Insulin-to-carbohydrate Ratio Research Articles

Toward a Run-to-Run Adaptive Artificial Pancreas: In Silico Results

Contemporary and future outpatient long-term artificial pancreas (AP) studies need to cope with the well-known large intra- and interday glucose variability occurring in type 1 diabetic (T1D) subjects. Here, we propose an adaptive model predictive control (MPC) strategy to account for it and test it in silico. A run-to-run (R2R) approach adapts the subcutaneous basal insulin delivery during the night and the carbohydrate-to-insulin ratio (CR) during the day, based on some performance indices calculated from subcutaneous continuous glucose sensor data. In particular, R2R aims, first, to reduce the percentage of time in hypoglycemia and, secondarily, to improve the percentage of time in euglycemia and average glucose. In silico simulations are performed by using the University of Virginia/Padova T1D simulator enriched by incorporating three novel features: intra- and interday variability of insulin sensitivity, different distributions of CR at breakfast, lunch, and dinner, and dawn phenomenon. After about two months, using the R2R approach with a scenario characterized by a random 30% variation of the nominal insulin sensitivity the time in range and the time in tight range are increased by 11.39% and 44.87%, respectively, and the time spent above 180 mg/dl is reduced by 48.74%. An adaptive MPC algorithm based on R2R shows in silico great potential to capture intra- and interday glucose variability by improving both overnight and postprandial glucose control without increasing hypoglycemia. Making an AP adaptive is key for long-term real-life outpatient studies. These good in silico results are very encouraging and worth testing in vivo.

Bolus Calculator Settings in Well-Controlled Prepubertal Children Using Insulin Pumps Are Characterized by Low Insulin to Carbohydrate Ratios and Short Duration of Insulin Action Time

The "500 rule" has been used extensively to find the insulin to carbohydrate ratio (ICR) for carbohydrate counting (CC). Duration of insulin action (DIA) is often recommended to be set to 4 hours. Data are lacking on validating these routines in young children. ICR was calculated by dividing carbohydrate grams by insulin units. Insulin sensitivity factor (ISF) was defined by the 100 rule (100 divided by total daily insulin dose [TDD]). DIA was set to 3 hours. ICR, ISF, and DIA were adjusted continuously. Data for this retrospective analysis were taken from pump downloads at a routine visit. ICR and ISF were recalculated to rules (ICR/ISF multiplied by TDD). A total of 21 prepubertal children aged 7.0 ± 2.3 (mean ± SD), range 2-10 years, with diabetes duration 3.0 ± 1.9, range 0.5-7.7 years, used the pump bolus calculator for CC. HbA1c IFCC (NGSP) was 53 ± 6 mmol/mol (7.0 ± 0.5%). None had experienced severe hypoglycemia (unconsciousness/seizures) since diabetes diagnosis. TDD was 0.7 ± 0.1 U/kg/24 h (range 0.5-1.0), and the percentage basal insulin 38 ± 11%. Median breakfast rule was 211 (Q, quartiles 162;310), and for other meals 434 (Q 301;496). Median ISF rule was 113 (Q 100;128) in the morning, and 120 (Q 104;134) during the rest of the day. DIA was 2.6 ± 0.5 h (range 2-3) and target BG 5.3 ± 0.4 mmol/l (range 5.0-6.0). Prepubertal children seem to need more bolus insulin for meals than calculated from the 500 rule, especially at breakfast, but less insulin for corrections than calculated from the 100 rule. Two to 3 hours seems to be the appropriate range for DIA in this age group.

A Review of Insulin-Dosing Formulas for Continuous Subcutaneous Insulin Infusion (CSII) for Adults with Type 1 Diabetes.

Dosing guidelines for patients with type 1 diabetes using continuous subcutaneous insulin infusion (CSII), which are historically based on clinical experience and retrospective studies of patients consuming an American diet, recommend that basal insulin should represent approximately 50 % of the total daily dose (TDD). Recent prospective studies in the USA and Japan conclude that the more appropriate proportion is closer to 30–40 % of TDD. In addition, currently used formulas for calculating the carbohydrate-to-insulin ratio (CIR) and correction factor (CF) may lead to underdosing of bolus insulin by as much as 12.8–50 % for a hypothetical patient. The discrepancies between traditional formulas and data from newer studies can be accounted for by the more rigorous design of the newer studies (e.g., prospective design, controlled diets, meal omission, and frequent glucose monitoring). International differences in diet composition may also be important to consider when developing dosing recommendations for CSII.

Nonlinear Insulin to Carbohydrate Rule for Treatment of Type 1 Diabetes

This paper develops a nonlinear insulin to carbohydrate rule for use by type 1diabetes patients. The goal is to refine the commonly used Insulin to Carbohydrate Ratio (ICR) formula. The latter is a strictly linear rule relating carbohydrates consumed to insulin infusion. The new relationship presented in this paper is nonlinear and depends on the availability of a nonlinear dynamic model describing a patient's blood glucose response to food and insulin. Such a model can be obtained by use of nonlinear system Identification tools applied to patient test data. The suggested procedure is of similar complexity to the existing standard ICR rule. Hence it has the potential to be of clinical importance especially in developing countries where sophisticated solutions such as an artificial pancreas are unlikely to be used due to excessive cost. Simulations are presented which show that there exists a significant difference between the suggested insulin provided by the rule developed here and that given by the standard ICR rule.

Performance assessment of estimation methods for CIR/ISF in bolus calculators

Type 1 diabetes patients typically determine their bolus insulin needs using a bolus calculator which requires patient- and daytime-specific values for the carbohydrate-to-insulin-ratio (CIR) as well as for the insulin-sensitivity-factor (ISF). The strong inter- and intra-patient variability of blood glucose dynamics and the myriad of influencing disturbances makes estimating these factors a difficult task that is normally executed by skilled diabetologists using high quality data. In the scientific literature different methods have been proposed that should help medical professionals in determining reliable estimates of CIR and ISF. In this paper some of these methods are first introduced and then applied on one dataset recorded in a recent clinical trial. Their performance is then evaluated by comparing the estimates of CIR and ISF with the patient- and daytime-specific values used by the patients in the clinical trial. It was found that methods based on detailed data analysis perform especially well for predicting CIR, whereas simple rules of thumb tend to give better results for predicting ISF.

Carbohydrate-to-Insulin Ratio in a Mediterranean Population of Type 1 Diabetic Patients on Continuous Subcutaneous Insulin Infusion Therapy.

The carbohydrate-to-insulin ratio (CIR) is initially calculated from the total daily insulin dose (TDID). However, CIR likely presents variations owing to different population characteristics and intraday variations not being taken into account by most formulas. No information is available concerning the Mediterranean population. We investigated the CIR used by patients with type 1 diabetes (T1DM) using continuous subcutaneous insulin infusion (CSII) therapy in a Mediterranean area, to identify possible intraday variations and establish an adequate formula to calculate CIR. Data from 170 T1DM patients from Barcelona were obtained retrospectively from the Spanish National Registry of CSII Therapy (SNR-CSII). Theoretical CIR was calculated using the formula: 500 divided by TDID. This theoretical CIR was compared to the real CIR. The real CIR was also compared between main meals. Patients with HbA1c < 7% (n = 44) were considered a reference group for accurate bolus calculation and were analyzed as a subgroup. The real CIR used was 11.5 g/UI for breakfast, 12 g/UI for lunch, and 13.3 g/UI for dinner. CIR obtained by the 500/TDID formula for all meals was 15.5 g/UI. We obtained similar results for the group with HbA1c < 7%. The real CIR differed significantly from the theoretical CIR values and between breakfast and the other main meals (P < .005). CIR in our population was significantly lower for breakfast than for other meals. CIR using the 500/TDID formula underestimated prandial insulin requirements. A calculation of 350/TDID for breakfast and 400/TDID for lunch and dinner would be more appropriate for this population.

Diurnal variation of carbohydrate insulin ratio in adult type 1 diabetic patients treated with continuous subcutaneous insulin infusion.

To estimate the carbohydrate-to-insulin ratio (CIR), a formula dividing a constant, usually 300-500, by the total daily dose (TDD) of insulin, is widely utilized. An appropriate CIR varies for each meal of the day, however. Here, we investigate diurnal variation of CIR in hospitalized Japanese type1 diabetic patients treated with continuous subcutaneous insulin infusion. After optimization of the insulin dose, TDD and total basal insulin dose (TBD) were 34.9±10.2 and 9.3±2.8 units, respectively, with a percentage of TBD to TDD of 27.3±6.0%. The products of CIR and TDD at breakfast, lunch and dinner were 311±63, 530±161, and 396±63, respectively, suggesting that in the formula estimating CIR using TDD, the constant should vary for each meal of the day, and that 300, 500, and 400 are appropriate for breakfast, lunch, and dinner, respectively.

Bolus Calculator Settings in Well-Controlled Type 1 Diabetes Patients (Glycated Hemoglobin &lt;7%) Treated with Insulin Pumps

Two regimens of insulin therapy are used to achieve the goal of near normoglycemia: multiple daily injections (MDI) and continuous subcutaneous insulin infusion (CSII). 1 Due to the apparent improvement in quality of life and metabolic control and the greater personal independence (compared with MDI), CSII is becoming an increasingly popular method of insulin delivery for people with type 1 diabetes mellitus (T1DM). 1–3 However, one of the major problems related to the use of CSII, or intensive insulin regimens in general, is the accurate calculation of insulin boluses. These calculations should take into account multiple factors, such as current and target blood glucose levels, carbohydrate intake, insulin-to-carbohydrate ratio (ICR), and insulin sensitivity. 3 Using the ICR to calculate meal bolus and insulin sensitivity factor (ISF) to correct hyperglycemia are accepted methods of optimization of metabolic control. 3–5 These rules are also used to program the bolus calculator (BC), which is an insulin pump function. 3–6 The BC uses preprogrammed settings to generate a recommendation of bolus dose.3 There is an agreement that these settings should be individualized for each person; however, some general rules as starting points do exist.4–6 The aim of this analysis was to evaluate BC settings used by CSII-treated T1DM patients, exclusively with good metabolic control [glycated hemoglobin (HbA1c) < 7.0%]. Thirty-nine patients (26 females and 13 males) with T1DM treated with CSII and using a BC (more than 50% of total daily boluses delivered via this function) were included in this analysis. The data regarding body mass index (BMI), HbA1c level, diabetes duration, insulin dose, blood glucose parameters, and other clinical data from the past 3 years were collected from all the patients. Insulin pump memory data were downloaded via the Carelink software. Statistical analysis was performed with the use of statistical package Statistica10.0 PL. The Pearson or Spearman correlation was applied when appropriate. The mean age of the patients was 35 years, diabetes duration was slightly over 17 years, and mean HbA1c level was 6.38%. The clinical characteristics of the patients is summarized in Table 1. Mean ICR was 1.58 IU/10 g carbohydrates, and mean ISF was 36.8 mg/dl/IU of insulin. The ICR correlated positively (r = 0.39, p =.013; r = 0.35, p =.032) and the ISF negatively (r = -0.57, p < .000; r = -0.41, p =.010), with total daily insulin dose and daily insulin dose per kilogram of body weight. Additionally, ISF correlated negatively with BMI (r = -0.34, p = .034). No significant correlation was found between ICR or ISF and any of the following parameters: HbA1c, mean glycemia, diabetes duration, percentage of basal insulin, number of measurements per day, and age. The results of our study indicate that the rule for counting ICR (per 10 g of carbohydrate) in well-controlled T1DM patients should be approximately 290 and, for ISF, 1670. Table 1 Clinical Characteristics of Study Participants In conclusion, we have shown that the ISF rule in Polish patients with good metabolic control is similar to rules used by other centers; however, the ICR rule should be much more stringent. We have also shown that the ISF rule should be considered with respect to patients’ BMI.

Carbohydrate-to-Insulin Ratio Is Estimated from 300–400 Divided by Total Daily Insulin Dose in Type 1 Diabetes Patients Who Use the Insulin Pump

To optimize insulin dose using insulin pump, basal and bolus insulin doses are widely calculated from total daily insulin dose (TDD). It is recommended that total daily basal insulin dose (TBD) is 50% of TDD and that the carbohydrate-to-insulin ratio (CIR) equals 500 divided by TDD. We recently reported that basal insulin requirement is approximately 30% of TDD. We therefore investigated CIR after adjustment of the proper basal insulin rate. Forty-five Japanese patients with type 1 diabetes were investigated during several weeks of hospitalization. The patients were served standard diabetes meals (25-30 kcal/kg of ideal body weight). Each meal omission was done to confirm basal insulin rate. Target blood glucose level was set at 100 and 150 mg/dL before and 2 h after each meal, respectively. After the basal insulin rate was fixed and target blood glucose levels were achieved, TBD, CIR, TDD, and their products were determined. Mean (±SD) blood glucose levels before and 2 h after meals were 121±47 and 150±61 mg/dL, respectively. TDD was 31.5±9.0 U, and TBD was 27.0±6.5% of TDD. CIR×TDD of breakfast was significantly lower than those of lunch and supper (288±73 vs. 408±92 and 387±83, respectively; P<0.01). CIR has diurnal variance and is estimated from the formula CIR=300/TDD at breakfast or CIR=400/TDD at lunch and supper in type 1 diabetes patients. These results indicate that the insulin dose has been underestimated by using previously established calculations.

The Number of Basal Rates Required to Achieve Near-Normal Basal Glucose Control in Pump-Treated Type 2 Diabetes

It has been reported that most pump-treated patients with type 2 diabetes require only two or fewer basal rates. Using daily continuous glucose monitoring (CGM)-directed titration, this premise was re-evaluated at near-normal glycemic control. Thirty subjects who were insulin-naive (n = 10), on basal insulin (n = 10), or on basal-bolus insulin therapy (n=10) ate a fixed diet. The basal rate was started as a single rate and then adjusted to a basal glucose goal of 70-130 mg/dL. The insulin-to-carbohydrate ratio (ICR) (in g/U) was adjusted to 2-4-h postmeal CGM glucose goal of 80-120% of premeal glucose. The mean (SE) CGM basal glucose was 99.9 (4.9) mg/dL, and 4.5% (1.4%) of the readings were <70 mg/dL. The mean 2-4-h postmeal glucose was 113.3% (4.8%) of the premeal glucose. Only six subjects (20%) required two basal rates, while the remainder needed only one. The mean (SE) dosing relationships were as follows: total basal dose (TBD) (in U/day) = 0.226(0.018) × weight (in kg); TBD (in U/day) = 0.339(0.012) × total daily dose (TDD) (in U/day); ICR (in g/U) = 126(8)/TBD (in U/day); and ICR (in g/U) = 365(14)/TDD (in U/day). This study confirms that one basal rate is adequate for the majority of subjects with type 2 diabetes. The mathematical proportionality between dosing factors closely agrees with those obtained in CGM-titrated pump-treated type 1 diabetes but differs from those derived from clinical studies in which insulin titration was based on infrequent self-monitored plasma glucose testing and while on an unstructured diet.

How Much do I Give? Dose Estimation Formulas for Once-Nightly Insulin Glargine and Premeal Insulin Lispro in type 1 Diabetes Mellitus

To evaluate the mathematical relationships between dosing factors in type 1 diabetic patients using multiple daily injections. In this single-center, prospective study in type 1 diabetic patients, the basal continuous glucose monitoring glucose target was less than 130 mg/dL with fewer than 10% of 24-hour readings at less than 70 mg/dL. Basal glucose for the 4-hour meal periods was obtained from once-daily serial meal omissions. On an isocaloric, 50% carbohydrate, fixed diet, the insulin to carbohydrate ratio was adjusted to achieve a 2- to 4-hour postbolus glucose value within ±20% of premeal glucose. For determining dosing formulas, the slope of the linear regression line comparing the variables of weight, total daily dose (TDD), total basal dose (TBD), insulin-to-carbohydrate ratio (ICR), and correction factor (CF) was determined. Forty-nine patients were included. Titrating insulin glargine to the morning glucose led to hypoglycemia during the rest of the day (2 PM to 4 AM). Therefore the basal glucose target was the nondawn phenomenon portion of the day. The resulting estimation formulas could be rounded to the following: TBD = 0.2 x weight (kg) | TBD = 0.33 x TDD | 90/TBD = ICR = CF/4.5. Smaller insulin glargine doses to achieve control are in contrast to those much larger doses reported in clinical trials in multiple daily injection-treated type 1 diabetes in which the morning fasting glucose is the basal insulin target.

Development of Optimal Kids Insulin Dosing System Formulas for Young Children with Type 1 Diabetes Mellitus

This study was designed to develop predictive formulas for precise insulin dosing in young children with type 1 diabetes (T1DM). Consecutive 1-year data from a group of 14 young patients (eight girls, six boys) 3.9 ± 0.8 years old with diabetes duration of 2.0 ± 0.8 years, transitioned from multiple daily injections (MDI) to continuous subcutaneous insulin infusion (CSII), were analyzed to identify parameters governing optimal insulin dosing. Body mass index (BMI), total daily dose (TDD), total basal dose, insulin-to-carbohydrate ratio (ICR), correction factor (CF), and mean amplitude of glycemic excursion (MAGE) by continuous glucose monitoring and hemoglobin A(1c) (HbA(1c)) level were evaluated at baseline and every 3 months. The slopes of CF versus 1/TDD, bolus versus TDD, ICR versus 1/TDD, and CF versus ICR were determined. Kids Insulin Dosing System (KIDS) slope constants at follow-up were associated with MAGE compared with baseline (P<0.0001) without significant changes in BMI (16.6 ± 1.5 vs. 16.7 ± 1.4 kg/m(2)) and HbA(1c) values (8.0 ± 0.50% vs. 7.8 ± 0.40%). The relationship between CF and TDD changed significantly during CSII compared with baseline MDI (P<0.0001), whereas the coefficients for ICR and TDD relationship remained relatively unchanged. The KIDS formulas estimated TDD=0.74×body weight, total basal dose=0.28×TDD, CF=2,800/TDD, and ICR=13.5×body weight/TDD. The interrelationships among ICR, CF, TBD, and TDD remained stable on CSII and were accompanied by decreased glycemic excursions. The KIDS formulas may yield consistent and easy estimates of insulin dosing factors in very young patients with T1DM.

How Much Do I Give? Reevaluation of Insulin Dosing Estimation Formulas Using Continuous Glucose Monitoring

To reevaluate current formulas for determining the total basal insulin dosage (TBD), insulin to carbohydrate ratio (ICR), and correction factor (CF) from weight or total daily dosage (TDD) in pump-treated patients with type 1 diabetes mellitus. From a post hoc analysis of data from 4 previously published studies, subjects who met the inclusion criteria were selected. No subject was duplicated. For all studies, the basal glucose target was to have fewer than 20%of glucose readings greater than 170 mg/dL and to have 10% or fewer glucose readings less than 70 mg/dL. Bolus insulin was adjusted to achieve a 2- to 4-hour postbolus glucose value within 20% of the premeal glucose (ICR) or 80 to 120 mg/dL from premeal hyperglycemia (CF). In the first 2 studies, dosing titration by CGM was performed from 72-hour CGM tracings every week to every 6 weeks. In the other 2 studies, 24- to 72-hour CGM downloads and insulin adjustments were done each weekday. Of 101 participants, 61 (59% women) met the inclusion criteria. Estimation formulas could be rounded to the following: TBD = 0.2 x weight (kg) or 0.4 x TDD; ICR = 300 / TDD; and CF = 1500 / TDD. In particular the relationship between all 3 dosing factors could be represented as 100 / TBD = ICR = CF / 4.5. These results suggest that current formulas give a higher estimate for TBD and a lower estimate for the bolus dose.

Minimal Reduction in Insulin Dosage with Pramlintide Therapy When Pretreatment Near-Normal Glycemia is Established and Square-Wave Meal Bolus is Used

To evaluate the effect of near-normal glucose control before initiation of pramlintide therapy and square-wave meal bolus on self-reported hypoglycemia and the percentage change in dosing parameters after attaining the maximum pramlintide dosage. In this prospective study, insulin pump-treated patients with type 1 diabetes had insulin dosages optimally titrated on the basis of daily continuous glucose monitoring (CGM). Pramlintide therapy was initiated, and the dosage was increased 15 mcg/meal per week. Insulin dosage was adjusted during 30-minute visits after review of self-monitored blood glucose records, adverse effects, and hypoglycemia diary. Within 2 weeks of achieving a pramlintide dosage of 60 mcg/meal, the second CGM-guided insulin dosage adjustment was done. The primary end point was the percentage change in total basal insulin dosage (TBD) from baseline. The secondary end points were the percentage change in the insulin to carbohydrate ratio (ICR) and the assessment of symptoms of nausea and hypoglycemia during the pramlintide dosing escalation. Nine patients were enrolled. The difference between before and during CGM-guided insulin dosing was a mean (+/- standard deviation) TBD change of -11.2 +/- 13.2% (P = 0.023) and mean ICR change of 7.8 +/- 13.4% (P = 0.053). Pramlintide was well tolerated and resulted in decrease in weight and hemoglobin A1c values. Hypoglycemia occurred in 6 patients during the study; the assistance of another person was not required in any of these cases. No hypoglycemia was reported in the first week of starting pramlintide. Mild to moderate nausea was reported in 6 patients during the titration phase. Patients with near-normal glucose control who use a square-wave bolus may not need initial bolus dosage reduction. With weight loss, small adjustments in both TBD and ICR may be required. Greater incidence of hypoglycemia seen in previous studies may in part be due to mismatched insulin dosing.

Analysis of Guidelines for Basal-Bolus Insulin Dosing: Basal Insulin, Correction Factor, and Carbohydrate-To-Insulin Ratio

To analyze and compare the underlying mathematical models for basal-bolus insulin-dosing guidelines in patients with type 1 diabetes in a retrospective controlled study. Algebraic model-development yielded several systems of models with unknown constants, including 3 systems currently in use. These systems were compared for logic and consistency. One of these systems was the accurate insulin management (AIM) system, which we developed in the setting of our large endocrine practice. Our database consisted of retrospective clinical records for a 7-month period. During this time, correction factor (CF), carbohydrate-to-insulin ratio (CIR), and basal insulin were being adjusted incrementally by titration. The variables studied were height, body weight in pounds (BWlb), CF, CIR, hemoglobin A1c (A1C), basal insulin, and 6-day mean total daily dose of insulin (TDD). The values of the variables used in the study were those determined on arrival of the patients at the office. The last 6 TDDs were entered into the database, and the mean was calculated by formulas within the database. We sorted our database into 2 groups, a well-controlled test group (n = 167; A1C <or=7%, time on pump >180 days, no severe hypoglycemic events since the last office visit, and C-peptide level <or=0.5 ng/mL) and a control group with poor control (n = 209; A1C >7% or time on pump <180 days). We obtained one office visit per patient, as follows: from the test group, we chose the visit with the lowest A1C value; from the control group, we chose one visit by use of a computer's random number generator. A significant difference was demonstrated between the correlation constants of the test group versus the control group by performing T tests between the means and F tests between the standard deviations. The least squares estimates of the correlation constants from the test group were recommended in the guidelines, in place of the means, to gain accuracy. By these methods, the guidelines used by the patients with good glycemic control are made available for all patients. With use of the AIM system, the TDD for continuous subcutaneous insulin infusion = 0.24 * BWlb; basal insulin = 0.47 * TDD; CF = 1,700/TDD; and CIR = 2.8 * BWlb/TDD. Three mathematical models for CIR are presented, with a rationale for supporting one of them (the AIM model). This model, together with 3 related AIM models, when provided with statistically correlated constants, constitutes the AIM system of guidelines, a consistent and convenient means of estimating insulin-dosing variables for patients with type 1 diabetes.