Virtual cohort of extreme and average four-chamber heart meshes from statistical shape model

Dataset Description: We present a database of four-chamber heart models derived from a statistical shape model (SSM) suitable for electro-mechanical (EM) simulations. Our database consists of 39 four-chamber heart models generated from end-diastolic CT-derived meshes (available in the repository called ("Virtual cohort of adult healthy four-chamber heart meshes from CT images"). These meshes were used for EM simulations. The output of the simulations and the weights of the SSM are also provided.

Cardiac meshes: To build the SSM, we rigidly aligned the CT cohort and extracted the surfaces, representing them as deRham currents. The registration between meshes and computation of the average shape was done using a Large Deformation Diffeomorphic Metric Mapping method. The deformation functions depend on a set of uniformly distributed control points in which the shapes are embedded, and on the deformation vectors attached to these points. It is in this spatial field of deformation vectors (one per each control point) where the Principal Component Analysis is applied. Case #20 of the CT cohort was not included. More information on the details can be found in Supplement 3 of the reference paper. We created two extra cohorts by modifying the weight of the modes explaining 90%of the variance in shape (corresponding to modes 1 to 9). We created these meshes with either ±2 or ±3 standard deviations (SD) of each mode added to the average mesh (extreme2 and extreme3 cohorts respectively). We also created two additional meshes with ±1 SD for mode 2 (extreme1 cohort). The elements of all the 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.

We provide the average mesh, and the extreme1, extreme2 and extreme3 cohorts. These correspond to the files of the form modeX±1SD for extreme 1, modeX±2SD for extreme2 and modeX±3SD for extreme3. These meshes have been used to interpret the anatomical meaning of modifying each mode.

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 diverged for cases mode2-3SD, mode3+3SD, mode6-3SD, mode9-3SD and mode2-2SD . 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".

SSM weights:  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. We provide the weights for each mesh in a comma-separated-values file.

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".