1. 1 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 Modeling of heart mechanics with adaptation of tissue to load

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

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

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

5. 5 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. Parameter reduction: Self-structuring by simulation of adaptation

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

7. 7 Myofiber structure and hypertrophy Result of local adaptation?

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

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

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

11. 11

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

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

14. 14 15 10 5 0 midwallradius( ) mm base apex -2020(mm) equator 0 model prediction 10 o 0 o -10 o transverse angle( ) Transverse angle, model  experiment (pig) left ventricle L. Geerts, AJP 2002

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

16. 16 Sheet structure

17. 17 Fiber-Sheet Structure endocardium midwall epicardium

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

19. 19 Sheet Angles 6 pooled experiments BASE rz rc APEX 0o0o 45 o 90 o 135 o 180 o 0o0o 45 o 90 o 135 o 180 o epi endo Arts, T, Am J Physiol. 280:H2222-H2229 (2001). model predicted: 2 solutions with different likelyhood

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

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

22. 22 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. 2 solutions for sheat orientation

23. 23 Cross-sheet slice Courtesy A. Young

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

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

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

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

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

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

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

31. 31 TSR in Control and AVS patients Inner wall strain ln(L/L Vc=Vw ) 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

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

33. 33 CircAdapt model a. Modeling of circulation - Lumped model in modules: chambers, tubes, valves b. Adaptation of modules to load Search: Google + keyword ‘CircAdapt’ hit ‘AJP’: Arts T et al. Am J Physiol. 2005;288:H1943-H1954 hit ‘Biophysics’: MatLab source code

34. 34 Circulation in modules

35. 35 1-fiber model of a thick-walled cavity (chamber or blood vessel) V lv p lv VwVw ventricle (LV) wrapped in 1 myofiber  f = myofiber stress  f = myofiber strain p lv = LV pressure V lv = LV volume V w = wall volume FEM model confirms: Shape is practically irrelevant

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

37. 37 Input to CircAdapt value SI-unit description

38. 38 Simulations after adaptation

39. 39 Pressure-Volume & Stress-Strain Loops

40. 40 Calculated parameters= Result

41. 41 Promising applications 1.Boundary conditions for FEM of heart 2.Patient specific modeling 3.“Non-invasive catheterization” Pressure difference over: - membrane → pressure transducer - valve with inertia doppler velocity and acceleration mass ~ dynamic membrane → pressure transducer

42. 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. 43 Adaptation rules with ‘deformation intervention’

44. 44 fiber direction torsion fiber direction torsion 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

45. 45 Situs Inversus Totalis Normal (pig SIT heart)

46. 46 Situs Solitus (normal) ?? Situs Inversus Totalis ?? Torsion (rad) -0.20-0.1000.100.20 Expected torsion in SIT NOT TRUE !

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

48. 48 -0.20 Situs Solitus (normal)Situs Inversus Totalis Torsion (rad) Torsion in SIT -0.1000.100.20 Delhaas, T. et al. Ann N Y Acad Sci 1015: 190-201.

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

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

51. 51 inverse Dualistic myofiber structure SIT Helix angle endo - epi inverse normal

52. 52 Efficency The structure of the SIT heart is different. Because each cell optimizes generation of mechanical work (= adaptation rule), all cells work close to their optimum. Since the only escape of mechanical work is pump work, the SIT heart works about just as optimal as the normal heart. stress- strain work The only escape of work: pump work (p-V)

53. 53 General conclusion: Self-structuring by adaptation “morphogenetic draft” result Self-adaptation until load is proper growing brick - works for cardiovascular modeling on all levels - adaptation can be modeled - should be used as prior knowledge in heart modeling

54. 54 That ’SIT