Modeling of Human Snoring - Case Study Example

MODELING OF HUMAN SNORING By (Name) Unit Professor’s name University (Name) Course Date Abstract Snoring occurs whenever the upper airways become obstructed then reopened in quick succession following vibrations from the soft palates as well as the adjoining tissues in circumstances when excess inspiratory effort overcomes obstruction in the upper airways. Essentially, very few published studies relied on an extensive three-dimensional geometrical model representing the entire human head in their studies of mechanisms associated with snoring. This study aims at conducting a biomechanical investigation of the snoring mechanisms using a three dimensional Finite Element model of the human head. The study also seeks to design a model that will be useful in the prediction of the intensity of snoring noises through the application of the vibro-acoustic model. The current study will investigate snoring mechanisms using a comprehensive three-dimensional finite element model representing the entire human head including the neck as well as the entire upper airways. Moreover, it will ascertain the levels of snoring noises consequently providing invaluable information that will form the basis of future studies on control options for snoring. Introduction Snoring occurs whenever the upper airways become obstructed then reopened in quick succession. This occurs when the soft palates as well as the adjoining tissues vibrate during circumstances when excess inspiratory effort overcomes obstruction in the upper airways. Some study model experiments have demonstrated aeroclastic instability of soft palate tissues as the precursor of snoring. Approximately 20% of the adult population experience snoring thus making it a significant concern to an individual’s health (Epstein et al., 2010, p.14). The oro-pharyngeal walls frequently collapse especially during rapid eye movement sleep, which is also characterized by generalized relaxation of the muscles. Altered breathing patterns result in periodicity similar to Chayne-Stroke patterns. A dwindling level of blood oxygen and an increase in that of carbon dioxide happens over a considerable period of time prior to stimulation of respiration. This triggers the diaphragm into action ahead of the muscles of the upper airways thus causing the inspiratory effort to suck the relaxed oro-pharyngeal walls (Elliott et al., 2011, p.95). Figure 1: Anatomy of the upper airways The subsequent inspiratory efforts manage to open the airways thereby pulling air in causing the vibrations observed during snoring. In the event there is a further obstruction of the upper airways either by an adenoid or blocked nostril, there occurs an exaggerated collapse of the oro-pharyngeal wall caused by the inspiratory effort (Brockmann et al., 2012, p.75). There are no documented harmful effects of loud snoring except for the fact that it is a nuisance to other persons within the same vicinity thus a potential source of disharmony especially amongst married couples. Snoring is very prevalent amongst adults with approximately 20% of them snoring habitually. Recent studies have established that snoring is amongst the cardinal symptoms preceding the occurrence of obstructive sleep apnoea syndrome. However, there is an unclear distinction as to what point obstructive sleep apnoea sets in following episodes of snoring(Dreher et al., 2007, p.789). Persistent heavy snoring potentially results in the narrowing of the upper airways due to the hypertrophy of the adjacent structures. Consequently, the snorer progressively begins to experience limitations in the respiratory flow coupled with an increasing respiratory effort. In some instances, suction caused by strong efforts during inspiration has the potential to cause total collapse of the upper airways. Advanced complications of snoring may include collapse of the upper airways and associated sleepiness during the day (Kaditis et al., 2010, p.276). Despite the recent focus on snoring during the recent years, clinical experts mainly pay attention on mitigating the unwanted effects that snoring poses to an individual’s health. Consequently, very few studies pay attention to understanding the mechanisms behind snoring thereby resulting into effective approaches to mitigate the problem (Elliott et al., 2011, p.97). Figure 2: Schematic representation of the upper airway Purpose of the study This study aims at conducting a biomechanical investigation of the snoring mechanisms using a three dimensional Finite Element model of the human head. The researcher will identify the sources as well as the sinks during snoring using the Structural Intensity Methodology. The sources as well as the sinks are very useful in the identification of treatment options for snoring. The study also seeks to design a model that will be useful in the prediction of the intensity of snoring noises through the application of the vibro-acoustic model. The study will provide simulated results detailing modes of vibration, Structural Intensity fields, as well as transmission of the energy flows that will indicate the potential sources and sinks during snoring. Moreover, it will ascertain the levels of snoring noises consequently providing invaluable information that will form the basis of future studies on control options for snoring. Previous Investigations In 2002, researchers developed models of the finite element (FE) for both females and males by utilizing anatomic data from subjects of different sexes at the Harvard School of Medicine. They drew analyses of the upper airways’ finite element using a two-dimensional model. According to Birch and Srodon, 2009 who conducted an experiment to clarify the acoustic properties associated with snoring, repetitive sequences originating from the sound structures characterize large snoring sounds at low frequencies intertwined with rapid oscillations. The analysis yielded two distinct patterns that were dominant namely the complex –waveform and the simple-waveform. A gap in this study was the failure to identify the mechanisms responsible for snoring as well as the proven methods for mitigating the condition (Birch and Srodon, 2009, p.270). Cheng et al., (2011) conducted a study that involved the assessing the intensity of snoring sounds from different individuals recorded during polysomnographic tests and their relationship with demographic or clinical attributes. They concluded that apneic snorers experienced high rates of air flow, increased turbulence of the flows, and intense forces on the soft palate thereby causing negative pressures when they resume breathing. In another study, Aittokallio et al., developed a model that is useful in the prediction of the airflow profile in the nose by relying on the three essential components which control the patency of the airways during sleep (Cheng et al., 2011, p.450). According to Gavriely and Jensen who used a theoretical model comprising of a mobile wall inside a channel linked to an airway opening through a conduit that exerted some resistance, they concluded that the resistance, collapsibility, and narrowing of the upper airways are the predisposing factors to snoring and subsequently lead to obstructive sleep apneoa. In another study, Brietzke and Mair, (2006) investigated the impact of gas density variations on snoring simulations as well as supraglottic resistance using theoretical models of upper airways associated with their instability. Their study established that increasing the gas density leads to snoring even during lower rates of airflow (Brietzke and Mair, 2006). In an investigation conducted by Huang (1995), the researcher developed a mechanical model representing the soft palate dynamics when oronasal snoring occurs. This was realized by conducting an analysis of the soft palate’s linear stability using a two-dimensional flow on elastic plates. Cavusoglu et al., (2008) conducted an investigation on the behavior of unsteady and steady system flows through collapsible channels that enhanced the understanding of mechanisms associated with self-excited oscillations (Cavusoglu et al., 2008, p.879). Due to the simplistic approaches adopted by previous researchers, the understanding of the resistance, collapsibility, and narrowing of the upper airways remains limited thus creating the need to undertake extensive investigations on the mechanisms associated with snoring. Despite the fact that several models demonstrating nasal turbulence, vocal cords, and the larynx have been designed, most of them are two-dimensional and only focus on one aspect of the actual problem (Mason et al., 2013, p.96). Other studies involved models demonstrating turbulent flows in constricted ducts, inhalation studies using three-dimensional simplified model of a rigid throat, and snoring mechanisms for a two-dimensional wall channel that is flexible. The limiting aspect of these studies was the fact that the models used were simple geometric models used in the investigation of a specific physical mechanism. Essentially, very few published studies relied on an extensive three-dimensional geometrical model representing the entire human head in their studies of mechanisms associated with snoring (Liu et al., 2007, p.872). Models of Human Snoring Snoring occurs during the vibration of the flexible soft palate that joins the buccal track to the nasal cavity and the pharynx. The diagram shown below demonstrates the location of the soft palate and the adjacent structures (Elliott et al., 2011, p.101). Figure 3: Location of the human pharynx and adjacent structures There are three models of human snoring namely the fluid model, the modal expansion model, and the quasi-stationary frictionless model. The subsequent section analyses the fluid model of human snoring and the modal expansion method (Lee et al., 2013, p.345). 1. Fluid Model There is a relationship between the difference of the aerodynamic pressure ∆P(x, t)and the fluid structure motion. The fluid model flowing the fluid through a narrow channel situated between a moving structure and a wall. The model assumes a parallel flow with a resultant uniform pressure distributed along the flow (Liu et al., 2007, p.867). The typical rate of inspiratory flow is approximately 11s-1 whereas the channels cross-sectional area is 2cm2 thereby creating a fluid velocity of 5m s-1. This translates to a maximum Reynolds number of about 3000 and ensures that friction losses induced by pressure drops along the soft tissue palate become negligible. The relevance of the friction effects is observed during the explanation of the sound produced by snoring thus preventing a single flow pattern when the channel closes. However, simplified studies rely on uniform flows to calculate the channel’s inertial effects (Elliott et al., 2011, p.103). The ratio of pressure drop upstream in the nasal stream and mouth is useful in the generation of the mean velocity of air in the two channels. In order to create a similar velocity in both channels, the simplified fluid model assumes a ratio of 1. It is possible to generalize this model to other scenarios such as when there is closure of one channel. This assumption has been used in previous studies to minimize complex calculations especially in situations of unsteadiness(Elliott et al., 2011, p.104) . The Strouhal number is defined by multiplying the fundamental frequency of snoring ratio estimated at 50Hz with the soft palate’s length (L) and dividing the result by the velocity of the fluid U0 to obtain 0.4 typical value. This confirms the importance of non-stationary effects during snoring. The small nature of the system in comparison to the acoustic wavelength that corresponds to f0 and a small Mach number make the flow incomprehensible locally (Liu et al., 2007, p.873). Figure 4: Fluid model notations 2. Modal Expansion The equation shown below forms the basis of the modal expansion method to realize an infinite expansion in relation to natural modes with spatial dimensions: The functions ᴪ satisfies similar boundary conditions as w(x, t) In situations where the geometries are compatible and sufficient and simple boundaries conditions exist, it is possible to ascertain the analytical eigenmodes expressions ᴪm(x). For instance when the palate free on one end and clamped on the other end, the eigenmodes result in orthogonal functions upon neglect of structure-associated dissipation. In complicated geometries, it is possible to use numerical methods in developing functions that satisfy the condition of orthogonality (Elliott et al., 2011, p.105). The Galerkin’s method is then used to change equation of partial differentiation to yield infinite differential equations for the amplitudes The variable Mn provides for the modal mass for every unit width whereby Mn=mnµeL as demonstrated in the equation below: The parameter Mn is dimensionless and depends on the shape of the modal, L, e, and µ, the length, thickness, and density of the soft palate with ᴪ representing natural frequencies in the equation where ∆P=0 Proposed Research The proposed study will involve a biomechanical investigation of the snoring mechanisms using a three dimensional Finite Element model of the human head. Through this investigation, the researcher will identify the sources as well as the sinks during snoring using the Structural Intensity Methodology. The sources as well as the sinks are very useful in the identification of treatment options for snoring. The three dimensional Finite Element model of the human head will be useful in the prediction of the intensity of snoring noises through the application of the vibro-acoustic model. The study will simulate results detailing modes of vibration, Structural Intensity fields, as well as transmission of the energy flows that will indicate the potential sources and sinks during snoring. Moreover, it will ascertain the levels of snoring noises consequently providing invaluable information that will form the basis of future studies on control options for snoring. The study will investigate snoring mechanisms using the three-dimensional finite element model representing the entire human head including the neck as well as the entire upper airways. The applicable model in this study will comprise of the head, nasal cavity, tongue, hard palate, soft palate as well as the adjacent pharyngeal walls. The researcher will apply the Structural Intensity Methodology (SI Methodology) in the identification of the characteristics of snoring through the vibro-acoustic concept of controlling noise. In this case, the SI will serve as the flow of energy or power per unit area in the cross-sectional elastic medium. This is similar to acoustic intensity because of structural vibrations in the fluid medium. Based on the fact that the SI is a reflection of the direction and magnitude of the flow of vibrational energy in different parts of the structure, investigating the Structural Intensity of the throat structures from the dimension of controlling the vibrations and noise remains imperative. The distribution of the SI will provide extensive information regarding the paths of transmitting energy as well as the location of the sinks and sources of the energy generated from vibrations. The researcher will control the soft tissue vibrations as well as the surface walls of the upper airways and the levels of snoring noise by effectively altering the upper airways energy flows as well as the energy transmitted to the structure of the soft tissues. Modeling the human head using Finite Element The investigation into the snoring mechanisms will involve modeling the whole human head using shell and solid Finite Elements to yield a model shown in the diagram below. The upper part of the model is in accordance established by the ISB library whereas the other parts including the nasal cavity, tongue, hard palate, and soft palate will be created manually subject to scientific literature on the descriptions of the anatomy of the human head (Liu et al., 2007, p.870). The crucial structures in the model namely the neck, tongue, and soft palate will be modeled through the use of solid elements for purposes of obtaining more accurate representations of the natural structures. The model human head created by the Finite Elements will adequately cover the main phenomenon of dynamic response for the structures of interest namely the nasal cavity, tongue, and the soft palate. The researcher will put in much effort to achieve a replication of the three-dimensional features of the natural airways and avoid geometrical simplifications unless otherwise inevitable (Brietzke and Mair, 2006, p.418). Figure 5: The human head model design using the Finite Elements Materials with elastic, homogeneous, and isotropic properties will be used in designing the upper part of the head. The structures responsible for vibration namely the cartilages, tongue, hard palate, and soft palate will be designed using solid elements. A Poisson’s ratio of 0.49 in respect to the tongue will apply to enable the modeling of quasi-incompressibility since water is the major constituent in the tongue’s structure. The soft palate will have a Poisson’s ratio of 0.42 and a Young’s Modulus of 25kPa (Liu et al., 2007, p.867). Visco-elastic materials will be used in designing the soft palate and the tongue in order to facilitate dynamic responses analysis. It is expected the soft palate’s mechanical behavior will be visco-elastic and nonlinear. The elastic stress will represent instantaneous response by the soft tissues whereas the viscous stress emanates from the delayed response by surrounding tissues. The equation shown below represents this constitutive relationship: Whereby t = time The soft palate’s visco-elastic behavior will be modeled using the function of stress relaxation whose basis is the Prony series as shown below: Whereby: G(t) = Instantaneous modulus G0 = Delayed modulus g1 = Stress relaxation ٢1 = Stress relaxation N = Number of stress relaxation terms Internal dissipative forces’ effects will be addressed by assuming a structural damping of 5% Conclusions This study will utilize a three-dimensional model of the human head and neck designed using the Finite Elements to represent the realistic and natural upper airways. By analyzing the resultant data, the study seeks to evaluate the usefulness of the Structural Intensity Methodology in the identification of vibro-acoustic noises during snoring as well as the tissue parts with the highest sensitivity during the application of pressure. In addition to developing a three-dimensional model for investigating the mechanisms of snoring, the study will also design a mechanism for predicting the level of snoring noise in varying pressure zones. The model may undergo further exploration to ascertain additional snoring mechanisms and develop evidence-based interventions for mitigating the problem. An understanding of the mechanisms underlying snoring is very useful in the identification of relevant treatments to the problem. References Birch, M.J., Srodon, P.D., 2009. Biomechanical properties of the human soft palate. Cleft Palate. Craniofac. J. 46, 268–274. Brietzke, S.E., Mair, E.A., 2006. Acoustical analysis of snoring: Can the probability of success be predicted? Otolaryngol.-Head Neck Surg. 135, 417–420. Brockmann, P.E., Bertrand, P., Pardo, T., Cerda, J., Reyes, B., Holmgren, N.L., 2012. Prevalence of habitual snoring and associated neurocognitive consequences among Chilean school aged children. Int. J. Pediatr. Otorhinolaryngol. 76, 1327–1331. Cavusoglu, M., Ciloglu, T., Serinagaoglu, Y., Kamasak, M., Erogul, O., Akcam, T., 2008. Investigation of sequential properties of snoring episodes for obstructive sleep apnoea identification. Physiol. Meas. 29, 879. Cheng, S., Gandevia, S.C., Green, M., Sinkus, R., Bilston, L.E., 2011. Viscoelastic properties of the tongue and soft palate using MR elastography. J. Biomech. 44, 450–454. Dreher, A., Klemens, C., Patscheider, M., Kramer, M., Feucht, N., Schultheiss, C., Baker, F., De la Chaux, R., 2007. Use of pharyngeal pressure measurement to localize the source of snoring. Laryngo-Rhino-Otol. 86, 789–793. Elliott, N.S.J., Lucey, A.D., Heil, M., Eastwood, P.R., Hillman, D.R., 2011. Modelling and simulation of fluid-structure interactions in human snoring, in: 19th International Congress on Modelling and Simulation (MODSIM 2011). pp. 530–536. Epstein, M.D., Segal, L.N., Ibrahim, S.M., Friedman, N., Bustami, R., 2010. Snoring and the risk of obstructive sleep apnea in patients with pulmonary embolism. Sleep 33, 1069. Kaditis, A.G., Kalampouka, E., Hatzinikolaou, S., Lianou, L., Papaefthimiou, M., Gartagani-Panagiotopoulou, P., Zintzaras, E., Chrousos, G., 2010. Associations of tonsillar hypertrophy and snoring with history of wheezing in childhood. Pediatr. Pulmonol. 45, 275–280. Lee, H.-K., Lee, J., Kim, H., Ha, J.-Y., Lee, K.-J., 2013. Snoring detection using a piezo snoring sensor based on hidden Markov models. Physiol. Meas. 34, N41. Liu, Z.S., Luo, X.Y., Lee, H.P., Lu, C., 2007. Snoring source identification and snoring noise prediction. J. Biomech. 40, 861–870. Mason, D.J., Leavitt, J.K., Chaffee, M.W., 2013. Policy and Politics in Nursing and Healthcare-Revised Reprint. Elsevier Health Sciences.  Read More

Recent studies have established that snoring is amongst the cardinal symptoms preceding the occurrence of obstructive sleep apnoea syndrome. However, there is an unclear distinction as to what point obstructive sleep apnoea sets in following episodes of snoring(Dreher et al., 2007, p.789). Persistent heavy snoring potentially results in the narrowing of the upper airways due to the hypertrophy of the adjacent structures. Consequently, the snorer progressively begins to experience limitations in the respiratory flow coupled with an increasing respiratory effort.

In some instances, suction caused by strong efforts during inspiration has the potential to cause total collapse of the upper airways. Advanced complications of snoring may include collapse of the upper airways and associated sleepiness during the day (Kaditis et al., 2010, p.276). Despite the recent focus on snoring during the recent years, clinical experts mainly pay attention on mitigating the unwanted effects that snoring poses to an individual’s health. Consequently, very few studies pay attention to understanding the mechanisms behind snoring thereby resulting into effective approaches to mitigate the problem (Elliott et al., 2011, p.97).

Figure 2: Schematic representation of the upper airway Purpose of the study This study aims at conducting a biomechanical investigation of the snoring mechanisms using a three dimensional Finite Element model of the human head. The researcher will identify the sources as well as the sinks during snoring using the Structural Intensity Methodology. The sources as well as the sinks are very useful in the identification of treatment options for snoring. The study also seeks to design a model that will be useful in the prediction of the intensity of snoring noises through the application of the vibro-acoustic model.

The study will provide simulated results detailing modes of vibration, Structural Intensity fields, as well as transmission of the energy flows that will indicate the potential sources and sinks during snoring. Moreover, it will ascertain the levels of snoring noises consequently providing invaluable information that will form the basis of future studies on control options for snoring. Previous Investigations In 2002, researchers developed models of the finite element (FE) for both females and males by utilizing anatomic data from subjects of different sexes at the Harvard School of Medicine.

They drew analyses of the upper airways’ finite element using a two-dimensional model. According to Birch and Srodon, 2009 who conducted an experiment to clarify the acoustic properties associated with snoring, repetitive sequences originating from the sound structures characterize large snoring sounds at low frequencies intertwined with rapid oscillations. The analysis yielded two distinct patterns that were dominant namely the complex –waveform and the simple-waveform. A gap in this study was the failure to identify the mechanisms responsible for snoring as well as the proven methods for mitigating the condition (Birch and Srodon, 2009, p.270). Cheng et al., (2011) conducted a study that involved the assessing the intensity of snoring sounds from different individuals recorded during polysomnographic tests and their relationship with demographic or clinical attributes.

They concluded that apneic snorers experienced high rates of air flow, increased turbulence of the flows, and intense forces on the soft palate thereby causing negative pressures when they resume breathing. In another study, Aittokallio et al., developed a model that is useful in the prediction of the airflow profile in the nose by relying on the three essential components which control the patency of the airways during sleep (Cheng et al., 2011, p.450). According to Gavriely and Jensen who used a theoretical model comprising of a mobile wall inside a channel linked to an airway opening through a conduit that exerted some resistance, they concluded that the resistance, collapsibility, and narrowing of the upper airways are the predisposing factors to snoring and subsequently lead to obstructive sleep apneoa.

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