Investigation of Shape Functions Role on the Mesh-free Method Application in Soft Tissue Elastography

Document Type : English


1 Islamic Azad University, Khomeinishahr Branch

2 Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

3 Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran


In current study, The Mesh-free method based on weak-form formulation coupled with the ultrasound imaging technique is developed. This problem consists in computing the deformation of an elastic non-homogenous phantom by numerical methods (both Mesh-free and Finite Element) and converge their results to the measured deformation by the ultrasound. The shape functions of Mesh-free are approximated by the Moving Least Square (MLS) method. The effect of Shape functions on the Mesh-free results are analyzed and discussed with the several simulations in 2D domain.


[1]     Bamber J, Cosgrove D, Dietrich CF, Fromageau J, Bojunga J, Calliada F, Cantisani V, Correas JM, D’onofrio M, Drakonaki EE, Fink M. EFSUMB guidelines and recommendations on the clinical use of ultrasound elastography. Part 1: Basic principles and technology. Ultraschall in der Medizin-European Journal of Ultrasound. 2013 Apr;34(02):169-84.
[2]     Glaser KJ, Manduca A, Ehman RL. Review of MR elastography applications and recent developments. Journal of Magnetic Resonance Imaging. 2012 Oct 1;36(4):757-74.
[3]     Manduca A, Oliphant TE, Dresner MA, Mahowald JL, Kruse SA, Amromin E, Felmlee JP, Greenleaf JF, Ehman RL. Magnetic resonance elastography: non-invasive mapping of tissue elasticity. Medical image analysis. 2001 Dec 31;5(4):237-54.
[4]     Asbach P, Klatt D, Hamhaber U, Braun J, Somasundaram R, Hamm B, Sack I. Assessment of liver viscoelasticity using multifrequency MR elastography. Magnetic Resonance in Medicine. 2008 Aug 1;60(2):373-9.
[5]     Sporea I, Gilja OH, Bota S, Sirli R, Popescu A. Liver elastography-an update. Medical ultrasonography. 2013 Dec 1;15(4):304.
[6]     Naeeni HA, Haghpanahi M. FE Modeling of Living Human Brain Using Multifrequency Magnetic Resonance Elastography. InApplied Mechanics and Materials 2011 (Vol. 66, pp. 384-389). Trans Tech Publications.
[7]     Chen Q, Ringleb SI, Manduca A, Ehman RL, An KN. A finite element model for analyzing shear wave propagation observed in magnetic resonance elastography. Journal of Biomechanics. 2005 Nov 30;38(11):2198-203.
[8]     Liu GR, Gu YT. An introduction to meshfree methods and their programming. Springer Science & Business Media; 2005 Dec 5.
[9]     Zhu T, Atluri SN. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics. 1998 Apr 1;21(3):211-22.
[10] Hall TJ, Bilgen M, Insana MF, Krouskop TA. Phantom materials for elastography. ieee transactions on ultrasonics, ferroelectrics, and frequency control. 1997 Nov;44(6):1355-65.
[11] Sinkus R, Tanter M, Xydeas T, Catheline S, Bercoff J, Fink M. Viscoelastic shear properties of in vivo breast lesions measured by MR elastography. Magnetic resonance imaging. 2005 Feb 28;23(2):159-65.