Fig 1.
PV ventilation system coupled to DIC.
(A) A unique global PV to local DIC interfaced system illustrates piston-actuated ventilation and overhead cameras capturing bulk pressures and volumes as associated with regional tissue strains. (B) Visualization of the speckling used to track the displacements and strains for DIC. (C) Various PV inflation trajectories continuously measured are exemplified for three donor lungs. (D) Inflation stages at 30%, 60%, and 100% of maximum pressure display non-trivial strain patterns.
Fig 2.
FEA geometry and mesh preparation.
(A) The commercial geometry was meshed and oriented to reproduce the positioning of the specimen during inflation within the apparatus. The mesh was generated using HyperMesh with refinement based on curvature [51]. On the left, a perspective cut shows the utilization of smaller elements on the edges, while larger elements fill the bulk of the lungs. The refinement aided in modeling the contact between the lobes. (B) Airways from the commercial geometry up to the 10th generation were used to extract centerlines and define the geometry.
Fig 3.
Experimental nominal stress-strain curves from the biaxial measurements on pleura samples used to inform the FE model.
A polynomial curve was fit to all the data resulting in an averaged response (red) which generated material parameters using the Abaqus evaluation tool [55] for a reduced polynomial (Eq 3). The orange curves represent limiting cases where λ = 3 and λ = 1e−6 as defined in Table 1.
Fig 4.
(A) Human lungs positioned medial face-down on the plate in the air-tight tank are inflated according to the experimentally recorded pressure evolution shown in (B). The pressure values are increased at each of the 220 parenchymal nodes (red) corresponding to the end of the airway branches (C), which then diffuse throughout the rest of the tissue. The trachea (green) is constrained, and the deformable airways (blue) are embedded into the solid elements of the lungs.
Fig 5.
General IFEA optimization process used to model human lung mechanics.
Experimental pressure values during inflation serve as the input, where nine model parameters were calibrated to minimize the difference between output global lung volume and local strain experiments.
Table 1.
Parameters used in the optimization process and their boundaries.
The parameters kUL,LL,UR,MR,LR refer to the permeabilities for the five lobes as illustrated in Fig 4A. μ, α and ν are the material properties defined in Eq 1. The airways are characterized by the stiffness C10 from Eq 2, and the coefficient λ drives the mechanical behavior of the pleura based on Eq 3.
Fig 6.
Errors between the experimental data and those obtained following the optimization process for three different solutions representing local minima.
The relative error was computed using Eq 5 for the volumes, the average strains, and the strain standard deviation (σ strains). Overall, the local minimum 1 provided a better solution.
Table 2.
Initial starting points and converged calibrated parameters obtained from optimization.
The MultiStart option was utilized to define a set of feasible starting points and search for local minima for each point [81]. The algorithm successfully converged to solutions for three of the local solutions. While the starting points 2 and 3 were suggested by the solver, starting point 1 was determined through a trial-and-error approach involving multiple simulations and a sensitivity analysis (S3 Appendix).
Fig 7.
Translucent schematic (A) showing the relative airway placement within lobes where significant displacements are noted primarily in the distal airways (B), while the trachea and the main bronchi remain stationary. Representation of pore pressure flow inside the lungs is shown in (C). Major strains for the five lobes are visible in (D), with an expanded view focusing on the middle right lobe, a region of interest that exhibits similar strain patterns to those observed in other human lungs with the same lobe configuration.
Fig 8.
Comparison between the numerical model and the representative experimental PV curve during inflation, following calibration for local minimum 1.
Early and late inflection characteristic response of the physiological curve is observed.
Fig 9.
Post-calibration results of the model to subject-specific experiments.
Comparisons between experimental data and the model results at inflation snapshots of 30%, 60%, and 100% of maximum pressure stages, respectively. (A) The regional distribution of strains is quantitatively contrasted between experiment (speckle points) and computational model (nodes) with 1000–2000 data points for each lobe shown with the average major strains and standard deviation bars. (B) illustrates the strain patterns and distributions across the lobes, while (C) quantifies the magnitude of strain distributions across the fractional surfaces of the entire lung where the vertical dashed lines represent the averages.