Newtonian and non-Newtonian food bolus behaviors obtained from validated swallowing simulator based on moving particle simulation

Abstract

This study compared the behavior of food boluses describing Newtonian and non-Newtonian fluids through a validated human swallowing simulator based on moving particle simulation. The simulation was qualitatively and quantitatively validated through comparisons with videofluorography images. The positions and configurations of the food boluses and normalized brightness of the simulated and videofluorography images during every timestep were similar, and we thought that the simulator can be used to study the mechanism of food bolus behavior. The validated swallowing simulator results show that the key factors for the optimal design of the thickener are the control of the bolus inflow velocity, which is influenced by rheological and tribological properties, prevention of small splash particles, and bolus discharge flow rate from the epiglottis to the esophagus. In addition, we propose an evaluation index for the degree of bolus coherence based on the bolus flow rate and velocity.

Introduction

The elderly community grows annually in many developed countries. In addition, aspiration pneumonia is an increasingly common cause of death. The emergence of swallowing difficulties is a part of aging related to this type of pneumonia. To improve the quality of life and health of elderly people, research and development on food safety and mechanisms of swallowing disorders should be conducted. The determination of food safety for people with swallowing disorders or difficulties conventionally involves trial-and-error food testing, which increases choking and aspiration problems.

In this study, we aimed to understand the behaviors of the food boluses and their interactions with organs considering Newtonian and non-Newtonian fluids during swallowing by developing a numerical simulator based on three-dimensional (3D) moving particle simulation (MPS). In MPS, particles are assumed to constitute the food bolus. The simulation accuracy was evaluated both qualitatively and quantitatively through comparisons with videofluorography (VF) examinations.

Several studies have been conducted on swallowing. Two-dimensional motion analysis has allowed to evaluate variations in a particular area of a sample material (Yamamoto et al., 2010). This method was based on the detection of changes in brightness, structural variations, and food bolus positions. Like other atraumatic methods, VF images have been obtained using a full-scale model of the oropharyngeal cavity (Iida et al., 2009) considering the effects of the viscosity of food bolus and swallowing position. However, this model was both solid and immobile, enabling only a qualitative evaluation. In a numerical simulation, the transformation of the jelly configuration among organs was studied using the 3D finite element method (FEM) (Mizunuma et al., 2004). However, the time-dependent forced transformation of organ structures caused by falling food boluses was neglected. A simulation that included the forced transformation of the pharyngeal wall was performed using Newtonian and non-Newtonian fluids (Meng et al., 2005), but the organs were assumed to have an axisymmetric geometry. In another medical-image-based simulation, researchers estimated forces from the organs and movement of the food bolus using VF images (Shimokasa and Mizunuma, 2006). A coupled simulation was carried out using FEM with accurate 3D organs and a food bolus with gelatinous properties (Mizunuma et al., 2009). A 3D FEM was later applied to a liquid bolus simulation (Suzuki et al., 2011), but the flow in the pharynx was assumed to be continuous. Hence, accurate 3D FEM models were required to consider the forced transformations in a coupled simulation of organs, liquid bolus, and splashes of liquid during calculations (Sonomura et al., 2011). Mainstream numerical simulations of swallowing have been performed using FEM and recently using MPS, which allows to calculate fluid splashes and large transformations. Although MPS has been applied to swallowing (Michiwaki et al., 2011), the simulation has not been validated.

Other particle-based methods, such as smoothed particle hydrodynamics, have been applied to swallowing (Ho et al., 2014; Farazi et al., 2015). Although these methods coupled simulations with the FEM and smoothed particle hydrodynamics, a detailed validation was not performed. Coupling 3D MPS with simulation of organs and food bolus may suitably describe the flow configuration around the epiglottis (Kikuchi et al., 2017). Kamiya et al. (2019) and Michiwaki et al. (2020) discussed the validity of simulation results of Newtonian fluid (water) or extracted values of several physical properties such as velocity and viscosity for healthy individuals, while the case study of non-Newtonian fluids and bolus quantity or flow rate at inflow and outflow has not been addressed.

In this study, we confirmed that a swallowing simulator based on 3D MPS is qualitatively and quantitatively accurate compared with VF images of healthy individuals. The proposed simulator can estimate changes in the food bolus during swallowing, allowing to determine food products with Newtonian and non-Newtonian properties according to the bolus quantity and flow rate changes. In addition, the simulator may be applicable to develop safe and convenient foods for individuals with swallowing difficulties or dysphagia.

Theoretical

The MPS method developed by Koshizuka et al. (1998) is well-known in the study of free surfaces or large fluid transformations. The governing equations are expressed using the laws of conservation of mass and momentum as follows:   

  

where ρ is the density, P is the pressure, u is the velocity, and f is the external force applied to the fluid. The governing equations are discretized as particle interaction models (Koshizuka et al., 1998). In addition, a particle interacts with a neighboring one via weight function w(r) defined as   

where r is the distance between two particles and r_e is the influence radius. These interactions are restricted to r_e (Koshizuka et al., 1998).

Surface tension is an important factor in calculating the free surface of a liquid bolus. The tribological effect between food bolus and organ surface is important in practice (Stokes et al., 2013; Funami and Nakauma, 2022; Gamonpilas et al., 2023). However, the tribological effect on organ surfaces has been rarely treated in numerical simulations. To simulate the wetness on an organ surface, we use a potential model (Kondo et al., 2007) for simulation, which requires the surface tension and contact angle for calculation. Using MPS, the surface tension and contact angle can be considered using the following potential coefficient:   

  

where C_f and C_fs are the potential coefficients for the fluid and solid, respectively, σ is the surface tension, l₀ is the initial distance of the particle, and θ is the contact angle (Prometech Software, 2012).

We consider a thickener as the calculation sample. It exhibits the characteristics of a non-Newtonian fluid, particularly owing to its shear-thinning flow. For swallowing ease, liquid foods should be rheologically structured fluids, defined as fluids with yield stress (Nakauma et al., 2011). Hence, we should use a shear-thinning flow with yield stress as the model for simulation. However, owing to limitations of our commercial software, we consider shear-thinning flow without yield stress. The non-Newtonian property can be described as follows (power-law model) (Prometech Software, 2012):   

where C₁, C₂, and C₃ are constants, γ̇ is the shear rate, and T is the absolute temperature.

Materials and Methods

VF imaging of swallowing VF images were used to validate the 3D human swallowing simulator based on MPS. The subject for VF imaging was a healthy volunteer (25-year-old male) who provided informed consent for participation in this study. VF imaging was approved by the Ethical Committee of the Japanese Red Cross Musashino Hospital (Approval No. 116) and could be compared with our previous findings (Michiwaki et al., 2018). A VF image was taken every 1/30 s from the front and side views.

Measurements of contact angle, surface tension and viscosity In general, the main food properties required for simulation are viscosity and density. In the employed commercial software, the wet conditions and deformation properties near the organ wall were set as functions of the contact angle and surface tension, respectively. An edible pig tongue purchased from a market was used to measure the contact angle between the organs and liquid. The measured parts and measurement system are shown in Fig. 1. The density was measured using a density hydrometer (DA-130 N, Kyoto Electronics, Kyoto, Japan), and the viscosity was measured using a rheometer (MCR301, Physica-Anton Paar, Austria). In addition, the surface tension was measured using a surface tensiometer (Kyowa Interface Science, Drop Master 500; needle diameter, 0.4 mm).

Fig. 1.

Measured parts and measurement system for contact angle. (A) Edible pig tongue purchased from market to (B) measure contact angle between organs and liquid.

Accurate human swallowing model and definition of moving parts An accurate human swallowing model for the simulation was designed based on the computed tomography (CT) images shown in Fig. 2A. The jawbone, vertebrae, hyoid bone, tongue, soft palate, and space of the pharynx were depicted semi-automatically by changing the brightness, as shown in Fig. 2B. These parts were used to guide the modeling of other organs, which were traced manually based on anatomical knowledge and structural relationships between organs, as shown in Fig. 2C. The detailed modeling is reported in (Michiwaki et al., 2018). The moving parts of the 3D swallowing model were defined by four objects (i.e., tongue, soft palate, larynx, and pharynx), as shown in Fig. 3A.

Fig. 2.

Modeling using medical images. CT images were used to guide the modeling of other organs, which were traced manually based on anatomical knowledge and structural relationships between organs and bones.

Fig. 3.

Moving parts of 3D swallowing model and ROI.

Each organ model was independently transformed over time. As shown in Fig. 3B, the region of interest (ROI) was a rectangular solid (X = 30 mm, Y = 40 mm, Z = 80 mm), and the upper end of the ROI was set with respect to the uvula. In the calculation, we defined the time at which the front of the food bolus flowed into the ROI as zero.

Solver and simulation A 3D numerical simulator was developed using a specialized commercial software (ParticleWorks 2.5, Prometech Software, Tokyo, Japan). Preprocessing resulted in a distance function file containing distance functions, and a customized solver was used for analysis. The simulation required a precise time interval of 1/300 s to accurately describe human swallowing. More than 700 distance function files were produced per body part to cover the entire period of each swallow. Thus, the total number of files was approximately 2 800. These time-dependent files were used to represent the forced transformations of the organs during swallowing.

Materials and properties The simulated food models are Newtonian fluid (water) and non-Newtonian fluid (2 % (w/w) thickener aqueous solution (Toromake SP, Meiji, Tokyo, Japan)), which included a contrast medium (OYPALOMIN; Fuji Pharma, Tokyo, Japan). In this paper, we described Newtonian fluid model as “water” and non-Newtonian fluid model as “thickener” in order to simplify explanation. The properties of food samples, input data, and solver settings are listed in Table 1. The potential coefficient was calculated using Eqs. 4 and 5. The particle diameter, which influenced the food bolus resolution, was 2 mm. The posture during swallowing for the model was assumed to be a standing position. In addition, the quantity of food bolus was fixed at 5 mL. We assumed that the food was put into the mouth and swallowed immediately considering a uniform sample temperature of 25 °C and neglecting any variation in temperature during swallowing. The effective diameter was a fitting parameter in the analysis and determined to be 4.1 from validation results.

Table 1 Physical properties of simulation sample

Food model	Water model : Newtonian fluid (Wter with contrast medium*)		Thickener model : Non-Newtonian fluid (2 % (w/w) thickener** aqueous solution with constrast medium*)
Swallowing volume, mL	5.0		5.0
Surface tension, N/m	0.058		0.024
Viscosity, mPa·s	Liquid: 2.6 Near the wall: 5.0		Power law model: C1 = 5.636, C2 = −0.724
	Contact angle*** ⚬	Potential Coefficient	Contact angle*** ⚬	Potential Coefficient
Pharynx	60	1.62	76.1	0.443
Larynx	85	1.174	85	0.388
Soft palate	60	1.62	76.1	0.433
Tongue	43	1.87	71.6	0.47
Fluid	90	2.16	90	0.715

Density 1 000 kg/m³, particle diameter 2 mm, effective radius 4.1.

^*  Contrast medium : OYPALOMIN 370 (mixing ratio 1 : 1), Fuji Pharma, Tokyo, Japan.

^**  Thickener : Toromake SP, Meiji, Tokyo, Japan.

^***  Measurement by pig's organs. Bold are fitting parameter.

Validation For the qualitative evaluation, the simulation results were compared with VF images at various timesteps. The images were synchronized based on the arrival time of the food bolus at the epiglottic valleys. To validate the simulation results, the normalized brightness, B_n, around the epiglottis vallecula was used as the evaluation parameter and defined as follows:   

where B_t is the brightness calculated using the ImageJ image processing software (National Institutes of Health, Bethesda, MD, USA) and B_max and B_min are the maximum and minimum brightness values across measurements, respectively. As shown in Fig. 4, the brightness of the ROI changed over time. The normalized brightness was used to quantitatively evaluate these changes. The simulated and VF images were compared at all the timesteps.

Fig. 4.

Brightness changes at ROI (surrounding of epiglottis vallecula) for validation.

Results and Discussion

Qualitative validation We qualitatively compared the images over time as a person swallowed different food models (water and thickener). The food bolus flowed into the ROI shown in Fig. 3B at time zero. The food bolus behaviors during swallowing of Newtonian fluid (water) and non-Newtonian fluid (thickener) are shown in Figs. 5 and 6, respectively. In the lateral view during water swallowing (Fig. 5), the VF images can be easily compared with the simulated images. In particular, the bolus front configuration at 0 s, quantity, and form of the bolus accumulating in the epiglottic vallecula in 0.066–0.132 s and bolus shape flowing out into the esophagus in 0.198–0.330 s are similar in configuration and timing for the simulated and real VF images. In the anteroposterior-view images of the water-swallowing model, the bolus configuration is difficult to visualize in the VF images initially (from 0 s to 0.132 s), whereas the simulated images allow to easily recognize the food bolus changes and occurrence of small splash particles. In addition, the bolus form and quantity of the VF and simulated images are relatively similar in the area where a bolus passes from the oral region to the esophagus in the anteroposterior view. Hence, our simulation can reproduce the water bolus behavior with a high accuracy.

Fig. 5.

Qualitative validation for Newtonian fluid (water). The first and third rows show VF images, while the second and fourth rows show simulated images corresponding to the VF images on top. Each image shows the lateral (left) and anteroposterior (right) views.

Fig. 6.

Qualitative validation for non-Newtonian fluid (thickener). The first and third rows show VF images, while the second and fourth rows show simulated images corresponding to the VF images on top. Each image shows the lateral (left) and anteroposterior (right) views.

Similar images for the non-Newtonian fluid (thickener) are shown in Fig. 6. Like the water simulation, during inflow (0–0.132 s), the thickener bolus forms and accumulates in the epiglottic vallecula, being similar for the VF and simulated images in the lateral view. In addition, the shape of bolus flowing out into the esophagus in 0.198–0.330 s is similar in configuration and timing for the VF and simulated images. Although the food bolus flows with no splash, we cannot observe the food bolus at the beginning of swallowing (from 0 s to 0.132 s) in the VF images from the anteroposterior view. The simulation can suitably describe the thickener bolus behavior in detail, which was not previously confirmed, as well as spray formation shown in the VF images above.

Quantitative validation To quantitatively evaluate the accuracy of the 3D swallowing simulator, the normalized brightness was compared between the VF and simulated images. Figs. 7 and 8 show comparisons of the normalized brightness over time for the Newtonian (water) and non-Newtonian (thickener) fluids, respectively. We quantified the bolus inflow and outflow in the ROI shown in Fig. 4. Time zero was defined as the instant at which the bolus flowed into the ROI. A lower brightness indicates that more liquid flows. When the bolus flows into the ROI, the brightness decreases. When the brightness changes calculated from the simulated and VF images overlap, the results agree.

Fig. 7.

Quantitative validation comparing normalized brightness of area around epiglottis for Newtonian fluid (water).

Fig. 8.

Quantitative validation comparing normalized brightness of area around the epiglottis for non-Newtonian fluid (thickener).

The quantitative validation for water (Fig. 7) shows a decreasing slope corresponding to the inflow velocity and timing of minimum brightness. The slope is consistent for the simulated and VF results. In addition, when outflow begins, the normalized brightness between the simulated and VF results shows a similar trend. In image processing for validation, we defined an initial image of VF in time zero as a reference image. To remove the movement of organs in the ROI, the reference image was subtracted from the images at all timesteps. Hence, we could extract only the food bolus from the VF images in principle, but this method could present some artifacts in practice. When the subject moved back and forth or waggled the head during swallowing, an unnecessary part was included in ROI. The differences between VF and the simulation results at 0.2–0.3 s and 0.45–0.5 s in Fig. 7 are related to an unnecessary part included in the ROI by head movement; consequently, the brightness did not recover despite the food bolus beginning to flow. Considering this image processing error, near the epiglottis, we think the simulation seems to describe the flow of food bolus relatively exactly. The quantitative validation for the thickener (Fig. 8) indicates that brightness changes, such as decreasing slope, timing of minimum brightness, and outflow, are consistent for the VF and simulation results. Overall, the normalized brightness in the 3D simulations agrees with that obtained from the VF images throughout swallowing. Hence, the proposed 3D swallowing simulator is accurate for Newtonian and non-Newtonian fluids.

Bolus behaviors of water and thickener The bolus behaviors during swallowing of water and the thickener are shown in Figs. 9 and 10. The food bolus flows into the ROI at time zero. From 0 s to 0.133 s, the thickener forms a lump, while water flows in while also forming spray.

Fig. 9.

Bolus behaviors for water. Within each frame, the left and right images show the lateral and anteroposterior views, respectively. Time zero indicates the entrance of water into the ROI.

Fig 10.

Bolus behaviors for thickener. Within each frame, the left and right images show the lateral and anteroposterior views, respectively. Time zero indicates the entrance of thickener into the ROI.

The food bolus images at 0.067 s show that the thickener bolus flows into the vicinity of the epiglottic vallecula along the tongue base surface at a decreasing velocity. On the other hand, part of the water collides with the rear wall of the pharynx without slowing by the surface of the dorsal tongue and tongue base but instead accelerating owing to small splash particles. The water front arrives faster than the thickener at the epiglottic vallecula, and the bolus end of the water extremity scatters (from 0.1 s to 0.133 s). In contrast, the rear end of the gathered thickener bolus flows with a wide and long tail (from 0.2 s to 0.267 s). When comparing the food bolus images from 0.067 s to 0.333 s, water remains in the epiglottic vallecula for a short period, and outflow begins when the esophagus opens. In contrast, the thickener outflow begins in a short time without accumulating in the epiglottic vallecula to cover the epiglottis tip (from 0.233 s to 0.333 s). For bolus discharge (from 0.4 s to 0.5 s), the water flows into esophagus with thick lines, whereas the thickener flows as one lump (coherent bolus). In (Kumagai et al., 2009, Nakauma et al., 2011, Kumagai et al., 2021), the flow pattern during swallowing was related to the maximum velocity, V_max, obtained by the ultrasonic pulse Doppler method, and the time required for the bolus to flow in the pharynx, t₂, was obtained from the acoustic swallowing sound. The bolus flow pattern became a coherent flow (coherent bolus) when the bolus velocity through the pharynx, V_max, was small and t₂ was short. The bolus flow pattern became an incoherent flow (scattered bolus) when the particle velocities through the pharynx were both high and low. The flow pattern of the thickener model (Fig. 10) shows the simulation of a coherent flow (coherent bolus) when the food bolus passes through the pharynx space. On the other hand, the flow pattern of the water model (Fig. 9) simulates incoherent flow (scattered bolus) when the food bolus hits the pharynx wall or flows along the tongue base. Overall, our simulator allows to visualize and compare bolus behaviors of water with its incoherent flow (scattered bolus) and the thickener with its coherent flow (coherent bolus) at high temporal and spatial resolutions.

Bolus volume evaluation In conventional evaluation or measurement of swallowing, such as VF or ultrasound imaging, only the two-dimensional bolus shape and average velocity can be obtained. As our simulator can provide 3D quantitative information, such as the bolus volume, it outperforms conventional methods. We evaluated the food volume changes in the bolus within the ROI. For simulation, a person swallowed a given volume while varying the remaining food volume in the oral space. Thus, the inlet volume to the ROI slightly differed among swallowing simulations. The normalized number of particles was used as the evaluation index. Normalization consisted of dividing the number of bolus particles by the number of all particles flowing into the ROI at each timestep.

Fig. 11 shows the normalized number of particles over time indicating the mass of food bolus in the ROI. The normalized number was extracted from the output files of the simulator. Visualization images were generated to verify the flow configuration and changes in the normalized number of particles.

Fig 11.

Normalized number of particles of Newtonian (water) and non-Newtonian (thickener) fluids over time. The simulated images show the behaviors of water bolus (top) and thickener bolus (bottom). Within each frame, the left and right images show the lateral and anteroposterior views, respectively. Labels a–d indicate the times of the images.

Bolus volume and configuration during inflow and outflow As shown in Fig. 11, during bolus inflow (0–0.3 s), the maximum particle inflow occurs at 0.167 s for water and 0.3 s for the thickener, and the water volume increases much faster than the thickener volume afterward.

The water inflow changes approximately linearly, and the maximum volume is kept for ~0.1 s (from 0.133 to 0.233 s). The thickener inflow volume is slightly slower and stays by a shorter time at the maximum value. Hence, the flow rate of the thickener food bolus decreases during inflow. This indicates that the thickener bolus is swallowed while spreading laterally into the vicinity of the epiglottic vallecula along the tongue base surface, with a decrease in velocity owing to the friction between the organ surface and bolus. In contrast, water maintains its inflow velocity and even accelerates, as indicated by the timing of maximum bolus volume.

Overall, the interaction between the tribological effect with friction and lubrication between the bolus and organs as well as the rheological effect with bolus flow and deformation are key factors determining the bolus behavior. Considering the bolus position when all the food bolus flows into the ROI, the water bolus is located near the epiglottic vallecula (0.133 s) and spreads widely, whereas the thickener bolus is located near the front end of the bending epiglottis and entrance of the esophagus (0.30 s).

Next, we focus on the outflow in Fig. 11. The water bolus begins to flow out after staying from 0.133 s to 0.233 s at the maximum volume. In contrast, the thickener bolus quickly flows out after its volume reaches the maximum at 0.3 s. In addition, the outflow behaviors of both boluses are similar after the bolus rear end is located over the epiglottis at 0.433 s. Hence, the thickener bolus is ready to be discharged in coherent bolus and quickly flows out from the epiglottis to the esophagus, which may explain the improved thickener prevention of aspiration compared with water.

Passage time and velocity of food bolus In simulation, when a person swallows the same volume of different foods, no difference is observed in the total swallowing time for a wide range of ROI, as shown in Fig. 3B. The only differences occur from 0.067 s to 0.433 s (= 0.366 s), when the food bolus passes near the epiglottis region. Before and after this region, the difference is negligible regarding the change in inflow and outflow volumes.

The average inflow velocity of water and the thickener are 0.54 m/s and 0.36 m/s, respectively. These velocities are calculated from the distance moved by the bolus front and elapsed time using the visualization results of our simulator. In (Kumagai et al., 2009; Kumagai and Tanigome, 2012), ultrasonic measurements revealed inflow velocities of 0.5–0.6 m/s for water and 0.37 m/s for a thickener (0.5% (w/w) xanthan gum solution and viscosity of 0.52 Pa·s at shear rate of 10 s⁻¹). Our simulated inflow velocities are thus consistent with those obtained from ultrasonic measurements.

Bolus flow rate evaluation The effect of thickeners has been reported experimentally regarding the food bolus velocity and sensory perception. However, the food bolus velocity obtained from the laser Doppler method and image processing of data such as VF rely on superficial measurements and lack spatial information of depth (mass or volume). Our simulator can provide information of the bolus volume, which contains the depth direction information of the bolus and is difficult to obtain from conventional experimental measurement methods, indicating its superior applicability and a unique feature. In this study, we focused on the flow rate (in milliliters per second) that contained three-dimensional spatial and temporal information and compared the behavior of water and thickener bolus. We consider the bolus behavior by flow rate, which defines the changes in the number of particles, as an evaluation index.

Fig. 12 shows the flow rate in milliliters per second of the food bolus. Positive and negative values indicate inflow and outflow rates, respectively. The simulated images allow to visualize the flow configuration and flow rate.

Fig. 12.

Bolus flow rate of Newtonian (water) and non-Newtonian (thickener) fluids over time. The simulated images show the behaviors of water (top) and thickener (bottom) boluses. Within each frame, the left and right images show the lateral and anteroposterior views, respectively. The positive and negative values indicate the inflow and outflow rates, respectively. Labels a–d indicate the times of the images.

Bolus inflow rate During inflow (from 0 s to 0.067 s, Fig. 12), the flow rate of the water and thickener food boluses are similar despite the varying inlet velocity of the bolus front (i.e., the water bolus front arrives at the epiglottis faster than the thickener bolus). For water swallowing, although the inflow velocity of a small bolus front in the pharynx space is faster than that of the thickener, the fast-moving bolus is only a small portion of the total volume, and the inflow rate is also small. However, for thickener swallowing, although the inflow velocity of the bolus front is slower than that of water, the thickener bolus flows into the pharynx as coherent bolus, explaining the similar flow rates of the thickener and water. Hence, the overall trends in Fig. 12 during inflow are similar, suggesting that the flow rate during inflow does not change when a person swallows a given quantity of food.

Bolus transport in the tongue resembles the operation of a mechanical volumetric piston pump. In human swallowing, the tongue plays a role of a piston in the oral cavity to transport food bolus as it sequentially contacts the hard palate, soft palate, and pharynx rear wall by the contentious wave-like motion of the tongue. This mechanism does not depend on the food properties. Like transportation by a mechanical volumetric piston pump, even at a fixed flow rate, the cross-section of the flow direction varies, changing the inflow velocity. In other words, food bolus experiences friction on the organ wall surface, and the volume of food bolus pushed by the tongue is similar despite the velocity decrease and bolus spreading while transforming it laterally and drifting.

The food bolus transport can be controlled using the friction of the wall surface and fluidity of the food in the flow field at a given flow rate to change the behavior of the food bolus and prevent responses such as aspiration in elderly persons or patients with dysphagia. The proposed simulator allows to examine the behavior of food bolus regarding the velocity and flow rate.

Timing to reach maximum inflow rate Next, the timing for the maximum flow rate is analyzed. For water swallowing, the maximum flow rate is reached at 0.133 s, corresponding to the timing of all the food bolus flow into the ROI, as shown in Fig. 11. This means that the water bolus flow rate does not decrease until the entire food bolus flows into the ROI. In contrast, for thickener swallowing, the maximum flow rate is reached at 0.10 s, before all the food bolus flows into the ROI at 0.300 s (Fig. 11). Hence, the thickener bolus flow rate decreases before the entire food bolus flows into the ROI. The food bolus receives friction from the organ wall surface, and the volume of food bolus is pushed by the tongue despite the velocity decreasing and the bolus spreading while transforming laterally and drifting. We can confirm this behavior clearly from the simulated images.

Outflow timing Finally, we focus on the timing of the food bolus outflow. In Fig. 12, the lower part of the image represents the outflow time zone from the ROI. For both food boluses, the flow rate decrease starts just after all the food bolus flows into the ROI (at 0.2 s for water and 0.3 s for the thickener). Comparing the flow rates at the time of outflow, the water bolus outflows with a smaller flow rate and over a longer outflow time than the thickener bolus, which rapidly changes the flow rate and flows quickly. These characteristics of food bolus may explain perceptions of “clearness” or “sharpness” on the throat.

As shown in Fig. 12, the ratio of the outflow time when swallowing water is 53.8 %, and that when swallowing the thickener is 30.7 %. Hence, the time ratios of inflow and outflow are similar for water (around 50 %), whereas inflow takes approximately 70 % and outflow takes approximately 30 % of the swallowing time for the thickener. The thickener inflow takes longer and possibly prevents aspiration, and a quick outflow as coherent bolus also contributes to aspiration restraint.

The effects of thickener have widely been reported from the experimental viewpoint of food bolus velocity and sensory perception. An effective thickener is believed to reduce the flow velocity. On the other hand, qualitative interpretations are still used because quantitative measurements and evaluations are difficult for the behavior of food bolus during outflow. We evaluated the behavior during outflow in terms of the flow rate.

For a person, considering a common quantity to eat, no considerable difference is observed in the swallowing time between water and the thickener (Fig. 11). An aspiration occurs because the movement of the epiglottis and food bolus are not correct when we reduce the inflow flow rate using the thickener if the outflow flow rate is also low. This was confirmed in our past case study through numerical experiments using an MPS swallowing simulation (Kamiya et al., 2023). As shown in Fig. 12, the major difference between the water and thickener behaviors is the outflow flow rate. On the other hand, the calculated average outflow bolus velocities of water and thickener are 0.22 m/s and 0.09 m/s, respectively. Consequently, we cannot verify that a food bolus of thickener flows out quickly in terms of velocity. Therefore, the flow rate is an important index for determining the outflow from the epiglottis to the esophagus.

Evaluation index for degree of bolus coherence From the calculated bolus flow rate and velocity, we can obtain the average cross-section and hydraulic diameter as characteristic parameters of a tube section to study the flow behavior through the tube. If the hydraulic diameter is high, the cross-section is also high. In fact, the cross-section increases by the square of the hydraulic diameter.

Fig. 13 shows the time profile of the hydraulic diameter. During inflow (water: 0.0–0.2 s; thickener: 0.0–0.3 s), the maximum hydraulic diameters of water and the thickener are approximately 10 mm and 16 mm, respectively (i.e., the thickener has a 1.60 times larger diameter). This indicates that the cross-section of the thickener flow is 2.56 times wider than that of water. Thus, the thickener has a more coherent flow than water. During outflow (water: 0.2–0.433 s; thickener: 0.3–0.433 s), the maximum hydraulic diameters of water and the thickener are approximately 10 mm and 26 mm, respectively (i.e., the thickener has a 2.60 times larger diameter). Hence, the cross-section of thickener flow is 6.76 times wider than that of water, and the thickener has a more coherent flow than water. Comparing the inflow and outflow of thickener, the hydraulic diameter for outflow is 1.63 times higher than that inflow, and the cross-sections between inflow and outflow differ by a factor of 2.66. Thus, the outflow bolus is considered as much coherent than the inflow bolus.

Fig. 13.

Hydraulic diameter of Newtonian (water) and non-Newtonian (thickener) fluids. The simulated images show the behaviors of water (top) and thickener (bottom) boluses. Within each frame, the left and right images show the lateral and anteroposterior views, respectively. Labels a–d indicate the time of the images.

From the physical interpretation of the hydraulic diameter and cross-section, the food bolus seems more coherent when these values are higher. Hence, the diameter and cross-section may be used for evaluating the degree of bolus coherence. These values can serve as evaluation indices obtained from numerical simulations according to the velocity and flow rate.

Key factors for optimal thickener design The bolus flow rate changes in Fig. 12 confirm that the flow rate over one swallowing action is at the same level regardless of the difference in food properties when a person swallows a given volume of food. In other words, we cannot consciously control the intake flow rate considering food properties. In our simulator, the food bolus behavior to prevent aspiration can be controlled by only 0.366 s from 0.067 s to 0.433 s during swallowing. Our simulation results clearly indicate that the thickener bolus exhibits a completely different behavior from the interaction of friction with the wall surface and transformation by the flow in limited time and space.

Our numerical and visual simulation results show that it is necessary to consider the rheological and tribological properties of food for optimal thickener design. We conclude that there are three key factors to design thickeners for elderly people or patients with dysphagia. The first factor is the control of bolus inflow velocity using friction on the organ surface and bolus deformation. The second factor is controlling the occurrence of small splash particles during swallowing by thickening and creating a coherent bolus. The third and most important finding of our simulation is the realization of a high discharge flow rate from the epiglottic region by making coherent bolus. These three key factors should be considered for optimized and personalized food design for elderly people or patients with dysphagia.

Limitations of simulation models and future work We describe limitations of our current simulator in terms of organ, food, and calculation models. The most important problem is the long time required to create an accurate human model because it is difficult to extract soft organs from medical images, and it is necessary to integrate the results of medical images with anatomic knowledge. An efficient procedure using 320-row CT and a specialized image processing system is currently under construction.

There are two problems associated with the food model. First, a food model can only consider a power law for bolus flow and deformation. Other fluid models, such as the Bingham fluid model or shear-thinning flow model with yield stress, are required for various food simulations. The development of this food model is the target of our next study. Second, the tribology model includes friction and lubrication effects between the organ surface and bolus. The current model uses the contact angle and slip coefficient near the wall as fitting parameters to describe tribological effects. However, a trial-and-error simulation may be required to determine additional parameters. In addition, we should develop a method and experimental system to set simulation parameters compliant with physical measurements.

Regarding calculation, the current simulator does not consider the negative pressure effect when the esophagus quickly opens, and it cannot calculate the airflow in the oral cavity and pharynx space. Another calculation scheme, such as a coupled simulation of the FEM with a level-set model, is thus required.

Despite its limitations, our simulator can provide diverse numerical data and visualization results that can be useful and important for understanding phenomena or finding insights for optimization and personalization of food design for elderly people or patients with dysphagia. Our simulator does not change the movement and deformation of organs to adjust to different food properties. However, it allows to easily perform a parametric study to change the parameters for considering and estimating tribological and rheological effects. We believe that the proposed simulator constitutes a valuable evaluation tool for studies such as estimating the effect of early screening and changes in food properties that facilitate swallowing.

Conclusions

We developed a 3D swallowing simulator using MPS that can handle liquid splashes and transformations of free surfaces with liquid and air. The accuracy of the simulator was confirmed using qualitative and quantitative methods for Newtonian and non-Newtonian fluids. The validated swallowing simulator involving different food and swallowing models for a healthy person revealed three important factors of optimal design of a thickener: 1) control of bolus inflow velocity, which is influenced by rheological and tribological properties, 2) prevention of small splash particles, and 3) bolus discharge flow rate from the epiglottis to the esophagus. In addition, we propose evaluation indices for the degree of bolus coherence based on the calculated bolus flow rate and velocity. Although the simulator shows various limitations regarding organ, food, and calculation models, it may support the development of appropriate food products for elderly people who have difficulty swallowing and for patients with dysphagia.

Conflict of interest There are no conflicts of interest to declare.

Ethical statement This study was approved by the Ethical Committee of the Japanese Red Cross Musashino Hospital (Approval No. 116).

Abbreviations

3D

three-dimensional

FEM

finite element method

MPS

moving particle simulation

ROI

region of interest

VF

videofluorography

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