Blood sugar behavior is very complicated. It is affected by
- Current blood sugar (complicated by the possible presence of ketones if the patient is hyperglycemic)
- recent food out to several hours depending on the type and how much
- recent fast acting insulin (with variety and patient dependent reaction profiles between 45 minutes and two hours long. Oh, and delivery mechanism)
- long-acting insulin out past 12 hours (again patient and variety dependent)
- activity levels
- stress levels
- illness
- basal insulin rate if the patient wears a pump
- ad nauseum
Very hard problem. Any heuristic---any heuristic---you chose would be highly misleading. So short answer:
Don't do it.
This comes, in part, from having compared a diabetic's 24-hour continous glucose log with the ~10 finger pricks taken during the same time. I.e. my suggestion is data driven.
Edit: Evidently I didn't make myself clear.
You can't even get close.
Nothing you can do with finger prick data can be remotely reliable.
Connecting the dots with any lines (even straight segments) is just plain wrong. It doesn't reflect reality. Not even a little bit.
I'm an experimental particle physicist. Complicated data sets are what I do. There is a diabetic in my life (did you guess?). This matters to me.
But I've seen the high frequency data logs, side-by-side with a log of the days finger-pricks, exercise, food, and insulin.
If you could get every-fifteen-minutes data, I'd say go ahead and use a spline. It won't be dangerously misleading. But, if you have 6-10 measurements across the day, you know nothing.
Good news: continuous monitoring is coming down in price. It's out of the lab and available with some pumps even now.
For those who aren't familiar with this: compliant diabetic patients do (results of extremely unscientific polling) 4-6+ glucose tests a day as a matter of course, and several additional ones in the 1-2 hours following any unexpected excursion (they get physical symptoms that allow them to detect severe excursions).
This serves to give the patient a rough idea of how they are doing at controlling their glucose levels, but they also go to a lab to get a Hemoglobin A1C drawn every quarter (or so). The A1C result is dependent mostly on their average blood glucose.
I've talked to people who clocked in a 80-110 (quite favorable numbers) four times a day for months, and got back an A1C suggesting an average above 150 (not desirable at all). Presumable they were going high in the night. And I've heard similar stories from people who we probably going low---very low---in their sleep.
The lesson is:
Finger prick readings have their place, but don't try to extrapolate them to times not well sampled.