It is helpful for verification.
Gary Schneier calculates with 240 minutes of activity. If my IOB formula (see below) is used the numbers will look slightly different:
Gary Schneier:
90%, 70%, 50%, 30%, 20%, 10%, 5%, 0%
My IOB:
97%, 88%, 74%, 56%, 37%, 19%, 5.5%, 0%
In comparison my IOB is overestimating the numbers in the first phase.
Is this IOB estimate for Regular? Your IOB suggests a peak in insulin at like 4 hours, resulting in a markedly different profile than Scheiner. Scheiner uses a fit which suggests a peak right away for a rapid insulin like Humalog or Novolog. I am not suggesting that your profile won’t be helpful, only that it may be better to adjust the peak to better represent rapid onset and extend the tail to be more conservative. Does that make sense?
Insulin absorption curve from your IOB model:
I also suspect that if you take into account your intended insulin response curve (for Humalog or Novolog), it won’t add up to 100 at all times and then when calculate the area under the curve, it will be different, suggesting that the curves represent markedly different total insulin doses. I think you are quite “godyly”, but you need to obey the “conservation of insulin” principle.
It is one insulin reaction model for all insulin types. You just set the duration and this represents the speed of the insulin. It does not represent different peak behaviours (as simple as some pumps will handle it).
I think your derived “Insulin absorption curve” is not correct. The percent numbers of IOB are for every 1/2 hour. So x must be read like 1=30, 2=60, 3=90, 4=120, 5= 150, 6=190, 7=210, 8=240. Furthermore the insulin absorption curve = 100% - IOB%
This will look like this:
It is conservative. I am sure there is a more appropriate function than f(x)=(x^2-10)^2.
With my current formula I have tried to emulate the IOB curve given in this paper (figure 1):
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2769860
Quote: “The action curves differ from each other by their duration of action and are being used by CSII pump bolus wizards to estimate the available insulin in plasma, modified from Walsh and associates”. This approach is slightly different from the curve of Gary Schneier.
Ok, fair enough, I’m just saying that Scheiners model peaks between like 0.5 hours and 2.5 hours, just like the claimed behavior of Humalog and Novolog. Your model suggests a flattened and delayed peak from 1.5 hrs to like 3 hours. If you have a peak in action that is actually 0.5-2 hrs, just like it says on the box, calculating a different peak with IOB would be an inconsistency. Does that make sense?
I found some interesting data on insulin action profile. It appears that in a rapid insulin, the GIR (glucose infusion rate) , essentially how much insulin enters the blood stream, rises linearly to a peak and then drops off.
I don’t think adding the linear scaling adds anything to your algorithm. In fact I think it makes it very unrealistic. Personally I don’t see any noticeable difference in action between one unit and 10 units of fast acting insulin. And I certainly do not see a factor of 10 difference in action time.
Thanks for thinking about the Dosage adjustment.
You made a good observation by comparing 1 unit to 10 units. I too got the impression that my proposed adjustment is unrealistic. It is just the fact that I experience a significant tail effect with higher dosages. Thus I wanted to have it in the model. Your response shows that there is no formula for all. Some have a prolonged activity with higher dosages and others don’t. It would be best to make this behaviour adjustable (with / without) to our own preferences. For simplicity I decided to begin with the implementation of the version 1 formula without the adjustment. One step after the other…
Great chart. Seeing it this way I can now understand why my formula reminded you of the action curve of regular insulin. I would say that my formula is a compromise - somewhere in between analog and regular.
Maybe some of the more mathmatically skilled people here will find a function that will decline steeper at the beginning than f(x) = (x^2-10)^2 for 0 ≤ x ≤ √10. In future version the user could then select the appropriate function for his metabolism.
I vote for person being able to refine. Yes, larger boluses can be accounted for by changing the DIA as they will last longer and also larger boluses are stronger (less ICR needed). How do you figure out the proper algorhythm? For instance, with Apidra I believe the peak is from one hour and fifteen minutes after bolus lasting until 2 hours and ten minutes to two and a half hours, after which time a lot less drop in blood sugar. How would you individualize it because this may not be the same for everyone. Her DIA on Apidra is always 3.5 hours, sometimes 4, though a lot less drop after hours 2.5.
To match the approach of Gary Schneier I have modified the original function to this:
f(x)=((x+1)^2-11)^2 = percent of active insulin per minute x
This function will reach 0 at x = -1+√11 ≈ 2.32. It is in this context only valid for x between 0 and 2.32.
Adjustment for different duration
The system should ask the user how long 5 units of his bolus insulin will be active.
This parameter k will be in minutes. Let us assume the aswer is that 5 units will last
240 minutes (4 hours): k = 240.
Scale factor c:
240*c = -1+√11 <=> c = (-1+√11)/240 <=> c = 0.009652603
If you like to use the formula f(x) with minutes you will use f(x*c) to adjust for the scale.
Examples
5 units of Apidra will last 240 minutes.
The injected dosage was 5 units.
k = 240 => c = 0.009652603
IOB
f(30*c) = 87.18 => 5 units * (87.18/100) = 4.36 IOB
f(60*c) = 72.36 => 5 units * (72.36/100) = 3.61 IOB
f(90*c) = 56.36 => 5 units * (56.36/100) = 2.82 IOB
f(120*c) = 40.22 => 5 units * (40.22/100) = 2.01 IOB
f(150*c) = 25.08 => 5 units * (25.08/100) = 1.25 IOB
f(180*c) = 12.29 => 5 units * (12.29/100) = 0.61 IOB
f(210*c) = 3.37 => 5 units * (3.37/100) = 0.17 IOB
f(240*c) = 0 => 5 units * (0/100) = 0 IOB
As a result the differences between the insulin action proposed by Gary Schneier and my IOB formula are getting smaller:
That document is very useful. Thanks a lot.
I just read page 5-8 and there I learned that the Duration of Insulin action (DIA) used by pumps IS NOT THE SAME as the insulin level in blood. I made the same mistake:
MANY pumpers and clinicians set the DIA too short.
Clinicians often mistake the insulin level in the blood (3-4 hr duration) for insulin’s glucose-lowering effect that lasts 4-8 hrs. When a pumper finds that recommended bolus doses do not bring high BGs down (often caused by a low basal rate), shortening the DIA is perceived to be easier or safer than raising basal rates or lowering the carb factor.
A DIA time less than 3.5 to 4 hours almost always indicates that basal rates or carb boluses are too low and is usually indicated by an elevated A1c level.
A short DIA forces insulin delivery toward boluses.
This algorhythm will work for Novolog, IMO. I don’t think it will work the same way for Apidra because Apidra is more “front loaded.” Apidra lasts 3.5 hours for her, but lasts shorter period of time in most people, I think. Gary did advise us how to handle left over IOB when we were newly dx’d and on Novolog. For instance, at hour 3 when we took postprandial check if her BS was normal he would advise us to cover each extra unit IOB with 8 grams of carbs to prevent hypoglycemia. With Apidra, at hour 2.5, when we check, I will cover only HALF the insulin on board, i.e, if three units, I will give carbs on a t to 8 basis… 8 grams but only cover 1.5 units, not 3. At the time I asked Gary about Apidra, he had tried it but it did not work very differently for him than Novolog. Our endo said a lot of patients say the same thng. So it would be good if the person could fiddle with the algorhythms, nothing static so that you could figure out that 5 units of insulin would be mostly gone by hour 2.5, with some lasting that last hour and if the bolus was larger, duration would last 4.5 hours. But there is MUCH less drop with Apidra after hour 2.5 than with Novolog for us. Minimed’s algorhyms are definitely off with Apidra, at least for us, but covering half the IOB at the 2.5 hour mark works well. And we do very ofter have to cover the IOB; we have always done this.
Now I know that the formula is not meant to emulate the insulin itself. It is meant to emulate the insulin action. Please look at the powerpoint presentation that Alan has pointed to (look below, page 5-8).
I think the mistake is to think that we need to model the insulin curve. Of course this would be good but until recently the pump manufacturers just used a simple IOB curve. In the pump the user just has to select the Duration of Insulin action (DIA) to make the curve fit to his metabolism. It is just a heuristic but I think for the first iteration I will stick to Walsh.
This means I will take the very first IOB formula because it fits to the algorithms in pumps (at least up to 2005): f(x)=(x^2-10)^2
This function is comparable to the curvelinear model used in the Animas and Paradigm. It will be adjusted to the metabolism of the user by setting the Duration of Insulin Action (DIA). Walsh recommends to set the DIA between 4 to 6 hours to get accurate bolus calculations from pumps.
I’m on Novorapid (Novolog) and an Animas pump.
It was recently recommended (by a DE) that I change my insulin duration to 2.5 hours, even to 2 hours. I was very skeptical, but thought about it some more and realised that I was almost never giving doses over 5 units. More like 2-3 units for a lower carb meal, 5-7 units for the very rare pizza or pasta. I think once in 18 months, have I needed to give more than 6-7 units. So it made sense. I changed to 2.5 hours to start with.
It is working much better for me. If I have to correct say 2-3 hours after a meal (if I haven’t counted carbs properly or if I eat more), or bolus for more food, I’m getting better results. Not sure if I’m game to go for 2 hours just yet.
My basals are pretty much perfect, so for me it’s very different to what Walsh recommends and I can’t see how I wouldn’t go low with larger boluses for meals (if the correct bolus was given in the first place) or more basal.
Dear Holger
To dodge the problem of dose size I tend to inject several times the apidra. For instance if I think I need 15 units ( I am very insulin resistant) I will do 3 times 5 units. I wears out the needle more and you have more holes in the tummy grease but one variable less. Although I do not really know how much difference it makes. The lantus I inject twice/24 hours 25 units in one go again not sure if it would be better with 2 smaller injections. What do you think ? I remember once calculating the time of water droplets to evaporate completely. The math was unbelievably complex and could not do this now. For the mass transfer of insulin there might be some dimensionless number that could maybe give us some insight as to the effect of dose vs absorption time. .
Anthony …what an excellent question ! Love to see Holger’s answer here …
My first post was kind of on this topic, although I’m math-averse so I don’t do that, I did try out splitting N shots for a short period of time (approved for pump—> reread Bernstein—> tried multi-shot approach—> got pump, no more shots…) and I felt like it worked better but I didn’t take notes or anything like that.
This guy I used to play guitar with sometimes had a class where they’d calculate a drop of water from a faucet pretty much for a whole semester. My Tae Kwon Do teacher also talked about noting a drop of water and working on improving the speed of his kicks by racing it. I was able to get to 21 in 10 seconds but not as fast as that!
Although the Minimed’s algorhythms are not at all perfect when using Apidra, they are good enough; same with Animas. You can’t go wrong using a similar model. Each person will, through experience, figure out how much IOB to cover or if they want to increase ICR or not. Only reason we need to figure out IOB often is because we give a more aggressive bolus when at home. Both pumps have good algorhythms. I don’t like Walsh’s model at all, though it is easy to remember.
Only with Novolog or Humalog. Apidra has a shorter DIA. And if you set a duration of 4 hours, the pump will not let you correct highs. Most set the DIA on the pump to 3 hours so the pump will figure out the calculations and let them correct.
My “workaround” for that is also to hit it w/ the 5-10 g of carbs I missed that caused the high in the first in the first place.