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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).

      Validity of the Engineering-Based Mathematical Models

      It is axiomatic that a mathematical model is only as strong as the number of assumptions on which it is based. Based on the methods reported in the development of these models, it is possible to identify several false assumptions which have been made, and incorporated into the models.

      Addressing the study by Elad et al. [20] first, one of their key conclusions (from the technique shown in Fig. 2A–C) is that milk removal from the breast is caused by the rigid up/down movement of the baby’s jaws (impacting on the base of the nipple), combined with intraoral negative suction pressure. As a consequence, their model is based solely on the action of negative suction pressure, without any consideration of the possible role for the positive pressure wave created by the dorsum of the baby’s tongue. It should therefore come as no surprise that their model predicts that negative suction pressure alone can fully account for milk removal from the breast; essentially, theirs is more a kinetic model of how a mechanical breast pump works.

      A key quality issue, likely to affect the validity of modelling studies, is the size of the sample on which any model is based. In the study by Elad et al. [20], 9 subjects, varying in age from 11 to 150 days were included, with a maximum of 15 s of sucking recorded. From these records, “four to six sucking cycles (i.e., about 150 frames) were selected for the analysis of tongue motion.” On the basis that six suck cycles last approximately 6 s, this signifies that data from a total of 54 s of feeding were used to generate the mathematical model. This may be a reason why Elad et al. [20] did not detect, or include in their analysis, the type of tongue movement described by Geddes and colleagues [11, 12–14].

      Certain assumptions may also be made to make a model less mathematically complex to compute. Mortazavi et al. [21] state that, in their study, the milk ducts are “assumed to be rigid.” An unstated corollary to this will be that the duct openings are also assumed to be rigid, being held open (patent) throughout the feed. This is recognized as a false assumption, as, in practice, the milk ducts are highly flexible and collapsible; it would not be easy to predict how they would behave dynamically under the combination of both positive pressure from the tongue and negative suction pressure from the oral cavity. Their model also assumes that negative suction pressure plays the sole role in milk removal. Perhaps as a consequence of this, a comparison of simulated data with clinical data from the same baby forces them to conclude that “suction pressure alone cannot account for milk removal from the breast” (the probable factors were discussed above).

      Key Physiological Features Not Included in Models

      A major physiological fact is overlooked by both these models, however, which is that the baby’s jaws repeatedly compress the nipple-breast/teat complex at its base, at the start of the suck cycle, and do so cyclically throughout the feed. This pressure (approx. 37.5 mm Hg) is likely to occlude the milk ducts with each suck, so it is not appropriate to assume that milk is drawn directly from the breast into the baby’s mouth, on the assumption that the milk ducts remain patent throughout. The milk-filled duct system of the mother’s breast represents a pressure gradient, confluent with the baby’s mouth, which is active at the onset of feeding. Hypothetically, this pressure gradient could ensure continuous movement of milk from within the breast into the baby’s mouth. At the start of the suck cycle, however, with closure of the baby’s jaws, it is no longer active and will only become active again at the end of the suck cycle, when the baby’s jaws reopen, and the teat ducts refill with milk from the breast.

      This jaw closure, which causes the pressure gradient to be de-activated, persists for 75–80% of the suck cycle; so the pressure gradient cannot be characterized as being active throughout feeding. This is perhaps the biggest limitation of the two engineering-based models published to date, making them approximate much better to how a mechanical breast pump works. Neither provides a satisfactory theoretical explanation of how breastfeeding works (or of manual breast expression for that matter). Further concern should be raised over the assumption that the milk duct apertures remain open throughout; this is unlikely given the close approximation of the nipple to the soft tissues of the baby’s mouth, and the high suction pressures generated within the oral cavity.

      Which Force Is Primary in Causing Milk Removal from the Breast?

      As suggested above, the active pressure gradient could make it possible for milk to be delivered continuously from the breast to the baby’s mouth, were it not for the “gating” effect of the baby’s jaws. Accordingly, the milk available on each suck is limited to that captured in the milk ducts lying within the baby’s mouth; milk cannot be extracted directly from the breast. A further fact, which should not be overlooked, is that the milk duct openings are very much narrower (by up to 50 times) than the dilated milk-filled ducts leading to them. So, an essential corollary to the question above is: “What force is responsible for opening the duct ends?”

      Based on the proposition of Geddes and colleagues [10–14], can