Health-e-Child - IST-2004-027749 - Deliverable D.11.4

Heart Diseases

Personalised Simulation of Myocardium Electromechanics
and Pulmonary Valve Replacement Surgery in
Repaired Tetralogy of Fallot: a Case Study

3. Personalising an Electromechanical Model to Simulate Patient Cardiac Function

Once the personalised anatomy is built, we can personalise the electromechanical model presented in Part II, section 1, to simulate patient cardiac function. This model is made up of three main building blocks: electrophysiology, to simulate the electrical command; biomechanics, to model the pump function; and boundary conditions, to place the virtual heart in the body. We must personalise each one of these elements to simulate patient cardiac function.

3.1. Electrophysiology

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Isochrones illustrating the propagating electrical wave.
Electrophysiology is synchronously activated at the bottom
of the Purkinje bundle.

Model

Simulating electrophysiology is important since tetralogy of Fallot patients may suffer from electrophysiological troubles, which can lead to sudden death. In particular, bundle-branch blocks are frequent, mainly due to the initial surgical repair and subsequent fibrosis. QRS duration can also be significantly longer than in healthy subjects.

Because we aim at simulating these abnormalities but also at personalising the model using clinical data, we require a model that is accurate but simple enough to be controlled by few clinical parameters. In Health-e-Child, we use an anisotropic multi-front Eikonal model (Sermesant et al., FIMH 2007). This model provides, in non-extreme cases, similar results as those obtained with more complex models. However, it is controlled by only two clinically meaningful parameters and it is significantly faster (of the order of the seconds). The parameters to be set are:


Personalisation

For our patient, only the electrocardiogram is available, where no evident abnormality is observed. Nominal values available in the literature are thus used: conductivity is set to 500 m/s and anisotropy to 3. As illustrated by the video on the left, the electrical wave is initialised at the end of the Purkinje bundles, near the apex.

3.2. Biomechanics

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Strength of the active force that leads to myocardium contraction.
Left ventricle is stronger than right ventricle.
Contractility of the dyskinetic area is purposely
disabled to simulate the pathological motion.

Model

Once the electrical command personalised, we must personalise the cardiac contraction to simulate patient heart motion. As presented in Part II, section 1, the biomechanical model is constituted of two main elements: a geometrical model and a biomechanical constitutive law that models the properties of the myocardium tissue (Sermesant et al., TMI 2006).

Regarding the geometrical model, we rely on a tetrahedral representation of the organ. This enables us to use the personalised anatomies described in the previous section. Linear elasticity is used to model cardiac motion.

The constitutive law used in Health-e-Child is based on a multi-scale model, from nano-motors to the organ (see Part II, section 1). This model is controlled by the following parameters:


Personalisation

The biomechanical model is personalised by alternatively modifying the elasticity and contractility parameters based on observations done from the cine-MRI and the dynamic segmentations. The other parameters are set according to the values found in the literature (mass=1070kg/m3, anisotropy=3). Elasticity and contractility are set independently for three myocardium regions: left ventricle, right ventricle and dyskinetic area. A trial-and-error strategy is carried out to estimate these parameters. Cardiac function is simulated and compared to the cine MRI, 3D segmentation and other clinical observations such as 2D-US end-systolic pressures. Then, contractility is increased or decreased, to retrieve the measured ejection fractions and blood pool volume variations. Elasticity is modified to calibrate the simulated motion to the observed motion. Finally, the contractility of the dyskinetic area is set to 0 to simulate the pathology.

3.3. Boundary Conditions

Model

The last step consists in placing the virtual heart in his environment, i.e. the body. We simulate the four cardiac phases: contraction, ejection, relaxation and filling (Sermesant et al., TMI 2006). Atrial and arterial pressures are also taken into considerations. Finally, pulmonary regurgitations are simulated using a simple model that relies on data measured from 2D ultrasound. The measured regurgitation flows are directly integrated in the virtual heart (Mansi et al., 3DPH 2008).

Personalisation

Regurgitation flows are measured using 2D ultrasound Doppler images and directly integrated into the model. Doppler measurements also provide us with the end-systolic right-ventricule pressure (15mmHg), which we use to personalise the pulmonary artery pressure. Finally, the atrial pressures are set to 5mmHg for the right atrium and 12mmHg for the left atrium. End-systolic aorta pressure is set to 75mmHg following Health-e-Child cardiologists suggestions.

3.4. Results

Several quantitative indexes are obtained from the personalised simulation. First, simulated blood pool volumes are computed. Of course, this data was already available from the segmentations but simulated volumes enable us to calibrate the model. In that way, the biomechanical parameters (elasticity and contractility) are set such that the simulation agrees with the observed volumes and ejection fractions.

However, the key advantage of performing personalised simulations is that parameters that are not readily available in clinical routine can be simulated. For instance, we can simulate the variation of the ventricular, atrial and arterial pressures during the cardiac cycle. We are also able to draw pressure-volume loops, which provide precious information about myocardium efficiency.

Simulated volume variations (right ventricle in blue, left ventricle in red) and segmented volume variations (in green). The electromechanical model of the heart managed to recover the global cardiac function of the patient. Vertical bars limit the four cardiac phases.
Simulated pressures in the left ventricle (solid red curve), in the right ventricle (solid blue curve), in the aorta (dashed red curve) and in the pulmonary artery (dashed blue curve)
Pressure-volume diagram deduced from the two previous diagrams.
Observe the effect of the pulmonary regurgitations during the "iso-volumetric"
phases

Simulated contractions and 3D strain can also be assessed, to understand what are the effects upon the cardiac function of local abnormalities such as the dyskinetic region we observed in the images. Finally, radial displacements can be calculated and compared to the ground truth to refine the personalisation.

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Observed (left) and simulated (right) radial displacements. Similar color patterns highlight similar motion patterns. In particular, the abnormal motion of the dyskinetic area has been successfully recovered, as well as the septal motion.

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Von Mises strain computed from the simulated cardiac motion.

3.5. Conclusions

We now have a personalised electromechanical model of the heart that qualitatively simulates the cardiac function of our patient. The virtual heart can now be used to simulate parameters that are difficult to obtain in clinics. But more importantly, the parameters can be modified to simulate the effects of a therapy, as we will describe in the following section.

References