Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors

Abstract

Background: Continuous glucose monitors (CGMs) collect a detailed time series of consecutive observations of the underlying process of glucose fluctuations. To some extent, however, the high temporal resolution of the data is accompanied by increased probability of error in any single data point. Due to both physiological and technical reasons, the structure of these errors is complex and their analysis is not straightforward. In this article, we describe some of the methods needed to obtain a description of the sensor error that is detailed enough for simulation. Methods: Data were provided by Abbott Diabetes Care and included two data sets collected by the FreeStyle Navigator™ CGM: The first set consisted of 1032 time series of glucose readings from 136 patients with type 1 diabetes and parallel time series of reference blood glucose (BG) collected via self-monitoring at irregular intervals. The average duration of a time series was 5 days; the total number of sensor-reference data pairs was approximately 20,600. The second data set consisted of 56 time series of glucose readings from 28 patients with type 1 diabetes and a parallel time series of reference BG measured via the YSI 2300 Stat Plus™ analyzer every 15 minutes. The average duration of a time series was 2 days; the total number of sensor-reference data pairs was approximately 7000. Results: Three sets of results are discussed: analysis of sensor errors with respect to the BG rate of change, mathematical modeling of sensor error patterns and distribution, and computer simulation of sensor errors: Sensor errors depend nonlinearly on the BG rate of change: Errors tend to be positive (high readings) when the BG rate of change is negative and negative (low readings) when the BG rate of change is positive, which is indicative of an underlying time delay. In addition, the sensor noise is non-white (non-Gaussian) and the consecutive sensor errors are highly interdependent. Thus, the modeling of sensor errors is based on a diffusion model of blood-to-interstitial glucose transport, which accounts for the time delay, and a time-series approach, which includes autoregressive moving average (ARMA) noise to account for the interdependence of consecutive sensor errors. Based on modeling, we have developed a computer simulator of sensor errors that includes both generic and sensor-specific error components. A χ2 test showed that no significant difference exists between the observed and the simulated distribution of sensor errors and the distribution of errors of the FreeStyle Navigator ( p > .46). Conclusions: CGM accuracy was modeled via diffusion and additive ARMA noise, which allowed for designing a computer simulator of sensor errors. The simulator, a component of a larger simulation platform approved by the Food and Drug Administration in January 2008 for pre-clinical testing of closed-loop strategies, has been successfully applied to in silico testing of closed-loop control algorithms, resulting in an investigational device exemption for closed-loop trials at the University of Virginia.

Assessing Sensor Accuracy for Non-Adjunct Use of Continuous Glucose Monitoring

“…The interpretation of autocorrelation is more complex: roughly, higher autocorrelation would result in longer stretches of sensor errors in the same direction, observed for example during transient loss of sensitivity. 55 To simulate realistic CGM errors, we used 280 actual CGM traces (12 h long) compared with frequent YSI glucose analyzer measurement (every 15 min). Each trace produces a ''signature'' in term of fluctuation of the error in time (time-dependent bias, drift, delay, low-frequency fluctuations, and high-frequency variability).…”

Proposed Procedure to Improve Performance of an Artificial Pancreas and Pancreas Transplant: Review

“…In 1974, Albisser, et al [15] developed the artificial pancreas, but it is only utilised for in clinical studies that time. According to Boiroux, et al [16] the time constant is related to glucose transport from blood to subcutaneous tissues was 15 min, where the parameters for the CGM model is given by Breton and Kovatchev [17]. However, this may not be accurate because the body of human still yet knows what time will respond for allowing the pancreas to give insulin.…”

Modeling the Error of Continuous Glucose Monitoring Sensor Data: Critical Aspects Discussed through Simulation Studies

“…Chase and colleagues, 14 after having pointed out that no studies about sensor error were previously available, proposed to model sensor errors in the simplest way, i.e., a random white noise Gaussian process with a constant coefficient of variation. Breton and Kovatchev 15 proposed a more sophisticated model, where sensor error is not white and also non-Gaussian. In particular, after analysis of a data set from 28 type 1 diabetic subjects consisting of both CGM data (1-minute sampling) and BG references measured frequently in parallel (15-minute sampling), they concluded that the time series of the reconstructed CGM sensor errors can be described as realization of the output of an autoregressive (AR) filter of order 1 driven by white noise.…”

“…In particular, after analysis of a data set from 28 type 1 diabetic subjects consisting of both CGM data (1-minute sampling) and BG references measured frequently in parallel (15-minute sampling), they concluded that the time series of the reconstructed CGM sensor errors can be described as realization of the output of an autoregressive (AR) filter of order 1 driven by white noise. The procedure adopted 15 included two major steps: (a) CGM data were recalibrated by fitting a linear regression model against all the available BG references 16 and (b) in order to take into account distortion due to BG-to-IG dynamics, data fit incorporated the linear time-invariant (LTI) model of BG-to-IG kinetics proposed elsewhere. 17 Notably, in step b, a "population" value of the time constant τ of the model of BG-to-IG kinetics was determined and used for all the 136 individuals of the data set.…”