Mechanistic population pharmacokinetics of total and unbound paclitaxel for a new nanodroplet formulation versus Taxol in cancer patients

Abstract

Purpose

Our objectives were (1) to compare the disposition and in vivo release of paclitaxel between a tocopherol-based Cremophor-free formulation (Tocosol Paclitaxel^®) and Cremophor^® EL-formulated paclitaxel (Taxol^®) in human subjects, and (2) to develop a mechanistic model for unbound and total paclitaxel pharmacokinetics.

Methods

A total of 35 patients (average ± SD age: 59 ±13 years) with advanced non-hematological malignancies were studied in a randomized two-way crossover trial. Patients received 175 mg/m² paclitaxel as 15 min (Tocosol Paclitaxel) or 3 h (Taxol) intravenous infusion in each study period. Paclitaxel concentrations were determined by LC–MS/MS in plasma ultrafiltrate and whole blood. NONMEM VI was used for population pharmacokinetics.

Results

A linear disposition model with three compartments for unbound paclitaxel and a one-compartment model for Cremophor were applied. Total clearance of unbound paclitaxel was 845 L/h (variability: 25% CV). The prolonged release with Tocosol Paclitaxel was explained by the limited solubility of unbound paclitaxel of 405 ng/mL (estimated) in plasma. The 15 min Tocosol Paclitaxel infusion yielded a mean time to 90% cumulative input of 1.14 ± 0.16 h. Tocosol Paclitaxel was estimated to release 9.8% of the dose directly into the deep peripheral compartment. The model accounted for the presence of drug-containing nanodroplets in blood.

Conclusions

Population pharmacokinetic analysis indicated linear disposition and a potentially higher bioavailability of unbound paclitaxel following Tocosol Paclitaxel administration due to direct release at the target site. The prolonged release of Tocosol Paclitaxel supports 15 min paclitaxel infusions. This mechanistic model may be important for development of prolonged release formulations that distribute in and from the systemic circulation.

Appendices

Appendix

Mechanistic model for drug release from Tocosol Paclitaxel nanodroplets

The following equations describe the amount of paclitaxel in nanodroplets (A _Nano) and in the unstirred water layer (A _Layer) (see also Fig. 1):

$$ \frac{{{\text{d}}A_{\text{Nano}} }}{{{\text{d}}t}} = F_{\text{Tocosol}} \cdot R_{\text{Input}} - {\text{ka}}_{1} \cdot \left( {1 - \frac{{C_{\text{Layer}} }}{{C_{\text{Sol}} }}} \right) \cdot A_{\text{Nano}} $$

(A1)

$$ \frac{{{\text{d}}A_{\text{Layer}} }}{{{\text{d}}t}} = {\text{ka}}_{1} \cdot \left( {1 - \frac{{C_{\text{Layer}} }}{{C_{\text{Sol}} }}} \right) \cdot A_{\text{Nano}} - {\text{ka}}_{2} \cdot A_{\text{Layer}} $$

(A2)

where C _Sol is the solubility of unbound paclitaxel in the volume of distribution for nanodroplets (V _Nano), C _Layer is the paclitaxel concentration in the unstirred water layer, R _Input is the zero-order input into the nanodroplet compartment, and F _Tocosol is the relative bioavailability of Tocosol Paclitaxel compared to Taxol. The release of drug from nanodroplets into the unstirred water layer is described by the first-order rate constant ka₁ and the transfer of drug from the unstirred water layer to the central and peripheral compartment by the first-order rate constant ka₂ (Fig. 1). Initial conditions for A _Nano and A _Layer are zero.

If ka₂ is much larger than ka₁, A _Layer will show a rapid initial rise and thereafter the differential dA _Layer/dt will be very small compared to dA _Nano/dt. In this situation, the quasi-stationary solution for A _Layer that is valid after the rapid initial rise can be calculated by setting the differential dA _Layer/dt to zero and solving for A _Layer. This yields:

$$ A_{\text{Layer}} = \frac{{{\text{ka}}_{1} \cdot A_{\text{Nano}} }}{{{\text{ka}}_{2} + \frac{{{\text{ka}}_{1} \cdot A_{\text{Nano}} }}{{C_{\text{Sol}} \cdot V_{\text{Layer}} }}}}. $$

(A3)

The V _Layer represents the volume of the unstirred water layer. Inserting this equation into Eq. A1 yields the following equation for the mixed-order (Michaelis–Menten) process from the nanodroplet to the central compartment:

$$ \begin{aligned} \frac{{{\text{d}}A_{\text{Nano}} }}{{{\text{d}}t}} = & F_{\text{Tocosol}} \cdot R_{\text{Input}} - \frac{{{\text{ka}}_{ 2} \cdot C_{\text{Sol}} \cdot V_{\text{Layer}} \cdot A_{\text{Nano}} }}{{\frac{{{\text{ka}}_{ 2} \cdot C_{\text{Sol}} \cdot V_{\text{Layer}} }}{{{\text{ka}}_{ 1} }} + A_{\text{Nano}} }} \\ = & F_{\text{Tocosol}} \cdot R_{\text{Input}} - \frac{{{\text{Vmax}} \cdot A_{\text{Nano}} }}{{{\text{AN}}_{ 5 0} + A_{\text{Nano}} }}. \\ \end{aligned} $$

(A4)

The maximum rate of drug transfer is denoted as V _max and is equal to the product of ka₂, C _Sol, and V _Layer. The amount of drug in the nanodroplet compartment (AN₅₀) that results in a transfer rate of 50% of V _max is V _max/ka₁. Based on the final estimates, we confirmed that this quasi-stationary solution is an accurate approximation of the full set of differential equations.

The product of ka₂ and V _Layer is the clearance from the unstirred water layer (CL_Layer) which is identifiable, whereas the individual terms are not. Therefore, a mixed-order transfer from the nanodroplet to the central compartment can be explained mechanistically by solubility-limited transfer through an unstirred water layer.

Output equation for plasma ultrafiltrate for nanodroplet formulation

Blood samples drawn during the release phase of Tocosol Paclitaxel nanodroplets contain nanodroplets with paclitaxel. This unreleased paclitaxel was assumed to be in part released during the processing of blood samples. Due to the vigorous conditions during centrifugation, we assumed that the unstirred water layer is less important. The release of paclitaxel from nanodroplets into plasma was described by a first-order process that becomes saturated, if the unbound plasma concentration approaches the estimated solubility limit (Fig. 1). This yields the following equations for the amounts of drug in nanodroplets in a blood sample (A _Nano,S) and in the blood sample excluding drug in nanodroplets (A _Blood,S):

$$ \frac{{{\text{d}}A_{{{\text{Nano}},{\text{S}}}} }}{{{\text{d}}t}} = - {\text{ka}} \cdot A_{{{\text{Nano}},{\text{S}}}} \cdot \left( {1 - \frac{{A_{{{\text{Blood}},{\text{S}}}} }}{{V_{\text{Sample}} \cdot {\text{BF}}_{\text{TOC}} \cdot C_{\text{Sol}} }}} \right) $$

(A5)

$$ \frac{{{\text{d}}A_{\text{Blood,S}} }}{{{\text{d}}t}} = {\text{ka}} \cdot A_{\text{Nano,S}} \cdot \left( { 1- \frac{{A_{\text{Blood,S}} }}{{V_{\text{Sample}} \cdot {\text{BF}}_{\text{TOC}} \cdot C_{\text{Sol}} }}} \right). $$

(A6)

The binding factor for Tocosol paclitaxel (BF_TOC) was assumed to be constant during sample handling, as the saturable component of protein binding was negligible for high unbound concentrations. The first-order release rate constant under sample handling conditions is denoted as ka. The paclitaxel amount in sampled blood excluding drug in nanodroplets (A _Blood,S) divided by the sample volume (V _Sample) and by the binding factor BF_TOC yields the unbound plasma concentration. The initial condition was A _Nano·V _Sample/V _Nano for A _Nano,S and the unbound concentration in central compartment (C1) multiplied by V _Sample and BF_TOC for A _Blood,S.

These two differential equations were solved in Maple and the solution was used as the output equation for the paclitaxel concentration in plasma ultrafiltrate for Tocosol Paclitaxel [E(t _Proc), N1, and N2 are intermediary variables to simplify the equations]:

$$ E\left( {t_{\text{Proc}} } \right) = { \exp }\left( {\frac{{{\text{ka}} \cdot \left( {A_{\text{Nano}} - V_{\text{Nano}} \cdot C_{\text{Sol}} \cdot {\text{BF}}_{\text{TOC}} + V_{\text{Nano}} \cdot {\text{BF}}_{\text{TOC}} \cdot {\text{C1}}} \right) \cdot t_{\text{Proc}} }}{{V_{\text{Nano}} \cdot {\text{BF}}_{\text{TOC}} \cdot C_{\text{Sol}} }}} \right) $$

(A7)

$$ {\text{N1}} = - C_{\text{Sol}} \cdot A_{\text{Nano}} + A_{\text{Nano}} \cdot {\text{C1}} - V_{\text{Nano}} \cdot C_{\text{Sol}} \cdot {\text{BF}}_{\text{TOC}} \cdot {\text{C1}} $$

(A8)

$$ {\text{N2}} = V_{\text{Nano}} \cdot {\text{BF}}_{\text{TOC}} \cdot {\text{C1}}^{ 2} + C_{\text{Sol}} \cdot E\left( {t_{\text{Proc}} } \right) \cdot {\rm A}_{\text{Nano}} $$

(A9)

$$ A_{\text{blood,S}} \left( {t_{\text{Proc}} } \right) = \frac{{V_{\text{Sample}} \cdot {\text{BF}}_{\text{TOC}} \cdot \left[ {{\text{N1}} + {\text{N2}}} \right]}}{{ - {\text{BF}}_{\text{TOC}} \cdot C_{\text{Sol}} \cdot V_{\text{Nano}} + V_{\text{Nano}} \cdot {\text{BF}}_{\text{TOC}} \cdot {\text{C1}} + E\left( {t_{\text{Proc}} } \right) \cdot A_{\text{Nano}} }}. $$

(A10)

Dividing the amount of paclitaxel in the blood sample (excluding the unreleased amount in nanodroplets) at the end of sample processing (t _Proc) by the sample volume and the binding factor yields the output equation for the concentration in plasma ultrafiltrate for Tocosol Paclitaxel:

$$ {\text{Cu}}\left( {t_{\text{Proc}} } \right) = \frac{{A_{\text{blood,S}} \left( {t_{\text{Proc}} } \right)}}{{V_{\text{Sample}} \cdot {\text{BF}}_{\text{TOC}} }}. $$

(A11)

We assumed an average time of sample processing of 30 min according to the procedures described in the clinical protocol and estimated the half-life of the first-order release rate constant ka. The sample volume (V _Sample) was arbitrarily set to 1 L, as this choice did not influence the results.