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Hao Gao 1 , Boyce E. Griffith 2 , David Carrick 3 , Colin Berry 3 , Xiaoyu Luo 1

Hao Gao 1 , Boyce E. Griffith 2 , David Carrick 3 , Colin Berry 3 , Xiaoyu Luo 1. Fluid structure interaction of left ventricle modelling from diastole to systole based on in-vivo CMR. School of mathematics and Statistics, University of Glasgow, UK

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Hao Gao 1 , Boyce E. Griffith 2 , David Carrick 3 , Colin Berry 3 , Xiaoyu Luo 1

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  1. Hao Gao1, Boyce E. Griffith2, David Carrick3, Colin Berry3, Xiaoyu Luo1 Fluid structure interaction of left ventricle modelling from diastole to systole based on in-vivo CMR School of mathematics and Statistics, University of Glasgow, UK Department of Medicine, University of New York, USA Institute of Cardiovascular and Medical Science, University of Glasgow, UK

  2. Challenges in LV Modelling Computer simulation offers unique opportunities for integrating multi-sets data, providing insights, even predicting outcomes, etc. • Multi-scale: • Multi-physics: • Patient specific: Immersed boundary method: https://code.google.com/p/ibamr

  3. Image Derived LV Model • Healthy LV (at early of diastole) (1) Short-axis cine images Manual Segmentation (2) Left ventricular outflow tracts Solid Reconstruction AV MV LV

  4. Image Derived LV Model outflow inflow Artificial extension MV AV Basal plane Image derived apex Remarks 1: 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)

  5. Myofibre-enforced Structure Laminar organization: Fibre—sheet—normal (f, s, n) Holzaple & Ogden 2009 Sheet-normal matrix fiber sheet sheet Passive stress shear Fibre 8 unknown parameters Hunter, Brieings in Bioinformatics, 2008

  6. Active Tension Model • Spatially uniform • simultaneous Niederer S, et al, 2006

  7. Boundary Conditions (1) • BCs for diastolic filling ejection isovolumetric relaxation isovolumetric contraction No flow fixed Inflow/outflow diastolic filling Valves fully fixation Partial fixation Non-contractile Only allowing radial expansion Fixed in long and circumferential axis Ramped P (8) Contractile LV Note: Diastolic pressure is directly applied to the endocardial surface to mimic the first sucking phase of the diastolic filling.

  8. Boundary Conditions (2) • BCs for isovolumetric contraction ejection isovolumetric relaxation isovolumetric contraction No flow No flow fixed Inflow/outflow diastolic filling Valves fully fixation Partial fixation Non-contractile Only allowing radial expansion Fixed in long and circumferential axis Contractile LV

  9. Boundary Conditions (3) Rp • BCs for ejection ejection PWk(t): initialized with 85mmHg (cuff) C isovolumetric relaxation isovolumetric contraction Rc No flow fixed Inflow/outflow diastolic filling Valves fully fixation Partial fixation Non-contractile Only allowing radial expansion Fixed in long and circumferential axis Contractile LV AV opens: out flow rate > 0 AV closes: out flow rate < 0

  10. Boundary Conditions (4) • BCs for isovolumetricrelaxiation ejection isovolumetric relaxation isovolumetric contraction No flow No flow fixed Inflow/outflow diastolic filling Valves fully fixation Partial fixation Non-contractile Only allowing radial expansion Fixed in long and circumferential axis Contractile LV

  11. Material Parameter Optimization Systolic contraction Published material parameters AdjustTref Matched ES volume Passive material parameters No Diastolic filling Adjust parameters (scale + fine adjust) End Matched ED volume No Tref = 256 kPa others from rat experiments

  12. Results: Pressure-Volume Loop (72mL,95.7mmHg) (139mL,119mmHg) ejection 161mmHg Cuff Pressure (85-150mmHg) isovolumetric contraction isovolumetric relaxation (78mL,0mmHg) diastolic filling (143mL,8mmHg)

  13. LV Dynamics

  14. Flow Patterns

  15. Aortic Flow Rates

  16. Validation: Strain Comparison Middle LV Red line: MR using deformable image registration method Black line: IBFE simulation

  17. Ongoing Work Coupling to electrophysiology (2) Adding mitral valve Mono/Bi-domain models

  18. 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

  19. Acknowledgement Collaborators: R. W. Ogden B. Griffith A. Allan W.W. Chen N Qi J. Ma H. Gao C. Berry W.G. Li H.M. Wang

  20. Active Tension T T Ca2+

  21. Peak Systolic Active Tension kPa basal kPa apex

  22. Brief Introduction of IBM Stress tensor Solid is immersed inside fluid (overlapped mesh) : fluid stress tensor : structure stress tensor

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