مدل تصادفي غلظت گلوكز در پلاسماي خون ، وقتي پارامترهاي مدل با زمان و نمونه ها تغيير مي كنند

The Stochastic Model for the Glucose Concentration in Plasma - the Model Parameters Vary with Time and Individuals

Purpose: The research presents an overview of a two - compartmental model describing the decay of an injected glucose tracer in the blood plasma of some female subjects. The research was performed in 1996 at St. Thomasʹ Hospital, London. Material & Methods: The subjects were in their post-partum period and some were suffering from gestational diabetes during pregnancy. The subjects, intravenously, received an injected glucose and glucose tracer and the blood samples were taken at various times between 2 to 180 minutes after injection. Thus, the research aims at building a stochastic model for the concentration of glucose tracer in plasma and intravascular tissues to substitute the current deterministic model that does not account for the random effects. In this new method, we assume the concentration of glucose tracer in blood plasma in different times and subjects are different (with fixed variance) and the concentration of glucose tracer in each fixed time has a random process with truncated normal distribution. Therefore, uncertainty incorporates with the whole system, specially the two fluxes between compartments, loss of the second compartment and the initial concentration of glucose tracer in blood plasma. The parameters vary with time and samples thus, using the deterministic model for the concentration of glucose tracer is not appropriate. Results: To build a stochastic model, differential equations were used and the final model for the concentration of glucose tracer in both compartments was built in combination of bi-compartmental matrix and the moments of the random process. Conclusion: The comparison of the stochastic and deterministic model for the concentration of glucose tracer has shown a little difference between two models and they are almost the same. This similarity can be due to the small sample size or the similarity of the random process.