Stochastic compartment models are widely used in modeling processes for biological populations. The residence time has been especially useful in describing the system dynamics in the models. The direct calculation of the distribution for the residence time of stochastic multi-compartment models is very complicated even with a relatively simple model and often impossible to calculate directly. This dissertation presents an analytical method to obtain the moment generating function for stochastic multi-compartment models and describe the distribution of the residence times, especially systems with nonexponential lifetime distributions. A common method for obtaining moments of the residence time is using the coefficient matrix, however it has a limitation in obtaining high order moments and moments for combined compartments in a system. In this dissertation, we first derive the bivariate moment generating function of the residence time distribution for stochastic two-compartment models with general lifetimes. It provides any order of moments and also enables us to approximate the density of the residence time using the saddlepoint approximation. The approximation method is applied to various situations including the approximation of the bivariate distribution of residence times in two-compartment models or approximations based on the truncated moment generating function. Special attention is given to the distribution of the residence time for multi-compartment semi-Markov models. The cofactor rule and the analytic approach to the two-compartment model facilitate the derivation of the moment generating function. The properties from the embedded Markov chain are also used to extend the application of the approach. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus provides an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.

<p>Positron Emission Tomography, PET, is a noninvasive medical imaging technique to get functional information of the kinetics of radioactive compound injected in the body. The data used in this thesis comes from a total of five H₂¹⁵O PET studies of one patient. This was done in order to study the blood flow in liver metastasis of the patient, before and after treatment.</p><p>A one compartment model was used to do the ROI based analyses. With a least square method in Matlab the unknown parameters in the model, such as the kinetic rate constants, the dispersion and the fraction of blood in the tissue, was extracted. Also a brief analysis of different parts of the metastases, edge and center, was done to see the variations within the metastases. The results show some increase of the blood flow after the treatment, and two of the three studied metastases showed a distinct difference of the activity in the center versus the edge. Given in the thesis are also some basic PET and compartmental modeling theory.</p> / <p>Positronemissionstomografi, PET, är en icke-invasiv medicinsk bildteknik för att få funktionell information om kinetiken av radioaktiva föreningar injicerade i kroppen. Det data som används i denna kandidatuppsats kommer från totalt fem H₂¹⁵O PET-studier av en patient. Detta gjordes för att studera blodflödet i levermetastaser hos patienten före och efter behandling.</p><p>En 1-kompartmentmodell användes för att göra ROI-baserade analyser. Med en minsta kvadrat-metod i Matlab kunde de okända parametrarna i modellen, såsom den kinetiska hastighetskonstanten, spridningen och andelen blod i vävnaden, fås ut. En kort analys gjordes också av olika delar av metastaserna, kanten och mitten, för att se variationerna inuti metastaserna. Resultaten visar en viss ökning av blodflödet efter behandlingen, och två av de tre studerade metastaser visade en tydlig skillnad av aktiviteten i mitten jämfört med kanten. I rapporten ges också grundläggande teori om bland annat PET och kompartmentmodellering.</p>

Positron Emission Tomography, PET, is a noninvasive medical imaging technique to get functional information of the kinetics of radioactive compound injected in the body. The data used in this thesis comes from a total of five H215O PET studies of one patient. This was done in order to study the blood flow in liver metastasis of the patient, before and after treatment. A one compartment model was used to do the ROI based analyses. With a least square method in Matlab the unknown parameters in the model, such as the kinetic rate constants, the dispersion and the fraction of blood in the tissue, was extracted. Also a brief analysis of different parts of the metastases, edge and center, was done to see the variations within the metastases. The results show some increase of the blood flow after the treatment, and two of the three studied metastases showed a distinct difference of the activity in the center versus the edge. Given in the thesis are also some basic PET and compartmental modeling theory. / Positronemissionstomografi, PET, är en icke-invasiv medicinsk bildteknik för att få funktionell information om kinetiken av radioaktiva föreningar injicerade i kroppen. Det data som används i denna kandidatuppsats kommer från totalt fem H215O PET-studier av en patient. Detta gjordes för att studera blodflödet i levermetastaser hos patienten före och efter behandling. En 1-kompartmentmodell användes för att göra ROI-baserade analyser. Med en minsta kvadrat-metod i Matlab kunde de okända parametrarna i modellen, såsom den kinetiska hastighetskonstanten, spridningen och andelen blod i vävnaden, fås ut. En kort analys gjordes också av olika delar av metastaserna, kanten och mitten, för att se variationerna inuti metastaserna. Resultaten visar en viss ökning av blodflödet efter behandlingen, och två av de tre studerade metastaser visade en tydlig skillnad av aktiviteten i mitten jämfört med kanten. I rapporten ges också grundläggande teori om bland annat PET och kompartmentmodellering.

A three-compartment model is extended to estimate the fate and transport of DEHP in a realistic residential environment. The model considered eight environmental media (i.e. air, particulate matter with six size fractions, vinyl flooring, carpet, furniture, dust, wall and ceiling). Particle movement (deposition and resuspension), dust removal (vacuuming), indoor cooking, and adsorption/absorption on indoor surfaces are included. The predicted airborne DEHP concentrations at steady state are within 0.1 [microgram]/m³ to 0.6 [microgram]/m³, which are similar to those measured in field studies. After vinyl flooring (the primary source) is removed, it takes 2 years for the indoor airborne DEHP level to reduce 0.01 [microgram]/m³, and the time increases significantly when carpet present. The results indicate that carpets as well as other interior surfaces may be important phthalate sinks and if the only removal mechanism is ventilation, strongly sorbing phthalate may persist for years. Phthalate amount in dust is strongly influenced by the deposition surface. The concentration of DEHP presents 10 times higher in dust on the source (vinyl flooring) than on the sink (furniture), and it takes more than a year for DEHP to reach equilibrium between bulk air and dust. The domestic activity of cooking is then included in the model and it shows that suspended particle concentration has a substantial impact on gas-phase DEHP level indoors, while the influence of ventilation is only to some extent. Three other SVOCs (DMP, BBP and DiDP) are also investigated and their environmental fates show that chemical’s vapour pressure and octanol/air partition coefficient have substantial influences on sorbing mechanisms and the gas phase and airborne concentrations. / text

The forced Oscillation Technique (FOT) can be used to measure lung impedance continuously during breathing. However, spectral overlap between the breathing waveform and the applied flow oscillation can be problematic if the frequency content of spontaneous breathing is unknown. This problem motivated us to develop a modification to the FOT system called the Tracked Breathing Trainer. The modification uses biofeedback to constrain subjects to breathe at a single predetermined frequency. This thesis investigates the engineering and physiological aspects of the modification we made. We studied 8 adult non-asthmatic and 8 adult asthmatic subjects. Three 16 s perturbatory flow oscillation signals ranging from 1-40 Hz were used on the subjects. Each subject received three trials per perturbation for both spontaneous and tracked breathing. We then fitted a resistance-elastance-inertance model of the lung to each data set. For non-asthmatic subjects, the average resistance (R) and elastance (E) values for the first spontaneous breathing trial were 2.5±0.15 cmH2O.s.ml-1 and 18.1±3.55 cmH2O.ml-1, and for the third spontaneous breathing trial were 2.4±0.12 cmH2O.s.ml-1 and 21.8±4 cmH2O.ml-1. R and E for the first tracked breathing trial were 2.3±0.21 cmH2O.s.ml-1 and 33.6±7.4 cmH2O.ml-1, and for the third tracked breathing trial were 2.4±0.14 cmH2O.s.ml-1 and 25.75±4.3 cmH2O.ml-1, respectively. For asthmatic subjects, the average R and E values for the first spontaneous breathing trial were 3.32±0.68 cmH2O.s.ml-1 and 39.13±9.8 cmH2O.ml-1, and for the third spontaneous breathing trial were 3.12±0.15 cmH2O.s.ml-1 and 39.91±6.2 cmH2O.ml-1. R and E for the first tracked breathing trial were 2.86±0.15 cmH2O.s.ml-1 and 32.47±4.1 cmH2O.ml-1, and for the third tracked breathing trial were 2.86±0.21 cmH2O.s.ml-1 and 33.89±10 cmH2O.ml-1, respectively. These results show that R was consistently lower during tracked breathing than spontaneous breathing in both non-asthmatic and asthmatic subjects. However, an increase in E was observed during tracked breathing. We suspect this effect may have resulted from dynamic hyperinflation. These results also show that R and E are reproducible with both spontaneous and tracked breathing, and that R and E were not noticeably different between both breathing maneuvers. We conclude that using biofeedback to control the breathing pattern during application of the FOT in normal subjects does not significantly affect impedance measurements, and thus may be useful for avoiding spectral overlap between FOT perturbations and the breathing pattern.

The objective of the present study was to explore the correlation between resting metabolic rate (RMR), body composition and physical activity in active and inactive men and women aged 20-30 years. In total, 13 active and 10 inactive women and 8 active and 5 inactive men were enrolled in this study. RMR was measured using an indirect respiratory calorimeter and body composition was obtained using a BodPod, anthropometric measurements (measurements of waist, weight, skin fold thickness etc.) and bioelectrical impedance analysis. From the BodPod were information obtained about fat-free mass (FFM) and fat mass (FM) and from the bioelectrical impedance analysis were data obtained about the total body water (TBW). By combining the data from these methods a three-compartment model could be produced. This gives a better value of the body composition. By using anthropometric measurements the muscle mass (MM) could be calculated. FFM measurements correlate best with RMR for both active men and women and for inactive women. For the inactive men MM correlates best with RMR. In conclusion, comparing the groups as a whole it is seen that the FFM correlates best with RMR for both women and men. Since the muscles are the metabolically active part of FFM it is concluded that muscles affects the RMR value and muscles can in turn be influenced by training.

<p>Pharmacometric modelling is an increasingly used method for analysing the outcome from clinical trials in drug development. The model building process is complex and involves testing, evaluating and diagnosing a range of plausible models aiming to make an adequate inference from the observed data and predictions for future studies and therapy. </p><p>The aim of this thesis was to advance the approaches used in pharmacometrics by introducing improved models and methods for application in essential parts of model building procedure: (i) structural model development, (ii) stochastic model development and (iii) model diagnostics. </p><p>As a contribution to the structural model development, a novel flexible structural model for drug absorption, a transit compartment model, was introduced and evaluated. This model is capable of describing various drug absorption profiles and yet simple enough to be estimable from data available from a typical trial. As a contribution to the stochastic model development, three novel methods for parameter distribution estimation were developed and evaluated; a default NONMEM nonparametric method, an extended grid method and a semiparametric method with estimated shape parameters. All these methods are useful in circumstances when standard assumptions of parameter distributions in the population do not hold. The new methods provide less biased parameter estimates, better description of variability and better simulation properties of the model. As a contribution to model diagnostics, the most commonly used diagnostics were evaluated for their usefulness. In particular, diagnostics based on individual parameter estimates were systematically investigated and circumstances which are likely to misguide modelers towards making erroneous decisions in model development, relating to choice of structural, covariate and stochastic model components were identified. </p><p>In conclusion, novel approaches, insights and models have been provided to the pharmacometrics community. </p><p>Implementation of these advances to make model building more efficient and robust has been facilitated by development of diagnostic tools and automated routines.</p>

Pharmacometric modelling is an increasingly used method for analysing the outcome from clinical trials in drug development. The model building process is complex and involves testing, evaluating and diagnosing a range of plausible models aiming to make an adequate inference from the observed data and predictions for future studies and therapy. The aim of this thesis was to advance the approaches used in pharmacometrics by introducing improved models and methods for application in essential parts of model building procedure: (i) structural model development, (ii) stochastic model development and (iii) model diagnostics. As a contribution to the structural model development, a novel flexible structural model for drug absorption, a transit compartment model, was introduced and evaluated. This model is capable of describing various drug absorption profiles and yet simple enough to be estimable from data available from a typical trial. As a contribution to the stochastic model development, three novel methods for parameter distribution estimation were developed and evaluated; a default NONMEM nonparametric method, an extended grid method and a semiparametric method with estimated shape parameters. All these methods are useful in circumstances when standard assumptions of parameter distributions in the population do not hold. The new methods provide less biased parameter estimates, better description of variability and better simulation properties of the model. As a contribution to model diagnostics, the most commonly used diagnostics were evaluated for their usefulness. In particular, diagnostics based on individual parameter estimates were systematically investigated and circumstances which are likely to misguide modelers towards making erroneous decisions in model development, relating to choice of structural, covariate and stochastic model components were identified. In conclusion, novel approaches, insights and models have been provided to the pharmacometrics community. Implementation of these advances to make model building more efficient and robust has been facilitated by development of diagnostic tools and automated routines.

Diese Arbeit beschäftigt sich sowohl mit der experimentell motivierten Fragestellung nach der Kontrolle der Einzelzellaktivität kortikaler Neurone sowie mit der theoretischen Beschreibung der neuronalen Dynamik und ihrer Transfereigenschaften anhand einfacher Neuronenmodelle. Hierfür werden in-vivo Daten, die mit Hilfe der juxtazellulären Stimulation mit weißem bandpass limitiertem Gaußschem Rauschen erhoben wurden, verwendet. Mit Parameterfits einfacher Neuronenmodelle werden die experimentell ermittelten Pulszugstatistiken sowie die präzisen Zeitpunkte der einzelnen Aktionspotentiale quantitativ reproduziert. Diese Untersuchungen zeigen, dass mit dynamischen Rauschstimuli in juxtazellulärer Stimulation verlässlich und reproduzierbar Pulszüge in einzelnen kortikalen Neuronen hervorgerufen werden können. Weiterhin offenbart die Analyse der Daten die Eigenschaft der untersuchten Neurone frequenzunabhängig, bishin zu Vielfachen der Feuerrate des Neurons, Information über Signalkomponenten zu transferieren. Diese Eigenschaft steht im Widerspruch zum Verhalten der einfachsten (und populärsten) integrate-and-fire Modelle, die die Zelle ohne Auflösung ihrer räumlichen Struktur näherungsweise beschreiben. Die Erweiterung solcher Ein-Kompartiment Modelle auf ein Zwei-Kompartiment Modell und die damit eingeführte Unterscheidung zwischen Soma und Dendrit ermöglicht es, für einzelne Neuronen sämtliche experimentell erhobenen Statistiken, einschließlich des Hochfrequenz- Transfers, quantitativ zu reproduzieren. Zusätzlich zu den obigen Untersuchungen wird eine Methode vorgestellt, um, anhand von Input-Output Statistiken konkreter Neurone, Gaußsche Stimuli zu berechnen, die in der jeweiligen Zelle einen vorgeschriebenen Pulszug hervorrufen. In Experimenten und Simulationen wird gezeigt, dass diese vorgeschriebenen Pulszüge mit einer Verlässlichkeit erzeugt werden können, die in etwa der intrinsischen Verlässlichkeit des untersuchten Neurons entspricht. / This work elaborates on the question to which extent experimental control about the activity of single cortical neurons can be achieved and deals with the theoretical description of the neuronal dynamics. To this end, in-vivo data that have been recorded from juxtacellular experiments in cortical neurons are used. By means of parameter optimization, simple neuron models are fitted in order to quantitatively reproduce the measured spike train statistics and specific action potential timings. The analysis reveals that dynamic noise-stimuli can be used in juxtacellular stimulation to reliably generate reproducible spike trains in single cortical neurons. The analysis also reveals that the cells show a marked broadband coding of information, up to frequencies that are multiples of the firing rate of the respective neuron. This is in contrast to what is known for the simplest (and most popular) integrate-and-fire models, for which the cellular dynamics are described by a single space-independent variable. The extension of these one-compartment models to two-compartment models introduces a spatially distinction between soma and dendrite and we could show that for particular neurons it is sufficient to quantitatively reproduce all experimentally measured spike-train and input-output statistics, including the highfrequency information-transfer. Therefore, the effect of the spatial structure can be an important (structural) mechanism that can have influence on the neuronal dynamics. Additionally to the above considerations, by means of input-output statistics of particular neurons, we propose a method to compute Gaussian stimuli that are supposed to evoke prescribed spike trains in the respective neuron. Using experiments and simulations, we show that the prescribed spike trains can be evoked with a reliability that is comparable to the intrinsic reliability of the neuron under investigation.

La simulation devient un outil incontournable pour concevoir ou optimiser les procédés en biotechnologies. Elle est particulièrement pertinente pour permettre le changement d'échelle de l'échelle laboratoire à la mise en œuvre de cultures biologiques industrielles. Cette thèse se concentre sur le développement d'une structure de modèle pour les fermenteurs, qui ne néglige ni les problématiques de mélange, ni la complexité biologique, tout en permettant des simulations rapides. Pour intégrer l'ensemble des phénomènes couplés et dynamiques interagissant dans les bioréacteurs, l'approche proposée couple (i) un modèle métabolique dynamique pour décrire le comportement des cellules, (ii) un modèle de bilan de population pour suivre la diversité biologique et (iii) un modèle de compartiments pour décrire l'hydrodynamique du fermenteur. Une structure de modèle métabolique, générique et numériquement peu couteuse a été appliquée à E. coli et S. cerevisiae et été confrontée avec succès à de nombreuses données expérimentales. Parmi plusieurs méthodes numériques permettant de traiter les équations de bilan de population, la méthode EQMOM a été sélectionnée pour sa stabilité et sa précision et son coût a été réduit d'un facteur 10. L'hydrodynamique gaz-liquide d'un fermenteur industriel a été obtenue par simulations CFD et des outils ont été développés pour en extraire des modèles de compartiments. Le couplage de ces différents aspects a finalement été illustré par la simulation d'une culture industrielle. Ce travail ouvre la voie à la création d'outil de simulation rapide, ce qui permettra des études d'ingénierie de design et d'optimisation de procédés industriels. / Simulations are becoming an essential tool to design and improve processes in the field of biotechnologies. They are especially relevant to facilitate the scale-up of biological cultures from laboratory to industrial scales which is a key difficulty as of now. This thesis focuses on developping a model structure for fermenters, which does not neglect either mixing issues known to occur in industrial bioreactor, nor biological complexity inherent to micro-organisms, while enabling fast and low-cost simulations. To account for all coupled and dynamic phenomena that occur in bioreactors, the developed approach couples (i) a dynamic metabolic model to describe cells behaviour, (ii) a population balance model tracking biological cell-to-cell diversity and (iii) a compartment model to account for fermenter hydrodynamics. A structure for low-cost dynamic metabolic model has been developed, applied to E. coli and S. cerevisiae and successfully challenged against experimental data. Among multiple numerical methods tackling population balance equations, the EQMOM method has been selected for its stability and precision, and its algorithm has been improved by reducing its cost by a factor 10. The gas-liquid hydrodynamics of an industrial fermenter has been obtained through CFD simulations, and tools have been developed to extract compartment model from these simulation results. Finally, the coupling between all these modeling blocks has been demonstrated by simulating an actual industrial culture. This work paves the way to the emergence of fast bioreactor simulation tools, which will then enable new enginnering studies for designing and optimising industrial bio-processes.