Dr. Treviño (1) has derived a mathematical formula for HbA1c (A1C) change in response to exponential plasma glucose decay. His analysis has shown a faster decay of A1C associated with a slower decay of plasma glucose and posed a question to the weighted-average relationship between plasma glucose and A1C, which we proposed in our previous study (2). Since his derived formula is very complicated and the detailed analytical method is not given, I cannot exactly reply to his question. However, I propose here a new physiological model, which deals with the kinetics of GHb production in red cells, and explain the relationship between plasma glucose and A1C.
GHb is not contained in the newly born red cells, formed every day in proportion to plasma glucose level during red cell life, and finally removed from blood together with the end of red cell life. Hemoglobin in the red cells aged 1 day is therefore glycated during the preceding 1 day, whereas hemoglobin in the red cells aged 2 days is glycated during the preceding 2 days, and so on. Thus, GHb produced on the day just before A1C measurement is contained in the red cells aged 1 to T days (T is the red cell life span), whereas GHb produced on the day 2 days before is contained in the red cells aged 2 to T days. Generally, GHb produced on the day s days before A1C measurement is contained in the red cells aged s to T days. This means that the total amount of GHb produced on the day s days before A1C measurement is proportional to the volume of the red cells aged s to T days. In a steady-state condition where the distribution function of red cell age is constant, the contributory rate of the plasma glucose in the day s days before A1C measurement is proportional to T−s, and is given by W(s) = 2(T−s)/T2 (0 ≤ s ≤ T), where the coefficient 2/T2 is a normalization factor.
This result is just the same as in our previous report (2). Area under the weight function curve shows contributory rate of plasma glucose for each period. For T = 120 days, 50% of A1C is determined by the plasma glucose level during the preceding 35 days, 25% by the plasma glucose level during 25 days before this period, and the remaining 25% by the plasma glucose level during the 2-month period before these periods. The present model clearly shows the relationship between plasma glucose and A1C. Introduction of distribution function of red cell age to this model further enables analysis of A1C behavior when the red cell kinetics is disturbed by various physiological or medical conditions.
