Background
Glycated hemoglobin A
1c (HbA
1c) has been used as an index of glycemic control in the management, clinical guidance, and clinical trials of diabetic patients for the past 35 years. In 2009, HbA1c became a diagnostic test for diabetes [
1]. In 2008, the multi-center A1C-Derived Average Glucose (ADAG) study was concluded, documenting the linear relationship between HbA
1c and mean blood glucose (MBG) [
2]. For an average individual, this relationship can be used to report HbA
1c as an estimated average glucose level over a period of 3 to 4 months (which is considered to be an approximate life span of erythrocytes) preceding HbA
1c test execution. According to the ADAG study assumptions, such an estimate should fall within ±15% of the study-wide calculated level for 90% of the individual patients [
2]. However, this average linear relationship cannot be combined with any additional knowledge about the particular patient (e.g., results of HbA
1c tests repeated within a short time period or information from a patient that she or he experienced a substantial improvement in glycemic control a few weeks ago) to narrow this 15% uncertainty range. Neither can it be used to study the influence of different glycemia profiles on the HbA
1c level. For this purpose, mathematical modeling has been applied, among other methodologies [
3]-[
12].
In 2011, Ladyzynski
et al. demonstrated that it was feasible to approximate the average relationship of HbA
1c and glycemia reported in the ADAG study using one of such models [
12]. The kinetics of hemoglobin glycation in this model can be characterized by an overall hemoglobin glycation rate constant (
k). Besides the kinetics of the hemoglobin glycation reaction, the release of erythrocytes to the blood stream from the bone marrow and the elimination of erythrocytes from circulation were taken into account while calculating the average HbA
1c level over all equal-aged cohorts of erythrocytes circulating in the vascular system at any given time.
Because the above-mentioned report [
12] was based on data from healthy volunteers, it seemed advisable to validate the model using data from patients with diabetes. We expected the mean values of
k to be similar in patients with type 1 and type 2 diabetes. However, we have not found any data in the literature confirming such an equality of the glycation rate constants in these two groups of patients. In reports available in the literature, the total number of cases studied so far in patients with diabetes is limited, making it difficult to draw conclusions about the mean values and the intersubject variability of
k in type 1 and type 2 diabetes. Contrarily, many clinical studies reported high variability of HbA
1c, which could hardly be explained by differences in glycemic control. Taking into consideration the different pathophysiology of type 1 and type 2 diabetes and considering all the factors other than glycemia that might influence the glycation rate (e.g., pH, oxidative stress, enzymatic deglycation, Schiff base inhibitors), the possibility that there are significant differences in formation of HbA
1c in these two groups of patients cannot be ruled out.
The aim of the current work was threefold: (1) to estimate and compare the mean k and its interindividual variability in patients with type 1 and type 2 diabetes, (2) to validate the ability of the mathematical model to predict HbA1c concentration based on different glucose levels and to reproduce the relationship of HbA1c and glycemia established in the ADAG study, and (3) to simulate different glycemia profiles and their influence on the HbA1c concentration and to use these simulations to support interpretation of HbA1c in different clinical situations.
Methods
In the first part of the study, an experimental procedure described in detail elsewhere [
7],[
12] was used to estimate
k and to evaluate the HbA
1c model. The procedure consisted of four phases, described below.
Blood glucose and HbA1c estimation in vivo
Glycemia course over a 120-day period was estimated based on CGM using a Guardian RT system (Medtronic Diabetes, Northridge, CA, USA) calibrated at least 4 times a day using capillary glucose measured with an Accu-Chek Go glucometer (Roche Diagnostics, Basel, Switzerland). Glucose concentrations measured with glucometers were rescaled to reflect the whole blood glucose concentrations as if they had been measured with the gold standard glucose analyzer YSI 2300 Stat Plus (Yellow Springs Instruments Inc., Yellow Springs, OH, USA) according to the linear regression reported by Cohen
et al.[
13]. Then the results were multiplied by 1.11, as recommended by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) [
14], to reflect blood glucose (BG) concentrations in plasma. Based on the DirectNet study, it was assumed that Guardian RT neither underestimates nor overestimates glucose concentration in relation to the calibrating results [
15]. In each participant, 3 glucose sensors were applied for 6 days, with an assumed time span of 4 and 2 weeks between application of the first two and the last two sensors, respectively.
Two methods were used to estimate 120-day glycemia profiles. In the first method, we calculated two separate daily glycemia profiles representing working days and weekends by a point-wise averaging of the daily recordings (WW method). Then we connected these profiles repeatedly to obtain the extrapolated 120-day course. In the second method, the rescaled-to-plasma daily profiles were repeatedly copied to build the whole 120-day course, without any intermediate averaging (ID method). Both 120-day profiles were used to identify the individual k value for each subject and to evaluate the sensitivity of this estimate on the short-term glycemia variability. The k value was also calculated based on an analytical solution of the model under the assumption that BG was equal to the mean value (MBG) for 120 days.
The HbA
1c was measured at the end of usage of the last sensor (5 repetitions were done) by applying the cation-exchange HPLC method with a D-10 analyzer (Bio-Rad Laboratories, Hercules, CA, USA). This analyzer measures HbA
1c according to the National Glycohemoglobin Standardization Programme (NGSP) as a percentage of the total hemoglobin [
16].
Cultivation of erythrocytes in vitro
At the end of glucose monitoring, 30 ml of blood was sampled for cultivation of erythrocytes. The erythrocytes isolated from the blood samples were cultured for up to 5 weeks at 37°C [
7],[
12]. Three glucose levels were maintained in culturing media corresponding to BG of 5.2 mmol/l, 10.5 mmol/l, and 15.7 mmol/l, respectively. Glucose concentrations measured in the medium using the YSI analyzer were divided by 1.06 to account for different water content in the plasma and in the medium [
14].
The following procedure was used every day to sustain the presumed constant concentrations of glucose. First, a sample of the medium was taken to measure the glucose concentration before the old medium was replaced by the fresh one. Second, the hemolized erythrocytes were removed together with the old medium from a cell-culture dish, and then the fresh medium containing the desirable glucose concentration was added into the culture. The difference between the glucose concentration at the beginning and at the end of each day was decreasing with time because the number of viable erythrocytes that were able to metabolize glucose was also decreasing. Therefore, the glucose concentration in each culture was not constant but instead was changing, in a sawtooth-like manner, each day. To minimize errors that were made during HbA1c modeling, we interpolated these intraday changes of glucose concentration and used the interpolated values in the model.
A series of preliminary experiments with different glucose concentrations in the medium [
7] confirmed that after 14 days of culturing, the molality of glucose in the medium and in the erythrocytes was the same (standard deviation of the absolute relative differences was equal to 3.6%). Glucose content in erythrocytes was not measured after the 14th day of culturing because of a limited volume of samples. Thus, it cannot be ruled out that glucose transport through the walls of the erythrocytes may be affected
in vitro as a result of changes in the availability of GLUT1, which enable the facilitated diffusion of glucose. However, the influence of such changes on the results must have been limited in the current study because the constant levels of glucose were maintained in the medium.
We also sampled the cultures to measure HbA
1c and to estimate the number of viable erythrocytes using Bürker’s chamber [
17]. Samples for HbA
1c testing were frozen at −80°C until erythrocyte cultivation ended, and then HbA
1c was assessed in all samples. To ensure the viability of erythrocytes
in vitro (or our ability to properly remove nonviable cells and to detect viable cells), in the preliminary tests we used two methods in parallel to estimate the number of the viable cells in the cultures: a microscopic method with Bürker’s chamber and a cytometric method applying the Annexin V binding protocol. In the preliminary tests, described above [
7], we conducted six
in vitro experiments using blood samples from the healthy volunteers. The apoptotic cells were detected (in 5 samples in each experiment) using a FACSCalibur cytometer and CellQuest software (Becton Dickinson, San Diego, CA, USA).
We found a good agreement between the results of the cytometric and the microscopic analyses. The mean difference of the viable erythrocytes count expressed in relation to the erythrocytes’ count at the day of blood sampling for the
in vitro experiments between the microscopic and the cytometric methods equaled 1.7 ± 2.8% (mean ± SD), p < 0.002 [
7]. This result confirmed that we were able to properly distinguish the apoptotic cells from the viable cells. Thus, we used the microscopic method in the main cycle of experiments.
Estimation of the overall glycation rate constant
The applied HbA
1c model assumes that HbA
1c level depends on three main processes: the kinetics of hemoglobin glycation, the release of the reticulocytes from bone marrow and the elimination of erythrocytes from circulation. The kinetics of hemoglobin glycation in the equal-aged cohort of erythrocytes was modeled with a simple differential equation [
12]:
where HbA denotes concentration of non-glycated hemoglobin and t is time.
The most important assumptions of the model are as follows: (1) the life span of erythrocytes is constant and equal to 120 days, (2) the turnover of erythrocytes is constant, (3) HbA
1c concentration in the newly generated reticulocytes is equal to zero [
4],[
18], (4) erythrocytes are eliminated in chronological order (“the oldest” ones are eliminated first) [
7], and (5) the influence of the spleen-facilitated vesiculation on HbA
1c is negligible [
7],[
10]. The influence of these assumptions on the modeled HbA
1c was assessed earlier [
7].
Based on these assumptions, a hemoglobin mass balance equation was utilized to calculate HbA
1c level in the equal-aged cohort of erythrocytes at any particular point in time, depending on BG. These calculations were performed in parallel in 120 cohorts of erythrocytes of different ages (ranging from 1 day to 120 days), and then the results were averaged over all the cohorts to obtain the modeled HbA
1c level that corresponds to the measured HbA
1c level. To estimate a value of
k, calculations were repeated with iteratively modified
k until the absolute difference between the calculated and the measured HbA
1c dropped below 0.046% (0.05 mmol/mol). To avoid overestimation of
k, the calculations were performed using the unbiased IFCC-aligned HbA
1c levels that were obtained from the NGSP-aligned ones according to the linear equation recommended by the IFCC [
16]. In this manuscript, HbA
1c concentrations are reported according to both scales, with the NGSP-aligned values expressed in percentages of the total hemoglobin (%), followed by the IFCC-aligned values in millimoles of HbA
1c per mol of the total hemoglobin (mmol/mol) given in parentheses.
The HbA
1c model has been described in detail elsewhere and it has been proven to be capable of predicting HbA
1c levels in nondiabetic individuals [
7],[
12]. In one of these reports [
12], an analytical solution of the model was presented under an assumption of a constant glycemia throughout the entire life span of erythrocytes (HbA1c is NGSP-aligned and LS stands for the life span of erythrocytes in the equation below):
This equation was used to calculate values of k for all the study participants, based on their individual MBG values, and to compare them with values of k estimated numerically, based on extrapolated continuous glycemia courses obtained using the WW and ID methods.
The most important simplification of the model was related to the assumed constant life span of erythrocytes equal to 120 days. To show an influence of this assumption on the estimated values of k we also identified the model (i.e., estimated values of k for all the study participants) for alternative values of the life span equal to 60, 80, 100, 140 and 160 days.
Assessment of the model performance based on in vitro data
It was assumed that hemoglobin glycation obeys the same kinetics
in vivo as it does
in vitro[
6]. The models with
k individualized for each subject were used to predict HbA
1c changes assuming 4 different mechanisms of erythrocyte apoptosis during the
in vitro cultivation: the chronological loss of cohorts, the uniform loss of erythrocytes from all cohorts, the combination of these two mechanisms, or the counter-chronological loss of erythrocytes (with the “youngest” erythrocytes being eliminated first). The percentage of the modeled erythrocytes that were left each day in the simulated cultures reflected the percentage of the viable erythrocytes measured in the real cultures. No new erythrocytes were added in the model to reflect the real-life conditions. A detailed description of the
in vitro modeling was reported earlier [
7],[
12]. The mean difference (MD) and the mean absolute difference (MAD) of the measured and the predicted HbA
1c levels were used to assess the model’s performance.
Modeling a relationship of HbA1c and blood glucose levels
In the second part of the study, the mean
k and its intersubject variability were estimated for patients with type 1 and type 2 diabetes. The mean
k was then used to model the linear relationship of HbA
1c and MBG. The obtained linear function was compared with the experimental one that was reported in the ADAG study [
2]. However, the ADAG study reported a regression line with HbA
1c as the independent variable, whereas the model-generated results should be compared with the line calculated with MBG as the independent variable (i.e., the one minimizing the prediction error of HbA
1c based on MBG). In both cases, the correlation coefficient is the same but the slopes and intercepts of regression lines differ.
We had no access to the raw data from the ADAG population. Therefore, we used the published summary statistics of the ADAG study to build a statistical model of the ADAG population and to draw a sample of 10,000 pairs of HbA
1c and MBG from this population with the Monte Carlo technique using the OpenBUGS 3.2.1 system [
19]. Based on these simulated data, a regression line of HbA
1c
vs. MBG was determined and compared with the relationship obtained using the HbA
1c model.
In the third part of the study, the model with the mean k was used to simulate the influence of different 120-day-long glucose profiles on HbA1c, assuming a 120-day life span of erythrocytes. Additionally, the model with the mean k value was used to predict steady-state HbA1c concentrations for constant MBG values in case of shortening (to 60, 80, and 100 days) and lengthening (to 140 and 160 days) of the survival of erythrocytes.
Participants
The study group consisted of 30 sequentially enrolled non-Hispanic white adults including 15 patients with type 1 diabetes and 15 with type 2 diabetes. Exclusion criteria were proliferative retinopathy or maculopathy requiring treatment, renal impairment (creatinine higher than 177 μmol/l), heart failure (class III or IV, according to NYHA, or cardiac infarction within past 3 months), and mental impairment.
Baseline characteristics of the study group are presented in Table
1. All of the subjects had stable metabolic control prior to the enrollment and a regular lifestyle as confirmed by the results of an interview. The study adhered to the Declaration of Helsinki, the subjects provided informed written consent, and the local ethical committee approved the study protocol.
Table 1
Baseline characteristics of the study group
n | 15 | 15 | 30 |
Sex (% female) | 8 (53) | 7 (47) | 15 (50) |
Age (years) | 36.4 ± 15.5 | 57.5 ± 15.8 | 47.0 ± 18.8 |
Duration of diabetes (years) | 11.8 ± 11.3 | 10.1 ± 10.7 | 10.9 ± 10.8 |
BMI (kg/m2) | 23.9 ± 5.6 | 29.1 ± 5.9 | 26.5 ± 6.2 |
C-peptide (nmol/l) | 0.11 ± 0.17 | 1.10 ± 0.63 | 0.61 ± 0.68 |
Hemoglobin (g/l) | 141 ± 11 | 139 ± 9 | 140 ± 10 |
Hematocrit (%) | 41.1 ± 3.1 | 41.1 ± 2.7 | 41.1 ± 2.8 |
RBC (× 1012/l) | 4.74 ± 0.38 | 4.65 ± 0.33 | 4.69 ± 0.35 |
WBC (× 109/l) | 6.78 ± 1.75 | 7.40 ± 1.78 | 7.09 ± 1.76 |
Fe (μmol/l) | 17.9 ± 8.6 | 16.6 ± 3.8 | 17.2 ± 6.6 |
Creatinine (μmol/l) | 76 ± 27 | 68 ± 14 | 72 ± 22 |
Statistical analysis
Normality of distribution of all variables was confirmed using the Shapiro-Wilk W test. Thus, the analysis of variance (ANOVA) or t-test was applied to analyze the data, using Statistica ver. 7.1 (StatSoft Inc., Tulsa, OK, USA). All results are presented as mean ± SD unless otherwise indicated. A p-value below 0.05 was considered statistically significant.
Discussion
The mean overall glycation rate constant values identified using 120-day glycemia courses that were extrapolated based on the CGM data in patients with type 1 and type 2 diabetes support the notion of the same mean rate of hemoglobin glycation in these two groups of diabetic patients. The mean
k reported in this study is just 3.1% higher than the mean
k obtained in 10 healthy volunteers, estimated earlier using the same methodology [
12], and 2.0% higher than the one that we calculated based on the results of the 3-month CGM data for 22 patients with diabetes and for 3 nondiabetic subjects presented by Nathan
et al.[
21]. The mean
k reported here is also in a good agreement with previously reported values estimated on the basis of a limited number of samples utilizing
in vivo or
in vitro experiments, when methodological differences are accounted for [
3],[
4],[
6],[
7],[
18].
The mean
k values were only marginally different for three methods of the long-term glycemia extrapolation that were used. This result confirms the data reported in the clinical studies showing that HbA
1c is sensitive to MBG level but not to glycemic short-term variations [
2],[
21]-[
23] because the MBG levels used in these three methods were very similar to each other, whereas the glucose variability measures were significantly different.
The life span of erythrocytes shorter or longer than the assumed 120-day would not change the conclusion that the mean k is similar in patients with type 1 and type 2 diabetes, provided that the mean erythrocyte survival was similar in these two groups. However, the mean value of k would be affected if the erythrocyte life span was different than 120 days.
The interindividual CV of
k was similar regardless of the type of diabetes, but it was higher than the value reported earlier in healthy volunteers [
12] (p = 0.025). The obtained CV is high, but it cannot be automatically attributed in full to variability of glycation rate. Ladyzynski
et al.[
12] demonstrated that a major part of variability of
k in healthy volunteers could be explained by random errors of HbA
1c and glycemia measurements and, more importantly, by a heterogeneity of erythrocyte life span [
12].
Furne
et al. [
24] estimated that by using the end-alveolar carbon monoxide technique, the standard deviation of the life span of erythrocytes in healthy subjects was equal to 23 days. This value is more than enough to explain the variability of
k obtained in the current study and to justify the resulting differences in HbA
1c corresponding to a given glucose concentration, which can be observed in Figure
4, where, for example, at an MBG equal to 15.5 mmol/l, HbA
1c varies from 8.3% (68 mmol/mol) to 13.8% (127 mmol/mol). Higher CV of
k noted in our study in comparison with the study concerning healthy volunteers [
12] suggests that the heterogeneity of the life span of the erythrocytes might be higher in patients with diabetes. This is in line with the results reported by Virtue
et al.[
25], who demonstrated that in a group of patients with type 2 diabetes, this parameter was equal to 25 days.
Higher CV noted in our study suggests that the other above-mentioned sources of variability might also be more pronounced or that
k is more significantly influenced by other factors (e.g., oxidative stress [
26]) in patients with diabetes than in healthy subjects. Further studies are required to confirm this hypothesis. Nevertheless, the model also can be individualized, applying the method used in this study, to fit a particular patient’s data more precisely.
The HbA
1c model with
k individually identified for each patient was used to predict HbA
1c in cultures of patients’ erythrocytes. We tested a few possible modes of erythrocyte removal, because of a lack of any method that could actually measure which erythrocytes are lost. The results indicated a high ability of the model to predict HbA
1c when two modes of erythrocyte removal – chronological loss and uniform loss – were combined. The results of
in vitro studies strengthen the validity of the model under
in vivo conditions, because both models share the same
k for a particular subject and the
in vitro simulation starts with the calculated HbA
1c levels in each equal-aged cohort of erythrocytes on the last day of the glucose monitoring
in vivo. This means that the two models are strongly interrelated [
7].
The average linear relationship of HbA1c as a function of MBG, which was modeled using the mean k and a constant 120-day life span of erythrocytes, reproduced the relationship of these variables obtained using the data sampled from the ADAG population despite differences between the groups (e.g., in terms of ethnicity, proportion of nondiabetic individuals and patients with type 1 and type 2 diabetes). This is yet another confirmation of the validity of the model.
More importantly, the fact that both linear relationships are almost identical has significant implications regarding the glycation rate, the life span of erythrocytes, and the glycemic control. On the one hand, if the life span of erythrocytes shortens with a worsening of glycemic control, as was suggested in a few reports [
25],[
27], then the mean
k must increase to compensate for the shorter time of glycation (otherwise the slopes of both lines would have to be different). Possible mechanisms responsible for such an increase include patients’ susceptibility to oxidative stress and an association of hyperglycemia with free-radical-mediated lipid peroxidation [
26] or the existence of high and low hemoglobin glycation phenotypes [
28],[
29]. On the other hand, some studies have indicated that the life span of erythrocytes is independent of glycemic control or even that it is longer in patients with poorer control [
18],[
30],[
31], implying that the mean glycation rate is not correlated or that it is negatively correlated with glycemic control.
Unfortunately, based solely on the hemoglobin glycation model, it is not possible to judge, whether the life span of erythrocytes and the glycation rate constant are negatively, positively, or not correlated with HbA
1c. This is related to the fact that in the model the glycation rate constant
k and the life span of erythrocytes are not present separately but as a product of these two variables (see, above, the second equation in section
Estimation of the overall glycation rate constant). Therefore, it is not possible to reach a conclusion about possible changes of one of these parameters as a function of HbA
1c without having prior knowledge about changes of the other parameter. A reliable method of measuring the survival of erythrocytes
in vivo is required to solve this problem. In the absence of such a method, mathematical modeling can be used to incorporate a description of the aging of erythrocytes into the glycation model [
32].
From a practical point of view, the most important conclusion, that can be drawn from a good agreement of both linear relationships considered above, is that changes in the life span must be balanced by changes in the glycation rate across the wide range of HbA1c levels to ensure nearly a constant product of these two variables; otherwise it would not be possible to reproduce the average relationship of HbA1c and MBG obtained in the ADAG study using the model with k equal to 1.296 × 10−9 l mmol−1 s−1 and the 120-day life span of erythrocytes. In fact, the same result would be achieved even if some other value of the life span of erythrocytes were assumed. This is related to the fact that k is estimated from the model based on the assumed life span of erythrocytes, that is, the shorter the life span, the higher the estimated value of k and vice versa.
Because of a good agreement of the simulated and the experimental relationship of HbA1c and MBG obtained using the mean k and the same mean life span of erythrocytes, the same values of these parameters can be used to obtain reliable predictions of HbA1c in response to different glycemic profiles in the average patient with diabetes. We conducted a few series of such predictions for different glycemic profiles preceding the HbA1c test execution. The conclusions from these predictions are as follows: (1) interpreting HbA1c as a measure of MBG is meaningful only in the case of stable glycemic control; (2) the HbA1c level might vary widely during sudden changes in glycemia, even in the case of glycemia profiles with the same MBG level; (3) HbA1c is not a sensitive indicator of short-term glycemic variability; and (4) there is a considerable ambiguity in interpreting the result of a single HbA1c measurement when no additional information about the patient is available (e.g., previous HbA1c or BG values).
These conclusions are in good agreement with observations known from clinical practice and demonstrated in clinical trials. However, using the model it is possible to assess what quantitative statements (for example, “HbA1c is not a sensitive indicator of the short-term glycemic variability”) really mean in terms of concrete numerical values of HbA1c and BG.
From a practical standpoint, the most important value of the presented work is that having a positively verified model, in which k can be identified for a particular patient, and taking into consideration the relative mathematical simplicity of the model, more frequent tests of HbA1c might be used together with the results of modeling to decrease ambiguity of interpreting HbA1c in terms of glycemic control. For example, one can calculate monthly estimates of MBG using the model and monthly HbA1c tests instead of assuming that BG was constant for the whole life span of erythrocytes. In other words, the model make it possible to improve interpretability of the most recent HbA1c value by combining all the evidence available within 3–4 months related to glycemia monitoring and HbA1c testing.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
PL conceived and designed the study, analyzed and interpreted the data and wrote the manuscript. PF acquired the data, performed the statistical analysis and wrote the manuscript. MIB designed the study and interpreted the data. SS acquired and analyzed the data. JKr interpreted the data and made critical revisions of the manuscript for important intellectual content. JKa researched the data and reviewed the manuscript. All authors read and approved the final manuscript.