Model based insulin absorption into intravenous infusion sets in adult and neonatal intensive care unit’s

10th IFAC Symposium on Biological and Medical Systems 10th IFAC Symposium on Biological and Medical Systems São Paulo, Brazil, September 3-5, 2018 10th Paulo, IFAC Symposium on Biological and Medical Systems Available online at www.sciencedirect.com São Brazil, September 3-5, 2018 10th Paulo, IFAC Symposium on Biological and Medical Systems São Brazil, September 3-5, 2018 São Paulo, Brazil, September 3-5, 2018

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IFAC PapersOnLine 51-27 (2018) 24–29

Model based insulin absorption into intravenous infusion sets in adult and Model based insulin absorption into intravenous infusion sets in adult and neonatal intensive care unit’s Model based insulin absorption into intravenous infusion sets in adult and Model based insulin absorption into intravenous infusion sets in adult and neonatal intensive care unit’s neonatal intensive care unit’s Anna R. intensive Hardy*. J. Geoffrey. Chase* neonatal care unit’s

Anna R. Jennifer Hardy*. L. J. Geoffrey. Knopp*. Chase* Anna R. Jennifer Hardy*. L. J. Geoffrey. Knopp*. Chase* Anna R. Jennifer Hardy*. L. J. Geoffrey. Chase* Knopp*.  Jennifer L. Knopp*. * *Department of Mechanical Engineering, Centre for Bio-Engineering, University of Canterbury, Private Bag 4800,  * *Department of Mechanical Engineering, Centre for Bio-Engineering, University of Canterbury, Private Bag 4800,  Christchurch 8140, New Zealand * *Department of Mechanical Engineering, Centre for Bio-Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand * *Department of Mechanical Engineering, Centre for Bio-Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand Christchurch 8140, New Zealand Abstract: Abstract: Abstract: Introduction: While still a contentious topic, some studies suggest regulating blood glucose (BG) Abstract: Introduction: still a improves contentious topic,outcomes. some studies regulating have bloodbeen glucose (BG) between 4.4 andWhile 8.0 mmol/L clinical Modelsuggest based approaches successful Introduction: While still a improves contentious topic,outcomes. some studies suggest regulating have bloodbeen glucose (BG) between 4.4 and 8.0 mmol/L clinical Model based approaches successful at modulating BG inmmol/L intensive care unit (ICU)outcomes. settingstudies using insulin. However, absorption by Introduction: While still a improves contentious topic, some suggest regulating insulin bloodbeen glucose (BG) between 4.4 and 8.0 clinical Model based approaches have successful at modulating BG inmmol/L intensive caretheunit (ICU)outcomes. setting using insulin. However, insulin absorption by infusion set materials may reduce quality of control. Previous studies highlight the occurrence of between 4.4 and 8.0 improves clinical Model based approaches have been successful at modulating BG in intensive care unit (ICU) setting using insulin. However, insulin absorption by infusion setabsorption, materials mayare reduce the quality control.using Previous studies the absorption occurrence of significant but highly variable inof methodology and results. Nohighlight study insulin considers or accounts at modulating BG in intensive care unit (ICU) setting insulin. However, by infusion setabsorption, materials but mayare reduce qualityinof control. Previous studies highlight the occurrence of highlythe variable methodology and results. NoThis study considers or accounts significant for all potential variables affecting insulin absorption by infusion tubing. study willoccurrence identify and infusion setabsorption, materials mayare reduce the quality of control. Previous studies highlight the of significant but highly variable in methodology and results. No study considers or accounts for all these potential variables affecting insulin absorption by potential infusion tubing.No This study will identify and model variables tobut better understand and for insulin losses. significant absorption, are highly variable inaccount methodology and results. study considers or accounts for all potential variables affecting insulin absorption by infusion tubing. This study will identify and model variables to better understand account for for all these potential variables affecting insulinand absorption by potential infusion insulin tubing.losses. This study will identify and model these variables to better and account for potential insulin losses. Modelling Methodology: Theunderstand insulin absorption model developed is a compartment model based on model these variables to better understand and account for potential insulin losses. Modelling Methodology: The insulin absorption model developed is a compartment model conservation of mass. Literature data was collected and the model was validated based on fitting based error. on K1 Modelling Methodology: The insulin absorption model developed isvalidated a compartment model based on conservation of mass. Literature data was collected and the model was based on fitting error. K1 absorption rates of insulin into the tubing and the rate of insulin release into free flow, and K 2 are the Modelling Methodology: The insulin absorption model developed is a compartment model based on conservation ofabsorption mass. Literature data was collected the and model validated based on fitting error. K11 insulin into the and tubing thewas rate of release into free flow, and K2 are the and K2Literature andrates wereof identified iteratively using Matlab to fit theinsulin model to literature data. respectively. K conservation of1 mass. data was collected and the model was validated based on fitting error. K 22 are the absorption rates of insulin into the tubing and the rate of insulin release into free flow,1 and K and K2 andrates wereof identified iteratively usingand Matlab to fitof theinsulin modelrelease to literature data.flow, respectively. K1absorption are the insulin into the tubing the rate into free and K 2 were identified usingdata Matlab thePVC modeltubes to literature data. respectively. 1 1 and K2 2 andThe Results and K Discussion: model fit theiteratively experimental for to PEfitand well, with a max were identified iteratively usingdata Matlab to fitand thePVC modeltubes to literature data. respectively. K 1 and K2 andThe Results and Discussion: model fit the experimental for PE well, with a max percentage difference of 8.54% between the fitted and experimental data. The model was more inaccurate Results anddifference Discussion: The model fit the the fitted experimental data for PE and PVC tubes well, with a max percentage of 8.54% between and experimental data. The model was more inaccurate values identified were similar magnitude for both materials, K for PVC tubes than PE tubes. K 1 2 awas Results anddifference Discussion: The model fit the the fitted experimental data for PE and PVC tubes well, with maxa percentage of 8.54% between and experimental data. The model was more inaccurate values identified were similar magnitude for both materials, K was a for PVC tubes than PE tubes. K 1 2 similar magnitude for PVC, but not PE. Limited data from other studies meant they could not be used percentage difference of tubes. 8.54%Kbetween the fitted and experimental data. Thefor model more inaccurate identified were similar magnitude bothwas materials, K22 wastoa for PVC tubes than PE 1 1 values similar magnitude for PVC, but not PE. Limited data from other studies meant they could not be used to test the model more completely. The assumption that the concentration of insulin in the syringe is what is identified were similar for they both could materials, K2 wastoa for PVCmagnitude tubes thanforPEPVC, tubes. 1 values similar butKnot PE. Limited data from other magnitude studiesofmeant not be test the model completely. Theof assumption the concentration insulin in carried the syringe istoused what is specified couldmore also be a source variability. More experiments to they be outbe make similar for PVC, but not Limited that data from other studiesneed could not to test the magnitude model more completely. ThePE. assumption that the concentration ofmeant insulin in the syringe is used what is specified could also be a source of variability. More experiments need to be carried out to make relative tovariability. specific that materials, but this first model of carried thissyringe phenomenon is conclusions onmore Kalso 1 and test the model completely. Theofassumption the concentration of insulin in the specified could be Ka2, source More experiments need to be out istowhat make Ka2, source relative specific materials, but this first model this phenomenon is conclusions onsounds, Kalso 1 and fundamentally justifying explicit validation testing.experiments specified could be ofto More need to beof out to make K22, relative tovariability. specific materials, but this first model of carried this phenomenon is conclusions onsounds, K11 and fundamentally justifying explicit validation testing. K2, relative to specific materials, but this first model of this phenomenon is conclusions onsounds, K1 andjustifying fundamentally explicit validation testing. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Glucose Control, Insulin Absorption, Insulin Delivery, Compartment Model, Infusion Tubing fundamentally sounds, justifying explicit validation testing. Keywords: Glucose Control, Insulin Absorption, Insulin Delivery, Compartment Model, Infusion Tubing Keywords: Glucose Control, Insulin Absorption, Insulin Delivery, Compartment Model, Infusion Tubing  Keywords: Glucose Control, Insulin Absorption, Insulin Delivery, Compartment Model, Infusion Tubing  infusion sets leading to poor control and increased risk may  1. INTRODUCTION infusion leading model to poorbased controlresults, and increased result in sets erroneous as this risk factormay is  1. INTRODUCTION infusion sets leading model to poorbased controlresults, and increased risk may result in erroneous as this factor is 1. INTRODUCTION not well recognised, and thus unaccounted for. Critically ill patients are susceptible to stress induced unknown, infusion sets leading to poor control and increased risk may result in erroneous model based results, as this factor is 1. INTRODUCTION unknown, not well recognised, and thus unaccounted for. Critically ill patients are susceptible to stress induced hyperglycaemia, even with previous history of diabetes. result in erroneous model based results, as this factor is Critically ill patients are no susceptible to stress induced unknown, not well recognised, and thus unaccounted for. hyperglycaemia, even the with no previous history of diabetes. Previous studies onrecognised, insulin absorption into infusion for. sets are Some studies suggest regulation of blood glucose (BG) unknown, not well and thus unaccounted Critically ill patients are susceptible to stress induced hyperglycaemia, even the withregulation no previous historyglucose of diabetes. studiesinon insulin absorption into infusion are Some suggest of blood (BG) Previous highly variable their methodology, results and theresets is little levels studies to normo-glycaemic levels (~4.4 and glucose 8.0 mmol/L) hyperglycaemia, even the withregulation no previous history of diabetes. studiesinon insulin absorption into infusion sets are Some studies suggest of blood (BG) Previous highly variable their methodology, results and there is little levels to normo-glycaemic levels (~4.4 and 8.0 mmol/L) agreement on the extent of absorption (Zahid et al., 2008, improves a range of clinical outcomes (Van den Berghe et al., studiesinon insulin absorption into infusion sets are Some studies suggest the regulation of blood glucose (BG) Previous highly variable their methodology, results and there is little levels to normo-glycaemic levels (~4.4 and 8.0 mmol/L) on the extent of absorption (Zahid et al.,iset 2008, improves anormo-glycaemic range of clinical outcomes (Van den 8.0 Berghe et al., agreement Fuloria et al., 1998, Hewson et al., results 2000, Jakobsson al., 2001, Van den Berghe et al., 2006, Chase et al., 2008, highly variable in their methodology, and there little levels to levels (~4.4 and mmol/L) agreement on the extent of absorption (Zahid et al., 2008, improves a range of clinical outcomes (Van den et Berghe et al., Fuloria et al., 1998, Hewson et al., 2000, Jakobsson et al., 2001, Van den Berghe et al., 2006, Chase al., 2008, 2009). Significantly, there is no agreement on whether the Krinsley, 2004, Penning et al., 2015, Reed et al., 2007, agreement on the extent of absorption (Zahid et al., et 2008, improves a range of clinical den et Berghe et al., Fuloria et al., 1998, Hewson et al., 2000, Jakobsson al., 2001, Van den Berghe et outcomes al., 2006,(Van Chase al., 2008, Significantly, there is no agreement on and whether Krinsley, Penning al., is 2015, Reed et al., absorption sites1998, on the tubing reach saturation, whether Uyttendaele et al.,Berghe 2017). Insulin a keyChase input in Fuloria et al., Hewson et al., 2000, Jakobsson et the al., 2001, Van2004, den etet al., 2006, et controlling al., 2007, 2008, 2009). 2009). Significantly, there is no agreement on whether the Krinsley, 2004, Penning et al., 2015, Reed et al., 2007, absorption sites on thethere tubing reach saturation, and whether Uyttendaele et al.,is 2017). Insulin is2015, a key input in controlling the steady states output insulin concentration equals the input glycaecmia, and typically delivered intravenously using a 2009). Significantly, is no agreement on whether the Krinsley, 2004, Penning et al., Reed et al., 2007, absorption sites on the tubing reach saturation, and whether Uyttendaele et 2017). Insulin is a key input in controlling glycaecmia, andal., typically intravenously using a concentration. the steady states output concentration equals input range of different infusion setsdelivered or is lines. absorption sites on the insulin tubing reach saturation, and the whether Uyttendaele et al.,is 2017). Insulin a key input in controlling the steady states output insulin concentration equals the input glycaecmia, and is typically delivered intravenously using a concentration. range of different infusion sets or lines. the steady states output insulin concentration equals the input glycaecmia, and isinfusion typically range of different setsdelivered or lines. intravenously using a concentration. However, there is agreement on the significance of insulin Modelofbased approaches, STAR and eMPC, have been concentration. range different infusion sets or lines. However, is agreement on care the significance of insulin Model based approaches, STAR and eteMPC, have been absorption there in neonatal intensive units (NICU’s). NICU successful (Amrein et al., 2010, Amrein al., 2012, Blaha et Model based approaches, STAR and eteMPC, have been However, there is agreement on care the significance of insulin absorption in neonatal intensive units (NICU’s). NICU successful (Amrein et al., 2010, Amrein al., 2012, Blaha et patients are given small volume, high concentration infusion al., 2009, Blaha et al., 2016, Evans et al., 2011, Evans et al., However, there is agreement on care the significance of insulin Model based approaches, STAR and eteMPC, have been ingiven neonatal intensive units (NICU’s). NICU successful (Amrein et al., 2010, Amrein al., 2012, Blaha et absorption patients are small volume, high concentration infusion al., 2009, Blaha et al., 2016, Evans et al., 2011, Evans et al., and thus insulin may sit in the tubing for longer periods of 2012, Fisk et al., 2012, Stewart et al., 2016). In particular, absorption ingiven neonatal intensive care units (NICU’s).infusion NICU successful (Amrein et al., 2010, Amrein et 2011, al., 2012, Blaha et patients are small volume, high concentration al., 2009, Blaha et al., 2016, Evans et al., Evans et al., and thus insulin may sit in the tubing for longer periods 2012, Fisk et al., 2012, Stewart et al., 2016). In particular, time than adult ICU’s. This difference can significantly alter STAR titrates insulin and nutrition using a well-validated patients are given small volume, high concentration infusion al., 2009, Blaha et 2012, al., 2016, Evans al.,2016). 2011, In Evans et al., and thus insulin may sit in the tubing for longer periods of of 2012, Fisk et al., Stewart et et al., particular, STAR titrates insulin and nutrition using a well-validated than insulin adult ICU’s. This can significantly alter the insulin delivered the fluid delivered, model Fisk based sensitivity metric (Chase et particular, al., 2010, time and thus maycompared sit in difference thetotubing for volume longer periods of 2012, et insulin al., 2012, Stewart et al., 2016). In time than adult ICU’s. This difference can significantly alter STAR titrates insulin and nutrition using a well-validated insulin delivered compared to the fluid volume delivered, model et based insulin sensitivity metric (Chase etet al., 2010, the which in turn increases uncertainty and variability in control. Chase al., 2011, Dickson et al., 2017, Stewart al., 2018, time than adult ICU’s. This difference can significantly alter STAR titrates insulin and nutrition using a well-validated insulin delivered compared to the volumeindelivered, model based insulin sensitivity metric (Chase et al., 2010, the in turn increases uncertainty andfluid variability control. Chase al., 2011, Dickson et al., 2017, Stewart al., 2018, McAuley et al., 2011, Docherty etmetric al., 2011, Lotzetet et al., 2006, the insulin delivered compared to the fluid volumeindelivered, model et based insulin sensitivity (Chase 2010, which which in turn increases uncertainty and variability control. Chase et al., 2011, Dickson et al., 2017, Stewart et al., 2018, McAuley et al., 2011, Docherty et al., 2011, Lotz et al., 2006, Suhaimi al., 2010). However, insulin absorption in2018, ICU which in turn increases uncertainty and variability in control. Chase et et al., 2011, Dickson et al., 2017, Stewart et al., McAuley et al., 2011, Docherty et al., 2011, Lotz et al., 2006, Suhaimi et al., 2010).Docherty However, insulin absorption ICU McAuley al., 2011, et al., 2011, Lotz et al.,in Suhaimi etet al., 2010). However, insulin absorption in2006, ICU Suhaimi © et 2018, al., IFAC 2010).(International However, Federation insulin absorption in Control) ICU 24 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 IFAC of Automatic Copyright © 2018 Peer review©under of International Federation of Automatic 2018 responsibility IFAC 24 Control. Copyright Copyright © 2018 IFAC 24 10.1016/j.ifacol.2018.11.602 Copyright © 2018 IFAC 24

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A number of studies have observed and defined the problem of insulin absorption. However, most studies consider only one problem variable, specifically, insulin concentration, and there are no known attempts to attempt to model absorption dynamics overall. In particular, infusion sets and their setup vary significantly in clinical situations, and thus there are several key variables involved, not all of which are reported in the existing studies. Key variables affecting insulin absorption are: insulin concentration, flow rate, tube length, radius and material, preconditioning (flushing, priming and priming solution) and carrier solution. Two key studies show the effect of some of these variables on insulin absorption, but with different results (Fuloria et al., 1998, Zahid et al., 2008). Fuloria et al (Fuloria et al., 1998) considered the effect of flow rate and preconditioning for PVC and PE tubes on insulin absorption in the NICU and concluded that priming resulted in significant increases in initial insulin recovery. Insulin never reached 100% steady state concentration. However, Zahid et al (Zahid et al., 2008) also considered insulin recovery in tubing based on flow rate and found 100% insulin recovery was achieved for some flow rates.

Fig 1: Basic schematic of insulin absorption model in infusion sets Using a conservation of mass basis, a first model for Figure 1 can be defined: (1) Where V is the volume of the tube (mL), q is the insulin flow rate (mL/hr) and F is the insulin concentration (U/mL) at any given time (t) at the output. However, Equation 1 does not consider absorption. It was thus assumed insulin can be absorbed and released from the “bore” sites and the rate they occur is different yielding:

These two studies highlight the necessity for an insulin absorption model that accounts for all relevant variables. Such a model would help to better understand insulin delivery, and thus glycaemic control. In addition, they could be added to model-based control systems to account for this effect, thus more accurately dosing insulin to patients. This paper develops models to capture these effects and are validated using literature data.

(2) SA is the internal surface area of the tube (m2), B is the number of units of insulin bound to the tube surface (U), K 1 represents the absorption rate of insulin into the tubing and K2 represents the rate of insulin release back into the free flow. From a unit balance on Equation 2 K1 and K2 have units

2. MODELLING METHODOLOGY Insulin absorption has not been previously modelled. Here. compartment models are used based on those described in (Carson et al., 2001, Cobelli et al., 1984). Physiological behaviour has a well-studied historical basis and most models build their root from basic compartment modelling with differential equations. It was assumed that the absorption of insulin into infusion tubing was similar to the transport of material in biological systems so compartment models could be applied.

of

. The rate of change of the number of units bound to

the surface can be represented by: (3)

Importantly, the model presented here does not consider preconditioning with insulin as a variable. Instead, it requires a known output insulin concentration at the beginning of the infusion. Equally, this aspect can be considered an initial condition, or one that can be modelled by the system to obtain an initial condition for the dynamic model presented.

Therefore, Equation 2 simplifies to: (4) A steady state analysis on Equations 2 and 3 gives:

The key variables to be considered are: insulin concentration, flow rate, and tube specifics (length, radius and material). It is likely environmental factors like temperature and humidity would have some effect (Nielsen et al., 2001), but they are assumed controlled or small for this first model. Figure 1 shows the basic model structure.

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K1 and K2 were identified from data using an iterative Matlab (The Mathworks, Notick, MA, USA) method and ODE solver until convergence to a tolerance was met (1 x 10-4). Extra data points were interpolated from the original data. The initial number of bound units was calculated using:

(5) This result is as expected and provides an initial model validation for the overall structure and dynamics. However, several previous studies report insulin concentration not returning to 100% of the input concentration even after long periods, resulting steady state less than 100% (Hewson et al., 2000, Jakobsson et al., 2009). Thus, a saturation on the output concentration may be required. Equally, the known input insulin concentration may be variable based on recent studies of insulin degradation in the pharmacy or logistics (Carter et al., 2017). Hence, in the absence of confirmation regarding this latter effect and potential insulin degradation before use, this study assumes 100% can be reached without further evidence to the contrary. Evaluation of this effect would not change the model but merely its input concentration, so the overall dynamics should still be valid.

(6) Recall that Fo is the insulin concentration in the syringe and Finit is the output insulin concentration after preconditioning. 4. RESULTS AND DISCUSSION Figures 2 through 5 show the plots of the fitted data using the model and the experimental data. Table 2 shows the fitted K1 and K2 values once convergence was met. The overall model fits in these figures is very good indicating all necessary dynamics are present in the model derived.

3. PARAMETER IDENTIFICATION The (Zahid et al., 2008) tests were selected to test the model because it was the only paper that supplied the tube radius and enough data points to fit the model. Due to disagreements between papers it is unclear if the results from these tests are entirely accurate. However, for the purposes of testing the model structure and dynamics it is assumed they are. The key model parameters for each of the four tests presented in this work are summarised in Table 1. The tests took place over 24 hours and the first measurement was taken 30 minutes after the infusion began. The measurement taken at 30 minutes was used as the initial condition for the model. Fig 2: Fitted model to the (Zahid et al., 2008) test 1 data

Table 1: Summary of the key parameters for the (Zahid et al., 2008) tests (#1-4) Test Parameter Flow Rate (mL/hr) Insulin Concentration (U/mL) Tube Material Carrier Solution Syringe Volume (mL) Tube Length (cm) Priming Volume (mL) Tube Radius (mm) Preconditioning

1

2

3

4

0.5

1

0.5

1

1

1

1

1

PE 0.9% saline

PE 0.9% Saline

PVC 0.9% Saline

PVC 0.9% Saline

50

50

50

50

200

200

150

150

1.6

1.6

0.4

0.4

0.9

0.9

0.5

0.5

NA

NA

NA

NA

Fig 3: Fitted model to the (Zahid et al., 2008) test 2 data

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absorption into a PVC tube. The model was effective at capturing the observed dynamics for both materials, and fit the experimental data well with low maximum percentage errors. In particular, it can capture the initial drop in Figure 5 with different values of the parameters, while maintaining their value as K1, K2 > 0, per Table 2. These results further validate the model structure’s ability to capture the observed dynamics using realistic parameter values. For both materials K1 was a similar order of magnitude for PE and PVC, but the two materials had very different K1 values. Similarly, K2 was similar for PVC but not PE. These results may indicate a poor model, other test differences, or errors which are unknown. One limitation is the limited data. Many papers (Fuloria et al., 1998, Hewson et al., 2000, Jakobsson et al., 2009) do not report enough data to model accurately create such a full model, limiting this initial model validation and overall knowledge of the results. Equally, input insulin concentration, FO, may be more variable than previously considered or known based on recent testing of pharmacy insulin (Carter et al., 2017). However, the overall results are good and indicate no significant missing dynamics at this point in model development and validation.

Fig 4: Fitted model to the (Zahid et al., 2008) test 3 data

Table 2: Identified K1 and K2 parameter values and max percentage difference between model and test data Test PE Parameter

PVC

1

2

3

4

K1

1.4

2.9

53.8

46.8

K2 Max Percentage difference between modelled and experimental data

34.1

99.5

25.3

28.5

1.49

0.64

5.6

8.54

A main limitation of this work is the very limited data available to date in this topic. Equally, the experimental data available is very limited in its control of variables and/or reporting of the key variables used in their studies. Thus, there is little data to begin model development. Hence, to overcome this limitation and further verify if this model is a good approximation of insulin absorption in infusion sets more experiments need to be carried out with greater structure and completeness. There is a lack of sufficient data to make any specific conclusions on the relationship between K1 and K2 and infusion set material and structural properties (length, radius and material) based on the limited but encouraging results here. However, sucha reliance, particularly if it was related solely to material properties and type would enable values of K1 and K2 to be developed for any material property used in these infusion sets. Equally, there have not been any known previous studies that investigate various tube lengths or radiuses which are critical and commonly variable parameters in clinical set up, but a validated model could provide these answers.

5. CONCLUSIONS Overall, these results present good fit to observed dynamics with a physics and mass conservation based approach related to known infusion set and infusion parameters. It is possible that this model has errors or limitations that are not yet exposed, but it is to the author’s knowledge the first such model. These results thus justify a more rigorous set of experiments designed to fully validate the model’s potential and limitations.

Fig 5: Fitted model to the (Zahid et al., 2008) test 4 data

Figures 2-5 show the fitted data versus the experimental data given an initial condition. Specifically, Figures 2 and 3 show the absorption into a PE tube and Figures 4 and 5 show the 27

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