IN-­‐SILICO COMPARISON OF INTRAVENOUS, INTRAPERITONEAL, SUBCUTANEOUS AND COMBINED APPROACHES FOR CLOSED-­‐LOOP GLUCOSE CONTROL Anders Fougner1,2,5, Konstanze Kölle1,2,5, Hans Erik Frøyen1,2, Reinold Ellingsen1,3,7, Sven Magnus Carlsen1,4,6, and Øyvind Stavdahl1,2 anderfo@itk.ntnu.no konstako@itk.ntnu.no hanserik.froyen@gmail.com reinold.ellingsen@ntnu.no sven.carlsen@ntnu.no ostavdahl@itk.ntnu.no 1Ar4ficial Pancreas Trondheim – The APT research group (www.apt-­‐norway.com) Norwegian University of Science and Technology (NTNU), Trondheim, Norway 2Department of Engineering Cyberne4cs 3Department of Electronics and Telecommunica4ons 4Department of Cancer Research and Molecular Medicine MOTIVATION 5Helse Midt-­‐Norge – The Central Norway Regional METHODS Health Authority, Norway 6St Olavs University Hospital, Trondheim, Norway 7GlucoSet AS, Trondheim, Norway Control methods •  Manually tuned propor4onal-­‐integra4ve-­‐deriva4ve (PID) control. Only tested for a double IP approach. Modeling •  Model-­‐predic4ve control (MPC). Tested for all approaches, including •  Modular mathema4cal model. combined approaches (e.g. IV insulin infusion and IP glucose sensing). •  Glucose and insulin dynamics based on •  The “controller model” used by MPC is simplified/linearized compared to exis4ng models [3,4]. the simulator model. Addi4onally, some parameters are perturbed in the •  Extended with IP insulin infusion [5]. simulator model: Insulin sensi4vity, insulin absorp4on and glucose •  Extended with IP glucose sensing [1,2]. dynamics (from blood to sensor site), in order to achieve more realis4c results. Equal percent-­‐wise perturba4on in all approaches (IV, IP, SC). •  Sensor dynamics for selected sensor types. •  Parameter sets for diabetes type 1 subjects •  Simulated for 24 hours including 3 typical meals. and for non-­‐diabe4c subjects. •  Compared with simula4ons of non-­‐diabe4c subjects, with the same meal input. Approaches for insulin infusion and glucose sensing •  Subcutaneous (SC) approach: Slow response, poor robustness towards local 4ssue effects (mechanical pressure, temperature etc), variable insulin absorp4on. •  Intravenous (IV) approach: Appealing, but only prac4cally possible inside the hospital/
clinic. Meal
1
Meal input
R_a
I_SC
•  Intraperitoneal (IP) approach: Faster dynamics at both ends [1,2], while being more prac4cally usable than intravascular sensors. G
Meal digestion model
I_1
Subcutaneous
glucose dynamics
R_a
Subcutaneous
insulin absorption
I_IP
2
Insulin bolus
G
G
Intraperitoneal
insulin absorption
Physiological model;
glucose & insulin dynamics
Intravenous
insulin infusion
RESULTS Intravenous
glucose
Approach
R*
Comparing IP-IP approach with PID control for diabetes type 1 with a non-diabetic simulation.
Blood gluc conc [mmol/L]
9
IIP , GIP
Non-diabetic
8.5
8
I_sc,.G_sc
7.5
7
6.5
6
5.5
I_ip,.G_sc
5
0
200
400
600
800
1000
1200
1400
Time [minutes]
1600
1800
2000
Examples of MPC simula6on results with model perturba6ons Glucose concentration for DM1, MPC, ISC GSC , comparing values of R when Np = 300, Q = 1, S = 200. Glucose concentration for DM1, MPC, IIP GIP , comparing values of R when Np = 300, Q = 1, S = 200.
10
10
r
r
r
r
r
Double SC approach 9
=2
= 16
= 25
= 80
= 300
I_ip,.G_ip
=2
= 16
= 25
= 80
= 300
8
Blood gluc conc [mmol/L]
Blood gluc conc [mmol/L]
r
r
r
r
r
Double IP approach 9
8
7
6
5
I_iv,.G_sc
7
6
4
3
3
0
200
400
600
800
1000
1200
1400
1600
1800
2000
I_iv,.G_iv
5
4
2
1
G_SC
2
G_IP
G_in
G_meas
Glucose sensor
dynamics
3
G_IV
4
G_meas
MPC simula6on results summarized PID control simula6on results 4.5
G_IP
Intraperitoneal
glucose dynamics
I
I_2
G_SC
2
0
200
400
600
800
Time [minutes]
CONCLUSION •  A simple PID controller may be sufficient for a double IP approach. •  A double intraperitoneal approach (IIPGIP) gives markedly smaller glucose excursions afer meals compared to the state-­‐
of-­‐the-­‐art double subcutaneous approach (ISCGSC) on MPC. •  The difference is larger when tested on a MPC with induced model errors; the double IP approach is more robust to model errors, compared to SC approaches (ISCGSC , IIPGSC). •  Our results suggest that a double IP approach should be inves4gated further on the way towards a robust ar4ficial pancreas. 1000
1200
1400
1600
1800
2000
Time [minutes]
2
16
25
80
300
2
16
25
80
300
2
16
25
80
300
2
16
25
80
300
2
16
25
80
300
Gmin.
(mmol/L)
2,67
3,14
3,19
3,23
4,07
3,35
4,49
4,49
4,49
4,49
4,15
4,49
4,49
4,49
4,49
4,19
4,49
4,49
4,49
4,49
4,21
4,49
4,49
4,49
4,49
Area.under.
Area.over.
Gmax.
Mean.glucose.
low.limit.......
high.limit......
(mmol/L)
level.(mmol/L)
(<.4.mmol/L)
(>.8.mmol/L)
7631
2074
3064
2242
0
904
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8,53
9,45
9,37
9,75
9,83
7,44
8,27
8,47
8,77
9,16
7,31
8,04
8,37
8,58
9,11
6,53
6,95
7,19
7,53
7,94
6,64
7,26
7,67
8,03
8,30
378
1717
1364
2635
4065
0
88
251
686
1427
0
5
164
380
1321
0
0
0
0
0
0
0
0
2
82
4,49
5,16
5,20
5,53
5,96
4,78
5,21
5,43
5,68
6,07
4,76
5,21
5,42
5,73
6,06
4,67
4,97
5,09
5,37
5,66
4,69
5,11
5,24
5,49
5,82
(*) The R tuning parameter represents the input weigh4ng for the MPC algorithm, but since Q (weigh4ng of the devia4on from reference, 4.5 mmol/L) is set to a constant value of 1, the varia4on of R is prac4cally adjus4ng the Q/R ra4o. The last parameter, S, is a weigh4ng of a slack variable (breaking of the low and high limits). REFERENCES [1] Velho, G., Froguel, P., and Reach, G., “Determina4on of Peritoneal Glucose Kine4cs in Rats: Implica4ons for the Peritoneal Implanta4on of Closed-­‐loop Insulin Delivery Systems,” Diabetologia, vol. 32, no. 6, pp. 331–336, 1989. [2] Burneo, D. R., Huyeo, L. M., Zisser, H. C., Doyle, F. J., and Mensh, B. D., “Glucose Sensing in the Peritoneal Space Offers Faster Kine4cs than Sensing in the Subcutaneous Space,” Diabetes, vol. 63, no. 7, pp. 2498–2505, July 2014. [3] Dalla Man, C., Raimondo, D. M., Rizza, R. A., and Cobelli, C., “GIM, Simula4on sofware of meal glucose-­‐insulin model,” Journal of Diabetes Science and Technology, vol. 1, no. 3, pp. 323–330, 2007. [4] Wilinska, M. E., Chassin, L. J., Schaller, H. C., Schaupp, L., Pieber, T., and Hovorka, R., “Insulin Kine4cs in Type-­‐1 Diabetes: Con4nuous and Bolus Delivery of Rapid Ac4ng Insulin,” IEEE Transac9ons on Biomedical Engineering, vol. 52, no. 1, pp. 3–12, 2005. [5] Matsuo, Y., Shimoda, S., Sakakida, M., Nishida, K., Sekigami, T., Ichimori, S., et al., “Strict Glycemic Control in Diabe4c Dogs with Closed-­‐loop Intraperitoneal Insulin Infusion Algorithm Designed for an Ar4ficial Endocrine Pancreas,” Journal of Ar9ficial Organs, vol. 6, no. 1, pp. 55–63, 2003.