An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations

Anand P. Santhanam; Yugang Min; Sudhir P. Mudur; Abhinav Rastogi; Bari H. Ruddy; Amish Shah; Eduardo Divo; Alain Kassab; Jannick P. Rolland; Patrick Kupelian

doi:10.1016/j.crme.2010.07.006

An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations
[Une formulation inverse reposant sur les harmoniques hypersphériques pour la reconstruction 3D du mouvement du poumon]

Anand P. Santhanam ^1,² ; Yugang Min ³ ; Sudhir P. Mudur ⁴ ; Abhinav Rastogi ¹ ; Bari H. Ruddy ⁵ ; Amish Shah ² ; Eduardo Divo ⁶ ; Alain Kassab ⁶ ; Jannick P. Rolland ⁷ ; Patrick Kupelian ⁸

¹ College of Optics and Photonics, University of Central Florida, Orlando, FL 32816 2450, USA
² Department of Radiation Oncology, M.D. Anderson Cancer Center, Orlando, USA
³ College of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816 2450, USA
⁴ Concordia University, Canada
⁵ Department of Health and Public Affairs, University of Central Florida, Orlando, FL 32816 2450, USA
⁶ Mechanical, Material and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 2450, USA
⁷ Institute of Optics, University of Rochester, USA
⁸ Department of Radiation Oncology, University of California, Los Angeles, USA

Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 461-473.

Résumé
Abstract

Une méthode d'estimation de l'opérateur associé à la description 3D des mouvements volumiques du poumon humain est présentée dans cet article. Pour des écoulements entrants d'air et des déplacements volumiques connus, l'opérateur et, ensuite, les propriétés élastiques du poumon sont estimés en termes d'une fonction de Green. L'opérateur est calculé à l'aide d'une transformation en harmoniques hypersphériques, qui facilite la prise en compte de l'hétérogénéité de l'opérateur au moyen d'un nombre fini de coefficients fréquentiels. Les écoulements entrants d'air sont estimés au moyen de données spirométriques. Au moyen d'une méthode optique 3D de mesure d'écoulements, les mouvements volumiques des poumons gauche et droit, représentant l'anatomie et les mouvements locaux d'un sujet humain, ont été estimès à l'aide de données 4D-CT. Les résultats issus de la mise en œuvre de la méthode comprennent l'estimation de l'opérateur de déformation pour les poumons gauche et droit d'un sujet humain atteint de cancer du poumon. La validation de la méthode montre que le module de Young peut être estimé dans chaque voxel à 2% près.

A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.

Publié le : 2010-07-01

DOI : 10.1016/j.crme.2010.07.006

Keywords: Biomechanics, Inverse problems, 3D lung dynamics, Hyper-spherical harmonics
Mot clés : Biomécanique, Problèmes inverses, Dynamique 3D du poumon, Harmoniques hypersphériques

Affiliations des auteurs :

Anand P. Santhanam ^{1, 2} ; Yugang Min ³ ; Sudhir P. Mudur ⁴ ; Abhinav Rastogi ¹ ; Bari H. Ruddy ⁵ ; Amish Shah ² ; Eduardo Divo ⁶ ; Alain Kassab ⁶ ; Jannick P. Rolland ⁷ ; Patrick Kupelian ⁸

¹ College of Optics and Photonics, University of Central Florida, Orlando, FL 32816 2450, USA
² Department of Radiation Oncology, M.D. Anderson Cancer Center, Orlando, USA
³ College of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816 2450, USA
⁴ Concordia University, Canada
⁵ Department of Health and Public Affairs, University of Central Florida, Orlando, FL 32816 2450, USA
⁶ Mechanical, Material and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 2450, USA
⁷ Institute of Optics, University of Rochester, USA
⁸ Department of Radiation Oncology, University of California, Los Angeles, USA

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     author = {Anand P. Santhanam and Yugang Min and Sudhir P. Mudur and Abhinav Rastogi and Bari H. Ruddy and Amish Shah and Eduardo Divo and Alain Kassab and Jannick P. Rolland and Patrick Kupelian},
     title = {An inverse hyper-spherical harmonics-based formulation for reconstructing {3D} volumetric lung deformations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {461--473},
     publisher = {Elsevier},
     volume = {338},
     number = {7-8},
     year = {2010},
     doi = {10.1016/j.crme.2010.07.006},
     language = {en},
}

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Anand P. Santhanam; Yugang Min; Sudhir P. Mudur; Abhinav Rastogi; Bari H. Ruddy; Amish Shah; Eduardo Divo; Alain Kassab; Jannick P. Rolland; Patrick Kupelian. An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations. Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 461-473. doi : 10.1016/j.crme.2010.07.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.006/

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