WHAT CAN WE LEARN FROM COMPUTER SIMULATION?

Transcription

1 WHAT CAN WE LEARN FROM COMPUTER SIMULATION? Ehud Raanani, MD Gil Marom, Phd Cardiothoracic Surgery, Sheba Medical Center Sackler School of Medicine, Biomechanical Engineering, Tel Aviv University Homburg, September 12, 2013 The Leviev Heart Center

2 Freedom from re-operation after 5 years (100PTS) 96.2% ± 2.6%

3 Freedom from 2+ AI 5 years 84% ± 6%

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5 Courtesy; H.J Schafers Surgical Solutions Geometry altered by non-pressurized state! Stay sutures

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10 Geometric Relationships of the Aortic Root Kunzelman et. al. 1994

11 What are the normal diameters of the aortic root? Roman 1987 Kim 1996 Nistri 1999 Varnous 2003 Maselli 2005 Babaee 2007 Tamas 2007 Soncini 2009 Bierbach 2010 Zhu 2011 N Annular Ø STJ Ø STJ/ annulus 24.5 (± 3) 27.5 (± 3) 23.4 (± 2.4) 28.1 (± 3.2) 22.7 (± 2.7) 24.7 (± 2.8) (± 3) 31.2 (± 3.7) 24.4 (± 4.1) 22.3±1,4 ( ) 25.4 (± 4.1) 26.7±2.2 ( ) 1.2±0.1 ( ) 21.8±2.4 21± 3 21,6 21±2,8 20,3±8,7 29.5±3.1 27± 4 27,3 25± 3,7 23.4±3, ,3 1,2 1,1 Courtesy E Lansac

12 Annular and Sinuses Dilataion

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14 The numerical model: fluid structure interaction (FSI)

15 Nominal stress [kpa] The structure model (14,000 shell elements) The cusps: AV cusps consists of collagen fibers embedded in an elastin matrix Anisotropic and hyperelastic behavior Different layers of Collagen and Elastin (CFN) 10 regions with different fiber orientations and diameters Collagen Elastin ,1 0,2 0,3 Eng. Strain

16 Nominal stress [kpa] The Root Average behaviour of porcine aortic sinuses from Gundiah et al. (Ann. Thorac. Surg., 2008; J. Heart Valve Disease, 2008) Aortic root tissue assumed to be isotropic and hyperelastic ,2 0,4 Eng. Strain

17 P [kpa] The flow model : Mesh ~700,000 Physiologic time dependent pressures were employed at the boundaries, representing pressures at the LV and the ascending aorta LV Aorta Rigid wall Compliant aortic root Rigid wall ,2 0,4 0,6 0,8 t [s] LV pressure left ventricle ascending aorta Aortic pressure

18 The non-pathologic FSI model

19 Parametric studies of aortic root geometry Influence of annulus diameter and cusp size Simplified linear elastic and isotropic model Solution duration of 10ms - constant BC Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: /j.jtcvs Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: /j.jtcvs

20 Effect of annulus diameter Six geometries with different annulus diameters Calculated by expanding or shrinking the AA of normal case (24mm) The other dimensions were not changed 20mm 22mm 24mm 26mm 28mm 30mm C-C section

21 Effect of cusp size Five cases with different cusp size The root dimensions are identical to the 24mm case Geometric height 15.4mm 15.9mm 16.2mm 17.6mm 18.9mm Relative cusp size 86% 92% 100% 108% 116% C-C section h G

22 Influence of the geometry on coaptation 5 4 average h c [mm] h C average h C [mm] geometric height [mm] 3,5 3 2,5 2 1,5 1 0, AA diameter [mm]

23 Influence of the geometry on the max. σ max [kpa] principal stress The average dimensions case (h G =16.2mm, d AA =24mm) has the lowest mechanical stress geometrial height [mm] σ max [kpa] AA diameter [mm] Maximum principal stress [kpa]

24 Coaptation vs. effective height Comparison of coaptation during diastole as a function of the effective height The effective height correlates well with valve coaptation The cusps in all the cases with h E <9mm prolapsed during 5 diastole h E h c [mm] 4,5 4 3,5 3 2,5 2 1,5 1 0, h E [mm] daa cusp area

25 Parametric studies of aortic root geometry The influence of graft size and STJ to AA ratio CFN model and hyperelastic material in the sinuses Time dependent and physiological BC

26 Dry parametric study Sixteen cases of aortic roots Were calculated from the base geometry with an applied outer pressure that expanded or shrank the initial AA and STJ

27 Stress distribution during diastole

28 Influence of d STJ /d AA on flow shear stress FSI parametric study with five cases of aortic roots Reducing d STJ /d AA increases the shear stress values To prevent AA expansion - valve-sparing with annuloplasty is preferable

29 Influence of asymmetry Effect of asymmetric BAV morphology on hemodynamics CFN model and hyperelastic material in the sinuses Time dependent and physiological BC

30 Effect of asymmetric BAV configuration Four morphologies of native AV: Tricuspid aortic valve (TAV) Asymmetric bicuspid aortic valve (BAV 1) with and without raphe Almost symmetric bicuspid aortic valve (BAV 2) TAV BAV 1 without raphe BAV 1 with raphe BAV 2

31 Stress during peak systole TAV has the largest opening area Highest stress values are found in BAVs with fused cusps Raphe region increases stress magnitudes The collagen fibers have higher stresses than the surrounding tissues BAV no. 2 has the lowest stress distribution but also very small opening area Max. principal stress [kpa] A TAV BAV no. 2 A BAV no.1 without raphe BAV no.1 with raphe

32 Velocity vectors and streamlines TAV BAV no. 1 without raphe Flow velocity magnitude [m/s] BAV no. 1 with raphe BAV no. 2

33 Flow shear stress during peak systole Higher systolic flow shear stresses are found on the cusps of BAVs The TAV model has the lowest shear stress, specifically on the coapting regions Flow shear stress [Pa] TAV BAV no. 2 BAV no.1 without raphe BAV no.1 with raphe

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35 Annuloplasty or Sub-comissural plication?

36 Summary of parametric studies: There is a normal or perfect symmetric case, that has the best combination of large coaptation, low diastolic tissue stress and low systolic flow shear stress Larger annulus and short cusps length results in higher tissue stress and less cusps coaptation Effective height measure correlates well with cusps coaptation Low STJ/annulus diameter results in high cusp tissue stress, annuloplasty should always be considered BAV have significant lower EOA Asymmetry of BAVs cause larger vortices near the cusps and higher flow shear stress on their tissue

37 Near Future?

38 Preservation of symmetric cusps 38 Geometric height (cusp length from nadir to free margin)

39 Thank you The Leviev Heart Center

40 Acknowledgments Gil Marom PhD Department of Biomechanical engineering, TAU Advisors: Prof. Moshe Rosenfeld Prof. Rami Haj-Ali Prof. Ehud Raanani Collaborators: Prof. Hans-Joachim Schäfers Prof. Hee-Sun Kim Dr. Sagit Ben Zekry Dr. Ashraf Hamdan Mechanics of composite materials lab members: Rotem Halevi Mor Peleg Support: Nicholas and Elizabeth Slezak Super Center for Cardiac Research and Biomedical Engineering at Tel Aviv University

41 Hammermeister et al, JACC 2000

42 Patients and methods From January 2001 to November patients underwent aortic valve preservation surgery (include dissections) 100 elective patients with AI greater than 2+ were includedluded

43 Dysfunction of Aortic Root

44 Aortic Cusps

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47 Objectives To develop a compliant FSI model with: Coaptation between the cusps of the valve Physiologic material properties and realistic BC Mesh refinement study To determine the influence of modeling simplifications FSI with rigid root, dry model Parametric studies of aortic root geometry Annulus diameter, cusp size, STJ to annulus ratio To find the influence of BAVs on hemodynamics To model the effect of asymmetric porcine-specific collagen fibers alignment

48 Previous FSI models of aortic valves Prosthetic mechanical valves - rigid cusps FSI models of flexible valves Arbitrary Lagrangian Eulerian (ALE) Eulerian approach 2D (Lai et al., 2002; Dumont et al., 2004) 3D (Sotiropoulos and Borazjani, 2009) (Van Loon, 2005; Morsi et al., 2007; Katayama et al., 2008) - coaptation was not modeled Fictitious domain (FD) (De Hart et al., 2003; Astorino et al., 2009) - unrealistic BC LS-Dyna (Nicosia et al., 2003; Weinberg and Mofrad, 2007; Carmody et al., 2006) - no coaptation, compressible flow, explicit solver Peskin s immersed boundary (IB) method (Griffith et al., 2009) - semi-rigid root, unrealistic material properties, cannot achieve numerically converged results.

49 Haj-Ali et al. (2012) J. Biomech. 45: Parametric 3D geometry Geometry based on parametric curves and average dimensions The cusps z=0 section: x l = r co cos θ 1 r fo r co sin θ 1 n y=0 section: z = h 1 + h 1 free edge: x = r f + r c cos θ 1 r f z = h f + r l h r c h f = h f cl The sinuses y l n r v x r v r fo y r c sin θ 1 m N z=0 section: r = r co + r s r co cos 3 2 θ y=0 section: circle arc

50 The numerical model: fluid structure interaction (FSI)

51 3D FSI model of native aortic valves with: Cusps Coaptation Physiologic blood pressure Compliant Aortic Root Realistic material properties (AV cusps)

52 Parametric studies of aortic root geometry Influence of cusp size and aortic annulus diameter Simplified linear elastic and isotropic model Solution duration of 10ms - constant BC Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: /j.jtcvs Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: /j.jtcvs

53 The structure model Implicit dynamic analysis Collagen Fiber Network (CFN) model Contact algorithm ~14,000 Shell elements Abaqus (Simulia)

54 P [kpa] The flow model Eulerian method + mesh adaptation Laminar flow ~700,000 elements FlowVision HPC (Capvidia) LV Aorta 0 0,2 0,4 0,6 0,8 t [s] LV pressure Rigid wall left ventricle Compliant aortic root Rigid wall ascending aorta Aortic pressure

55 Nominal stress [kpa] The structure model the cusp Radial stress-strain from Mavrilas & Missirlis (1978) 10 regions with different fiber orientations and diameters Collagen Elastin ,1 0,2 0,3 Eng. Strain

56 Nominal stress [kpa] The structure model the root Average behaviour of porcine aortic sinuses from Gundiah et al. (Ann. Thorac. Surg., 2008; J. Heart Valve Disease, 2008) ,2 0,4 Eng. Strain

57 The non-pathologic FSI model (cont.) 30 Pressure [mmhg] Stress [KPa] [ms] 30 Pressure [mmhg] Max. Principal Stress [KPa] Hemodynamics Tissue mechanics Pressure [mmhg] Max. Principal Stress [KPa] t [ms] Hemodynamics Tissue me 30 Pressure [mmhg] Max. Principal Stress [KPa] t [ms] Hemodynamics Tissue mechanics 30 Pressure [mmhg] Max. Principal Stress [KPa]

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59 Model verification and comparison with simplified model Simplified linear elastic and isotropic model Solution duration of 10ms - constant BC Marom et al. (2012) Med. Biol. Eng. Comput. 50: , doi: /s

60 Verification of the model - mesh Refinement studies of the structure and flow meshes The solution is independent on the mesh Flow Structure 700,000 elements 14,000 elements w z / w r [mm] w r 700,000 w z 700,000 w r 2,000,000 w z 2,000,000 w z / w r [mm] w r 14,300 w z 14,300 w r 125,000 w z 125, t [ms] t [ms]

61 FSI model with compliant root t=0 t=2ms t=4ms t=6ms t=8ms 350 C Maximum principal stress [kpa] C C-C section Pressure on LV side [mmhg] Pressure on aorta side [mmhg] 20 0

62 Simplified models

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64 Influence of asymmetry FSI model with porcine-specific collagen fibers alignment Native CFN model and hyperelastic material in the sinuses Time dependent and physiological BC

65 Native CFN model The network was mapped from digital microscope photos The CFN defined by: length, thickness, alignment Simplified CFN Symmetric circular arcs, identical for all three cusps The mapped collagen Left cusp Posterior cusp Right cusp Simplified CFN fiber network (CFN) Native cusps The mapped collagen fiber network (CFN) Simplified CFN

66 Asymmetric vs. symmetric valves

67 Asymmetric effect on the kinematics

68 Computer Finite Element Model, FSI

69 Summary 3D FSI model of native aortic valves with: Coaptation Compliant root Physiologic blood pressure Realistic material properties Dry vs. FSI models: larger displacement and stress values Parametric studies: the normal case has the best combination of large coaptation, low diastolic tissue stress and low systolic flow shear stress Asymmetry of BAVs cause larger vortices near the cusps and higher flow shear stress on their tissue Asymmetric fibers alignment: different stress distribution in each cusps and asymmetric hemodynamics

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