Modeling of heart mechanics with adaptation of tissue to load

1. Modeling of heart mechanics with adaptation of tissue to load Theo Arts t.arts@bf.unimaas.nl Frits Prinzen, Tammo Delhaas*, Peter Bovendeerd**, J. Lumens, W. Kroon (Biophysics, Physiology, Pediatric Cardiology, Engineering) Maastricht University, *Maastricht University Hospital **University of Technology, Eindhoven The Netherlands IPAM Feb 06

2. Models Modeling:- Finite Element Model Electro-Mechanics of the heart- CircAdapt = whole circulation model- Incorporation of adaptation with Self-structuring

3. left+right ventricle movie:sarcomere length & pV FEM of LV+RV- paced, depolarization wave with pacing- full cardiac cycle(R. Kerckhoffs, 2003)

4. CircAdapt model of heart and circulation lungs aorta RA LA RV LV system Dynamic(t)CompliancesInertiasNon-linear

5. Parameter reduction: Self-structuring by simulation of adaptation Modeling structure of myocardial wall with adaptation:- mechanical load determines wall mass fiber orientation sheet orientation - size and shape of blood vessels Enormous reduction of number of parameters Especially in pathology: Generally 1 basic cause of pathology, followed by physiological adaptation processes.

6. Cardiovascular adaptation to mechanical load Whole organ function tissue stress & strain (pump) function pressure flow load gene expression protein formation adaptation tissue properties structure geometry Local tissue adaptation Implication: Cell adaptation determines organ structure

7. Myofiber structure and hypertrophy Result of local adaptation?

8. apical view, upper layers peeled off(randomly?) Cardiac fiber structure LV RV F. Torrent-Guasp

9. What signals to the cells can be used for adaptation? Filling/Rest Activation Force/Stretch Synchrony Shortening Relaxation

10. Used adaptation rules of cardiac tissue extra-cellular matrix myocyte orientation (fiber structure) in myocyte optimum: - principal stress alingment - sarcomere shortening fibroblast myocyte stretch contractility deformation extra-cellular matrix strain softening tissue mass (wall mass) (filling) Arts, 1994, Biophys J. 66:953-961.

12. 1/2 Diffusion Tensor Imaging Myofiber orientation components in cross-section of the goat heart. perpendicular posterior anterior in plane Base to apex In plane

13. model predicted Transmural course of helix angle (goat) L. GeertsAJP 2002

14. Transverse angle, model experiment (pig) left ventricle tr ans ver se angle ( ) midwall radius ( ) 1 5 m m o 1 0 10 equator 5 0 o 0 -20 0 (mm) 20 ap ex ba se model prediction o -10 L. Geerts, AJP 2002

15. Myofiber structure Proposed adaptation rules for local tissue → Realistic helical and transverse fiber structure

16. Sheet structure

17. Fiber-Sheet Structure endocardium midwall epicardium

18. Hypothesis Sheets split on plane of maximum shear 45o directions of maximum shear, Fiber direction not in one of those planes 2 planes Find plane with maximum shear Constraint:Sheet planes also contain the fiber direction

19. 6 pooledexperiments Sheet Angles APEX BASE 180o 135o 90o 45o 0o rz rc rz rc model predicted: 2 solutions with different likelyhood 180o 135o 90o 45o 0o epi endo Arts, T, Am J Physiol. 280:H2222-H2229 (2001).

20. Simulation of short axis sheet cross-sections seems realistic

21. Sheets facilitate wall thickening and shortening by shear (and rotation) (J. Covell)

22. 2 solutions for sheat orientation Unloading for shear by 90º sheet rotation has same macroscopic effect on mechanics, ab= ba ≈ 0 So, sheet orientation itself is quite irrelevant for modeling, as long as it unloads the major component of shear stress.

23. Cross-sheet slice Courtesy A. Young

24. Sheet structure - Sheet plane contains myofiber direction - Designed to facilitate cross­fiber deformation, thus minimizing chamber stiffness

25. Application of predicted structure in analysis Non-invasive determination of transmural difference in myofiber shortening with aortic stenosis

26. Aortic stenosis Subendocardial dysfunction region with high intramyocardial pressure, causing coronary flow obstruction aortic stenosis high left ventricular pressure endo epi

27. Wall segment model (cylindrical) Determination of transmural differences inner outer Shortening only inner - - - outer - Torsion only inner + outer - • Torsion tuned to Shortening • IF Subendocardial  • TSR=( Torsion / Shortening )   Shortening & Torsion inner - - outer - -

28. Magnetic Resonance Tagging (MRT) ribs RV cavity lung Rotation and deformation of the heart can be quantified LV wall

29. Torsion/Shortening measurement shortening MRT Definitions shortening = D ln(Cavity Area) torsion torsion

30. Mri-Software: Midwall motion and circumferential strain Normal human left ventricle

31. TSR in Control and AVS patients TSR=slope of torsion versus inner wall strain in systole: - Dimensionless- Species independent- Expresses transmural difference in contractile function Control= healthy young AVSten= Aortic Valve Stenosis AVRepl= 3 mo after aortic valve replacement Inner wall strain ln(L/LVc=Vw)

32. From TSR to TransDif Model: Torsion/Shortening (TSR)↓ normalized transmural difference in myofiber shortening (TransDif) TransDif=Difference/Mean Stunned subendocardial myocardium regains function Van der Toorn A et al. Am J Physiol. 2002;283:H1609-1615

33. CircAdapt model a. Modeling of circulation - Lumped model in modules: chambers, tubes, valvesb. Adaptation of modules to load Search: Google + keyword ‘CircAdapt’ hit ‘AJP’: Arts T et al. Am J Physiol. 2005;288:H1943-H1954hit ‘Biophysics’: MatLab source code

34. Circulation in modules

35. 1-fiber model of a thick-walled cavity (chamber or blood vessel) ventricle (LV) wrapped in 1 myofiber Vlvplv f= myofiber stressf= myofiber strainplv= LV pressureVlv= LV volumeVw= wall volume Vw FEM model confirms: Shape is practically irrelevant

36. Laws of adaptation Adaptation of Cavity • Contractility+diastolic stretch → Hypertrophy • Deformation → Dilatation Adaptation of Blood vessel • Shear stress → Diameter ↑ • Wall stress → Wall thickness ↑

37. Input to CircAdapt value SI-unit description

38. Simulations after adaptation

39. Pressure-Volume & Stress-Strain Loops

40. Calculated parameters= Result

41. Promising applications • Boundary conditions for FEM of heart • Patient specific modeling • “Non-invasive catheterization” Pressure difference over: - membrane → pressure transducer - valve with inertia doppler velocity and acceleration mass ~ dynamic membrane → pressure transducer

42. Hypertrophy in12 wks myofiber mechanics in AV-block Systolic fiber stress is not the stimulus to hypertrophy. More likely: end-diastolic stress (Donker et al, Basic Res Cardiol, 2005).

43. Adaptation rules with‘deformation intervention’

44. Situs Solitus (normal) Situs Inversus Totalis (SIT) Hypothesis SIT heart with mirrored fiber structure is an alternative solution satisfying adaptation rules of cardiac cells. Test SIT heart should have equal torsion but in opposite direction. occurrence 8000 : 1 fiber direction fiber direction torsion torsion

45. Situs Inversus Totalis Normal (pig SIT heart)

46. Expected torsion in SIT -0.20 -0.10 0 0.10 0.20 ?? Situs Inversus Totalis ?? Situs Solitus (normal) Torsion (rad) NOT TRUE !

47. Human torsion Situs Solitus (normal) Situs Inversus Totalis (n=14) Rotation 0.20 5 base [rad] 4 0.10 3 2 0.00 1 apex -0.10 Torsion 0.10 d base 0.00 c b -0.10 a apex -0.20 0.5 s

48. Torsion in SIT Situs Solitus (normal) Situs Inversus Totalis -0.20 -0.10 0 0.10 0.20 Torsion (rad) Delhaas, T. et al. Ann N Y Acad Sci1015: 190-201.

49. Myofiber structure in SIT Normal adaptation rules Start conditions for fiber structure: - normal apex - inverse base Development to SIT structure → RESULT

50. Situs Inversus Totalis boundary conditions A natural in vivo ‘experiment’ to investigate cell’s long term response to a variety of deformations