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This article is from the Diabetes FAQ, by Edward Reid edward@paleo.org with numerous contributions by others.
Hb = hemoglobin, the compound in the red blood cells that transports
oxygen. Hemoglobin occurs in several variants; the one which composes
about 90% of the total is known as hemoglobin A. A1c is a specific
subtype of hemoglobin A. The 1 is actually a subscript to the A, and
the c is a subscript to the 1. "Hemoglobin" is also spelled
"haemoglobin", depending on your geographic allegiance.
Glucose binds slowly to hemoglobin A, forming the A1c subtype. The
reverse reaction, or decomposition, proceeds relatively slowly, so any
buildup persists for roughly 4 weeks. Because of the reverse reaction,
the actual HbA1c level is strongly weighted toward the present. Some of
the HbA1c is also removed when erythrocytes (red blood cells) are
recycled after their normal lifetime of about 90-120 days. These
factors combine so that the HbA1c level represents the average bG level
of approximately the past 4 weeks, strongly weighted toward the most
recent 2 weeks. It is almost entirely insensitive to bG levels more
than 4 weeks previous.
In non-diabetic persons, the formation, decomposition and destruction of
HbA1c reach a steady state with about 3.0% to 6.5% of the hemoglobin
being the A1c subtype. Most diabetic individuals have a higher average
bG level than non-diabetics, resulting in a higher HbA1c level. The
actual HbA1c level can be used as an indicator of the average recent bG
level. This in turn indicates the possible level of glycation damage to
tissues, and thus of diabetic complications, if continued for years.
Interpreting HbA1c values can be tricky for several reasons. See the
following section for more details.
 
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