Analysis Of 4-D Cardiac Mr Data With Nurbs Deformable Models: Temporal Fitting Strategy And Nonrigid Registration

  • Nicholas J. Tustison
  • Amir A. Amini
Part of the Topics in Biomedical Engineering. International Book Series book series (ITBE)

We present research in which both left- and right-ventricular deformation is estimated from tagged cardiac mgnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered and compared for the left ventricle include two Cartesian NURBS models — one with a cylindrical parameter assignment and one with a prolate spheroidal parameter assignment. The remaining two are non-Cartesian, i.e., prolate spheroidal and cylindrical, each with their respective prolate spheroidal and cylindrical parameter assignment regime.


Control Point Longitudinal Strain Nonrigid Registration Deformation Gradient Tensor Normal Human Volunteer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8 References

  1. 1.
    S. Masood, Yang G-Z, Pennell DJ, Firmin DN. 2000. Investigating intrinsic myocardial me- chanics: the role of MR tagging, velocity phase mapping, and diffusion imaging. J Magn Reson Imaging 12:873-883.CrossRefGoogle Scholar
  2. 2.
    Amini AA, Prince JL, eds. 2001. Measurement of cardiac deformations from mri: physical and mathematical models. Dordrecht: Kluwer AcademicMATHGoogle Scholar
  3. 3.
    Frangi AF, Niessen WJ, Viergever MA. 2001. Three-dimensional modeling for functional analysis of cardiac images: a review. IEEE Trans Med Imaging 20(1):2-25.CrossRefGoogle Scholar
  4. 4.
    Haber I, Metaxas DN. 2000. Three-dimensional motion reconstruction and analysis of the right ventricle using tagged MRI. Med Image Anal 4:335-355.CrossRefGoogle Scholar
  5. 5.
    Klein SS, Graham TP, Lorenz CH. 1998. Noninvasive delineation of normal right ventricular contractile motion with magnetic resonance imaging myocardial tagging. Ann Biomed Eng 26:756-763.CrossRefGoogle Scholar
  6. 6.
    Naito H, Arisawa J, Harada K, Yamagami H, Kozuka T, Tamura S. 1995. Assessment of right ventricular regional contraction and comparison with the left ventricle in normal humans: a cine magnetic resonance study with presaturation myocardial tagging. Br Heart J 74:186-191.CrossRefGoogle Scholar
  7. 7.
    Young A, Fayad ZA, Axel L. 1996. Right ventricular midwall surface motion and deformation using magnetic resonance tagging. Am J Physiol 271:H2677-H2688.Google Scholar
  8. 8.
    Axel L, Dougherty L. 1989. MR imaging of motion with spatial modulation of magnetisation. Radiology 171:841-845.Google Scholar
  9. 9.
    Zerhouni E, Parish D, Rogers W, Yang A, Shapiro E. 1988. Human heart: tagging with MR imaging: a method for noninvasive assessment of myocardial motion. Radiology 169:59-63.Google Scholar
  10. 10.
    Amini AA, Chen Y, Curwen RW, Mani V, Sun J. 1998. Coupled B-snake grids and constrained thin-plate splines for analysis of 2-D tissue deformations from tagged MRI. IEEE Trans Med Imaging 17(3):344-356.CrossRefGoogle Scholar
  11. 11.
    Wang Y-P, Chen Y, Amini AA. 2001. Fast LV motion estimation using subspace approximation techniques. IEEE Trans Med Imaging 20(6):499-513.CrossRefGoogle Scholar
  12. 12.
    Chandrashekara R, Mohiaddin RH, Rueckert D. 2002. Analysis of myocardial motion in tagged MR images using nonrigid image registration. Proc SPIE 4684:1168-1179.CrossRefGoogle Scholar
  13. 13.
    Chen Y, Amini AA. 2002. A MAP framework for tag line detection in SPAMM data using Markov random fields on the B-spline solid. IEEE Trans Med Imaging 21(9):1110-1122.CrossRefGoogle Scholar
  14. 14.
    Huang J, Abendschein D, D ávila-Rom án V, Amini A. 1999. Spatiotemporal tracking of my- ocardial deformations with a 4D B-spline model from tagged MRI. IEEE Trans Med Imaging 18 (10):957-972.Google Scholar
  15. 15.
    Ozturk C, McVeigh ER. 1999. Four dimensional b-spline based motion analysis of tagged cardiac mr images. Proceedings SPIE 3660:46-56.CrossRefGoogle Scholar
  16. 16.
    Radeva P, Amini AA, Huang J. 1997. Deformable B-solids and implicit snakes for 3D local- ization and tracking of SPAMM MRI data. Comput Vision Image Understand 66(2):163-178.CrossRefGoogle Scholar
  17. 17.
    Chandrashekara R, Mohiaddin RH, Rueckert D. 2003. Analysis of myocardial motion and strain patterns using a cylindrical B-spline transformation model. In Proceedings of the inter- national symposium on surgery simulation and soft tissue modeling (IS4TM). Lecture notes in computer science, vol. 2673, pp. 88-99. New York: Springer.Google Scholar
  18. 18.
    Deng X, Denney Jr TS. 2002. 3D myocardial strain reconstruction from tagged MR image data using a cylindrical B-spline model. In Proceedings of the IEEE international symposium on biomedical imaging, pp. 609-612. Washington, DC: IEEE Computer Society.Google Scholar
  19. 19.
    Piegl L. 1991. On NURBS: a survey. IEEE Comput Graphics Appl 10(1):55-71.CrossRefGoogle Scholar
  20. 20.
    L. Piegl, Tiller W. 1997. The NURBS book. New York: Springer.Google Scholar
  21. 21.
    Figueiredo MAT, Let ão JMN, Jain AK. 2000. Unsupervised contour representation and es- timation using B-splines and a minimum description length criterion. IEEE Trans Image Process 9(6):1075-1087.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Ma W, Kruth JP. 1994. Mathematical modelling of free-form curves and surfaces from discrete points with NURBS. In Curves and surfaces in geometric design, pp. 319-326. Ed PJ Laurent, A Le M éhaut é , LL Schumaker. Wellesley, MA: A.K. PetersGoogle Scholar
  23. 23.
    Gertz EA, Wright S. 2001. OOQP user guide. Argonne, IL: Argonne National Laboratory. swright/ooqp/.
  24. 24.
    Schoenberg IJ, Whitney A. 1953. On P ólya frequency functions, III: the positivity of trans- lation determinants with an application to the interpolation problem by spline curves. Trans Am Math Soc 74:246-259.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Ma W, Kruth JP. 1995. Parameterization of randomly measured points for least-squares fitting of B-spline curves and surfaces. Comput Aided Design 27(9):663-675.MATHCrossRefGoogle Scholar
  26. 26.
    Tustison NJ, D ávila-Rom án VG, Amini AA. 2003. Myocardial kinematics from tagged MRI based on a 4-D B-spline model. IEEE Trans Biomed Eng 50:1038-1040.Google Scholar
  27. 27.
    Press WH, Flannery BP, Teukolsky SA, Vetterling WT. 1988. Numerical recipes in C: the art of scientific computing. Cambridge: Cambridge UP.MATHGoogle Scholar
  28. 28.
    Horn B, Schunck B. 1981. Determining optical flow. Artif Intell 17:185-203.CrossRefGoogle Scholar
  29. 29.
    Cerqueira MD, Weissman NJ, Dilsizian V. 2002. Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart: a statement for healthcare professionals from the Cardiac Imaging Committee of the Council on Clinical Cardiology of the American Heart Association. Circulation 105:539-542.CrossRefGoogle Scholar
  30. 30.
    Arts T, Hunter WC, Douglas A, Muijtjens AMM, Reneman RS. 1992. Description of the deformation of the left ventricle by a kinematic model. J Biomech 25:1119-1127.CrossRefGoogle Scholar
  31. 31.
    Waks E, Prince JL, Douglas AS. 1996. Deformable Fourier models for surface finding in 3D images. Proceedings of the IEEE workshop on mathematical methods in biomedical image analysis (MMBIA’96), pp. 182-191. Washington, DC: IEEE Computer Society.Google Scholar
  32. 32.
    Suter D, Chen F. 2000. Left ventricular motion reconstruction based on elastic vector splines. IEEE Trans Med Imaging 19(4):295-305.CrossRefGoogle Scholar
  33. 33.
    Moore C, Lugo-Olivieri C, McVeigh E, Zerhouni E. 2000. Three-dimensional systolic strain patterns in the normal human left ventricle: characterization with tagged MR imaging. Radi- ology 214(2):453-466.Google Scholar
  34. 34.
    Bland JM, Altman DG. 2003. Applying the right statistics: analyses of measurements studies. Ultrasound Obstet Gynecol 22:85-93.CrossRefGoogle Scholar
  35. 35.
    Spiegel M, Luechinger R, Weber O, Scheidegger M, Schwitter J, Boesiger P. 2000. Ring- Tag: assessment of myocardial midwall motion in volunteers and patients with myocardial hypertrophy. Proc ISMRM 6:1607.Google Scholar
  36. 36.
    Aletras AH, Balaban RS, Wen H. 1999. High-resolution strain analysis of the human heart with fast-DENSE. J Magn Reson Imag 140:41-57.Google Scholar
  37. 37.
    Osman NF, McVeigh ER, Prince JL. 2000. Imaging heart motion using harmonic Phase MRI. IEEE Trans Med Imaging 19(3):186-202.CrossRefGoogle Scholar
  38. 38.
    Kuijer JPA, Jansen E, Marcus JT, van Rossum AC, Heethaar RM. 2001. Improved harmonic phase myocardial strain maps. Magn Reson Med 46:993-999.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Nicholas J. Tustison
    • 1
  • Amir A. Amini
    • 1
  1. 1.Cardiovascular Image Analysis LaboratoryWashington UniversitySt. LouisUSA

Personalised recommendations