# Models

## UVA/Padova model with exercise (Breton 2008)

More detail will be provided soon.

### Disclaimer

It must be expressly pointed out that this is only a mathematical model which can at most describe the real processes in the human body approximately and in parts. Therefore, although the simulation results qualitatively resemble clinical curves, they must be interpreted with caution and are not suitable for deriving individual treatment strategies from them (see disclaimer). We do not assume any responsibility for the correctness of the results or damages of any kind resulting from the use of the simulator (see license).

### References

Breton, Marc D.: Physical activity – the major unaccounted impediment to closed loop control. Journal of Diabetes Science and Technology Volume 2 Issue 1, 2008.

## Cambridge Model

This model is taken from the work of Hovorka et al [1], with implementation based on [2].

### Specifics and deviations

With the default parameters, this model has a very high insulin sensitivity and implies a very low basal rate.

In [1], the glucose absorption rate resulting from a meal was measured as a time signal

$U_G(t) = \dfrac{D_G\,A_G\,t\,e^{-t/t_{max,G}}}{t^2_{max,G}}$

This approach is only suitable for a single meal. It is more elegant to formulate glucose absorption as a solution of an initial value problem, as done in [2]. For this purpose, the original model must be extended by two compartments.

### Block diagram

The following scheme visualizes the state variables included in the model and the interactions between them:

## Disclaimer

It must be expressly pointed out that this is only a mathematical model which can at most describe the real processes in the human body approximately and in parts. Therefore, although the simulation results qualitatively resemble clinical curves, they must be interpreted with caution and are not suitable for deriving individual treatment strategies from them (see disclaimer). We do not assume any responsibility for the correctness of the results or damages of any kind resulting from the use of the simulator (see license).

### References

[1] Hovorka, R.; Canonico, V.; Chassin, L. J.; Haueter, U.; Massi-Benedetti, M.; Federici, M. O.; Pieber, T. R.; Schaller, H. C., Schaupp, L.; Vering, T.; Wilinska, M. E.: Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Journal of Phyiological Measurement, Volume 25, 2004.

[2] Andersen, S. H.: Software for in Silico Testing of an Artificial Pancreas. Master’s Thesis at Technical University of Denmark. 2014.

The arrangement of the block diagram was inspired by a template by Clara Furió Novejarque, Universitat Politècnica de València.

This model was described by Dalla Man et al. in [3, 4]. Its equations are also the basis of the UVA/PADOVA Type 1 Diabetes Simulator (T1DMS).

### Specifics and deviations

• For the digestion rate (kempt), different models are described in [3,4]. For simplicity, an average of maximum and minimum digestion rates was provisionally used instead of the complex calculation rules.
• Hepatic gluconeogenesis ([3], Eq. (4)) was limited to avoid singularity ([3], Eq. (5)) at high insulin concentrations.
• Subcutaneous insulin kinetics included in T1DMS [4] are not described in [3]; they were taken from [2], including the associated parameters

The default values of the parameters are taken from the “Normal Value” column in [3, Table 1] and describe the behavior of a healthy person.

### Block diagram

The following scheme visualizes the state variables included in the model and the interactions between them:

### Disclaimer

It must be expressly pointed out that this is only a mathematical model which can at most describe the real processes in the human body approximately and in parts. Therefore, although the simulation results qualitatively resemble clinical curves, they must be interpreted with caution and are not suitable for deriving individual treatment strategies from them (see disclaimer). We do not assume any responsibility for the correctness of the results or damages of any kind resulting from the use of the simulator (see license).

### References

[1] Dalla Man, Ch.; Camilleri, M.; Cobelli, C.: A System Model of Oral Glucose Absorption: Validation on Gold Standard Data. IEEE Transactions on Biomedical Engineering, Volume 53, Number 12, December 2006

[2] Dalla Man, Ch.; Raimondo, D.M.; Rizza, R. A.; Cobelli, C.: GIM, Simulation Software of Meal Glucose-Insulin Model. Journal of Diabetes Science and Technology, Volume 1, Issue 3, May 2007

[3] Dalla Man, C.; Rizza, R. A.; Cobelli, C.: Meal simulation model of the glucose-insulin system. IEEE Transactions on biomedical engineering, 54(10), 2007.

[4] Dalla Man, C.; Micheletto, F.; Lv, D.; Breton, M.; Kovatchev, B.; Cobelli, C.: The UVA/PADOVA Type 1 Diabetes Simulator: New Features. Journal of Diabetes Science and Technology, Volume 8, Issue 1, 2014.

The arrangement of the block diagram was inspired by a template by Clara Furió Novejarque, Universitat Politècnica de València.