Hæmodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D¿numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional¿numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D¿scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D¿blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional¿numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D¿models and numerical schemes.
This paper presents a methodological review of models for predicting blood glucose (BG) concentration, risks and BG events. The surveyed models are classified into three categories, and they are presented in summary tables containing the most relevant data regarding the experimental setup for fitting and testing each model as well as the input signals and the performance metrics. Each category exhibits trends that are presented and discussed. This document aims to be a compact guide to determine the modeling options that are currently being exploited for personalized BG prediction. This paper presents a methodological review of models for predicting blood glucose (BG) concentration, risks, and BG events. The surveyed models are classified into three categories, and they are presented in summary tables containing the most relevant data regarding the experimental setup for fitting and testing each model as well as the input signals and the performance metrics. Each category exhibits trends that are presented and discussed. This document aims to be a compact guide to determine the modeling options that are currently being exploited for personalized BG prediction.
The immersed boundary method is an approach to fluid‐structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid‐structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian‐Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. We employ a nodal FE discretization of the structural equations while retaining a finite difference discretization of the Eulerian equations, and we apply this new scheme to benchmark problems involving elastic, rigid, and actively contracting structures of left ventricle. The primary contribution of this work is that it introduces a novel approach to coupling the Lagrangian and Eulerian variables that enables Independent Lagrangian and Eulerian spatial discretizations and thus the effective use of coarse structural meshes with the IB method.
Protein‐ligand binding is a fundamental biological process that is paramount to many other biological processes, such as signal transduction, metabolic pathways, enzyme construction, cell secretion, and gene expression. Accurate prediction of protein‐ligand binding affinities is vital to rational drug design and the understanding of protein‐ligand binding and binding induced function. Existing binding affinity prediction methods are inundated with geometric detail and involve excessively high dimensions, which undermines their predictive power for massive binding data. Topology provides the ultimate level of ion and thus incurs too much reduction in geometric information. Persistent homology embeds geometric information into topological invariants and bridges the gap between complex geometry and topology. However, it oversimplifies biological information. This work introduces element specific persistent homology (ESPH) or multicomponent persistent homology to retain crucial biological information during topological simplification. The combination of ESPH and machine learning gives rise to a powerful paradigm for macromolecular analysis. Tests on 2 large data sets indicate that the proposed topology‐based machine‐learning paradigm outperforms other existing methods in protein‐ligand binding affinity predictions. ESPH reveals protein‐ligand binding mechanism that can not be attained from other conventional techniques. The present approach reveals that protein‐ligand hydrophobic interactions are extended to 40Å away from the binding site, which has a significant ramification to drug and protein design. Most physical models are based on geometry, which leads to high number of degrees of freedom for biomolecular data sets. In contrast, topology is often too to be practically useful. Persistent homology bridges the gap between geometry and topology but neglects biological information. This work introduces element‐specific persistent homology to retain essential biological information during topological simplification. The integration of element‐specific persistent homology and machine learning sheds light on the molecular mechanism of protein‐ligand binding that cannot obtain from other conventional techniques.
Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient‐specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid–structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient‐specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian–Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient‐specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta. In this work, we present a framework for designing patient‐specific prosthetic heart valves using parametric design and immersogeometric fluid–structure interaction (FSI) analysis. Leaflet geometry is generated from several design parameters, while conforming to a medical image derived aortic root geometry at the attached edge. Each design is analyzed using our immersogeometric FSI methodology. A parametric study investigates the influence of geometry on valve performance. Simulation results are compared with phase contrast magnetic resonance imaging data.
Mechanical ventilation is a key therapy for patients who cannot breathe adequately by themselves, and dynamics of mechanical ventilation system is of great significance for life support of patients. Recently, models of mechanical ventilated respiratory system with 1 lung are used to simulate the respiratory system of patients. However, humans have 2 lungs. When the respiratory characteristics of 2 lungs are different, a single‐lung model cannot reflect real respiratory system. In this paper, to illustrate dynamic characteristics of mechanical ventilated respiratory system with 2 different lungs, we propose a mathematical model of mechanical ventilated respiratory system with 2 different lungs and conduct experiments to verify the model. Furthermore, we study the dynamics of mechanical ventilated respiratory system with 2 different lungs. This research study can be used for improving the efficiency and safety of volume‐controlled mechanical ventilation system. Because coupling effects of 2 lungs has a significant influence on safety and efficiency of mechanical ventilation, a pneumatic model with 2 lungs has been built in this paper to study the coupling effects of 2 lungs in volume‐controlled ventilation. It can be concluded that a change of compliance or air resistance of one lung can affect both lungs and an unbalance of 2 lungs may result in overly high pressure in the trachea and overventilation.
Bronchial diameter is a key parameter that affects the respiratory treatment of mechanically ventilated patients. In this paper, to reveal the influence of bronchial diameter on the airflow dynamics of pressure‐controlled mechanically ventilated patients, a new respiratory system model is presented that combines multigeneration airways with lungs. Furthermore, experiments and simulation studies to verify the model are performed. Finally, through the simulation study, it can be determined that in airway generations 2 to 7, when the diameter is reduced to half of the original value, the maximum air pressure (maximum air pressure in lungs) decreases by nearly 16%, the maximum flow decreases by nearly 30%, and the total airway pressure loss (sum of each generation pressure drop) is more than 5 times the original value. Moreover, in airway generations 8 to 16, with increasing diameter, the maximum air pressure, maximum flow, and total airway pressure loss remain almost constant. When the diameter is reduced to half of the original value, the maximum air pressure decreases by 3%, the maximum flow decreases by nearly 5%, and the total airway pressure loss increases by 200%. The study creates a foundation for improvement in respiratory disease diagnosis and treatment. We propose a novel mathematical model of mechanical ventilated respiratory system with multigeneration airways. The mathematical model was verified through experimental study. Influence of bronchial diameter on airflow dynamics of pressure‐controlled ventilation system is illustrated. The bronchial diameter change in generations 2 to 7 has a greater impact on airflow dynamics than that in generations 8 to 16. The study lays a foundation for the improvement in respiratory disease diagnosis and treatment.