A constrained genetic approach for computing material property of elastic objects

This paper presents a constrained genetic approach for reconstructing the material properties of elastic objects. The considered reconstruction problem is ill-posed and must be constrained properly so that a unique and stable numerical solution can be obtained. Qualitative prior information is incorporated using a rank-based scheme to constrain the admissible solutions. Experiments show that the proposed approach is robust when presented with noisy data and can reconstruct the elastic property accurately and reliably. In a comparison study with the deterministic Gauss-Newton methods, the constrained genetic approach also shows very consistent performance.

[1]  G Crosta.  Mathematical Review: MR2044619 (2005b:74051) Barbone, Paul E.; Gokhale, Nachiket H. Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions , 2005 .

[2]  M. Burger,et al.  Level set methods for geometric inverse problems in linear elasticity , 2004 .

[3]  Armando Manduca,et al.  Imaging elastic properties of biological tissues by low-frequency harmonic vibration , 2003, Proc. IEEE.

[4]  L. D. Chiwiacowsky,et al.  A variational approach for solving an inverse vibration problem , 2006 .

[5]  J. Bishop,et al.  Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography. , 2000, Physics in medicine and biology.

[6]  Dimitris N. Metaxas.  Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging , 1996 .

[7]  Ralf Salomon,et al.  Evolutionary algorithms and gradient search: similarities and differences , 1998, IEEE Trans. Evol. Comput..

[8]  M. O'Donnell,et al.  Model-based reconstructive elasticity imaging of deep venous thrombosis , 2004, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[9]  Alain Blouin,et al.  All-optical measurement of in-plane and out-of-plane Young's modulus and Poisson's ratio in silicon wafers by means of vibration modes , 2004 .

[10]  Nail Gumerov,et al.  Application of a Hybrid Genetic/PowellAlgorithm and a Boundary Element Methodto Electrical Impedance Tomography , 2001 .

[11]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[12]  Frédérique Frouin,et al.  Ultrasound elastography based on multiscale estimations of regularized displacement fields , 2004, IEEE Transactions on Medical Imaging.

[13]  K. Miller.  Least Squares Methods for Ill-Posed Problems with a Prescribed Bound , 1970 .

[14]  K D Paulsen,et al.  An overlapping subzone technique for MR‐based elastic property reconstruction , 1999, Magnetic resonance in medicine.

[15]  Antoni John,et al.  Material Coefficients Identification of Bone Tissues Using Evolutionary Algorithms , 2003 .

[16]  A.R. Skovoroda,et al.  Measuring the nonlinear elastic properties of tissue-like phantoms , 2004, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[17]  Genki Yagawa,et al.  INELASTIC CONSTITUTIVE PARAMETER IDENTIFICATION USING AN EVOLUTIONARY ALGORITHM WITH CONTINUOUS INDIVIDUALS , 1997 .

[18]  V. Morozov.  On the solution of functional equations by the method of regularization , 1966 .

[19]  Jonathan Bishop,et al.  A constrained modulus reconstruction technique for breast cancer assessment , 2001, IEEE Transactions on Medical Imaging.

[20]  J. Ophir,et al.  Elastography: A Quantitative Method for Imaging the Elasticity of Biological Tissues , 1991, Ultrasonic imaging.

[21]  Ron Kikinis,et al.  Registration of 3-d intraoperative MR images of the brain using a finite-element biomechanical model , 2000, IEEE Transactions on Medical Imaging.

[22]  Christoph H. Arns,et al.  Computation of linear elastic properties from microtomographic images: Methodology and agreement between theory and experiment , 2002 .

[23]  Gary G. Yen,et al.  A simple elitist genetic algorithm for constrained optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[24]  H. Saunders.  Book Reviews : The Finite Element Method (Revised): O.C. Zienkiewicz McGraw-Hill Book Co., New York, New York , 1980 .

[25]  Jingfeng Jiang,et al.  A finite-element approach for Young's modulus reconstruction , 2003, IEEE Transactions on Medical Imaging.

[26]  Carlos A. Coello Coello,et al.  An Improved Diversity Mechanism for Solving Constrained Optimization Problems Using a Multimembered Evolution Strategy , 2004, GECCO.

[27]  G. Uhlmann,et al.  IDENTIFICATION OF LAME PARAMETERS BY BOUNDARY MEASUREMENTS , 1993 .

[28]  Cheng-Hung Huang,et al.  A non‐linear inverse vibration problem of estimating the time‐dependent stiffness coefficients by conjugate gradient method , 2001 .

[29]  Faouzi Kallel,et al.  Tissue elasticity reconstruction using linear perturbation method , 1996, IEEE Trans. Medical Imaging.

[30]  Chikayoshi Sumi,et al.  A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements , 1998, IEEE Transactions on Medical Imaging.

[31]  K. Paulsen,et al.  A computational model for tracking subsurface tissue deformation during stereotactic neurosurgery , 1999, IEEE Transactions on Biomedical Engineering.

[32]  Nail A. Gumerov,et al.  Application of a hybrid gentic/powell algorithm and a boundary element method to electical , 2001 .

[33]  S. Priori,et al.  A genetic algorithm approach to image reconstruction in electrical impedance tomography , 2000, IEEE Trans. Evol. Comput..

[34]  M. M. Carroll,et al.  Foundations of Solid Mechanics , 1985 .

[35]  Dmitry B. Goldgof,et al.  A vision-based technique for objective assessment of burn scars , 1998, IEEE Transactions on Medical Imaging.

[36]  C. G. Shaefer,et al.  The ARGOT Strategy: Adaptive Representation Genetic Optimizer Technique , 1987, ICGA.

[37]  M. Sato.  [Mechanical properties of living tissues]. , 1986, Iyo denshi to seitai kogaku. Japanese journal of medical electronics and biological engineering.

[38]  G. Wahba.  Spline models for observational data , 1990 .

[39]  James Ralston,et al.  On the inverse boundary value problem for linear isotropic elasticity , 2002 .

[40]  M. Doyley,et al.  Evaluation of an iterative reconstruction method for quantitative elastography , 2000 .

[41]  Jonathan Ophir,et al.  Elastography: Imaging the elastic properties of soft tissues with ultrasound , 2002, Journal of Medical Ultrasonics.

[42]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[43]  Peter L. Munk.  Imaging of AIDS , 1992 .

[44]  R L Ehman,et al.  Complex‐valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation , 2001, Magnetic resonance in medicine.

[45]  Robert G. Reynolds,et al.  A Survey of Constraint Handling Techniques in Evolutionary Computation Methods , 1995 .

[46]  Kevin J. Parker,et al.  Techniques for elastic imaging: a review , 1996 .

[47]  A. Manduca,et al.  Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. , 1995, Science.

[48]  Piotr Orantek.  Hybrid Evolutionary Algorithms in Optimization of Structures under Dynamical Loads , 2004 .

[49]  Michael I Miga.  A new approach to elastography using mutual information and finite elements. , 2003, Physics in medicine and biology.

[50]  Christian Laugier,et al.  Constrain-based identification of a dynamic model , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[51]  Muneo Hori,et al.  Inverse Analysis Method for Identification of Local Elastic Properties by Using Displacement Data , 2003 .

[52]  Lawrence O. Hall,et al.  A constrained genetic approach for reconstructing Young's modulus of elastic objects from boundary displacement measurements , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[53]  Ling Guan,et al.  Application of evolutionary programming to adaptive regularization in image restoration , 2000, IEEE Trans. Evol. Comput..

[54]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[55]  A.R. Skovoroda,et al.  Prospects for elasticity reconstruction in the heart , 2004, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[56]  Christoph H. Arns,et al.  Computation of Linear Elastic Properties from Microtomographic Images: Methodology and Match to Theory and Experiment. , 2002 .

[57]  Michel Bertrand,et al.  Noninvasive vascular elastography: theoretical framework , 2004, IEEE Transactions on Medical Imaging.

[58]  Joyce R. McLaughlin,et al.  Recovery of the Lamé parameter μ in biological tissues , 2003 .

[59]  Pier Paolo Delsanto,et al.  A Genetic Algorithm for the determination of the elastic constants of a monoclinic crystal , 2000 .

[60]  Assad A. Oberai,et al.  INVERSE PROBLEMS PII: S0266-5611(03)54272-1 Solution of inverse problems in elasticity imaging using the adjoint method , 2003 .

[61]  Otmar Scherzer,et al.  Finite-dimensional approximation of tikhonov regularized solutions of non-linear ill-posed problems , 1990 .

[62]  Demetri Terzopoulos,et al.  Analysis and Synthesis of Facial Image Sequences Using Physical and Anatomical Models , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[63]  D E Robinson,et al.  Elastography--the movement begins. , 2000, Physics in medicine and biology.

[64]  Edward J. Garboczi,et al.  An algorithm for computing the effective linear elastic properties of heterogeneous materials: Three-dimensional results for composites with equal phase poisson ratios , 1995 .

[65]  Markus H. Gross,et al.  Simulating facial surgery using finite element models , 1996, SIGGRAPH.

[66]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[67]  H. W. Engl.  Identification Of Parameters In Polymer Crystallization, Semiconductor Models And Elasticity Via Iterative Regularization Methods H. W. Engl , 2002 .

[68]  Zbigniew Michalewicz,et al.  A Survey of Constraint Handling Techniques in Evolutionary Computation Methods , 1995 .

[69]  Sean J. Kirkpatrick.  Optical assessment of tissue mechanical properties , 2000, Saratov Fall Meeting.

[70]  K. R. Raghavan,et al.  Forward and inverse problems in elasticity imaging of soft tissues , 1994 .