Numerical simulation of blood flow in an anatomically-accurate cerebral venous tree

Numerical coupling of 0D and 1D models in networks of vessels including transonic flow conditions. Application to short-term transient and stationary hemodynamic simulation of postural changes

When modeling complex fluid networks using one-dimensional (1D) approaches, boundary conditions can be imposed using zero-dimensional (0D) models. An application case is the modeling of the entire human circulation using closed-loop models. These models can be considered as a tool to investigate short-term transient and stationary hemodynamic responses to postural changes. The first shortcoming of existing 1D modeling methods in simulating these sudden maneuvers is their inability to deal with rapid variations in flow conditions, as they are limited to the subsonic case. On the other hand, numerical modeling of 0D models representing microvascular beds, venous valves or heart chambers is also currently modeled assuming subsonic flow conditions in 1D connecting vessels, failing when transonic and supersonic flow conditions appear. Therefore, if numerical simulation of sudden maneuvers is a goal in closed-loop models, it is necessary to reformulate the current methodologies used when coupling 0D and 1D models, allowing the correct handling of flow evolution for both subsonic and transonic conditions. This work focuses on the extension of the general methodology for the Junction Riemann Problem (JRP) when coupling 0D and 1D models. As an example of application, the short-term transient response to head-up tilt (HUT) from supine to upright position of a closed-loop model is shown, demonstrating the potential, capability and necessity of the presented numerical models when dealing with sudden maneuvers.

Study on Performance Simulation of Vascular-like Flow Channel Model Based on TPMS Structure

In medical validation experiments, such as drug testing and clinical trials, 3D bioprinted biomimetic tissues, especially those containing blood vessels, can be used to replace animal models. The difficulty in the viability of printed biomimetic tissues, in general, lies in the provision of adequate oxygen and nutrients to the internal regions. This is to ensure normal cellular metabolic activity. The construction of a flow channel network in the tissue is an effective way to address this challenge by both allowing nutrients to diffuse and providing sufficient nutrients for internal cell growth and by removing metabolic waste in a timely manner. In this paper, a three-dimensional TPMS vascular flow channel network model was developed and simulated to analyse the effect of perfusion pressure on blood flow rate and vascular-like flow channel wall pressure when the perfusion pressure varies. Based on the simulation results, the in vitro perfusion culture parameters were optimised to improve the structure of the porous structure model of the vascular-like flow channel, avoiding perfusion failure due to unreasonable perfusion pressure settings or necrosis of cells without sufficient nutrients due to the lack of fluid passing through some of the channels, and the research work promotes the development of tissue engineering in vitro culture.

A Solution of the Junction Riemann Problem for 1D Hyperbolic Balance Laws in Networks including Supersonic Flow Conditions on Elastic Collapsible Tubes

The numerical modeling of one-dimensional (1D) domains joined by symmetric or asymmetric bifurcations or arbitrary junctions is still a challenge in the context of hyperbolic balance laws with application to flow in pipes, open channels or blood vessels, among others. The formulation of the Junction Riemann Problem (JRP) under subsonic conditions in 1D flow is clearly defined and solved by current methods, but they fail when sonic or supersonic conditions appear. Formulations coupling the 1D model for the vessels or pipes with other container-like formulations for junctions have been presented, requiring extra information such as assumed bulk mechanical properties and geometrical properties or the extension to more dimensions. To the best of our knowledge, in this work, the JRP is solved for the first time allowing solutions for all types of transitions and for any number of vessels, without requiring the definition of any extra information. The resulting JRP solver is theoretically well-founded, robust and simple, and returns the evolving state for the conserved variables in all vessels, allowing the use of any numerical method in the resolution of the inner cells used for the space-discretization of the vessels. The methodology of the proposed solver is presented in detail. The JRP solver is directly applicable if energy losses at the junctions are defined. Straightforward extension to other 1D hyperbolic flows can be performed.

Seven Mathematical Models of Hemorrhagic Shock

Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject's responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.

Uncertainty quantification implementations in human hemodynamic flows

BACKGROUND AND OBJECTIVE

Human hemodynamic modeling is usually influenced by uncertainties occurring from a considerable unavailability of information linked to the boundary conditions and the physical properties used in the numerical models. Calculating the effect of these uncertainties on the numerical findings along the cardiovascular system is a demanding process due to the complexity of the morphology of the body and the area dynamics. To cope with all these difficulties, Uncertainty Quantification (UQ) methods seem to be an ideal tool.

RESULTS

This study focuses on analyzing and summarizing some of the recent research efforts and directions of implementing UQ in human hemodynamic flows by analyzing 139 research papers. Initially, the suitability of applying this approach is analyzed and demonstrated. Then, an overview of the most significant research work in various fields of biomedical hemodynamic engineering is presented. Finally, it is attempted to identify any possible forthcoming directions for research and methodological progress of UQ in biomedical sciences.

CONCLUSION

This review concludes that by finding the best statistical methods and parameters to represent the propagated uncertainties, while achieving a good interpretation of the interaction between input-output, is crucial for implementing UQ in biomedical sciences.

Influence of Hemodialysis Catheter Insertion on Hemodynamics in the Central Veins

Central venous catheter (CVC) related thrombosis is a major cause of CVC dysfunction in patients under hemodialysis. The aim of our study was to investigate the impact of CVC insertion on hemodynamics in the central veins and to examine the changes in hemodynamic environments that may be related to thrombus formation due to the implantation of CVC. Patient-specific models of the central veins with and without CVC were reconstructed based on computed tomography images. Flow patterns in the veins were numerically simulated to obtain hemodynamic parameters such as time-averaged wall shear stress (TAWSS), oscillating shear index (OSI), relative residence time (RRT), and normalized transverse wall shear stress (transWSS) under pulsatile flow. The non-Newtonian effects of blood flow were also analyzed using the Casson model. The insertion of CVC caused significant changes in the hemodynamic environment in the central veins. A greater disturbance and increase of velocity were observed in the central veins after the insertion of CVC. As a result, TAWSS and transWSS were markedly increased, but most parts of OSI and RRT decreased. Newtonian assumption of blood flow would overestimate the increase in TAWSS after CVC insertion. High wall shear stress (WSS) and flow disturbance, especially the multidirectionality of the flow, induced by the CVC may be a key factor in initiating thrombosis after CVC insertion. Accordingly, approaches to decrease the flow disturbance during CVC insertion may help restrain the occurrence of thrombosis. More case studies with pre-operative and postoperative modeling and clinical follow-up need to be performed to verify these findings. Non-Newtonian blood flow assumption is recommended in computational fluid dynamics (CFD) simulations of veins with CVCs.

Fluid-Structure Interaction Analysis of Perfusion Process of Vascularized Channels within Hydrogel Matrix Based on Three-Dimensional Printing

The rise of three-dimensional bioprinting technology provides a new way to fabricate in tissue engineering in vitro, but how to provide sufficient nutrition for the internal region of the engineered printed tissue has become the main obstacle. In vitro perfusion culture can not only provide nutrients for the growth of internal cells but also take away the metabolic wastes in time, which is an effective method to solve the problem of tissue engineering culture in vitro. Aiming at user-defined tissue engineering with internal vascularized channels obtained by three-dimensional printing experiment in the early stage, a simulation model was established and the in vitro fluid-structure interaction finite element analysis of tissue engineering perfusion process was carried out. Through fluid-structure interaction simulation, the hydrodynamic behavior and mechanical properties of vascularized channels in the perfusion process was discussed when the perfusion pressure, hydrogel concentration, and crosslinking density changed. The effects of perfusion pressure, hydrogel concentration, and crosslinking density on the flow velocity, pressure on the vascularized channels, and deformation of vascularized channels were analyzed. The simulation results provide a method to optimize the perfusion parameters of tissue engineering, avoiding the perfusion failure caused by unreasonable perfusion pressure and hydrogel concentration and promoting the development of tissue engineering culture in vitro.

Blood flow in the cerebral venous system: modeling and simulation

The development of a software platform incorporating all aspects, from medical imaging data, through three-dimensional reconstruction and suitable meshing, up to simulation of blood flow in patient-specific geometries, is a crucial challenge in biomedical engineering. In the present study, a fully three-dimensional blood flow simulation is carried out through a complete rigid macrovascular circuit, namely the intracranial venous network, instead of a reduced order simulation and partial vascular network. The biomechanical modeling step is carefully analyzed and leads to the description of the flow governed by the dimensionless Navier-Stokes equations for an incompressible viscous fluid. The equations are then numerically solved with a free finite element software using five meshes of a realistic geometry obtained from medical images to prove the feasibility of the pipeline. Some features of the intracranial venous circuit in the supine position such as asymmetric behavior in merging regions are discussed.

A global multiscale mathematical model for the human circulation with emphasis on the venous system

We present a global, closed-loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one-dimensional hyperbolic systems while the rest of the components are described by zero-dimensional models represented by differential-algebraic equations. Robust, high-order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient-specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. A merit of our model is its global, closed-loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers.