Frequency analysis of food bolus fragmentation through a vertical pipe

Abstract

The behavior of a raw carrot bolus through a vertical pipe was investigated with a laser detector. To investigate the effect of cohesiveness, samples were pre-processed in various stages, as follows: no compression, 50 % and 80 % compression, and blending with xanthan gum. First, the transit time of the bolus was measured from the time series signal of the voltage drop corresponding to the density of the food fragments. The results showed that the transit time was shorter for the bolus with greater assumed cohesiveness. Next, we analyzed the structure of the bolus flow by obtaining the power spectrum of the time series signal, which exhibited a power-law relationship of the form P(f) ~ f^−α. The value of the exponent α, reflecting the structure of the bolus flow, was also shown to be correlated with the assumed cohesiveness. Therefore, we propose that α can be used as an index to evaluate bolus cohesiveness under shear conditions.

Introduction

The process of eating can be divided into three stages: the oral stage, in which the bolus is formed by mastication, the pharyngeal stage, in which the bolus is transported to the pharynx by swallowing, and the esophageal stage, in which the bolus is transported to the stomach (Chen and Engelen, 2012). The bolus that passes through the pharynx is subject to shear forces (Gilbert et al, 2007; Steele et al., 2015), and the behavior of the bolus under such conditions is considered to be an important factor that determines the safety of swallowing. In other words, the food bolus is required to move through the pharynx at a speed that is neither too fast nor too slow, and it should form an aggregate that is minimally adhesive (Hadde and Chen, 2021; Kumagai et al., 2021). For example, Kumagai et al. showed that the maximum velocity at which the bolus passes through the pharynx is a function of the viscosity of a liquid food, suggesting that the fluidity of the bolus can be adjusted by controlling the rheology of the food (Kumagai et al., 2009). In addition, regarding the cohesiveness of the bolus, a videofluoroscopy swallow study (VFSS) experimentally gave the relationship between the viscosity of the liquid and its resistance to stretching, namely its cohesiveness (Hadde et al., 2019). Both of these were studies on liquid food, and studies on the behavior of bolus of solid food under shear are comparatively lacking (Prinz and Lucas, 1997; Moritaka and Nakazawa, 2010; Peyron et al., 2011; Rodrigues et al., 2013). The bolus formation itself of solid food is considered to be very complicated, even if it is not limited to shearing. Texture profile analysis (TPA) (Bourne, 2003), an established technique used to evaluate textures of solid food materials, is now being used to evaluate the textures of food boluses (Shiozawa et al., 2003; Peyron et al., 2011; Sagawa et al., 2011; Moritaka et al., 2019).

If the food bolus is defined as a mixture of masticated food fragments and saliva (Bourne 2003), it is necessary for safe swallowing to discuss the fragment size distribution and salivary rheology (Hutchings and Lillford, 1988; Prinz and Lucas, 1997; Chen, 2009; Nishinari et al., 2023). In previous studies, we reported that the masticated fragments of raw carrots and fish sausages follow a lognormal distribution (Kobayashi et al., 2006; Kobayashi et al., 2010). Although it is unclear how the fragment-size distribution contributes to ease of swallowing, some studies have shown that its importance varies depending on the type of food and its moisture content (Peyron et al., 2011; Nishinari et al., 2019). Chen and Lolivret suggested that mixing a sufficient amount of saliva to significantly improve the flowability and elasticity of the bolus is a requirement for safe swallowing (Chen and Lolivret, 2011). The moisture content of both the food and saliva act to bind the food fragments, and these rheological properties are thought to influence the behavior of the food bolus under shear. As the Hutchings-Lillford model (Hutchings and Lillford, 1988) comprehensively explains, swallowing is considered to occur when the size of fragments of food and the texture of the food bolus (adhesiveness or cohesiveness) meet certain criteria. Although the raw carrots used in the authors’ previous study have been well studied in terms of fragment size, the cohesiveness and adhesiveness of the carrot bolus have not been well studied, except by TPA. It is believed that the development of a new index of the texture of solid food boluses will make a significant contribution to the design of foods for safe swallowing.

It is important to study the physical properties of the food bolus of solid food by considering them as aggregates of wet fragments and evaluating how they split and deform under shear conditions in model experiments such as by artificially generating a bolus and dropping it. It is possible to directly investigate the behavior of the bolus when it falls using a high-speed camera. However, it is expensive to construct a system to quantitatively analyze the results. Another method to quantify the fragment-flow under gravity is to measure the time-series signal of transmitted light intensity across the pipe using a laser light and detection system (Horikawa et al., 1995; Nakahara and Isoda, 1997; Moriyama et al., 1998; Yamazaki et al., 2002). Horikawa et al. (Horikawa et al., 1995) were the first to study a density flow experimentally in a particle-flow. Their experiment showed the formation of density flow by the creation of counter air flow from the friction between granular materials produced by closing the bottom-end of the vertical pipe through which the particles were flowing. They showed that the power spectrum P(f) of the frequency f obtained from the time series of the density flow exhibits a power-law relationship in the form of P(f) ~f^−α. Moreover, there is a clear difference in the power spectrum between the uniform flow (at a low inflow rate) and the density flow (at a high inflow rate), which reveals the existence of a critical rate (Yamazaki et al., 2002). Thus, the shape of the power spectrum is sensitive to the pattern formation of the particle-flow.

In this paper, we report the results of our model experiment in which an artificially generated food bolus was dropped in a vertical pipe. The bolus used in the drop experiment was pre-compressed to mimic chewing and was also tested in an uncompressed state. In order to investigate the disintegration process of the dropped food bolus, we placed a laser detector at the bottom of the vertical pipe and measured the size of the food fragments passing through the detector by using the transmitted light intensity. Based on the results of these measurements, we discuss how the presence or absence of pre-compression is related to the stability of the bolus. In addition, a similar drop experiment was performed with a bolus mixed with xanthan gum as a simulated saliva to investigate the effect of saliva’s cross-linking properties on the bolus’ integrity during its fall, although this was a very rough approximation.

Materials and Methods

Materials Solid foods can be categorized into four groups: sponge-like foods, gels, raw fruits and vegetables, and dry crispy foods (Kohyama et al., 2004). In the present study, we chose to investigate raw carrot from the raw fruit and vegetable group. Raw carrots harvested in Japan were used as solid food samples. The samples were cut into 7–9 g cylinders (diameter and height of 4 cm and 0.5 cm, respectively) and then crushed in a food mixer (IFM-C20G, Iwatani, Osaka, Japan) for approximately 1 s. Fig. 1 shows a typical example of the crushed samples. In a previous study, we experimentally studied the fragment-size distribution of crushed raw carrots and found it to follow the power-law distribution (Kobayashi and Shibayama, 2021). The size of fragments was nonuniform and was distributed over a wide range from 10⁻² to 10 cm².

Fig. 1

Typical snapshot of the food fragment samples of raw carrot crushed using a food. mixer.

In this experiment, a comparison was made between a pre-compressed and an uncompressed food bolus to examine the effect of mastication on the stability of the food bolus. This was performed to allow us to simulate the control of the ease of bolus aggregation, or cohesiveness. Cohesiveness is a particularly important parameter in TPA for determining the texture of a food bolus (Szczesniak, 1963; Szczesniak, 2002). In TPA, cohesiveness is defined as the ratio of the work required when the food sample is first compressed to the work required when it is compressed a second time (Rosenthal, 1999). It should be noted that it is unclear whether the ease of bolus aggregation assessed in our experiments is equivalent to cohesiveness as defined by TPA. However, the compression method in our experiments was performed according to the TPA method as follows. A raw carrot sample weighing 5 g was placed in a glass petri dish with an inner diameter of 45 mm and compressed to 50 % and 80 % of the height of the sample at a constant rate of 10 mm/s using a 30 mm diameter cylindrical plunger attached to a rheometer combined with a vertical motorized test stand (EMX-1000N-FA, IMADA, Toyohashi, Japan) and a force gauge (ZTA-200N, IMADA) and held for 10 seconds. Oral moisture, such as saliva and moisture released from food, has a significant effect on bolus cohesion (Chen and Engelen, 2012). It is thought that increasing the compression releases the water content of the carrot, thereby increasing the cohesiveness of the carrot bolus. The drop test was performed using a pseudo-food bolus prepared in this manner.

Xanthan gum is a material often used as a simulated saliva (van der Reijden et al., 1996). In this study, 0.1 g of xanthan gum (FUJIFILM Wako Pure Chemical Corporation, Osaka, Japan) was put into 50 mL of distilled water and stirred for 1 h at room temperature. After that, the mixture was stirred while being heated to 80 °C, and allowed to stand at room temperature for 40 minutes. A pseudo food bolus was prepared by mixing 0.5 mL of the xanthan gum aqueous solution thus prepared and 5 g of crushed raw carrot prepared in advance. The bolus to which xanthan gum was added was not compressed before the experiment and was dropped as it was.

Experimental Procedure The experimental setup is schematically shown in Fig. 2. We set up a vertical square acrylic pipe of height 75 cm and width 5 cm (inner width: 4 cm). This acrylic pipe is used to block external influences such as from wind. We placed raw carrot fragments (approximately 5.0 g) in a spoon and poured them from the top of the square pipe to observe the bolus flow under gravity. As the bolus fell through the square pipe, we measured density fluctuations as the transmission light intensity across a fixed location just below the square pipe using a laser detection system (IB-30, KEYENCE, Osaka, Japan). The beam had a constant light intensity and a rectangular profile. This beam was narrowed by a slit to height 1.5 mm and width 40 mm. The voltage was adjusted to a suitable baseline value (approximately 2 V or 5 V) with the measurement position of the square pipe being empty, i.e., with no carrot fragments being present at the measurement position. The time series signal output of the IB-30 (laser detectors) was observed with a digital oscilloscope (TDS 1012C-EDU, Tektronix, Beaverton, OR, USA).

Fig. 2

Schematic illustration of the experimental setup.mixer.

A voltage drop occurs as food fragments pass through the laser beam, and the magnitude of this drop depends on the density of the food fragment aggregate. When small food fragments pass through the beam, voltage drops occur intermittently with a short period (Fig. 3 (a)). On the other hand, a voltage drop with a long period occurs when a large aggregation food fragments passes through (Fig. 3 (b)). In the actual experiment, since pieces of different sizes were dropped, the time series signal was a mixture of voltage drops of different periods corresponding to the sizes of the pieces. Conversely, using fast Fourier transform (FFT) of the obtained time series signals and calculation of the power spectrum, it is possible to analyze the period, given as the frequency, and the strength of the voltage drops in the signals. That is, this analysis allows us to examine how the food bolus disintegrated into aggregations of different sizes during the falling process.

Fig. 3

Illustration of the relationship between the voltage drop and the density of the food fragment population for (a) small and (b) large size.

Data Analysis The time series signals were input to a computer in order to carry out FFT analysis performed using OriginPro 9.0 (OriginLab, Northampton, MA, USA) and the power spectra of the time-series signals of bolus flow through a square pipe. Each spectrum was obtained by averaging over 23 (uncompressed), 25 (50 %compressed), 24 (80 % compressed) and 16 (mixed xanthan gum) independent data sets with a length of 1 250 discrete points each.

Results

Bolus transit time Fig2. 4(a)–(d) show typical examples of time series signals of voltage drops corresponding to a group of fragments passing through the laser when they were dropped into a vertical pipe for uncompressed, 50 % compressed, 80 % compressed, and xanthan gum mixed food boluses, respectively. The oscilloscope used for the measurement has a sample interval of 0.0004 s, which means that 2 500 data points can be obtained over 1 s.

By measuring the time from the start to the end of the voltage drop in the time series signal in Fig. 4, the transit time of each bolus can be obtained. Fig. 5 shows the transit time of the bolus for each of the conditions shown in Fig. 4. These results are averages of transit times measured from 16–25 independent trials, and error bars indicate standard errors. Compared to the food bolus without any pre-compression, it can be observed that the transit time decreases with increasing compression. The xanthan gum cross-linked bolus was found to have an even shorter transit time than the other boluses.

Fig. 4

Typical time series signals of the voltage drop: (a) uncompressed, (b) 50 % compressed, (c) 80 % compressed, and (d) mixed xanthan gum. Note that the voltage is adjusted to (a) 2.3 or (b)–(d) 5.0 V when no fragments are at the measuring position, respectively.

Fig. 5

Transit time corresponding to each condition in Fig. 4. The corresponding transit times are as follow: uncompressed (N = 23) 0.39 ± 0.03, 50 % compressed (N = 25) 0.18 ± 0.02, 80 % compressed (N = 24) 0.14 ± 0.02, mixed xanthan gum (N = 16) 0.08 ± 0.01, respectively.

Power spectrum To analyze the bolus flow statistically, we focused on the power spectrum of the time series signal representing the bolus flow. Fig. 6 shows the power spectrum corresponding to bolus flow under gravity. For all power spectra in Fig. 6, a power-law relationship of P(f) ~ f^−α with α can be observed in the low-frequency region of approximately 2 Hz to 30 Hz. Note that the low frequency range corresponds to the long period component of the time series signals. On the other hand, in the high frequency range above approximately 100 Hz, a sharp decrease in power can be observed. As mentioned above, the height of the laser is 1.5 mm, and the cutoff at 100 Hz indicates that the average speed of passage of a food fragment comprising a food bolus is 0.15 m/s. This means that the measurement limit of the frequency in our system is around 100 Hz, rendering it impossible to make measurements above 100 Hz (Nakahara and Isoda, 1997).

Fig. 6

Log-log plots of the power spectrum P(f) versus the frequency f obtained by Fourier analysis on the time series signals of (a) uncompressed, (b) 50 % compressed, (c) 80 % compressed, and (d) mixed xanthan gum. The straight line in each figures indicates the slope of that part to be (a) 0.96, (b) 0.64, (c) 0.47 and (d) 0.23, respectively. The error bars show the standard error in each figs.

As shown in Fig. 6, the value of α was 0.96 for the uncompressed, 0.64 for the 50 % compressed, 0.47 for the 80 % compressed, and 0.23 for the mixed xanthan gum samples. As is known from previous studies on granular materials (Horikawa et al., 1995; Nakahara and Isoda, 1997; Moriyama et al., 1998; Yamazaki et al., 2002), the value of α in the power spectrum of the time series signal takes a large value when the difference in density of the granular flow, i.e. incoherent flow, is large, and a small value when the flow is coherent. In other words, our experiments confirmed that the relative difference in density tended to become larger in the following order: uncompressed bolus sample flow, 50 % compressed bolus sample flow, 80 % compressed sample bolus flow, and the sample bolus flow mixed with xanthan gum.

Discussion

The present paper reports the study of drop experiments to quantify the bolus flow of raw carrots through a vertical pipe. The experiment was conducted using four different conditions: sample without pre-compression, sample with 50 % compression, sample with 80 % compression, and sample mixed with xanthan gum, to investigate the effect of the material that cross-links the food bolus. These conditions can be thought of as controlling the cohesiveness of the food bolus (assuming increasing cohesiveness in the order of uncompressed, 50 % compressed, 80 % compressed, and mixing with xanthan gum). First, the transit time of the food bolus was measured from the time series signal of the voltage drop corresponding to the density of the falling food fragments (Fig. 5). The results showed that transit time was shorter for boluses with greater assumed cohesiveness. Next, we analyzed the structure of the bolus flow by obtaining the power spectrum of the time series signal (Fig. 6). The low-frequency part of the power spectrum of the bolus flow was found to exhibit power-law behavior of the form P(f) ~ f^−α. The value of the exponent α obtained in these experiments was α ≃ 0.96 for the uncompressed condition, α ≃ 0.64 and 0.47 for the 50 and 80 % compressed conditions, and α ≃ 0.23 for the condition with mixing with xanthan gum. As in the case of the transit time, the value of the exponent α was shown to be correlated with the assumed cohesiveness. When the value of α is small, as in the case of a bolus mixed with xanthan gum, the bolus flow becomes a coherent flow. In this case, considering that the transit time is also short, it can be inferred that the bolus falls in a coherent manner with almost no splitting. On the other hand, the bolus with a large value of α and a long transit time, such as an uncompressed bolus, is expected to break into small and large fragments during its transit. The dynamics of this fragmentation process depends on the degree of compression applied to the bolus prior to falling, and it is shown that as the degree of compression increases from 50 to 80 %, the bolus falls more coherently. These results are consistent with those of Kumagai et al. who analyzed the flowability of the food in the pharynx using ultrasonic pulse Doppler and found that the “ease to form bolus in the mouth” can be evaluated by the maximum flow velocity and the transit time of the bolus in the pharynx (Kumagai et al., 2021).

The value of α discussed in this experiment can be considered an index for evaluation of the cohesiveness of the food bolus in terms of the ability of food fragments to maintain aggregation under shear. In general, when applying the TPA-defined cohesiveness to a bolus, the bolus is packed into a container and evaluated by a 2-bite compression test. However, some concerns have been expressed about the validity of expanding the scope of TPA-based evaluation beyond solid foods (Nishinari et al., 2013; Nishinari et al., 2019). For example, during the swallowing process, the bolus boundary is not limited by the container and TPA cohesiveness is unnaturally defined. Recent studies have attempted to generate an overall interpretation of cohesiveness based on how the food itself changes shape and disintegrates at the free boundary, without being limited by the shape of the container or other factors (Nishinari et al., 2019; Peleg, 2020; Hadde et al., 2020; Kumagai et al., 2021). Our method, like those in these previous studies, may be a more natural assessment of bolus cohesiveness. In addition, although our method cannot be used to directly evaluate the behavior of a bolus in vivo, it is possible to easily change various parameters that may be related to bolus formation, such as the fragment size distribution, the viscosity of the cross-linking material, and the type of food in our experiments.

Our method is only intended to assess cohesiveness and there is no discussion of the mechanism by which cohesiveness occurs: it is mentioned above that increasing the degree of compression increases the amount of water released from the raw carrot, which contributes to cohesiveness, but no quantitative assessment of how much water was released from the food as a result of compression was performed. Moisture contributes not only to the cohesiveness of the bolus but also to its flowability, and it is very important to investigate its effects for a basic understanding of swallowing (Chen and Engelen, 2012). As the water content increases, the effects of the physical properties of the water, such as viscosity, should also be considered (Prinz and Lucas, 1997). It is easy to investigate the mechanical properties of such bolus-bridging substances using the present method, after systematically varying the water content and viscosity, and this is one of the issues to be addressed in the future.

As one of the potential applications of the present findings, we propose its use to evaluate individual mastication and swallowing abilities. This could be done by having a subject chew a food and then perform a drop experiment with a bolus collected from the subject’s oral cavity. It is well known that salivary properties closely related to bolus formation, such as viscosity, vary between individuals and even within a single subject depending on conditions at the time of measurement (Schipper et al., 2007). It will be very interesting to see how much effect these differences in the properties of the bolus have on the value of α, and this presents an issue for future study.

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

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