Fluid structure interaction of left ventricle modelling from diastole to systole based on in-vivo CMR Hao Gao 1, Boyce E. Griffith 2, David Carrick 3, Colin Berry 3, Xiaoyu Luo 1 1.School of mathematics and Statistics, University of Glasgow, UK 2.Department of Medicine, University of New York, USA 3.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 19 Immersed boundary method:

Image Derived LV Model  Healthy LV (at early of diastole) (1) Short-axis cine images (2) Left ventricular outflow tracts MV AV LV Manual Segmentation Solid Reconstruction 3 out of 19

Image Derived LV Model AV MV 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) Basal plane apex inflow outflow 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 stress 5 out of 19

Active Tension Model Niederer S, et al, 2006 Spatially uniform simultaneous 6 out of 19

Boundary Conditions (1) Contractile LV Non-contractile Valves 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-contractile Valves 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-contractile Valves 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 P Wk (t): initialized with 85mmHg (cuff) Rc fully fixation Partial fixation AV opens: out flow rate > 0 AV closes: out flow rate < 0

Boundary Conditions (4) Contractile LV Non-contractile Valves 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 kPa others from rat experiments

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

LV Dynamics 13 out of 19

Flow Patterns 14 out of 19

Aortic Flow Rates 15 out of 19

Validation: Strain Comparison Middle LV Red line: MR using deformable image registration method Black 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 Ca 2+ T

Peak Systolic Active Tension 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