# A Distribution-Based Metric for Quantifying Dispersibility in Dry Powder Inhalers

## TL;DR

This paper introduces a new method using the Wasserstein distance to measure how well dry powder inhalers disperse medication, enabling better formulation and device comparisons.

## Contribution

The paper introduces a mathematically rigorous, distribution-based metric using the Wasserstein distance to quantify dispersibility in dry powder inhalers.

## Key findings

- Wasserstein-1 distance (W1) captured formulation- and device-dependent differences in dispersibility not visible in raw particle size distributions.
- Crystalline mannitol showed the largest W1 values, while amorphous trehalose and inulin had distinct pressure responses.
- W1 aligned with cascade impaction metrics, showing its potential as a reproducible and interpretable dispersibility metric.

## Abstract

Background/Objectives: Reproducible evaluation of aerosol dispersibility remains a key challenge in the development of dry powder inhalers (DPIs), where small variations in particle cohesion, morphology, or device resistance can lead to large differences in aerodynamic performance. In passive DPIs, the forces required for powder fluidization and aerosolization arise from the interaction of patient inspiratory airflow with device geometry and must overcome strong interparticle cohesive forces to enable effective lung delivery. Cascade impaction is the gold standard for determining aerodynamic particle size distribution (APSD), but its low throughput and experimental burden limit its utility for systematic formulation and device screening. Prior studies have explored laser diffraction-based particle sizing under varying dispersion energies as indirect metrics of powder dispersibility. Here, we extend this approach by introducing a mathematically rigorous, distribution-based framework that applies the first-order Wasserstein distance (Earth Mover’s Distance) to quantify relative dispersibility with respect to a material-specific maximally dispersed reference state. Methods: Mannitol, trehalose, and inulin were spray-dried under matched conditions to generate model dry powders. Particle size distributions were measured by laser diffraction (Sympatec HELOS/R) using both a RODOS dry dispersion module to define a maximally dispersed reference state and an INHALER module to generate aerosols under clinically relevant dispersion conditions spanning multiple device resistances and pressure drops. For each condition, the Wasserstein-1 distance (W1) was computed between cumulative volume-based size distributions obtained under reference and inhaler-based dispersion. Cascade impaction was used as an orthogonal method to characterize aerodynamic performance under a representative dispersion condition. Results: W1 captured formulation-, device-, and flow-dependent differences in dispersibility that were not readily separable by visual inspection of particle size distributions alone. Crystalline mannitol exhibited the largest and most flow-rate-dependent W1 values, whereas amorphous trehalose and polymeric inulin showed smaller W1 values with distinct, non-monotonic pressure responses that depended on device resistance. W1 qualitatively aligned with cascade impaction metrics, exhibiting a positive association with mass median aerodynamic diameter and an inverse association with fine particle fraction, while also demonstrating that efficient dose emission can occur despite incomplete deagglomeration. Conclusions: This study establishes the Wasserstein distance as a physically interpretable, formulation-agnostic metric for quantifying aerosol dispersibility relative to a material-specific reference state. This framework enables systematic comparison of dispersion efficiency across devices and operating conditions using standard laser diffraction data and provides a reproducible basis for mechanistic optimization of DPI formulations and inhaler designs.