title: A novel formulation for Neumann inflow boundary conditions in biomechanics.
abstract: Neumann boundary conditions prescribing the total momentum flux at inflow boundaries of biomechanical problems are proposed in this study. This approach enables the simultaneous application of velocity/flow rate and pressure curves at inflow boundaries. As the basic numerical method, a residual-based variational multiscale (or stabilized) finite element method is presented. The focus of the numerical examples in this work is on respiratory flows with complete flow reversals. However, the proposed formulation is just as well suited for cardiovascular flow problems with partial retrograde flow. Instabilities, which were reported for such problems in the literature, are resolved by the present approach without requiring the additional consideration of a Lagrange multiplier technique. The suitability of the approach is demonstrated for two respiratory flow examples, a rather simple tube and complex tracheobronchial airways (up to the fourth generation, segmented from end-expiratory CT images). For the latter example, the boundary conditions are generated from mechanical ventilation data obtained from an intensive care unit patient suffering from acute lung injury. For the tube, analytical pressure profiles can be replicated, and for the tracheobronchial airways, a correct distribution of the prescribed total momentum flux at the inflow boundary into velocity and pressure part is observed.
authors.affiliation: Emmy Noether Research Group on "Computational Multiscale Methods for Turbulent Combustion", Technische Universität München, Boltzmannstr. 15, D-85747 Garching, Germany; Institute for Computational Mechanics, Technische Universität München, Boltzmannstr. 15, D-85747 Garching, Germany. vgravem@lnm.mw.tum.de.
authors.forename: Volker
authors.initials: V
authors.lastname: Gravemeier
authors.forename: Andrew
authors.initials: A
authors.lastname: Comerford
authors.forename: Lena
authors.initials: L
authors.lastname: Yoshihara
authors.forename: Mahmoud
authors.initials: M
authors.lastname: Ismail
authors.forename: Wolfgang A
authors.initials: WA
authors.lastname: Wall
mesh_terms: D055371:Acute Lung Injury / Q000503:physiopathology / Q000628:therapy; D001696:Biomechanical Phenomena / Q000502:physiology*; D001980:Bronchi / Q000033:anatomy & histology / Q000502:physiology; D020342:Finite Element Analysis; D006801:Humans; D008954:Models, Biological; D012121:Respiration, Artificial; D015656:Respiratory Mechanics / Q000502:physiology*; D014132:Trachea / Q000033:anatomy & histology / Q000502:physiology
keywords: Neumann inflow boundary conditions; cardiovascular mechanics; residual-based variational multiscale finite element method; respiratory mechanics