Home glucose meters: How accurate should they be to avoid dysglycemia in patients using carbohydrate counting?

. Accurate self-monitoring of blood glucose is the key to an e ﬀ ective and safe intensive insulin therapy. Indeed, most insulin dosing decisions are made based on the blood glucose values obtained from home glucose meters, in particular for those using diet planning and carbohydrate counting. Patients on that therapeutic regimen depend not only on their ability to accurately estimate the carbohydrate content of each meal but also on the accuracy of the glucose meter being used. Therefore, in order to avoid postprandial hypoglycemia and hyperglycemia, it is of great importance to realize how important is the accuracy of blood glucose meters according to the particular characteristics of each patient. In this regard, we propose an analytic method to ﬁnd the limits of the blood glucose meters accuracy according to the insulin-to-carb ratio, the insulin sensitivity factor and the ability of each patient to estimate the carbohydrate content of each meal. hyperglycemic


INTRODUCTION
Self-Monitoring of Blood Glucose (SMBG) is the mainstay of proper diabetes management, supporting tight blood glucose control in patients on intensive insulin regimens, e.g., patients using diet planning and carbohydrate counting. However, to be useful and safe SMBG needs to be accurate. The accuracy of SMBG systems relies on several factors, being the accuracy of the blood glucose meters one of the most important [1]. As reported by Ekhlaspour et al in [2], the accuracy of commercially available blood glucose meters varies significantly. Regarding this study, 17 glucose meters were tested and it was found that their mean absolute relative difference (MARD) range from 5.6% to 20.8%.
Inaccurate blood glucose measurements may lead to incorrect dosing calculations which may result in dangerous variations of insulin doses and negatively influence glycemic control [1,3]. Indeed, Campos-Náñez et al conducted a 30-day in-silico study and found that blood meters accuracy clearly affect the glycemic control in type 1 diabetes patients. Moreover, the study shows that the meters' accuracy has a significant impact not only on the occurrence of severe hypoglycemic events but also on long-term average glycemia (HbA1c) [4].
In this context, it is of great importance to choose the correct blood glucose meter taking into account the particular characteristics and glycemic goals of each patient. Therefore, we propose an analytic method to find the limits of the blood glucose meters accuracy that considers the ability of each patient to estimate the carbohydrate content of each meal 1 along with its' insulin-to-carb ratio and insulin sensitivity factor. 1 The ability of each patient to accurately estimate the carbohydrate content of each meal could be quantified considering the average absolute error committed by the patient while evaluating a set of N meals, by:

MATHEMATICAL METHODS
The equation allows patients using carbohydrate counting to calculate the insulin bolus (i.e., prandial and correctional insulin) for each meal, according to the carbohydrates planned to be consumed in that meal (CHO), the insulin-to-carb ratio (ICR), the preprandial blood glucose target (G T ), the preprandial blood glucose value (G), the insulin sensitivity factor (IS F), the physiologic status of the patient represented by K, and the insulin remaining active from the last bolus (IOB, Insulin-on-Board) [5,6]. In the subsequent analysis, we will consider K = 1 (i.e., the impact of illness, physical activity or medication on insulin and glucose metabolism of patients will not be addressed in this study) and IOB = 0 (i.e., it will be considered that the time between meals is larger than the duration of the insulin action, and there is no insulin stacking). Moreover, we also assume that patient's ICR and IS F are physiologically appropriate. Let's consider CHO =ĈHO ± ΔCHO and G =Ĝ ± ΔG to be variables of Equation 1, whereĈHO is an estimate of CHO with an absolute error ΔCHO > 0, andĜ is an estimate of G with an absolute error ΔG > 0. The remaining variables of Equation 1 are considered to be exact values. In such conditions, the absolute error of ., ICR and IS F are positive values). Therefore, we have: The bolus' absolute error, ΔB, will perform as an unplanned and inappropriate correction bolus, with the consequent undesired effect on the patient's postprandial glycemia (G postprandial ) given by: where ΔG postprandial is the variation on the patient postprandial blood glucose. By denoting the hyperglycemia and hypoglycemia limits as G Hyper and G Hypo , respectively, it is possible to conclude that the maximum value of ΔG postprandial allowed, in order to avoid hyperglycemia and hypoglycemia episodes, is given by min G Hyper − G T , G T − G Hypo (n.b., the function min{·} returns the minimum value of a set of elements) and, therefore, it is sufficient to satisfy the following condition to avoid them: Equation 2 shows that the sufficient limits of accurate carbohydrate counting, in order to avoid dysglycemia, depend not only on each patient data but also on the accuracy of the blood glucose meter being used. Therefore, taking into account the ability of each patient to correctly estimate the carbohydrate content of each meal, along with it's IS F, ICR, and glycemic targets, the blood glucose meter absolute error, ΔG, should satisfy the following conditions:

DISCUSSION
To assess and discuss the implications of the proposed method let's consider a hypothetical patient of 75 kg body weight, consuming a total of 50 U of insulin each day, having a preprandial glucose target of G T = 110 mg/dL, and the following glycemic thresholds for hyperglycemia and hypoglycemia, respectively: G Hyper = 150 mg/dL, G Hypo = 70 mg/dL. Suppose, without loss of generality, that the ICR and IS F for this patient are calculated according to the recommendations of the American Association of Clinical Endocrinologists/American College of Endocrinology (AACE/ACE) [7], using the following rules: ICR = 450/T DD and IS F = 1700/T DD, where TDD is the Total Daily Dose of insulin that, in this case, is equal to 50 U. Therefore, under these assumptions, the patient's ICR and IS F are 9 g/U and 34 mg/dL/U, respectively. Finally, this patient is able to estimate the carbohydrate content of each meal with an average absolute error of 10 g (i.e., ΔCHO = 10 g). According to Equation 2, the maximum absolute error allowed while estimating the carbohydrate content of each meal depends on the meter accuracy and on the patient data, as shown Figure 1. Let us consider first the use of an ideal blood glucose meter, i.e., having no error. In that case, the maximum admissible absolute error while estimating the carbohydrates is given by ΔCHO max = 9 × 40/34 ≈ 10.59 g. Hence, since ΔCHO ≤ ΔCHO max , the risk of the patient facing dysglycemic events is reduced. However, such an ideal meter does not exist. Moreover, the accuracy of the blood glucose meters available on the market varies significantly, as can be seen in Table 1. Taking into account the accuracy of the blood glucose meters, the value of ΔCHO max could be significantly smaller. Table 1 shows the value of ΔCHO max for several blood glucose meters and, makes clear that none of them fits into the diabetes management strategy of this patient. Therefore, this patient must improve their carbohydrates counting skills or change their glycemic targets. As an example, if the patient glycemic goals change to G T = 120 mg/dL, G Hyper = 170 mg/dL, and G Hypo = 70 mg/dL, it will be safe to use any of the first four blood glucose meters listed in Table 1, under the range 20 ≤ BS < 180.
Therefore, the accuracy of the blood glucose meters is a determinant factor for a proper glycemic control and must be taken into account while fitting the diabetes management strategy of each patient.

CONCLUSION
Patients with diabetes make their insulin dosing decisions based on the glycemic values obtained from home glucose meters. Indeed, patients on intensive insulin regimens, particularly those using meal planning and carbohydrate counting, heavily depend not only on their ability to accurately estimate the carbohydrate content of each meal but also on the accuracy of the blood glucose meters to achieve a rigorous glycemic control. Therefore, to avoid dysglycemic events, it is fundamental to understand the impact of the blood glucose meters accuracy on the insulin bolus. To that end, we propose an analytic method to find the limits of the blood glucose meters accuracy according to the insulin-to-carb ratio, the insulin sensitivity factor and the ability of each patient to estimate the carbohydrate content of each meal. By using the proposed method, healthcare professionals are able to make informed decisions about the best blood glucose meter for each patient according to their particular characteristics. Moreover, this method allows healthcare professionals to optimize the glycemic goals of each patient according to their characteristics and meter accuracy in order to lessen the risk of hypoglycemic and hyperglycemic episodes.