Difference between revisions of "Team:UNAM-CU/Modeling"

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Modeling

Introduction

The main objective of our modeling section was to create a mathematical system that could explain the relationship between blood glucose levels, the size of the bacterial population, and the resulting insulin production, for different conditions related to state of energy homeostasis in the human body. The relevance of our model is such that it provides a theoretical framework that can be applied to the development of our device for people that depend on insulin, while predicting the behaviour of their blood glucose when using it, ensuring a proper insulin administration.

Bacteria

We obtained experimental data from laboratory section of bacterial population growth over time. After observing the growth curves, we assumed a logistic growth based in a qualitative approach, and what has been reported in previous works [1] Using linear regression and applying limits to estimate the variables to generate the corresponding values for the minimum and maximum regions of the equations, it was possible to develop a function that was similar to the experimental results.

Glucose

The glucose that is being considered is, primordially, correspondent to the levels that are present on the human blood, the main reason is that the sensor that is present at the bacteria membrane is thought to detect the levels on the surroundings, which should be at an equilibrium with the glucose levels on blood. Our system is thought to detect the glucose that the user has assimilated in his/her blood, in order to produce an adequate transcriptional response resulting in insulin that might be beneficial for the user’s metabolism. Glucose is considered as being negatively regulated by the amount of insulin in bloodstream and is consumed at a basal level at a rate proportional to the glucose already present.

The process of ingesting is considered as very chaotic and specific to each person , we decided to elaborate a system of pulses with an aleatory amplitude and periodicity. This aleatory amplitude was considered as following a Poisson distribution. The decision to implement a Poisson distribution was made under the considerations that we had to generate pulses that represented a general person from a certain population, the Poisson allows to have values related to the population average without generating values that would be unrealistic such as negative or extremely high that would surge from other distributions like the normal distribution. These pulses were taken as the following:

We also take into account that there is an amount of time between food eating and sugar level changes associated with them, so we are planning to build a system that uses delay equations to represent this period. Other important instances that could influence the glucose levels are the starving response and the glucose-consuming activity, those factors are dependent on the glucose levels given for a certain time and vary along the day, these equations were developed using a delay equations system, which might be helpful because these changes are not instantaneously taking place after its application.. Activity was thought to a function that causes a reduction on the glucose levels according to a certain person’s physiology. There is a constant consumption of glucose in the body that is not related to sport activity, like the consumption used to sustain the brain and other metabolic pathways [2]. We expected a differential response according to the glucose levels already present, when those levels are low, an

specific person has low energy levels, which could be correlated to a deficit on energy supplies like glucose. On the other hand, when glucose levels are too high, people tend to feel a lethargy sensation, it is commonly known as “el mal del cerdo” (the pig’s disease) in our region. Under that theoretical basis, we assumed that our activity function would have an optimum glucose burn at a medium glucose rate, which might be different inter and intra population because of the metabolic variances that could arise when changing our study subject. The two tails of the function should be asymmetric since both have different origins, considering these circumstances, we assumed that the graphic that represents this behaviour should be like the Figure 3.

The starving function followed a different approach, the response for each glucose level scenario were also analyzed and compiled at a single function with its respective graphic. When a certain person reaches extremely low levels of glucose, the body uses the glucose stocked in the body as a emergency resource, resulting in an increase in blood glucose. This response is dependent in the amount of glucose, which reduces considerably with medium levels of glucose [3]

The conjunction of these factors emulates the influence of lifestyle on glucose dynamics, these must be considered with the dynamics that result from the metabolism, which also involve the protein regulation of the insulin. The glucose regulation was considered as being the result of an exponential equation with a steady state at an specific vale xb, which should be considered as the value