Page 173 - Advances in Biomechanics and Tissue Regeneration

8.5 PATIENT-SPECIFIC CARDIAC PODI COMPUTATION 169

TABLE 8.8 Cube Grid With Different Mesh Discretizations
Cube grid CG-1 CG-2 CG-3 CG-4 CG-5 CG-6
Nodes 294 336 448 504 720 990

0.5
Displacement
LV-PV
0.45
0.4

L 2 error 0.35
0.3
0.25

0.2
0.15
200 300 400 500 600 700 800 900 1000
Num of grid nodes
FIG. 8.31 Change in ε BV R -norm as the number of grid nodes increases.
‘ 2

TABLE 8.9 Change in the Error and Calculation Time as the Number of Grid Nodes Increases
L 2 -error Calculation time (s)
Displacement Visual Total Projection
CG-2 0.45 Deformations 232 219
CG-6 0.36 Deformations 643 628

as shown in Fig. 8.32, with the nodes lying inside the wall showing improvement while the lateral wall of the RV
exhibits more expansion. However, when the deformed state is more closely investigated, the localized nonphysical
deformations are still dominant on the surfaces of the geometry and the magnitude of the displacement field is notice-
ably lower, as depicted in Fig. 8.30C. The most significant solution improvements can be found at the epicardium sur-
face of the RV.
Regarding the PODI calculation time, it is found to be increasing almost linearly because more grid nodes are pre-
sent, as shown in Fig. 8.33. This is due to the fact that the PIP algorithm and the template projections require more time.
The three most dominant POMs are found to be needed in order to reach the minimum specified energy limit for the
displacement, strain and stress field data. Further investigation of the POVs reveals that the energy of the first, second,
and third POMs is about 61.6%, 30.5%, and 7.8%, respectively. The fourth POM is below 1.04 10 14 %. This is in
contrast to Rama et al. [34], where the first POM already accounted for about 99% of the energy. The cube standard-
ization method obviously has a scattering effect leading to dataset matrices, U i , with disorganized data due to the

Displacement
1.588e+01
11.909
7.9394
3.9697
2.201e-05
(A) (B) (C)
FIG. 8.32 PODI displacement field plot based on the cube template standardization method for different numbers of grid nodes. (A) PODI with
294 grid nodes. (B) PODI with 990 grid nodes. (C) EFG.

I. BIOMECHANICS