Combined in Vitro-in Silico Approach to Predict Deposition and Pharmacokinetics of Budesonide Dry Powder Inhalers

Abstract

Purpose

A combined in vitro – in silico methodology was designed to estimate pharmacokinetics of budesonide delivered via dry powder inhaler.

Methods

Particle size distributions from three budesonide DPIs, measured with a Next Generation Impactor and Alberta Idealized Throat, were input into a lung deposition model to predict regional deposition. Subsequent systemic exposure was estimated using a pharmacokinetic model that incorporated Nernst-Brunner dissolution in the conducting airways to predict the net influence of dissolution, mucociliary clearance, and absorption.

Results

DPIs demonstrated significant in vitro differences in deposition, resulting in large differences in simulated regional deposition in the central conducting airways and the alveolar region. Similar but low deposition in the small conducting airways was observed with each DPI. Pharmacokinetic predictions showed good agreement with in vivo data from the literature. Peak systemic concentration was tied primarily to the alveolar dose, while the area under the curve was more dependent on the total lung dose. Tracheobronchial deposition was poorly correlated with pharmacokinetic data.

Conclusions

Combination of realistic in vitro experiments, lung deposition modeling, and pharmacokinetic modeling was shown to provide reasonable estimation of in vivo systemic exposure from DPIs. Such combined approaches are useful in the development of orally inhaled drug products.

Appendices

Appendix 1 – Volumetric Flowrates

The Delvadia et al. semi-idealized inhalation profiles are presented in terms of the volumetric flowrate exiting the inhaler mouthpiece. The setup in Fig. 1 can provide an indirect measure of this flowrate by considering a mass balance of flow. Consider a control volume encompassing the supply line, the breathing machine line, the vacuum line downstream of the NGI, and the airflow entering the DPI. The equation for conservation of mass in this control volume is: $\frac{dm}{dt}=\sum {\dot{m}}_{\mathrm{in}}-\sum {\dot{m}}_{\mathrm{out}}$ (A-1).

The time rate of change of mass inside the control volume, dm/dt, is considered negligible relative to the magnitudes of the inlet and outlet flows. This assumption is justified by noting that all flows here have Mach numbers less than 0.3 (i.e. flow can be considered incompressible, so changes in density are small) and the walls of the control volume are rigid (i.e. the actual volume of gas contained in the control volume remains constant). Noting that m = ρV (mass equals density times volume), expanding with the product rule for differentiation, and using the above physical reasoning (incompressible flow and a rigid control volume), dm/dt is:

$$ \frac{d m}{d t}=\frac{d\left(\rho V\right)}{d t}=\rho \frac{d V}{d t}+V\frac{d\rho}{d t}=0 $$

(A-2)

The equation for conservation of mass becomes, after expressing the inlet and outlet flows in terms of their volumetric flowrates Q_vol,supply, Q_vol,HBM, Q_vol,vacuum, and Q_vol,DPI:

$$ {\rho}_{\mathrm{supply}}{Q}_{\mathrm{vol},\mathrm{supply}}+{\rho}_{\mathrm{DPI}}{Q}_{\mathrm{vol},\mathrm{DPI}}={\rho}_{\mathrm{HBM}}{Q}_{\mathrm{vol},\mathrm{HBM}}+{\rho}_{\mathrm{vacuum}}{Q}_{\mathrm{vol},\mathrm{vacuum}} $$

(A-3)

Equation A - 3 can be recast in terms of standard flowrates using the ideal gas law as follows. The volumetric flowrate at a particular temperature and pressure relates to the standard flowrate as

$$ {Q}_{\mathrm{vol},\mathrm{m}}(t)={Q}_{\mathrm{std},\mathrm{m}}(t)\frac{P_{\mathrm{ref}}}{T_{\mathrm{ref}}}\frac{T_{\mathrm{m}}}{P_{\mathrm{m}}} $$

(A-4)

From the ideal gas law:

$$ {\rho}_{\mathrm{m}}=\frac{P_{\mathrm{m}}}{R_{\mathrm{specific}}{T}_{\mathrm{m}}} $$

(A-5)

Equation A - 4 can then be expressed as

$$ {\rho}_{\mathrm{m}}{Q}_{\mathrm{vol},\mathrm{m}}(t)={\rho}_{\mathrm{ref}}{Q}_{\mathrm{std},\mathrm{m}}\left(t\ \right) $$

(A-6)

Here ρ_m is the air density at which the volumetric flowrate is desired (dependent on temperature and pressure), while ρ_ref is a reference density (equal to approximately 1.2 kg/m^3 for TSI calibrated flowmeters). With suitable substitutions, Eq. A - 3 takes a simple form as all density terms become ρ_ref. Further rearranging to solve for the unmeasured flowrate entering the DPI, Eq. A - 3 becomes:

$$ {Q}_{\mathrm{std},\mathrm{DPI}}(t)={Q}_{\mathrm{std},\mathrm{HBM}}(t)+{Q}_{\mathrm{std},\mathrm{vacuum}}(t)-{Q}_{\mathrm{std},\mathrm{supply}}(t) $$

(A-7)

Flowrates on the right hand side of Eq. A - 7 are known, allowing for the straightforward calculation of the standard flowrate generated through the DPI, Q_{std, DPI}. Calculation of the volumetric flowrate exiting the DPI mouthpiece can then be performed using A - 8 (Ruzycki et al., J Aerosol Med Pulm Drug Deliv 2019;32 (6):405–417).

$$ {Q}_{\mathrm{vol},\mathrm{DPI}\kern0.15em \mathrm{exit}}(t)={Q}_{\mathrm{std},\mathrm{DPI}}(t)\frac{T_{\mathrm{m}}}{T_{\mathrm{ref}}}\frac{P_{\mathrm{ref}}}{\left({P}_{\mathrm{m}}-{\left[R{Q}_{\mathrm{std},\mathrm{DPI}}(t)\frac{T_{\mathrm{m}}}{T_{\mathrm{ref}}}\frac{P_{\mathrm{ref}}}{P_{\mathrm{m}}}\kern0.10em \right]}^2\right)} $$

(A-8)

P_ref equals 101.3 kPa, T_ref equals 21.11°C (294.26 K), and R is the device resistance (taken as the reference value measured at sea level). Eq. A - 8 assumes that the effect of ambient pressure on inhaler resistance is negligible (reasonable for moderate altitudes; Titosky et al., J Pharm Sci 2014;103:2116–2124; Ruzycki et al., J Aerosol Med Pulm Drug Deliv 2018;31 (4):221–236). Furthermore, the derivation assumes that the relation between pressure drop and flowrate is quasi-steady, a reasonable assumption given the small volume of the inhaler relative to the inhalation flowrate.

Appendix 2 – Equations Describing the Pharmacokinetic Model

The equations describing the pharmacokinetic model shown schematically in Fig. 2 of the main text are summarized in this Appendix. Note that initial deposited masses in each generation of the tracheobronchial airways and in the alveolar region (F_i, 0 ≤ i ≤ 14, and F_ALV, respectively) come directly from the regional deposition model discussed in the main text, while the initial dose in the gastrointestinal tract is taken as the dose measured in the Alberta Idealized Throat in vitro. Rate constants describing mucociliary clearance (k_muc,i) and the volume of the airway surface liquid in each generation V_ASL,i come from the airway surface liquid model discussed in the main text. Values for other rate constants and critical parameters are provided in the main text with references to the literature.

Gastrointestinal tract compartment drug mass, m _A :

$$ \frac{d{m}_{\mathrm{A}}}{dt}=-{k}_{\mathrm{a}}{m}_{\mathrm{A}}+{k}_{\mathrm{muc},0}\left({m}_{0,1}+{m}_{0,2}\right) $$

(B-1)

Equation B - 1 is subject to the initial condition m_A equal to the dose measured in the Alberta Idealized Throat at time t = 0

Central compartment drug mass, m _X :

$$ \frac{d{m}_{\mathrm{X}}}{dt}=-\left({k}_{12}+{k}_{01}\right){m}_{\mathrm{X}}+{F}_{\mathrm{BA}}{k}_{\mathrm{a}}{m}_{\mathrm{A}}+{k}_{21}{m}_{\mathrm{P}}+{k}_{\mathrm{A}\mathrm{LV}}{m}_{\mathrm{A}\mathrm{LV},2}+{k}_{\mathrm{TB}}\sum \limits_{i=0}^{14}{m}_{i,2} $$

(B-2)

Equation B - 2 is subject to the initial condition m_X = 0 at time t = 0

Central compartment drug concentration, c _X :

$$ {c}_{\mathrm{X}}=\frac{m_{\mathrm{X}}}{V_{\mathrm{C}}} $$

(B-3)

Where the volume of distribution, V_C, was calculated via Eq. 3 as discussed in the main text.

Peripheral compartment drug mass, m _P :

$$ \frac{d{m}_{\mathrm{P}}}{dt}={k}_{12}{m}_{\mathrm{X}}-{k}_{21}{m}_{\mathrm{P}} $$

(B-4)

Equation B - 4 is subject to the initial condition m_P = 0 at time t = 0

i^th tracheobronchial airway compartment drug mass, m_i (0 ≤ i < 14):

$$ \frac{d{m}_{\mathrm{i},1}}{dt}=-{K}_{\mathrm{diss},\mathrm{TB}}{m}_{\mathrm{i},1}\left({c}_{\mathrm{S}}-{c}_{\mathrm{i}}\right)-{k}_{\mathrm{muc},\mathrm{i}}{m}_{\mathrm{i},1}+{k}_{\mathrm{muc},\mathrm{i}+1}{m}_{\mathrm{i}+1,1} $$

(B-5)

$$ \frac{d{m}_{\mathrm{i},2}}{dt}={K}_{\mathrm{diss},\mathrm{TB}}{m}_{\mathrm{i},1}\left({c}_{\mathrm{S}}-{c}_{\mathrm{i}}\right)-{k}_{\mathrm{muc},\mathrm{i}}{m}_{\mathrm{i},2}+{k}_{\mathrm{muc},\mathrm{i}+1}{m}_{\mathrm{i}+1,2}-{k}_{\mathrm{TB}}{m}_{\mathrm{i},2} $$

(B-6)

i^th tracheobronchial airway compartment drug mass, m_i (i = 14):

$$ \frac{d{m}_{\mathrm{i},1}}{dt}=-{K}_{\mathrm{diss},\mathrm{TB}}{m}_{\mathrm{i},1}\left({c}_{\mathrm{S}}-{c}_{\mathrm{i}}\right)-{k}_{\mathrm{muc},\mathrm{i}}{m}_{\mathrm{i},1} $$

(B-7)

$$ \frac{d{m}_{\mathrm{i},2}}{dt}={K}_{\mathrm{diss},\mathrm{TB}}{m}_{\mathrm{i},1}\left({c}_{\mathrm{S}}-{c}_{\mathrm{i}}\right)-{k}_{\mathrm{muc},\mathrm{i}}{m}_{\mathrm{i},2}-{k}_{\mathrm{TB}}{m}_{\mathrm{i},2} $$

(B-8)

i^th tracheobronchial airway compartment drug concentration, c_i (0 ≤ i ≤ 14):

$$ {c}_{\mathrm{i}}=\frac{m_{\mathrm{i},2}}{V_{\mathrm{ASL},\mathrm{i}}} $$

(B-9)

Alveolar compartment drug mass, m _ALV :

$$ \frac{d{m}_{\mathrm{ALV},1}}{dt}=-{k}_{\mathrm{diss},\mathrm{ALV}}{m}_{\mathrm{ALV},1} $$

(B-10)

$$ \frac{d{m}_{\mathrm{ALV},2}}{dt}={k}_{\mathrm{diss},\mathrm{ALV}}{m}_{\mathrm{ALV},1}-{k}_{\mathrm{ALV}}{m}_{\mathrm{ALV},2} $$

(B-11)

Equation B – 5, B – 7, and B – 10 are subject to the initial condition m_i,1 = F_i at time t = 0. Eq. B – 6, B – 8, and B – 11 are subject to the initial condition m_i,2 = 0 at time t = 0