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The study on storage of breastmilk and its effect on antioxidant levels  was well designed and provided some interesting information. However, the conclusions that the authors drew are based on conjecture about the clinical relevance of the findings. There is a potential risk to infant health if mothers follow their recommendations and abandon the pumping and storage of their milk.
The authors demonstrated that term and preterm human milk had high levels of antioxidant activity but that some of this activity was lost with refrigeration while even more was lost with freezing, especially after 7 days. It should be noted, however, that antioxidant levels only decreased by 5% and 11% at 48hrs and 7 days of refrigeration respectively, while the corresponding drops for freezing were 13% and 19%. These drops may be statistically significant, but their clinical significance is unknown. For example, the authors cited necrotising enterolitis as one condition that could be prevented by antioxidants. One of the earliest studies demonstrating a protective effect against necrotising enterocolitis  used pooled, banked, pasteurised donor human milk. Presumably the processing and storage of this type of donor milk was much harsher on the antioxidants than the conditions under which the authors tested their mothers' milk samples, and yet there was significant protection conferred on the infants who consumed it.
The authors compared the antioxidant levels of various infant formulas against human milk, finding that even though formula did not lose antioxidant activity with storage, its levels were consistently significantly lower than those of human milk. Even at 7 days of freezing, human milk had 25% greater antioxidant activity than formula.
Despite their findings, the authors recommend: "To preserve antioxidant capacity, [human] milk should only be stored for a short time at refrigerator temperature and not frozen." Human milk has been demonstrated to retain many of its beneficial immunoprotective properties with refrigeration for as long as 8 days [3,4] and also to a lesser extent with pasteurization and freezing for donor banking . The current study shows that human milk also retains most of its antioxidant activity to the extent that even after 7 days of freezing it still has significantly more than formula. Whether due to its antioxidant activity or its many other immunoprotective factors, the fact remains that human milk protects infants against a variety of illnesses.
Pumping milk is a time-consuming endeavour, especially for mothers of premature infants. In order to maintain an adequate milk supply by pumping, mothers must pump frequently and in the early weeks their infants often don't consume as much milk as their mothers produce. The excess must be stored. It would be unfortunate if mothers who read the authors' recommendation concluded that their milk had no value if not fed within a couple of days. There are too many other beneficial factors that are stable for longer periods of storage, and even the levels of antioxidants preserved with longer storage are still better than formula.
Instead of recommending that mothers' milk be refrigerated for only brief periods and not frozen, it would be better to acknowledge that freshly expressed milk is ideal and should be fed whenever available, but that in its absence refrigerated milk, followed by frozen milk, are the next best alternatives. That way, the babies would get the most beneficial milk during their most vulnerable period but still have many benefits of their mothers' milk later on.
(1) N Hanna et al. Effect of storage on breast milk antioxidant activity. Arch. Dis. Child. Fetal Neonatal Ed. 2004; 89: F518-F520
(2) Lucas A and Cole T. Breast milk and neonatal necrotizing enterocolitis. Lancet 1990;336:1519-23. Letters Lancet 1991;337:435-6.
(3) Pardou et al. human milk banking: influence of storage processes and of bacterial contamination on some milk constituents. Biol Neonate 1994;65:302-9.
(4) Hamosh M. Bioactive factors in human milk. Pediatr Clin North Am 2001;48:69-86.
(5) Arnold LDW. Donor Human Milk Banking. Chapter 14 in Breastfeeding and Human Lactation, Riordan J, Ed, 3rd ed. 2005. Jones and Bartlett. Pp 424-5.