Parametric Identification of Sorensen model for glucose-insulin-carbohydrates dynamics using evolutive algorithms

Velázquez, Eduardo Ruiz; Sánchez, Oscar D.; Quiroz, G.; Pulido, Guillermo O.

doi:10.14736/kyb-2018-1-0110

Cited by 1 publication

(2 citation statements)

References 27 publications

(36 reference statements)

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“…In accordance with the methodology used in [33], the problem of parametric identifiability can be treated as a case of observability problem. Under some consideration, a parameter is treated as a state variable with time derivative zero, i.e.…”

Section: Analysis Of the Modelmentioning

confidence: 99%

“…Then the problem of observability of the x variables disappears [32]. For the analytical system (1), the rank test gives the rank of the following Jacobian

O_{N} = (][, \begin{matrix} 1em4pt \\ \frac{\partial h false(x false)}{\partial p} \\ \frac{\partial L_{f} h false(x false)}{\partial p} \\ ⋮ \\ \frac{\partial L_{f}^{n - 1} h false(x false)}{\partial p} \end{matrix})

where

L_{f} h = true \frac{\partial h false(x false)}{\partial x} f (bold-italicx, bold-italicp)

is the Lie derivative [33]. Then, (5) is locally identifiable if

rank false(O_{N} false(p false) false) = q

Consider

p^{*} \in P

and note that for all

p

in the neighbourhood of

p^{*} false(i . e . p \in V false(p^{*} false) false)

y = O_{N} false(p false) p

Then, condition (6) implies that for

p \in V false(p^{*} false)

…”

Section: Analysis Of the Modelmentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation of a meal glucose–insulin model for TIDM patients from therapy historical data

Sánchez

Ruı́z-Velázquez

Alanís

et al. 2019

IET Systems Biology

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The effect of meal on blood glucose concentration is a key issue in diabetes mellitus because its estimation could be very useful in therapy decisions. In the case of type 1 diabetes mellitus (T1DM), the therapy based on automatic insulin delivery requires a closed-loop control system to maintain euglycaemia even in the postprandial state. Thus, the mathematical modelling of glucose metabolism is relevant to predict the metabolic state of a patient. Moreover, the eating habits are characteristic of each person, so it is of interest that the mathematical models of meal intake allow to personalise the glycaemic state of the patient using therapy historical data, that is, daily measurements of glucose and records of carbohydrate intake and insulin supply. Thus, here, a model of glucose metabolism that includes the effects of meal is analysed in order to establish criteria for data-based personalisation. The analysis includes the sensitivity and identifiability of the parameters, and the parameter estimation problem was resolved via two algorithms: particle swarm optimisation and evonorm. The results show that the mathematical model can be a useful tool to estimate the glycaemic status of a patient and personalise it according to her/his historical data.

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Section: Analysis Of the Modelmentioning

confidence: 99%

“…Then the problem of observability of the x variables disappears [32]. For the analytical system (1), the rank test gives the rank of the following Jacobian