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Computational Modelling of the Whole-Heart Electrical Activity
Siniša Sovilj, PhD University of Zagreb, Faculty of
Electrical Engineering and Computing, Zagreb, CROATIA
Računalno modeliranje električne aktivnosti srca
dr.sc. Siniša Sovilj, dipl.ing.
Sveučilište u Zagrebu, Fakultet elektrotehnike i računarstva
1$ = 6 HRK UNSW UNIZG
Osnovano 1949. 1669.
Studenata 50.516 65.592
Zaposlenika 5300 8080
Fond (endowment)
1.520 M$ 328 M HRK ( 55 M$)
Školarina 4000 $/kolegiju 50.000 $/god.
8000 HRK/god. (1333 $/god.)
Smještaj 200-400$/tjedno 10-20 k$/god.
3000 kn/mjesečno
Bruto plaća • Research
associate • Assistant Prof. • Associate Prof. • Professor
• 60-80 k$
• 80-100 k$ • 100-120 k$ • 125-140 k$
• 13.800 kn*12
=165.600 HRK (27.600 $)
• •
Neto plaća -25% -45%
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Outline
• Previous work
• 0) single cell model
• 1) simplified 2D model
• 2) simplified 3D model
• 3) realistic 3D model
• Future work
Previous work
• Prediction of postoperative AF
Previous work
• Prediction of postoperative AF
Previous work
• Prediction of postoperative AF
Previous work
• Prediction of postoperative AF
Previous work
• Prediction of postoperative AF
0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
40,00
1 2 3 4 5 6 7 8 9
AF
pre
vela
nce %
Postoperative day
Previous work
• Prediction of postoperative AF
0) Single Cell model
• FitzHugh-Nagumo (FHN) model
1 2
1 2
1 SAN
1
mio
e ie e ion
i ei i ion
m i e
m m
ion m
n
i n
m
m m
o m
V VV i
t t
V VV i
t t
V V V
V B V Bi k c V B a k c u
A A
V B V Bi k c V B a k c u V
Vi
t
V Buk d
t A
A
e b
A
u
non-SANm B
0) Single Cell model
• FitzHugh-Nagumo (FHN) model
0) Single Cell model
• FitzHugh-Nagumo (FHN) model
1 2
1 2
1 SAN
1
mio
e ie e ion
i ei i ion
m i e
m m
ion m
n
i n
m
m m
o m
V VV i
t t
V VV i
t t
V V V
V B V Bi k c V B a k c u
A A
V B V Bi k c V B a k c u V
Vi
t
V Buk d
t A
A
e b
A
u
non-SANm B
1) Simplified 2D model
e
σ /
0
σ /
0
e
i
b
e
b
i
V V on H
V on
V i
H
V on H
V i
n
n
B
B
n 0
n n J
n
0
I LA RA
II LF RA
III LF LA
GND
V V V
V V V
V V V
V X
Transmembrane potential (Vm)
Transmembrane potential (Vm)
2) Simplified 3D model
𝑉𝐼 = 𝑉𝐿 − 𝑉𝑅
𝑉𝐼𝐼 = 𝑉𝐹 − 𝑉𝑅
𝑉𝐼𝐼𝐼 = 𝑉𝐹 − 𝑉𝐿
𝑎𝑉𝑅 = (2𝑉𝑅 − 𝑉𝐿 − 𝑉𝐹)/2
𝑎𝑉𝐿 = (2𝑉𝐿 − 𝑉𝑅 − 𝑉𝐹)/2
𝑎𝑉𝐹 = (2𝑉𝐹 − 𝑉𝑅 − 𝑉𝐿)/2
𝑉𝐶𝑇 = (𝑉𝐿 + 𝑉𝑅 + 𝑉𝐹)/3
𝑋 = 0.610 ∙ 𝐴 + 0.171 ∙ 𝐶 − 0.781 ∙ 𝐼
𝑌 = 0.655 ∙ 𝐹 + 0.345 ∙ 𝑀 − 1.000 ∙ 𝐻
𝑍 = 0.133 ∙ 𝐴 + 0.736 ∙ 𝑀 − 0.264 ∙ 𝐼 −0.374 ∙ 𝐸 − 0.231 ∙ 𝐶
Transmembrane potential (Vm)
heart surface cross-section
Normal Anterior MI Inferior MI
Normal Anterior MI Inferior MI
3) Realistic 3D model
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Visual Human Project
• Voxel size (torso): 0.9mm x 0.9mm x 3mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Segmentation
• 0.9mm x 0.9mm x 6mm/slice
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Heart
• Heart + Aorta + Sup.&Inf. Vena Cava + Pulmonary Trunk
Mesh
Mesh
Mesh
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Result
Conclusion
• 3 torso-embedded whole-heart models
• applications: new diagnostic tools (predictive, preventive, personalisied)
Simplified 2D Simplified 3D Realistic 3D
Tetrahedral Elements
8.174 21.106 298.728
DoF 28.403 51.680 682.768
Simul. Time (1 sec @ 1 ms)
~ 5 min ~ 1 h ~ 12 h
* Intel Core i7-970 workstation, 24GB RAM, 100 Gflops
Future Work
• realistic 3D model, finer geometry, details
• induction of arrhythmias, defibrillation
• inverse problem estimation (patient-specific)
• more detailed cell models e.g. generic
• coupling with other cardiac models:
– electro-mechanical
– cardiac flow models
Thank you!