Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves

This paper presents a new concentrated parameter model for cardiovascular dynamics that includes an innovative model of heart valve dynamics, which is embedded in the overall model of the four chambers of the heart and the systemic and pulmonary circulation loops. The heart chambers are described with a variable elastance model, and the systemic and pulmonary loops are described with modified Windkessel models. In modelling the heart valve dynamics, the various factors that influence the valve motion are examined, and the governing differential equation for valve motion is derived. The heart valve model includes the influence of the blood pressure effect, the friction effect from the tissue, and from blood motion. As improvement from previous works, the contribution of the blood vortex effect in the vicinity of the valve leaflets to valve motion is specially considered. The proposed model is then used in simulation of healthy and certain pathological conditions such as mitral valve stenosis and aortic regurgitation. The predicted results agree well with results illustrated in cardiology textbooks.     

Mechanical aspects of the development of artificial heart valves

The development of an antithrombogenic coating permits a hybrid design for artificial heart valves. A substrate material optimized for its application is coated to meet the electrochemical requirements of improved hemocompatibility. But future progress in artificial heart valves requires an improvement in design as well as of the material. The basis of both aspects is the determination of such fundamental mechanical properties as the elasticity and plasticity of the valve ring and the deformation and fraction behaviour of the occluder. Analytical and numerical calculations of various different models result in different requirements for the substrate of ring and occluder. A combination of high elastic temper and low resistance to flow requires a ring material with a Young's modulus of 40 GPa or more, and a 0.2% proof stress to (Young's modulus)2/3 ratio of 0.3 MPa1/3. The best occluder materials should have a Young's modulus of more than 50 GPa and a flexural strength of at least 800 MPa. On the basis of these criteria, a heart valve consisting of a TiA15Fe2,5 ring and occluders made partially stabilized zirconia is introduced.     

Numerical simulation of flow in mechanical heart valves: grid resolution and the assumption of flow symmetry

A numerical method is developed for simulating unsteady, 3-D, laminar flow through a bileaflet mechanical heart valve with the leaflets fixed. The method employs a dual-time-stepping artificial-compressibility approach together with overset (Chimera) grids and is second-order accurate in space and time. Calculations are carried out for the full 3-D valve geometry under steady inflow conditions on meshes with a total number of nodes ranging from 4 x 10(5) to 1.6 x 10(6). The computed results show that downstream of the leaflets the flow is dominated by two pairs of counter-rotating vortices, which originate on either side of the central orifice in the aortic sinus and rotate such that the common flow of each pair is directed away from the aortic wall. These vortices intensify with Reynolds number, and at a Reynolds number of approximately 1200 their complex interaction leads to the onset of unsteady flow and the break of symmetry with respect to both geometric planes of symmetry. Our results show the highly 3-D structure of the flow; question the validity of computationally expedient assumptions of flow symmetry; and demonstrate the need for highly resolved, fully 3-D simulations if computational fluid dynamics is to accurately predict the flow in prosthetic mechanical heart valves.     

Non-linear rotation-free shell finite-element models for aortic heart valves

Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann–Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves.     

Relative risk regression: reliable and flexible methods for log-binomial models

Relative risks (RRs) are generally considered preferable to odds ratios in prospective studies. However, unlike logistic regression for odds ratios, the standard log-binomial model for RR regression does not respect the natural parameter constraints and is therefore often subject to numerical instability. In this paper, we develop a reliable and flexible method for fitting log-binomial models. We use an Expectation-Maximization (EM) algorithm where the multiplicative event probability is viewed as the joint probability for a collection of latent binary outcomes. This gives a simple iterative scheme that provides stable convergence to the maximum likelihood estimate. In addition to reliability, the method offers some flexible generalizations, including models with unspecified isotonic regression functions. We examine the method's performance using simulations and data analyses of the age-specific RR of mortality following heart attack. These analyses demonstrate the potential for numerical instability in RR regression and show how this can be overcome using the proposed approach. Source code to implement the method in R is provided as supplementary material available at Biostatistics online.     

Numerical simulation of steady flow in a two-dimensional total artificial heart model.

In this paper, a numerical simulation of steady laminar and turbulent flow in a two-dimensional model for the total artificial heart is presented. A trileaflet polyurethane valve was simulated at the outflow orifice while the inflow orifice had a trileaflet or a flap valve. The finite analytic numerical method was employed to obtain solutions to the governing equations in the Cartesian coordinates. The closure for turbulence model was achieved by employing the k-epsilon-E model. The SIMPLER algorithm was used to solve the problem in primitive variables. The numerical solutions of the simulated model show that regions of relative stasis and trapped vortices were smaller within the ventricular chamber with the flap valve at the inflow orifice than that with the trileaflet valve. The predicted Reynolds stresses distal to the inflow valve within the ventricular chamber were also found to be smaller with the flap valve than with the trileaflet valve. These results also suggest a correlation between high turbulent stresses and the presence of thrombus in the vicinity of the valves in the total artificial hearts. The computed velocity vectors and turbulent stresses were comparable with previously reported in vitro measurements in artificial heart chambers. Analysis of the numerical solutions suggests that geometries similar to the flap valve (or a tilting disk valve) results in a better flow dynamics within the total artificial heart chamber compared to a trileaflet valve.     

Three-dimensional visualization of stationary flow behind artificial heart valves]

The visualization and quantitative analysis of flow offers a possibility for the hydrodynamic characterization of artificial heart valves. Different types of valves can be compared if velocity profile and the turbulent shear stress caused by the prosthesis are known. The tracer technique was selected, since it permits visualization also of turbulent flow through the valve. With the aid of a simple optical device the three-dimensional flow pattern behind the valve is determinable. The main features of the method are: The regions of interest can easily be identified. Velocity profiles can be determined and shear stress and turbulence intensities estimated. The experimental setup is simple, calibration is not necessary, and it can be used for turbulent flows. The method can be used only with transparent fluids and vessels; measurements in blood are not possible. Because of the large number of measuring points required the method is very time-consuming. The use of an automatic picture analyzing system would make it possible to increase the number of pictures processed, and thus increase resolution. The velocity profile of a three-finger-valve, the TAD 29, was established at a distance of 20 mm from the ring, and compared with known profiles from the literature. The valve has an opening angle of 70 degrees. All typical regions for the flow of an artificial heart valve, such as jet, stagnation gone, backflow and turbulence were demonstrated.     

A patient with four artificial heart valves after ergotamine therapy

A 67-year-old female was evaluated in the out-patient clinic because of shortness of breath on exertion and regular spells of fever. She had been taking ergotamine tartrate to treat migraine for more than 30 years. The patient had undergone aortic-valve replacement for aortic insufficiency three years before. On echocardiographic evaluation, severe retraction and insufficiency of the remaining native heart valves was demonstrated. Endocarditis and carcinoid syndrome were excluded. The mitral, tricuspid and pulmonary valves were all replaced by a mechanical valvular prosthesis. Pathological-anatomical evaluation of the three replaced valves and the aortic valve replaced three years earlier disclosed identical findings, compatible with long-term ergotamine use. Nine months after surgery, a sick sinus syndrome developed necessitating implantation of a DDDR pacemaker with a right atrial and a coronary sinus lead. Functional class according to the New York Heart Association improved from class III to I. After stopping the ergotamine, the fever disappeared. However, the migraine spells reoccurred which are now being treated with paracetamol.     

Nonparametric models and methods for designs with dependent censored data: part I

We consider a nonparametric (NP) approach to the analysis of repeated measures designs with censored data. Using the NP model of Akritas and Arnold (1994, Journal of the American Statistical Association 89, 336-343) for marginal distributions, we present test procedures for the NP hypotheses of no main effects, no interaction, and no simple effects. This extends the existing NP methodology for such designs (Wei and Lachin, 1984, Journal of the American Statistical Association 79, 653-661). The procedures do not require any modeling assumptions and should be useful in cases where the assumptions of proportional hazards or location shift fail to be satisfied. The large-sample distribution of the test statistics is based on an i.i.d. representation for Kaplan-Meier integrals. The testing procedures apply also to ordinal data and to data with ties. Useful small-sample approximations are presented, and their performance is examined in a simulation study. Finally, the methodology is illustrated with two real life examples, one with censored and one with missing data. It is indicated that one of the data sets does not conform to any set of assumptions underlying the available methods and also that the present method provides a useful additional analysis even when data sets conform to modeling assumptions.     

Implicit solvent models for flexible protein-protein docking by molecular dynamics simulation

The suitability of three implicit solvent models for flexible protein-protein docking by procedures using molecular dynamics simulation is investigated. The three models are (i) the generalized Born (GB) model implemented in the program AMBER6.0; (ii) a distance-dependent dielectric (DDD) model; and (iii) a surface area-dependent model that we have parameterized and call the NPSA model. This is a distance-dependent dielectric model modified by neutralizing the ionizable side-chains and adding a surface area-dependent solvation term. These solvent models were first tested in molecular dynamics simulations at 300 K of the native structures of barnase, barstar, segment B1 of protein G, and three WW domains. These protein structures display a range of secondary structure contents and stabilities. Then, to investigate the performance of the implicit solvent models in protein docking, molecular dynamics simulations of barnase/barstar complexation, as well as PIN1 WW domain/peptide complexation, were conducted, starting from separated unbound structures. The simulations show that the NPSA model has significant advantages over the DDD and GB models in maintaining the native structures of the proteins and providing more accurate docked complexes.     

BglBricks: A flexible standard for biological part assembly

Background  

Standard biological parts, such as BioBricks™ parts, provide the foundation for a new engineering discipline that enables the design and construction of synthetic biological systems with a variety of applications in bioenergy, new materials, therapeutics, and environmental remediation. Although the original BioBricks™ assembly standard has found widespread use, it has several shortcomings that limit its range of potential applications. In particular, the system is not suitable for the construction of protein fusions due to an unfavorable scar sequence that encodes an in-frame stop codon.     

Numerical integration of population models satisfying conservation laws: NSFD methods

Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models.     

Parameter inversion estimation in photosynthetic models: Impact of different simulation methods

When we apply ecological models in environmental management, we must assess the accuracy of parameter estimation and its impact on model predictions. Parameters estimated by conventional techniques tend to be nonrobust and require excessive computational resources. However, optimization algorithms are highly robust and generally exhibit convergence of parameter estimation by inversion with nonlinear models. They can simultaneously generate a large number of parameter estimates using an entire data set. In this study, we tested four inversion algorithms (simulated annealing, shuffled complex evolution, particle swarm optimization, and the genetic algorithm) to optimize parameters in photosynthetic models depending on different temperatures. We investigated if parameter boundary values and control variables influenced the accuracy and efficiency of the various algorithms and models. We obtained optimal solutions with all of the inversion algorithms tested if the parameter bounds and control variables were constrained properly. However, the efficiency of processing time use varied with the control variables obtained. In addition, we investigated if temperature dependence formalization impacted optimally the parameter estimation process. We found that the model with a peaked temperature response provided the best fit to the data.     

Likelihoods and simulation methods for a class of nonneutral population genetics models

Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.