Insulin activity

[scottleibrand]

How hard would it be to also return the level of insulin activity (first derivative of IOB)? That is the other thing we need to be able to incorporate this into oref0 or similar.

[beached]

All the curves I have seen use body mass as a factor. But a quick hack might be to take the total insulin/DIA and get a U/min or use a normal distribution.

[scottleibrand]

I think it should be literally as "simple" as also returning the derivative of the curves already in this code. (I'd have to get help from WolframAlpha to figure out the derivatives, though. I don't remember any of that from HS calc.) :-)

[bustavo]

If my math is not that bad ( and please don't trust me...test test test ), the derivative should be:
(constant_a * 4) * time_from_bolus^3 + (constant_b * 3) * time_from_bolus^2 + (constant_c * 2) * time_from_bolus + constant_d

Make sure to maintain each constant symbol ( plus or minus )...

[beached]

I am not sure that is the correct way(formula above is fine a_x^b becomes ab_x^(b-1) for each term).

I may be wrong too, but that will give your the instantanious rate of change for iob left at time t in percentage. But don't we really want the amount changed between time t and the last measurement.

[bustavo]

If you need to get the difference of IOB between t and ( t-1 ), then you can do that with the actual formula as it is just manually getting the two values for each time and then subtracting the amounts... is that what you need @scottleibrand?

[kenstack]

as @bustavo says its really asy to do it by simply taking a backward difference or a forward difference
since the step times change I dont use the old value - I simply do

(iob (t+1)-iob(t))/1.0 (you can skip the divide by 1 of course :)) that will give you the local slope of iob, and if you multiple that by your sensitivity at that moment it gives you the iob velocity

[cjo20]

I've been looking at ways of changing the maths behind iob/activity in oref0 to something easier to maintain. As part of the comparison, I looked at the 3 hour formula from here.

I calculated the derivative (everything /100, derivative sign flipped to make the comparison easier) and compared to the existing oref0 results.

poly = -3.203e-9 * pow(i,4) + 1.354e-6 * pow(i,3) - 1.759e-4 * pow(i,2) + 9.255e-4 * i + 0.99951
polyDeriv = 4*3.203e-9 * pow(i,3) - 3*1.354e-6 * pow(i,2) + 2*1.759e-4 * i - 9.255e-4

This was the result - the tail end of the derivative doesn't fit very well with what would be expected. Is this potentially a problem with the polynomials currently being used?

[bustavo]

I think I could explain this with two interesting things I've seen with my own personal data:

1. It could make sense that the curve goes back up in the end if you consider that sensitivity goes up as your bg goes down. If you keep your sensitivity fixed ( ie always 22 points per insulin Unit ), this curve shape could make sense... if you keep your sensitivity variable it doesn't ( ie 15 at 150 / 20 at 120 / 30 at 100 / 40 at 80 / etc ) because the sensitivity variability will already be accounting for the increment you are trying to show with the curve tail going up again.

2. It could make sense that the curve goes back up in the end if you consider that maybe your IOB curve is a little bit longer... @kenstack & I observed that after 180 minutes we had about other 30 minutes of activity ( bg still lowering ) and the only reason we found for this was a longer IOB curve, hence the new IOB 3.5 hour curve which now fits perfectly with the observed data.

I'd like to read @kenstack others opinion on this curve for discussion...

[cjo20]

Just to be absolutely clear, the grey line above is purely from taking the derivative of this polynomial: https://github.com/Perceptus/iob/blob/master/insulin_on_board_pct.js#L71

The orange line is what is currently used by oref0.

I'm not sure where exactly the polynomial equations came from, but if it was just from trying to fit a curve to published ones then I could imagine it would be very easy to get something that looks right but with weird behaviours in the derivatives.

Trying to model things like changing insulin resistance as part of this equation doesn't feel right, mainly because there isn't actually a guarantee that BG will be lower 150 minutes after any bolus.

[bustavo]

Yes there is absolutely no need at all to integrate insulin resistance into this curve as this curve just measures the effect of the insulin.

The referenced polynomial is a fit from Walsh's published insulin activity curves which come from a clamp study where a person got insulin put into its body and then glucose was used to try to level the bg according to the insulin activity... the resulting curve ( glucose used to maintain the bg level with the used insulin ) is this IOB curve.

I don't really still understand why there is a need to get a derivative from IOB curves... could you please explain?