Predicting Pulmonary Pharmacokinetics from In Vitro Properties of Dry Powder Inhalers

Abstract

Purpose

The ability of two semi-mechanistic simulation approaches to predict the systemic pharmacokinetics (PK) of inhaled corticosteroids (ICSs) delivered via dry powder inhalers (DPIs) was assessed for mometasone furoate, budesonide and fluticasone propionate.

Methods

Both approaches derived the total lung doses and the central to peripheral lung deposition ratios from clinically relevant cascade impactor studies, but differed in the way the pulmonary absorption rate was derived. In approach 1, the rate of in vivo drug dissolution/absorption was predicted for the included ICSs from in vitro aerodynamic particle size distribution and in vitro drug solubility estimates measured in an in vivo predictive dissolution medium. Approach 2 derived a first order absorption rate from the mean dissolution time (MDT), determined for the test formulations in an in vitro Transwell^® based dissolution system.

Results

Approach 1 suggested PK profiles which agreed well with the published pharmacokinetic profiles. Similarly, within approach 2, input parameters for the pulmonary absorption rate constant derived from dissolution rate experiments were able to reasonably predict the pharmacokinetic profiles published in literature.

Conclusion

Approach 1 utilizes more complex strategies for predicting the dissolution/absorption process without providing a significant advantage over approach 2 with regard to accuracy of in vivo predictions.

Appendices

Appendix 1: Fitting MF’s absorption profile to the Nernst-Brunner Equation

The absorption profile of MF derived by deconvouting the PK profile (see main text) was fitted to the Nernst-Brunner equation. Using information from cascade impactor studies (amount of drug deposited on stages 1 through 7) saturation solubility Cs could be easily determined as only unknown parameter.

$$ \frac{d{X}_{sum}}{dt}=\sum \limits_{i=1}^n\frac{D{S}_i(t)}{h_i(t)}\ \left( Cs-\frac{Xd}{V}\right) $$

(2)

X_sum - total amount of undissolved drug (g).

D – diffusion coefficient (cm²/s).

S_i – surface area of particle associated with each stage of the NGI, i(cm²), calculated from amounts deposited on a given stage by applying eq. 3–6.

h_i – diffusion layer thickness of the particle associated with each stage i (cm).

Cs – saturation solubility (g/ml).

Xd – amount dissolved (g).

V – volume (840 ml, representing the lung volume (37)).

r: radius.

The surface area (S_i) associated with particles on a given NGI stage was calculated from the amounts of undissolved drug present on a given NGI stage (X_i), the starting geometric diameter (d_geo) of particles of a given NGI stage, the related starting radius of particles (r), the remaining radius during dissolution of the particles (r_i), the number of particles (N_i), the density of particles (ρ) as follows:

$$ r=\frac{d_{geo}}{2} $$

(3)

$$ {r}_i(t)={\left(\frac{3{X}_i}{4\pi \rho {N}_i}\right)}^{\frac{1}{3}} $$

(4)

$$ N={X}_i\left(t=0\right){\left(\frac{4\pi r{\left(t=0\right)}^2\rho }{3}\right)}^{-1} $$

(5)

$$ {S}_i(t)=N4\pi {r}_i{(t)}^2 $$

(6)

Considering that ICSs are non-ionized, the diffusion coefficient D in eq. 2 was based on the Hayduk-Laudie equation (equation 7) (40) assuming that the viscosity η of water is similar to that of the lung, as data for the lung environment are not available.

$$ D=\frac{13.26^{\ast }{10}^{-5}}{\ {\eta_{water}^{1.4}}^{\ast }{V}_M^{0.589}}\kern1.25em $$

(7)

The molecular volume V_M for the corticosteroids was calculated using the approach described by Zhao et al. (41). Fitting was performed using the differential form of the Nernst-Brunner equation (eq. 2) with a dt of 0.01 min. The radii of the particles (r_i) and their surface areas (S_i) were updated for each time point by calculating the change in amount dissolved and consequently the reduction in radius and surface area of particles at each time t. The shape of the particles was assumed to be spherical.

Appendix 2: Differential Equations describing Approach 1

Change in undissolved drug (LC1) in central lung:

$$ \frac{dLC1}{dt}=-\left(\sum \limits_{i=1}^n\frac{D\ast {S}_{i,c}(t)}{h_{i,c}(t)}\left({C}_s-\frac{X{d}_C}{V}\right)+{k_{muc}}^{\ast } LC1\right) $$

(8)

Parameters related to the Nernst-Brunner equation are identical to those of eq. 2, subscript C indicates central lung compartment; k_muc represents mucociliary clearance rate; LC1 amount of solid drug remaining in the central compartment. S_i,c – surface area of particle associated with each stage i of the NGI (cm²). Surface area was not treated as constant but adjusted during the dissolution process as outlined in eqs. 2–7.

h_i,c – diffusion layer thickness of the particle associated with each stage i (cm); Cs – saturation solubility (g/ml); D – diffusion coefficient (cm²/s); Xd_C: amount dissolved in central lung; V: Volume of lung (840 ml equivalent to the aqueous volume of the lung (37)).

Change in dissolved drug (LC2) in central lung:

$$ \frac{dLC2}{dt}=\sum \limits_{i=1}^n\frac{D^{\ast }{S}_{i,c}}{h_{i,c}}\left({C}_s-\frac{X{d}_C}{V}\right)-{k_{pulC}}^{\ast } LC2 $$

(9)

Parameters related to the Nernst-Brunner equation are identical to those of eq. 2; subscript C indicates central lung compartment, k_pulC: absorption rate from central lung, set to 10 h⁻¹ to achieve sink conditions. LC2 amount of dissolved drug remaining in the central compartment. V: Volume of lung (840 ml equivalent to the aqueous volume of the lung (37)).

Change in undissolved drug (LP1) in peripheral lung:

$$ \frac{dLP1}{dt}=-\sum \limits_{i=1}^n\frac{D\ast {S}_{i,P}(t)}{h_{i,P}(t)}\left({C}_s-\frac{Xd_P}{V}\right) $$

(10)

Parameters related to the Nernst-Brunner equation are identical to those of eq. 2, subscript P indicates peripheral lung compartment; LP1 amount of solid drug remaining in the peripheral compartment; S_i,p – surface area of particles associated with each stage of the NGI, i(cm²). Surface area was not treated as constant but adjusted during the dissolution process as outlined in equations 2–7); h_i,p – diffusion layer thickness of the particle associated with each stage i (cm); Cs – saturation solubility (g/ml); D – diffusion coefficient (cm²/s); Xd_p: amount dissolved in peripheral lung; Volume of lung (840 ml equivalent to the aqueous volume of the lung (37)).

Change in dissolved drug (LP2) in peripheral lung:

$$ \frac{dLP2}{dt}=\sum \limits_{i=1}^n\frac{D^{\ast }{S}_{i,P}}{h_{i,P}}\left({C}_s-\frac{Xd_P}{V}\right)-{k_{pulP}}^{\ast } LP2 $$

(11)

Parameters related to the Nernst-Brunner equation are identical to those of eq. 2; subscript P indicates peripheral lung compartment, k_pulP indicates the absorption rate from peripheral lung, which was set to 20 h⁻¹ to achieve sink conditions. LP2 represents the amount of dissolved drug remaining in the peripheral compartment, while V denotes the volume of the lung (840 ml).

Change in undissolved drug (A) present in GIT (only relevant for BUD in the absence of charcoal):

$$ \frac{dA}{dt}=-{ka}^{\ast }A+{k_{muc}}^{\ast } LC1 $$

(12)

ka-first order oral absorption rate constant, A-amount of undissolved drug in GIT, k_muc-mucociliary clearance rate, LC1- amount of undissolved drug remaining in the central lung.

Change in drug (X) present in the central systemic compartment:

$$ \frac{dX}{dt}=-{k_{10}}^{\ast }X-{k_{12}}^{\ast }X+{k_{21}}^{\ast }P+{k_{pulC}}^{\ast } LC2+{k_{pulP}}^{\ast } LP2+{k_a}^{\ast }{F}^{\ast }A $$

(13)

k₁₂, k₂₁-intercompartmental rate constants, describing two compartment body model, F-oral bioavailability, P-amount in peripheral systemic compartment, A-amount of drug in GIT tract.

Change in drug (P) present in the peripheral systemic compartment:

$$ \frac{dP}{dt}={k_{12}}^{\ast }X-{k_{21}}^{\ast }P $$

(14)

k₁₂, k₂₁-intercompartmental rate constants, describing two compartment body model

Appendix 3: Differential Equations describing Approach 2

The following differential equations describe modeling approach 2 (see also Scheme 1 and 2):

Change in undissolved drug (LC1) in the central lung compartment:

$$ \frac{dLC1}{dt}=-{ka_L}^{\ast } LC1-{k_{muc}}^{\ast } LC1 $$

(15)

ka_L: absorption rate from lung. LC1-amount of undissolved drug remaining in the central compartment; K_muc-mucociliary clearance rate.

Change in undissolved drug in the peripheral lung compartment:

$$ \frac{dLP1}{dt}=-k{a_L}^{\ast } LP1 $$

(16)

ka_L: absorption rate from lung. LC1-amount of undissolved drug remaining in the peripheral compartment.

Change in drug (X) present in the central systemic compartment:

$$ \frac{dX}{dt}=-{k_{10}}^{\ast }X-{k_{12}}^{\ast }X+{k_{21}}^{\ast }P+{ka_L}^{\ast } LC1+{ka_L}^{\ast } LP1+{k_a}^{\ast }{F}^{\ast }A $$

(17)

k₁₂, k₂₁-intercompartmental rate constants, describing two compartment body model, F-oral bioavailability, P-amount in peripheral systemic compartment, A-amount of drug in GIT tract; ka_L: absorption rate from lung; LC1-amount of undissolved drug remaining in the central lung; LP1-amount of undissolved drug remaining in the peripheral lung; k_a-absorption rate constant from GIT.

Change in drug (P) present in the peripheral systemic compartment:

$$ \frac{dP}{dt}={k_{12}}^{\ast }X-{k_{21}}^{\ast }P $$

(18)