Download Intra-cardiac turbulence in a realistic human left heart

3rd International Conference on Computational and Mathematical Biomedical Engineering - CMBE2013
16-18 December 2013, Hong-Kong
P. Nithiarasu and R. Löhner (Eds.)
Intra-cardiac turbulence in a realistic human left heart
Franck Nicoud? , Christophe Chnafa?? and Simon Mendez??
Montpellier 2, CNRS 5149 I3M , 34095 Montpellier, France,
[email protected]
?? CNRS 5149 I3M , 34095 Montpellier, France
? University
SUMMARY
A numerical framework designed to compute the blood flow in patient-specific human hearts is
presented. The geometry of the heart cavities and associated wall motion are extracted from ECG
gated 3D medical images while the valves of the heart are accounted for thanks to low order
geometrical models. The resulting blood flow equations are solved using a fourth-order lowdissipative finite-volume scheme and a mixed Arbitrary Lagrangian-Eulerian / Immersed Boundary framework. On top of retrieving the main fluid flow phenomena commonly observed in the
left heart, the methodology allows studying the heart flow dynamics, including the turbulence
characteristics and cycle-to-cycle variations.
Key Words: blood flow, left heart, turbulence.
1
INTRODUCTION
Phase-contrast magnetic resonance imaging (PC-MRI) is nowadays able to provide 3D in-vivo images of the haemodynamics in heart chambers in a non-invasive way [1]. Nevertheless, accuracy
of the velocity field is questionable in disturbed flows [2]. In addition, flow quantities such as wall
shear stresses and pressure, which constitute relevant clinical information, cannot be measured
directly with the PC-MRI method. Computational fluid dynamics (CFD) constitutes a possible,
yet challenging, alternative for patient-specific non-invasive flow characterization. The blood flow
domain variations over the cardiac cycle can theoretically be computed by solving an appropriate fluid-structure-bioelectric interaction problem. However, the mechanical/electrical properties
of the heart muscle are patient specific and can hardly be assessed in practice; besides, the outer
boundary conditions for such coupled problem stem from the interactions between the heart and
its environment and are thus virtually unknown. An alternative consists in using dynamic medical
images (4D) for the computation of the heart deformations. In this view, endocardium movements
are extracted from morphological medical images and prescribed as boundary conditions of the
fluid problem, thus avoiding solving a coupled multiphysics problem [3]. The present work describes a CFD framework based on this principle and its application to an actual patient left heart.
2
METHOD
The YALES2BIO solver (http://www.math.univ-montp2.fr/ yales2bio/) used in this study is a fully
explicit 3D CFD in-house code dedicated to the resolution of microscopic and macroscopic cardiovascular flows. It relies heavily on the YALES2 solver widely validated for complex engineering
applications [4]. It is based on fourth-order finite-volume approximation and an explicit fourthorder Runge-Kutta scheme for time integration. Due to the expected transitional nature of the
flow, large eddy simulations are performed to represent turbulence, using advanced subgrid scale
models able to handle transitional wall bounded flows in complex geometries [5-6].
The numerical domain is extracted from a set of 10 computed tomography (CT) images available
along the cardiac cycle of an actual patient. One native cardiac phase is first selected among the
available phases; the corresponding volumetric data is imported into an image processing software
(ScanIP; Simpleware Ltd., Exeter, UK). The region of interest is isolated and segmentation process
is made by the thresholding method. The extracted geometry is imported in a commercial mesh
generator (Gambit, ANSYS) to generate the finite volumes mesh of the native numerical domain.
As shown in Fig. 1, the computational domain includes the left atrium (LA), left ventricle (LV),
the aortic root (AO) and the pulmonary veins. Note that the papillary muscles were not accounted
for to ease the ventricle desciption, although they could influence the vortex breakdown during the
diastole. Smaller geometrical elements like the aortic valve (AV) and the mitral valve (MV) are
handled by an immersed boundary method [7]. Their exact shape and dynamics are approximated
using the partial information contained in the medical images. The AV which has a moderate
impact on the ventricular flow is modeled as a planar region being alternatively permeable and
impermeable depending on the phase in the cardiac cycle. Its location can be easily determined
thanks to the aortic valve annulus, visible in the medical images. The MV is modelled by a more
realistic geometry based on measurements (open surface, leaflets lengths) extracted from the medical images. Moreover, the AV and MV are assumed to be alternatively closed/opened in phase
opposition during the cardiac cycle: MV open-AV closed during diastole (LV volume increasing)
and MV closed-AV open during systole (LV volume decreasing). The flow waveform imposed
to the four inlet conditions of the computational domain can then be calculated by applying the
mass conservation principle to the time evolving LV/LA volumes. The resulting inlet velocity is
periodic and displayed in Fig. 1A. A nearly isotropic grid with spatial resolution close to 0.8 mm
and approx. three-million tetrahedral elements is used. In order to make the computational grid
follow the physiological heart deformations over time, fields of deformations between the native
image and the other images taken at different phases of the cardiac cycle are first computed by a
non-linear image registration algorithm [3]. Applied to the native mesh, these deformations allow
generating a time evolving mesh consistent with the 4D medical images and whose connectivity
remains unchanged over the cardiac cycle. This enables to use the Arbitrary Lagrangian-Eulerian
methodology to account for the grid motion when solving the fluid flow equations. The simulation time step is fixed by a CFL condition consistent with the explicit time integration used in
YALES2BIO and leading to ∆t ≈ 10−4 s in the present case. Blood is modeled as an incompressible Newtonian fluid with kinematic viscosity 4 × 10−6 m2 s−1 and density close to 1000 kg
m−3 .
3
RESULTS
The peak Reynolds numbers based on flow rate and cross sections mean diameters are indicated
in Fig. 1B at different locations within the computational domain; the computed values are in the
range 2000-5000 and clearly correspond to transitional flow regime where turbulent effects are
expected to occur. This is an a posteriori justification of the choice made to use an appropriate
LES framework (low dissipative, high order scheme [4], advanced sub-grid scale model [5-6]) to
account for the turbulence activity within the heart flow.
Due to the transitional nature of this complex cyclic flow, the velocity pattern changes from one
cycle to the other. 20 cardiac cycles were computed and phase averages were gathered over the
Figure 1: A: computational mesh of the luminal surface of the left heart and zoom on the grid.
The inlets (pulmonary veins) are indicated by black arrows, the outlet (aorta) by the gray arrow.
The inlet waveform is sketched. B: AV and MV modeled valves are visible by transparency. Peak
Reynolds numbers at different locations are indicated.
Figure 2: Slices of the left heart simulation. Velocity vectors are represented during the entering
of the jet through the MV at time t = 530 ms (A) and during the late diastole phase, t = 690 ms,
(B,C). (B) is an instantaneous view of the flow while (C) is the phase-averaged flow.
last 15 cycles. Cycle-to-cycle variations are not observed during the whole cycle. During flow
acceleration, the jet formed at the mitral valve is very stable (Fig. 2A). On the contrary, during
phases of deceleration, the instantaneous velocity (Fig. 2B) and phase-averaged velocity (Fig. 2C)
are clearly different. While a highly disturbed flow is seen for the instantaneous view of the
velocity field in the LV, a large recirculation cell and two others smaller recirculation zones (below
the AV and next to the apex) are visible in the phase-averaged view. Interestingly, phase-averaged
velocity flow fields are very similar to recent PC-MRI measurement of the flow in a left heart
[1]. In the common description of the LV, the large recirculation cell is characteristic of late
diastole. The present results show that this description is true only in the phase-averaged sense,
while instantaneous velocity fields reflect the turbulent nature of the intra-cardiac blood flow.
2 +w 2 )/2 (the fluctuations are defined with respect
Fields of turbulent kinetic energy (u2rms +vrms
rms
to the phase averaged velocity fields) extracted from the simulations (not shown) show that the
turbulence intensity can be as high as 20 % during the late diastole while the flow is virtually
laminar during the ventricle filling.The intra-cardiac turbulence is thus highly intermittent and
should only be represented by large-eddy simulations techniques rather than classical ReynoldsAveraged Navier-Stokes (RANS) turbulence models (e.g.: k-; k-ω among many others) designed
to handle fully developed, ergodic turbulent flows.
4
CONCLUSIONS
A numerical method developed for the computations of the flow in patient-specific human hearts
has been exposed and applied to an actual human left heart. The motions of the ventricle, atrium
and ascending aorta were deduced from medical images while a rough model of the mitral valve
was used, with only two possible states (open or closed). Still, the flow obtained is consistent with
the current knowledge regarding the intra-cardiac blood flow. In addition, cycle-to-cycle variations
are observed, demonstrating that averaged information as provided by MRI only partially describes
the flow structure in the left heart.
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