Continuous Subcutaneous Insulin Infusion (CSII) Pumps are not “truly” Continuous: Web Based Simulations of Different Pumps at Low Basal Rates

When Continuous Subcutaneous Insulin Infusion (CSII) pumps deliver a continuous basal rate of fast acting insulin, they are not truly "continuous": they are not always active and turning, administering a truly continuous flow rate of insulin all the time. Instead, a series of discrete pulses or boluses are given periodically based on the desired basal rate, the “stroke volume” and “sleep period” of the pump due to the electromechanical attributes of the pump as well as to conserve battery. The stroke volume is the minimum amount of insulin that can be given by the pump at any point in time. The sleep period is a period where the pump does nothing and operates in low power mode. The sleep mode also makes the pump quiet and inconspicuous most of the time. Three major diabetes technology companies I had worked for in the past had asked me to simulate how different stroke volumes and sleep times affect the plasma insulin concentration for different desired basal rates based on a pharmacokinetic model. Then, I had coded and designed these simulators with a combination of either LabVIEW, Matlab, Java and/or Python that included a GUI for the end user.

Here, I have simulated the model with WikiModel just by entering model equations and parameters without any code in a web browser that anyone can interact with: http://www.wikimodel.com/workspace/5081879929683968/Pulsatile Versus Continuous Delivery. A screenshot of the model equations and parameters is shown in Figure 1. The model is based on a two-compartment model consisting of two single order differential equations (each with their own time constant, tau_1 and tau_2) cascaded together that describes the transport of insulin via subcutaneous delivery to the plasma. This model is a subset of the virtual patient model described by Sami Kanderian, Stu Weinzimer, Gayane Voskanyan, and Garry M. Steil (1) where the average values of the larger time constant, tau_1 and smaller time constant tau_2 were identified as 70 ± 28 min and 45 ± 20 min respectively. This two-compartment differential equation model accepts insulin inputs as true continuous delivery as well as series of pulses or boluses. The model is simulated twice; the first five equations in Figure 1 simulate a truly continuous basal rate (black lines) for reference, and the remaining equations simulate a series of boluses calculated at specific times by a CSII pump in order to achieve the desired basal rate based on its specified stroke volume and sleep time (tan lines).  

Figure 1: WikiModel web page with a model simulating the pharmacokinetics of insulin delivery. Model equations and parameters are shown on the left, simulated output variables are plotted on the right. Both true continuous insulin delivery (black) and a series of intermittent boluses (tan) are simulated with a desired basal rate of 0.05 U/hr. Here the tan lines are simulating the Omnipod pump that has a stroke volume of 0.05U and a sleep period of 1 min. The first plot contains the simulated plasma insulin, profiles (uU/ml), the second plot contains the series of boluses (U) in order to achieve the desired basal rate, the third plot contains the accumulated residual over time. The fifth plot shows the true continuous input (U/hr) which is only there for the black plot.

The stroke volume and sleep time along with the desired basal rate parameters can be altered to observe the resulting plasma insulin concentration profile and how it compares to a truly continuous pump. The stroke volume and sleep periods for several insulin pumps are shown in Table 1.

Table 1: stroke volumes and sleep times of several insulin pumps

Each time the pump briefly wakes up, it may or may not deliver one or more strokes depending on the residual insulin to be delivered based on the desired basal rate to give BolusU_b units of insulin. The residualU is incremented by desiredBasalUPerHr*Δt/60, where desiredBasalUPerHr is the desired basal rate in Units per hour and Δt is the elapsed time in minutes between simulated data points. When the pump wakes up, if residualU exceeds the stroke volume of the pump the pump delivers one or more strokes of insulin, as many as required to reduce residualU as close to 0 as possible. A factor is included to account for bit discretization of the accumulated residual.

A comparison of the different pump outputs as well as a truly continuous pump for different desired basal rates are shown in Figure 2 by running simulations for various desiredBasalUPerHr, strokeVolumeU, and sleepTime values. Note that the simulated results for the Omnipod and the YpsoPump are identical for the chosen basal rates. Despite the Omnipod having a shorter sleep time (1 min versus 3 min), all strokes happened to be administered at 3-minute multiples.

Figure 2: Simulated plasma insulin concentrations for various desired basal rates (rows) delivered by different insulin pumps as well as true continuous insulin infusion for reference. Plots on the right are zoomed in to the time period from 480 min to 600 min with the insulin concentration values at a larger scale to show the size of the pulsatile fluctuations relative to the true steady state value.

All simulations assume a starting plasma insulin concentration of 0 uU/ml where the pumps desired basal rate is set at time t=0 min. As shown, the larger the ratio of stroke volume relative to the desired basal rate, the greater the difference in plasma insulin concentration as a result of the series of boluses delivered by the pump and the “true continuous” value. Note that the clearance parameter (ml/min) inversely scales the plasma concentration output (uU/ml) but different clearance values do not change the relative magnitude of the oscillations of plasma insulin concentration undulations from CSII pump delivery to the true continuous steady state value. The true continuous steady state value can be calculated as the ratio of the basal rate to clearance (with some unit conversions to get the result in uU/ml). The size of the oscillations (peak to valley magnitude) relative to the true continuous steady state value for different pumps at different basal rates are shown in Figure 3.

 Figure 3: Plasma insulin oscillation swing size relative to true steady value simulated for different pumps at various basal rates. The minimal selectable basal rate for each pump is indicated with an Asterix.

The maximum deviation from the true continuous steady state value is approximately half the oscillation size. As evident in Figure 2, for any pump, as the basal rates increase, the relative magnitude of the oscillations decreases. For any basal rate, the t:slim X2 pump has the lowest simulated oscillation magnitude of all the pumps due to the fact that it has the lowest stroke volume, however all pumps have small plasma insulin concentration oscillations at their respective lowest selectable basal rate (denoted by the Asterix). So why even do this exercise then? Well, here we did the experiment backwards; when designing a new pump, such simulations would help us define those appropriate design parameters in order to achieve oscillations no bigger than a specified magnitude for the lowest basal rate users for a target pediatric patient group with a very low basal requirement, for example as described by Christof Klinkert, Bettina Heidtmann, Matthias Grabert, and Reinhard Holl (2). On the flip side, what this shows us is that for users that administer 0.1 Units of basal insulin or more per hour, there’s not much benefit in developing a pump with a stroke volume of less than 0.05 U considering the added cost and complexity of parts in order to achieve a finer resolution. 

References

1.      Kanderian SS, Weinzimer S, Voskanyan G, Steil GM. Identification of intraday metabolic profiles during closed-loop glucose control in individuals with type 1 diabetes. J Diabetes Sci Technol. 2009 Sep 1;3(5):1047-57. doi: 10.1177/193229680900300508. PMID: 20144418; PMCID: PMC2769900.

2.      Klinkert C, Bachran R, Heidtmann B, Grabert M, Holl RW; DPV-Initiative. Age-specific characteristics of the basal insulin-rate for pediatric patients on CSII. Exp Clin Endocrinol Diabetes. 2008 Feb;116(2):118-22. doi: 10.1055/s-2007-990296. Epub 2007 Oct 31. PMID: 17973210.