Advertisement

Quantifying Tensor Field Similarity with Global Distributions and Optimal Transport

  • Arnold D. GomezEmail author
  • Maureen L. Stone
  • Philip V. Bayly
  • Jerry L. Prince
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11071)

Abstract

Strain tensor fields quantify tissue deformation and are important for functional analysis of moving organs such as the heart and the tongue. Strain data can be readily obtained using medical imaging. However, quantification of similarity between different data sets is difficult. Strain patterns vary in space and time, and are inherently multidimensional. Also, the same type of mechanical deformation can be applied to different shapes; hence, automatic quantification of similarity should be unaffected by the geometry of the objects being deformed. In the pattern recognition literature, shapes and vector fields have been classified via global distributions. This study uses a distribution of mechanical properties (a 3D histogram), and the Wasserstein distance from optimal transport theory is used to measure histogram similarity. To evaluate the method’s consistency in matching deformations across different objects, the proposed approach was used to sort strain fields according to their similarity. Performance was compared to sorting via maximum shear distribution (a 1D histogram) and tensor residual magnitude in perfectly registered objects. The technique was also applied to correlate muscle activation to muscular contraction observed via tagged MRI. The results show that the proposed approach accurately matches deformation regardless of the shape of the object being deformed. Sorting accuracy surpassed 1D shear distribution and was on par with residual magnitude, but without the need for registration between objects.

Keywords

Strain Tensor fields Tagged MRI Organ deformation 

References

  1. 1.
    Ibrahim, E.S.H.: Myocardial tagging by cardiovascular magnetic resonance: evolution of techniques-pulse sequences, analysis algorithms, and applications. J. Cardiovasc. Magn. Reson. 13(1), 36–42 (2011)CrossRefGoogle Scholar
  2. 2.
    Moerman, K.M., Sprengers, A.M.J., Simms, C.K., Lamerichs, R.M., Stoker, J., Nederveen, A.J.: Validation of tagged MRI for the measurement of dynamic 3D skeletal muscle tissue deformation. Med. Phys. 39(4), 1793–1810 (2012)CrossRefGoogle Scholar
  3. 3.
    Parthasarathy, V., Prince, J.L., Stone, M., Murano, E.Z., NessAiver, M.: Measuring tongue motion from tagged cine-MRI using harmonic phase (HARP) processing. J. Acoust. Soc. Am. 121(1), 491–504 (2007)CrossRefGoogle Scholar
  4. 4.
    Ganpule, S., et al.: A 3D computational human head model that captures live human brain dynamics. J. Neurotrauma 34(13), 2154–2166 (2017)CrossRefGoogle Scholar
  5. 5.
    Gomez, A.D., Xing, F., Chan, D., Pham, D.L., Bayly, P., Prince, J.L.: Motion estimation with finite-element biomechanical models and tracking constraints from tagged MRI. In: Wittek, A., Joldes, G., Nielsen, P.M.F., Doyle, B.J., Miller, K. (eds.) Computational Biomechanics for Medicine: From Algorithms to Models and Applications, pp. 81–90. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-54481-6_7CrossRefGoogle Scholar
  6. 6.
    Wenk, J.F., et al.: Regional left ventricular myocardial contractility and stress in a finite element model of posterobasal myocardial infarction. J. Biomech. Eng. 133(4), 1–14 (2011)CrossRefGoogle Scholar
  7. 7.
    Henninger, H.B., Reese, S.P., Anderson, A.E., Weiss, J.A.: Validation of computational models in biomechanics. Proc. Inst. Mech. Eng. Part H 224(7), 801–812 (2010)CrossRefGoogle Scholar
  8. 8.
    Tian, Y., Nearing, G.S., Peters-Lidard, C.D., Harrison, K.W., Tang, L.: Performance metrics, error modeling, and uncertainty quantification. Mon. Weather Rev. 144(2), 607–613 (2016)CrossRefGoogle Scholar
  9. 9.
    Woo, J., Xing, F., Lee, J., Stone, M., Prince, J.L.: Construction of an unbiased spatio-temporal atlas of the tongue during speech. In: Ourselin, S., Alexander, D.C., Westin, C.-F., Cardoso, M.J. (eds.) IPMI 2015. LNCS, vol. 9123, pp. 723–732. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-19992-4_57CrossRefGoogle Scholar
  10. 10.
    Maas, S.A., Ellis, B.J., Ateshian, G.A., Weiss, J.A.: FEBio: finite elements for biomechanics. J. Biomech. Eng. 134(1), 011005 (2012)CrossRefGoogle Scholar
  11. 11.
    Keszei, A.P., Berkels, B., Deserno, T.M.: Survey of non-rigid registration tools in medicine. J. Digit. Imaging 30(1), 102–116 (2017)CrossRefGoogle Scholar
  12. 12.
    Spencer, A.J.M.: Continuum Mechanics, 1995th edn. Dover Books, Essex (1985)zbMATHGoogle Scholar
  13. 13.
    Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. ACM Trans. Graph. 21(4), 807–832 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ohbuchi, R., Minamitani, T., Takei, T.: Shape-similarity search of 3D models by using enhanced shape functions. Int. J. Comput. Appl. Technol. 23(2/3/4), 70–78 (2005)CrossRefGoogle Scholar
  15. 15.
    Dinh, H.Q., Xu, L.: Measuring the similarity of vector fields using global distributions. In: da Vitoria, L.N. (ed.) SSPR/SPR 2008. LNCS, vol. 5342, pp. 187–196. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-89689-0_23CrossRefGoogle Scholar
  16. 16.
    Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transportation distances. Adv. Neural Inf. Process. Syst. 26, 2292–2299 (2013)Google Scholar
  17. 17.
    Su, Z., et al.: Optimal mass transport for shape matching and comparison. IEEE Trans. Pattern Anal. Mach. Intell. 37(11), 2246–2259 (2015)CrossRefGoogle Scholar
  18. 18.
    ur Rehman, T., Haber, E., Pryor, G., Melonakos, J., Tannenbaum, A.: 3D nonrigid registration via optimal mass transport on the GPU. Med. Image Anal. 13(6), 931–940 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Arnold D. Gomez
    • 1
    Email author
  • Maureen L. Stone
    • 2
  • Philip V. Bayly
    • 3
  • Jerry L. Prince
    • 1
  1. 1.Electrical and Computer Engineering DepartmentJonhs Hopkins UniversityBaltimoreUSA
  2. 2.Department of Neural and Pain SciencesUniversity of MarylandBaltimoreUSA
  3. 3.Mechanical Engineering DepartmentWashington University in St. LouisSt. LouisUSA

Personalised recommendations