# Calculating the Glycemic Index using an AUC Glucose/Blood curve?

Does anyone know the mathematics to calculate the Glycemic Index using a AUC Glucose/Blood curve? Is there an article documenting the process? I understand that algebra and integral calculus is involved.

For instance, here is an AUC Glucose/Blood graph of foods against a Glucose reference: I know the definition of the Glycemic Index is the relative rise in blood glucose level two hours after consuming food. It is the area under a 2 hours glucose/blood response curve, following a 12 hour fast and 50 g ingestion of a carbohydrate.

I know Glucose has a Glycemic Index of 100 and I'm unsure how this relates to the integral of (area under) the Glucose curve in the above graph. Also, the Glycemic Index appears to be unit-less, which is further confusing.

I try a rough calculation as follows and the results appear off. I draw a rectangle where the glucose curve is pictured here between 0-60 min, it comes out to 10 mmol/L - 6 mmol/L = 4 mmol/L y-axis, 60 min - 0 min = 60 min x-axis. The resulting area of the GI is 4 mmol/L * 60 min = 220 mmol/L * min and when the GI for Glucose should be 100.

Appreciate guidance here.

Glycemic index is the ratio of blood glucose AUC for some carbohydrate source to a reference source, usually either glucose or white bread.

It's unitless because it's a ratio of numbers with the same units:

(concentration/time) / (concentration/time)

Glucose is defined as having a glycemic index of 100. This is an entirely arbitrary choice. It could have been 1, it could have been 42. 100 is convenient, because it will tend to make most foods have numbers in an easy range, basically the same reason that proportions are often expressed as percentages ("20%" rather than ".20").

To calculate area under the curve from a set of discrete measurements like in the graph above, typically one would use the trapezoid rule though any other integration approximation would give similar results.

An example from the methods section in one paper:

The incremental area under the blood glucose response curves (IAUCG) to test and reference foods were calculated geometrically using the trapezoid rule, ignoring the area below the fasting baseline

So, for the above curve, the first step would be to subtract the fasting baseline which appears to be around 5.8 mmol/L, then use the trapezoid rule to get the AUC in units of mmol/L * time for glucose and each fruit, and express the glycemic index for each as 100 * fruit/glucose.

• For above graph using the glucose curve with two sides, Baseline: 10 mmol/L - 6 mmol/L = 4 mmol/L. Trap Rules: 30 min -0 min * .5(0 mmol/L + 4 mmol/L) = 60 min * mmol/L, 120 min - 30 min * .5(0 mmol/L + 4 mmol/L) = 180 min * mmol/L, 60 min * mmol/L + 180 min * mmol/L = 250 min * mmol / L, then GI for glucose is 100 * (250 min * mmol / L) fruit / (250 min * mmol / L) glucose = 100. Does this calculation appear correct?
– Nick
Nov 18, 2022 at 19:37
• Another question, if the Glycemic Index of a fruit is 50, the fruit/glucose ratio is 1/2. Does this imply the fruit has less glucose over time than the reference glucose? Or perhaps the integral of the fruit extends past the 2 hour window?
– Nick
Nov 18, 2022 at 19:39
• If you go to the paper they report the AUC for glucose to be 259+/-15 mmol x min/L from the actual data, so yes it seems like your 250 is a pretty good estimate from the figure but I'm not going to bother auditing your math in this format. Nov 18, 2022 at 19:45
• Glycemic index is a measure of how much a food affects blood glucose. That's it. If you want to know how much total energy a food contributes, better to look at calories. Glycemic index doesn't measure anything else about metabolism, just blood glucose. Nov 18, 2022 at 19:48
• @Nick Importantly, blood glucose is under homeostatic control, so it's not as if every molecule of glucose in the diet causes a proportional change to blood glucose. GI is just a simple measure based on something easily measurable by a lab (blood/plasma glucose), it's not an attempt to create a full metabolic model. Nov 18, 2022 at 20:00