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

FINITE ELEMENT ANALYSIS ON FLUID FILTRATION IN SYSTEM OF PERMEABLE CURVED CAPILLARY AND TISSUE

Fluid filtration across a capillary wall, which is associated with many diseases, is noteworthy for its significant role in cancer treatment. In this study, the coupled fluid dynamic phenomenon within a capillary and its surrounding tissues has been numerically analyzed in order to investigate the effect of capillary geometry, filtration coefficient, and tissue pressure on capillary filtration. The computational domain is composed of a fluid capillary subdomain coupled with a porous tissue subdomain. The flows in the sub-domains are described by the Stokes and Darcy equations, respectively, which are solved in a coupled manner by applying a nodal replacement scheme at the capillary wall. Distributions of pressure and flow velocity are presented, which show that the interfacial pressure drop is strongly influenced by permeability, tissue boundary pressure, and capillary radii. These results provide useful information on the relationship between the interstitial flow pattern and oxygen transport.

A finite element method to correct deformable image registration errors in low-contrast regions

Image-guided adaptive radiotherapy requires deformable image registration to map radiation dose back and forth between images. The purpose of this study is to develop a novel method to improve the accuracy of an intensity-based image registration algorithm in low-contrast regions. A computational framework has been developed in this study to improve the quality of the 'demons' registration. For each voxel in the registration's target image, the standard deviation of image intensity in a neighborhood of this voxel was calculated. A mask for high-contrast regions was generated based on their standard deviations. In the masked regions, a tetrahedral mesh was refined recursively so that a sufficient number of tetrahedral nodes in these regions can be selected as driving nodes. An elastic system driven by the displacements of the selected nodes was formulated using a finite element method (FEM) and implemented on the refined mesh. The displacements of these driving nodes were generated with the 'demons' algorithm. The solution of the system was derived using a conjugated gradient method, and interpolated to generate a displacement vector field for the registered images. The FEM correction method was compared with the 'demons' algorithm on the computed tomography (CT) images of lung and prostate patients. The performance of the FEM correction relating to the 'demons' registration was analyzed based on the physical property of their deformation maps, and quantitatively evaluated through a benchmark model developed specifically for this study. Compared to the benchmark model, the 'demons' registration has the maximum error of 1.2 cm, which can be corrected by the FEM to 0.4 cm, and the average error of the 'demons' registration is reduced from 0.17 to 0.11 cm. For the CT images of lung and prostate patients, the deformation maps generated by the 'demons' algorithm were found unrealistic at several places. In these places, the displacement differences between the 'demons' registrations and their FEM corrections were found in the range of 0.4 and 1.1 cm. The mesh refinement and FEM simulation were implemented in a single thread application which requires about 45 min of computation time on a 2.6 GHz computer. This study has demonstrated that the FEM can be integrated with intensity-based image registration algorithms to improve their registration accuracy, especially in low-contrast regions.

A novel breast software phantom for biomechanical modeling of elastography

PURPOSE

In developing breast imaging technologies, testing is done with phantoms. Physical phantoms are normally used but their size, shape, composition, and detail cannot be modified readily. These difficulties can be avoided by creating a software breast phantom. Researchers have created software breast phantoms using geometric and/or mathematical methods for applications like image fusion. The authors report a 3D software breast phantom that was built using a mechanical design tool, to investigate the biomechanics of elastography using finite element modeling (FEM). The authors propose this phantom as an intermediate assessment tool for elastography simulation; for use after testing with commonly used phantoms and before clinical testing. The authors design the phantom to be flexible in both, the breast geometry and biomechanical parameters, to make it a useful tool for elastography simulation.

METHODS

The authors develop the 3D software phantom using a mechanical design tool based on illustrations of normal breast anatomy. The software phantom does not use geometric primitives or imaging data. The authors discuss how to create this phantom and how to modify it. The authors demonstrate a typical elastography experiment of applying a static stress to the top surface of the breast just above a simulated tumor and calculate normal strains in 3D and in 2D with plane strain approximations with linear solvers. In particular, they investigate contrast transfer efficiency (CTE) by designing a parametric study based on location, shape, and stiffness of simulated tumors. The authors also compare their findings to a commonly used elastography phantom.

RESULTS

The 3D breast software phantom is flexible in shape, size, and location of tumors, glandular to fatty content, and the ductal structure. Residual modulus, maps, and profiles, served as a guide to optimize meshing of this geometrically nonlinear phantom for biomechanical modeling of elastography. At best, low residues (around 1-5 KPa) were found within the phantom while errors were elevated (around 10-30 KPa) at tumor and lobule boundaries. From our FEM analysis, the breast phantom generated a superior CTE in both 2D and in 3D over the block phantom. It also showed differences in CTE values and strain contrast for deep and shallow tumors and showed significant change in CTE when 3D modeling was used. These changes were not significant in the block phantom. Both phantoms, however, showed worsened CTE values for increased input tumor-background modulus contrast.

CONCLUSIONS

Block phantoms serve as a starting tool but a next level phantom, like the proposed breast phantom, will serve as a valuable intermediate for elastography simulation before clinical testing. Further, given the CTE metrics for the breast phantom are superior to the block phantom, and vary for tumor shape, location, and stiffness, these phantoms would enhance the study of elastography contrast. Further, the use of 2D phantoms with plane strain approximations overestimates the CTE value when compared to the true CTE achieved with 3D models. Thus, the use of 3D phantoms, like the breast phantom, with no approximations, will assist in more accurate estimation of modulus, especially valuable for 3D elastography systems.

CONSTRUCTION OF ANATOMICALLY ACCURATE FINITE ELEMENT MODELS OF THE HUMAN HAND AND A RAT KIDNEY

The aim of the paper is to develop a method for generating three-dimensional (3D) models of organs from medical images (computerized tomography (CT) images, magnetic resonance imaging (MRI), etc.). There were three main steps in the development of the model: the first step was image processing. Different image-processing operators including blurring, sharpening, edge detection, region segmentation, mathematical morphology transformation, rotation, and movement of the kidney slices were performed to automatically construct the accurate boundary information. The second step was mesh generation of each slice based on the boundary information by using the transfinite interpolation (TFI) technique. In this paper, the TFI method was improved to create grids from images directly. The last step was reconstructing the models by stacking the 2D grid models and visualizing the result in the Advanced Visual System (AVS) software. In order to verify the effectiveness of this method, the finite element (FE) models of a rat kidney, human hand, and blood vessels were reconstructed and good results were obtained.

An analysis of the mechanical parameters used for finite element compression of a high-resolution 3D breast phantom

PURPOSE

The authors previously introduced a methodology to generate a realistic three-dimensional (3D), high-resolution, computer-simulated breast phantom based on empirical data. One of the key components of such a phantom is that it provides a means to produce a realistic simulation of clinical breast compression. In the current study, they have evaluated a finite element (FE) model of compression and have demonstrated the effect of a variety of mechanical properties on the model using a dense mesh generated from empirical breast data. While several groups have demonstrated an effective compression simulation with lower density finite element meshes, the presented study offers a mesh density that is able to model the morphology of the inner breast structures more realistically than lower density meshes. This approach may prove beneficial for multimodality breast imaging research, since it provides a high level of anatomical detail throughout the simulation study.

METHODS

In this paper, the authors describe methods to improve the high-resolution performance of a FE compression model. In order to create the compressible breast phantom, dedicated breast CT data was segmented and a mesh was generated with 4-noded tetrahedral elements. Using an explicit FE solver to simulate breast compression, several properties were analyzed to evaluate their effect on the compression model including: mesh density, element type, density, and stiffness of various tissue types, friction between the skin and the compression plates, and breast density. Following compression, a simulated projection was generated to demonstrate the ability of the compressible breast phantom to produce realistic simulated mammographic images.

RESULTS

Small alterations in the properties of the breast model can change the final distribution of the tissue under compression by more than 1 cm; which ultimately results in different representations of the breast model in the simulated images. The model properties that impact displacement the most are mesh density, friction between the skin and the plates, and the relative stiffness of the different tissue types.

CONCLUSIONS

The authors have developed a 3D, FE breast model that can yield high spatial resolution breast deformations under uniaxial compression for imaging research purposes and demonstrated that small changes in the mechanical properties can affect images generated using the phantom.

Advances in finite element simulations of elastosonography for breast lesion detection

Among the available tools for the early diagnosis of breast cancer, the elastographic technique based on ultrasounds has many advantages such as the noninvasive measure, the absence of ionizing effects, the high tolerability by patients, and the wide diffusion of the ecographic machines. However this diagnostic procedure is strongly affected by many subjective factors and is considered not reliable enough even to reduce the number of biopsies used to identify the nature of lesions. Therefore in the literature experimental and numerical simulations on physical and virtual phantoms are presented to test and validate procedures and algorithms and to interpret elastosonographic results. In this work, first a description of the elastographic technique and a review of the principal finite element (FE) models are provided and second diagnostic indexes employed to assess the nature of a lump mass are presented. As advances in FE simulations of elastosonography, axisymmetric phantom, and anthropomorphic models are described, which, with respect to the literature, include some features of breast mechanics. In particular deterministic analyses were used to compare the various details of virtual elastograms and also to investigate diagnostic indexes with respect to the regions where strains were considered. In order to improve the reliability of the elastosonographic procedure, univariate and multivariate sensitivity analyses, based on a probabilistic FE approach, were also performed to identify the parameters that mostly influence the deformation contrast between healthy and cancerous tissues. Moreover, synthetic indicators of the strain field, such as the strain contrast coefficient, were evaluated in different regions of interest in order to identify the most suitable for lesion type assessment. The deterministic analyses show that the malignant lesion is characterized by a uniform strain inside the inclusion due to the firmly bonding condition, while in the benign inclusion (loosely bonded) a strain gradient is observed independently from the elastic modulus contrast. The multivariate analyses reveal that the strain contrast depends linearly on the relative stiffness between the lesion and the healthy tissue and not linearly on the interface friction coefficient. The anthropomorphic model shows other interesting features, such as the layer or curvature effects, which introduce difficulties in selecting a reference region for strain assessment. The results show that a simple axisymmetric model with linear elastic material properties can be suitable to simulate the elastosonographic procedure although the breast curvature and layer distinction play a significant role in the strain assessment.

Customized planning of augmentation mammaplasty with silicon implants using three-dimensional optical body scans and biomechanical modeling of soft tissue outcome

The aesthetic results of augmentation mammaplasty are essentially determined by the size and the shape of the implant as well as its position on the chest. To achieve successful aesthetic results, customized surgery planning based on a reliable visual concept of the prospective surgery outcome and quantitative methods for assessment of three-dimensional (3D) breast shape could be of considerable additional value. This report evaluates a novel method for customized planning and quantitative optimization of breast augmentation based on 3D optical body scanning of the patient's breast and computational modeling of soft tissue mechanics. This method allows a 3D photo-realistic appearance of postsurgery breasts to be simulated for different surgical scenarios. It also allows the result of a virtual simulation to be implemented using measurements derived from a computationally predicted breast model. A series of clinical studies are presented that demonstrate the feasibility and accuracy of the proposed approach for customized 3D planning of breast augmentation, including direct comparison between simulated and postsurgery results. Our experimental results show that for 89% of the breast surface, the average difference between the simulated and postsurgery breast models amounts to less than 1 mm. The presented method for customized planning of augmentation mammaplasty enables realistic prediction and quantitative optimization of postsurgery breast appearance. Based on individual 3D data and physical modeling, the described approach enables more accurate and reliable predictions of surgery outcomes than conventionally used photos of prior patients, drawings, or ad hoc data manipulation. Moreover, it provides precise quantitative data for bridging the gap between virtual simulation and real surgery.

Correlating locations in ipsilateral breast tomosynthesis views using an analytical hemispherical compression model

To improve cancer detection in mammography, breast examinations usually consist of two views per breast. In order to combine information from both views, corresponding regions in the views need to be matched. In 3D digital breast tomosynthesis (DBT), this may be a difficult and time-consuming task for radiologists, because many slices have to be inspected individually. For multiview computer-aided detection (CAD) systems, matching corresponding regions is an essential step that needs to be automated. In this study, we developed an automatic method to quickly estimate corresponding locations in ipsilateral tomosynthesis views by applying a spatial transformation. First we match a model of a compressed breast to the tomosynthesis view containing a point of interest. Then we estimate the location of the corresponding point in the ipsilateral view by assuming that this model was decompressed, rotated and compressed again. In this study, we use a relatively simple, elastically deformable sphere model to obtain an analytical solution for the transformation in a given DBT case. We investigate three different methods to match the compression model to the data by using automatic segmentation of the pectoral muscle, breast tissue and nipple. For validation, we annotated 208 landmarks in both views of a total of 146 imaged breasts of 109 different patients and applied our method to each location. The best results are obtained by using the centre of gravity of the breast to define the central axis of the model, around which the breast is assumed to rotate between views. Results show a median 3D distance between the actual location and the estimated location of 14.6 mm, a good starting point for a registration method or a feature-based local search method to link suspicious regions in a multiview CAD system. Approximately half of the estimated locations are at most one slice away from the actual location, which makes the method useful as a mammographic workstation tool for radiologists to interactively find corresponding locations in ipsilateral tomosynthesis views.

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

Large breast compressions: observations and evaluation of simulations

PURPOSE

Several methods have been proposed to simulate large breast compressions such as those occurring during x-ray mammography. However, the evaluation of these methods against real data is rare. The aim of this study is to learn more about the deformation behavior of breasts and to assess a simulation method.

METHODS

Magnetic resonance (MR) images of 11 breasts before and after applying a relatively large in vivo compression in the medial direction were acquired. Nonrigid registration was employed to study the deformation behavior. Optimal material properties for finite element modeling were determined and their prediction performance was assessed. The realism of simulated compressions was evaluated by comparing the breast shapes on simulated and real mammograms.

RESULTS

Following image registration, 19 breast compressions from 8 women were studied. An anisotropic deformation behavior, with a reduced elongation in the anterior-posterior direction and an increased stretch in the inferior-superior direction was observed. Using finite element simulations, the performance of isotropic and transverse isotropic material models to predict the displacement of internal landmarks was compared. Isotropic materials reduced the mean displacement error of the landmarks from 23.3 to 4.7 mm, on average, after optimizing material properties with respect to breast surface alignment and image similarity. Statistically significantly smaller errors were achieved with transverse isotropic materials (4.1 mm, P=0.0045). Homogeneous material models performed substantially worse (transverse isotropic: 5.5 mm; isotropic: 6.7 mm). Of the parameters varied, the amount of anisotropy had the greatest influence on the results. Optimal material properties varied less when grouped by patient rather than by compression magnitude (mean: 0.72 vs. 1.44). Employing these optimal materials for simulating mammograms from ten MR breast images of a different cohort resulted in more realistic breast shapes than when using established material models.

CONCLUSIONS

Breasts in the prone position exhibited an anisotropic compression behavior. Transverse isotropic materials with an increased stiffness in the anterior-posterior direction improved the prediction of these deformations and produced more realistic mammogram simulations from MR images.

Modeling static and dynamic thermography of the human breast under elastic deformation

An abnormal thermogram has been shown to be a reliable indicator of increased risk of breast cancer. Numerical modeling techniques for thermography are proposed to quantify the complex relationships between the breast thermal behaviors and the underlying physiological/pathological conditions. Previous thermal modeling techniques did not account for gravity-induced elastic deformation arising from various body postures, nor did they suggest that a dynamic thermal procedure may be used to enhance clinical diagnosis. In this paper, 3D finite element method (FEM)-based thermal and elastic modeling techniques are developed to characterize comprehensively both the thermal and elastic properties of normal and tumorous breast tissues during static and dynamic thermography. In the steady state, gravity-induced breast deformation is found to cause an upper-lower asymmetric surface temperature contrast for sitting/standing up body posture, even though all the thermal and elastic properties are assumed uniform. Additionally, the tumor-induced surface temperature alterations are found to be caused primarily by shallow tumors and to be less sensitive to tumor size than to tumor depth. In the dynamic state, the breast exhibits distinctive temporal patterns that are associated with distinct thermal events: cold stress and thermal recovery induced by changes in the ambient temperature. Specifically, the tumor-induced thermal contrast shows an opposite initial change and delayed peak as compared with the deformation-induced thermal contrast. These findings are expected to provide a stronger foundation for, and greater specificity and precision in, thermographic diagnosis, and treatment of breast cancer.

Matrix density-induced mechanoregulation of breast cell phenotype, signaling and gene expression through a FAK-ERK linkage

Mammographically dense breast tissue is one of the greatest risk factors for developing breast carcinoma, yet the associated molecular mechanisms remain largely unknown. Importantly, regions of high breast density are associated with increased stromal collagen and epithelial cell content. We set out to determine whether increased collagen-matrix density, in the absence of stromal cells, was sufficient to promote proliferation and invasion characteristic of a malignant phenotype in non-transformed mammary epithelial cells. We demonstrate that increased collagen-matrix density increases matrix stiffness to promote an invasive phenotype. High matrix stiffness resulted in increased formation of activated three-dimensional (3D)-matrix adhesions and a chronically elevated outside-in/inside-out focal adhesion (FA) kinase (FAK)-Rho signaling loop, which was necessary to generate and maintain the invasive phenotype. Moreover, this signaling network resulted in hyperactivation of the Ras-mitogen-activated protein kinase (MAPK) pathway, which promoted growth of mammary epithelial cells in vitro and in vivo and activated a clinically relevant proliferation signature that predicts patient outcome. Hence, the current data provide compelling evidence for the importance of the mechanical features of the microenvironment, and suggest that mechanotransduction in these cells occurs through a FAK-Rho-ERK signaling network with extracellular signal-regulated kinase (ERK) as a bottleneck through which much of the response to mechanical stimuli is regulated. As such, we propose that increased matrix stiffness explains part of the mechanism behind increased epithelial proliferation and cancer risk in human patients with high breast tissue density.

A finite element infant eye model to investigate retinal forces in shaken baby syndrome

BACKGROUND

Shaken baby syndrome (SBS) is a form of abuse in which an infant, typically 6 months or less, is held and submitted to repeated acceleration-deceleration forces. One of the indicators of abuse is bilateral retinal hemorrhaging. A computational model of an infant eye, using the finite element method, is built in order to assess forces at the posterior retina for a shaking and an impact motions.

METHOD

The eye model is based on histological studies, diagrams, and materials from previous literature. Motions are applied to the model to simulate a four-cycle shaking motion in 1 second with maximum extension/flexion of the neck. The retinal forces of the shaking motion, at the posterior eye, are compared to an impact pulse (60G) simulating a fall for a total duration of 100 ms.

RESULTS

The shaking motion, for the first cycle, shows retinal force means at the posterior eye to be around 0.08 N sustained from the time range of 50 to 200 ms, into the shake, with a peak in excess of 0.2 N. The impulse, area under the curve, is 15 N-ms for 250 msec for the first cycle. The impact simulation reveals a mean retinal force around 0.025 N for a time range of 0 to 26 ms, with a peak force around 0.11 N. Moreover, the impulse for the impact simulation is 13 times lower than the shaking motion.

CONCLUSION

The results suggest that shaking alone may be enough to cause retinal hemorrhaging, as there are more sustained and higher forces in the posterior retina, compared to an impact due to a fall. This is in part due to the optic nerve causing more localized stresses in a shaking motion than an impact.

Creating individual-specific biomechanical models of the breast for medical image analysis

RATIONALE AND OBJECTIVES

Anatomically realistic biomechanical models of the breast potentially provide a reliable way of mapping tissue locations across medical images, such as mammograms, magnetic resonance imaging (MRI), and ultrasound. This work presents a new modeling framework that enables us to create biomechanical models of the breast that are customized to the individual. We demonstrate the framework's capabilities by creating models of the left breasts of two volunteers and tracking their deformations across MRIs.

MATERIALS AND METHODS

We generate customized finite element models by automatically fitting geometrical models to segmented data from breast MRIs, and characterizing the in vivo mechanical properties (assuming homogeneity) of the breast tissues. For each volunteer, we identified the unloaded configuration by acquiring MRIs of the breast under neutral buoyancy (immersed in water). Such imaging is clearly not practical in the clinical setting; however, these previously unavailable data provide us with important data with which to validate models of breast biomechanics. Internal tissue features were identified in the neutral buoyancy images and tracked to the prone gravity-loaded state using the modeling framework.

RESULTS

The models predicted deformations with root-mean-square errors of 4.2 and 3.6 mm in predicting the skin surface of the gravity-loaded state for each volunteer. Internal tissue features were tracked with a mean error of 3.7 and 4.7 mm for each volunteer.

CONCLUSIONS

The models capture breast shape and internal deformations across the images with clinically acceptable accuracy. Further refinement of the framework and incorporation of more anatomic detail will make these models useful for breast cancer diagnosis.

Automated finite-element analysis for deformable registration of prostate images

Two major factors preventing the routine clinical use of finite-element analysis for image registration are: 1) the substantial labor required to construct a finite-element model for an individual patient's anatomy and 2) the difficulty of determining an appropriate set of finite-element boundary conditions. This paper addresses these issues by presenting algorithms that automatically generate a high quality hexahedral finite-element mesh and automatically calculate boundary conditions for an imaged patient. Medial shape models called m-reps are used to facilitate these tasks and reduce the effort required to apply finite-element analysis to image registration. Encouraging results are presented for the registration of CT image pairs which exhibit deformation caused by pressure from an endorectal imaging probe and deformation due to swelling.

A new validation method for X-ray mammogram registration algorithms using a projection model of breast X-ray compression

Establishing spatial correspondence between features visible in X-ray mammograms obtained at different times has great potential to aid assessment and quantitation of change in the breast indicative of malignancy. The literature contains numerous nonrigid registration algorithms developed for this purpose, but existing approaches are flawed by the assumption of inappropriate 2-D transformation models and quantitative estimation of registration accuracy is limited. In this paper, we describe a novel validation method which simulates plausible mammographic compressions of the breast using a magnetic resonance imaging (MRI) derived finite element model. By projecting the resulting known 3-D displacements into 2-D and generating pseudo-mammograms from these same compressed magnetic resonance (MR) volumes, we can generate convincing images with known 2-D displacements with which to validate a registration algorithm. We illustrate this approach by computing the accuracy for two conventional nonrigid 2-D registration algorithms applied to mammographic test images generated from three patient MR datasets. We show that the accuracy of these algorithms is close to the best achievable using a 2-D one-to-one correspondence model but that new algorithms incorporating more representative transformation models are required to achieve sufficiently accurate registrations for this application.

Breast image registration techniques: a survey

Breast cancer is the most common type of cancer in women worldwide. Image registration plays an important role in breast cancer detection. This paper gives an overview of the current state-of-the-art in the breast image registration techniques. For the intramodality registration techniques, X-ray, MRI, and ultrasound are the primary focuses of interest. Intermodality techniques will cover the combination of different modalities. Validation of breast registration methods is also discussed.

Elastic moduli of normal and pathological human breast tissues: an inversion-technique-based investigation of 169 samples

Understanding and quantifying the mechanical properties of breast tissues has been a subject of interest for the past two decades. This has been motivated in part by interest in modelling soft tissue response for surgery planning and virtual-reality-based surgical training. Interpreting elastography images for diagnostic purposes also requires a sound understanding of normal and pathological tissue mechanical properties. Reliable data on tissue elastic properties are very limited and those which are available tend to be inconsistent, in part as a result of measurement methodology. We have developed specialized techniques to measure tissue elasticity of breast normal tissues and tumour specimens and applied them to 169 fresh ex vivo breast tissue samples including fat and fibroglandular tissue as well as a range of benign and malignant breast tumour types. Results show that, under small deformation conditions, the elastic modulus of normal breast fat and fibroglandular tissues are similar while fibroadenomas were approximately twice the stiffness. Fibrocystic disease and malignant tumours exhibited a 3-6-fold increased stiffness with high-grade invasive ductal carcinoma exhibiting up to a 13-fold increase in stiffness compared to fibrogalndular tissue. A statistical analysis showed that differences between the elastic modulus of the majority of those tissues were statistically significant. Implications for the specificity advantages of elastography are reviewed.

Finite Element Modelling of Breast Biomechanics: Finding a Reference aState

Non-rigid-body registration techniques, that constrain the set of possible soft tissue deformations to be consistent with the basic laws of physics, offer a means of providing realistic and accurate estimates of breast movement under mammographic compression. Such constraints can be imposed by the use of anatomically accurate finite element models that predict soft tissue deformations. The overarching aim is to develop tools for tracking regions of interest across multiple images (different views taken at different times) for image-guided surgeries and reliable diagnostic and therapy monitoring. Due to the nonlinear deformations imposed on the breast under the various imaging modalities, the finite element reference geometry from which deformations are predicted is important. Gravity loads act on the breast in all imaging modalities. In this paper, we propose a method of identifying a stress-free reference state of the breast given a series of loaded deformed configurations that have been derived from images of a patient placed in different orientations with respect to the direction of gravity.

An inverse problem solution for measuring the elastic modulus of intactex vivobreast tissue tumours

Soft tissue elasticity has been a subject of interest in biomedical applications as an aid to medical diagnosis since the dawn of medicine. More recently, this has led to the concept of elastography with the aim of imaging the spatial distribution of tissue elasticity. Interpreting elastography images requires reliable information pertaining to elastic properties of normal and pathological tissues. Such information is either very limited or not available in the literature. Elastic modulus measurement techniques developed for soft tissues generally require tissue excision to prepare samples for testing. While this may be done with normal tissues, tumour tissue excision is generally not permissible because tumour pathological assessment requires that the tumour be kept intact. To address this limitation, we developed a system to measure the Young's modulus of tumour specimens. The technique consists of indenting the tumour specimen while measuring indentation force and displacements. To obtain the Young's modulus from the measured force-displacement slope, we developed an iterative inversion technique that uses a finite element model of the piecewise homogeneous tissue slice in each iteration. Preliminary elasticity measurement results of various breast tumours are presented and discussed. These results indicate that the proposed method is robust and highly accurate. Furthermore, they indicate that a benign lesion and malignant tumours are roughly five times and ten times stiffer than normal breast tissues respectively.

A biomechanical model of mammographic compressions

A number of biomechanical models have been proposed to improve nonrigid registration techniques for multimodal breast image alignment. A deformable breast model may also be useful for overcoming difficulties in interpreting 2D X-ray projections (mammograms) of 3D volumes (breast tissues). If a deformable model could accurately predict the shape changes that breasts undergo during mammography, then the model could serve to localize suspicious masses (visible in mammograms) in the unloaded state, or in any other deformed state required for further investigations (such as biopsy or other medical imaging modalities). In this paper, we present a validation study that was conducted in order to develop a biomechanical model based on the well-established theory of continuum mechanics (finite elasticity theory with contact mechanics) and demonstrate its use for this application. Experimental studies using gel phantoms were conducted to test the accuracy in predicting mammographic-like deformations. The material properties of the gel phantom were estimated using a nonlinear optimization process, which minimized the errors between the experimental and the model-predicted surface data by adjusting the parameter associated with the neo-Hookean constitutive relation. Two compressions (the equivalent of cranio-caudal and medio-lateral mammograms) were performed on the phantom, and the corresponding deformations were recorded using a MRI scanner. Finite element simulations were performed to mimic the experiments using the estimated material properties with appropriate boundary conditions. The simulation results matched the experimental recordings of the deformed phantom, with a sub-millimeter root-mean-square error for each compression state. Having now validated our finite element model of breast compression, the next stage is to apply the model to clinical images.

Phenomenological model of diffuse global and regional atrophy using finite-element methods

The main goal of this work is the generation of ground-truth data for the validation of atrophy measurement techniques, commonly used in the study of neurodegenerative diseases such as dementia. Several techniques have been used to measure atrophy in cross-sectional and longitudinal studies, but it is extremely difficult to compare their performance since they have been applied to different patient populations. Furthermore, assessment of performance based on phantom measurements or simple scaled images overestimates these techniques' ability to capture the complexity of neurodegeneration of the human brain. We propose a method for atrophy simulation in structural magnetic resonance (MR) images based on finite-element methods. The method produces cohorts of brain images with known change that is physically and clinically plausible, providing data for objective evaluation of atrophy measurement techniques. Atrophy is simulated in different tissue compartments or in different neuroanatomical structures with a phenomenological model. This model of diffuse global and regional atrophy is based on volumetric measurements such as the brain or the hippocampus, from patients with known disease and guided by clinical knowledge of the relative pathological involvement of regions and tissues. The consequent biomechanical readjustment of structures is modelled using conventional physics-based techniques based on biomechanical tissue properties and simulating plausible tissue deformations with finite-element methods. A thermoelastic model of tissue deformation is employed, controlling the rate of progression of atrophy by means of a set of thermal coefficients, each one corresponding to a different type of tissue. Tissue characterization is performed by means of the meshing of a labelled brain atlas, creating a reference volumetric mesh that will be introduced to a finite-element solver to create the simulated deformations. Preliminary work on the simulation of acquisition artefacts is also presented. Cross-sectional and longitudinal sets of simulated data are shown and a visual classification protocol has been used by experts to rate real and simulated scans according to their degree of atrophy. Results confirm the potential of the proposed methodology.

Factors influencing the accuracy of biomechanical breast models

Recently it has been suggested that finite element methods could be used to predict breast deformations in a number of applications, including comparison of multimodality images, validation of image registration and image guided interventions. Unfortunately knowledge of the mechanical properties of breast tissues is limited. This study evaluated the accuracy with which biomechanical breast models based on finite element methods can predict the displacements of tissue within the breast in the practical clinical situation where the boundaries of the organ might be known reasonably accurately but there is some uncertainty on the mechanical properties of the tissue. For two datasets, we investigate the influence of tissue elasticity values, Poisson's ratios, boundary conditions, finite element solvers and mesh resolutions. Magnetic resonance images were acquired before and after compressing each volunteer's breast by about 20%. Surface displacement boundary conditions were derived from a three-dimensional nonrigid image registration. Six linear and three nonlinear elastic material models with and without skin were tested. These were compared to hyperelastic models. The accuracy of the models was evaluated by assessing the ability of the model to predict the location of 12 corresponding anatomical landmarks. The accuracy was most sensitive to the Poisson's ratio and the boundary condition. Best results were achieved for accurate boundary conditions, appropriate Poisson's ratios and models where fibroglandular tissue was at most four times stiffer than fatty tissue. These configurations reduced the mean (maximum) distance of the landmarks from 6.6 mm (12.4 mm) to 2.1 mm (3.4 mm) averaged over all experiments.

Feasibility of a novel deformable image registration technique to facilitate classification, targeting, and monitoring of tumor and normal tissue

PURPOSE

To investigate the feasibility of a biomechanical-based deformable image registration technique for the integration of multimodality imaging, image guided treatment, and response monitoring.

METHODS AND MATERIALS

A multiorgan deformable image registration technique based on finite element modeling (FEM) and surface projection alignment of selected regions of interest with biomechanical material and interface models has been developed. FEM also provides an inherent method for direct tracking specified regions through treatment and follow-up.

RESULTS

The technique was demonstrated on 5 liver cancer patients. Differences of up to 1 cm of motion were seen between the diaphragm and the tumor center of mass after deformable image registration of exhale and inhale CT scans. Spatial differences of 5 mm or more were observed for up to 86% of the surface of the defined tumor after deformable image registration of the computed tomography (CT) and magnetic resonance images. Up to 6.8 mm of motion was observed for the tumor after deformable image registration of the CT and cone-beam CT scan after rigid registration of the liver. Deformable registration of the CT to the follow-up CT allowed a more accurate assessment of tumor response.

CONCLUSIONS

This biomechanical-based deformable image registration technique incorporates classification, targeting, and monitoring of tumor and normal tissue using one methodology.

Application of soft tissue modelling to image-guided surgery

The deformation of soft tissue compromises the accuracy of image-guided surgery based on preoperative images, and restricts its applicability to surgery on or near bony structures. One way to overcome these limitations is to combine biomechanical models with sparse intraoperative data, in order to realistically warp the preoperative image to match the surgical situation. We detail the process of biomechanical modelling in the context of image-guided surgery. We focus in particular on the finite element method, which is shown to be a promising approach, and review the constitutive relationships which have been suggested for representing tissue during surgery. Appropriate intraoperative measurements are required to constrain the deformation, and we discuss the potential of the modalities which have been applied to this task. This technology is on the verge of transition into clinical practice, where it promises to increase the guidance accuracy and facilitate less invasive interventions. We describe here how soft tissue modelling techniques have been applied to image-guided surgery applications.

Anisotropic multi-scale fluid registration: evaluation in magnetic resonance breast imaging

Registration using models of compressible viscous fluids has not found the general application of some other techniques (e.g., free-form-deformation (FFD)) despite its ability to model large diffeomorphic deformations. We report on a multi-resolution fluid registration algorithm which improves on previous work by (a) directly solving the Navier-Stokes equation at the resolution of the images, (b) accommodating image sampling anisotropy using semi-coarsening and implicit smoothing in a full multi-grid (FMG) solver and (c) exploiting the inherent multi-resolution nature of FMG to implement a multi-scale approach. Evaluation is on five magnetic resonance (MR) breast images subject to six biomechanical deformation fields over 11 multi-resolution schemes. Quantitative assessment is by tissue overlaps and target registration errors and by registering using the known correspondences rather than image features to validate the fluid model. Context is given by comparison with a validated FFD algorithm and by application to images of volunteers subjected to large applied deformation. The results show that fluid registration of 3D breast MR images to sub-voxel accuracy is possible in minutes on a 1.6 GHz Linux-based Athlon processor with coarse solutions obtainable in a few tens of seconds. Accuracy and computation time are comparable to FFD techniques validated for this application.

Tomography-based 3-D anisotropic elastography using boundary measurements

While ultrasound- and magnetic resonance-based elastography techniques have proved to be powerful biomedical imaging tools, most approaches assume isotropic material properties. In this paper, a general framework is developed for tomography-based anisotropic elastography. An anatomically well-motivated piece-wise homogeneous model is proposed to represent a class of biological objects consisting of different regions. With established tomography modality, static displacements are measured on the entire external and internal boundaries, and the force distribution is recorded on part of the external surface. A principle is proposed to identify the anisotropic elastic moduli of the constituent regions with the obtained boundary measurements. The reconstruction procedure is optimization-based with minimizing an objective function that measures the difference between the predicted and observed displacements. Analytic gradients of the objective function with respect to the elastic moduli are calculated using an adjoint method, and are utilized to significantly improve the numerical efficiency. Simulations are performed to identify the elastic moduli in a breast phantom consisting of soft tissue and a hard tumor. For isotropic phantom, one set of the boundary measurements enables unique reconstruction results for the tissue and tumor. For anisotropic phantom, however, multiple sets of the measurements corresponding to different deformation modes become necessary.

Accuracy of finite element model-based multi-organ deformable image registration

As more pretreatment imaging becomes integrated into the treatment planning process and full three-dimensional image-guidance becomes part of the treatment delivery the need for a deformable image registration technique becomes more apparent. A novel finite element model-based multiorgan deformable image registration method, MORFEUS, has been developed. The basis of this method is twofold: first, individual organ deformation can be accurately modeled by deforming the surface of the organ at one instance into the surface of the organ at another instance and assigning the material properties that allow the internal structures to be accurately deformed into the secondary position and second, multi-organ deformable alignment can be achieved by explicitly defining the deformation of a subset of organs and assigning surface interfaces between organs. The feasibility and accuracy of the method was tested on MR thoracic and abdominal images of healthy volunteers at inhale and exhale. For the thoracic cases, the lungs and external surface were explicitly deformed and the breasts were implicitly deformed based on its relation to the lung and external surface. For the abdominal cases, the liver, spleen, and external surface were explicitly deformed and the stomach and kidneys were implicitly deformed. The average accuracy (average absolute error) of the lung and liver deformation, determined by tracking visible bifurcations, was 0.19 (s.d.: 0.09), 0.28 (s.d.: 0.12) and 0.17 (s.d.: 0.07) cm, in the LR, AP, and IS directions, respectively. The average accuracy of implicitly deformed organs was 0.11 (s.d.: 0.11), 0.13 (s.d.: 0.12), and 0.08 (s.d.: 0.09) cm, in the LR, AP, and IS directions, respectively. The average vector magnitude of the accuracy was 0.44 (s.d.: 0.20) cm for the lung and liver deformation and 0.24 (s.d.: 0.18) cm for the implicitly deformed organs. The two main processes, explicit deformation of the selected organs and finite element analysis calculations, require less than 120 and 495 s, respectively. This platform can facilitate the integration of deformable image registration into online image guidance procedures, dose calculations, and tissue response monitoring as well as performing multi-modality image registration for purposes of treatment planning.