Mahmoud Ismail

A novel formulation for Neumann inflow boundary conditions in biomechanics

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.

Coupled and reduced dimensional modeling of respiratory mechanics during spontaneous breathing

In this paper, we develop a total lung model based on a tree of 0D airway and acinar models for studying respiratory mechanics during spontaneous breathing. This model utilizes both computer tomography-based geometries and artificially generated lobe-filling airway trees to model the entire conducting region of the lung. Beyond the conducting airways, we develop an acinar model, which takes into account the alveolar tissue resistance, compliance, and the intrapleural pressure. With this methodology, we compare four different 0D models of airway mechanics and determine the best model based on a comparison with a 3D-0D coupled model of the conducting airways; this methodology is possible because the majority of airway resistance is confined to the lower generations, that is, the trachea and the first few bronchial generations. As an example application of the model, we simulate the flow and pressure dynamics under spontaneous breathing conditions, that is, at flow conditions driven purely by pleural space pressure. The results show good agreement, both qualitatively and quantitatively, with reported physiological values. One of the key advantages of this model is the ability to provide insight into lung ventilation in the peripheral regions. This is often crucial because this is where information, specifically for studying diseases and gas exchange, is needed. Thus, the model can be used as a tool for better understanding local peripheral lung mechanics without excluding the upper portions of the lung. This tool will be also useful for in vitro investigations of lung mechanics in both health and disease.

Adjoint-based inverse analysis of windkessel parameters for patient-specific vascular models

A human circulatory system is composed of more than 50,000 miles of blood vessels. Such a huge network of vessels is responsible for the elevated pressure values within large arteries. As such, modeling of large blood arteries requires a full modeling of circulatory system. This in turn is computationally not affordable. Thus, a multiscale modeling of the arterial network is a necessity. The multiscale approach is achieved through, first, modeling the arterial regions of interest with 3D models and the rest of the circulatory network with reduced-dimensional (reduced-D) models, then coupling the multiscale domains together. Though reduced-D models can well reproduce physiology, calibrating them to fit 3D patient-specific Fluid Structure Interaction (FSI) geometries has received little attention. For this reason, this work develops calibration methods for reduced-D models using adjoint based methods. We also propose a reduced modeling complexity (RMC) approach that reduces the calibration cost of expensive FSI models using pure fluid modeling. Finally, all of the developed calibration techniques are tested on patient-specific arterial geometries, showing the power and stability of the proposed calibration methods.

A stable approach for coupling multidimensional cardiovascular and pulmonary networks based on a novel pressure‐flow rate or pressure‐only Neumann boundary condition formulation

In many biomedical flow problems, reversed flows along with standard treatment of Neumann boundary conditions can cause instabilities. We have developed a method that resolves these instabilities in a consistent way while maintaining correct pressure and flow rate values. We also are able to remove the necessary prescription of both pressure and velocities/flow rates to problems where only pressure is known. In addition, the method is extended to coupled 3D/reduced-D fluid and fluid-structure interaction models. Numerical examples mainly focus on using Neumann boundary condition in cardiovascular and pulmonary systems, particularly, coupled with 3D-1D and 3D-0D models. Inflow pressure, traction, and impedance boundary conditions are first tested on idealized tubes for various Womersley numbers. Both pressure and flow rate are shown to match the analytical solutions for these examples. Our method is then tested on a coupled 1D-3D-1D artery example, demonstrating the power and simplicity of extending this method toward fluid-structure interaction. Finally, the proposed method is investigated for a coupled 3D-0D patient-specific full lung model during spontaneous breathing. All coupled 3D/reduced-D results show a perfect matching of pressure and flow rate between 3D and corresponding reduced-D boundaries. The methods are straight-forward to implement in contrast to using Lagrange multipliers as previously proposed in other studies.

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

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

CFD challenge: hemodynamic simulation of a patient-specific aortic coarctation model with adjoint-based calibrated windkessel elements

This work presents our approach for modelling the CFD challenge example of the aortic coarctation of an 8 year old child. The three-dimensional fluid domain was modeled as described in the challenge as an incompressible Newtonian fluid. A residual-based variational multiscale finite element method is used to solve the 3D fluid field. The boundaries were treated with 3-element windkessel models. The windkessel elements were tuned using an adjoint based method to fit the pressure and flowrate values reported by the challenge. A mesh refinement was performend to ensure the spatial convergence of the presented results. Finally, pressure values at π1 and π2 slices are reported.

Bridging Scales in Respiratory Mechanics

In this paper, we review different types of overall lung models developed recently in our group. The first approach is based on three-dimensional (3D) continuum models of both the airways and the tissue. As only parts of the lung can be resolved in detail in the model, advanced multi-scale techniques are utilized to adequately consider the unresolved parts. Alternatively, we have proposed a comprehensive reduced-dimensional lung model allowing to effectively study pressure and flow characteristics in the entire conducting region of the lung, albeit at the cost of detailed information on local tissue stresses and strains. To combine the advantages of detailed and simplified lung models, we have developed a novel approach for the coupling of 3D and 0D airway models.

Adjoint Based Calibration of Coupled Simulation Approaches of Patient-Specific Vascular Models

In recent years, computational methods have often been utilized for a better understanding of cardiovascular systems. They can be used to analyze vascular disease development [1], predict life threatening risk factors [2], and help improve vascular treatments.Copyright