On estimating intraventricular hemodynamic forces from endocardial dynamics: A comparative study with 4D flow MRI.

Intraventricular pressure gradients or hemodynamic forces, which are their global measure integrated over the left ventricular volume, have a fundamental importance in ventricular function. They may help revealing a sub-optimal cardiac function that is not evident in terms of tissue motion, which is naturally heterogeneous and variable, and can influence cardiac adaptation. However, hemodynamic forces are not utilized in clinical cardiology due to the unavailability of simple non-invasive measurement tools. Hemodynamic forces depend on the intraventricular flow; nevertheless, most of them are imputable to the dynamics of the endocardial flow boundary and to the exchange of momentum across the mitral and aortic orifices. In this study, we introduce a simplified model based on first principles of fluid dynamics that allows estimating hemodynamic forces without knowing the velocity field inside the LV. The model is validated with 3D phase-contrast MRI (known as 4D flow MRI) in 15 subjects, (5 healthy and 10 patients) using the endocardial surface reconstructed from the three standard long-axis projections. Results demonstrate that the model provides consistent estimates for the base-apex component (mean correlation coefficient r=0.77 for instantaneous values and r=0.88 for root mean square) and good estimates of the inferolateral-anteroseptal component (r=0.50 and 0.84, respectively). The present method represents a potential integration to the existing ones quantifying endocardial deformation in MRI and echocardiography to add a physics-based estimation of the corresponding hemodynamic forces. These could help the clinician to early detect sub-clinical diseases and differentiate between different cardiac dysfunctional states.

Asymptotic Model of Fluid-Tissue Interaction for Mitral Valve Dynamics.

The vortex formation process inside the left ventricle is intrinsically connected to the dynamics of the mitral leaflets while they interact with the flow crossing the valve during diastole. The description of the dynamics of a natural mitral valve still represents a challenging issue, especially because its material properties are not measurable in vivo. Medical imaging can provide some indications about the geometry of the valve, but not about its mechanical properties. In this work, we introduce a parametric model of the mitral valve geometry, whose motion is described in the asymptotic limit under the assumption that it moves with the flow, without any additional resistance other than that given by its shape, and without the need to specify its material properties. The mitral valve model is coupled with a simple description of the left ventricle geometry, and their dynamics is solved numerically together with the equations ruling the blood flow. The intra-ventricular flow is analyzed in its relationship with the valvular motion. It is found that the initial valve opening anticipates the peak velocity of the Early filling wave with little influence of the specific geometry; while subsequent closure and re-opening are more dependent on the intraventricular vortex dynamics and thus on the leaflets' geometry itself. The limitations and potential applications of the proposed model are discussed.

Left ventricular fluid mechanics: the long way from theoretical models to clinical applications.

The flow inside the left ventricle is characterized by the formation of vortices that smoothly accompany blood from the mitral inlet to the aortic outlet. Computational fluid dynamics permitted to shed some light on the fundamental processes involved with vortex motion. More recently, patient-specific numerical simulations are becoming an increasingly feasible tool that can be integrated with the developing imaging technologies. The existing computational methods are reviewed in the perspective of their potential role as a novel aid for advanced clinical analysis. The current results obtained by simulation methods either alone or in combination with medical imaging are summarized. Open problems are highlighted and perspective clinical applications are discussed.

Comparative numerical study on left ventricular fluid dynamics after dilated cardiomyopathy.

INTRODUCTION: The role of flow on the progression of left ventricular (LV) remodeling has been presumed, although measurements are still limited and the intraventricular flow pattern in remodeling hearts has not been evaluated in a clinical setting. Comparative evaluation of intraventricular fluid dynamics is performed here between healthy subjects and dilated cardiomyopathy (DCM) patients. METHODS: LV fluid dynamics is evaluated in 20 healthy young men and 8 DCM patients by combination of 3D echocardiography with direct numerical simulations of the equation governing blood motion. Results are analyzed in terms of quantitative global indicators of flow energetics and blood transit properties that are representative of the qualitative fluid dynamics behaviors. RESULTS: The flow in DCM exhibited qualitative differences due to the weakness of the formed vortices in the large LV chamber. DCM and healthy subjects show significant volumetric differences; these also reflect inflow properties like the vortex formation time, energy dissipation, and sub-volumes describing flow transit. Proper normalization permitted to define purely fluid dynamics indicators that are not influenced by volumetric measures. CONCLUSION: Cardiac fluid mechanics can be evaluated by a combination of imaging and numerical simulation. This pilot study on pathological changes in LV blood motion identified intraventricular flow indicators based on pure fluid mechanics that could potentially be integrated with existing indicators of cardiac mechanics in the evaluation of disease progression.

Functional strain-line pattern in the human left ventricle.

Analysis of deformations in terms of principal directions appears well suited for biological tissues that present an underlying anatomical structure of fiber arrangement. We applied this concept here to study deformation of the beating heart in vivo analyzing 30 subjects that underwent accurate three-dimensional echocardiographic recording of the left ventricle. Results show that strain develops predominantly along the principal direction with a much smaller transversal strain, indicating an underlying anisotropic, one-dimensional contractile activity. The strain-line pattern closely resembles the helical anatomical structure of the heart muscle. These findings demonstrate that cardiac contraction occurs along spatially variable paths and suggest a potential clinical significance of the principal strain concept for the assessment of mechanical cardiac function. The same concept can help in characterizing the relation between functional and anatomical properties of biological tissues, as well as fiber-reinforced engineered materials.

Intraventricular vortex flow changes in the infarcted left ventricle: numerical results in an idealised 3D shape.

The cardiac diagnostic process is primarily based on the evaluation of myocardial mechanics whereas little is known about blood dynamics that is rarely considered to this purpose. The intraventricular blood flow is analysed here for akinetic and dyskinetic myocardial motion corresponding to the presence of an ischaemic pathology. This study is performed through a 3D numerical model of the left ventricular flow. Results show that the presence of an anterior-inferior wall infarction leads to the shortening and weakening of the diastolic mitral jet. A region of stagnating flow is found near the apex and close to the ischaemic wall. These results are in agreement with previous clinical findings based on echographic imaging. The described phenomena are also noticed for moderate degrees of the ischaemic pathology and suggest a potential value of the study of the intraventricular flow to develop early diagnostic indicators.

On the left ventricular vortex reversal after mitral valve replacement.

The blood flow in the human left ventricle is known to develop a vortical motion that should facilitate the ejection of blood into the primary circulation. This study shows that such a rotary motion can be totally reversed after the implant of a prosthetic valve. This phenomenon, in agreement with clinical observation, appears mostly imputable to the symmetry of the implant. The reversed rotation increases energy dissipation and modifies the pressure distribution with the potential development of new pathologies. The results provide preliminary, physically based, elements for the improvement of surgical procedures or prosthesis.

Asymmetric opening of a simple bileaflet valve.

The opening motion of a bileaflet valve driven by a pulsed stream is studied in the limiting condition of rigid massless leaflets closing a two-dimensional channel. This simple arrangement allows us to write simple dynamical equations for the solid that are solved numerically with the Navier-Stokes equation for the fluid. The analysis is focused on the influence of asymmetry on the coupled fluid-valve dynamics when parameters are taken with references to cardiac valves. Results show that the wake generation from the leaflet's trailing edge can be partly inhibited; the primary vortex downstream does not occur in an intermediate range of asymmetry. The potential emergence of such a phenomenon in realistic cases would present implications in development of diagnostic schemes.

Nature optimizes the swirling flow in the human left ventricle.

The asymmetry of the blood flow in the human left ventricle is commonly assumed to facilitate the following ejection of blood in the primary circulation. The intraventricular flow is here studied by the numerical solution of the governing equations written in a prolate spheroid geometry with moving walls. The physiological parameters are taken from pediatric clinical data; then, the entering jet is artificially displaced to modify the asymmetry of the flow. The analysis of flow patterns confirms that the physiological case looks to best comply with the transition from the filling to the ejection phase. The flow energy dissipation is found to be minimized about the physiological conditions. An unnatural asymmetry, as given by cardiac diseases or valvular replacement, could reduce the efficiency of the heart pump by over 10%, thus augmenting the work required by the cardiac muscle.

Model and influence of mitral valve opening during the left ventricular filling.

The flow inside a model left ventricle during filling (diastole) is simulated by the numerical solution of the equations of motion under the axisymmetric approximation. The left ventricle is taken with a truncated ellipsoid geometry, and a simple conceptual model is introduced to simulate the presence of the moving mitral valve. A relevant role during the left ventricle diastolic flow, as already discussed by other authors, is played by the travelling vortex wake that is formed from the transmitral jet during the early filling acceleration phase. The presence of a moving valve is found to produce a non-simultaneous spatial development of the entering bulk flow and a slightly more complex vortex wake structure; the results are discussed in comparison with fixed valve ones. They are analysed also in terms of M-mode representation suggesting a physical interpretation of the pattern detected in the clinical measurements that extends the one given previously on the basis of fixed valve models.

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.

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.