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Computational Fluid Dynamics or CFD is the analysis of systems involving fluid flow, heat transfer and associated phenomena such as chemical reactions by means of computer-based simulation (Versteeg & Malalasekera, 1995). This technique spans a wide range of industrial and non-industrial applications which include aerodynamics of aircraft and vehicles, turbomachinary and in this case, biofluid mechanics. CFD use in the medical field has seen a growing success mainly due it providing several unique advantages over experiment based approaches to fluid system design.
These advantages include:
A substantial reduction of lead times and costs of new designs;
The ability to study systems where controlled experiments are difficult or impossible to perform (e.g. very large or small systems);
The ability to study systems under hazardous conditions at and beyond their normal performance limits and
A practically unlimited level of detail of results.
The upper airway (UA) is a complex structure that has a critical role in providing inspiratory and expiratory airflow to and from the trachea and lungs during respiration (Young, T, Palta, M, Dempsey). The pharynx, the collapsible region of the upper respiratory tract, is usually subdivided into three segments as presented in Figure 1-1 below: nasopharymx (NP, From the end of the nasal septum to the free margin of the soft palate), oropharynx (OP, from the margin of the soft palate to the tip of the epiglottis) and hypopharynx (HP, from the tip of the epiglottis to the vocal cords) (Young, T, Palta, M, Dempsey).
Figure 1-1. Major structure of upper airway, reprinted from http://connection.lww.com
Obstructive sleep apnea syndrome (OSAS) is a disorder characterized by repetitive pharyngeal collapse and occlusion during sleep. This sleep disorder affects affecting 4% of men and 2% of women (Young, Palta et al. 1993). The short-term consequences of sleep apnea include sleep fragmentation, loud snoring, increases in daytime sleepiness and fatigue-related accident. Children who suffer from OSAS may show a variety of signs including behavioral disturbance, learning deficits and a slower body growth. Without prompt treatments in the early stage of OSAS, long term adverse effects on neurocognitive and cardiovascular functions may develop and have negative impacts on multiple organs and system.
This thesis will analyse OSAS using CFD. Investigations on the fluid dynamics through the upper airway will be closely examined with particular attention to transitional turbulent flow of air. In Chapter 2, some background information will be presented with examples of previous techniques used to investigate OSAS. The effects of airway geometry on upper airway pressure and flow resistance in the respiratory cycle are also analyzed. Chapter 3 will follow and the methods used will be discussed.
Three dimensional computational fluid models based on the anatomies of OSAS patients and controls are discussed and effects of airway geometry on upper airway pressure and flow resistance in the respiratory cycle are analyzed. Although confined by the rigid wall assumption, the CFD model makes the interpretation of airway fluid mechanics tractable since the airway compliance is time-varying and usually unknown. The resistance to flow resulting from these structural abnormalities leads to negative intraluminal pressures on the order of the reported collapse pressure and critical pressure () measured in OSAS patients.
CHAPTER 2: Literature Review
2.1 Background information
2.1.1 Sleep Disorder and Obstructive Sleep Apnea Syndrome (OSAS)
The abnormalities in airway dimension, muscle tone and ability of airway components to open make up the complex group of conditions which are known to cause sleep disordered breathing. Growing interest in sleep disorders have led to increased research (Sher, Schechtman et al. 1996). The initial identification of OSAS was followed by studies characterizing snoring, hypopneas, respiratory effort-related arousal and flow limitation events. Currently more sophisticated tests have been developed to differentiate OSAS from other sleep disorders (Polysomnography Task Force 1997). Among them the overnight full-channel polysomnography (PSG) is the most commonly used method to diagnose sleep apnea (Polysomnography Task Force 1997).
Snoring is a stable respiratory act characterized by increased inspiratory effort and increased endothoracic negative pressure due to narrowing of the upper airways. Snoring is accompanied by noise produced by vibration of the soft palate research (Cirignoita 2004).
Apneas and hypopneas are referred to as sleep-disordered breathing events. They cause asphyxia and provoke arousal from sleep. The severity of asphyxia depends on baseline gas exchange and the duration of the apnea or hypopnea . Apnea is commonly defined as airflow cessation for at least 10 seconds while hypopnea is applied when airflow decreases enough to lower oxygen saturation . Obstructive apnea and hypopnea have the same pathophysiology and determine the same effects on sleep fragmentation and oxygenation research (Cirignoita 2004).
If there is respiratory effort to resume airflow, the apnea is considered to be obstructive. Under such condition the upper airway is generally susceptible to collapse or narrowing during sleep due to increases in the size of soft tissue structures (tonsils, tongue base, soft palate, lateral pharyngeal walls, and parapharyngeal fat), or by craniofacial or nasal abnormalities (Cirignoita 2004). Absence of respiratory effort indicates that the brain is not responding to signals from the respiratory tract, classified as central sleep apnea. There are also mixed sleep apneas, in which both central and obstructive apnea are present (Cirignoita 2004).
2.1.2 Pathogenesis of OSAS and Available Treatments
Although understanding of the pathogenesis of OSAS is still limited, various treatment options have been developed for OSAS, depending upon the site(s) of the obstruction or collapse, symptom severity, and extent of clinical complications. Selection of treatment(s) for individual OSAS patient should be based upon balanced consideration of multiple factors, and the treatment effectiveness is variable and must be evaluated over time.
Behavioral and Medical Treatments: Severity of OSAS can be lessened by repositioning the body (sleeping on the side instead of in supine position). Behavioral changes might help reduce exacerbations of OSAS, but are not a cure. For OSAS caused by nasal obstruction, nasal decongestants can be used as medical treatments. Some oral appliances can help patients to maintain an open airway during sleep (Sher, Schechtman et al. 1996).
Weight Control: Clinic-based and epidemiological studies demonstrate a strong association between obesity and obstructive sleep apnea (Grunstein 1996). However, the exact mechanisms whereby weight loss results in improvements in OSAS are unknown, which may be associated with changes in upper body structure and decreases in upper airway collapsibility (Grunstein 1996). Increased adipose tissue deposits in the lateral pharyngeal fat pads and the increased muscle mass associated with weight gain are believed to cause airway obstruction.
Nasal Positive Airway Pressure (nasal CPAP) is often used to offset the increase in pharyngeal collapsibility during sleep. Nasal continuous positive airway pressure (CPAP) has become the nonsurgical treatment of choice for obstructive sleep apnea syndrome (OSAS) (Kribbs, Pack et al. 1993). This treatment is very effective at opening the pharynx during sleep, provided that an appropriate level of nasal CPAP is prescribed. However, up to 35% of patients receiving nasal CPAP discontinue its use, and those who continue treatment do not use it consistently (Sullivan, Jones et al. 1981).
Surgical Treatments may be appropriate for patients who cannot comply with or are not appropriate candidates for conservative therapies or nasal CPAP alone. The type of surgery performed should be based upon the specific pathophysiology of the patient's condition. The airway obstruction site(s) can be identified by radiography or other visualization method before surgery. Prior to 1980, tonsillectomy, adenoidectomy, nasal surgery, and tracheostomy were the main surgical treatments for OSAS. More options became available after 1980, including uvulopalotopharyngoplasty (UPPP), pharyngeal surgeries, laser
assisted uvulopalatoplasty (LAUP), and maxillomandibular advancement (MMA) (Sullivan, Jones et al. 1981).
UPPP is most efficacious for patients with oropharyngeal obstruction. However, the response rates to UPPP decrease over time. The failure rate increases when it is performed alone in the presence of retrolingual obstruction. Multiple surgical treatments including UPPP should be considered for those patients who have more than one obstruction site or craniofacial skeletal abnormalities. Laser-assisted uvulopalatoplasty (LAUP) have been shown to improve snoring and EDS (excessive daytime somnolence), by removing parts of the uvula and soft palate bilaterally. LAUP does not require general anesthesia or hospitalization, but no evidence based guidelines are available that suggest LAUP is effective or safe as a treatment for OSAS (Sullivan, Jones et al. 1981).
2.2 Mechanical models of OSAS
2.2.1 Starling resistor model
Figure 1-2. Diagram of a collapsible tube. The collapsible segment between and is exposed to external pressure . is the nasal resistance in the nasal passage. and represent the upstream pressure and downstream pressure, respectively.
In previous studies, the upper airway during sleep is usually modeled as a simple, collapsible conduit called a Starling Resistor (Figure 1-2). This model provides a generalized approach for determining the critical pressure () during inspiration and expiration, based on the pressure-flow relationships in the upper airway segment. The model predicts that the airway would be occluded completely whenever pressure both upstream () and downstream () fall below a . No flow could pass through the airway as long as > >. Flow initiates after is raised above . A flow-limited state would occur as long as the < (> >) (Schwab 1998). Under the flow limitation condition, flow through the upper airway rises linearly with elevation in , but is not influenced by .
The Starling resistor model can be used to describe airflow dynamics in the upper airway throughout the respiratory cycle. During inspiration, nasal pressure is upstream pressure (=) and trachea pressure is downstream pressure (=). As long as the trachea pressure is below , upstream pressure will determine if the upper airway occludes (<, ) or is flow-limited (>>). During expiration, nasal pressure is downstream pressure (=) and trachea pressure is upstream pressure (=). The upper airway will be either flow-limited or occluded whenever >0, provided that the downstream pressure remains atmospheric. Under these circumstances, airflow will cease whenever the upstream pressure falls below (>>), and airflow will increase linearly as is increased above the (>>=0).
The concepts of the Starling resistor model have several therapeutic implications. By increasing upstream pressure or decreasing either or , sleep hypopneas and apnea might be ameliorated. Furthermore, decreases in or in OSAS patients should decrease the flow resistance and thus increase inspiratory flow. However, it is unclear whether can be reduced sufficiently though mechanical, eletrophysiological, or pharmacological manipulation to abolish apnea.
2.2.2 Modeling Interactions Between the Air Flow and the Distensible Tissues
The Starling resistor model serves as a lumped parameter model that considers the upper airway as a single compliant segment. Its advantage is being able to recreate the flow limitation phenomenon or choking in a single compliant tube element in which model parameters are axially distributed. However, due to the discrete (non-homogeneous) nature of the upper airway, such assumptions are physiologically unreasonable. Fodil et al. described a model in which two singularities can be individualized in the airways (Fodil, Ribreau et al. 1997). These two elements have their own compliances, which enable the consideration of local differences in anatomical and physiological properties between pharyngeal regions. By controlling downstream pressure, inspiratory flow and area variations were predicted. The results revealed an area evolution following a doubly folded shape, and the occurrence of maximum and minimum flows in close succession, which can be considered as a physiological "flow plateau".
An improved version of this multi-element model, composed of 14 individualized compliant elements, has been used to simulate pressure-flow relationships in the nasal passages. Given an inspiratory pressure and a known compliance distribution, the model predicts the area profile and inspiratory flow. Initial geometric area and mechanical characteristics of each element were determined by acoustic rhinometry and posterior rhinomanometry. Under steady-state conditions, this model is able to simulate the pressure-flow relationship observed in vivo under normal conditions and pathological conditions.
2.2.3 Finite Element Model from Mid-Sagittal MR Images
To simulate the tongue and uvular movements in the anteroposterior direction, and the relative motions of surrounding structures such as tongue, mandible, hard palate, soft palate, uvula, hyoid bone, epiglottis, and pharyngeal airway, Malhotra et al. generated two dimensional finite element models from signal averaged mid-sagittal MRI for both a male and a female (Malhotra, Huang et al. 2002). As shown in Figure 1-3, a number of key points along the boundaries of the structures on MRI were identified (Figure 1-3, left), and the mean structures were defined for two-dimensional FE analysis afterwards (Figure 1-3, right).
Figure 1-3. A reproduced 2D finite element airway model. (original from (Malhotra, Huang et al. 2002) . Left: mid-saggital MRI of upper airway with surrounding structures; right: an illustration of the two-dimensional finite element model of the upper airway with mesh removed. is the pressure at the airway entrance and is the pressure at the airway exit.
The finite element models were run under conditions of primarily laminar and fully developed flow. The models demonstrated that the males' airways are substantially more collapsible than the females' airways, solely on the basis of anatomic differences. The model considered representative anatomies from the pool of MRI studies, tested the relative collapsibility under both sleeping (with some muscle activity) and passive (no muscle activity) conditions, as well as the effects of airway length, soft palate area and pharyngeal volumes on pharyngeal collapsibility.
2.3 Mechanical Environments of the Respiratory System
2.3.1 Structural Effects on the Airflow and Resistance in Upper Airway
Clearly OSAS involves flow limitation and a collapsible airway may be actively dilated by genioglossus and other upper airway muscles (Schwartz, Smith et al. 1988). Previous observations have demonstrated that the upper airway resists collapse during wakefulness, and the velopharynx is a highly compliant segment of pharynx when the pharyngeal muscles are relaxed (Isono, Feroah et al. 1997). Thus structural or anatomic alterations may contribute to a positive when neuromuscular activity declines at sleep. Distinguishing the relative contribution of each abnormality to airway closure could help researchers interpret experimental results and clinicians design better diagnostic and treatment tools to eliminate pharyngeal narrowing and closure.
Smith et al examined the pressure-flow relationships in patients with OSAS by applying incremental levels of positive pressure through a nasal mask during non-rapid-eye-movement sleep (Smith, Wise et al. 1988). The results are consistent with the view that the upper airway functions as a Starling resistor with a collapsible segment in the oropharnyx, and OSAS patients have a positive critical pressure. With total muscle paralysis produced by administration of muscular blockade under general anesthesia, Isono et al assessed the static mechanics of the passive pharynx by endoscopically measuring the cross-sectional area of the pharynx (A) at various pharyngeal luminal pressures () during complete airway closure (Isono, Shimada et al. 1998). The relationship between these two factors can be fitted by an exponential function, , where B and K are constants.
Maximum area was determined as mean values of measured area at the highest three values of. The value of K controls the shape of the curve; the higher the K value, the more round the curve. Most study subjects had a primary site of closure at the velopharynx instead of oropharynx. The curves for the apneic group were below those for normal controls, having a smaller and higher. The shape of the curve was more rounded in apneics, indicating the passive pharynx of OSAS patients was more vulnerable to pressure change independent of the pharyngeal size (more collapsible) as well as more structurally narrowed.
Children were also studied using a similar protocol. Cross-sectional area of the narrowest segment was significantly smaller in OSAS children and the collapsibility of the retropalatal and retroglossal segments significantly increased in OSAS children, indicating a significant role of the anatomic factors in the pathogenesis of pediatric OSAS patients (Isono et al, 1998)
2.3.2 Airway wall mechanics
Among the structural factors, dimensions, composition, and stiffness of the airway wall are essential determinants of airway cross-sectional area during dynamic collapse in a forced expiration. The interaction between the forces acting to open the airway (parenchymal tension and wall stiffness) and those to close it (negative airway internal pressure) determines the airway caliber. Historically the airway was viewed merely as conduit to convey airflow into and out of the gas exchange region of the lung and was paid little attention except for its contribution to airflow resistance (Mead 1961). 1986 marked the first review to investigate the mechanics of flow limitation, in which expiratory flow becomes independent of respiratory effort at low to intermediate lung volumes (Hyatt 1986). Pressure-area relationship measurements were obtained to study the effects of transmural pressure on lower airway luminal cross-sectional area (tube law), so that the airway compliance could be obtained.
Lambert et al derived the relaxed airway wall tube law from the trachea to the terminal bronchioles by matching experimentally observed flow-volume curves (Kamm 1999):
, when >0 Eq. (1-1)
, when >0 Eq. (1-2)
where and , and transmural pressure is the difference between and the effective tissue pressure acting on the outer wall. is the maximum cross-sectional area, is the value of at , is its slope at the point
There is some argument about whether the upper airway is more compliant in patients with OSAS. During respiratory efforts against airway occlusion, changes in upper airway size are significantly greater in snoring subjects with OSAS compared to weight matched snorers without OSAS (Brown, Bradley et al. 1985). This result indicates that OSAS patients have a more compliant airway. Significantly larger percentage changes in oropharyngeal size in awake patients with OSAS also suggest higher distensibility exists in OSAS group (Galvin, Rooholamini et al. 1989). It's also observed that awake patients with OSAS not only have smaller oropharyngeal airways, but larger expansion of this airway, particularly in the retropalatal region (Schwab, Gefter et al. 1993). However, such observations are only apparent on expiration, when the pharyngeal dilator muscles become less active, and further study is needed to determine whether the differences in upper airway size changes during breathing in awake subjects result from differences in upper airway dilator muscle activation during inspiration, and/or result from actual differences in the compliance of airway walls. Increased genioglossus activity is observed in OSAS patients, suggesting larger volume changes in expiration might occur as a consequence when these muscles become less active (Mezzanotte, Tangel et al. 1992). Therefore, it is questionable if OSAS patients have intrinsic mechanical abnormality compared with normal subjects. This reminds us that the measured upper airway "compliance" in many studies is actually influenced by the respiratory cycle and the negative pressure used to measure the compliance, and to access the upper airway compliance we need to exclude muscle activation effects.
Upper airway muscles such as the genioglossus are skeletal muscles. Skeletal muscle is a combination of characteristic fiber type(s) and its mechanical function is directly related to the intrinsic contractile properties of the muscle, such as force-velocity relationship and length-tension relationship (Mezzanotte, Tangel et al. 1992). Therefore, development and shortening during maximal voluntary contractions of inspiratory and expiratory muscles are determined primarily by the intrinsic contractile properties of the muscles (Mognoni, Saibene et al. 1968)
2.3.3 Control of Pharyngeal Musculature
OSAS patients generally have a narrower and more collapsible upper airway relative to others (Arens, McDonough et al. 2002). Such abnormal upper airway mechanics may be overcome by increased activation of upper airway dilators during wakefulness, but cause OSAS in sleep because of a reduction in basal upper airway activity (Brouillette and Thach 1979) and attenuation of dilator muscle activation in response to negative pressure (Gleadhill, Schwartz et al. 1991). It has been proposed in the "balance of forces" model that upper airway collapse occurs when the intraluminal negative pressures generated by the respiratory pump muscles during inspiration are inadequately opposed by pharyngeal dilator muscle activation (Remmers, Deegroot et al. 1978). Soft palate and tongue are believed to take an important role in the pathogenesis of OSAS (Horner 1996).
2.3.4 Upper Airway Muscles
The upper airway is composed of complex muscle groups. Only some major muscles are summarized here. In the nose and palate region, the main muscles groups are: alae nasi (to dilate the nares), tensor veli palatine (to stiffen palate), levator veli palatine (to raise palate), palatoglossus (to open retropalatal space) and palatopharyngeus (to close pharynx). In the oropharynx, the main muscle groups are: genioglossus (GG), (to protrude the tongue and typically recorded with intramuscular electrode (Sauerland and Mitchell 1970)), hyoglossus (to retract the tongue), styloglossus (to retract the tongue), constrictors (to constrict pharynx), styiopharyngeus (to elevate pharynx), and digastric (to dilate pharynx). In the larynx region, there are muscles to abduct vocal cords.
2.3.5 Mechanical Consequences of UA muscle Activation
Increased genioglossus activity has been associated with anterior tongue protrusion, pharyngeal airspace enlargement, and a net upper airway dilating force during inspiration (Bennett and Hutchinson 1946). Such dilating effects of upper airway muscle activation might be offset by negative inspiratory pressure(Wheatley, Kelly et al. 1991). The increases in retropalatal airway resistance associated with decreased tensor palatine (TP) activity suggests a mechanical role of TP in affecting airway patency (Tangel, Mezzanotte et al. 1991). However, activity of other palatal muscles are also probably involved and correlation coefficients between TP activity and retropalatal resistance are not clear (Tangel, Mezzanotte et al. 1991). Nasal resistance may not be changed significantly by alae nasi activity, while pharyngeal patency might be changed by hyoid muscles (Wheatley, Tangel et al. 1993). The relative importance of the individual palatal muscle to the maintenance of upper airway patency, awake and asleep, and the mechanical consequences of its activation, are still not well understood. Electrical activation of muscles may be effective in preventing upper airway collapse, and the clinical applications of airway muscle stimulation are an active area of research (Brennick, Pickup et al. 2004).
2.3.6 Effects of UA muscle Activation on UA Compliance
It has been suggested that upper airway muscle activation increases the ability of the airway to resist collapse. However, the mechanisms of airway stability improvements by increase airway stiffness and by airway muscle activation are fundamentally different . Compared with muscle activation, in which a more negative closing pressure results from an increase in airway size, the change in airway wall compliance changes the slope of upper airway pressure-volume relationship, thereby changing the closing pressure . In anesthetized animals, abolition of upper airway muscle activity makes closing pressure less negative and decreases upper airway volume, but it does not change the slope of the upper airway pressure-volume relationship . Such slope is the same in the live and post-mortem animal  despite the absence of muscle activity after death and much more positive closing pressure . These studies suggest that an increase in upper airway muscle activity might result in a more negative closing pressure due to the changes on airway size rather than wall stiffness. However, Isono et al.  has shown a change in the slope of upper airway pressure-volume relationship after applying electrical stimulation of genioglossus during hyperventilation-induced apnea in anesthetized OSAS patients, indicating a potential for increased genioglossus activity to exert a measurable effect on wall stiffness if the activation is large enough.
The method chapter describes the specific procedures that you undertook in or- der to produce your results. This should include schematic diagrams, governing equations, details of numerical methods, description of technical software, de- scription of experimental rig and operating procedure, a description and list of input parameters, and any other details specific to the methods employed in your project, as appropriate. It is in this chapter that you will make the greatest use of the mathematical features of LATEX and probably find the first need for tables.
3.1.1 Single equations
+ v · âˆ‡v
= âˆ’âˆ‡p + µâˆ‡2v + f (3.1)
3.1.2 Grouped equations
EÎ½ Î» =
(1 + Î½ )(1 âˆ’ 2Î½ )
2(1 + Î½ )
3.1.3 Side-by-side equations
EÎ½ Î» =
(1 + Î½ )(1 âˆ’ 2Î½ )
, µ =
2(1 + Î½ )
3. Methods 5
Table 3.1: A table of parameter values
Parameter Value Description
Lâˆ- 40.5 mm Length of channel
H âˆ- 5.0 mm Height of channel
âˆ-lrigid 6.0 mm Length of rigid central
âˆ-lflexible 8.0 mm Length of flexible plate
hâˆ- 0.25 mm Thickness of flexible
f 1.1774 kg/m
Density of fluid
µâˆ- 1.98Ã-10âˆ’5 kg/(m·s) Dynamic viscosity of
Î½ 0.3333 Poisson's ratio of solid
Mass per unit area of solid
Bâˆ- 1.87Ã-10âˆ’8 N·m Flexural rigidity of flex-
U âˆ- 0.08488 m/s Mean inlet velocity
âˆ-Î·0 0.08 mm Amplitude of initial
flexible plate eigen-
You can refer to equations individually, e.g., (3.1), (3.2a), (3.3a), or collectively
3.2 Tables and Figures
Here we have an example of a table (Table 3.1) and also of a figure containing subfigures (Figure 3.1).
3.3 Reference material
For general concepts you should refer to well-known books on the topic (and include the chapter and/or page), not websites. For example (but not limited to):
â€¢ Fluid mechanics: Massey (1983), Houghton & Carpenter (2003), Pope
(2000), Versteeg & Malalasekera (2007);
â€¢ Solid mechanics: Achenbach (1973), Mase (1970);
3. Methods 6
(a) velocity magnitude
Figure 3.1: Example of a figure with two subfigures using the minipage environment. Alternatively the subfigure package can be used.
â€¢ Medical: Marieb (2000).
Software should be referenced and in most cases there exists a user manual; e.g.
â€¢ OpenFOAM: Open FOAM: User Guide (2010);
â€¢ oomph-lib: Heil & Hazel (2006).
For more specific concepts you will need to cite relevant journal papers. NEVER CITE WIKIPEDIA.
This chapter should stick to the title-results. Your aim here is to describe what you found, which you will convey through graphs/plots, and possibly photos if you have an experimental project; i.e., pictures. As a suggestion, you may find it easiest to choose which pictures best demonstrate your results and then simply describe what is in each of the pictures. Use sections and subsections to group your results as appropriate.
This is perhaps the most important chapter of your thesis as it is here that you demonstrate your understanding of your results. To do this it is helpful to relate your results to the results of the papers that you introduced in the Literature Review. Suggested points to address are the limitations of your work (typically related to the method; i.e., assumptions made, simplifications of the model, accuracy of the equipment), the meaning of your results, how your results compare with those of your peers, and what contribution you have made to the field. This last point may seem daunting but the value of your work may simply be that no one has done it before, or that you have demonstrated that a particular piece of software is a useful tool for studying the problem at hand, or that useful insight can be gained even from a relatively simple model, or that your project lays the foundation for a more detailed investigation. This chapter should be somewhere between 5 and 10 pages.
This chapter should begin with a brief summary of what your project was about followed by a list of conclusions that you can draw from your results and discus- sion. As a guide, if you can make a single-sentence statement beginning with "I conclude that . . . " then this statement is probably a conclusion (you do not, of course, need to begin each conclusion with those three words). As a suggestion for how to write this chapter, reread your Discussion chapter and, of the points you discussed and speculated upon, find those statements that you made with conviction-these are likely your conclusions. This chapter should answer any questions that were raised in the Introduction thereby giving your thesis closure.
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Practice parameters for the indications for polysomnography and related procedures. Polysomnography Task Force, American Sleep Disorders Association Standards of Practice Committee. Sleep, 1997. 20(6): p. 406-22.
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Grunstein, R. R. (1996). "Metabolic aspects of sleep apnea." Sleep 19(10): 218-220.
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Isono, S., T. R. Feroah, et al. (1997). "Interaction of cross-sectional area, driving pressure, and airflow of passive velopharynx." Journal of Applied Physiology 83(3): 851-859.
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Mead, J., Mechanical properties of the lung. Physiol. Rev., 1961. 41: p. 281-330.
Hyatt, R., Forced expiration, in Handbook of physiology, A. Fishman, Editor. 1986. p. 295-314.
Brown, I. G., T. Bradley, et al. (1985). "Pharyngeal compliance in snoring subjects with and without obstructive sleep apnea." The American review of respiratory disease 132: 211-215.
Galvin, J., S. Rooholamini, et al. (1989). "Obstructive sleep apnea: diagnosis with ultrafast CT." Radiology 171: 775-778.
Mezzanotte, W., D. Tangel, et al. (1992). "Waking genioglossal electromyogram in sleep apnea patients versus normal controls (a neuromuscular compensatory mechanism)." The Journal of Clinical Investigation 89(5): 1571-1579.
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Kamm, R. D. (1999). "Airway wall mechanics." Annual Review of Biomedical Engineering 1: 47-72.
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Gleadhill, I. C., A. R. Schwartz, et al. (1991). "Upper airway collapsibility in snorers and in patients with obstructive hypopnea and apnea." The American review of respiratory disease 143(6): 1300-1303.
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