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From Fellrnr.com, Running tips
Caffeine
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* A milk intake of 500 to 900 ml/day<ref name="CaffBabyMilk"/>
* The nursing mother's caffeine intake of 200mg/day (one double shot espresso),
We get a resulting caffeine concentration in the milk of 4ug/ml to 8ug/ml<ref name="Stavchansky-"/>, which is a total caffeine intake of between 2mg to 13mg, or 0.6 to 4 mg/Kg body weight. The upper end of that level is quite high. However, the baby's half-life for caffeine is 6031-100 132 hours(average 82 hours)<ref name="Parsons-1981"/>, compared with an adult's 2-10 hour half-life, so the caffeine will build up over time. A 24 hour half live (which is easier to calculate) would result in about a 3mg to 26mg, which is 1 to 8 mg/Kg. I'm guessing that would result in the baby not sleeping well! Conversely, a baby whose mother takes caffeine during pregnancy and is then given formula milk may undergo caffeine withdrawal after birth<ref name="McGowan-1988"/>. Even if the mother breast feeds, the varying levels of caffeine may cause withdrawal symptoms<ref name="Martín-2007"/>. Also, caffeine has been shown to increase fetal heart rate<ref name="Buscicchio-2012"/>.
=References=
<references>
<ref name="Graboys-1989"> {{Cite journal | last1 = Graboys | first1 = TB. | last2 = Blatt | first2 = CM. | last3 = Lown | first3 = B. | title = The effect of caffeine on ventricular ectopic activity in patients with malignant ventricular arrhythmia. | journal = Arch Intern Med | volume = 149 | issue = 3 | pages = 637-9 | month = Mar | year = 1989 | doi = | PMID = 2465748 }}</ref>
<ref name="Pettitt-2012"> {{Cite journal | last1 = Pettitt | first1 = RW. | last2 = Niemeyer | first2 = JD. | last3 = Sexton | first3 = PJ. | last4 = Lipetzky | first4 = A. | last5 = Murray | first5 = SR. | title = Do the non-caffeine ingredients of energy drinks affect metabolic responses to heavy exercise? | journal = J Strength Cond Res | volume = | issue = | pages = | month = Oct | year = 2012 | doi = 10.1519/JSC.0b013e3182736e31 | PMID = 23037611 }}</ref>
<ref name="Parsons-1981">Parsons, William D., and Allen H. Neims. "Prolonged half-life of caffeine in healthy term newborn infants." Journal of Pediatrics 98.4 (1981): 640-641.</ref>
</references>