Chemical Concentration Model in a Breathing Lung
by Mike Martin

This page allows you to iterate a model, given below, for a chemical's concentration, ct, in a pumping lung for a total of N steps/breaths using selected values of the ambient concentration, k, of the chemical in the environment. The q variable is a number between 0 and 1 that can be interpreted as the ratio of the volume of a breath to the total volume of the lung or, more simply, the ratio of air exchanged. The model is given by the following first-order difference equation:

ct+1 = ( 1 - q ) ct + q k

c0 is the initial condition -- the initial value of the concentration in the lung. Enter in the value of the parameters, then press the "Plot/Evaluate" button.



k =

q =

c0 =

N =

M =


The graphs are given by:


Numerical values for the last M terms of a sequence that is T terms long are given by:


The equilibrium values, along with their stability type, are given below: