Team:UCL London/Modeling/Model1

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=Oxygen and Cell concentration model=

Description
At a later stage we will consider another stress independently, then build a model on this stress in order to determine the characteristic parameters. Ultimately we will have a joint model for the two stresses and will eventually obtain a recommendation on the environment.

Objectives
The objectives of this model is to determine Oxygen stress levels at which the cells are put at a stress they can not cope with so that the cells begin to decrease in number. Therefore the ultimate objective is to create a model of the kinetics of the E-coli cells in relation to the oxygen stress levels; determining the minimum level of oxygen (kept constant) at which the size of the colony is stable.

From the lab we will verify that the parameters taken are correct. We will also define the percentage error judged admissible.

Equations
We will assume the following equations:


 * Equation of growth: x(t)=x0*exp(mu*t)
 * x0 is the initial concentration of E Coli
 * mu is the growth rate specific to the E Coli


 * Growth and decline phases: rx=mu*x(t)
 * rx is the volumetric rate of biomass production


 * Number of cells at a time t: N=N0*Exp(-kd*t)
 * kd is the specific death constant
 * N0 is the initial number of cells


 * Rate of cells death: rd=kd*N
 * N is the number of viable cells
 * kd is the specific death constant


 * Oxygen uptake rate: Q(t)=Q0*x(t)
 * Q0 is the specific O2 uptake rate
 * x is the cell concentration


 * Rate of oxygen transfer per unit of volume of fluid: Na=kl*a*(Cal*-Cal*)
 * kl is the liquid phase mass transfer coefficient
 * a is the gas liquid interfacial area per unit of volume of liquid
 * Cal* is the oxygen concentration in broth on equilibrium with gas phase
 * Cal oxygen concentration in broth