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The fluid mechanics of bolus ejection from the oral cavity
Journal of Biomechanics 34 (2001) 1537–1544
The fluid mechanics of bolus ejection from the oral cavity Mark A. Nicosiaa,c,*, JoAnne Robbinsa,b,c a Institute on Aging, University of Wisconsin, Madison, WI 53792, USA Department of Medicine, University of Wisconsin, Madison, WI 53792, USA c William S. Middleton Veterans Affairs Medical Center, Madison, WI 53705, USA b
Accepted 19 July 2001
Abstract The squeezing action of the tongue against the palate provides driving forces to propel swallowed material out of the mouth and through the pharynx. Transport in respose to these driving forces, however, is dependent on the material properties of the swallowed bolus. Given the complex geometry of the oral cavity and the unsteady nature of this process, the mechanics governing the oral phase of swallowing are not well understood. In the current work, the squeezing flow between two approaching parallel plates is used as a simplified mathematical model to study the fluid mechanics of bolus ejection from the oral cavity. Driving forces generated by the contraction of intrinsic and extrinsic lingual muscles are modeled as a spatially uniform pressure applied to the tongue. Approximating the tongue as a rigid body, the motion of tongue and fluid are then computed simultaneously as a function of time. Bolus ejection is parameterized by the time taken to clear half the bolus from the oral cavity, t1=2 : We find that t1=2 increases with increased viscosity and density and decreases with increased applied pressure. In addition, for low viscosity boluses (moapproximately 100 cP), density variations dominate the fluid mechanics while for high viscosity boluses (m>approximately 1000 cP), viscosity dominates. A transition region between these two regimes is found in which both properties affect the solution characteristics. The relationship of these results to the assessment and treatment of swallowing disorders is discussed. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fluid mechanics; Oral cavity; Swallowing
1. Introduction The sequential contact of the tongue against the palate plays an important role in the transport of swallowed material out of the oral cavity and through the pharynx (Cerenko et al., 1989; Dodds, 1987). Flow in response to these propulsive forces, however, depends on the physical properties of the bolus, such as viscosity and density. The dual role of the oropharynx in respiration and deglutition requires its rapid reconfiguration to accommodate bolus transport while protecting against bolus invasion into the airway. Despite the importance of this portion of the swallow, a general understanding of the effects of material property
*Corresponding author. Cardiothoracic Surgery Division, University of Wisconsin, H4/383 Clinical Sciences Center, 600 Highland Avenue, Madison, WI 53792, USA. Tel.: +1-608-265-0500; fax: +1608-263-0547. E-mail address: mnicosia@facstaff.wisc.edu (M.A. Nicosia).
variations on the dynamics of bolus ejection from the oral cavity is lacking. In addition to their impact on bolus ejection during normal swallowing, bolus material properties also play a role in the assessment and treatment of individuals with swallowing disorders. For example, the fluid intake of individuals who aspirate thin liquids (the most common type of material aspirated) is commonly restricted to ‘‘thickened liquids’’, a treatment strategy thought to slow bolus flow through the oropharynx and increase the time that the airway may use to protect itself against invasion by the bolus (Curran and Groher, 1990; Logemann, 1998). The aspiration of ingested material may transport oral bacteria to the lungs and is a risk factor for aspiration pneumonia, a serious and often lifethreatening health concern for the institutionalized and hospitalized geriatric population (Feinberg, 1991). Furthermore, deficiencies in swallowing function are often diagnosed using a videofluoroscopic swallowing study (Robbins et al., 1990), during which the flow of swallowed barium sulfate mixtures is studied using
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videofluoroscopy. These barium mixtures, however, are up to 3 times denser than non-barium liquids such as those normally ingested (Dantas et al., 1989, 1990). Extrapolating videofluoroscopic findings to the behavior of common dietary liquids requires an understanding of the effect that material property variations have on the oropharyngeal swallow, especially in a research setting where variables regarding bolus motion are often quantified (Robbins et al., 1992). In the current study, mathematical modeling is used to study the fluid mechanics of bolus ejection from the oral cavity. Our model, which is based on parallel plate squeezing flow to represent the tongue-palate contact, predicts the ejection time of the bolus for given material properties and applied pressure. We hypothesize that bolus ejection time will increase with increased viscosity and increased density and decrease with increased pressure applied by the tongue. 2. Methods Fig. 1 shows a schematic of the head and oral cavity along with the geometry and axisymmetric coordinate system used in the current analysis. The initial distance between the plates is denoted H and the radii, R: R is approximated as large enough to ignore edge effects (i.e., H=R51; the validity of this approximation will be explored later in this section). In the physiological system, the action of the tongue to eject the bolus from the oral cavity is generated by the contraction of
intrinsic and extrinsic lingual musculature. Here, that action is idealized as a spatially uniform pressure applied to the tongue (Pappl ). The incompressible flow of a Newtonian liquid is governed by the balances of mass and linear momentum, given by (respectively), r u ¼ 0;
ð1Þ
rðut þ u ruÞ ¼ rP þ mr2 u;
ð2Þ
where u is the velocity vector, P is the pressure, m is the viscosity, and r is the density. Subscripts are used to denote differentiation, a convention that will be used throughout this work. Applying a force balance to the tongue yields, Z R pR2 Pappl þ mg þ 2p P½hðtÞ; r; t r dr ¼ mhtt ; ð3Þ 0
where m and htt denote the mass and acceleration of the tongue. Note that Eqs. (1) and (2) are coupled to Eq. (3) through the hydrodynamic pressure term, P; and that the tongue is modeled as a rigid body (i.e., deformations of the tongue are not considered). The goal of the solution procedure is to compute the motion of the tongue along with the bolus flow characteristics for a given applied pressure. To describe the fluid flow between the tongue and palate, a stream function is introduced, of the form, cðr; z; tÞ ¼ r2 f ðz; tÞ: Radial and axial velocity components (u and w; respectively) are obtained by differentiating c with respect to z and r; 1 u ¼ cz ¼ rfz ð4Þ r 1 w ¼ cr ¼ 2f : ð5Þ r Eq. (5) shows that the axial velocity w does not depend on r; which follows from the geometric approximation that H=R is small. No-slip boundary conditions and initial conditions in terms of f are given by f ð0; tÞ ¼ fz ð0; tÞ ¼ 0; f ½hðtÞ; t ¼ ht =2;
fz ½hðtÞ; t ¼ 0;
f ðz; 0Þ ¼ 0; ht ð0Þ ¼ 0;
Fig. 1. Schematic of a lateral view of the head and oral cavity and the geometry and axisymmetric coordinate system used to model bolus ejection. The region of interest focuses on the central portion of the tongue, where its contact with the hard palate can accurately be approximated as parallel plate squeezing flow.
hð0Þ ¼ H;
ð6Þ
It can be shown that inserting Eqs. (4) and (5) into Eq. (2) and combining with the force balance on the plate1 (Eq. (3)) leads to the following set of equations (Weinbaum et al., 1985); mathematical details are included as supplemental information for interested 1 As they are derived from a stream function, the velocity components identically satisfy the continuity equation.
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readers (see Webpage of the Journal of Biomechanics at http://www.elsevier.com/locate/jbiomech), fzt þ fz2 2ffzz f ½hðtÞ; t ¼ ht =2:
1 fzzz ¼ bhtt þ 1 Re
ð7Þ ð8Þ
The following normalizations were used: r% ¼ r=R; z% ¼ z=H; h% ¼ h=H; f% ¼ fT=H; t% ¼ t=T; T ¼ ðprR4 =4QÞ1=2 ; where Q ¼ ½pR2 ðPappl Patm Þ mg is the net applied force on the lower plate. The overbar refers to nondimensional quantities; it is then dropped for convenience. The non-dimensional parameters, Re (Reynolds number) and b are defined by (Weinbaum et al., 1985), pffiffiffiffiffiffi 2H 2 Pr Re ¼ ; ð9Þ mR b¼
4Hm : prR4
ð10Þ
Physically, Re represents the ratio of inertial to viscous effects within the fluid, and b is related to inertia of the tongue. Consider typical values for b during swallowing. The mass of the tongue is approximated by m ¼ prt R2 L; where rt is the density of tongue muscle and L is the thickness, which yields H L rt : ð11Þ b¼4 RRr Approximating the density of tongue muscle as the same as the density of water gives values of rt =r between approximately 1 and 13; depending on the working fluid. Given that L=Ro1 (i.e., the tongue is wider than it is thick), b ¼ OðH=RÞ51 for either fluid. Thus, consistent with the other approximations, the inertia of the tongue is neglected in the current analysis. To facilitate the numerical solution of Eqs. (7) and (8), the following transformations are introduced, Z ¼ z=hðtÞ;
ð12Þ
g ¼ fZ =hðtÞ:
ð13Þ
This substitution leads to the modified governing equations, 2f gZ ZhgZ gZZ 2 1¼0 ð14Þ gt þ g2 h h h Re ht ¼ 2f :
ð15Þ
The Z-direction was discretized using second-order accurate finite differencing and time marching was accomplished using a fully implicit method, leading to a tridiagonal matrix. The solution algorithm is shown in Fig. 2. Note that at the first time step, the small time asymptotic solution given by Lawrence et al. (1985) was used to initiate the solution.
Fig. 2. Flow chart of the algorithm used to compute the fluid velocity profile along with the motion of the tongue. TOL represents a tolerance required for convergence. This value was set at 1 108.
A uniform grid of 100 points in the Z-direction and a non-dimensional time-step of 0.001 were used in all simulations. These values were first tested with mesh refinement studies and found to give grid-independent solutions. The tolerance for time step advance was set at 1 108. All calculations were carried out on a Pentium desktop computer (Compaq Computer Corporation, Houston, TX). For each simulation, the time required for the distance between the plates to decrease to H=2; denoted t1=2 ; was quantified. This half closing time is a measure of the speed with which the fluid is ejected. To validate the numerical solution, the nondimensional t1=2 was first compared to asymptotic solutions in the limit of infinite and zero Re: Thesepsolutions are ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi given by hðtÞ ¼ 1=cosh2 ðtÞ and hðtÞ ¼ 3=ðtRe þ 3Þ; respectively (Weinbaum et al., 1985). t1=2 is easily obtained by setting h ¼ 12 and solving for t: Although our model considers Newtonian fluids, many swallowed materials exhibit some degree of nonNewtonian behavior (Li et al., 1992). These materials are typically shear-thinning, with variations in viscosity becoming less pronounced with increased shear rate. To study the effect that such non-Newtonian characteristics might have on our numerical model, the wall shear rate was also computed for each simulation, according to, qw qu g’ ¼ þ ¼ rfzz jwall : ð16Þ qr qz wall A series of different materials was considered in this study, selected to span the range of liquids commonly encountered in normal swallowing as well as in
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swallowing evaluation and treatment (Coster and Schwarz, 1987; Dantas et al., 1989, 1990; Glassburn and Deem, 1998; Li et al., 1992). Viscosity values between 1 and 100 000 cP and densities of 1000 and 3000 kg/m3 were studied. Values for pressure applied by the tongue were estimated from data in the literature based on experiments using strain gauge sensors (Shaker et al., 1988; Pouderoux and Kahrilas, 1995) or bulb pressure sensors (Pouderoux and Kahrilas, 1995; Nicosia et al., 2000). Such data likely overestimate the applied pressure, as peak values occur after the bolus has exited the oral cavity and represent maximal tongue-palate contact pressure. Thus, a large range of applied pressures was studied, between 50 and 250 mmHg. To estimate the initial fluid height between the tongue surface and hard palate ðHÞ; the following relationship between the bolus volume and H was used: H¼
bolus volume ; pR2
ð17Þ
where R is the radius of the central portion of the tongue (see Fig. 1). The width and length of the tongue were estimated to be 3 and 5 cm, respectively (Kahrilas et al., 1993), yielding an average radius of 2 cm. For a bolus volume of 3 cm3, H was calculated to be 0.25 cm. This gives H=R ¼ 0:125; which is consistent with the approximations in the current model. To put these parameters into a fluid mechanical perspective, Fig. 3 shows the Reynolds number as a function of viscosity for several different values of
applied pressure and for r ¼ 1000 and 3000 kg/m3. Note that the Reynolds number varies over several orders of magnitude as viscosity is varied over the range appropriate for swallowed boluses. Also note that neither the applied pressure nor density has a large effect on Reynolds number, due to these terms appearing as a square root in the expression for Reynolds number (Eq. (9)).
3. Results The numerical solution showed excellent agreement to the asymptotic solutions in the limit of zero and infinite Re (Fig. 4). As both limits were approached, the difference between numerical and analytical solutions decreased to less than 1%. For low viscosity boluses (viscosity between approximately 1 and 100 cP), variations in density have a greater effect on t1=2 than variations in viscosity; a three-fold increase in density leads to a greater change in t1=2 than a ten-fold increase in viscosity (Fig. 5; note that here the dimensional t1=2 is plotted). This region corresponds to high Reynolds number flows in which viscous forces are dominated by (density modulated) inertial effects. The situation is reversed for higher viscosity boluses (viscosity greater than approximately 1000 cP), where viscosity plays the dominant role (Fig. 5). In effect, as viscosity increases, the flow reduces to a lubrication theory-type situation with no dependence on density. Finally, note that the applied pressure does not have a
Fig. 3. Reynolds number as a function of viscosity for different values of applied lingual pressure and for r ¼ 1000 kg/m (top) and r ¼ 3000 kg/m3 (bottom). Note the large range of Reynolds number for different combinations of bolus types and applied pressure.
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Fig. 4. Nondimensional half-closing time, t1=2 ; plotted as a function of Reynolds number (&), along with the asymptotic solutions for infinite (- - -) and zero Reynolds number (F). The numerical solution shows excellent agreement in these limiting cases.
Fig. 5. Half-closing time, in seconds, plotted versus bolus viscosity for two different values of density (1000 and 3000 kg/m3) and two different values of applied pressure (50 and 100 mm Hg). Note that logarithmic scales are used for both axes in these plots.
Fig. 6. Dimensional half-ejection time as a function of applied lingual pressure for a 50000 cP, 1000 kg/m3 bolus. Whereas the ejection time is unphysiologically large for low pressure, t1=2 reduces to physiological levels with increasing applied pressure. Many studies have shown that lingual pressure is increased with increasingly thick boluses.
large effect on the viscosity values corresponding to the transition from inertial to viscous dominance (Fig. 5). In general, as viscosity increases (for values >100 cP), bolus ejection time increases; at a viscosity of 100 000 cP, the half-closing time has increased to greater than 1 second for both values of applied pressure (Fig. 5). Although the time taken to clear a bolus from the oral cavity increases with increased viscosity (Robbins et al., 1992), even so-called semi-solids are cleared in approximately 500–600 ms (Dantas et al., 1989). To understand this discrepancy, we note that boluses of increased viscosity have been shown to elicit higher pressures from the tongue (Nicosia et al., 2000; Pouderoux and Kahrilas, 1995). As applied pressure increases, our model predicts that bolus ejection time reduces to more physiological values (Fig. 6).
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Fig. 7. Wall shear rate as a function of time for two different bolus viscosities (r ¼ 1000 kg/m3 and Pappl ¼ 100 mmHg). Note the different scale used for the y-axis in each plot, due to the large difference in shear rates between these two cases.
Fig. 8. Maximum shear rate as a function of bolus viscosity (r ¼ 1000 kg/m3 and Pappl ¼ 100 mmHg). Note the large range of shear rates in response to alterations in bolus viscosity.
The shear rate profile shows a similar qualitative behavior for different boluses, with peak shear rate during bolus ejection decreasing with increased viscosity (Fig. 7). The peak shear rate is highly dependent on the type of bolus being swallowed, varying over several orders of magnitude with variations in viscosity (Fig. 8).
4. Discussion The objective of the current work was to study the effect of material property variations (viscosity and density) and of applied lingual pressure on the dynamics of bolus ejection from the oral cavity. The time taken to clear half the bolus from the oral cavity, t1=2 ; was computed for a range of different materials and applied pressures. Our results show that for viscosity less than approximately 100 cP, variations in density have a stronger influence on t1=2 than variations in viscosity. A transition region occurs between viscosity values of
approximately 100 and 1000 cP, where density and viscosity both affect t1=2 : With further increases in viscosity, viscous forces overcome inertial effects, and variations in density have no influence at all on t1=2 : In studies considering the effects of material property variations on oropharyngeal swallowing, viscosity has traditionally been considered the primary mechanical variable. In fact, only a pair of studies considered the effect of variations in both density and viscosity on the oropharyngeal swallow (Dantas et al., 1989, 1990). In these studies, oral transit duration2 increased with increased density, suggesting that variations in density have an effect on the oral phase of swallowing. The current analysis is consistent with these previous studies and illustrates that density and viscosity interact to govern the mechanics of parallel plate squeezing flow. 2
In that study, oral transit time was defined as the interval between the first posterior motion of the bolus and the time which the bolus tail reaches the faucial pillars.
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These basic results have important implications with respect to swallowing evaluation and treatment, especially given the difference in density between barium sulfate mixtures commonly used in clinical swallowing studies and liquids which are normally ingested on a daily basis. In particular, care must be taken in extrapolating the results of videofluoroscopic swallowing studies to make inferences concerning commonly swallowed materials for low viscosity boluses (oapproximately 1000 cP). Furthermore, both viscosity and density should be routinely reported with videofluoroscopic swallowing studies, especially for comparison among work by different groups. Note that although the difference in t1=2 between the high- and low-density boluses in the low viscosity region was very small (Fig. 5), bolus ejection typically occurs quite rapidly. For example, Kahrilas et al. (1993) found that the tongue pulsion phase (defined as the time from the onset of tongue-palate approximation to complete closure) occurs in approximately 100 msec, independent of bolus volume. Perhaps more subtly, the results of this study suggest a complex interaction among variations in bolus material properties, applied lingual pressure, and the resulting fluid motions. As shown by several investigators (Nicosia et al., 2000; Pouderoux and Kahrilas, 1995; Shaker et al., 1988), the propulsive force applied by the tongue increases with increased ‘‘viscosity’’.3 However, as shown in Fig. 6, different values of applied pressure lead to different bolus ejection times for a given material. Consider the importance of this interaction on the use of ‘‘thickened liquids’’ as a treatment for individuals who aspirate thin liquids. The goal of this treatment methodology is to vary bolus material properties in an attempt to obtain optimal bolus flow characteristics. The current results suggest that the mechanical effect of thickened liquids may be nonuniform among different dysphagic populations, with different bolus flow outcomes related to the degree to which tongue pressure generation is compromised. More research is required to understand these complex interactions, but simply altering material properties without considering the interaction of these variations with the oropharyngeal swallowing system may be too simplistic. Density (or ‘‘mass density’’ for emphasis) is the parameter governing transient effects within a material. This fact comes directly from Newton’s Second Law of motion (force=mass * acceleration), which states that the acceleration of a body in a given direction is proportional to the net applied force in that direction and to the mass. Note that the momentum equation 3
The quotation marks are used because the actual viscosity values were not reported. All studies considered ‘‘semi-solid’’ versus liquid boluses.
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governing fluid flow (Eq. (2)) is simply Newton’s Law applied to a control volume and expressed per unit volume. Thus, the rate of change of velocity (i.e., acceleration) for a body is directly linked to its density. Since a bolus starts from rest and is accelerated through the oral cavity and into the pharynx during swallowing, it follows that this inherently transient process should be affected by density. With increasing viscosity, viscous forces damp these transient effects; indeed for values of viscosity above approximately 1000 cP density variations have virtually no effect on the flow characteristics. Previous studies have used both inertia-free parallel plate squeezing flow (Kokini et al., 1977; Campanella and Peleg, 1987) and inertia-free flow within a closing wedge (Chen, 1993) to model flow between the tongue and hard palate. These studies did not consider the swallowing process but rather focused on the oral sensory discrimination of fluid viscosity. The current model, based on parallel-plate squeezing flow, considered the tongue as a rigid (non-deformable) body. Although it is clear that the tongue undergoes large deformations during the oral phase of swallowing, the current analysis focuses on the final, propulsive phase of swallowing, which is driven by the squeezing action of the tongue against the palate. In this case, it is not necessary to consider the complex motions of the tongue during bolus manipulation and the rigid approximation is an appropriate simplification. Whereas the current analysis considered Newtonian liquids (constant viscosity, independent of shear rate), many swallowed materials exhibit some degree of nonNewtonian behavior (Li et al., 1992). However, most swallowed materials are ‘‘shear-thinning’’, which is typical of suspensions. Such liquids show non-Newtonian characteristics at low shear rates and approach a constant viscosity with increased shear. Given the highshear rate occurring during the ejection of a bolus (Figs. 7 and 8), the inclusion of non-Newtonian material behavior is not likely to significantly affect the conclusions of the current study. The current study was limited to the ejection phase of a bolus from the oral cavity. Extension of these results to a complete understanding of the entire oral phase of swallowing will necessarily require more complex models, including a realistic material and geometric representation of the tongue and its motions during swallowing. Such an extension is vital to extend the current results to understand oral mechanics in dysphagic individuals, who often show complex lingual motions during the oral phase of swallowing that could potentially influence bolus ejection characteristics. In summary, the current study has demonstrated that viscosity and density interact with applied lingual pressure to govern the fluid mechanics of bolus ejection from the oral cavity during swallowing. Variations in density play the dominant role for low viscosity boluses
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(o100 cP) while viscous forces dominate for high viscosity boluses (>1000 cP). These results enhance our understanding of the effects of material property variations on the oropharyngeal swallowing system and offer the potential to aid in the clinical evaluation and treatment of individuals with swallowing disorders.
Acknowledgements This work was supported in part by the National Institutes of Health, National Research Service Award #TG AG00213 from the National Institute on Aging and R01 NS24427. This is GRECC manuscript 01-01.
References Campanella, O.H., Peleg, M., 1987. Lubricated squeezing flow of a Newtonian liquid between elastic and rigid plates. Rheologica Acta 26, 396–400. Cerenko, D., McConnel, F.M.S., Jackson, R.T., 1989. Quantitative assessment of pharyngeal driving forces. Otolaryngology, Head Neck Surgery 100, 57–63. Chen, X.D., 1993. Slip and no-slip squeezing flow of liquid food in a wedge. Rheologica Acta 32, 477–482. Coster, B.S., Schwarz, W.H., 1987. Rheology and the swallow-safe bolus. Dysphagia 1, 113–118. Curran, J., Groher, M., 1990. Development and dissemination of an aspiration risk education diet. Dysphagia 5, 6–12. Dantas, R.O., Dodds, W.J., Massey, B.T., Kern, M.K., 1989. The effect of high- vs low-density barium preparations on the quantitative features of swallowing. American Journal of Roentgenology 153, 1191–1195. Dantas, R.O., Kern, M.K., Massey, B.T., Dodds, W.J., Kahrilas, P.J., Brasseur, J.G., Cook, I.J., Lang, I.M., 1990. Effect of swallowed
bolus variables on the oral and pharyngeal phases of swallowing. American Journal of Physiology 258, G675–G681. Dodds, W.J., 1987. The physiology of swallowing. Dysphagia 3, 171– 178. Feinberg, M., 1991. Aspiration and the elderly. Dysphagia 5, 61–71. Glassburn, D., Deem, J., 1998. Thickener viscosity in dysphagia management: variability among speech-language pathologists. Dysphagia 13, 218–222. Kahrilas, P.J., Lin, S., Logemann, J.A., Ergun, G.A., Facchini, F., 1993. Deglutitive tongue action: volume accomodation and bolus propulsion. Gastroenterology 104, 152–162. Kokini, J.L., Kadane, J.B., Cussler, E.L., 1977. Liquid texture perceived in the mouth. Journal of Texture Studies 8, 195–218. Lawrence, C.J., Kuang, Y., Weinbaum, S., 1985. The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 2. Boundary layer and exact numerical solution. Journal of Fluid Mechanics 156, 479–494. Li, M., Brasseur, J.G., Kern, M.K., Dodds, W.J., 1992. Viscosity measurements of barium sulfate mixtures for use in motility studies of the pharynx and esophagus. Dyphagia 7, 17–30. Logemann, J., 1998. Evaluation and Treatment of Swallowing Disorders, Pro-Ed. Nicosia, M.A., Hind, J.A., Roecker, E.B., Carnes, M., Doyle, J., Dengel, G.A., Robbins, J., 2000. Age effects on the temporal evolution of isometric and swallowing pressure. Journal of Gerontology: Medical Sciences 55, M634–M640. Pouderoux, P., Kahrilas, P.J., 1995. Deglutitive tongue force modulation by volition, volume, and viscosity in humans. Gastroenterology 108, 1418–1426. Robbins, J.A., Sufit, R., Rosenbeck, J., Levine, R., Hyland, J., 1990. A modification of the modified barium swallow. Dysphagia 2, 83–86. Robbins, J., Hamilton, J.W., Lof, G.L., Kempster, G.B., 1992. Oropharyngeal swallowing in normal adults of different ages. Gastroenterology 103, 823–829. Shaker, R., Cook, I.J.S., Dodds, W.J., Hogan, W.J., 1988. Pressureflow dynamics of the oral phase of swallowing. Dysphagia 3, 79–84. Weinbaum, S., Lawrence, C.J., Kuang, Y., 1985. The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 1. Analytic solutions; inviscid and small- but finiteReynolds limits. Journal of Fluid Mechanics 156, 463–477.
The fluid mechanics of bolus ejection from the oral cavity Mark A. Nicosiaa,c,*, JoAnne Robbinsa,b,c a Institute on Aging, University of Wisconsin, Madison, WI 53792, USA Department of Medicine, University of Wisconsin, Madison, WI 53792, USA c William S. Middleton Veterans Affairs Medical Center, Madison, WI 53705, USA b
Accepted 19 July 2001
Abstract The squeezing action of the tongue against the palate provides driving forces to propel swallowed material out of the mouth and through the pharynx. Transport in respose to these driving forces, however, is dependent on the material properties of the swallowed bolus. Given the complex geometry of the oral cavity and the unsteady nature of this process, the mechanics governing the oral phase of swallowing are not well understood. In the current work, the squeezing flow between two approaching parallel plates is used as a simplified mathematical model to study the fluid mechanics of bolus ejection from the oral cavity. Driving forces generated by the contraction of intrinsic and extrinsic lingual muscles are modeled as a spatially uniform pressure applied to the tongue. Approximating the tongue as a rigid body, the motion of tongue and fluid are then computed simultaneously as a function of time. Bolus ejection is parameterized by the time taken to clear half the bolus from the oral cavity, t1=2 : We find that t1=2 increases with increased viscosity and density and decreases with increased applied pressure. In addition, for low viscosity boluses (moapproximately 100 cP), density variations dominate the fluid mechanics while for high viscosity boluses (m>approximately 1000 cP), viscosity dominates. A transition region between these two regimes is found in which both properties affect the solution characteristics. The relationship of these results to the assessment and treatment of swallowing disorders is discussed. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fluid mechanics; Oral cavity; Swallowing
1. Introduction The sequential contact of the tongue against the palate plays an important role in the transport of swallowed material out of the oral cavity and through the pharynx (Cerenko et al., 1989; Dodds, 1987). Flow in response to these propulsive forces, however, depends on the physical properties of the bolus, such as viscosity and density. The dual role of the oropharynx in respiration and deglutition requires its rapid reconfiguration to accommodate bolus transport while protecting against bolus invasion into the airway. Despite the importance of this portion of the swallow, a general understanding of the effects of material property
*Corresponding author. Cardiothoracic Surgery Division, University of Wisconsin, H4/383 Clinical Sciences Center, 600 Highland Avenue, Madison, WI 53792, USA. Tel.: +1-608-265-0500; fax: +1608-263-0547. E-mail address: mnicosia@facstaff.wisc.edu (M.A. Nicosia).
variations on the dynamics of bolus ejection from the oral cavity is lacking. In addition to their impact on bolus ejection during normal swallowing, bolus material properties also play a role in the assessment and treatment of individuals with swallowing disorders. For example, the fluid intake of individuals who aspirate thin liquids (the most common type of material aspirated) is commonly restricted to ‘‘thickened liquids’’, a treatment strategy thought to slow bolus flow through the oropharynx and increase the time that the airway may use to protect itself against invasion by the bolus (Curran and Groher, 1990; Logemann, 1998). The aspiration of ingested material may transport oral bacteria to the lungs and is a risk factor for aspiration pneumonia, a serious and often lifethreatening health concern for the institutionalized and hospitalized geriatric population (Feinberg, 1991). Furthermore, deficiencies in swallowing function are often diagnosed using a videofluoroscopic swallowing study (Robbins et al., 1990), during which the flow of swallowed barium sulfate mixtures is studied using
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videofluoroscopy. These barium mixtures, however, are up to 3 times denser than non-barium liquids such as those normally ingested (Dantas et al., 1989, 1990). Extrapolating videofluoroscopic findings to the behavior of common dietary liquids requires an understanding of the effect that material property variations have on the oropharyngeal swallow, especially in a research setting where variables regarding bolus motion are often quantified (Robbins et al., 1992). In the current study, mathematical modeling is used to study the fluid mechanics of bolus ejection from the oral cavity. Our model, which is based on parallel plate squeezing flow to represent the tongue-palate contact, predicts the ejection time of the bolus for given material properties and applied pressure. We hypothesize that bolus ejection time will increase with increased viscosity and increased density and decrease with increased pressure applied by the tongue. 2. Methods Fig. 1 shows a schematic of the head and oral cavity along with the geometry and axisymmetric coordinate system used in the current analysis. The initial distance between the plates is denoted H and the radii, R: R is approximated as large enough to ignore edge effects (i.e., H=R51; the validity of this approximation will be explored later in this section). In the physiological system, the action of the tongue to eject the bolus from the oral cavity is generated by the contraction of
intrinsic and extrinsic lingual musculature. Here, that action is idealized as a spatially uniform pressure applied to the tongue (Pappl ). The incompressible flow of a Newtonian liquid is governed by the balances of mass and linear momentum, given by (respectively), r u ¼ 0;
ð1Þ
rðut þ u ruÞ ¼ rP þ mr2 u;
ð2Þ
where u is the velocity vector, P is the pressure, m is the viscosity, and r is the density. Subscripts are used to denote differentiation, a convention that will be used throughout this work. Applying a force balance to the tongue yields, Z R pR2 Pappl þ mg þ 2p P½hðtÞ; r; t r dr ¼ mhtt ; ð3Þ 0
where m and htt denote the mass and acceleration of the tongue. Note that Eqs. (1) and (2) are coupled to Eq. (3) through the hydrodynamic pressure term, P; and that the tongue is modeled as a rigid body (i.e., deformations of the tongue are not considered). The goal of the solution procedure is to compute the motion of the tongue along with the bolus flow characteristics for a given applied pressure. To describe the fluid flow between the tongue and palate, a stream function is introduced, of the form, cðr; z; tÞ ¼ r2 f ðz; tÞ: Radial and axial velocity components (u and w; respectively) are obtained by differentiating c with respect to z and r; 1 u ¼ cz ¼ rfz ð4Þ r 1 w ¼ cr ¼ 2f : ð5Þ r Eq. (5) shows that the axial velocity w does not depend on r; which follows from the geometric approximation that H=R is small. No-slip boundary conditions and initial conditions in terms of f are given by f ð0; tÞ ¼ fz ð0; tÞ ¼ 0; f ½hðtÞ; t ¼ ht =2;
fz ½hðtÞ; t ¼ 0;
f ðz; 0Þ ¼ 0; ht ð0Þ ¼ 0;
Fig. 1. Schematic of a lateral view of the head and oral cavity and the geometry and axisymmetric coordinate system used to model bolus ejection. The region of interest focuses on the central portion of the tongue, where its contact with the hard palate can accurately be approximated as parallel plate squeezing flow.
hð0Þ ¼ H;
ð6Þ
It can be shown that inserting Eqs. (4) and (5) into Eq. (2) and combining with the force balance on the plate1 (Eq. (3)) leads to the following set of equations (Weinbaum et al., 1985); mathematical details are included as supplemental information for interested 1 As they are derived from a stream function, the velocity components identically satisfy the continuity equation.
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readers (see Webpage of the Journal of Biomechanics at http://www.elsevier.com/locate/jbiomech), fzt þ fz2 2ffzz f ½hðtÞ; t ¼ ht =2:
1 fzzz ¼ bhtt þ 1 Re
ð7Þ ð8Þ
The following normalizations were used: r% ¼ r=R; z% ¼ z=H; h% ¼ h=H; f% ¼ fT=H; t% ¼ t=T; T ¼ ðprR4 =4QÞ1=2 ; where Q ¼ ½pR2 ðPappl Patm Þ mg is the net applied force on the lower plate. The overbar refers to nondimensional quantities; it is then dropped for convenience. The non-dimensional parameters, Re (Reynolds number) and b are defined by (Weinbaum et al., 1985), pffiffiffiffiffiffi 2H 2 Pr Re ¼ ; ð9Þ mR b¼
4Hm : prR4
ð10Þ
Physically, Re represents the ratio of inertial to viscous effects within the fluid, and b is related to inertia of the tongue. Consider typical values for b during swallowing. The mass of the tongue is approximated by m ¼ prt R2 L; where rt is the density of tongue muscle and L is the thickness, which yields H L rt : ð11Þ b¼4 RRr Approximating the density of tongue muscle as the same as the density of water gives values of rt =r between approximately 1 and 13; depending on the working fluid. Given that L=Ro1 (i.e., the tongue is wider than it is thick), b ¼ OðH=RÞ51 for either fluid. Thus, consistent with the other approximations, the inertia of the tongue is neglected in the current analysis. To facilitate the numerical solution of Eqs. (7) and (8), the following transformations are introduced, Z ¼ z=hðtÞ;
ð12Þ
g ¼ fZ =hðtÞ:
ð13Þ
This substitution leads to the modified governing equations, 2f gZ ZhgZ gZZ 2 1¼0 ð14Þ gt þ g2 h h h Re ht ¼ 2f :
ð15Þ
The Z-direction was discretized using second-order accurate finite differencing and time marching was accomplished using a fully implicit method, leading to a tridiagonal matrix. The solution algorithm is shown in Fig. 2. Note that at the first time step, the small time asymptotic solution given by Lawrence et al. (1985) was used to initiate the solution.
Fig. 2. Flow chart of the algorithm used to compute the fluid velocity profile along with the motion of the tongue. TOL represents a tolerance required for convergence. This value was set at 1 108.
A uniform grid of 100 points in the Z-direction and a non-dimensional time-step of 0.001 were used in all simulations. These values were first tested with mesh refinement studies and found to give grid-independent solutions. The tolerance for time step advance was set at 1 108. All calculations were carried out on a Pentium desktop computer (Compaq Computer Corporation, Houston, TX). For each simulation, the time required for the distance between the plates to decrease to H=2; denoted t1=2 ; was quantified. This half closing time is a measure of the speed with which the fluid is ejected. To validate the numerical solution, the nondimensional t1=2 was first compared to asymptotic solutions in the limit of infinite and zero Re: Thesepsolutions are ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi given by hðtÞ ¼ 1=cosh2 ðtÞ and hðtÞ ¼ 3=ðtRe þ 3Þ; respectively (Weinbaum et al., 1985). t1=2 is easily obtained by setting h ¼ 12 and solving for t: Although our model considers Newtonian fluids, many swallowed materials exhibit some degree of nonNewtonian behavior (Li et al., 1992). These materials are typically shear-thinning, with variations in viscosity becoming less pronounced with increased shear rate. To study the effect that such non-Newtonian characteristics might have on our numerical model, the wall shear rate was also computed for each simulation, according to, qw qu g’ ¼ þ ¼ rfzz jwall : ð16Þ qr qz wall A series of different materials was considered in this study, selected to span the range of liquids commonly encountered in normal swallowing as well as in
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swallowing evaluation and treatment (Coster and Schwarz, 1987; Dantas et al., 1989, 1990; Glassburn and Deem, 1998; Li et al., 1992). Viscosity values between 1 and 100 000 cP and densities of 1000 and 3000 kg/m3 were studied. Values for pressure applied by the tongue were estimated from data in the literature based on experiments using strain gauge sensors (Shaker et al., 1988; Pouderoux and Kahrilas, 1995) or bulb pressure sensors (Pouderoux and Kahrilas, 1995; Nicosia et al., 2000). Such data likely overestimate the applied pressure, as peak values occur after the bolus has exited the oral cavity and represent maximal tongue-palate contact pressure. Thus, a large range of applied pressures was studied, between 50 and 250 mmHg. To estimate the initial fluid height between the tongue surface and hard palate ðHÞ; the following relationship between the bolus volume and H was used: H¼
bolus volume ; pR2
ð17Þ
where R is the radius of the central portion of the tongue (see Fig. 1). The width and length of the tongue were estimated to be 3 and 5 cm, respectively (Kahrilas et al., 1993), yielding an average radius of 2 cm. For a bolus volume of 3 cm3, H was calculated to be 0.25 cm. This gives H=R ¼ 0:125; which is consistent with the approximations in the current model. To put these parameters into a fluid mechanical perspective, Fig. 3 shows the Reynolds number as a function of viscosity for several different values of
applied pressure and for r ¼ 1000 and 3000 kg/m3. Note that the Reynolds number varies over several orders of magnitude as viscosity is varied over the range appropriate for swallowed boluses. Also note that neither the applied pressure nor density has a large effect on Reynolds number, due to these terms appearing as a square root in the expression for Reynolds number (Eq. (9)).
3. Results The numerical solution showed excellent agreement to the asymptotic solutions in the limit of zero and infinite Re (Fig. 4). As both limits were approached, the difference between numerical and analytical solutions decreased to less than 1%. For low viscosity boluses (viscosity between approximately 1 and 100 cP), variations in density have a greater effect on t1=2 than variations in viscosity; a three-fold increase in density leads to a greater change in t1=2 than a ten-fold increase in viscosity (Fig. 5; note that here the dimensional t1=2 is plotted). This region corresponds to high Reynolds number flows in which viscous forces are dominated by (density modulated) inertial effects. The situation is reversed for higher viscosity boluses (viscosity greater than approximately 1000 cP), where viscosity plays the dominant role (Fig. 5). In effect, as viscosity increases, the flow reduces to a lubrication theory-type situation with no dependence on density. Finally, note that the applied pressure does not have a
Fig. 3. Reynolds number as a function of viscosity for different values of applied lingual pressure and for r ¼ 1000 kg/m (top) and r ¼ 3000 kg/m3 (bottom). Note the large range of Reynolds number for different combinations of bolus types and applied pressure.
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Fig. 4. Nondimensional half-closing time, t1=2 ; plotted as a function of Reynolds number (&), along with the asymptotic solutions for infinite (- - -) and zero Reynolds number (F). The numerical solution shows excellent agreement in these limiting cases.
Fig. 5. Half-closing time, in seconds, plotted versus bolus viscosity for two different values of density (1000 and 3000 kg/m3) and two different values of applied pressure (50 and 100 mm Hg). Note that logarithmic scales are used for both axes in these plots.
Fig. 6. Dimensional half-ejection time as a function of applied lingual pressure for a 50000 cP, 1000 kg/m3 bolus. Whereas the ejection time is unphysiologically large for low pressure, t1=2 reduces to physiological levels with increasing applied pressure. Many studies have shown that lingual pressure is increased with increasingly thick boluses.
large effect on the viscosity values corresponding to the transition from inertial to viscous dominance (Fig. 5). In general, as viscosity increases (for values >100 cP), bolus ejection time increases; at a viscosity of 100 000 cP, the half-closing time has increased to greater than 1 second for both values of applied pressure (Fig. 5). Although the time taken to clear a bolus from the oral cavity increases with increased viscosity (Robbins et al., 1992), even so-called semi-solids are cleared in approximately 500–600 ms (Dantas et al., 1989). To understand this discrepancy, we note that boluses of increased viscosity have been shown to elicit higher pressures from the tongue (Nicosia et al., 2000; Pouderoux and Kahrilas, 1995). As applied pressure increases, our model predicts that bolus ejection time reduces to more physiological values (Fig. 6).
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Fig. 7. Wall shear rate as a function of time for two different bolus viscosities (r ¼ 1000 kg/m3 and Pappl ¼ 100 mmHg). Note the different scale used for the y-axis in each plot, due to the large difference in shear rates between these two cases.
Fig. 8. Maximum shear rate as a function of bolus viscosity (r ¼ 1000 kg/m3 and Pappl ¼ 100 mmHg). Note the large range of shear rates in response to alterations in bolus viscosity.
The shear rate profile shows a similar qualitative behavior for different boluses, with peak shear rate during bolus ejection decreasing with increased viscosity (Fig. 7). The peak shear rate is highly dependent on the type of bolus being swallowed, varying over several orders of magnitude with variations in viscosity (Fig. 8).
4. Discussion The objective of the current work was to study the effect of material property variations (viscosity and density) and of applied lingual pressure on the dynamics of bolus ejection from the oral cavity. The time taken to clear half the bolus from the oral cavity, t1=2 ; was computed for a range of different materials and applied pressures. Our results show that for viscosity less than approximately 100 cP, variations in density have a stronger influence on t1=2 than variations in viscosity. A transition region occurs between viscosity values of
approximately 100 and 1000 cP, where density and viscosity both affect t1=2 : With further increases in viscosity, viscous forces overcome inertial effects, and variations in density have no influence at all on t1=2 : In studies considering the effects of material property variations on oropharyngeal swallowing, viscosity has traditionally been considered the primary mechanical variable. In fact, only a pair of studies considered the effect of variations in both density and viscosity on the oropharyngeal swallow (Dantas et al., 1989, 1990). In these studies, oral transit duration2 increased with increased density, suggesting that variations in density have an effect on the oral phase of swallowing. The current analysis is consistent with these previous studies and illustrates that density and viscosity interact to govern the mechanics of parallel plate squeezing flow. 2
In that study, oral transit time was defined as the interval between the first posterior motion of the bolus and the time which the bolus tail reaches the faucial pillars.
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These basic results have important implications with respect to swallowing evaluation and treatment, especially given the difference in density between barium sulfate mixtures commonly used in clinical swallowing studies and liquids which are normally ingested on a daily basis. In particular, care must be taken in extrapolating the results of videofluoroscopic swallowing studies to make inferences concerning commonly swallowed materials for low viscosity boluses (oapproximately 1000 cP). Furthermore, both viscosity and density should be routinely reported with videofluoroscopic swallowing studies, especially for comparison among work by different groups. Note that although the difference in t1=2 between the high- and low-density boluses in the low viscosity region was very small (Fig. 5), bolus ejection typically occurs quite rapidly. For example, Kahrilas et al. (1993) found that the tongue pulsion phase (defined as the time from the onset of tongue-palate approximation to complete closure) occurs in approximately 100 msec, independent of bolus volume. Perhaps more subtly, the results of this study suggest a complex interaction among variations in bolus material properties, applied lingual pressure, and the resulting fluid motions. As shown by several investigators (Nicosia et al., 2000; Pouderoux and Kahrilas, 1995; Shaker et al., 1988), the propulsive force applied by the tongue increases with increased ‘‘viscosity’’.3 However, as shown in Fig. 6, different values of applied pressure lead to different bolus ejection times for a given material. Consider the importance of this interaction on the use of ‘‘thickened liquids’’ as a treatment for individuals who aspirate thin liquids. The goal of this treatment methodology is to vary bolus material properties in an attempt to obtain optimal bolus flow characteristics. The current results suggest that the mechanical effect of thickened liquids may be nonuniform among different dysphagic populations, with different bolus flow outcomes related to the degree to which tongue pressure generation is compromised. More research is required to understand these complex interactions, but simply altering material properties without considering the interaction of these variations with the oropharyngeal swallowing system may be too simplistic. Density (or ‘‘mass density’’ for emphasis) is the parameter governing transient effects within a material. This fact comes directly from Newton’s Second Law of motion (force=mass * acceleration), which states that the acceleration of a body in a given direction is proportional to the net applied force in that direction and to the mass. Note that the momentum equation 3
The quotation marks are used because the actual viscosity values were not reported. All studies considered ‘‘semi-solid’’ versus liquid boluses.
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governing fluid flow (Eq. (2)) is simply Newton’s Law applied to a control volume and expressed per unit volume. Thus, the rate of change of velocity (i.e., acceleration) for a body is directly linked to its density. Since a bolus starts from rest and is accelerated through the oral cavity and into the pharynx during swallowing, it follows that this inherently transient process should be affected by density. With increasing viscosity, viscous forces damp these transient effects; indeed for values of viscosity above approximately 1000 cP density variations have virtually no effect on the flow characteristics. Previous studies have used both inertia-free parallel plate squeezing flow (Kokini et al., 1977; Campanella and Peleg, 1987) and inertia-free flow within a closing wedge (Chen, 1993) to model flow between the tongue and hard palate. These studies did not consider the swallowing process but rather focused on the oral sensory discrimination of fluid viscosity. The current model, based on parallel-plate squeezing flow, considered the tongue as a rigid (non-deformable) body. Although it is clear that the tongue undergoes large deformations during the oral phase of swallowing, the current analysis focuses on the final, propulsive phase of swallowing, which is driven by the squeezing action of the tongue against the palate. In this case, it is not necessary to consider the complex motions of the tongue during bolus manipulation and the rigid approximation is an appropriate simplification. Whereas the current analysis considered Newtonian liquids (constant viscosity, independent of shear rate), many swallowed materials exhibit some degree of nonNewtonian behavior (Li et al., 1992). However, most swallowed materials are ‘‘shear-thinning’’, which is typical of suspensions. Such liquids show non-Newtonian characteristics at low shear rates and approach a constant viscosity with increased shear. Given the highshear rate occurring during the ejection of a bolus (Figs. 7 and 8), the inclusion of non-Newtonian material behavior is not likely to significantly affect the conclusions of the current study. The current study was limited to the ejection phase of a bolus from the oral cavity. Extension of these results to a complete understanding of the entire oral phase of swallowing will necessarily require more complex models, including a realistic material and geometric representation of the tongue and its motions during swallowing. Such an extension is vital to extend the current results to understand oral mechanics in dysphagic individuals, who often show complex lingual motions during the oral phase of swallowing that could potentially influence bolus ejection characteristics. In summary, the current study has demonstrated that viscosity and density interact with applied lingual pressure to govern the fluid mechanics of bolus ejection from the oral cavity during swallowing. Variations in density play the dominant role for low viscosity boluses
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(o100 cP) while viscous forces dominate for high viscosity boluses (>1000 cP). These results enhance our understanding of the effects of material property variations on the oropharyngeal swallowing system and offer the potential to aid in the clinical evaluation and treatment of individuals with swallowing disorders.
Acknowledgements This work was supported in part by the National Institutes of Health, National Research Service Award #TG AG00213 from the National Institute on Aging and R01 NS24427. This is GRECC manuscript 01-01.
References Campanella, O.H., Peleg, M., 1987. Lubricated squeezing flow of a Newtonian liquid between elastic and rigid plates. Rheologica Acta 26, 396–400. Cerenko, D., McConnel, F.M.S., Jackson, R.T., 1989. Quantitative assessment of pharyngeal driving forces. Otolaryngology, Head Neck Surgery 100, 57–63. Chen, X.D., 1993. Slip and no-slip squeezing flow of liquid food in a wedge. Rheologica Acta 32, 477–482. Coster, B.S., Schwarz, W.H., 1987. Rheology and the swallow-safe bolus. Dysphagia 1, 113–118. Curran, J., Groher, M., 1990. Development and dissemination of an aspiration risk education diet. Dysphagia 5, 6–12. Dantas, R.O., Dodds, W.J., Massey, B.T., Kern, M.K., 1989. The effect of high- vs low-density barium preparations on the quantitative features of swallowing. American Journal of Roentgenology 153, 1191–1195. Dantas, R.O., Kern, M.K., Massey, B.T., Dodds, W.J., Kahrilas, P.J., Brasseur, J.G., Cook, I.J., Lang, I.M., 1990. Effect of swallowed
bolus variables on the oral and pharyngeal phases of swallowing. American Journal of Physiology 258, G675–G681. Dodds, W.J., 1987. The physiology of swallowing. Dysphagia 3, 171– 178. Feinberg, M., 1991. Aspiration and the elderly. Dysphagia 5, 61–71. Glassburn, D., Deem, J., 1998. Thickener viscosity in dysphagia management: variability among speech-language pathologists. Dysphagia 13, 218–222. Kahrilas, P.J., Lin, S., Logemann, J.A., Ergun, G.A., Facchini, F., 1993. Deglutitive tongue action: volume accomodation and bolus propulsion. Gastroenterology 104, 152–162. Kokini, J.L., Kadane, J.B., Cussler, E.L., 1977. Liquid texture perceived in the mouth. Journal of Texture Studies 8, 195–218. Lawrence, C.J., Kuang, Y., Weinbaum, S., 1985. The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 2. Boundary layer and exact numerical solution. Journal of Fluid Mechanics 156, 479–494. Li, M., Brasseur, J.G., Kern, M.K., Dodds, W.J., 1992. Viscosity measurements of barium sulfate mixtures for use in motility studies of the pharynx and esophagus. Dyphagia 7, 17–30. Logemann, J., 1998. Evaluation and Treatment of Swallowing Disorders, Pro-Ed. Nicosia, M.A., Hind, J.A., Roecker, E.B., Carnes, M., Doyle, J., Dengel, G.A., Robbins, J., 2000. Age effects on the temporal evolution of isometric and swallowing pressure. Journal of Gerontology: Medical Sciences 55, M634–M640. Pouderoux, P., Kahrilas, P.J., 1995. Deglutitive tongue force modulation by volition, volume, and viscosity in humans. Gastroenterology 108, 1418–1426. Robbins, J.A., Sufit, R., Rosenbeck, J., Levine, R., Hyland, J., 1990. A modification of the modified barium swallow. Dysphagia 2, 83–86. Robbins, J., Hamilton, J.W., Lof, G.L., Kempster, G.B., 1992. Oropharyngeal swallowing in normal adults of different ages. Gastroenterology 103, 823–829. Shaker, R., Cook, I.J.S., Dodds, W.J., Hogan, W.J., 1988. Pressureflow dynamics of the oral phase of swallowing. Dysphagia 3, 79–84. Weinbaum, S., Lawrence, C.J., Kuang, Y., 1985. The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 1. Analytic solutions; inviscid and small- but finiteReynolds limits. Journal of Fluid Mechanics 156, 463–477.