A semilogarithmic scale for glucose provides a balanced view of hyperglycemia and hypoglycemia

Abstract

Objective: It would be desirable to improve the ability of physicians and patients to identify hypoglycemic episodes when viewing displays of glucose by date, time of day, or day of the week.

Research design and methods: A logarithmic scale is utilized for display of glucose versus date and time of day using a range of 40 to 400 mg/dl. Several plausible alternatives are considered for transformation of the glucose data.

Result: Use of a semilogarithmic plot triples the percentage of the vertical axis allocated to hypoglycemia (e.g., 40-80 mg/dl) from 10% to 30.1% while compressing the hyperglycemic region. The log scale improves the symmetry of the glucose distribution. Transformations were evaluated corresponding to the Schlichtkrull M(100) value, the high blood glucose index/low blood glucose index of Kovatchev and associates, an index of glycemic control developed by the present author, and the GRADE score of Hill and coworkers. Results are similar for all four transformations. This approach is applicable both to self-monitoring of blood glucose (SMBG) and continuous glucose monitoring (CGM). Based on preliminary results, it is proposed that the log transform could potentially facilitate analysis of glucose patterns and may facilitate rapid and consistent detection and appreciation of the severity and consistency of hypoglycemic episodes, even in the presence of complex overlapping patterns commonly observed in both SMBG and CGM glucose profiles.

Conclusion: Display of glucose on a logarithmic scale can potentially improve the accuracy of analysis and interpretation of popular methods for graphic display of glucose values. Device manufacturers should consider including options for semilogarithmic display of glucose on SMBG meters, CGM sensors, and software for retrospective analyses of glucose data.

Figure 1.

(A) Display of glucose by date for CGM data of one patient for 8 days (linear scale). Vertical axis, glucose (mg/dl); horizontal axis, date. The daily mean glucose is also shown for each day (pink line). (B) Display of glucose profile by time of day for the data of 1A (linear scale). Vertical axis, glucose (mg/dl); horizontal axis, time of day. (C) Glucose by date with glucose displayed on semilogarithmic scale for the same data as 1A. Vertical axis, glucose (mg/dl) on logarithmic scale; horizontal axis, date. (D) Glucose profile by time of day (glucose displayed on logarithmic scale) for the same data as shown in 1B. Vertical axis, glucose (mg/dl) on logarithmic scale; horizontal axis, time of day. The target range of 80–140 mg/dl is shaded light green with red horizontal lines at the upper and lower limits of that range. Values of 50, 100, 200, and 400 mg/dl are emphasized because they are equally spaced on a logarithmic scale. Glucose is shown in units of mg/dl on the left vertical axes and in units of mmol/liter on the right vertical axes of 1C and 1D.

Figure 2.

Comparison of several types of transformations of the glucose scale. Abscissa, glucose on semilogarithmic scale from 40 to 400 mg/dl; ordinate, transformations, including logarithmic transform with an arbitrary linear scaling factor, G' = 200*log(glucose/126.5) (black straight line, no data points); use of a criterion that glucose should be in the range 80 to 200 mg/dl (pink step function); IGC1 (yellow, black diamonds) using parameters LLTR = 80, ULTR = 140, b = 2.0, a = 1.1, and c = d = 30; IGC₂, (green, open triangles) using parameters LLTR = ULTR = 100 mg/dl (a target level of 100), b = 1.8, a = 1.5, c = d = 30; Schlichtkrull M_R index with R = 100 mg/dl (M₁₀₀, red curve with black closed circles), Kovatchev and colleagues' HBGI and LBGI transformations (blue curve with closed black squares with superimposed white plus sign), and Hill and coworkers' GRADE score transformation (brown curve with superimposed closed brown circles) multiplied by a constant scaling factor of five to facilitate comparison with the other transformations. Of the transformations included here, the GRADE transformation most closely approximates a simple log transformation.