Inhaled Aerosol Deposition as Regional Lung Dose

From an Inhaled Dose to Regional Lung Dose

An inhaler dose is not automatically a lung dose. Some material may remain in the device, fail to enter the mouth, deposit in the upper airways, or be exhaled. Even the portion deposited in the lung is not necessarily distributed uniformly: particle size and the way a person inhales can change how much reaches different regions. For PBPK modeling, the useful starting point is therefore a mass balance that connects the inhaled amount to deposited amounts in specified regions.

This tutorial concerns where and how much aerosol deposits. A deposited amount is a regional input to a subsequent model; deposition alone does not specify how quickly drug leaves that region or enters systemic circulation.

Definition: Let \(D_{\mathrm{in}}\) be the aerosol mass inhaled during a specified administration, in mass units such as micrograms. For lung region \(r\), the regional deposition fraction \(f_r\) is the fraction of \(D_{\mathrm{in}}\) that deposits in that region under the specified aerosol and breathing conditions. The regional deposited dose is \(D_r=f_rD_{\mathrm{in}}\). If the regions are mutually exclusive, their fractions sum to at most 1; the remainder represents inhaled mass not assigned to those deposited regions, often including exhaled mass.

A practical regional partition might distinguish the extrathoracic region (such as the mouth and upper airway), the conducting airways, and the pulmonary region. The exact partition should match the intended model. If only lung deposition is being tabulated, upper-airway deposition should be reported separately rather than silently counted as lung dose.

It is also important to specify which dose is used. A nominal or metered dose is the amount intended to leave the device; an emitted dose is the amount that actually leaves it; and an inhaled dose is the amount that enters the respiratory tract. If \(D_{\mathrm{nom}}\) is nominal dose, and \(f_{\mathrm{emit}}\) and \(f_{\mathrm{capture}}\) are the fractions emitted and then inhaled, respectively, a simple accounting relationship is \(D_{\mathrm{in}}=D_{\mathrm{nom}}f_{\mathrm{emit}}f_{\mathrm{capture}}\). These fractions must not be applied again if the supplied dose is already the inhaled dose.

Regional Fractions and Mass Balance

Regional fractions are conditional on the specified situation: aerosol formulation and particle-size distribution, device, and breathing conditions. They are not universal constants for a drug or a lung region. For a consistent accounting, define the fractions with a common denominator, usually the mass inhaled into the respiratory tract. If \(f_{\mathrm{ET}}\), \(f_{\mathrm{cond}}\), and \(f_{\mathrm{pulm}}\) are fractions of inhaled mass depositing in the extrathoracic, conducting-airway, and pulmonary regions, then

f_{\mathrm{ET}}+f_{\mathrm{cond}}+f_{\mathrm{pulm}}+f_{\mathrm{exh}}=1, \qquad D_r=f_rD_{\mathrm{in}},

where \(f_{\mathrm{exh}}\) is the fraction exhaled without depositing in the specified regions. If a model tracks only selected regions, the tracked fractions may sum to less than 1; the untracked remainder should be stated, not reassigned by assumption. A sum above 1 is a warning that fractions with different denominators have been mixed, regions overlap, or a calculation is wrong.

Worked Example: Separating Device Losses From Regional Deposition

Suppose a hypothetical inhaler has a nominal dose of 500 micrograms. Assume 80% is emitted from the device and 75% of that emitted mass is inhaled. For this breathing condition, suppose the inhaled-mass fractions are 0.30 extrathoracic, 0.25 conducting-airway, 0.35 pulmonary, and 0.10 exhaled. Calculate the inhaled dose and regional amounts.

Inhaled dose. Applying the device and inhalation fractions once gives \(D_{\mathrm{in}}=500\ \text{micrograms}\times0.80\times0.75=300\ \text{micrograms}\).

Regional deposition. The extrathoracic amount is \(0.30\times300=90\) micrograms; the conducting-airway amount is \(0.25\times300=75\) micrograms; and the pulmonary amount is \(0.35\times300=105\) micrograms. The exhaled amount is \(0.10\times300=30\) micrograms.

The check is \(90+75+105+30=300\) micrograms, and the fractions sum to \(0.30+0.25+0.35+0.10=1.00\). The pulmonary deposited dose is 105 micrograms, not 35% of the nominal dose: the stated fractions were defined relative to inhaled mass.

Accounting for Particle-Size Distributions

An aerosol contains particles over a range of sizes. A single representative size can hide important differences in deposition. One transparent calculation divides the aerosol into size bins, records the mass share in each bin, and applies a regional deposition fraction for each bin. Here, particle size is represented by aerodynamic diameter, which accounts for how a particle behaves aerodynamically rather than only its geometric dimensions.

Definition: Let \(w_j\) be the fraction of inhaled aerosol mass in size bin \(j\), with \(\sum_j w_j=1\). Let \(F_{rj}\) be the fraction of mass in bin \(j\) that deposits in region \(r\) under the stated conditions. The total inhaled-mass fraction depositing in region \(r\) is \(f_r=\sum_j w_jF_{rj}\), and the regional dose is \(D_r=D_{\mathrm{in}}\sum_jw_jF_{rj}\).

This weighted sum follows directly from mass accounting. The inhaled mass in bin \(j\) is \(D_{\mathrm{in}}w_j\); the amount of that bin deposited in region \(r\) is \(D_{\mathrm{in}}w_jF_{rj}\). Adding the deposited amounts across non-overlapping bins gives

D_r=\sum_j D_{\mathrm{in}}w_jF_{rj} =D_{\mathrm{in}}\sum_jw_jF_{rj}.

The calculation assumes that the bin mass shares refer to inhaled aerosol, that the bins cover the full inhaled size distribution, and that each \(F_{rj}\) uses the same regional definitions and inhaled-mass accounting. For each bin, the fractions assigned to all tracked deposited regions plus the non-deposited remainder should sum to 1. The fractions are inputs to this calculation; they must be appropriate to the particular aerosol and breathing scenario.

Worked Example: Combining Size Bins Into Regional Doses

Consider a hypothetical 400-microgram inhaled dose with 25% of its mass in a 1-micrometre bin, 50% in a 3-micrometre bin, and 25% in a 6-micrometre bin. Suppose the following illustrative fractions apply within each bin:

Size bin	Mass share \(w_j\)	Extrathoracic \(F_{\mathrm{ET},j}\)	Conducting \(F_{\mathrm{cond},j}\)	Pulmonary \(F_{\mathrm{pulm},j}\)	Exhaled remainder
1 micrometre	0.25	0.20	0.10	0.55	0.15
3 micrometres	0.50	0.35	0.30	0.25	0.10
6 micrometres	0.25	0.55	0.25	0.08	0.12

Each row's regional fractions and remainder sum to 1, and the mass shares sum to 1. The overall extrathoracic fraction is \(0.25(0.20)+0.50(0.35)+0.25(0.55)=0.3625\), giving \(400(0.3625)=145\) micrograms. The conducting-airway fraction is \(0.25(0.10)+0.50(0.30)+0.25(0.25)=0.2375\), giving 95 micrograms.

The pulmonary fraction is \(0.25(0.55)+0.50(0.25)+0.25(0.08)=0.2825\), giving \(400(0.2825)=113\) micrograms. The weighted exhaled fraction is \(0.25(0.15)+0.50(0.10)+0.25(0.12)=0.1175\), giving 47 micrograms. The amounts sum to \(145+95+113+47=400\) micrograms. The small apparent discrepancy between rounded regional amounts and exact fractions is avoided here because these amounts are exact to the nearest microgram.

Breathing Conditions and Regional Input Profiles

The same inhaled mass can yield different regional doses under different breathing conditions. For example, a hypothetical deposition calculation might assign different fractions to a shallow, faster inhalation than to a slower, deeper inhalation. The fractions should be selected or estimated for the relevant conditions; they should not be transferred between scenarios without justification.

For a PBPK input, a regional deposited amount may be treated as an input at the time of deposition, or represented as a time-varying deposition rate if the inhalation period is resolved. Let \(R_{\mathrm{in}}(t)\) be the inhaled mass rate, in micrograms per minute, and let \(f_r(t)\) be the regional fraction applicable at time \(t\). Then the regional deposition input rate is

R_r(t)=f_r(t)R_{\mathrm{in}}(t), \qquad D_r=\int R_r(t)\,dt.

If the regional fractions are constant over the administration, integration gives \(D_r=f_rD_{\mathrm{in}}\), where \(D_{\mathrm{in}}=\int R_{\mathrm{in}}(t)\,dt\). If inhalation conditions change during the dose, use condition-specific fractions over the corresponding intervals and add the resulting deposited amounts. This constructs a deposition input; it does not describe subsequent regional absorption or clearance.

Worked Example: Comparing Breathing Conditions and Building an Input

Suppose two hypothetical breathing conditions each deliver 300 micrograms into the respiratory tract. Under shallow inhalation, use fractions of 0.35 extrathoracic, 0.25 conducting-airway, 0.20 pulmonary, and 0.20 exhaled. Under slow, deep inhalation, use 0.20, 0.20, 0.50, and 0.10, respectively. Calculate the regional amounts and, for slow, deep inhalation, construct a simple time-dependent input for two inhalation intervals.

Shallow inhalation. The regional amounts are \(300(0.35)=105\) micrograms extrathoracic, \(300(0.25)=75\) micrograms conducting-airway, and \(300(0.20)=60\) micrograms pulmonary. The remaining 60 micrograms are exhaled. These amounts sum to 300 micrograms.

Slow, deep inhalation. The corresponding amounts are \(300(0.20)=60\) micrograms extrathoracic, \(300(0.20)=60\) micrograms conducting-airway, and \(300(0.50)=150\) micrograms pulmonary; 30 micrograms are exhaled. Again the total is 300 micrograms. Under the supplied hypothetical fractions, the slow, deep condition deposits 90 micrograms more in the pulmonary region than the shallow condition.

Now suppose the slow, deep inhaled rate is 120 micrograms per minute from time 0 to 1 minute and 180 micrograms per minute from time 2 to 3 minutes, with no inhaled dose between intervals. The total is \(120(1)+180(1)=300\) micrograms. With constant regional fractions, the pulmonary input rate is \(0.50(120)=60\) micrograms per minute from 0 to 1 minute and \(0.50(180)=90\) micrograms per minute from 2 to 3 minutes. Integrating gives \(60(1)+90(1)=150\) micrograms deposited in the pulmonary region. The same construction gives extrathoracic rates of 24 and 36 micrograms per minute, and conducting-airway rates of 24 and 36 micrograms per minute, over the respective intervals.

Assumptions, Diagnostics, and Alternatives

These calculations are mass-allocation models. Their usefulness depends on whether the input fractions represent the intended aerosol and conditions. The fractions may come from an appropriate deposition model, measurement, or justified scenario specification; a table of numbers alone does not make them transferable to another device or breathing pattern.

Check denominators. Confirm whether each fraction is relative to nominal, emitted, or inhaled dose. Regional fractions defined against inhaled mass cannot be multiplied directly by nominal dose unless the earlier dose conversions are included exactly once.
Check mass conservation. For each size bin or condition, sum all mutually exclusive regional fractions and the stated remainder. A sum above 1 indicates an accounting problem; a sum below 1 requires an explicit unassigned category.
Check size-bin coverage. Mass shares should sum to 1 for the inhaled aerosol. Omitting a size range without accounting for its mass can bias all regional estimates.
Check scenario matching. A change in particle-size distribution or breathing condition may alter regional fractions. Reusing one set of fractions without checking its applicability can produce plausible-looking but unsupported regional inputs.
Check regional definitions. Ensure that the regions do not overlap and that any extrathoracic deposition is not counted again as lung deposition.

A single overall regional fraction is the simplest alternative and can be adequate when only a coarse estimate is needed and the aerosol and breathing scenario are fixed. A size-bin calculation is more informative when particle-size composition matters and suitable bin-specific fractions are available. A more detailed deposition model may represent additional aerosol and respiratory features, but greater detail does not remove the need to define dose denominators, regions, and mass balance. All approaches remain limited by the quality and relevance of their deposition inputs.

Common pitfall: Multiplying the nominal dose by a regional fraction that is defined relative to inhaled mass, while also treating that product as a lung dose, skips the device-emission and inhalation steps. The correction is to establish \(D_{\mathrm{in}}\) first, apply regional fractions to that amount, and report any upstream dose fractions separately. Also, a deposited pulmonary dose is not automatically an absorbed dose.

Check Your Understanding

Answer each question, then compare with the worked solutions below.

An inhaled dose is 240 micrograms. Fractions are 0.25 extrathoracic, 0.30 conducting-airway, and 0.35 pulmonary. What is the unassigned or exhaled fraction, and what pulmonary amount is deposited?
An inhaled aerosol has 60% of its mass in bin A and 40% in bin B. The pulmonary fractions are 0.40 and 0.20. Calculate the overall pulmonary fraction.
Why is it incorrect to multiply a nominal dose by regional fractions defined relative to inhaled mass without first accounting for emission and inhalation?
If a regional deposition fraction is constant during an inhalation and the inhaled rate doubles for the same time interval, what happens to the regional deposition rate during that interval?

Solutions. (1) The remainder is \(1-(0.25+0.30+0.35)=0.10\), or 10%; the pulmonary amount is \(240(0.35)=84\) micrograms. (2) The weighted pulmonary fraction is \(0.60(0.40)+0.40(0.20)=0.32\), or 32%. (3) The regional fraction applies to inhaled mass, not nominal mass; first convert nominal dose to inhaled dose using the applicable emission and inhalation fractions, then apply the regional fraction. (4) Since \(R_r(t)=f_rR_{\mathrm{in}}(t)\) with constant \(f_r\), doubling \(R_{\mathrm{in}}(t)\) doubles the regional deposition rate.