Numerical models for the simulation of flexible artificial heart valves: part I--computational methods

A numerical model of the coupled motion of a flexing surface in a high Reynolds number flow is presented for the simulation of flexible polyurethane heart valves in the aortic position. This is achieved by matching a Lagrangian dynamic leaflet model with a panel method based flow solver. The two models are coupled via the time-dependent pressure field using the unsteady Bernoulli equation. Incorporation of sub-cycling in the dynamic model equations and fast pre conditioning techniques in the panel method solver yields efficient convergence and near real-time simulations of valve motion. The generality of dynamic model allows different material properties and/or geometries to be studied easily and interactively. This interactivity is realized by embedding the models within a design environment created using the software IRIS Explorer. Two flow domains are developed, an infinite domain and an internal domain using conformal mapping theory. In addition bending stress on the valve is computed using a simple stress model based on spline and circle equation techniques.     

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part II - Valve Studies

Abstract

Using a coupled Lagrangian dynamic leaflet model and an unsteady potential flow solver the motion of a polyurethane type heart valve is simulated in the aortic position. The simulations incorporate two flow domains; the first comprises only the leaflets which are embedded within an unsteady flow of infinite expanse, and the second incorporates the influence of the aortic geometry via a conformal mapping. Simulations are performed for a cardiac output of 51itres/min and a beat period of 72 b.p.m. corresponding to a typical aortic pulse. Resulting valve motions are computed for various leaflet bending stiffnesses in both flow domains. In addition both the bending stress and strain and their time rate of change are evaluated. Valve motion displays the characteristic rapid opening, stable opening and slow closing phases as detailed in the literature. The computed stress values along the leaflet surface are of the order of those found experimentally.     

A fully coupled fluid-structure interaction model of the secondary lymphatic valve

Abstract

The secondary lymphatic valve is a bi-leaflet structure frequent throughout collecting vessels that serves to prevent retrograde flow of lymph. Despite its vital function in lymph flow and apparent importance in disease development, the lymphatic valve and its associated fluid dynamics have been largely understudied. The goal of this work was to construct a physiologically relevant computational model of an idealized rat mesenteric lymphatic valve using fully coupled fluid-structure interactions to investigate the relationship between three-dimensional flow patterns and stress/deformation within the valve leaflets. The minimum valve resistance to flow, which has been shown to be an important parameter in effective lymphatic pumping, was computed as 268?g/mm⁴?s. Hysteretic behavior of the lymphatic valve was confirmed by comparing resistance values for a given transvalvular pressure drop during opening and closing. Furthermore, eddy structures were present within the sinus adjacent to the valve leaflets in what appear to be areas of vortical flow; the eddy structures were characterized by non-zero velocity values (up to ～4?mm/s) in response to an applied unsteady transvalvular pressure. These modeling capabilities present a useful platform for investigating the complex interplay between soft tissue motion and fluid dynamics of lymphatic valves and contribute to the breadth of knowledge regarding the importance of biomechanics in lymphatic system function.     

Structural analysis of the natural aortic valve in dynamics: From unpressurized to physiologically loaded

A novel finite element model of the natural aortic valve was developed implementing anisotropic hyperelastic material properties for the leaflets and aortic tissues, and starting from the unpressurized geometry. Static pressurization of the aortic root, silicone rubber moulds and published data helped to establish the model parameters, while high-speed video recording of the leaflet motion in a left-heart simulator allowed for comparisons with simulations. The model was discretized with brick elements and loaded with time-varying pressure using an explicit commercial solver. The aortic valve model produced a competent valve whose dynamic behavior (geometric orifice area vs. time) closely matched that observed in the experiment. In both cases, the aortic valve took approximately 30 ms to open to an 800 mm² orifice and remained completely or more than half open for almost 200 ms, after which it closed within 30–50 ms. The highest values of stress were along the leaflet attachment line and near the commissure during diastole. Von Mises stress in the leaflet belly reached 600–750 kPa from early to mid-diastole. While the model using the unpressurized geometry as initial configuration was specially designed to satisfy the requirements of continuum mechanics for large deformations of hyperelastic materials, it also clearly demonstrated that dry models can be adequate to analyze valve dynamics. Although improvements are still needed, the advanced modeling and validation techniques used herein contribute toward improved and quantified accuracy over earlier simplified models.     

An integrated fluid–structure interaction and thrombosis model for type B aortic dissection

False lumen thrombosis (FLT) in type B aortic dissection has been associated with the progression of dissection and treatment outcome. Existing computational models mostly assume rigid wall behavior which ignores the effect of flap motion on flow and thrombus formation within the FL. In this study, we have combined a fully coupled fluid–structure interaction (FSI) approach with a shear-driven thrombosis model described by a series of convection–diffusion reaction equations. The integrated FSI-thrombosis model has been applied to an idealized dissection geometry to investigate the interaction between vessel wall motion and growing thrombus. Our simulation results show that wall compliance and flap motion can influence the progression of FLT. The main difference between the rigid and FSI models is the continuous development of vortices near the tears caused by drastic flap motion up to 4.45 mm. Flap-induced high shear stress and shear rates around tears help to transport activated platelets further to the neighboring region, thus speeding up thrombus formation during the accelerated phase in the FSI models. Reducing flap mobility by increasing the Young’s modulus of the flap slows down the thrombus growth. Compared to the rigid model, the predicted thrombus volume is 25% larger using the FSI-thrombosis model with a relatively mobile flap. Furthermore, our FSI-thrombosis model can capture the gradual effect of thrombus growth on the flow field, leading to flow obstruction in the FL, increased blood viscosity and reduced flap motion. This model is a step closer toward simulating realistic thrombus growth in aortic dissection, by taking into account the effect of intimal flap and vessel wall motion.

     

A two way fully coupled fluid structure simulation of human ureter peristalsis

Abstract

Numerical simulations of ureter peristalsis have been carried out in the past to understand both the flow field and ureter wall mechanics. The main objective of the current investigations is to have a better understanding of the urine transport due to the peristalsis in the ureter, thus making the information helpful for a better treatment and diagnosis of ureteral complications like urine reflux. In the current study, a numerical simulation is performed using a finite-element-based solver with a two-way fully coupled fluid structure interaction approach between the ureter wall and urine. For the first time, the ureter wall is modeled as an anisotropic hyper-elastic material based on experiments performed in previous literature on the human ureter. Peristalsis in the ureter is modeled as a series of isolated boluses. By observing the flow field it is clear that the peristalsis mechanism has a natural tendency to create a backflow as the isolated bolus moves forward. As a result, the urine can flow back from the bladder to the ureter at the ureterovesical (ureter-bladder) junctions, if the one-way valve starts to malfunction.     

Validation of a proteomic biomarker panel to diagnose minor-stroke and transient ischaemic attack: phase 2 of SpecTRA,a large scale translational study

Abstract

OBJECTIVE: To validate our previously developed 16 plasma-protein biomarker panel to differentiate between transient ischaemic attack (TIA) and non-cerebrovascular emergency department (ED) patients.

METHOD: Two consecutive cohorts of ED patients prospectively enrolled at two urban medical centers into the second phase of SpecTRA study (training, cohort 2A, n?=?575; test, cohort 2B, n?=?528). Plasma samples were analyzed using liquid chromatography/multiple reaction monitoring-mass spectrometry. Logistic regression models which fit cohort 2A were validated on cohort 2B.

RESULTS: Three of the panel proteins failed quality control and were removed from the panel. During validation, panel models did not outperform a simple motor/speech (M/S) deficit variable. Post-hoc analyses suggested the measured behaviour of L-selectin and coagulation factor V contributed to poor model performance. Removal of these proteins increased the external performance of a model containing the panel and the M/S variable.

CONCLUSIONS: Univariate analyses suggest insulin-like growth factor-binding protein 3 and serum paraoxonase/lactonase 3 are reliable and reproducible biomarkers for TIA status. Logistic regression models indicated L-selectin, apolipoprotein B-100, coagulation factor IX, and thrombospondin-1 to be significant multivariate predictors of TIA. We discuss multivariate feature subset analyses as an exploratory technique to better understand a panel’s full predictive potential.     

The effect of implantation orientation of a bileaflet mechanical heart valve on kinematics and hemodynamics in an anatomic aorta

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.     

Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture

This work presents a validation of a fluid-structure interaction computational model simulating the flow conditions in an in vitro mock heart chamber modeling mitral valve regurgitation during the ejection phase during which the trans-valvular pressure drop and valve displacement are not as large. The mock heart chamber was developed to study the use of 2D and 3D color Doppler techniques in imaging the clinically relevant complex intra-cardiac flow events associated with mitral regurgitation. Computational models are expected to play an important role in supporting, refining, and reinforcing the emerging 3D echocardiographic applications. We have developed a 3D computational fluid-structure interaction algorithm based on a semi-implicit, monolithic method, combined with an arbitrary Lagrangian-Eulerian approach to capture the fluid domain motion. The mock regurgitant mitral valve corresponding to an elastic plate with a geometric orifice, was modeled using 3D elasticity, while the blood flow was modeled using the 3D Navier-Stokes equations for an incompressible, viscous fluid. The two are coupled via the kinematic and dynamic conditions describing the two-way coupling. The pressure, the flow rate, and orifice plate displacement were measured and compared with numerical simulation results. In-line flow meter was used to measure the flow, pressure transducers were used to measure the pressure, and a Doppler method developed by one of the authors was used to measure the axial displacement of the orifice plate. The maximum recorded difference between experiment and numerical simulation for the flow rate was 4%, the pressure 3.6%, and for the orifice displacement 15%, showing excellent agreement between the two.     

Effect of turbulent models on left ventricle diastolic flow patterns simulation

Abstract

Vortex structures, as one of the most important features of cardiac flow, have a crucial impact on the left ventricle function and pathological conditions. These swirling flows are closely related to the presence of turbulence in left ventricle which is investigated in the current study. Using an extended model of the left heart, including a fluid-structure interaction (FSI) model of the mitral valve with a realistic geometry, the effect of using two numerical turbulent models, k-ε and Spalart-Allmaras (SA), on diastolic flow patterns is studied and compared with results from laminar flow model. As a result of the higher dissipation rate in turbulent models (k-ε and SA), vortices are larger and stronger in the laminar flow model. Comparing E/A ratio in the three models (Laminar, k-ε, and SA) with experimental data from healthy subjects, it is concluded that the results from k-ε model are more accurate.     

Pulsatile Flow Inside Moderately Elastic Arteries,Its Modelling and Effects of Elasticity

Pulsatile flow inside a moderately elastic circular conduit with a smooth expansion is studied as a model to understand the influence of wall elasticity in artery flow. The solution of the simultaneous fluid-wall evolution is evaluated by a perturbative method, where the zeroth order solution is represented by the flow in a rigid vessel; the first order correction gives the wall motion and induced flow modification without the need to solve the difficult coupled problem. Such an approach essentially assumes a locally infinite celerity, therefore it represent a good approximation for the fluid-wall interaction in sites of limited extent (branches, stenosis, aneurism, etc.), which include typical situations associated with vascular diseases. The problem is solved numerically in the axisymmetric approximation; the influence of wall elasticity on the flow and on the unsteady wall shear stress is studied in correspondence of parameters taken from realistic artery flow. Attention is posed to the role of phase difference between the incoming pressure and flow pulses.     

Development of An Accurate Three-dimensional Finite Element Knee Model

This paper presents the development of a detailed articulating three-dimensional finite-element model of the human knee, derived from MRI scan images. The model utilises precise material models and many contact interfaces in order to produce a realistic kinematic response. The behaviour of the model was examined within two fields of biomechanical simulations: general life and car-crash. These simulations were performed with the non-linear explicit dynamic code PAM-SAFE?. The knee model produced results that compared favourably with existing literature. Such a model (together with other joint models that could be constructed using the same techniques) would be a valuable tool for examining new designs of prosthesis and mechanisms of injury.     

Patient-specific CFD models for intraventricular flow analysis from 3D ultrasound imaging: Comparison of three clinical cases

BackgroundAs the intracardiac flow field is affected by changes in shape and motility of the heart, intraventricular flow features can provide diagnostic indications. Ventricular flow patterns differ depending on the cardiac condition and the exploration of different clinical cases can provide insights into how flow fields alter in different pathologies.MethodsIn this study, we applied a patient-specific computational fluid dynamics model of the left ventricle and mitral valve, with prescribed moving boundaries based on transesophageal ultrasound images for three cardiac pathologies, to verify the abnormal flow patterns in impaired hearts. One case (P1) had normal ejection fraction but low stroke volume and cardiac output, P2 showed low stroke volume and reduced ejection fraction, P3 had a dilated ventricle and reduced ejection fraction.ResultsThe shape of the ventricle and mitral valve, together with the pathology influence the flow field in the left ventricle, leading to distinct flow features. Of particular interest is the pattern of the vortex formation and evolution, influenced by the valvular orifice and the ventricular shape. The base-to-apex pressure difference of maximum 2 mmHg is consistent with reported data.ConclusionWe used a CFD model with prescribed boundary motion to describe the intraventricular flow field in three patients with impaired diastolic function. The calculated intraventricular flow dynamics are consistent with the diagnostic patient records and highlight the differences between the different cases. The integration of clinical images and computational techniques, therefore, allows for a deeper investigation intraventricular hemodynamics in patho-physiology.     

Exploring continuity equation via a modeling activity: in the context of crowd science

Abstract

Using problems from real life contexts which is related to learners’ environment or their culture plays an important role in their learning that concept. In this regard, science educators especially physics educators search for real-life domain of theoretical concepts for effective science teaching and they consider analogical and physical models as an opportunity in their instruction. In the presented activity, we worked with 66 senior pre-service science teachers from our science teaching methods course. We used crowd movements as a real-life domain of our analogical models to scientifically explain a stampede case, then utilized physical model to explore continuity equation. Real life problem based scenarios could be used while taking advantage of the 3?D modeling in teaching of scientific principle. As a result, we found that pre-service teachers were able to make scientific explanation for causes of stampedes by using modeling activity. High school teachers and upper-level instructors could benefit from including the modeling activity introduced in this study to help their students understand the concepts related to continuity equation by designing a physical model based on an analogical model. Via the physical model, students are able to make predictions, observations, interpretations and explanations of a complex and abstract scientific phenomenon.     

Experimental measurement of dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. Although exact causes and mechanisms of AV calcification are unclear, previous studies suggest that mechanical forces play a role. Since calcium deposits occur almost exclusively on the aortic surfaces of AV leaflets, it has been hypothesized that adverse patterns of fluid shear stress on the aortic surface of AV leaflets promote calcification. The current study characterizes AV leaflet aortic surface fluid shear stresses using Laser Doppler velocimetry and an in vitro pulsatile flow loop. The valve model used was a native porcine valve mounted on a suturing ring and preserved using 0.15% glutaraldehyde solution. This valve model was inserted in a mounting chamber with sinus geometries, which is made of clear acrylic to provide optical access for measurements. To understand the effects of hemodynamics on fluid shear stress, shear stress was measured across a range of conditions: varying stroke volumes at the same heart rate and varying heart rates at the same stroke volume. Systolic shear stress magnitude was found to be much higher than diastolic shear stress magnitude due to the stronger flow in the sinuses during systole, reaching up to 20 dyn/cm² at mid-systole. Upon increasing stroke volume, fluid shear stresses increased due to stronger sinus fluid motion. Upon increasing heart rate, fluid shear stresses decreased due to reduced systolic duration that restricted the formation of strong sinus flow. Significant changes in the shear stress waveform were observed at 90 beats/min, most likely due to altered leaflet dynamics at this higher heart rate. Overall, this study represents the most well-resolved shear stress measurements to date across a range of conditions on the aortic side of the AV. The data presented can be used for further investigation to understand AV biological response to shear stresses.     

Assessment of valve implantation in the descending aorta as an alternative for aortic regurgitation patients not treatable with conventional procedures

Background:

Aortic Regurgitation (AR) produces the entrance of an abnormal amount of blood in the left ventricle. This disease is responsible for high morbidity and mortality worldwide and may be caused by an aortic valve dysfunction. Surgical and transcatheter aortic valve replacement (TAVR) are the current options for treating AR. They have replaced older procedures such as Hufnagel’s one. However, some physicians have reconsidered this procedure as a less aggressive alternative for patients not eligible for surgical or TAVR. Although Hufnagel suggested a 75% regurgitation reduction when a valve is placed in the descending aorta, a quantification of this value has not been reported.

Methods:

In this paper, CFD/FSI numerical simulation is conducted on an idealized geometry. We quantify the effect of placing a bileaflet mechanical heart valve in the descending aorta on a moderate-severe AR case. A three-element Windkessel model is employed to prescribe pressure outlet boundary conditions. We calculate the resulting flow rates and pressures at the aorta and first-generation vessels. Moreover, we evaluate several indices to assess the improvement due to the valve introduction.

Results and conclusions:

Regurgitation fraction (RF) is reduced from 37.5% (without valve) to 18.0% (with valve) in a single cardiac cycle. This reduction clearly shows the remarkable efficacy of the rescued technique. It will further ameliorate the left ventricle function in the long-term. Moreover, the calculations show that the implantation in that location introduces fewer incompatibilities’ risks than a conventional one. The proposed methodology can be extended to any particular conditions (pressure waveforms/geometry) and is designed to assess usual clinical parameters employed by physicians.

     

Investigation of left heart flow using a numerical correlation to model heart wall motion

A three-dimensional computational fluid dynamics (CFD) method has been developed to model the flow in the left heart including atrium and ventricle. Since time resolution of the medical scans does not fit the requirements of the CFD calculations, the main challenge in a numerical simulation of heart chambers is wall motion modeling. This study employs a novel three-dimensional approximation scheme to correlate the wall boundary and grid movement in systole and diastole. It uses a geometry extracted from medical images in the literature and deformed based on the reported flow rates. The opening and closing of the mitral (MV) and the aortic valve (AV) considered as simultaneous events. Unstructured tetragonal grids were used for the meshing of the domain. The calculation was performed by a Navier–Stokes solver using the arbitrary Lagrange–Euler (ALE) formulation. Results show that the proposed correlation for the wall motion could predict the main features of heart flows.     

Experimental measurement of dynamic fluid shear stress on the ventricular surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. The exact causes and mechanisms of AV calcification are unclear, although previous studies suggest that mechanical forces play a role. It has been clinically demonstrated that calcification preferentially occurs on the aortic surface of the AV. This is hypothesized to be due to differences in the mechanical environments on the two sides of the valve. It is thus necessary to characterize fluid shear forces acting on both sides of the leaflet to test this hypothesis. The current study is one of two studies characterizing dynamic shear stress on both sides of the AV leaflets. In the current study, shear stresses on the ventricular surface of the AV leaflets were measured experimentally on two prosthetic AV models with transparent leaflets in an in vitro pulsatile flow loop using two-component Laser Doppler Velocimetry (LDV). Experimental measurements were utilized to validate a theoretical model of AV ventricular surface shear stress based on the Womersley profile in a straight tube, with corrections for the opening angle of the valve leaflets. This theoretical model was applied to in vivo data based on MRI-derived volumetric flow rates and valve dimension obtained from the literature. Experimental results showed that ventricular surface shear stress was dominated by the streamwise component. The systolic shear stress waveform resembled a half-sinusoid during systole and peaks at 64–71 dyn/cm², and reversed in direction at the end of systole for 15–25?ms, and reached a significant negative magnitude of 40–51 dyn/cm². Shear stresses from the theoretical model applied to in vivo data showed that shear stresses peaked at 77–92 dyn/cm² and reversed in direction for substantial period of time (108–110?ms) during late systole with peak negative shear stress of 35–38 dyn/cm².