2003;1021:93C104. component competitive adsorption model. Supraphysiologic IL-6 concentrations were necessary to obtain adequate CLSM transmission, therefore unknown model parameters were fit to CLSM data at high IL-6 concentrations, and the fitted model was used to simulate cytokine adsorption behavior at physiologically relevant levels which were below the microscopy detection threshold. CLSM intraparticle IL-6 adsorption profiles agreed with predictions of the competitive adsorption model, indicating displacement of cytokine by high affinity serum solutes. However, competitive adsorption effects were predicted using the model to be U 95666E negligible at physiologic cytokine concentrations associated with hemoadsorption therapy. within a single sorbent bead FLJ25987 is usually: is the mass density of adsorbed species per bead mass, at radial position, is the effective intraparticle diffusion coefficient of species is the mass concentration of species within the liquid phase of the sorbent pores. The following assumptions are made: (1) film diffusion effects are negligible, (2) concentration in the liquid phase U 95666E of the pores is much smaller than concentration in the adsorbed phase, (3) intraparticle adsorption is usually fast compared to diffusion, such that local equilibrium applies, (4) adsorption is usually modeled using the multicomponent Langmuir isotherm, where is the average particle radius, is the maximum adsorbed mass of species per bead mass, is the initial bulk concentration of species is usually a time level corresponding to the experimental conditions used in the study. Dropping asterisks and combining parameters: terms are derived from the two component Langmuir isotherm equation: as a dimensionless relative affinity coefficient, given by is the concentration required to saturate 50% of sorbent sites. We can consider cytokine adsorption to be in a low relative affinity regime ( 1) given ~ O(10?6 mg/ml) and for protein adsorption in common sorbent beads ~ O(10?1mg/ml) [29]. Hence, cytokine concentrations in our application are much less than those necessary to reach ? bead saturation ( is usually proportional to is usually proportional to and term negligible in Eq. 3, i.e. adsorption of species (serum) is usually impartial of adsorption of species (cytokine). The term in Eq. 4 gives rise to cytokine displacement by the higher relative affinity serum species. Our previously published single component model is usually a subset of the current model, where cytokine displacement is considered negligible ( 0). 2.4. Model Fitted to CLSM Data Given the set of coupled equations describing mass transport of serum components and cytokine (Eq. 3 & 4, respectively), the unknown model parameters are: and only appear as a product, and therefore the two parameters cannot be fitted independently. A value of = 11012 mlmgbead?1cm?2s was calculated as a reasonable estimate, using cbin = 1g/ml (spiked IL-6 concentration), qbmax = 1mg/mgbead (order of magnitude approximation), and Db = 110?9 cm2/s (calculated in previous CLSM work [12]); thereby permitting independent fitting of the remaining parameters. The system of equations was solved for (adsorbed cytokine) using 219 the finite element method with Comsol Multiphysics?, and a parameter optimization technique was developed as follows: numerical solutions from Comsol were imported into Matlab?, and the three unknown model parameters (is the number of incubation time points, is the number of radii data points, and and radius segment values. CLSM intensities are directly proportional to adsorbed cytokine within the particle, therefore normalized CLSM and simulation data can be compared in this manner. Normalized CLSM intensity values [values were varied within a nominal range for each parameter, and best fit parameter values were 242 estimated for all combinations using the iterative error minimization algorithm (Table 2). Parameter sensitivity was examined by running model simulations using a subset range of parameter values (Table 3), and then plotting parameter values vs. SSE to quantify model sensitivity to parameter perturbations. All parametric analyses were run using solutions to the 2hr and 5.5hr time points. Table 2 Initial guess parameter values used within the parameter optimization routine, and resulting range of best fit parameter U 95666E estimates. vs. (Fig. 4(a)), vs. (Fig. 4(b)), vs. (Fig. 4(c)). For each case, eleven separate graphs were generated using values for the third variable which was not plotted, but model behavior was comparable between each of the eleven graphs for all cases. In Fig. 4(a-b), changes in have minimal effects on SSE, indicating negligible.