Matematisk Model for Mavesækkens Tømning - Danmarks Tekniske ...

Abstract
The aim of this assignment is to advance a mathematical model of the gastric
emptying which takes the blood glucose concentration into account. The hypothesis
is that the blood glucose affects the gastric emptying to such an extent,
that it is necessary to take this feedback-mechanism into account in a model of
the gastric emptying rate.
Studies of the physiology of the stomach indicate that the hormones somastostatin
and cholecystokinin may slow gastric emptying during hyperglycemia,
whereas the hormone ghrelin may accelerate the emptying during hypoglycemia.
To set up a model of the gastric emptying in euglycemia, a clinical clampexperiment
was performed in which the blood glucose of the subject was held
constant at 5 mmol/L while the gastric emptying was monitored using a gammacamera.
To obtain quantified data from the gastric emptying measurement, a borderfinding
programme was developed in order to find the stomach boundaries automatically
and efficiently, and to graphically show the amount of food in the
stomach as a function of time.
Existing models of the gastric emptying were fitted to data from a routine gastric
emptying measurement. New models were likewise fitted to data from the
experiment with the euglycemic clamp. The existing models did not fit the data
satisfactorily, whereas several of the new, simple linear models provided accurate
fits to the data from the experiment.
In order to simulate clamped gastric emptying measurements of a healthy subject,
a model of the pancreas was implemented in a model of the glucoregulatory
system.
In conclusion, more research needs to be performed before a mathematical
expression of the gastric emptying rate’s dependence on the ambient blood