Pediatric inhalation therapy and the aerodynamic rationale for age-based aerosol sizes

KEYWORDS:

• Inhalation therapy
• children
• infants
• pulmonary drug delivery
• aerosols

1. Introduction

Inhalation aerosols represent a cornerstone in treating pediatric respiratory conditions and may be administered as soon as following birth in preterm neonates or shortly after in babies. Yet, deposition efficiencies (DE) of inhaled aerosols in the lungs of infants and young children are underwhelming, with typical outcomes <30% of the administered dose, and not uncommonly <5% depending on age and disease [1]. Despite progress in improving delivery devices, current reviews still stress the same upsetting message [2,3]. The rule of thumb might easily read: the younger the patient the worse the targeting efficiency to the lungs.

The selection of an appropriate inhaler holds important ramifications in the effective dose delivered to a young patient’s lungs [4]. For example, infants and young children are unable to coordinate the inhalation maneuver necessary with metered dose inhalers (MDI). Concurrently, dry powder inhalers (DPIs) are typically advocated in older children as these require patient compliance through vigorous suction to de-aggregate the drug powder. Together these limitations, including the limited ability of young patients to hold their breath to increase the action of gravitational settling, hinder pulmonary DE and device options. For the youngest that are nose breathers, the practice of adapting face masks and intranasal prongs represents only incremental improvements. The underlying picture remains fundamentally unchanged.

Treatment options and inhalation guidelines are broadly derived from devices and protocols established for adults whereby dosage adaptations in children, if any, are based on extrapolations often according to bodyweight [5]. Clinicians may prescribe inhaled medications that are disease appropriate but not necessarily approved for these young ages as the majority of inhalers and drug formulations are based on adult studies, or at the very least in older children [6]. This reality underscores a lack in considering more significantly the physical determinants of inhaled aerosol transport that influence pulmonary deposition. In improving pediatric inhalation therapy, we advocate below the mechanistic argument to adapt pharmaceutical aerosol sizes according to age rather than adhere to a ‘one-size-fits-all’ approach.

2. Inhalation airflows: children are not miniature adults

Beyond the challenges of pediatric aerosol administration due to regimen and device compliance, as well as cognitive development (e.g. passive tidal breathing, coordination of inhalation with device actuation), we must first recognize that children are not simply miniature adults when considering anatomical and physiological differences with adults [7–9]. The ramifications are significant as neither weight- nor tidal breath-based parameter adaptations alone can achieve therapeutic efficiency in terms of dosimetry [10].

The coupling between children’s narrower airways (with small cross-sectional areas A) and higher breathing rates gives rise to airflow velocities that are faster in children's lungs compared to adults’, as supported by recent computational fluid dynamics (CFD) studies [11,12]. Here, it is critical to distinguish between bulk inhalation flow rates (e.g. Q in L/min) and local airflow velocities (i.e. U=Q/A in m/s). Despite lower inhalation flow rates in children, relatively faster airflow velocities in airways ensue from significantly smaller A and the relatively greater fraction of tidal volume with respect to functional residual capacity [12] (FRC). While our initial perception might be misled to assume that smaller lungs equate with weaker airflow velocities since inhalation flow rates are weaker, age-based differences imply that for a given airborne particle inhaled an aerosol will travel relatively faster in a child’s lungs compared to an adult as the particle is locally carried by relatively faster surrounding airflow velocities.

3. Inertia of inhaled airborne particles

For an inhaled aerosol traveling along the respiratory tract, its inclination to depart from a given trajectory can be assessed by comparing the (im)balance between (i) the particle’s inertia at a given flight speed (i.e. velocity) to (ii) the aerodynamic drag imparted from the surrounding airflow. As long as these two forces are balanced the particle will continue along its given trajectory at constant speed (not accounting for gravity or other forces such as electrostatic effects, etc.). We recall that a particle begins its airborne flight by accelerating to a given speed due to the aerodynamic drag exerted by the inhaled airflow. If the airflow accelerates further, the particle will attempt to ‘catch up’ with the new airspeed or conversely slow down if the airflow weakens. The ability for an aerosol to react quickly to such changes depends on the inertia it carries.

We may heuristically compare the magnitude of the forces emanating from (i) inertia to that resulting from (ii) frictional drag. The former is quantified from a particle’s momentum P = mv, (m is its mass and v its velocity). Assuming for easiness a spherical particle of diameter d_p such that mass is proportional to volume, we write m~ρd_p³ where ρ is the particle density (often close to that of water). In turn, the particle’s momentum scales as P~ρd_p³v. The resulting inertial force follows from Newton’s second law as the change in momentum over time (F_momentum = dP/dt). To estimate the rate (d/dt), we consider a representative timescale (t) corresponding to the travel time over a characteristic distance. In the lungs, this may be evaluated from the local airflow speed in an airway of diameter D such that t~ D/v. It then follows that F_momentum ~ ρd_p³v²/D.

The aerodynamic drag force experienced by this aerosol is directly proportional to the viscosity (µ) of the surrounding fluid (i.e. air). Considering the units of force (kg∙m/s²) and viscosity (kg/m-s), dimensional arguments impose that F_drag scales as ~µvd_p; this expression is nearly identical to the rigorous expression from Stokes’ drag law for small aerosols. We can compare the magnitude of each force by constructing the ratio:

(1) $\frac{F_{momentum}}{F_{drag}}\sim \frac{\rho d_p^3{v}^2/D}{\mu d_{p}v}=\frac{\rho d_p^{2}v}{\mu D}.$(1)

This force ratio is essentially the exact definition of the particle’s Stokes number, i.e. Stk~F_momentum/F_drag. A more rigorous derivation would lead to an algebraic constant multiplying the expression in Equation (1)(1) $\frac{F_{momentum}}{F_{drag}}\sim \frac{\rho d_p^3{v}^2/D}{\mu d_{p}v}=\frac{\rho d_p^{2}v}{\mu D}.$(1) , e.g. 1/18 for a sphere. We can gain some initial insight by considering that if Stk is larger than unity, the particle’s momentum will be larger than the ‘stabilizing’ effect of the aerodynamic drag. For a fixed d_p, the Stokes number at a given airway generation will be comparatively larger in a child as v is larger and D is smaller compared to adults (both parameters act to increase Stk). Conversely, for fixed values of v and D, decreasing the Stokes number requires significantly reducing the aerosol size as Stk ~ d_p².

The Stokes number thus represents the (in)ability of an aerosol to stay on course in the advent of changes along its trajectory. In the lungs, this ensues most notably from anatomical deviations (e.g. oropharyngeal region, glottal constriction, bifurcating airways). If an aerosol cannot swiftly adapt to dynamic changes along its trajectory, it will tend to keep course and eventually impact. Hence, the combination of faster speeds and smaller airways in pediatric populations favors impaction.

4. Expert opinion

The concept of the Stokes number is well established in pharmaceutical research and development. It serves as the basis of measurement apparatuses (e.g. cascade impactor) to optimize, for example, the fraction of fine particles manufactured. However, this physical concept has not transcended clinical guidelines for pediatric inhalation therapy. While our mechanistic considerations do not account for disease specificities or intra-subject differences, delivering aerosols to the respiratory regions requires minimizing impaction to circumvent superfluous losses and avoid undesired side effects. In pediatric populations, impaction leads to relatively higher losses of a nominal therapeutic dose in extra-thoracic and the proximal conducting regions. While this results in a higher deposition efficiency (DE) at the whole-lung level, it comes at the undesirable cost of a higher deposition ratio of conductive to respiratory regions [10] (Figure 1a).

Figure 1. (a) Schematic of aerosol deposition trends as a function of age groups (i.e. adult, child and infant) and highlighted in the different lung regions (i.e. extra-thoracic, conducting and respiratory). By and large pediatric deposition is confined to the upper and extra-thoracic airways. (b) Deposition efficiency (DE) as a function of the particle Stokes number (Stk); curve trends are displayed according to the respective lung regions.

Recognizing that DE curves for the extra-thoracic, conducting and respiratory regions follow broadly a similar trend according to age when plotted as a function of Stk [11] (Figure 1b), the physical underpinnings introduced here support the rationale to use smaller aerosols in younger populations (i.e. a given Stokes number corresponds to a smaller aerosol diameter at younger ages). Customizing inhaled particle sizes according to age groups can thus increase their chance to ‘go with the flow’ and adhere to the sinuous changes along the respiratory tract. Advocating for smaller aerosol sizes is however not a boundless recommendation. Indeed, our heuristic treatment of the Stokes number does not consider other concurrent deposition mechanisms, foremost gravitational settling (or diffusion for aerosols <0.1–0.2 µm). Moreover, the number and size of aerosols are known to be flow rate-dependent in some devices (e.g. DPIs) such that increased inhalation flow rates yield both higher emitted dose and smaller particles. In turn, the correlation of lung dose with flow rate is complex and can be both positive or negative depending on the formulation of the drug and the characteristics of the inhaler [13]. Despite the limitations of our mechanistic analysis, when considering typical pharmaceutical aerosol size ranges (~0.1 to 10 µm) inhalation therapy guidelines should favor delivering smaller sizes for pediatric inhalation therapy and could potentially be realized by more convenient drug formulations or modifications in device design. While straightforward solutions are not yet widely available, the overarching delivery strategy should aim to mitigate superfluous losses from impaction such that aerosols reach the deeper airways where gravity can guarantee deposition (or avoid losses due to exhalation for sub-micron aerosols). For example, recent condensational growth techniques rely on inhaling very fine aerosols (<1 µm), thereby eliminating extrathoracic depositional loss while providing a means to minimize exhaled loss following aerosol size growth along the respiratory tract [14,15].

Looking back, clinical recommendations have been repeatedly voiced to use smaller aerosol sizes for pediatric patients [9]. Not only did past studies over two decades ago acknowledge that smaller airway diameters lead to increased central lung deposition due to increased impaction [16], the notion that lung deposition increases with age while oropharyngeal deposition decreases was clearly advanced [17]. Significantly, higher amounts of lung dose have been achieved both in vivo and in vitro using smaller aerosol sizes in early childhood [18]. While these conclusions have not directly been attributed to aerodynamic considerations, our discussion is motivated by the same reality undermining the success of pediatric inhalation therapy. Here, we have adopted a simple yet mechanistic argument to further support these seminal studies and ultimately accelerate changes in current clinical guidelines.

Declaration of interest

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

Reviewer disclosures

Peer reviewers on this manuscript have no relevant financial or other relationships to disclose.

Additional information

Funding

J. Sznitman thanks funding support from the Israel Science Foundation (ISF Grant no. 1840/21). J.M. Oakes was supported by the Bill and Melinda Gates Foundation (INV-018835).