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!