Modeling of the oxygen transfer in the respiratory process

Little is known about transport throughout the respiration cycle in the conducting airways. It is challenging to appropriately describe the time-dependent number of particles entering back into the model during exhalation. Modeling the entire lung is not feasible; therefore, multidomain methods must be used. Here, we present a new framework that is designed to simulate particles throughout the respiration cycle, incorporating realistic airway geometry and respiration. This framework is applied for a healthy rat lung exposed to ∼ 1μm diameter particles, chosen to facilitate parameterization and validation. The flow field is calculated in the conducting airways (3D domain) by solving the incompressible Navier-Stokes equations with experimentally derived boundary conditions. Particles are tracked throughout inspiration by solving a modified Maxey-Riley equation. Next, we pass the time-dependent particle concentrations exiting the 3D model to the 1D volume conservation and advection-diffusion models (1D domain). Once the 1D models are solved, we prescribe the time-dependent number of particles entering back into the 3D airways to again solve for 3D transport. The coupled simulations highlight that about twice as many particles deposit during inhalation compared to exhalation for the entire lung. In contrast to inhalation, where most particles deposit at the bifurcation zones, particles deposit relatively uniformly on the gravitationally dependent side of the 3D airways during exhalation. Strong agreement to previously collected regional experimental data is shown, as the 1D models account for lobe-dependent morphology. This framework may be applied to investigate dosimetry in other species and pathological lungs.

Section: Methodsmentioning

confidence: 99%

{normalΩ}_{1 D_{l}}

\frac{\partial Q_{1 D_{l}}}{\partial z} = - \frac{\partial A_{E_{l}}}{\partial t} for 0 ⩽ z ⩽ l_{T_{l}} and 0 ⩽ t ⩽ T,

where z is the longitudinal spatial coordinate along the length of the airway tree,

Q_{1 D_{l}}

is the total longitudinal flow rate for all the airways within each generation in the lobe l at position z , and

A_{E_{l}}

is the total volume, normalized by its length, of all the airways within each generation. Note that

A_{E_{l}}

evolves throughout the respiration cycle to account for the inhaled/exhaled air volume and the expression is presented later (Equation ).…”

Section: Methodsmentioning

confidence: 99%

“…Particle transport in the 1D domain,

{normalΩ}_{1 D_{l}}

: to ensure mass conservation, a semi‐implicit finite volume scheme is chosen to solve the 1D transport model, Equation .

{false(A_{E} c false)}_{l, i}^{n + 1} + \frac{normalΔ t}{normalΔ z_{l}} true[{normalΦ}_{l, i + 1 false/ 2}^{n + 1} - {normalΦ}_{l, i - 1 false/ 2}^{n + 1} true] = {false(A_{E_{l}} c false)}_{l, i}^{n} - normalΔ t L_{l, i}^{n},

where

\begin{matrix} left \\ Φ_{l, i + 1 / 2}^{n + 1} = {[Q_{l, D_{l, i}}^{n + 1} c_{l, i}^{n + 1}]}_{Q_{1 D_{l, i}}^{n + 1} > 0} + {[Q_{l, D_{l, i} + 1}^{n + 1} c_{l, i + 1}^{n + 1}]}_{Q_{l, D_{l, i}}^{n + 1} > 0} \\ - D_{E_{l, i} + 1 / 2}^{n + 1} A_{_{l, i} + 1 / 2} [\frac{c_{l, i + 1}^{n + 1} - c_{l, i}^{n + 1}}{Δ_{Z l}}] \\ Φ_{l,} \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Aerosol transport throughout inspiration and expiration in the pulmonary airways

Oakes

Shadden

Grandmont

et al. 2017

“…For mechanical ventilation or spirometric tests modeling, Robin boundary conditions can be applied to model the action of the surrounding tissue. On the basis of another study, we propose nonlinear boundary conditions that take into account the chest and the diaphragm resistance to lung expansion. One can consider f given by

bold-italicf = - k ((),, V) bold-italicu italicon \partial italicΩ

where k is a lobar dependant function that can be for instance be defined by

italick ((),, V) = k_{i} ((),, {italicV}_{italici}) = c_{i} \frac{((),, {italicV}_{italictlc}_{i} - V_{italicfr c_{i}}) V_{i}}{{italicV}_{italictlc}_{i} - V_{italicfr c_{i}} - V_{i}}, if bold-italicx \in \partial L_{i} ⋂ \partial italicΩ,

with ∂ L i as the outer surface of lobe i and V i

{, V}_{italicfr c_{i}}

, and V tlci , respectively, as the current inhaled volume in lobe i , its volume at functional residual capacity, and TLC.…”

Section: Modelmentioning

confidence: 99%

A tree‐parenchyma coupled model for lung ventilation simulation

Pozin

Montesantos

Katz

et al. 2017

In this article, we develop a lung ventilation model. The parenchyma is described as an elastic homogenized media. It is irrigated by a space-filling dyadic resistive pipe network, which represents the tracheobronchial tree. In this model, the tree and the parenchyma are strongly coupled. The tree induces an extra viscous term in the system constitutive relation, which leads, in the finite element framework, to a full matrix. We consider an efficient algorithm that takes advantage of the tree structure to enable a fast matrix-vector product computation. This framework can be used to model both free and mechanically induced respiration, in health and disease. Patient-specific lung geometries acquired from computed tomography scans are considered. Realistic Dirichlet boundary conditions can be deduced from surface registration on computed tomography images. The model is compared to a more classical exit compartment approach. Results illustrate the coupling between the tree and the parenchyma, at global and regional levels, and how conditions for the purely 0D model can be inferred. Different types of boundary conditions are tested, including a nonlinear Robin model of the surrounding lung structures.

“…Each acinus is assumed to be filled with a tree of alveolar ducts as illustrated in Figure 6(c). This approach allows to model the whole acinus as a 0D element while maintaining its viscoelastic mechanical properties (e.g., investigated in ). The resulting acinar model, as presented in , is linear and has been sufficient to reproduce the mechanical behavior of healthy lung tissue during spontaneous breathing reading

B \frac{d^{2} P (t)}{d t^{2}} + E_{2} \frac{dP (t)}{dt} = B_{normala} B \frac{d^{2} Q_{i}}{d t^{2}} + ((), E_{1} B + E_{2} B + E_{2} B_{normala}) \frac{d Q_{i} (t)}{dt} + E_{1} E_{2} Q_{i} ((), t),

where Q i is the air flow rate into an alveolar duct and B , B a , E 1 , and E 2 are the various components of the four‐element Maxwell model (Figure 6(b)).…”

Section: Mathematical Modelsmentioning

confidence: 99%

A comprehensive computational human lung model incorporating inter‐acinar dependencies: Application to spontaneous breathing and mechanical ventilation

Roth

Ismail

Yoshihara

et al. 2016

In this article, we propose a comprehensive computational model of the entire respiratory system, which allows simulating patient-specific lungs under different ventilation scenarios and provides a deeper insight into local straining and stressing of pulmonary acini. We include novel 0D inter-acinar linker elements to respect the interplay between neighboring alveoli, an essential feature especially in heterogeneously distended lungs. The model is applicable to healthy and diseased patient-specific lung geometries. Presented computations in this work are based on a patient-specific lung geometry obtained from computed tomography data and composed of 60,143 conducting airways, 30,072 acini, and 140,135 inter-acinar linkers. The conducting airways start at the trachea and end before the respiratory bronchioles. The acini are connected to the conducting airways via terminal airways and to each other via inter-acinar linkers forming a fully coupled anatomically based respiratory model. Presented numerical examples include simulation of breathing during a spirometry-like test, measurement of a quasi-static pressure-volume curve using a supersyringe maneuver, and volume-controlled mechanical ventilation. The simulations show that our model incorporating inter-acinar dependencies successfully reproduces physiological results in healthy and diseased states. Moreover, within these scenarios, a deeper insight into local pressure, volume, and flow rate distribution in the human lung is investigated and discussed. Copyright © 2016 John Wiley & Sons, Ltd.