Three-dimensional overall lung model
Ventilator-associated lung injuries (VALI) are known to occur primarily in the respiratory zone of the lung. Therefore, a detailed three-dimensional (3D) model of lung parenchyma is needed. However, for a reasonable investigation of respiratory mechanics during mechanical ventilation, the conducting part of the lung also has to be included in the model. After all, local parenchyma deformations are governed by the distribution of airﬂow into the peripheral domains.
To combine the conducting and the respiratory domains in one overall lung model, we have proposed a novel coupling approach. Since only parts of both the airway tree and the alveolar structures can be resolved in 3D, the transport of air down to the respiratory zone cannot be simulated explicitly but has to be modeled. The developed methodology is based on dividing the parenchyma model into subdomains associated with the outlets of the resolved 3D airway tree. The volume of air passing through each outlet has to equal the change in volume of the corresponding tissue subdomain. To enforce this constraint within the framework of monolithic fluid-structure interaction (FSI) problems, the Lagrange multiplier technique has been utilized. For the parallel and iterative solution of the resulting linear systems, a speciﬁc preconditioning algorithm has been proposed.
The volume coupling approach can be easily combined with the multiscale parenchyma model. Hence, we have established a 3D overall lung model comprising the conducting and the respiratory part of the lung down to single alveoli.
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