ANALYSIS OF PERMEATION DATA - EVALUATION OF THE LAG TIME METHOD

Equations derived previously for penetration (C(x,t) and J(x,t) vs t), flux and permeation (A vs t) profiles were evaluated numerically to study the process of development of steady-state diffusion across the membrane. The concentration and flux profiles of the diffusant within the membrane indicated that at least three lag times were required to achieve a linear concentration gradient and a steady-state flux across the membrane. The permeation profile becomes truly linear at time greater than three lag times implying that the permeation experiment should be conducted for at least three lag times to achieve steady state which may not be possible with biological membranes. Also, if the experiments were conducted for a duration less than three lag times, the estimated J(ss) and T(lag) may be in error. To determine the error introduced, the simulated permeation profile was broken down into data subsets as if the experiments had been conducted for time equal to one to six lag times. The data subsets were then analyzed by the lag time method to estimate the parameters. The error in estimates of J(ss) and lag time increased significantly as the total experimental time was reduced from six to one lag time. The J(ss) and T(lag) were highly underestimated, and for the experiment conducted for one lag time, the percentage errors in J(ss) and T(lag) were -60 and -54% from the theoretical values, respectively. The errors in derived values of D, the diffusion coefficient and K(m), the membrane/water partition coefficient were significantly higher (116 and -82%) than the errors in J(ss) and T(lag). These results demonstrated the limitations of the lag time method for analysis of permeation data with particular reference to the duration of the experiment, which should be at least three lag times to achieve steady-state diffusion.