A Three-Compartment Pharmacokinetic Model to Predict the Interstitial Concentration of Talaporfin Sodium in the Myocardium for Photodynamic Therapy: A Method Combining Measured Fluorescence and Analysis of the Compartmental Origin of the Fluorescence

Abstract

To evaluate the effectiveness of photodynamic therapy occurring in the interstitial space of the myocardium, we estimated the interstitial concentration of talaporfin sodium in the canine myocardium by constructing a three-compartment pharmacokinetic model based on measured changes in talaporfin sodium plasma concentration and myocardial fluorescence. Differential rate equations of talaporfin sodium concentration in the plasma, interstitial space, and cell compartment were developed with individual compartment volume, concentration, and rate constants. Using measured volume ratios based on histological examinations, we defined that the myocardial fluorescence consisted of the linear addition of fluorescence generated from these three compartments. The rate constants were obtained by fitting to minimize the sum of the squared errors between the measured talaporfin sodium concentrations and the calculated concentrations divided by the number of data points using the conjugate gradient method in MATLAB. We confirmed that this fitting operation may be appropriate, because a coefficient of determination between the measured talaporfin sodium changes and the calculated concentrations using our equations was 0.99. Consequently, to estimate the interstitial concentration in the canine myocardium, we propose a three-compartment pharmacokinetic model construction methodology using measured changes in talaporfin sodium plasma concentration and changes in myocardial fluorescence.