Influence of dilated cardiomyopathy and a left ventricular assist device on vortex dynamics in the left ventricle

Together with new developments in mechanical cardiac support, the analysis of vortex dynamics in the left ventricle has become an increasingly important topic in literature. The aim of this study was to develop a method to investigate the influence of a left ventricular assist device (LVAD) on vortex dynamics in a failing ventricle. An axisymmetric fluid dynamics model of the left ventricle was developed and coupled to a lumped parameter model of the complete circulation. Simulations were performed for healthy conditions and dilated cardiomyopathy (DCM). Vortex structures in these simulations were analysed by means of automated detection. Results show that the strength of the leading vortex ring is lower in a DCM ventricle than in a healthy ventricle. The LVAD further influences the maximum strength of the vortex and also causes the vortex to disappear earlier in time with increasing LVAD flows. Understanding these phenomena by means of the method proposed in this study will contribute to enhanced diagnostics and monitoring during cardiac support.     

Intraventricular flow patterns and stasis in the LVAD-assisted heart

Left ventricular assist device (LVAD) support disrupts the natural blood flow path through the heart, introducing flow patterns associated with thrombosis, especially in the presence of medical devices. The aim of this study was to quantitatively evaluate the flow patterns in the left ventricle (LV) of the LVAD-assisted heart, with a focus on alterations in vortex development and stasis. Particle image velocimetry of a LVAD-supported LV model was performed in a mock circulatory loop. In the Pre-LVAD flow condition, a vortex ring initiating from the LV base migrated toward the apex during diastole and remained in the LV by the end of ejection. During LVAD support, vortex formation was relatively unchanged although vortex circulation and kinetic energy increased with LVAD speed, particularly in systole. However, as pulsatility decreased and aortic valve opening ceased, a region of fluid stasis formed near the left ventricular outflow tract. These findings suggest that LVAD support does not substantially alter vortex dynamics unless cardiac function is minimal. The altered blood flow introduced by the LVAD results in stasis adjacent to the LV outflow tract, which increases the risk of thrombus formation in the heart.     

Effect of spatial inlet velocity profiles on the vortex formation pattern in a dilated left ventricle

Despite the advancement of cardiac imaging technologies, these have traditionally been limited to global geometrical measurements. Computational fluid dynamics (CFD) has emerged as a reliable tool that provides flow ?eld information and other variables essential for the assessment of the cardiac function. Extensive studies have shown that vortex formation and propagation during the filling phase acts as a promising indicator for the diagnosis of the cardiac health condition. Proper setting of the boundary conditions is crucial in a CFD study as they are important determinants, that affect the simulation results. In this article, the effect of different transmitral velocity profiles (parabolic and uniform profile) on the vortex formation patterns during diastole was studied in a ventricle with dilated cardiomyopathy (DCM). The resulting vortex evolution pattern using the uniform inlet velocity profile agreed with that reported in the literature, which revealed an increase in thrombus risk in a ventricle with DCM. However the application of a parabolic velocity profile at the inlet yields a deviated vortical flow pattern and overestimates the propagation velocity of the vortex ring towards the apex of the ventricle. This study highlighted that uniform inlet velocity profile should be applied in the study of the filling dynamics in a left ventricle because it produces results closer to that observed experimentally.     

Jet collisions and vortex reversal in the human left ventricle

Unnatural dynamics of the notorious vortex in the left ventricle is often associated with cardiac disease. Understanding how different cardiac diseases alter the flow physics in the left ventricle may therefore provide a powerful tool for disease detection. In this work, the fluid dynamics in the left ventricle subject to different severities of aortic regurgitation is experimentally investigated by performing time-resolved particle image velocimetry in a left heart duplicator. Diastolic vortex reversal was observed in the left ventricle accompanied by an increase in viscous energy dissipation. Vortex dynamics and energy dissipation may provide useful insights on sub-optimal flow patterns in the left ventricle.     

The effect of vortex formation on left ventricular filling and mitral valve efficiency

A new mechanism for quantifying the filling energetics in the left ventricle (LV) and past mechanical heart valves (MHV) is identified and presented. This mechanism is attributed to vortex formation dynamics past MHV leaflets. Recent studies support the conjecture that the natural healthy left ventricle (LV) performs in an optimum, energy-preserving manner by redirecting the flow with high efficiency. Yet to date, no quantitative proof has been presented. The present work provides quantitative results and validation of a theory based on the dynamics of vortex ring formation, which is governed by a critical formation number (FN) that corresponds to the dimensionless time at which the vortex ring has reached its maximum circulation content, in support of this hypothesis. Herein, several parameters (vortex ring circulation, vortex ring energy, critical FN, hydrodynamic efficiencies, vortex ring propagation speed) have been quantified and presented as a means of bridging the physics of vortex formation in the LV. In fact, the diastolic hydrodynamic efficiencies were found to be 60, 41, and 29%, respectively, for the porcine, anti-anatomical, and anatomical valve configurations. This assessment provides quantitative proof of vortex formation, which is dependent of valve design and orientation, being an important flow characteristic and associated to LV energetics. Time resolved digital particle image velocimetry with kilohertz sampling rate was used to study the ejection of fluid into the LV and resolve the spatiotemporal evolution of the flow. The clinical significance of this study is quantifying vortex formation and the critical FN that can potentially serve as a parameter to quantify the LV filling process and the performance of heart valves.     

Cardiac protein changes in ischaemic and dilated cardiomyopathy: a proteomic study of human left ventricular tissue

The development of heart failure (HF) is characterized by progressive alteration of left ventricle structure and function. Previous works on proteomic analysis in cardiac tissue from patients with HF remain scant. The purpose of our study was to use a proteomic approach to investigate variations in protein expression of left ventricle tissue from patients with ischaemic (ICM) and dilated cardiomyopathy (DCM). Twenty-four explanted human hearts, 12 from patients with ICM and 12 with DCM undergoing cardiac transplantation and six non-diseased donor hearts (CNT) were analysed by 2DE. Proteins of interest were identified by mass spectrometry and validated by Western blotting and immunofluorescence. We encountered 35 differentially regulated spots in the comparison CNT versus ICM, 33 in CNT versus DCM, and 34 in ICM versus DCM. We identified glyceraldehyde 3-phophate dehydrogenase up-regulation in both ICM and DCM, and alpha-crystallin B down-regulation in both ICM and DCM. Heat shock 70 protein 1 was up-regulated only in ICM. Ten of the eleven differentially regulated proteins common to both aetiologies are interconnected as a part of a same network. In summary, we have shown by proteomics analysis that HF is associated with changes in proteins involved in the cellular stress response, respiratory chain and cardiac metabolism. Although we found altered expression of eleven proteins common to both ischaemic and dilated aetiology, we also observed different proteins altered in both groups. Furthermore, we obtained that seven of these eleven proteins are involved in cell death and apoptosis processes, and therefore in HF progression.     

Modeling the relationship between LVAD support time and gene expression changes in the human heart by penalized partial least squares

MOTIVATION: Heart failure affects more than 20 million people in the world. Heart transplantation is the most effective therapy, but the number of eligible patients far outweighs the number of available donor hearts. The left mechanical ventricular assist device (LVAD) has been developed as a successful substitution therapy that aids the failing ventricle while a patient is waiting for the donor heart. We obtained genomics data from paired human heart samples harvested at the time of LVAD implant and explant. The heart failure patients in our study were supported by the LVAD for various periods of time. The goal of this study is to model the relationship between the time of LVAD support and gene expression changes. RESULTS: To serve the purpose, we propose a novel penalized partial least squares (PPLS) method to build a regression model. Compared with partial least squares and Breiman's random forest method, PPLS gives the best prediction results for the LVAD data.     

Computational fluid dynamics analysis of surgical adjustment of left ventricular assist device implantation to minimise stroke risk

Background. Currently, mechanical support is the most promising alternative to cardiac transplantation. Ventricular assist devices (VADs) were originally used to provide mechanical circulatory support in patients awaiting planned heart transplantation (‘bridge-to-transplantation’ therapy). The success of short-term bridge devices led to clinical trials evaluating the clinical suitability of long-term support (‘destination’ therapy) with left ventricular assist devices (LVADs). The first larger scale, randomised trial that tested long-term support with an LVAD reported a 44% reduction in the risk of stroke or death in patients with an LVAD. In spite of the success of LVADs as bridge-to-transplantation and long-term support, patients managed by these devices are still at risk of several adverse events. The most devastating complication is caused by embolisation of thrombi formed within the LVAD or inside the heart into the brain. Prevention of thrombi formation is attempted through anticoagulation management and by improving LVADs design; however, there is still significant occurrence of thromboembolic events in patients. Investigators have reported that the incidence of thromboembolic cerebral events ranges from 14% to 47% over a period of 6–12 months.

Methods and approach. An alternative method to reduce the incidence of cerebral embolisation is proposed by the co-authors, and the hypothesis is that it is possible to minimise the number of thrombi flowing into the carotid and vertebral arteries by an optimal placement of the LVAD outflow conduit, with or without the addition of aortic bypass connecting the ascending aorta and the innominate artery (IA), or left carotid artery. This paper presents the computational fluid dynamics (CFD) analysis of the aortic arch haemodynamics using a representative geometry of the human aortic arch with or without an alternative aortic bypass. In order to study the trajectory of the thrombi within the aortic arch bed, the CFD code, Fluent 6.3, is utilised to resolve the flow field and to solve the Lagrangian particle tracking of thrombi released randomly at the inlet of the LVAD cannula.

Results. Results are presented for simulations of thrombi in the range of 2–5 mm. The percentage of individual diameter as well as aggregate diameter thrombi flowing to the carotid and vertebral arteries as a function of LVAD conduit placement and aortic bypass implantation is reported. The influence of the LVAD conduit implantation and bypass reveals a nearly 50% variation in predicted cerebral embolism rates.

Conclusions. The adjustment of the location of the anastomosis of the LVAD outflow cannula as well as its angle of incidence plays a significant role in the level of thromboembolisms. By proper adjustment in this CFD study of a synthetic model of an aortic arch bed, we found that nearly a 50% reduction in cerebral embolism could be achieved for a configuration consisting of a shallow angle of implantation over a baseline normal incidence of the LVAD cannula. Within the limitations of our model, we have established that the LVAD implantation geometry is an important factor and should be taken into consideration when implanting an LVAD. It is possible that other parameters such as distance of the LVAD outflow cannula to the root of the IA could affect the thrombi embolisation probabilities. However, the results of this study suggest that the risk of stroke may be significantly reduced by as much as 50% by tailoring the VAD implantation by a simple surgical manoeuvre. The results of this line of research may ultimately lead to techniques that can be used to estimate the optimal LVAD configuration in a patient-specific manner by pre-operative imaging.     

Theoretical approach to blood ejection from the human left ventricle

An ejection dynamics mathematical model of human left ventricle (LV) based on physiological data of human heart is proposed in this study. The mathematical equations were expressed in terms of vorticity-stream function equations in a prolate spheroidal coordinate system. These equations combined with specified boundary conditions were numerically solved by using an alternating-direction-implicit (ADI) algorithm with second order accuracy. The unsteady aspects of the ejection process were subsequently introduced into the numerical simulation. The numerical results have shown that the present ellipsoidal model could be available to simulate the ejection process of the human LV. Such a model combined with cardiac muscle mechanics could be studied further to determine altered left ventricular function in cardiac diseases.     

Velocity and turbulence measurements past mitral valve prostheses in a model left ventricle

Thrombogenesis and hemolysis have both been linked to the flow dynamics past heart valve prostheses. To learn more about the particular flow dynamics past mitral valve prostheses in the left ventricle under controlled experimental conditions, an in vitro study was performed. The experimental methods included velocity and turbulent shear stress measurements past caged-ball, tilting disc, bileaflet, and polyurethane trileaflet mitral valves in an acrylic rigid model of the left ventricle using laser Doppler anemometry. The results indicate that all four prosthetic heart valves studied create at least mildly disturbed flow fields. The effect of the left ventricular geometry on the flow development is to produce a stabilizing vortex which engulfs the entire left ventricular cavity, depending on the orientation of the valve. The measured turbulent shear stress magnitudes for all four valves did not exceed the reported value for hemolytic damage. However, the measured turbulent shear stresses were near or exceeded the critical shear stress reported in the literature for platelet lysis, a known precursor to thrombus formation.     

Left ventricular assist device as a bridge to recovery in a young woman admitted with peripartum cardiomyopathy

Left ventricular assist devices (LVAD) are an effective therapeutic option for end-stage heart failure patients as a bridge to cardiac transplantation in those who deteriorate despite maximal therapy and when a donor heart is not ready available. In some patients, cardiac recovery has been reported while supported by an LVAD. In this case report, we describe a 29-year-old female who was admitted to our centre because of peripartum cardiomyopathy (PPCM). Despite intensive treatment with intravenous inotropes and intra-aortic balloon counter-pulsation she had a persisting low cardiac index and an LVAD was implanted. In the months following implantation the left ventricular systolic function improved and the left ventricular dimensions normalised. Eventually the LVAD could be ex-planted nine months after implantation. At this moment, three years after explantation, echo-cardiography shows a normal-sized left ventricle and almost completely recovered systolic function. (Neth Heart J 2008;16:426-8).     

Determinants of the occurrence of vortex rings in the left ventricle during diastole

This study employs classical inviscid fluid dynamics theory to investigate whether LV diastolic inflow volume and the size of the LV play a role in vortex ring formation. Fluid injection across an orifice into a large container results in the generation of a vortex ring having a constant size and speed. Relations between the vortex size and speed and the injection were obtained by applying conservation laws regarding kinetic energy, impulse and vorticity; the initial state was computed using a bolus injection model, and the final state by using the Kelvin vortex model. An important parameter in the equations is the relative injection length, i.e., the ratio of the length of the injected bolus and the radius of the orifice (L/R). Its estimated highest value in man, L/R = 15, produces a rather thick vortex ring (relative thickness 0.77). Comparable results following from the Hill vortex model convinced us that the Kelvin vortex model can be applied in the whole range of injection lengths in the human left ventricle. In an in vitro model it is shown experimentally that vortex rings can be generated for L/R in the range from 2 to 16. The measured traveling speed of the vortex ring is in fair agreement with the theory, as well as the ring radius for large injections. A vortex ring located in a narrow channel cannot reach its proper traveling speed. The method of images is used to estimate the speed reduction of vortex rings within a cylinder. It turns out that propagation of vortex rings is possible when the ratio of orifice to cylinder radius is less than about 0.5.(ABSTRACT TRUNCATED AT 250 WORDS)     

Flow patterns in three-dimensional left ventricular systolic and diastolic flows determined from computational fluid dynamics

A realistic model of the left ventricle of the heart was previously constructed, using a cast from a dog heart which was in diastole. Previous studies of the three-dimensional heart model were conducted in systole only. The purpose of this investigation was to extend the model to both systole and diastole, and to determine what the effect of a previous cardiac cycle was on the next cardiac cycle. The 25.8 cc ventricular volume was reduced by 40% in 0.25 seconds, then increased to the original volume in another 0.25 seconds and then allowed to rest for 0.25 seconds. Runs done with an ejection fraction of 60% showed little variation from one cardiac cycle to another after the third cardiac cycle was completed; the maximum velocity could vary by over 30% between the first and second cardiac cycles. In systole, centerline and cross-sectional velocity vectors greatly increased in magnitude at the aortic outlet. Most of the pressure drop occurred in the top 15% of the heart. The diastolic phase showed complex vortex formation not seen in the systolic contractions; these complex vortices could account for experimentally observed turbulent blood flow fluctuations in the aorta.     

In vivo porcine left atrial wall stress: Computational model

Most computational models of the heart have so far concentrated on the study of the left ventricle, mainly using simplified geometries. The same approach cannot be adopted to model the left atrium, whose irregular shape does not allow morphological simplifications. In addition, the deformation of the left atrium during the cardiac cycle strongly depends on the interaction with its surrounding structures. We present a procedure to generate a comprehensive computational model of the left atrium, including physiological loads (blood pressure), boundary conditions (pericardium, pulmonary veins and mitral valve annulus movement) and mechanical properties based on planar biaxial experiments. The model was able to accurately reproduce the in vivo dynamics of the left atrium during the passive portion of the cardiac cycle. A shift in time between the peak pressure and the maximum displacement of the mitral valve annulus allows the appendage to inflate and bend towards the ventricle before the pulling effect associated with the ventricle contraction takes place. The ventricular systole creates room for further expansion of the appendage, which gets in close contact with the pericardium. The temporal evolution of the volume in the atrial cavity as predicted by the finite element simulation matches the volume changes obtained from CT scans. The stress field computed at each time point shows remarkable spatial heterogeneity. In particular, high stress concentration occurs along the appendage rim and in the region surrounding the pulmonary veins.     

Effect of left atrial ligation-driven altered inflow hemodynamics on embryonic heart development: clues for prenatal progression of hypoplastic left heart syndrome

Congenital heart defects (CHDs) are abnormalities in the heart structure present at birth. One important condition is hypoplastic left heart syndrome (HLHS) where severely underdeveloped left ventricle (LV) cannot support systemic circulation. HLHS usually initiates as localized tissue malformations with no underlying genetic cause, suggesting that disturbed hemodynamics contribute to the embryonic development of these defects. Left atrial ligation (LAL) is a surgical procedure on embryonic chick resulting in a phenotype resembling clinical HLHS. In this study, we investigated disturbed hemodynamics and deteriorated cardiac growth following LAL to investigate possible mechanobiological mechanisms for the embryonic development of HLHS. We integrated techniques such as echocardiography, micro-CT and computational fluid dynamics (CFD) for these analyses. Specifically, LAL procedure causes an immediate flow disturbance over atrioventricular (AV) cushions. At later stages after the heart septation, it causes hemodynamic disturbances in LV. As a consequence of the LAL procedure, the left-AV canal and LV volume decrease in size, and in the opposite way, the right-AV canal and right ventricle volume increase. According to our CFD analysis, LAL results in an immediate decrease in the left AV canal WSS levels for 3.5-day (HH21) pre-septated hearts. For 7-day post-septated hearts (HH30), LAL leads to further reduction in WSS levels in the left AV canal, and relatively increased WSS levels in the right AV canal. This study demonstrates the critical importance of the disturbed hemodynamics during the heart valve and ventricle development.

     

A modified mathematical model of the anatomy of the cardiac left ventricle

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.     

Combined experimental and numerical analysis of the flow structure into the left ventricle

Fluid dynamics is used for diagnosis in cardiology only to a partial extent. Indeed several aspects of cardiac flows and their relation with pathophysiology are unknown. The flow that develops into the left ventricle is here studied by using a combination of numerical and experimental models. The former allows a detailed three-dimensional analysis, the latter can be used in conditions, like in presence of turbulence, that are out of reach of the current computational power. The three-dimensional flow dynamics is analyzed in terms of its vortical structure. The study, within its limitations, provides further physical understanding about the intraventricular flow structure. This could eventually support the development of cardiac diagnostic indicators based on fluid dynamics.     

An elongation model of left ventricle deformation in diastole

A numerical method of the left ventricle (LV) deformation, an elongation model, was put forth for the study of LV fluid mechanics in diastole. The LV elongated only along the apical axis, and the motion was controlled by the intraventricular flow rate. Two other LV models, a fixed control volume model and a dilation model, were also used for model comparison and the study of LV fluid mechanics. For clinical sphere indices (SIs, between 1.0 and 2.0), the three models showed little difference in pressure and velocity distributions along the apical axis at E-peak. The energy dissipation was lower at a larger SI in that the jet and vortex development was less limited by the LV cavity in the apical direction. LV deformation of apical elongation may represent the primary feature of LV deformation in comparison with the secondary radial expansion. The elongation model of the LV deformation with an appropriate SI is a reasonable, simple method to study LV fluid mechanics in diastole.     

Estimation of aortic distensibility and instantaneous left ventricular volume in living man

A method is presented in this paper for the estimation of aortic distensibility and instantaneous systolic left ventricular volume in living man in the absence of valvular regurgitation. The method is based on a simple, elastic-reservoir-theory, model of the circulatory system and requires no assumption concerning the geometry of the left ventricle. The input data required for this mathematical model consists of stroke volume, an aortic pressure record over an entire cardiac cycle and end diastolic ventricular volume. The procedure developed here for the estimation of aortic distensibility and instantaneous left ventricular volume is very practical from a computational point of view. It is believed that it will yield useful information concerning two clinically important quantities which cannot be measured directly in living man and will facilitate the study of correlations between these quantities and various physiological and pathological states. Results are presented in the paper for six cardiac patients. The requisite data in each case was obtained in the Cardiac Research Laboratory at the Peter Bent Brigham Hospital.     

Fluid dynamics of the left ventricular filling in dilated cardiomyopathy

Modifications in diastolic function occur in a broad range of cardiovascular diseases and there is an increasing evidence that abnormalities in left ventricular function may contribute significantly to the symptomatology. The flow inside the left ventricle during the diastole is here investigated by numerical solution of the Navier-Stokes equations under the axisymmetric assumption. The equation are written in a body-fitted, moving prolate spheroid, system of coordinates and solved using a fractional step method. The system is forced by a given volume time-law derived from clinical data, and varying the two-degrees-of-freedom ventricle geometry on the basis of a simple model. The solution under healthy conditions is analysed in terms of vorticity dynamics, showing that the flow field is characterised by the presence of a vortex wake; it is attached to the mitral valve during the accelerating phase of the E-wave, and it detaches and translate towards the ventricle apex afterwards. The flow evolution is discussed, results are also reported as an M-mode representation of colour-coded Doppler velocity maps. In the presence of ventricle dilatation the mitral jet extends farther inside the ventricle, propagation velocity decreases, and the fluid stagnates longer at the apex.