advertisement

Langmuir model without transport In this worksheet I am working on the identifiability of the parameters of a model of antibody binding. create usefull sets In this worksheet we shall obtain results and look at the case where the inlet concentration, is known or alternately unknown set up equations B equations Notably I present this equation in terms of the output y_ij set up y_ij equations. We label the equation for the nth derivative of as (2.1) (2.2) obtain y and derivatives multinomial eliminate B1 take a derivative substitute in the definition of Substitute an equation for obtained by rearanging y1 Put it in a form that is easy to read (3.1) look at coefficients We know that if two multinomials on the same variables are equal for all vlaues of these variables, then their coefficents will also be equal. Now we consider only the coefficients (4.1) (4.2) (4.3) Evaluate for the two stages of the model We also know that for two models too give the same outputs, the coefficients of the multinomials when C is 0 (4.1.1.1) (4.1.1.2) (4.1.1.3) (4.1.1.3) when C is C_T (4.1.2.1) (4.1.2.2) (4.1.2.3) Create equation lists and solve For known C_T (5.1.1) For unknown C_T (5.2.1)