Tahara and colleagues (1–3) have reported results of experimental investigations concluding a relationship between plasma glucose level and HbA1c (A1C), defined as
Their expression for W(s) is
The experimental mean fasting plasma glucose (MFPG) results reported in ref. 1 were analytically modeled and then used to determine the corresponding mean A1C curve (Eq. 1). Excellent correlation was obtained between experimental mean A1C and analytical A1C curves. The specific curve for MFPG is
where γ is constant in time but nonetheless adjustable to designate different decay rates. The MFPG curve reported in ref. 1 is found from Eq. 3 for Gs= 6.6, Gd= 6.2, and γ = 1. The related expression for A1C derived from Eq.1 is
Values of H(t) versus t obtained using Eq. 4, with K = 0.75, T = 17 weeks, and γ = 1 were subtracted from the mean of patient-admission A1C values to approximate the mean A1C curve reported in ref. 1.
Adjusting γ to designate different decay rates, as would be the case for patients using only diet and exercise to control their plasma glucose levels, it is evident from Eq. 3 that as γ decreases from (say) γ = 1 to γ = 0.1, e.g., γ = 0.8, 0.4, 0.2, 0.1, a family of G(t) curves will be generated whose corresponding decay is slower. Given that 50% of the GHb level at any time is determined by the plasma glucose level during the preceding 1-month period, 25% by the plasma glucose level during the 1-month period before that, and the remaining 25% by the plasma glucose level during the 2-month period before the first 2 months (1–3), it follows that if the plasma glucose curve decays, the corresponding A1C curve will also decay. Results reported in ref. 1 confirm this, as do results from a study by Rohlfing et al. (4), where an algebraic relationship between FPG and A1C is reported.
However, the γ curves of A1C determined from Eq. 4 display a faster decay as γ decreases. This inverted decay suggests the weighted-average relationship between plasma glucose and A1C reported in ref. 1 is questionable. As functions of γ, both plasma glucose and A1C curves should decay faster as γ increases and slower as γ decreases, not one slower and the other faster (or vice versa).
