batch-recirculation system, where a dimensional stable anode (DSA(©)) coated with Ti/TiO2 and RuO2 film oxide were used. The effects of three variables, current density (milliampere per square centimeter), time of treatment (minutes), and supporting electrolyte dosage (moles per liter) upon the total organic carbon removal were evaluated. Optimized conditions were obtained for the highest desirability at 244.11 mA/cm(2), 41.78 min, and 0.07 mol/L of NaCl and 242.84 mA/cm(2), 37.07 min, and 0.07 mol/L of Na2SO4. Under the optimal conditions, 54.99 % of chemical oxygen demand (COD) and 71.07 ammonia nitrogen (NH3-N) removal was achieved with NaCl and 45.50 of COD and 62.13 NH3-N with Na2SO4. A new kinetic model predicted obtained from the relation between BBD and the kinetic model was suggested.

Effect of impeller type and mechanical agitation on the mass transfer and power consumption aspects of ASBR operation treating synthetic wastewater

The effect of flow type and rotor speed was investigated in a round-bottom reactor with 5 L useful volume containing 2.0 L of granular biomass. The reactor treated 2.0 L of synthetic wastewater with a concentration of 800 mgCOD/L in 8-h cycles at 30 degrees C. Five impellers, commonly used in biological processes, have been employed to this end, namely: a turbine and a paddle impeller with six-vertical-flat-blades, a turbine and a paddle impeller with six-45 degrees-inclined-flat-blades and a three-blade-helix impeller. Results showed that altering impeller type and rotor speed did not significantly affect system stability and performance. Average organic matter removal efficiency was about 84% for filtered samples, total volatile acids concentration was below 20 mgHAc/L and bicarbonate alkalinity a little less than 400 mgCaCO(3)/L for most of the investigated conditions. However, analysis of the first-order kinetic model constants showed that alteration in rotor speed resulted in an increase in the values of the kinetic constants (for instance, from 0.57 h(-1) at 50 rpm to 0.84 h(-1) at 75 rpm when the paddle impeller with six-45 degrees-inclined-flat-blades was used) and that axial flow in mechanically stirred reactors is preferable over radial-flow when the vertical-flat-blade impeller is compared to the inclined-flat-blade impeller (for instance at 75 rpm, from 0.52 h(-1) with the six-flat-blade-paddle impeller to 0.84 h(-1) with the six-45 degrees-inclined-flat-blade-paddle impeller), demonstrating that there is a rotor speed and an impeller type that maximize solid-liquid mass transfer in the reaction medium. Furthermore, power consumption studies in this reduced reactor volume showed that no high power transfer is required to improve mass transfer (less than 0.6 kW/10(3) m(3)). (C) 2008 Elsevier Ltd. All rights reserved.

Effects of temperature at different organic loading levels on the performance of a fluidized-bed anaerobic sequencing batch bioreactor

An investigation was performed on the effect of temperature and organic load on the stability and efficiency of a 1.8-L fluidized-bed anaerobic sequencing batch reactor (ASBR), containing granulated biomass. Assays were carried out employing superficial up How velocity of 7 m/h, total cycle length of 6 h and synthetic wastewater volume of 1.3 L per cycle. The fluidized-bed ASH was operated at 15, 20, 25 and 30 degrees C with influent organic matter concentrations of 500 and 1000 mgCOD/L The system showed stability under all conditions and presented filtered samples removal efficiency ranging from 79 to 86%. A first-order kinetic model could be fitted to the experimental values of the organic matter concentration profiles. The specific kinetic parameter values of this model ranged from 0.0435 to 0.2360 L/(gTVS h) at the implemented operation conditions. in addition, from the slope of an Arrhenius plot, the activation energy values were calculated to be 16,729 and 12,673 cal/mol for operation with 500 and 1000 mgCOD/L, respectively. These results show that treatment of synthetic wastewater. with concentration of 500 mgCOD/L, was more sensitive to temperature variations than treatment of the same residue with concentration of 1000 mgCOD/L. Comparing the activation energy value for operation at 500 mgCOD/L with the value obtained by Agibert et al. (S.A. Agibert, M.B. Moreira, S.M. Ratusznei, J.A.D. Rodrigues, M. Zaiat, E. Foresti. Influence of temperature on performance of an ASBBR with circulation applied to treatment of low-strength wastewater. journal of Applied Biochemistry and Biotechnology, 136 (2007) 193-206) in an ASBBR treating the same wastewater at the same concentration, the value obtained in the fluidized-bed ASBR showed to be superior, indicating that treatment of synthetic wastewater in a reactor containing granulated biomass was more sensitive to temperature variations than the treatment using immobilized biomass. (c) 2008 Elsevier B.V. All rights reserved.

Effects of bed materials on the performance of an anaerobic sequencing batch biofilm reactor treating domestic sewage

The objective of this study was to determine the best performance of an anaerobic sequencing batch biofilm reactor (AnSBBR) based on the use of four different bed materials as support for biomass immobilization. The bed materials utilized were Polyurethane foam (PU), vegetal carbon (VC), synthetic pumice (SP), and recycled low-density polyethylene (PE). The AnSBBR. with I total volume Of 7.2 L, was operated in 8-h batch cycles over 10 months, and fed with domestic sewage with an average influent chemical oxygen demand (COD) of 358 +/- 110 mg/L. The average effluent COD values were 121 +/- 31, 208 +/- 54, 233 +/- 52, and 227 +/- 51 mg/L. for PU, VC, SP, and PE, respectively. A modified first-order kinetic model was adjusted to temporal profiles of COD during a batch cycle, and the apparent kinetic constants were 0.52 +/- 0.05, 0.37 +/- 0.05, 0.80 +/- 0.04, and 0.30 +/- 0.021h(-1) for PU, VC, SP, and PE, respectively. Specific substrate utilization rates of 1.08, 0.11, and 0.86 mg COD/mg VS day were obtained for PU, VC, and PE, respectively. Although SP yielded the highest kinetic coefficient, PU was considered the best support, since SP presented loss of chemical constituents during the reactor`s operational phase. In addition, findings oil the microbial community were associated with the reactor`s performance data. Although PE did not show a satisfactory performance, an interesting microbial diversity was found oil its surface. Based oil the morphology and denaturing gradient gel electrophoresis (DGGE) results, PE showed the best capacity for promoting the attachment of methanogenic organisms, and is therefore a material that merits further analysis. PU was considered the Most suitable material showing the best performance in terms of efficiency of solids and COD removal. (C) 2007 Elsevier Ltd. All rights reserved.

Fluidized ASBR treating synthetic wastewater: Effect of recirculation velocity

An investigation has been performed on the effect of liquid phase recirculation velocity and increasing influent concentration on the stability and efficiency of an anaerobic sequencing batch reactor (ASBR) containing granular biomass. The reactor treated 1.3 L synthetic wastewater at 30 degrees C in 6 h cycles. Initially the effect of recirculation velocity was investigated employing velocities of 5, 7 and 10 m/h and influent concentration of 500 mg COD/L. At these velocities, filtered sample organic matter removal efficiencies were 83, 85 and 84%, respectively. A first order kinetic model could also be fitted to the experimental organic matter concentration profiles. The kinetic parameter values of this model were 1.35, 2.36 and 1.00 h(-1) at the recirculation velocities of 5, 7 and 10 m/h, respectively. The recirculation velocity of 7 m/h was found to be the best operating strategy and this value was maintained while the influent concentration was altered in order to verify system efficiency and stability at increasing organic load. Influent concentration of 1000 mg COD/L resulted in filtered sample organic matter removal efficiency of 80%, and a first order kinetic parameter value of 1.14 h(-1), whereas the concentration of 1500 mg COD/L resulted in an efficiency of 82% and a kinetic parameter value of 1.31 h(-1). (C) 2007 Elsevier B.V. All rights reserved.

Metabolite mean transit times in the liver as predicted by various models of hepatic elimination

Predicted area under curve (AUC), mean transit time (MTT) and normalized variance (CV2) data have been compared for parent compound and generated metabolite following an impulse input into the liver, Models studied were the well-stirred (tank) model, tube model, a distributed tube model, dispersion model (Danckwerts and mixed boundary conditions) and tanks-in-series model. It is well known that discrimination between models for a parent solute is greatest when the parent solute is highly extracted by the liver. With the metabolite, greatest model differences for MTT and CV2 occur when parent solute is poorly extracted. In all cases the predictions of the distributed tube, dispersion, and tasks-in-series models are between the predictions of the rank and tube models. The dispersion model with mixed boundary conditions yields identical predictions to those for the distributed tube model (assuming an inverse gaussian distribution of tube transit times). The dispersion model with Danckwerts boundary conditions and the tanks-in series models give similar predictions to the dispersion (mixed boundary conditions) and the distributed tube. The normalized variance for parent compound is dependent upon hepatocyte permeability only within a distinct range of permeability values. This range is similar for each model but the order of magnitude predicted for normalized variance is model dependent. Only for a one-compartment system is the MIT for generated metabolite equal to the sum of MTTs for the parent compound and preformed metabolite administered as parent.

The folding of knotted proteins: insights from lattice simulations

We carry out systematic Monte Carlo simulations of Go lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system.

A regulação endócrina dos balanços de cálcio

RESUMO: As concentrações circulantes de cálcio são notavelmente constantes a despeito das variações diárias na absorção intestinal e na eliminação renal deste elemento. A regulação da calcémia é um sistema complexo que compreende vários factores controladores (a calcémia, a fosforémia, as concentrações circulantes de paratormona (PTH) e calcitriol além de muitos outros factores como hormonas esteróides em geral, outros iões como o magnésio e outros factores hormonais) e vários órgãos alvo (glândulas paratiroideias, osso, rim e intestino). As respostas dos órgãos alvo também são muito variadas. No caso mais simples, a cristalização de sais de cálcio corresponde a uma mudança de fase em que participam moléculas orgânicas que a iniciam, aceleram ou inibem. Em geral a combinação de um factor controlador com o respectivo receptor de membrana (para polipeptídeos ou iões) ou intracelular (hormonas esteróides) é apenas o primeiro passo de uma cadeia bioquímica que introduz uma enorme amplificação na resposta. A esta variedade de mecanismos de resposta correspondem grandes diferenças nos tempos de resposta que podem ser de minutos a semanas. É hoje possível “observar” (medir) com apreciável rigor nos líquidos biológicos (sangue, urina, fezes, etc.) os factores mais importantes do sistema de regulação da calcémia (cálcio, fósforo, paratormona e calcitriol) assim como administrar estes factores em experiências agudas. Esta possibilidade reflecte – se na literatura neste campo que tem vindo a crescer. O advento das técnicas da biologia molecular tem permitido a caracterização molecular de algumas das disfunções da homeostase do cálcio e é de esperar um diagnóstico fisiopatológico cada vez mais rigoroso dessas disfunções. Com o avanço dos conhecimentos nesta área que não cessa de aumentar temos cada vez maiores capacidades para fazer diagnósticos e é cada vez mais difícil interpretar com rigor os correspondentes quadros metabólicos. A análise ou síntese de sistemas complexos é a actividade mais nobre dos engenheiros que lhes permite desenhar pontes, diques, barcos, aviões ou automóveis. Com o aparecimento de computadores de médio ou grande porte foi – lhes possível utilizar descrições matemáticas não só para desenhar sistemas como ainda para interpretar eventuais falhas na sua operação. Essas descrições matemáticas consistem numa sequência de operações realizadas num computador segundo um “programa informático” que receberam a designação genérica de modelos, por analogia com as famosas leis (equações) da física que foram deduzidas a partir de um certo número de postulados e que permitem representar matematicamente processos físicos. As famosas leis de Newton são talvez os exemplos mais famosos de “modelos” de sistemas físicos. A introdução de modelos matemáticos em biologia e particularmente em medicina só se deu recentemente.MÉTODOS No trabalho que aqui se apresenta construiu - se um modelo simplificado da homeostase do cálcio destinado ao cálculo de variáveis observáveis (concentrações de cálcio, fósforo, PTH e calcitriol) de modo a poderem comparar-se valores calculados com valores observados. A escolha dos componentes do modelo foi determinada pela nossa experiência clínica e pela informação fisiopatológica e clínica publicada. Houve a preocupação de construir o modelo de forma modular de modo a ser possível a sua expansão sem grandes transformações na descrição matemática (e informática) já existente. Na sua fase actual o modelo não pode ser usado como instrumento de diagnóstico. É antes uma ferramenta destinada a esclarecer “em princípio” mecanismos fisiopatológicos. Usou – se o modelo para simular um certo número de observações publicadas e para exemplificar a sua eventual aplicação clínica na simulação de situações hipotéticas e na análise de possíveis mecanismos fisiopatológicos responsáveis por situações de hipo ou hipercalcémias. Simultaneamente fez – se uma análise dos dados acumulados relativos a doentes vistos no Serviço de Endocrinologia do Instituto Português de Oncologia de Francisco Gentil – Centro Regional Oncológico de Lisboa, S.A. CONCLUSÕES Numa população de 894 doentes com patologias variadas do Instituto Português de Oncologia de Lisboa os valores da calcémia tiveram uma distribuição normal unimodal com uma média de 9.56 mg/dl, e um erro padrão de 0.41 mg/dl. Estas observações sugerem que a calcémia está sujeita a regulação. A partir dos resultados publicados em que o metabolismo do cálcio foi perturbado por infusões de cálcio, calcitriol ou PTH, de estudos bioquímicos e fisiológicos sobre os mecanismos de acção de factores controladores da calcémia e do estudo do comportamento de órgãos alvo (paratiroideias, intestino, osso e rim) foi possível construir um modelo matemático de parâmetros concentrados do sistema de regulação da calcémia. As expressões analíticas usadas foram baseadas na cinética enzimática de modo a que os seus parâmetros tivessem um significado físico ou fisiológico simples. O modelo revelou apreciável robustez e flexibilidade. É estável quando não perturbado e transita entre estados estacionários quando perturbado. Na sua forma actual gera simulações que reproduzem satisfatoriamente um número apreciável de dados experimentais colhidos em doentes. Isto não significa que possa ser usado como instrumento de diagnóstico aplicável a doentes individuais. O desenho do modelo comporta a adição posterior de novas relações quando surgirem situações para as quais se revele insuficiente. A utilização exaustiva do modelo permitiu explicitar aspectos do metabolismo do cálcio que ou não estão contidas na sua formulação actual – o aparecimento de hipertrofia ou de adenomas das paratiroideias e as alterações na estrutura óssea , a participação de outros factores controladores – magnésio, ou estão insuficientemente descritas – alterações do metabolismo do fósforo nos hipoparatiroidismos. A análise dos dados relativos aos doentes do Serviço de Endocrinologia do IPO permitiu o início da caracterização dos tipos de patologia que representam e de possíveis mecanismos fisiopatológicos subjacentes. Estas observações são o ponto de partida para análises futuras. São exemplos das relações encontradas: a distribuição dos doentes por dois grandes grupos conforme a calcémia é determinada pelas concentrações circulantes de PTH ou estas são determinadas pela calcémia; a distribuição sazonal das concentrações de Vit. D25. no sangue; a correlação negativa entre estas e as concentrações de PTH no sangue. Também foi possível extrair a cinética do controlo da PTH sobre a síntese de calcitriol. O estudo dos níveis circulantes de PTH no pós-operatório imediato de doentes paratiroidectomizados permitiu determinar as suas taxas de degradação metabólica. O modelo permitiu simular as relações Ca/PTH no sangue, Ca/Fracção excretada da carga tubular, Ca/P no sangue para valores normais ou altos de Ca. Foram feitas simulações de situações fisiopatológicas (em “doentes virtuais”): infusões crónicas de cálcio, PTH e calcitriol; alterações no comportamento de receptores. Estas simulações correspondem a experiências que não podem ser realizadas em humanos. São exemplos da utilização do modelo na exploração de possíveis mecanismos fisiopatológicos através da observação de resultados quantitativos inacessíveis à intuição. O modelo foi útil em duas fases do trabalho: Primeiro, durante a sua síntese implicou uma escolha criticamente selectiva de informação, sua análise quantitativa e processamento, uma explicitação rigorosa (analítica) das relações funcionais entre os controladores e as variáveis e da sua integração numa estrutura global; Segundo, a simulação de situações experimentais ou clínicas (dados do Serviço de Endocrinologia do IPO) em doentes obrigou a explicitar raciocínios fisiopatológicos habitualmente formulados em bases puramente intuitivas. Esta prática revelou comportamentos óbvios após as simulações – acção reduzida das infusões PTH (simulação de hiperparatiroidismos primários) enquanto não há inibição total da respectiva secreção, necessidade de aumento da massa secretora da paratiroideia nas insuficiências renais avançadas, etc. A síntese e utilização do modelo não implicaram uma preparação matemática avançada e foram possíveis mercê da disponibilidade de “software” interactivo especificamente desenhado para a simulação de sistemas dinâmicos em que os programas se escrevem em inglês usando a simbologia simples da álgebra elementar. A função nobre de modelos desta natureza é semelhante à dos modelos usados pelos físicos desde o século XVII: permitir explicações de carácter geral funcionando como uma ferramenta intelectual para manipulação de conceitos e para a realização de “experiências pensadas” (“thought experiments”) respeitando certos princípios físicos (princípios de conservação) que estabelecem as fronteiras da realidade. -------ABSTRACT: Calcium blood levels are remarkably constant despite great variations in calcium daily intake, intestinal absorption and renal excretion. The regulation of the calcium concentration in the blood is achieved by a complex system that includes several controller factors (mainly the serum levels of calcium, phosphorus, parathyroid hormone (PTH) and calcitriol but also of steroid hormones, ions such as magnesium and other hormonal factors) and several target organs (parathyroid glands, bone, kidney and intestine). The functional response to the controlling factors obeys a variety of kinetics. The precipitation of calcium salts is a simple phase transition in which organic molecules may provide nucleation centres or inhibit the process. The combination of a controller factor with its receptor located in the cell membrane (for peptides or ions) or in the nucleus (for steroid hormones) is only the first step of a biochemical chain that introduces a huge amplification in the response. To this great variability of response we have to add the times of response that vary from minutes to weeks. It is possible to “observe” (measure) with great accuracy in biological fluids (blood, urine, faeces, etc.) the most important factors intervening in the calcium regulation (calcium, phosphorus, PTH and calcitriol). The response of the system to acute infusions of the controlling factors has also been studied. Using molecular biology techniques it has been possible to characterize some calcium homeostasis dysfunctions and better physiopathological diagnosis are expected. With the increasingly new knowledge in this area we have better capacity to diagnose but it is harder to explain correctly the underlying metabolic mechanisms. The analysis or synthesis of complex systems is the noble activity of engineers that enables them to draw bridges, dams, boats, airplanes or cars. With the availability of medium-large frame computers it was possible to use mathematical descriptions not only to draw systems but also to explain flaws in its operations. These mathematical descriptions are generally known as models by analogy with the laws (equations) of physics that allow the mathematical description of physical processes. In practice it is not possible to find general solutions for the mathematical descriptions of complex systems but (numeric) computations for specific situations can be obtained with digital computers. The introduction of mathematical models in biology and particularly in medicine is a recent event. METHODS In this thesis a simplified model of calcium homeostasis was built that enables the computation of observable variables (concentrations of calcium, phosphorus, PTH and calcitriol) and allows the comparison between the simulation values and observed values. The choice of the model���s components was made according to our clinical experience and to the published clinical and physiopathological data. The model has a modular design that allows future expansions with minor alterations in its structure. In its present form the model cannot be used for diagnosis. It is a tool designed to enlighten physiopathological processes. To exemplify its possible clinical application in the simulation of hypothetical situations and in the analysis of possible mechanisms responsible for hypo or hypercalcemias the model was used to simulate a certain number of published observations. An analysis of clinical and laboratory data from the Endocrinology Department of the Portuguese Cancer Institute (I.P.O.F.G.-C.R.O.L.,S.A.) is also presented. CONCLUSIONS In a population of 188 patients without an identifiable disease of the calcium metabolism at the Portuguese Cancer Institute the calcemia levels had a unimodal distribution with an average of 9.56 mg/dL and a S.E.M of 0.41 mg/dL. This observation confirms that serum calcium is regulated. Using published data; in which calcium metabolism was disrupted by calcium, PTH or calcitriol infusions; from biochemical and physiological studies of the action of controller factors on the calcemia; in which the response of target organs (parathyroid glands, intestine, bone, kidney) was studied it was possible to build a mathematical model of concentrated parameters of the calcium homeostasis. Analytical expressions used were based on enzymatic kinetics. The model is flexible and robust. It is stable when not disturbed and changes between steady states when disturbed. In its present form it provides simulations that reproduce closely a number of experimental clinical data. This does not mean that it can be used as a diagnostic tool for individual patients. The exhaustive utilisation of the model revealed the need of future expansions to include aspects of the calcium metabolism not included in its present form –hypertrophy or adenomas of the parathyroid glands, bone structure changes, participation of other controller factors such as magnesium – or insufficiently described – phosphate metabolism in hypoparathyroidism. The analysis of the data collected from the I.P.O.’s Endocrinology Department allowed the initial characterization of the different pathologies represented and of their possible physiopathological mechanisms. These observations are a starting point for future analysis. As examples of the relations found were: the distribution of patients in two groups according to the dependency of calcium by PTH levels or PTH levels by calcium concentration; the seasonal distribution of the serum concentrations of D25; its negative correlation with PTH concentration. It was also possible to extract the kinetics of the control of the synthesis of calcitriol by PTH. The analysis of immediate post-surgical levels of PTH in parathyroidectomized patients allowed the determination of its metabolic clearance. The model also allowed the simulation of the relations between Ca/PTH in blood, serum Ca/Fraction of tubular load excreted and Ca/P in blood for normal and high values of calcium. Simulations were made of pathological situations (in “virtual patients”): chronic infusions of calcium, PTH and calcitriol; changes in the characteristics of receptors. These simulations are not possible in real persons. They are an example of the use of this model in exploring possible mechanisms of disease through the observation of quantitative results not accessible to simple intuition. This model was useful in two phases: Firstly, its construction required a careful choice of data, its quantitative analysis and processing, an analytical description of the relations between controller factors and variables and their integration in a global structure. Secondly, the simulation of experimental or clinical (I.P.O.’s Endocrinology Department) data implied testing physiopathological explanations that previously were based on intuition. The construction and utilisation of the model didn’t demand an advanced mathematical preparation since user-friendly interactive software was used. This software was specifically designed for the simulation of dynamic systems. The programs are written in English using elementary algebra symbols. The essential function of this type of models is identical to that of those used by physicists since the XVII century which describe quantitatively natural processes and are an intellectual tool for the manipulation of concepts and the performance of “thought experiments” based in certain physical principles (conservation principles) that are the frontiers of reality.------------------RESUMÉE: Les concentrations circulantes de calcium sont constantes même pendant des variations de l’absorption intestinale et de l’élimination rénale de cet élément. La régulation de la calcémie est un système complexe qui comprend plusieurs éléments contrôleurs (la calcémie, la phosphorémie, les concentrations circulantes de l’hormone parathyroïdienne (PTH) e du calcitriol et d’autres comme les hormones stéroïdes ou des ions comme le magnésium) et plusieurs organes (glandes parathyroïdiennes, l’os, le rein et l’intestin). Les réponses de ces organes sont variées. Dans le cas plus simple, la cristallisation des sels de calcium correspond à un changement de phase dans lequel y participent des molécules organiques que la débutent, l’accélèrent ou l’inhibent. Généralement la combinaison d’un élément contrôleur avec leur récepteur de membrane (pour les peptides ou les ions) ou intracellulaire (pour les hormones stéroïdes) n’est que le premier pas d’une chaîne biochimique qu’introduit une grande amplification de la réponse. A cette variété de réponses correspondent des grandes différences des temps de réponses qu’y vont des minuits a semaines. Il est possible « observer » (mesurer) dans les fluides biologiques (sang, urine, fèces, etc.) les éléments plus importants du système de régulation de la calcémie (calcium, phosphate, PTH et le calcitriol) et les administrer en expérimentes aigus. Cette possibilité est visible dans la littérature publiée dans ce domaine qui est en croissance permanente. L’avenir des techniques de biologie moléculaire a permis caractériser des nombreuses dysfonctions de la régulation de la calcémie et on attend un diagnostique physiopathologique de ces dysfonctions chaque fois plus rigoureuses. Les connaissances dans ce domaine s’agrandissent et on a de plus de capacités pour faire des diagnostiques et il est chaque fois plus difficile les interpréter. L’analyse ou synthèse de systèmes complexes est l’activité plus noble des ingénieurs qui les permit dessiner des ponts, bateaux, avions ou automobiles. Avec des ordinateurs de médium ou grand port il les est possible utiliser descriptions mathématiques pour dessiner les systèmes et interpréter des éventuelles fautes d’opération. Ces descriptions mathématiques sont une séquence d’opérations réalisées dans un ordinateur selon « un programme informatique » qui ont reçu la désignation générique de modèles, pour analogie avec les équations de la physique qui ont été déduits d’un nombre de postulées et qu’ont permit représenter des processus physiques en équations mathématiques. Les fameuses équations de Newton sont peut-être les exemples plus connus des systèmes physiques. L’introduction des modèles mathématiques en biologie et en particulier en médecine est un évènement récent. Dans ce travaille, on a construit un modèle simplifié de l’homéostasie du calcium pour calculer les variables observables (concentrations de calcium, phosphate, PTH et calcitriol) pour les comparer. Les choix des components a été déterminés par notre expérience clinique et par l’information physiopathologique et clinique publiée. Le modèle a été construit de façon modulaire ce que permit leur postérieur expansion sans des grandes altérations dans la description mathématique et informatique déjà existante. Dans cette forme le modèle ne peut être utilisé comme un instrument de diagnostique. Il est un outil pour éclairer la physiopathologie. Le modèle a été utilisé pour simuler un certain nombre d’observations publiées et pour exemplifier leur possible utilisation clinique dans la simulation des hypothèses et de la physiopathologie des situations d’hypo ou hypercalcémie. On a fait une analyse des éléments des procès cliniques des malades observées dans le Service d’Endocrinologie de l’IPOFG-CROL, SA. Dans une population de 894 malades avec des différentes pathologies les valeurs de calcémie on une distribution uni modale avec une Médie de 9.56 mg/dL et une erreur standard de 0.41 mg/dL. Ces observations suggèrent que la calcémie soit sujette de régulation. En utilisant des résultats de travaux publiés dans lesquels le métabolisme du calcium a été changé par des infusions de calcium, calcitriol ou PTH, des études biochimiques et physiologiques sur des mécanismes d’action des éléments contrôleurs de la calcémie et de l’étude du comportement des organes cible (parathyroïdes, intestin, rein, os), il a été possible de construire un modèle mathématique de paramètres concentrés du système de régulation de la calcémie. Les expressions analytiques utilisées ont été basées sur la cinétique enzymatique de façon à que les paramètres aient eu une signification physique ou biologique. Le modèle est stable quand il n’est pas perturbé et transit entre états stationnaires quand il est sujet a des perturbations. A ce moment il fait des simulations qui reproduisent de façon satisfaisant un nombre d’observations expérimentales. La construction du modèle permit l’addiction de nouvelles relations dans les cas ou il est insuffisant. L’utilisation exhaustive du modèle a permit expliciter des aspects du métabolisme du calcium qui y ne sont pas compris – l’hyperplasie ou la formation des adénomes des parathyroïdes, les altérations de la structure des os, la participation d’outres éléments régulateurs (magnésium), ou sont insuffisamment décrites – les altérations du métabolisme des phosphates dans l’hypoparathyroidism. L’analyse de l’information des malades du Service d’Endocrinologie a permit caractériser les pathologies représentées et leurs possibles mécanismes physiopathologiques. Ces observations sont le point de départ pour les analyses futures. Sont des exemples des relations trouvées: la distribution des malades par deux groupes: ceux dans lequel la calcémie est déterminée par la PTH ou ceux dans lesquels la PTH est déterminée par la calcémie; la distribution sazonale de la concentration de la vitamine D; la corrélation négative entre la vitamine D et la PTH. On a eu la possibilité de déduire la cinétique de control de la PTH sur la synthèse du calcitriol. L’étude des niveaux circulants de PTH sur des sujets parathyroidectomisées a permit déduire leur taux de dégradation métabolique. Le modèle a permit simuler les relations Ca/PTH dans le sang, Ca/fraction éliminée par le rein, Ca/P dans le sang pour des valeurs normales ou hautes de calcium. On a fait des simulations de situations physiopathologiques (dans “malades virtuelles”): Infusions chroniques de calcium, PTH ou calcitriol; altérations des récepteurs. Ces simulations ne peuvent pas être réalisées dans les humains. Sont des exemples d’utilisation du modèle dans l’exploration des possibles mécanismes de la physiopathologie en observant des résultats quantitatifs inaccessibles à l’intuition. Le modèle a été utile pendant deux étapes des travaux: La première, dans sa construction on a choisi l’information disponible, son analyse quantitative, l’explicitation rigoureuse (analytique) des relations fonctionnelles entre les contrôleurs et les variables et sa intégration dans une structure globale. La deuxième, la simulation de situations expérimentales ou cliniques (du Service d’Endocrinologie) a obligé d’expliciter des raisonnements physiopathologiques généralement formulés utilisant l’intuition. Cette pratique a montré des comportements – action réduite des infusions de PTH (jusqu’à l’inhibition totale de leur respective sécrétion), nécessité d’augmenter la masse sécréteuse de la parathyroïde dans les insuffisants rénales, etc. La synthèse et utilisation du modèle n’ont pas besoin d’une formation avancée en mathématique et sont possibles grâce à un programme interactif qui a été conçu pour la simulation des systèmes dynamiques dans lesquels le programme se construit en anglais en utilisant la symbolique élémentaire de l’algèbre. La fonction noble de ces modèles est semblable à celles des physiques du XVII siècle: Permettre établir explications générales en fonctionnant comme un outil intellectuel pour manipuler des concepts et pour la réalisation d’expérimentes pensées en respectant certains principes de la physique (principe de la conservation) qu’établissent les frontières de la réalité.