1 / 18

Friday: Cardiac Mechanics and Electromechanics

NBCR Summer Institute 2006: Multi-Scale Cardiac Modeling with Continuity 6.3 Friday: Cardiac Biomechanics Andrew McCulloch, Fred Lionetti and Stuart Campbell. Friday: Cardiac Mechanics and Electromechanics. Modeling Ventricular Wall Mechanics Analysis of ventricular wall stress

base
Download Presentation

Friday: Cardiac Mechanics and Electromechanics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. NBCR Summer Institute 2006:Multi-Scale Cardiac Modeling with Continuity 6.3Friday:Cardiac BiomechanicsAndrew McCulloch, Fred Lionetti and Stuart Campbell

  2. Friday: Cardiac Mechanics and Electromechanics • Modeling Ventricular Wall Mechanics • Analysis of ventricular wall stress • Galerkin FEM for ventricular stress analysis • Newton’s method • Examples • homogeneous cube • prolate spheroid • Ventricular-Vascular Coupling

  3. Passive Stress (kPa) Soft Tissue Biomechanics • Conservation of mass, momentum and energy for finite elasticity • 3-D geometry and tissue structure • Boundary conditions: displacement pressure, impedance, isovolumic • Nonlinear, anisotropic stress-strain relations • Active systolic stress development as a function of time, intracellular calcium and sarcomere length history • Myofiber angle dispersion and transverse active stress • Residual strain • Growth • Perfusion

  4. E = ½(FTF– I ) ¶ x i = F iR ¶ X R W W 1 = ( ) P + RS E E 2 RS SR Nonlinear Elasticity: Governing Equations kinematics Strain-displacement relation constitutive law Stress-strain relation equilibrium divT + rb= 0 T=T T Force balance equation Moment balance

  5. 1. Formulate the weighted residual (weak) form 2. Divergence (Green-Gauss) Theorem Note: Taking w=du*, we have the virtual work equation

  6. Lagrangian Virtual Work Equations for Large Deformation Elasticity Virtual Work Divergence Theorem

  7. Newton’s Method in n Dimensions f’(x) is an n  n Jacobian matrix J Gives us a linear system of equations for x(k+1)

  8. Newton’s Method • Each step in Newton’s method requires the solution of the linear system • At each step the n2 entries of Jij have to be computed • In elasticity, the method of incremental loading is often useful • It might be preferable to reevaluate Jij only occasionally (Modified Newton’s Method) • Matrix-updating schemes: In each iteration a new approximation to the Jacobian is obtained by adding a rank-one matrix to the previous approximation • Often the derivatives in J are evaluated by finite differences

  9. Fiber Coordinates X X F Boundary Conditions C X R  endocardium (+83°) epicardium (-37°) P L V P = 0 e x t Strain Energy Function

  10. 11.0 10.5 10.0 9.5 9.0 0 100 200 300 400 500 600 Numerical Convergence Cubic Hermite interpolation 3 elements 104 d.o.f. 14 sec/iteration Total Strain Energy (Joules) 70 elements 340 d.o.f. 12 sec/iteration Linear Lagrange interpolation Total Degrees of Freedom

  11. Inflation of a High-order Passive Anisotropic Ellipsoidal Model of Canine LV

  12. Coupling FE Models to the Circulation Pulmonary circulation Atria FE ventricles Systemic circulation

  13. Methods: Ventricular-Vascular Coupling • Pressure protocol in finite element (FE) model • Maximum and minimum elastances • Time-varying elastance (VE) model • Run VE model coupled to circulation • Run fully coupled FE – circulation model • Test case: normal heart followed by LV ischemia

  14. Elastances

  15. Methods: Coupling Estimate LV & RV cavity pressure FE model Circulatory model Circ Cavity volumes FE Cavity volumes Calculate difference R R < criterion? no yes Update Jacobian Do not update Jacobian next timestep

  16. Methods: coupling Circ compliance matrix FE compliance matrix Estimation 1: Estimate pressure from history Estimation 2: Perturb LV pressure Estimation 3: Perturb RV pressure Estimations >3: Update pressures

  17. ischemia ischemia Resultsnormal beat followed by regional LV ischemia

  18. Resultsnormal beat followed by regional LV ischemia stroke volume [ml] Beat number

More Related