Biomechanical 3-D finite element modeling of the human breast using MRI data

The Solution of Inverse Non-Linear Elasticity Problems That Arise When Locating Breast Tumours

Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse problem. Other than for situations where classical linear elasticity theory may be applied, the simple approach for solving the inverse problem of reversing the direction of gravity and modelling the deformed body as an undeformed body does not give the correct solution. In this study, we derive equations that may be used to solve inverse problems. The solution of these equations may be used for a wide range of inverse problems in non-linear elasticity.

ImageParser: a tool for finite element generation from three-dimensional medical images

Background

The finite element method (FEM) is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures) of interest (ROIs) may be irregular and fuzzy.

Methods

A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements.

Results

The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues.

Conclusion

The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information.

A method to measure the hyperelastic parameters ofex vivobreast tissue samples

Over the past decade, there has been increasing interest in modelling soft tissue deformation. This topic has several biomedical applications ranging from medical imaging to robotic assisted telesurgery. In these applications, tissue deformation can be very large due to low tissue stiffness and lack of physical constraints. As a result, deformation modelling of such organs often requires a treatment, which reflects nonlinear behaviour. While computational techniques such as nonlinear finite element methods are well developed, the required intrinsic nonlinear mechanical parameters of soft tissues that are critical to develop reliable tissue deformation models are not well known. To address this issue, we developed a system to measure the hyperelastic parameters of small ex vivo tissue samples. This measurement technique consists of indenting an unconfined small block of tissue using a computer controlled loading system while measuring the resulting indentation force. The nonlinear tissue force-displacement response is used to calculate the hyperelastic parameters via an appropriate inversion technique. This technique is based on a nonlinear least squares formulation that uses a nonlinear finite element model as the direct problem solver. The features of the system are demonstrated with two samples of breast tissue and typical hyperelastic results are presented.

Measuring the elastic modulus of ex vivo small tissue samples

Over the past decade, several methods have been proposed to image tissue elasticity based on imaging methods collectively called elastography. While progress in developing these systems has been rapid, the basic understanding of tissue properties to interpret elastography images is generally lacking. To address this limitation, we developed a system to measure the Young's modulus of small soft tissue specimens. This system was designed to accommodate biological soft tissue constraints such as sample size, geometry imperfection and heterogeneity. The measurement technique consists of indenting an unconfined small block of tissue while measuring the resulting force. We show that the measured force-displacement slope of such a geometry can be transformed to the tissue Young's modulus via a conversion factor related to the sample's geometry and boundary conditions using finite element analysis. We also demonstrate another measurement technique for tissue elasticity based on quasi-static magnetic resonance elastography in which a tissue specimen encased in a gelatine-agarose block undergoes cyclical compression with resulting displacements measured using a phase contrast MRI technique. The tissue Young's modulus is then reconstructed from the measured displacements using an inversion technique. Finally, preliminary elasticity measurement results of various breast tissues are presented and discussed.

A new approach to elastography using mutual information and finite elements

Historically, increased mechanical stiffness during tissue palpation exams has been associated with assessing organ health as well as with detecting the growth of a potentially life-threatening cell mass. As such, techniques to image elasticity parameters (i.e., elastography) have recently become of great interest to scientists. In this work, a new method of elastography will be introduced within the context of mammographic imaging. The elastography method proposed represents a non-rigid iterative image registration algorithm that varies material properties within a finite element model to improve registration. More specifically, regional measures of image similarity are used within an objective function minimization framework to reconstruct elasticity images of tissue stiffness. Numerical simulations illustrate: (1) the encoding of stiffness information within the context of a regional image similarity criterion, (2) the methodology for an iterative elastographic imaging framework and (3) elasticity reconstruction simulations. The real strength in this approach is that images from any modality (e.g., magnetic resonance, computed tomography, ultrasound. etc) that have sufficient anatomically-based intensity heterogeneity and remain consistent from a pre- to a post-deformed state could be used in this paradigm.

Validation of nonrigid image registration using finite-element methods: application to breast MR images

This paper presents a novel method for validation of nonrigid medical image registration. This method is based on the simulation of physically plausible, biomechanical tissue deformations using finite-element methods. Applying a range of displacements to finite-element models of different patient anatomies generates model solutions which simulate gold standard deformations. From these solutions, deformed images are generated with a range of deformations typical of those likely to occur in vivo. The registration accuracy with respect to the finite-element simulations is quantified by co-registering the deformed images with the original images and comparing the recovered voxel displacements with the biomechanically simulated ones. The functionality of the validation method is demonstrated for a previously described nonrigid image registration technique based on free-form deformations using B-splines and normalized mutual information as a voxel similarity measure, with an application to contrast-enhanced magnetic resonance mammography image pairs. The exemplar nonrigid registration technique is shown to be of subvoxel accuracy on average for this particular application. The validation method presented here is an important step toward more generic simulations of biomechanically plausible tissue deformations and quantification of tissue motion recovery using nonrigid image registration. It will provide a basis for improving and comparing different nonrigid registration techniques for a diversity of medical applications, such as intrasubject tissue deformation or motion correction in the brain, liver or heart.

MR validation of soft tissue mimicing phantom deformation as modeled by nonlinear finite element analysis

A study of the applicability of nonlinear finite element analysis (FEA) to predict soft tissue deformation was validated with phase contrast magnetic resonance velocity imaging. A phantom of varying stiffness was placed in a special purpose, computer controlled MR compatible compression apparatus which provided precise, time varying compression with surface deformations on the order of 11%. The resulting motion was measured with MR velocity images acquired throughout the cycle of compression. The phantom geometry was modeled with a finite element mesh and the mechanical properties of the phantom material were measured and incorporated in the FEA model. The motion as calculated by the FEA model was compared to the motion measured with MRI and the results were found to vary with the material's Poisson's ratio and the coefficient of friction. A minimum difference was reached when the Poisson's ratio and coefficient of friction were set to 0.485 and 0.3, respectively. Under these conditions, the root mean square difference was found to be 14.4%.

A constrained modulus reconstruction technique for breast cancer assessment

A reconstruction technique for breast tissue elasticity modulus is described. This technique assumes that the geometry of normal and suspicious tissues is available from a contrast-enhanced magnetic resonance image. Furthermore, it is assumed that the modulus is constant throughout each tissue volume. The technique, which uses quasi-static strain data, is iterative where each iteration involves modulus updating followed by stress calculation. Breast mechanical stimulation is assumed to be done by two compressional rigid plates. As a result, stress is calculated using the finite element method based on the well-controlled boundary conditions of the compression plates. Using the calculated stress and the measured strain, modulus updating is done element-by-element based on Hooke's law. Breast tissue modulus reconstruction using simulated data and phantom modulus reconstruction using experimental data indicate that the technique is robust.