We thank Mehvar (2015) for comments on our recently published article on the estimation of the fractional hepatic clearance of verapamil (VER) that forms norverapamil (NOR) (Yang et al., 2015), and we appreciate this opportunity to respond. In our recent article, we misquoted the values reported by Mehvar et al. 1994 regarding the fraction of infused VER (0.21 and 0.18 for S-VER and R-VER, respectively; eq. 1) and the fraction of extracted VER converted to NOR (0.23 and 0.19 for S-VER and R-VER, respectively; eq. 2) during a single passage through a perfused rat liver preparation at steady state (Mehvar et al., 1994).

In eqs. 1 and 2 below, E is the extraction ratio of VER; Q is the hepatic blood flow rate; is the steady-state outflow concentration of NOR originating from single-pass studies, with as the input VER concentration; are the outflow and inflow concentrations of NOR, respectively, after single-pass perfusion with preformed NOR; and is the hepatic availability of NOR that is assumed to be identical for formed and preformed NOR (Mehvar et al., 1994). Equations 1 and 2 are based on the premise that the formed metabolite suffers immediate sequential removal within the metabolite formation organ; what was detected as the outflow metabolite concentration needs to be corrected for the organ availability of the metabolite, F{mi} (Pang and Gillette, 1979).(1)(2)As noted above, the same term was used by Mehvar et al. (1994) to describe the fraction of infused or extracted VER that is converted to NOR (eq. 1 versus eq. 2). In our experience, the first set of F_m values is not meaningful because these values are influenced by the amount of infused drug as well as by the competing pathways and their saturability. We estimated the second set of F_m values after correction for E or (1 − 0.069) for S-VER and (1 − 0.046) for R-VER in eq. 2 (F values in Table 1 of Mehvar et al. (1994)). The second set of values was 0.23 and 0.19, according to eq. 2. These values are indeed equivalent to h_mi, the fraction of hepatic clearance that forms the primary metabolite, mi (eq. 3), according to our study (Yang et al., 2015) and a study by Pang and Kwan (1983) under first-order conditions.(3)We misquoted Mehvar’s F_m value as 0.12 (Yang et al., 2015), when, in fact, their values were 0.23 and 0.19. These E-corrected F_m values would have defined h_mi (eq. 3) under first-order conditions. It must be noted, however, that Mehvar used the same term, F_m, for two different occasions; moreover, the term can be confusing because in pharmacokinetic terminology, F indicates availability, whereas f indicates fraction. Mehvar (2015) stated that the estimate of 0.23 did not differ much from 0.31, a value based on the ratio of intrinsic clearance (CL_int), and that any difference was due to variability. This may not be the case here, since Mehvar et al. (1994) did not include the appreciable loss of VER and NOR due to adsorption to tubing (loss of 10%–25% of the dose of VER and NOR) and nonlinearity in the data from our study (Yang et al., 2015).

Mehvar (2015) stated that we had misquoted the value of h_mi perhaps because we had misunderstood how to interpret single-pass versus recirculating data. Equation 3 is the proper definition of h_mi, regardless of the route of drug administration. In our experience, it is not necessary to stipulate oral or intravenous administration for single-pass perfusion, as described in the response by Mehvar (2015). We have performed many perfusion studies and are equipped to interpret the data appropriately. In the single-pass situation, both VER and preformed NOR could be administered into the portal vein and the outflow concentration, C_out, is not returned to the reservoir. The rate of appearance of mi (QC_out{mi}) after drug administration in single-pass studies (eq. 2) may be used for the estimation of h_mi, when corrected for F{mi}and E, defined by (C_in − C_out)/C_in. By contrast, when an infusion is made into the portal vein in recirculating liver experiments, the condition would mimic oral administration in vivo. When an infusion is made into the reservoir, the condition would mimic intravenous infusion.

Mehvar (2015) stated that use of plasma data to define h_mi, with correction for the blood to plasma ratios (Mehvar and Reynolds, 1996), should yield h_mi values based on blood data. This is in contrast with our study, in which we stated that blood, and not plasma, concentrations should be used to relate to blood flow and blood clearance in the estimation of h_mi (Yang et al., 2015). We recalculated the h_mi values (0.23 and 0.19) of Mehvar et al. (1994) and found that, after correction with the B:P ratios (0.758 and 0.66 for S-VER and R-VER and 0.733 and 0.614 for S-NOR and R-NOR, respectively; Robinson and Mehvar, 1996), h_mi values did remain similar to those (0.22 and 0.18) based on plasma. However, one could also discuss the effect of fast uptake into red cells but slow release from bound red cells or the possibility of a red cell carriage effect (Pang et al., 1995) on VER metabolism. This could materially affect h_mi. We thoroughly investigated this via red cell distribution studies and found that red cell carriage was absent for VER, revealed by estimates of the apparent “on” and “off” rate constants for binding to red cells (Yang et al., 2015). In our recent study, we not only verified the absence of red cell carriage, but we also accounted for the nonlinear red blood cell distribution and protein binding. However, in comparing our plasma protein unbound fraction with the literature, we mistakenly cited the study by Mehvar et al. (1994), instead of the correct study by Mehvar and Reynolds (1996). Mehvar (2015) further commented that in our recent study (Yang et al., 2015), we misquoted the value of () as 50–130 ml/min, instead of 260 and 430 ml/min (from Mehvar et al., 1994). To gain a clearer view, we recalculated these values, as shown in Table 1.

Our analysis revealed that Mehvar et al. (1994) estimated f_PCL_int as 260 and 430 ml/min for S-VER and R-VER, respectively. We recalculated f_BCL_int(cal) and found these values to be 234 and 491 ml/min, respectively, for S-VER and R-VER (Table 1). The f_BCL_int(cal) values are similar (234 and 491 ml/min versus 260 and 430 ml/min). However, these are not the free CL_int values. The CL_int values (approximately 1475 ml/min, obtained upon division by f_B) relate to the free or unbound drug; f_PCL_int or f_BCL_int corrects for the binding in plasma or blood, if there is binding. We acknowledge that we should have compared the CL_int estimates at 30 ml/min versus the 1475 ml/min in our recent study (Yang et al., 2015), as shown in Table 1.

In conclusion, our recent article contained a few misquotes and these will be corrected in an erratum. These errors, however, were minor and did not materially detract from the original study design, the elegant physiologically based pharmacokinetic fitting that considered nonlinear metabolism and biliary excretion, and the nonlinear distribution into red cells and protein binding. Most importantly, these minor errors did not affect the authors’ final interpretation of h_mi.

• Copyright © 2015 by The American Society for Pharmacology and Experimental Therapeutics