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The evidence gleaned from multiple imaging studies has since been expanded by employing engineering-based models of the milk duct structure of the breast, and the baby’s sucking pattern, in order to generate theoretical data on milk flow, for comparison with real clinical data.

The first substantive attempt to develop a mathematical model of milk extraction during breastfeeding was undertaken by Zoppou et al. [19]. Drawing on knowledge current at the time, they compared the action of a breast pump, which used a cyclic pattern of suction, with that of a baby using both suction and expression. Their theoretical model caused them to conclude that there was an optimal time during the suck cycle to apply a compressive force, which increased milk flow over that produced by suction alone. Given their conclusion, it is somewhat surprising that recent models have not included a compressive component.

Two recent studies of milk removal from the breast have adopted an engineering-based approach [20, 21]. These studies have sought to create mathematical models which simulate the dynamic relationship between suction generated in the baby’s oral cavity, and the milk-filled duct system of the breast [20, 21]; both studies use data recorded directly during breastfeeding. They are elegant, complex, and sophisticated, although it can prove difficult to evaluate them fully, in order to determine if any of the assumptions made might create erroneous conclusions. Modelling of the milk duct system of the breast is complex and will be bypassed in the discussion below, assuming them to be essentially accurate – that of Mortazavi et al. [21] is claimed to be more elaborate.

Elad et al. [20] have made some expansive claims about their work, but critical analysis of their study suggests some shortcomings. One noteworthy beneficial feature of their study is that their data analysis process allows them to use the hard palate as a register for movements of the tongue (Fig. 2). A relative weakness, in contrast, is that their data are derived from review of a relatively small selection of ultrasound images.

In brief, their methodology is as follows: 5–8 points are digitized on the hard palate (this is a manual process), to which a smooth curve is fitted by interpolation (red line in their Fig. 1A); the same process is applied to the tongue surface (green line). A set of tracings of the hard palate is collected for 4–6 suck cycles, which are then aligned with reference to the Hard-Soft Palate Junction, so that movement of the tongue relative to the hard palate can be visualized (identified as Fig 1A in their figure (Fig. 2A)).

Superimposed on this image (their Fig. 1C (Fig. 2A)) is a set of 28 equally spaced radiating lines (referred to as “polar coordinates,” numbered 1–27 in the figure), which radiate out from the scan head to above the hard and soft palate. The movement of the tongue surface is then plotted along every 5th or 6th polar coordinate, enabling the time lag, relative to the preceding focal coordinate to be visualized.

One apparent limitation of their approach is that 28 polar coordinates do not fully encompass the whole of the oral cavity. This might be regarded as a trivial issue, but the full passage of a suck across the oral cavity determines the overall suck duration, so that more lines would be required, up to at least 36, in order to embrace a full suckling action, including the prepharyngeal phase of swallowing.

Evaluating movement of the tongue surface relative to the hard palate, across four focal polar coordinates – #8, #13, #17, and #22 (illustrated), shows evidence of a phase shift between these separated lines (their Fig. 1E (Fig. 2B)).

In marked contrast, the time shift between ALL of the first 8 polar coordinates is evaluated and no phase shift is seen between individual lines. Based on their Fig. 1D (reproduced in my Fig. 2C), they assert that there is no phase shift between the lines, indicating that the “anterior tongue moves as a rigid body … ruling out the hypothesis of a peristaltic squeezing of the nipple” [20].

Personally, this line of argument appears misleading to me. Certainly, movement along the first three coordinates closest to the mandible (#1–3) is likely to be determined largely by up/down movement of the jaw, but beyond this point, there is evidence of propagation of a peristaltic wave from as early as polar coordinate #4, right through to #28.

Fig. 2. A Figure taken from Elad et al. [20] – a full description is contained in the text. B, C After Elad et al. [10], highlighted enlargement of their their Fig. 1C–E.

Fig. 3. Frame of ultrasound recording showing three user-applied rectangles, in which movements can be automatically tracked and compared.

The study by Monaci and Woolridge [22] merits discussion in this context, as it adopted a similar approach, but used signal processing techniques to analyze ultrasound records in real-time, thereby generating fully objective, automated results. They arbitrarily divided the oral cavity into three, spatially separated, non-overlapping sectors, equating to: (1) the anterior sector of the oral cavity, including nipple and front part of tongue (excluding lower jaw); (2) the middle sector of the oral cavity, comprising the mid-surface of the tongue and the space at the tip of the nipple in which milk accumulates; and (3) the posterior sector, comprising the oropharynx, where swallowing can be detected (Fig. 3).

These authors also examined the time shift between movements in each of these three areas. Ultrasound recordings from 29 mother/baby pairs (46 complete breastfeeds) were analyzed, although analysis was restricted to those periods when active sucking was taking place. Nonetheless, over 1 million frames of active sucking were analyzed in real-time by this technique.

If movement occurred in sector 1 first, a negative phase shift was recorded relative to sector 2; a zero phase shift indicated an absence of a phase shift between sectors 1 and 2; while a positive phase shift indicated movement in sector 2 preceded that in sector 1. In practice, this was caused by the movement in sector 2 being of larger amplitude than that in sector 1 and was commonly evidence for the presence of an ETD being inserted (i.e., an “added” suction element being superimposed on a peristaltic wave).

Figure 4 encompasses approximately 70 sucks, and illustrates the transition from a period of almost pure “peristaltic” sucking (frames 0–1,000), to a “vacuum” phase where ETDs predominate (alongside PTMs) (frames 1,000–1,500).

Fig. 4. Section of analysis over a time frame of 60 s, embracing 70 sucks, which captures the transition from one style of suckling to another.

Table 1. Automated analysis of ultrasound recordings, exploring the phase shift in movement between the anterior and mid-sections of the oral cavity

The “movement detection rectangles” were manually drawn, so needed to be redrawn when there was movement artefact. Despite this limitation, the signal processing approach was applied to all 46 breastfeeding episodes, totaling 16 h of recording. Overall results of the analysis are shown in Table 1.¹

PTMs were present throughout active sucking (100%), being: highly conspicuous for 78% of feeding, and predominating for over half of the time spent feeding, to the exclusion of ETDs (“suction/vacuum”). For a substantial period of feeding (27.5%), both PTMs and ETDS were equally visible, with no one method predominating over the other. For 22% of feeding, the added suction elements (ETDs) appeared to predominate. This analysis shows that ETDs [7, 12] were observable for roughly half of the time spent feeding.

Fig. 5. This figure shows the progression of a peristaltic wave from left (anterior) to right (posterior), across nine consecutive frames.

The same authors used a second analytical technique involving automated mapping of the contour of the surface of the tongue. This technique is capable of showing the progression, across successive frames, of a peristaltic wave from the anterior to posterior of the oral cavity. In Figure 5, the peristaltic wave is seen rising in amplitude, then declining, as it transitions (left to right) from the front to the back of the oral cavity.

One final piece of evidence supplied by this latter technique is that when an ETD is generated, the space created is generated as part of the standard peristaltic wave, as it progresses across the zone where the ETD appears; it is both opened at its leading edge initially, then closed off again from its anterior edge (Fig. 6).

The two pictures show the contour of the dorsum of the tongue, which is automatically tracked (using the purpose-built software); the tongue outline is compressed left to right in this figure. The dotted line shows the tongue’s outline in the current frame, while the continuous line shows that in the previous frame. The circle circumscribes the mid-section of the baby’s tongue where the ETD is generated.

The upper picture shows the precise moment the ETD starts to be generated, as the continuous line shows an absence of any indentation, while the dotted line peels away markedly to create an indentation (marked with an X), representing the start of the formation of an ETD “pocket.” In the lower picture, just four frames later, the ETD “pocket” is clear in the continuous line, and it is just starting to be closed off again, from the front (marked with a Y). This is the clearest evidence to date that added suction elements (ETDs) are created by the same core peristaltic process.

Fig. 6. This figure shows a localized added suck or extractive tongue depression, which is created from the front backwards. Four frames later, it is closed off again from the front backwards.

Returning to the most recent engineering-based study, Mortazavi et al. [21] created a complex model of the milk duct system of the breast, which they then combined with directly measured suction pressure data (Fig. 7) (from several babies), to define the parameter boundaries of the mathematical model. Modelled milk output was then compared with clinical data on milk transfer for a single baby.

Fig. 7. Phases of natural suckling (by 1 infant) transformed to a sequence of standardized sinusoidal waveforms (see inset). From Mortazavi et al. [21].

No data were collected on positive stripping pressure, so axiomatically, any such element was excluded from the model, despite it being an explicit component of one of the key studies they cited [19]. Any theoretical model which only assumes that the baby behaves like a mechanical suction pump is likely either to verify that presumption [20], or find that it is inadequate to explain clinical data on milk transfer [21].

In order to use sucking data in their model as parameter boundaries, sucking profiles were transformed into single harmonic, sinusoidal waveforms, seemingly all with a periodic frequency approaching 1 Hz (1 suck/s) (Fig. 8). The need to simplify natural data for incorporation into their model was no doubt necessary, but this constrains the baby’s sucking pattern to even more closely resemble an electric breast pump.

Their theoretical model simulated milk transfer by one baby, which was then compared with clinical data on intake by that baby. Based on this, the authors were forced to conclude that either sucking pressure alone, or total feed duration, did not account for: (a) the volume of milk removed, (b) the flow rate per unit time, or (c) the flow rate per suck.

This finding is unsurprising as it agrees with that of an earlier detailed study of the parameters of sucking pressure during breastfeeding [23], which was unable to find any association between suction and the 58% difference in intake between the first and second breast. Additionally, several authors have shown an inverse relationship between sucking pressure and milk flow during bottle-feeds: the greater the resistance to milk flow caused by teat hole size, the greater the pressure exerted by the baby to remove milk [15].

Fig. 8. A selection of pressure profiles enlarged from Figure 7. The rate of nutritive sucking for all profiles is 0.92 sucks/s; the non-nutritive rate is not statistically different at 0.95 sucks/s.

A range of other factors are believed to explain the difference in milk intake between the first and second breast, including the “mother’s physiological response to sucking” [21], although no consideration appears to have been given to the fact that satiation by the baby can most commonly be observed when feeding from the second breast [24], and/or that less milk is available from the second breast as a result of the tendency to start breastfeeds on the breast offered last at the previous feed.

Both of the engineering-based theoretical models discussed above [20, 21] projected milk flow to be 1.85–3 times greater than measured intake by the baby, despite using many fewer branching ductal milk lobes than are naturally found in the lactating breast (the 5-lobe model [21] produced less of a discrepancy than the 2-lobe model [20]). Seeking to explain why milk flow was slower in reality, Mortazavi et al. [21] concluded that resistance to milk flow was greater than predicted in their model. They concluded this was likely to have been caused by factors including: the “deformed region of the areola-nipple,” a “reduction of ducts cross-sectional area,” and/or “elasticity of the tissue.” More generally, they alluded to other parameters, which included: “suckling” (mouthing or chewing movements were otherwise ignored), swallowing, and “breathing interruptions” (coordinating swallows with breathing may retard the rate of milk acquisition).