Modeling hemodynamics in vascular networks using a geometrical multiscale approach: numerical aspects

An Objective and Repeatable Sac Isolation Technique for Comparing Biomechanical Metrics in Abdominal Aortic Aneurysms

(1) Abdominal aortic aneurysm (AAA) biomechanics-based metrics often reported may be over/under-estimated by including non-aneurysmal regions in the analyses, which is typical, rather than isolating the dilated sac region. We demonstrate the utility of a novel sac-isolation algorithm by comparing peak/mean wall stress (PWS, MWS), with/without sac isolation, for AAA that were categorized as stable or unstable in 245 patient CT image sets. (2) 245 patient computed tomography images were collected, segmented, meshed, and had subsequent finite element analysis performed in preparation of our novel sac isolation technique. Sac isolation was initiated by rotating 3D surfaces incrementally, extracting 2D projections, curve fitting a Fourier series, and taking the local extrema as superior/inferior boundaries for the aneurysmal sac. The PWS/MWS were compared pairwise using the entire aneurysm and the isolated sac alone. (3) MWS, not PWS, was significantly different between the sac alone and the entire aneurysm. We found no statistically significant difference in wall stress measures between stable (n = 222) and unstable (n = 23) groups using the entire aneurysm. However, using sac-isolation, PWS (24.6 ± 7.06 vs. 20.5 ± 8.04 N/cm2; p = 0.003) and MWS (12.0 ± 3.63 vs. 10.5 ± 4.11 N/cm2; p = 0.022) were both significantly higher in unstable vs. stable groups. (4) Our results suggest that evaluating only the AAA sac can influence wall stress metrics and may reveal differences in stable and unstable groups of aneurysms that may not otherwise be detected when the entire aneurysm is used.

Fluid structure computational model of simulating mitral valve motion in a contracting left ventricle

BACKGROUND

Fluid structure interaction simulations h hold promise in studying normal and abnormal cardiac function, including the effect of fluid dynamics on mitral valve (MV) leaflet motion. The goal of this study was to develop a 3D fluid structure interaction computational model to simulate bileaflet MV when interacting with blood motion in left ventricle (LV).

METHODS

The model consists of ideal geometric-shaped MV leaflets and the LV, with MV dimensions based on human anatomical measurements. An experimentally-based hyperelastic isotropic material was used to model the mechanical behaviour of the MV leaflets, with chordae tendineae and papillary muscle tips also incorporated. LV myocardial tissue was prescribed using a transverse isotropic hyperelastic formulation. Incompressible Navier-Stokes fluid formulations were used to govern the blood motion, and the Arbitrary Lagrangian Eulerian (ALE) method was employed to determine the mesh deformation of the fluid and solid domains due to trans-valvular pressure on MV boundaries and the resulting leaflet movement.

RESULTS

The LV-MV generic model was able to reproduce physiological MV leaflet opening and closing profiles resulting from the time-varying atrial and ventricular pressures, as well as simulating normal and prolapsed MV states. Additionally, the model was able to simulate blood flow patterns after insertion of a prosthetic MV with and without left ventricular outflow tract flow obstruction. In the MV-LV normal model, the regurgitant blood flow fraction was 10.1 %, with no abnormality in cardiac function according to the mitral regurgitation severity grades reported by the American Society of Echocardiography.

CONCLUSION

Our simulation approach provides insights into intraventricular fluid dynamics in a contracting LV with normal and prolapsed MV function, as well as aiding in the understanding of possible complications after transcatheter MV implantation prior to clinical trials.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980’s and early 1990’s. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

Computational model of cardiovascular response to centrifugation and lower body cycling exercise

Short-radius centrifugation combined with exercise has been suggested as a potential countermeasure against spaceflight deconditioning. Both the long-term and acute physiological responses to such a combination are incompletely understood. We developed and validated a computational model to study the acute cardiovascular response to centrifugation combined with lower body ergometer exercise. The model consisted of 21 compartments, including the upper body, renal, splanchnic, and leg circulation, as well as a four-chamber heart and pulmonary circulation. It also included the effects of gravity gradient and ergometer exercise. Centrifugation and exercise profiles were simulated and compared with experimental data gathered on 12 subjects exposed to a range of gravitational levels (1 and 1.4G measured at the feet) and workload intensities (25-100 W). The model was capable of reproducing cardiovascular changes (within ± 1 SD from the group-averaged behavior) due to both centrifugation and exercise, including dynamic responses during transitions between the different phases of the protocol. The model was then used to simulate the hemodynamic response of hypovolemic subjects (blood volume reduced by 5-15%) subjected to similar gravitational stress and exercise profiles, providing insights into the physiological responses of experimental conditions not tested before. Hypovolemic results are in agreement with the limited available data and the expected responses based on physiological principles, although additional experimental data are warranted to further validate our predictions, especially during the exercise phases. The model captures the cardiovascular response for a range of centrifugation and exercise profiles, and it shows promise in simulating additional conditions where data collection is difficult, expensive, or infeasible.NEW & NOTEWORTHY Artificial gravity combined with exercise is a potential countermeasure for spaceflight deconditioning, but the long-term and acute cardiovascular response to such gravitational stress is still largely unknown. We provide a novel mathematical model of the cardiovascular system that incorporates gravitational stress generated by centrifugation and lower body cycling exercise, and we validate it with experimental measurements from human subjects. Simulations of experimental conditions not used for model development corroborate the model's predictive capabilities.

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

A multiscale computational modeling for cerebral blood flow with aneurysms and/or stenoses

A 1-dimensional (1D)-3-dimensional (3D) multiscale model for the human vascular network was proposed by combining a low-fidelity 1D modeling of blood circulation to account for the global hemodynamics with a detailed 3D simulation of a zonal vascular segment. The coupling approach involves a direct exchange of flow and pressure information at interfaces between the 1D and 3D models and thus enables patient-specific morphological models to be inserted into flow network with minimum computational efforts. The proposed method was validated with good agreements against 3 simplified test cases where experimental data and/or full 3D numerical solution were available. The application of the method in aneurysm and stenosis studies indicated that the deformation of the geometry caused by the diseases may change local pressure loss and as a consequence lead to an alteration of flow rate to the vessel segment.

An effective model of cerebrovascular pressure reactivity and blood flow autoregulation

Understanding cerebral blood flow dynamics is crucial for the care of patients at risk of poor cerebral perfusion. We describe an effective model of cerebral hemodynamics designed to reveal important macroscopic features of cerebral blood flow without having to resolve the detailed microvasculature of the brain. Based on principles of fluid and elastic dynamics and vascular pressure-reactivity, the model quantifies the physical means by which the vasculature executes autoregulatory reflexes. We demonstrate that the frequency response of the proposed model matches experimental measurements and explains the influence of mechanical factors on the autoregulatory performance. Analysis of the model indicates the existence of an optimal mean arterial pressure which minimizes the sensitivity of the flow to changes in perfusion pressure across the frequency spectrum of physiological oscillations. We highlight the simplicity of the model and its potential to improve monitoring of brain perfusion via real-time computational simulations of cerebro- and cardio-vascular interventions.

Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator

Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary Lagrangian-Eulerian Techniques for the Mesh Representation

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results.

An effective model of blood flow in capillary beds

In this article we derive applicable expressions for the macroscopic compliance and resistance of microvascular networks. This work yields a lumped-parameter model to describe the hemodynamics of capillary beds. Our derivation takes into account the multiscale nature of capillary networks, the influence of blood volume and pressure on the effective resistance and compliance, as well as, the nonlinear interdependence between these two properties. As a result, we obtain a simple and useful model to study hypotensive and hypertensive phenomena. We include two implementations of our theory: (i) pulmonary hypertension where the flow resistance is predicted as a function of pulmonary vascular tone. We derive from first-principles the inverse proportional relation between resistance and compliance of the pulmonary tree, which explains why the RC factor remains nearly constant across a population with increasing severity of pulmonary hypertension. (ii) The critical closing pressure in pulmonary hypotension where the flow rate dramatically decreases due to the partial collapse of the capillary bed. In both cases, the results from our proposed model compare accurately with experimental data.

Characterisation of mixing in the proximal duodenum of the rat during longitudinal contractions and comparison with a fluid mechanical model based on spatiotemporal motility data

The understanding of mixing and mass transfers of nutrients and drugs in the small intestine is of prime importance in creating formulations that manipulate absorption and digestibility. We characterised mixing using a dye tracer methodology during spontaneous longitudinal contractions, i.e. pendular activity, in 10 cm segments of living proximal duodenum of the rat maintained ex-vivo. The residence time distribution (RTD) of the tracer was equivalent to that generated by a small number (8) of continuous stirred tank reactors in series. Fluid mechanical modelling, that was based on real sequences of longitudinal contractions, predicted that dispersion should occur mainly in the periphery of the lumen. Comparison with the experimental RTD showed that centriluminal dispersion was accurately simulated whilst peripheral dispersion was underestimated. The results therefore highlighted the potential importance of micro-phenomena such as microfolding of the intestinal mucosa in peripheral mixing. We conclude that macro-scale modeling of intestinal flow is useful in simulating centriluminal mixing, whereas multi-scales strategies must be developed to accurately model mixing and mass transfers at the periphery of the lumen.