Combining a Genetic Algorithm with Fitness Function Analysis to Improve the Elastodynamic Inverse Problem
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Digital Image Elastic Tomography (DIET) is a breast imaging technique based on the contrast in stiffness between diseased and healthy tissue. DIET is intended to be a low cost pre-screening method for breast cancer, with the aim of identifying stiff areas within the breast that require further investigation. The DIET inverse problem is to reconstruct stiffness based on steady-state harmonic surface motion data measured by a calibrated 3D imaging array. The ill-posed inverse problem of reconstructing tissue stiffness from surface motion data is simplified by using a shape based description assuming a high stiffness inclusion of unknown position within a less stiff background material. This study examines the three-dimensional problem using both numerical simulation and phantom data. Finite element methods (FEM) are used to model the motion. A parallel genetic algorithm (GA) has been developed for the DIET inverse problem. GAs evaluate the fitness of many solution estimates over successive generations. Each estimate along with its associated error provides information on the shape of the surface of the fitness function. The results of this study demonstrate the feasibility of using the fitness function analysis to improve the DIET solution process.Keywords:
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The aim of this study is the estimation of the three dimensional strain occurring in soft biological tissues under compressive forces, through the processing of radiofrequency ultrasound volumes. This work is one of the first attempts to deal with the 3D problem of tissue motion under load. In this article, we propose a new adaptive and iterative numerical model, allowing full-resolved strain parameters estimation. This model is based on an objective function minimization with linear inequalities constraints. An original technique of adaptive displacement of the region of study is also considered. Preliminary tests are performed on a volume of ultrasound data obtained from a 3D numerical phantom. Axial, lateral, and elevational displacements and axial strain fields are estimated, and compared with the theory
Minification
Strain (injury)
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Soft tissue models are of many types, but each type has its own problems in terms of realistic appearance and computational efficiency. In this study, we propose a hybrid model based on dynamic volume splines which combine the advantages of these models. To simulate a realistic appearance, biomechanical properties of the real tissue are obtained by force–displacement experiments and used to tune the parameters of the model. Unlike the usual types described in the literature, a new experiment is proposed where displacement is measured not only for the point of force application but also for the region around the applied force. In our study, multiple camera views were used to enable 3D reconstruction of the surface. The differences arising between the surfaces obtained before and after the application of force were then used in optimization-based inverse solution methods, and the estimated parameters were found to be consistent with the biomechanical tissue properties described in the literature.
Spline (mechanical)
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Basis (linear algebra)
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Results from the application of three nonlinear stiffness reconstruction algorithms to two simple cylindrical geometries are presented in this paper. Finite-element simulated harmonic motion data with added noise were initially used to represent a measured surface displacement dataset for each geometry. This motion was used as input to gradient-descent, combinatorial optimization, and hybrid reconstruction algorithms that aimed to reconstruct two shape-based parameters describing the internal stiffness of the geometry. Both the combinatorial optimization and hybrid algorithms showed significant advantages in reconstructed parameter accuracy when compared with the traditional gradient-descent approach, with success metrics improving by 13-28%. Results from the hybrid algorithm applied to silicone phantom displacements demonstrated for the first time the ability of this type of algorithm to reconstruct internal stiffness using only experimentally measured surface motion data. Improvements in the sophistication of the hybrid approach should lead to improved accuracy in reconstructed solutions, as well as enabling reconstructions where the geometry is less straightforward.
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The finite element method is commonly used to model tissue deformation in order to solve for unknown parameters in the inverse problem of viscoelasticity. Typically, a (regular-grid) structured mesh is used since the internal geometry of the domain to be identified is not known a priori. In this work, the generation of problem-specific meshes is studied and such meshes are shown to significantly improve inverse-problem elastic parameter reconstruction. Improved meshes are generated from axial strain images, which provide an approximation to the underlying structure, using an optimization-based mesh adaptation approach. Such strain-based adapted meshes fit the underlying geometry even at coarse mesh resolutions, therefore improving the effective resolution of the reconstruction at a given mesh size/complexity. Elasticity reconstructions are then performed iteratively using the reflective trust-region method for optimizing the fit between estimated and observed displacements. This approach is studied for Young's modulus reconstruction at various mesh resolutions through simulations, yielding 40%-72% decrease in root-mean-square reconstruction error and 4-52 times improvement in contrast-to-noise ratio in simulations of a numerical phantom with a circular inclusion. A noise study indicates that conventional structured meshes with no noise perform considerably worse than the proposed adapted meshes with noise levels up to 20% of the compression amplitude. A phantom study and preliminary in vivo results from a breast tumor case confirm the benefit of the proposed technique. Not only conventional axial strain images but also other elasticity approximations can be used to adapt meshes. This is demonstrated on images generated by combining axial strain and axial-shear strain, which enhances lateral image contrast in particular settings, consequently further improving mesh-adapted reconstructions.
Elasticity
Volume mesh
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A finite element based nonlinear inverse scheme is presented to reconstruct the elastic properties of soft tissues subjected to an external compression. An objective function relating the least-square difference of model-predicted and measured displacement or strain fields from a sequence of images (B-mode or MRI) is minimized with respect to the unknown material parameters. To obtain physically meaningful solutions, the material properties (Young's modulus, Poisson's ratio etc.) are bounded with lower and upper limits. The solution of the ensuing linearly constrained nonlinear optimization problem, is performed by means of a modified Levenberg-Marquardt method and an active set strategy. To demonstrate the effectiveness of the method, simulated data was studied by adding up to 20% noise. The method has also been used to determine the Young's modulus of a three-layer phantom. Preliminary numerical results with both simulated and experimental data suggest that the method is robust for reconstructing the elastic properties of soft tissues. If the boundary between normal tissues and suspicious tissues could be defined via image segmentation techniques, this method might accommodate more noise.
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Elasticity
Linear elasticity
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Manual breast exams are widely used for early detection of breast cancer. These exams rely heuristically on the significant stiffness (elastic modulus) difference between cancerous tissue and normal tissue. We wish to systematize this approach by developing an inverse technique which is capable of inferring the elastic modulus throughout the breast tissue based on the application of known surface forces. In this study, we proposed appropriate inverse computational algorithms and examined their performance on two-dimensional model problems. Finite element methods were used to model the tissue response for the forward problem–solving for the surface tissue displacements for a given forcing function. A variety of tumour locations were assumed, and 'measured results' were created with numerical noise added to simulate measurement errors. A genetic algorithm was then developed to solve the inverse problem–given the measured surface displacements, what is the distribution of tissue material properties within the breast? We developed an eigenvector expansion technique to create effective force test patterns for use in concert with the genetic algorithm. A series of test cases at various noise levels for a coarse and a fine mesh were examined. When a tumour was present, a tumour was always detected. When a tumour was absent, the algorithm always correctly reported no cancer.
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Hyperelastic material
Robustness
Pulsatile flow
Intravascular Ultrasound
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A novel material reconstruction method combining finite element (FE)-based direct inverse method and non-linear optimization algorithm is proposed for elasticity imaging of biological soft tissue. The biological soft tissue is represented using Neo-Hookean hyperelastic model. The FE-based direct inverse method provides an estimation of material parameter distribution which serves as the initial guess of the Levenberg–Marquardt optimization algorithm. Direct calculation of Jacobian matrix is proposed to improve the computational efficiency of the combined algorithm. Computer simulation demonstrated that the material parameters of soft tissue can be determined rapidly and accurately within a small tolerance using the proposed method. Our experimental results on a human lower leg demonstrated the clinical viability of this method.
Hyperelastic material
Elasticity
Linear elasticity
Biological tissue
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