Improved method for estimating Ca uptake in vascular smooth muscle using compartmental analysis

A comparative study on the modeling aspects of Ca uptake in vascular smooth muscle is presented with particular emphasis on determination of the influx rate and its standard error for one- and two-compartment models. Experimental data from our laboratory of 45Ca uptake by dog carotid arteries were optimally fitted to a one-compartment model and were used to compare different estimation methods and experiment designs. Reparameterization of the model equation yielded an expression that allows direct estimation of the influx rate and its standard error. Experiment design with replicated sampling at three to four times were found to provide the highest estimation precision and successful comparisons of influx rates under treatment and control conditions. Two-compartment model data reported in the literature for Ca uptake by cells were reprocessed, yielding standard errors for the rate constant of the fast component an order of magnitude larger than the mean estimate. For this case, a three-parameter variant of the one-compartment model was developed that described the data with acceptable standard errors. Overall we found that the choice of the model that fitted Ca uptake data best required consideration of parameter estimate precision comparisons in addition to F tests of significance between alternate models.