Virtual cohort of adult healthy four-chamber heart meshes from CT images

Dataset Description: We present the first database of four-chamber healthy heart models suitable for electro-mechanical (EM) simulations. Our database consists of twenty four-chamber heart models generated from end-diastolic CT acquired from patients who went to the emergency room with acute chest pains. Since no cardiac conditions were detected in follow-up, these patients were taken as representative of "healthy" (or asymptomatic) hearts. These meshes were used for EM simulations and to build a statistical shape model (SSM). The output of the simulations and the weights of the SSM are also provided.

Cardiac meshes: We segmented end-diastolic CT. The segmentation was then upsampled and smoothed. The final multi-label segmentation was used to generate a tetrahedral mesh. The resulting meshes had an average edge length of 1 mm. The elements of all the twenty meshes are labelled as follows:

1. Left ventricle myocardium
2. Right ventricle myocardium
3. Left atrium myocardium
4. Right atrium myocardium
5. Aorta wall
6. Pulmonary artery wall
7. Mitral valve plane
8. Tricuspid valve plane
9. Aortic valve plane
10. Pulmonary valve plane
11. Left atrium appendage "inlet"
12. Left superior pulmonary vein inlet
13. Left inferior pulmonary vein inlet
14. Right inferior pulmonary vein inlet
15. Right superior pulmonary vein inlet
16. Superior vena cava inlet
17. Inferior vena cava inlet
18. Left atrial appendage border
19. Right inferior pulmonary vein border
20. Left inferior pulmonary vein border
21. Left superior pulmonary vein border
22. Right superior pulmonary vein border
23. Superior vena cava border
24. Inferior vena cava border

Ventricular fibres were generated using a rule-based method, with a fibre orientation varying transmurally from endocardium to epicardium from 80˚ to -60˚, respectively.  We defined a system of universal ventricular coordinates on the meshes: an apico-basal coordinate (Z) varying continuously from 0 at the apex to 1 at the base (defined with the mitral and tricuspid valve); a transmural coordinate (\(\rho\)) varying continuously from 0 at the endocardium to 1 at the epicardium; a rotational coordinate (\(\phi\)) varying continuously from – π at the left ventricular free wall, 0 at the septum and then back to + π at the left ventricular free wall; intra-ventricular coordinate (V) defined at -1 at the left ventricle and +1 at the right ventricle. This coordinate system was assigned to the ventricles in the four-chamber meshes and all the other labels were assigned with -10.  

 We provide a zipped folder for each mesh, A VTK file for each mesh was included (in ASCII) as an UNSTRUCTURED GRID. In all the cases the following fields were included:

• POINTS, with the coordinates of the points in mm.
• CELL_TYPES, having all of the points the value 10 since they are tetrahedra.
• CELLS, with the indices of the vertices of every element.
• CELL_DATA, corresponding to the meshing tags. 
• VECTORS, with the directions of the fibres.
• POINT_DATA, with four LOOKUP_TABLE subfields corresponding to the UVC in the order \(\rho\), \(\phi\), Z and V.

Cardiac simulations: For the cardiac EM simulations we used CARP (Cardiac Arrhythmia Research Package). We used the reaction-eikonal model for electrophysiology, stimulating as initial condition the bottom third (Z < 0.33) of the endocardium. We simulated the large deformation mechanics in a Lagrangian reference system. The ventricular myocardium was modelled as a hyperelastic transversely isotropic material with Guccione's strain energy function. The remaining tissues were modelled as non-contracting neo-Hookean materials. Simulations of meshes #09 and #10 failed to converge. Details on the specific parametrisation can be found in the supplements of the reference paper.

We provide comma-separated-values files with the output of the simulations used in the reference paper for validation purposes. The simulations of the cases that did not converge were not included. The acronyms used in the names of columns are:

• EDP: End-diastolic pressure
• EDV: End-diastolic volume
• Myo_vol: Myocardial volume of the ventricle (as sum of its elements)
• ESV: End-systolic volume
• SV: Stroke volume 
• EF: Ejection fraction
• V1: Volume at time of peak flow
• EF1: First-Phase Ejection Fraction
• ESP: End-systolic pressure
• dPdtmax: Maximum increase of pressure
• dPdtmin: Maximum decrease of pressure
• PeakP: Peak pressure
• tpeak: Time to peak pressure
• ET: Ejection time
• ICT: Isovolumic contraction time
• IRT: Isovolumic relaxation time
• tsys: Duration of systole
• QRS: QRS duration
• AT1090: Time taken to activate from 10% to 90% of the mesh
• AT: Activation time of the left ventricle

Besides the output value name, in each column is specified the ventricle where that output was extracted from with the suffixes "_LV" or "_RV".

Statistical shape model: All the meshes but #20 were used to build a statistical shape model of four-chambers cardiac meshes. In short, we rigidly aligned the meshes and extracted the surfaces, representing them as deRham currents. The registration between meshes and computation of the average shape (also called atlas or template) was done using a Large Deformation Diffeomorphic Metric Mapping method. Each one of the meshes can be approximated as a linear combination of the shape modes, extracted using Principal Component Analysis on the space where the meshes are located. More details on the Statistical Shape Model are provided in the supplement of the reference paper. The average heart and extreme cases are provided in the repository named "Virtual cohort of extreme and average four-chamber heart meshes from statistical shape model". We have added 1000 more meshes from the same statistical shape model, modifying the weights from the PCA randomly within the 2SD range. These meshes are provided in the repository named "Virtual cohort of 1000 synthetic heart meshes from the adult human healthy population".

We provide the weights of the modes for each of the 19 meshes in a comma-separated-values file.