Mark Brouns

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    Abstract

    In medical applications it is important that aerosols reach the alveolarzone of the respiratory tract, to be effective. Before this region is reached,the aerosols have to pass the upper airway (UA), starting with the mouthand a 90-degree bend leading into the trachea. The UA geometrys irreg-ularity and constrictions (such as the vocal cords) potentially affect thedeposition of inhaled aerosols.

    The goal of this dissertation was to develop from the available CT-scans,a simplified yet realistic human UA geometry. From this computer gener-ated UA geometry, a suitable physical model was created for Particle ImageVelocimetry (PIV) measurements. Via Reynolds similitude, a seeded water-glycerine mixture, matching the refraction index of the transparent modelwas measured in a central sagittal plane of the model at four flow rates (cor-responding to 10, 15, 30 and 45 L/min air breathing flow rate). These PIVmeasurements were compared with Computational Fluid Dynamics (CFD)simulations of the fluid phase. Of the various available turbulence mod-els that were combined with the Reynolds Averaged Navier-Stokes (RANS)equations to compute the fluid phase in this UA model, the k

    Shear-

    Stress Transport (SST) turbulence model best reproduced the experimentalresults.

    For the simulation of the particle phase, particles with diameter rangingfrom 1 to 20 micrometer were tracked in a Lagrangian frame of referencethrough the obtained converged flow field. Simulations of total depositioncompared well with experimental deposition data, for particles with a valuefor the non-dimensional parameterStk.Re0.37 higher than 0.1(Stokesnumber.Reynoldsnumber0.37 > 0.1). Total deposition of particleswith a smaller value was overpredicted, probably due to exaggerated turbu-lence simulated at low flow rates. Simulations of local particle deposition

    patterns in the UA model were much more realistic than local depositionpatters previously reported in simplified geometries. In particular, simu-lated mouth deposition more closely resembled that obtained experimen-tally in realistic upper airway geometries. The influences of gravity, of car-rier gas, of degree of turbulence at the model entrance, and of consideringnon-steady flow at particle injection were discussed.

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    Finally a clinical problem of tracheal stenosis was tackled by introducingvarious degrees of constriction in the upper third of the trachea in the UAmodel. CFD simulations of pressure drops across the stenosis allowed usto propose a rule of thumb from which pressure drops over the stenosiscan be estimated, simply on the basis of breathing flow and stenosis crosssection. In addition, the best-fit exponent in the power law that relatespressure drop to breathing flow was proposed as a diagnostic tool in thenon-invasive monitoring of tracheal stenosis patients.

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    Acknowledgements

    Doing a Phd is a strenuous and cumbersome work, which I was not ableto finish without the help and support of many people. Therefore I want tothank everyone who contributed in any way to the making of my thesis.

    I wish to thank the head of the research group Fluid Mechanics andThermodynamics, Prof. Dr. Ir. Chris Lacor for giving me the opportunityto work on this very interesting field of research. Im particular grateful

    that he gave me the chance to develop my own ideas, which helped me togrow as a researcher.

    Secondly, I would like to thank my co-promotor, Prof. Dr. Sylvia Ver-banck, who always helped me to focus not only on the computational partof the research but also the physiological side of the research. For not beinga CFD-specialist, she posed many questions, which helped me to look in acritical way to the obtained results.

    Thirdly, I would like to thank my colleagues and former colleagues atthe Fluid Mechanics research group: Kris Van den Abeele, Sergey Smirnov,Patryk Widera, Santosh Jayaraju, Ghader Ghorbaniasl, Matteo Parsani,Mahdi Zakyani Roudsari, Dean Vucinic and former colleagues Jan Ram-

    boer and Tim Broeckhoven. First, Tim and Santhosh thanks a lot for theproofreading of this dissertation. I know you both had a lot work and read-ing someones Phd can be quite strenuous. Tim, also thanks for sharing anoffice during 4 years, we had a lot of fun together. Jan, you always helpedme to put things into perspective. Things are quite different without ouroffice-ninja. Kris, you are now almost 2 years in the department but it looksa lot longer... We had and hopefully will have a lot of fun together. Sergey,Patryk, Ghader, thanks for the nice discussions during the coffee breaks. Iwould express my gratitude to Alain Wery for his unlimited help with allthe computer problems and lab problems, I encountered over the past years

    and also our secretary Jenny Dhaes for her administrative support.I also want to thank my family and friends, who always reminded methat there was more in life than upper human airways.

    Last but certainly not least I want to thank my girlfriend Annemie. Youalways put up with my bad mood after an unsuccessful day and gave me

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    the courage to finish my Phd. Like you supported me during my Phd, I willhelp you to go through the upcoming difficult time.

    Mark Brouns, Vilvoorde,Oktober 2007

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    Contents

    Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

    Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

    1 Introduction 11.1 Asthma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 History of asthma . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Asthma in the world . . . . . . . . . . . . . . . . . . . . . . 2

    2 Anatomy of the Human Respiratory Tract 4

    2.1 The respiratory system . . . . . . . . . . . . . . . . . . . . . 42.1.1 Function of the respiratory system . . . . . . . . . . 42.1.2 The structure of the respiratory system . . . . . . . 6

    3 Theoretical Background of Particle Image Velocimetry (PIV) 123.1 Historical background of fluid measurements . . . . . . . . . 123.2 The principle of particle image velocimetry . . . . . . . . . . 153.3 Mathematical background of PIV evaluation . . . . . . . . . 17

    3.3.1 Auto-correlation . . . . . . . . . . . . . . . . . . . . 193.3.2 Cross-correlation of a pair of two single exposed record-

    ings . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.3 Optimization of the correlation . . . . . . . . . . . . 22

    3.4 Evaluation of PIV images . . . . . . . . . . . . . . . . . . . 233.4.1 Error estimation . . . . . . . . . . . . . . . . . . . . 263.4.2 Detection of spurious vectors (outliers) . . . . . . . . 26

    3.5 Tracer particles . . . . . . . . . . . . . . . . . . . . . . . . . 29

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    4 Theoretical Background of Computational Fluid Dynamics(CFD): The Particle Phase 324.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2 Geometric properties of particles . . . . . . . . . . . . . . . 32

    4.2.1 Particle size . . . . . . . . . . . . . . . . . . . . . . . 334.3 Dilute and dense flows . . . . . . . . . . . . . . . . . . . . . 344.4 Phase coupling . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 Modeling two-phase flows . . . . . . . . . . . . . . . . . . . 35

    4.5.1 Eulerian continuum approach . . . . . . . . . . . . . 354.5.2 Lagrangian trajectory approach . . . . . . . . . . . . 36

    4.6 Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . 364.7 Momentum Balance . . . . . . . . . . . . . . . . . . . . . . . 37

    4.7.1 Interphase Force . . . . . . . . . . . . . . . . . . . . 374.7.2 Body Force . . . . . . . . . . . . . . . . . . . . . . . 41

    4.8 Stochastic trajectory approach . . . . . . . . . . . . . . . . . 41

    5 Theoretical background of Computational Fluid Dynamics(CFD): The Fluid Phase 435.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 History of CFD . . . . . . . . . . . . . . . . . . . . . . . . . 445.3 The Navier-Stokes equations . . . . . . . . . . . . . . . . . . 45

    5.4 The Reynolds Averaging . . . . . . . . . . . . . . . . . . . . 465.5 Turbulence modeling . . . . . . . . . . . . . . . . . . . . . . 485.5.1 k turbulence models . . . . . . . . . . . . . . . . 495.5.2 k turbulence models . . . . . . . . . . . . . . . . 535.5.3 The Reynolds Stress Model (RSM) . . . . . . . . . . 56

    6 State-of-the-Art of the Research in Upper Airway Geome-tries 58

    7 PIV of the Flow in a Model of the Upper Human Airways 697.1 Creation of the phantom . . . . . . . . .