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Sándor J Kovács PhD MD Washington University, St. Louis

Discovering (predicting) new cardiac physiology/function from cardiac imaging, mathematical modeling and first principles. Sándor J Kovács PhD MD Washington University, St. Louis. UCLA/IPAM 2/6/06. Imaging and modeling allows us to go beyond. correlation to…. causality!.

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Sándor J Kovács PhD MD Washington University, St. Louis

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  1. Discovering (predicting) new cardiac physiology/function from cardiac imaging, mathematical modeling and first principles Sándor J Kovács PhD MD Washington University, St. Louis UCLA/IPAM 2/6/06

  2. Imaging and modeling allows us to go beyond correlation to… causality! UCLA/IPAM 2/6/06

  3. Focus: How the Heart Works When it Fills The physiologic process by which the heart fills has confused cardiologists, physiologists, biomedical engineers, medical students and graduate students for generations. UCLA/IPAM 2/6/06

  4. How the Heart Works When it Fills Why does it matter? The recent recognition that up to 50% of patients admitted to hospitals with congestive heart failure have ‘normal systolic function’ as reflected by ejection fraction, has further emphasized the need to more fully understand the physiology of diastole. UCLA/IPAM 2/6/06

  5. How the Heart Works When it Fills In an effort to quantitate diastolic function using a number or an index, the filling process has been characterized via correlations of selected features of either fluid (blood) flow or tissue displacement or motion to LV ejection fraction, end-diastolic pressure and other observables or clinical correlates such as exercise tolerance or mortality. UCLA/IPAM 2/6/06

  6. How the Heart Works When it Fills What do we know? Anatomy UCLA/IPAM 2/6/06

  7. How the Heart Works:anatomy Pericardial anatomy UCLA/IPAM 2/6/06

  8. How the Heart Works: anatomy Pericardial anatomy UCLA/IPAM 2/6/06

  9. How the Heart Works When it Fills Anatomy and terminology UCLA/IPAM 2/6/06

  10. How the Heart Works: anatomy Pericardial anatomy UCLA/IPAM 2/6/06

  11. How the Heart Works When it Fills What else do we know? Physiology UCLA/IPAM 2/6/06

  12. Doppler echocardiography reveals physiology: Method by which transmitral Doppler flow velocity data is acquired UCLA/IPAM 2/6/06

  13. Echocardiographically observed patterns of filling: S2 = second heart sound, IR = isovolumic relaxation, AT = acceleration time, DT= deceleration time. (Note: velocity scales differ slightly among images) Waveform features (Epeak, E/A, DT, …) are correlated with clinical aspects. UCLA/IPAM 2/6/06

  14. Cardiac catheterization reveals physiology: Simultaneous, high fidelity LAP, LVP and transmitral Doppler in closed chest canine. Note reversal of sign of A-V pressure gradient As flow accelerates (LAP > LVP) and decelerates (LAP < LVP). Isovolumic Relaxation Rapid Filling Atrial Systole Diastasis UCLA/IPAM 2/6/06

  15. Cardiac catheterization reveals physiology: Simultaneous aortic root, LV pressure and LV volume as a function of time for one cardiac cycle as measured in the cardiac catheterization laboratory. dP/dV<0 at MVO UCLA/IPAM 2/6/06

  16. Cardiac catheterization reveals physiology: AO AVC IVR AVO MVO MVC LA LV diastasis atrial systole Doppler A-wave rapid filling Doppler E-wave UCLA/IPAM 2/6/06

  17. Mechanics of filling: Ventricle fills in 2 phases: 1) Early, rapid-filling (dP/dV< 0) 2) Atrial filling (dP/dV > 0) (Actually, diastole has 4 phases: isovolumic relaxation, early rapid filling, diastasis, atrial contraction) UCLA/IPAM 2/6/06

  18. Catheterization and echo -combined Abnormal Pseudo- Restriction Restriction relaxation normalization (reversible) (irreversible) Normal 40 0 N- Mean LAP TAU NYHA I-II II-III III-IV IV Grade I II III IV UCLA/IPAM 2/6/06

  19. How the Heart Works When it Fills Recall key physiologic fact: At -(and for a while after) - MVO, the LV simultaneously decreases its pressure while increasing its volume! UCLA/IPAM 2/6/06

  20. How the Heart Works When it Fills We must therefore conclude that: The heart is a suction pump in early diastole! UCLA/IPAM 2/6/06

  21. To go from correlation to causality devise a kinematic model of suction initiated filling: Newton’s Law: md2x/dt2 + c dx/dt + kx = 0 Initial conditions: x(0) = xo  stored elastic strain to power suction v(0) = 0  no flow prior to valve opening Recall SHO has 3 regimes of motion,underdampedc2-4mk<0, critically dampedc2=4mk, overdampedc2 - 4mk>0. VALIDATION: Compare model-predicted velocity of oscillator to velocity of blood entering the ventricle through mitral valve. UCLA/IPAM 2/6/06

  22. Model of suction initiated filling: Block-diagram of operational steps Result: 1) re-express all E-and A-waves in terms of parameters AND 2) compute physiologic indexes UCLA/IPAM 2/6/06

  23. Model of suction initiated filling: does it fit the data? Examples of model’s ability to fit in-vivo Doppler data UCLA/IPAM 2/6/06

  24. Model prediction compared to actual data: Observed patterns of mitral valve inflow and superimposed model fits S2 = second heart sound, IR = isovolumic relaxation, AT = acceleration time, DT= deceleration time. (Note: velocity scales differ slightly among images) UCLA/IPAM 2/6/06

  25. Kinematic model of suction initiated filling compared to non-linear, coupled PDE models of filling: Comparison of the PDF (red), Meisner (blue) and Thomas (green) models for a clinical Doppler image. Note that all three models reproduce the contour of the image with comparable accuracy, and that the three models’ predictions are essentially indistinguishable graphically from one another. UCLA/IPAM 2/6/06

  26. Kinematic model of suction initiated filling: Indexes from model parameters: Mechanical Physiologic kxo Force in spring Maximum A-V pressure k Spring constant Chamber stiffness 1/2kxo2Stored energy Stored elastic strain xoSpring displacement Velocity-time integral of E-wave c2-4mk Regime of motion Stiff vs. delayed relaxation UCLA/IPAM 2/6/06

  27. Kinematic model of suction initiated filling: Predictions from kinematic modeling: 1) The spring is linear and it is bi-directional 2) Underdamped, critically damped, overdamped regimes 3) Existence of ‘load independentindex’ of filling 4) Equilibrium volume of LV is diastasis 5) Tissue oscillations 6) Resonance UCLA/IPAM 2/6/06

  28. Kinematic model of suction initiated filling: Physiologic analog and prediction of model: Q: What is the spring? UCLA/IPAM 2/6/06

  29. What is the ‘spring’? How the experiment that shows that cells can push was done! Titin Develops Restoring Force in Rat Cardiac Myocytes Michiel Helmes, Károly Trombitás, Henk Granzier Circulation Research. 1996;79:619-626. UCLA/IPAM 2/6/06

  30. What is the ‘spring’? Experimental data proving that titin acts as a linear, bi-directional spring It is hinged between thick and thin filaments. UCLA/IPAM 2/6/06

  31. Model of suction initiated filling: Model can be used to fit and (?) explain heretofore unexplained mechanism of biphasic E-waves. Early portion is governed by k dominance, (underdamped) later portion is governed by c dominance (overdamped). UCLA/IPAM 2/6/06

  32. Kinematic modeling of filling: “When you solve one difficulty, other new difficulties arise. You then try to solve them. You can never solve all difficulties at once.” P.A.M. Dirac UCLA/IPAM 2/6/06

  33. Modeling how the heart works: Recall a physiologic fact - Although the heart is an oscillator: It is possible to remain (essentially) motionless! UCLA/IPAM 2/6/06

  34. Modeling how the heart works: Hence: The four-chambered heart is a constant- volume pump! UCLA/IPAM 2/6/06

  35. How the Heart Works :(constant volume) • Constant-volume attribute of the four-chambered heart - • Hamilton and Rompf -1932 Hamilton W, Rompf H. Movements of the Base of the Ventricle and the Relative Constancy of the Cardiac Volume. Am J Physiol. 1932;102:559-65. • Hoffman and Ritman -1985 Hoffman EA, Ritman E. Invariant Total Heart Volume in the Intact Thorax. Am J Physiol. 1985;18:H883-H890. Also showed that Left heart and Right heart are very nearly constant volume! • Bowman and Kovács - 2003 Bowman AW, Kovács SJ. Assessment and consequences of the constant-volume attribute of the four-chambered heart. American Journal of Physiology, Heart and Circulatory Physiology 285:H2027-H2033, 2003. UCLA/IPAM 2/6/06

  36. How the Heart Works When it Fills : (constant volume) Cardiac MRI Cine Loop ‘four-chamber view” Note relative absence of ‘radial’ or ‘longitudinal’ pericardial surface displacement or motion UCLA/IPAM 2/6/06

  37. How the Heart Works When it Fills : (constant volume) Cardiac MRI Cine Loop ‘LV outflow track view” Note relative absence of ‘radial’ or ‘longitudinal’ pericardial surface displacement or motion UCLA/IPAM 2/6/06

  38. How the Heart Works When it Fills : (constant volume) Cardiac MRI Cine Loop ‘short-axis view” Note slight ‘radial’ motion of pericardial surface UCLA/IPAM 2/6/06

  39. How the Heart Works:(constant volume) Cardiac MRI Cine Loop ‘four-chamber view” Normal, human UCLA/IPAM 2/6/06

  40. How the Heart Works:(constant volume) Cardiac MRI Cine Loop ‘short-axis view” UCLA/IPAM 2/6/06

  41. How the Heart Works:(constant volume) Plot of # of pixels vs. frame number for 4-chamber slice Diastole Systole Area (in Pixels) Frame # UCLA/IPAM 2/6/06

  42. Rat heart - note almost ‘constant-volume’ feature UCLA/IPAM 2/6/06

  43. How the Heart Works:(constant volume) Plot of # of voxels vs. fraction R-R interval for 3-D data set Voxels Fraction of R-R Interval UCLA/IPAM 2/6/06

  44. How the Heart Works:(constant volume) Constant-Volume Attribute of the Four-Chambered Heart Via MRI - how are images analyzed? (with Bowman, Caruthers, Watkins) Conclusion: In normal, healthy subjects, the total volume enclosed within the pericardial sack remains constant to within a few percent. The pericardial surface exhibits only slight radial displacement throughout the cardiac cycle most notably along its diaphragmatic aspect. UCLA/IPAM 2/6/06

  45. How the Heart Works:(constant volume) Cine MRI loop of pericardium for one cardiac cycle UCLA/IPAM 2/6/06

  46. How the Heart Works:(constant volume) Right heart vs. left heart (n=20) UCLA/IPAM 2/6/06

  47. How the Heart Works:(constant volume) What are predictable consequences of a constant volume, four-chambered heart as they pertain to diastole? (In light of the previous slide showing that the volumes of left and right heart are also independently constant.) UCLA/IPAM 2/6/06

  48. How the Heart Works:(constant volume) Consider the motion of the mitral valve plane relative to the fixed apex and base. Caltech 3/10/05

  49. How the Heart Works:(constant volume) One dimensional analog of mitral valve plane motion atriumventricle UCLA/IPAM 2/6/06

  50. How the Heart Works:(constant volume) Normalized MVP displacement vs. cardiac cycle Normalized displacement Percentage of cardiac cycle UCLA/IPAM 2/6/06

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