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Kyoungju Park

A Finite Element Model Generation and Simulation for Functional Analysis of 4D Cardiac Tagged-MR Images. Kyoungju Park. Goals. Functional analysis of cardiac images: Realistic Generic Real-time Clinically useful. Why functional analysis?. Important to: Normal physiology study

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Kyoungju Park

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  1. A Finite Element Model Generation and Simulation for Functional Analysis of 4D Cardiac Tagged-MR Images Kyoungju Park

  2. Goals Functional analysis of cardiac images: • Realistic • Generic • Real-time • Clinically useful

  3. Why functional analysis? Important to: • Normal physiology study • Heart diseases and their causes • Alteration in heart shape and motion is a reasonable indicator of heart diseases

  4. Difficult due to • Realistic • Non-homogeneous motion of the complete heart • Generic • Different hearts • Real-time • Pre-processing such as manual boundary segmentation ( about 200 images ) • Clinically useful • Large number of parameters • Correspondence between subjects

  5. About cardiac imaging • Angiography • Echocardiography(2DE or 3DE) • CT • SPECT • PET • MRI

  6. Cardiac MR Cardiac MR allows more accurate measurements and also provides an insight into myocardial functions • MR tagging techniques • Velocity encoding techniques

  7. MR tagging The most promising non-invasive technology to evaluate regional myocardial contraction • SPAMM • CSPAMM • DANTE

  8. Displacement measures • Modified Snakes Algorithm • interactive scheme for tag tracking • B-Spline Surfaces • HARP MRI • fast, fully automatic and dense material points • so far has been applied to 2-D images

  9. Tag localization Phase 1 Phase 3 Phase 5 Phase 7 The top four figures are short-axis images, whereas the bottom four figures are long-axis images

  10. Work to date on heart modeling • Surface models • Geometric models • Generalized ellipsoids, cylinders etc. • Spherical coordinates, planispheric coordinates • Statistical models • Volumetric models • Deformation models

  11. Volumetric models

  12. Deformation models

  13. Fundamental questions? • Imaging techniques? • SPAMM • Modeling techniques? • The FE model with underlying geometry and physical constraints • Estimation techniques? • Hierarchical estimation • Functional analysis? =>Shape/motion parameters and strain analysis =>Global/Regional/Local

  14. System overview Three parts • Shape model generation • Motion estimation • Functional analysis

  15. System overview Three parts • Shape model generation • Motion estimation • Functional analysis

  16. Shape model generation “We use a generic heart to automatically build finite element meshes from tagged MR images” • A generic model • Represent the anatomical structure mathematically • Incorporate the prior knowledge • Include the LV and the RV up to its basal area

  17. Anatomic orientation right left LV RV

  18. Model coordinates We define a heart shape model with three surfaces

  19. u Material coordinates Spherical coordinates latitude u, longitude v v

  20. Model geometry The RV is composed of one tube and two ellipsoidal primitives.

  21. Mapping parameters The rs and rt parameters represent the relative location of septum area w.r.t. the LV center

  22. Axial scaling parameters Axial scaling parameters, r1, r2, r3 are defined along the x,y,z-axes respectively

  23. Shape feature vector

  24. Model dynamics Simplified Lagrangian dynamics equation of motion External forces, parameter forces, are computed from image-derived forces Regularizing term rigidity elasticity

  25. xc p xa xb Edge forces Forces from edge data points • For each edge point, find the closest triangular face from a point z • Let p be the projected point of z onto the plane defined by the triangle • The force that z exerts is computed and linearly distributed to the nodes of triangle xaxbxc z

  26. xa Image plane p xb xc z Edge forces Forces from model points • For each intersection point of image planes and triangle elements, find the closest edge from a point p • Let z be the closest edge point of p on the image plane • The force is computed and linearly distributed to the nodes of triangle xaxbxc

  27. Hierarchical estimation • Hierarchical representation is introduced to describe deformation • The algorithm incrementally adapts the shape parameters • global axial scaling parameters • piecewise shape parameters along u • local shape parameters at each u,v

  28. Generated model at t=0

  29. Overview Three • Model generation • Motion estimation • Functional analysis

  30. FEM generation Automatic volumetric element generation endocardium RV LV

  31. FEM generation Automatic volumetric element generation endocardium RV LV epicardium

  32. FEM generation Automatic volumetric element generation endocardium RV LV epicardium

  33. A single element v w v u u w Material Coordinates Physical Location

  34. Deformation descriptors • Deformation • Twisting • Longitudinal function • Radial function l r t

  35. FEM dynamics • External forces • Tagging forces • Edge forces • Internal strain energy • Transversely isotropic material (Stiffness) • Parametric constraints (Regularizing) Lagrangian dynamics equation of motion

  36. External forces • Tag data are embedded in the FE model

  37. Model tags Tag plane Model Tag: intersection of tag planes and elements

  38. Model Tag Stripe: intersection of model tag and image plane Image plane Force from tags xb Image plane xa xi xp xp nt xc

  39. Local position (e,n,s) Global position (x,y,z) Element coordinate systems n z e x s y

  40. Internal strain energy • The linear elastic theory • Regularization in material property domain • Isotropic and homogeneous material property • Parametric constraints • Regularization in geometric domain • Bending and stretching constraints The element stiffness matrix

  41. Reconstructed motion T=1 T=6

  42. System overview Three parts • Shape model generation • Motion estimation • Functional analysis

  43. Motion parameters:radial contraction RV LV Outer wall

  44. Motion parameters:longitudinal displacements RV LV Outer wall

  45. Motion parameters:twisting motion anterior LV free wall RV free wall posterior LV septum RV septum

  46. Quantification of deformation • Strain / strain ratio analysis • Volume • Cardiac output • Ejection fraction • Stroke • LVM, RVM

  47. Segmental analysis Divide into segments and perform analysis

  48. Proposing work • Test and modify • Realistic outflow tract • Deformation analysis • Combine the framework • Boundary delineation at t=1 • FEM generation • Tag tracking and motion analysis • Experiment and evaluate

  49. Contributions • Generic and comprehensive model • Less post-processing • Clinically useful information

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