Class: BE310
Group: M1
Members: Matthew DeNardo, Nicholas Fawzi, Courtney Morgan, Angela
Xavier
Date: May 2002
Abstract:
A two-compartment model of KCl solutions was created and compared to
mass balance mathematical models for the concentration of KCl in each compartment.
Flow between the compartments was modeled for steady-flow and sinusoidal-flow
cases. Plots of analytical equations predicting the concentration
in each compartment were compared by visual inspection as well as by taking
the mean difference and mean percent difference between the theoretical
and actual concentrations. For both conditions, the actual and theoretical
curves had the same shape and time decay. For steady flow, the mean
percent difference in concentration between experimental and mathematical
model was 0.44% for compartment 1, and 2.7% for compartment 2. For
sinusoidal flow, the mean percent difference was 4.5% for compartment 1
and 3.8% for compartment 2. Based on the resulting low mean percent differences,
this modeling of a two-compartment system with mathematical equations was
determined to be accurate. By varying the conditions of the mathematical
model, it was determined that the peak concentration in compartment 2 is
linearly proportional to the initial concentration in compartment 1 and
inversely related to the volume of compartment 2 by a multi-term logarithmic
function. These mathematical models can now be applied to modeling
biological systems such as drug delivery and lactation.