Glycated Hemoglobin (HbA1c): Clinical Applications of a Mathematical Concept

Glycated hemoglobin (HbA1c) reflects the cumulative glucose exposure of erythrocytes over a preceding time frame proportional to erythrocyte survival. HbA1c is thus an areal function of the glucose-time curve, an educationally useful concept to aid teaching and clinical judgment.

An ordinary differential equation is formulated as a parsimonious model of HbA1c. The integrated form yields HbA1c as an area-under-the-curve (AUC) of a glucose-time profile. The rate constant of the HbA1c model is then derived using the validated regression equation in the ADAG study that links mean blood glucose and HbA1c with a very high degree of goodness-of-fit.

This model has didactic utility to enable patients, biomedical students and clinicians to appreciate how HbA1c may be conceptually inferred from discrete blood glucose values using continuous glucose monitoring system (CGMS) or self-monitored blood glucose (SMBG) glucometer readings as shown in the examples. It can be appreciated how hypoglycemia can occur with rapid HbA1c decline despite poor glycemic control.

Being independent of laboratory assay pitfalls, computed 'virtual' HbA1c serves as an invaluable internal consistency cross-check against laboratory-measured HbA1c discordant with SMBG readings suggestive of inaccurate/fraudulent glucometer records or hematologic disorders including thalassemia and hemoglobinopathy. This model could be implemented within portable glucometers, CGMS devices and even smartphone apps for deriving tentative 'virtual' HbA1c from serial glucose readings as an adjunct to measured HbA1c. Such predicted 'virtual' HbA1c readily accessible via glucometers may serve as feedback to modify behavior and empower diabetic patients to achieve better glycemic control.