Fluid structure interaction of left ventricle modelling from diastole to systole based on in-

vivo CMR

Hao Gao1, Boyce E. Griffith2, David Carrick3, Colin Berry3, Xiaoyu Luo1

1. School of mathematics and Statistics, University of Glasgow, UK2. Department of Medicine, University of New York, USA3. Institute of Cardiovascular and Medical Science, University of Glasgow, UK

Challenges in LV Modelling

Multi-scale:

Computer simulation offers unique opportunities for integrating multi-sets data, providing insights, even predicting outcomes, etc.

Multi-physics:

Patient specific:

2 out of 19Immersed boundary method: https://code.google.com/p/ibamr

Image Derived LV Model

Healthy LV (at early of diastole) (1) Short-axis cine images

(2) Left ventricular outflow tracts

MVAV

LV

Manual Segmentation

Solid Reconstruction

3 out of 19

Image Derived LV Model

AV

MV

Remarks1: No valves (with positions indicated);2: Regions above MV and AV are artificially constructed for outflow and inflow BCs;3: circular inflow and outflow shapes (easy for applying BC)

Basal plane

apex

inflowoutflow

Artificial extension

Image derived

4 out of 19

Myofibre-enforced Structure

Laminar organization: Fibre—sheet—normal (f, s, n)

Hunter, Brieings in Bioinformatics, 2008

Fibre

sheet

Sheet-normal

Holzaple & Ogden 2009

shear

sheet

fiber

matrix

8 unknown parameters

Passive stress5 out of 19

Active Tension Model

Niederer S, et al, 2006

•Spatially uniform •simultaneous

6 out of 19

Boundary Conditions (1)

Contractile LV

Non-contractileValves

Inflow/outflow

Ramped P (8)Only allowing radial expansion Fixed in long and circumferential axis

fixed

fully fixation Partial fixation

7 out of 19

• BCs for diastolic filling

Note: Diastolic pressure is directly applied to the endocardial surface to mimic the first sucking phase of the diastolic filling.

No flow

diastolic filling

isovolumetric relaxation

isovolumetric contraction

ejection

Boundary Conditions (2)

Contractile LV

Non-contractileValves

Inflow/outflow

Only allowing radial expansion Fixed in long and circumferential axis

fixed

8 out of 19

• BCs for isovolumetric contraction

No flow

diastolic filling

isovolumetric relaxation

isovolumetric contraction

ejection

No flow

fully fixation Partial fixation

Boundary Conditions (3)

Contractile LV

Non-contractileValves

Inflow/outflow

Only allowing radial expansion Fixed in long and circumferential axis

fixed

9 out of 19

• BCs for ejection

diastolic filling

isovolumetric relaxation

isovolumetric contraction

ejection

No flow

Rp

C

PWk(t): initialized with 85mmHg (cuff)

Rc

fully fixation Partial fixation

AV opens: out flow rate > 0AV closes: out flow rate < 0

Boundary Conditions (4)

Contractile LV

Non-contractileValves

Inflow/outflow

Only allowing radial expansion Fixed in long and circumferential axis

fixed

10 out of 19

• BCs for isovolumetric relaxiation

No flow

diastolic filling

isovolumetric relaxation

isovolumetric contraction

ejection

No flow

fully fixation Partial fixation

Material Parameter Optimization

Published material parameters

Passive material parameters

Diastolic filling

Matched ED volume

No

Adjust parameters (scale + fine

adjust)

Systolic contraction

Matched ES volume

End

Adjust Tref

No

11 out of 19

Tref = 256 kPaothers from rat experiments

Results: Pressure-Volume Loop

60 80 100 120 140 160-20

0

20

40

60

80

100

120

140

160

180

200

LV cavity volume (mL)

LV c

avity

pre

ssur

e (m

mH

g)

diastolic filling

isovolumetric relaxation

isovolumetric contraction

ejection

12 out of 19

161mmHg

Cuff Pressure (85-150mmHg)

(78mL,0mmHg)

(143mL,8mmHg)

(139mL,119mmHg)

(72mL,95.7mmHg)

LV Dynamics

13 out of 19

Flow Patterns

60 80 100 120 140 160-20

0

20

40

60

80

100

120

140

160

180

200

LV cavity volume (mL)

LV c

avity

pre

ssur

e (m

mH

g)

14 out of 19

Aortic Flow Rates

15 out of 19

Validation: Strain Comparison

Middle LV

Red line: MR using deformable image registration methodBlack line: IBFE simulation

16 out of 19

Ongoing Work

(1) Coupling to electrophysiology

Mono/Bi-domain models

(2) Adding mitral valve

17 out of 19

Discussion & Conclusion

• The developed IB/FE LV model is capable of simulating LV dynamics with fluid-structure interaction

• Results are consistent with clinical measurements, a potential way to understand heart functions with new biomarkers

• Limitations

18 out of 19

Acknowledgement

Collaborators:

R. W. Ogden

B. Griffith

W.W. Chen

J. Ma N Qi

H. Gao

W.G. Li

A. Allan

H.M. Wang

C. Berry

19 out of 19

Active Tension T

20 out of 22

Ca2+

T

Peak Systolic Active Tension

kPa

kPa

21 out of 20

basal

apex

Brief Introduction of IBM

Solid is immersed inside fluid (overlapped mesh)

22 out of 22

: fluid stress tensor: structure stress tensor

Stress tensor