A quasi-3D model of the whole lung: airway extension to the tracheobronchial limit using the constrained constructive optimization and alveolar modeling, using a sac–trumpet model

Abstract

Existing computational models used for simulating the flow and species transport in the human airways are zero-dimensional (0D) compartmental, three-dimensional (3D) computational fluid dynamics (CFD), or the recently developed quasi-3D (Q3D) models. Unlike compartmental models, the full CFD and Q3D models are physiologically and anatomically consistent in the mouth and the upper airways, since the starting point of these models is the mouth–lung surface geometry, typically created from computed tomography (CT) scans. However, the current resolution of CT scans limits the airway detection between the 3rd–4th and 7th–9th generations. Consequently, CFD and the Q3D models developed using these scans are generally limited to these generations. In this study, we developed a method to extend the conducting airways from the end of the truncated Q3D lung to the tracheobronchial (TB) limit. We grew the lung generations within the closed lung lobes using the modified constrained constructive optimization, creating an aerodynamically optimized network aiming to produce equal pressure at the distal ends of the terminal segments. This resulted in a TB volume and lateral area of ∼165 cc and ∼2000 cm2, respectively. We created a “sac–trumpet” model at each of the TB outlets to represent the alveoli. The volumes of the airways and the individual alveolar generations match the anatomical values by design: with the functional residual capacity at 2611 cc. Lateral surface areas were scaled to match the physiological values. These generated Q3D whole lung models can be efficiently used for conducting multiple breathing cycles of drug transport and deposition simulations.

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways

“…However, the most commonly used simplification is the adoption of rigid airway walls. 39,47,61 While this enables the simulation of dynamic flows in the 3D od quasi-3D patient-specific structures of the bronchial tree by means of computational fluid dynamics (CFD), 7,9,12,13,[29][30][31][32][33][34][35]36,[51][52][53][54][55][56][57] it does not take into account the aforementioned changes in the bronchial properties caused by variations in pressures and flow, or the associated lung volume. This disadvantage is not present in simulations using fluid-structure interactions (FSI) that allow for the 3D geometry and flexibility of the bronchi to be taken into account.…”

“…The second type of simplifications was based on the assumption of rigid walls of the airways, 13,32,33,35,47,48,51–55 analyzing the system for a single lung volume or constant flow 10,19,21,53,55,58 . Among these approaches, the quasi‐3D model using plenty of wires to simplify fluid dynamics simulations, 56 has proved particularly successful 12,36,57 . In other cases, the wave‐speed limitation was omitted when including FL by dissipative pressure loss in flexible airways 15,37 .…”

“…10,19,21,53,55,58 Among these approaches, the quasi-3D model using plenty of wires to simplify fluid dynamics simulations, 56 has proved particularly successful. 12,36,57 In other cases, the wave-speed limitation was omitted when including FL by dissipative pressure loss in flexible airways. 15,37 Finally, even when the full FL mechanism was considered, flow was treated as quasi-static when simulating data only in discrete lung volumes 14,16,17 or for discrete time increments, 22 instead of using numerical solvers of differential equations, resulting from tissue and air compliances or inertances.…”

Predicting systemic and pulmonary tissue barrier concentration of orally inhaled drug products

“…A 1D model of a tubing network distributed in a 3D space is well suited to solve such a problem, as previously shown by authors. [26][27][28] The major advantages of this approach are the ease of model setup, high computational speed, simple visualization of results, and an easy link to compact models such as spring/mass/damper devices, valves, pumps, controllers, and 0D compartmental models. This method is referred to as the Q3D model, since it solves for all the 3D flow variables of {u,v,w,p}x (unlike 1D models) while maintaining the fully developed wall boundary condition.…”

“…To address the aforementioned challenges, we present here a multiscale computational framework (Fig 1) that involves: i) our recently published full-scale 24 generation (Gen) 3D lung model with distinct barrier regions spanning trachea (Gen 0) to tracheobronchial (Gen 1-15) to alveolar (Gen [16][17][18][19][20][21][22][23] and to the terminal alveolar sacs (Gen 24); [26] ii) our previously published and modified computational fluid dynamics (CFD) module, called quasi-3D (Q3D), to calculate inhalation flow profile and PSD-based drug deposition, [27,28] iii) a first-principles-based and lung region-specific dissolution and absorption module, iv) a tracheobronchial-region specific MCC module, and v) a gut absorption module, all connected to whole-body PBPK. Our simulation outcomes were validated on two distinct ICSs: budesonide (conditions specific to the Novolizer® device, which under normal inspiratory flow rates shows similar deposition of budesonide in the lungs of healthy volunteers as the Turbuhaler®) [29]) and fluticasone propionate (conditions specific to the Diskus® device).…”