A biomechanical model of mammographic compressions

Estimation of the biomechanical mammographic deformation of the breast using machine learning models

BACKGROUND

A typical problem in the registration of MRI and X-ray mammography is the nonlinear deformation applied to the breast during mammography. We have developed a method for virtual deformation of the breast using a biomechanical model automatically constructed from MRI. The virtual deformation is applied in two steps: unloaded state estimation and compression simulation. The finite element method is used to solve the deformation process. However, the extensive computational cost prevents its usage in clinical routine.

METHODS

We propose three machine learning models to overcome this problem: an extremely randomized tree (first model), extreme gradient boosting (second model), and deep learning-based bidirectional long short-term memory with an attention layer (third model) to predict the deformation of a biomechanical model. We evaluated our methods with 516 breasts with realistic compression ratios up to 76%.

FINDINGS

We first applied one-fold validation, in which the second and third models performed better than the first model. We then applied ten-fold validation. For the unloaded state estimation, the median RMSE for the second and third models is 0.8 mm and 1.2 mm, respectively. For the compression, the median RMSE is 3.4 mm for both models. We evaluated correlations between model accuracy and characteristics of the clinical datasets such as compression ratio, breast volume, and tissue types.

INTERPRETATION

Using the proposed models, we achieved accurate results comparable to the finite element model, with a speedup of factor 240 using the extreme gradient boosting model. These proposed models can replace the finite element model simulation, enabling clinically relevant real-time application.

A novel finite element model-based navigation system-supported workflow for breast tumor excision

In the case of female breast cancer, a breast-conserving excision is often desirable. This surgery is based on preoperatively gathered MRI, mammography, and sonography images. These images are recorded in multiple patient positions, e. g., 2D mammography images in standing position with a compressed breast and 3D MRI images in prone position. In contrast, the surgery happens in supine or beach chair position. Due to these different perspectives and the flexible, thus challenging, breast tissue, the excision puts high demands on the physician. Therefore, this publication presents a novel eight-step excision support workflow that can be used to include information captured preoperatively through medical imaging based on a finite element (FE) model. In addition, an indoor positioning system is integrated in the workflow in order to track surgical devices and the sonography transducer during surgery. The preoperative part of the navigation system-supported workflow is outlined exemplarily based on first experimental results including 3D scans of a patient in different patient positions and her MRI images. Graphical Abstract Finite Element model based navigation system supported workflow for breast tumor excision is based on eight steps and allows inclusion of information from medical images recorded in multiple patient positions.

Surface deformation tracking and modelling of soft materials

Many computer vision algorithms have been presented to track surface deformations, but few have provided a direct comparison of measurements with other stereoscopic approaches and physics-based models. We have previously developed a phase-based cross-correlation algorithm to track dense distributions of displacements over three-dimensional surfaces. In the present work, we compare this algorithm with one that uses an independent tracking system, derived from an array of fluorescent microspheres. A smooth bicubic Hermite mesh was fitted to deformations obtained from the phase-based cross-correlation data. This mesh was then used to estimate the microsphere locations, which were compared to stereo reconstructions of the microsphere positions. The method was applied to a 35 mm × 35 mm × 35 mm soft silicone gel cube under indentation, with three square bands of microspheres placed around the indenter tip. At an indentation depth of 4.5 mm, the root-mean-square (RMS) differences between the reconstructed positions of the microspheres and their identified positions for the inner, middle, and outer bands were 60 µm, 20 µm, and 19 µm, respectively. The usefulness of the strain-tracking data for physics-based finite element modelling of large deformation mechanics was then demonstrated by estimating a neo-Hookean stiffness parameter for the gel. At the optimal constitutive parameter estimate, the RMS difference between the measured microsphere positions and their finite element model-predicted locations was 143 µm.

Towards an in-plane methodology to track breast lesions using mammograms and patient-specific finite-element simulations

In breast cancer screening or diagnosis, it is usual to combine different images in order to locate a lesion as accurately as possible. These images are generated using a single or several imaging techniques. As x-ray-based mammography is widely used, a breast lesion is located in the same plane of the image (mammogram), but tracking it across mammograms corresponding to different views is a challenging task for medical physicians. Accordingly, simulation tools and methodologies that use patient-specific numerical models can facilitate the task of fusing information from different images. Additionally, these tools need to be as straightforward as possible to facilitate their translation to the clinical area. This paper presents a patient-specific, finite-element-based and semi-automated simulation methodology to track breast lesions across mammograms. A realistic three-dimensional computer model of a patient's breast was generated from magnetic resonance imaging to simulate mammographic compressions in cranio-caudal (CC, head-to-toe) and medio-lateral oblique (MLO, shoulder-to-opposite hip) directions. For each compression being simulated, a virtual mammogram was obtained and posteriorly superimposed to the corresponding real mammogram, by sharing the nipple as a common feature. Two-dimensional rigid-body transformations were applied, and the error distance measured between the centroids of the tumors previously located on each image was 3.84 mm and 2.41 mm for CC and MLO compression, respectively. Considering that the scope of this work is to conceive a methodology translatable to clinical practice, the results indicate that it could be helpful in supporting the tracking of breast lesions.

Breast tissue stiffness estimation for surgical guidance using gravity-induced excitation

Tissue stiffness interrogation is fundamental in breast cancer diagnosis and treatment. Furthermore, biomechanical models for predicting breast deformations have been created for several breast cancer applications. Within these applications, constitutive mechanical properties must be defined and the accuracy of this estimation directly impacts the overall performance of the model. In this study, we present an image-derived computational framework to obtain quantitative, patient specific stiffness properties for application in image-guided breast cancer surgery and interventions. The method uses two MR acquisitions of the breast in different supine gravity-loaded configurations to fit mechanical properties to a biomechanical breast model. A reproducibility assessment of the method was performed in a test-retest study using healthy volunteers and was further characterized in simulation. In five human data sets, the within subject coefficient of variation ranged from 10.7% to 27% and the intraclass correlation coefficient ranged from 0.91-0.944 for assessment of fibroglandular and adipose tissue stiffness. In simulation, fibroglandular content and deformation magnitude were shown to have significant effects on the shape and convexity of the objective function defined by image similarity. These observations provide an important step forward in characterizing the use of nonrigid image registration methodologies in conjunction with biomechanical models to estimate tissue stiffness. In addition, the results suggest that stiffness estimation methods using gravity-induced excitation can reliably and feasibly be implemented in breast cancer surgery/intervention workflows.

Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation

PURPOSE

The authors are developing a series of computational breast phantoms based on breast CT data for imaging research. In this work, the authors develop a program that will allow a user to alter the phantoms to simulate the effect of gravity and compression of the breast (craniocaudal or mediolateral oblique) making the phantoms applicable to multimodality imaging.

METHODS

This application utilizes a template finite-element (FE) breast model that can be applied to their presegmented voxelized breast phantoms. The FE model is automatically fit to the geometry of a given breast phantom, and the material properties of each element are set based on the segmented voxels contained within the element. The loading and boundary conditions, which include gravity, are then assigned based on a user-defined position and compression. The effect of applying these loads to the breast is computed using a multistage contact analysis in FEBio, a freely available and well-validated FE software package specifically designed for biomedical applications. The resulting deformation of the breast is then applied to a boundary mesh representation of the phantom that can be used for simulating medical images. An efficient script performs the above actions seamlessly. The user only needs to specify which voxelized breast phantom to use, the compressed thickness, and orientation of the breast.

RESULTS

The authors utilized their FE application to simulate compressed states of the breast indicative of mammography and tomosynthesis. Gravity and compression were simulated on example phantoms and used to generate mammograms in the craniocaudal or mediolateral oblique views. The simulated mammograms show a high degree of realism illustrating the utility of the FE method in simulating imaging data of repositioned and compressed breasts.

CONCLUSIONS

The breast phantoms and the compression software can become a useful resource to the breast imaging research community. These phantoms can then be used to evaluate and compare imaging modalities that involve different positioning and compression of the breast.

An Anthropometric-Based Subject-Specific Finite Element Model of the Human Breast for Predicting Large Deformations

The large deformation of the human breast threatens proper nodules tracking when the subject mammograms are used as pre-planning data for biopsy. However, techniques capable of accurately supporting the surgeons during biopsy are missing. Finite element (FE) models are at the basis of currently investigated methodologies to track nodules displacement. Nonetheless, the impact of breast material modeling on the mechanical response of its tissues (e.g., tumors) is not clear. This study proposes a subject-specific FE model of the breast, obtained by anthropometric measurements, to predict breast large deformation. A healthy breast subject-specific FE parametric model was developed and validated by Cranio-caudal (CC) and Medio-Lateral Oblique (MLO) mammograms. The model was successively modified, including nodules, and utilized to investigate the effect of nodules size, typology, and material modeling on nodules shift under the effect of CC, MLO, and gravity loads. Results show that a Mooney–Rivlin material model can estimate healthy breast large deformation. For a pathological breast, under CC compression, the nodules displacement is very close to zero when a linear elastic material model is used. Finally, when nodules are modeled, including tumor material properties, under CC, or MLO or gravity loads, nodules shift shows ~15% average relative difference.

Multi-axis dose accumulation of noninvasive image-guided breast brachytherapy through biomechanical modeling of tissue deformation using the finite element method

PURPOSE

Noninvasive image-guided breast brachytherapy delivers conformal HDR (192)Ir brachytherapy treatments with the breast compressed, and treated in the cranial-caudal and medial-lateral directions. This technique subjects breast tissue to extreme deformations not observed for other disease sites. Given that, commercially-available software for deformable image registration cannot accurately co-register image sets obtained in these two states, a finite element analysis based on a biomechanical model was developed to deform dose distributions for each compression circumstance for dose summation.

MATERIAL AND METHODS

The model assumed the breast was under planar stress with values of 30 kPa for Young's modulus and 0.3 for Poisson's ratio. Dose distributions from round and skin-dose optimized applicators in cranial-caudal and medial-lateral compressions were deformed using 0.1 cm planar resolution. Dose distributions, skin doses, and dose-volume histograms were generated. Results were examined as a function of breast thickness, applicator size, target size, and offset distance from the center.

RESULTS

Over the range of examined thicknesses, target size increased several millimeters as compression thickness decreased. This trend increased with increasing offset distances. Applicator size minimally affected target coverage, until applicator size was less than the compressed target size. In all cases, with an applicator larger or equal to the compressed target size, > 90% of the target covered by > 90% of the prescription dose. In all cases, dose coverage became less uniform as offset distance increased and average dose increased. This effect was more pronounced for smaller target-applicator combinations.

CONCLUSIONS

The model exhibited skin dose trends that matched MC-generated benchmarking results within 2% and clinical observations over a similar range of breast thicknesses and target sizes. The model provided quantitative insight on dosimetric treatment variables over a range of clinical circumstances. These findings highlight the need for careful target localization and accurate identification of compression thickness and target offset.

A tissue stabilization device for MRI-guided breast biopsy

We present a breast tissue stabilization device that can be used in magnetic resonance imaging-guided biopsy. The device employs adjustable support plates with an optimized geometry to minimize the biopsy target displacement using smaller compression than the conventional parallel plates approach. It is expected that the reduced compression will cause less patient discomfort and improve image quality by enhancing the contrast intake. Precomputed optimal positions of the stabilization plates for a given biopsy target location are provided in a look-up table. The results of several experiments with a prototype of the device carried out on chicken breast tissue demonstrate the effectiveness of the new design when compared with conventional stabilization methods. The proposed stabilization mechanism provides excellent flexibility in selecting the needle insertion point and can be used in manual as well as robot-assisted biopsy procedures.

Experimental and numerical analysis of soft tissue stiffness measurement using manual indentation device--significance of indentation geometry and soft tissue thickness

BACKGROUND

Indentation techniques haves been applied to measure stiffness of human soft tissues. Tissue properties and geometry of the indentation instrument control the measured response.

METHODS

Mechanical roles of different soft tissues were characterized to understand the performance of the indentation instrument. An optimal instrument design was investigated. Experimental indentations in forearm of human subjects (N = 11) were conducted. Based on peripheral quantitative computed tomography imaging, a finite element (FE) model for indentation was created. The model response was matched with the experimental data.

RESULTS

Optimized values for the elastic modulus of skin and adipose tissue were 130.2 and 2.5 kPa, respectively. The simulated indentation response was 3.9 ± 1.2 (mean ± SD) and 4.9 ± 2.0 times more sensitive to changes in the elastic modulus of the skin than to changes in the elastic modulus of adipose tissue and muscle, respectively. Skin thickness affected sensitivity of the instrument to detect changes in stiffness of the underlying tissues.

CONCLUSION

Finite element modeling provides a feasible method to quantitatively evaluate the geometrical aspects and the sensitivity of an indentation measurement device. Systematically, the skin predominantly controlled the indentation response regardless of the indenter geometry or variations in the volume of different soft tissues.

An H∞ strategy for strain estimation in ultrasound elastography using biomechanical modeling constraint

The purpose of ultrasound elastography is to identify lesions by reconstructing the hardness characteristics of tissue reconstructed from ultrasound data. Conventional quasi-static ultrasound elastography is easily applied to obtain axial strain components along the compression direction, with the results inverted to represent the distribution of tissue hardness under the assumption of constant internal stresses. However, previous works of quasi-static ultrasound elastography have found it difficult to obtain the lateral and shear strain components, due to the poor lateral resolution of conventional ultrasound probes. The physical nature of the strain field is a continuous vector field, which should be fully described by the axial, lateral, and shear strain components, and the clinical value of lateral and shear strain components of deformed tissue is gradually being recognized by both engineers and clinicians. Therefore, a biomechanical-model-constrained filtering framework is proposed here for recovering a full displacement field at a high spatial resolution from the noisy ultrasound data. In our implementation, after the biomechanical model constraint is integrated into the state-space equation, both the axial and lateral displacement components can be recovered at a high spatial resolution from the noisy displacement measurements using a robust H∞ filter, which only requires knowledge of the worst-case noise levels in the measurements. All of the strain components can then be calculated by applying a gradient operator to the recovered displacement field. Numerical experiments on synthetic data demonstrated the robustness and effectiveness of our approach, and experiments on phantom data and in-vivo clinical data also produced satisfying results.

Deformable medical image registration: a survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

Computer assisted planning of autologous fat grafting in breast

Autologous fat grafting is an emerging and promising surgical technique in regenerative medicine, and its application is quickly spreading in plastic and reconstructive surgery of the breast. However, despite the advantages of the technique, surgical complications may occur, such as implanted tissue necrosis and resorption and onset of microcalcifications. In view of the hypothesis that the uniformity of the lipoaspirate transplantation is related to graft survival and a lower probability of complications, we developed an interactive lipomodeling planning software application based on a genetic algorithm that allows automatic optimization of the uniformity of fat tissue distribution. The input dataset consists of a 3D model of the patient's thorax, created from MRI scans, on which relevant structures are segmented. The developed software was tested starting from either an automatically generated plan or an initial guess of the optimal surgical plan, and in both cases the application yielded a consistent improvement in the planned fat tissue distribution by optimizing the position of the insertion points and the direction of the insertion pathways. On the basis of the simulations performed, the use of genetic algorithms for optimization of the geometry of autologous fat transfer in the breast proved to be effective. These results will foster further activities focused on the comparison of predicted optimized geometries and those obtained in real surgical cases as a means of obtaining a deeper knowledge of the potential influence of a uniform fat tissue distribution on the quality of the surgical outcome. The presented application is also put forward as representing a noteworthy step towards the clinical application of computer assisted planning tools in breast surgery.

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.

Identification of the material parameters of soft tissues in the compressed leg

Elastic compression is recommended in prophylaxis and the treatment of venous disorder of the human leg. However, the mechanisms of compression are not completely understood and the response of internal tissues to the external pressure is partially unknown. To address this later issue, a 3D FE model of a human leg is developed. The geometry is derived from 3D CT scans. The FE model is made up of soft tissues and rigid bones. An inverse method is applied to identify the properties of soft tissues which are modelled as hyperelastic, near-incompressible, homogeneous and isotropic materials. The principle is to calibrate the constitutive properties using CT scans carried out with and without the presence of a compression sock. The deformed geometry computed by the calibrated FE model is in agreement with the geometry deduced from the CT scans. The model also provides the internal pressure distribution, which may lead to medical exploitation in the future.

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.

Mixed experimental and numerical approach for characterizing the biomechanical response of the human leg under elastic compression

Elastic compression is the process of applying an elastic garment around the leg, supposedly for enhancing the venous flow. However, the response of internal tissues to the external pressure is still partially unknown. In order to improve the scientific knowledge about this topic, a slice of a human leg wearing an elastic garment is modeled by the finite-element method. The elastic properties of the tissues inside the leg are identified thanks to a dedicated approach based on image processing. After calibrating the model with magnetic resonance imaging scans of a volunteer, the pressure transmitted through the internal tissues of the leg is computed. Discrepancies of more than 35% are found from one location to another, showing that the same compression garment cannot be applied for treating deficiencies of the deep venous system or deficiencies of the large superficial veins. Moreover, it is shown that the internal morphology of the human leg plays an important role. Accordingly, the approach presented in this paper may provide useful information for adapting compression garments to the specificity of each patient.

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.

Frictional contact mechanics methods for soft materials: Application to tracking breast cancers

Mammography is currently the most widely used screening and diagnostic tool for breast cancer. Because X-ray images are 2D projections of a 3D object, it is not trivial to localise features identified in mammogram pairs within the breast volume. Furthermore, mammograms represent highly deformed configurations of the breast under compression, thus the tumour localisation process relies on the clinician's experience. Biomechanical models of the breast undergoing mammographic compressions have been developed to overcome this limitation. In this study, we present the development of a modelling framework that implements Coulomb's frictional law with a finite element analysis using a C(1)-continuous Hermite mesh. We compared two methods of this contact mechanics implementation: the penalty method, and the augmented Lagrangian method, the latter of which is more accurate but computationally more expensive compared to the former. Simulation results were compared with experimental data from a soft silicon gel phantom in order to evaluate the modelling accuracy of each method. Both methods resulted in surface-deformation root-mean-square errors of less than 2mm, whilst the maximum internal marker prediction error was less than 3mm when simulating two mammographic-like compressions. Simulation results were confirmed using the augmented Lagrangian method, which provided similar accuracy. We conclude that contact mechanics on soft elastic materials using the penalty method with an appropriate choice of the penalty parameters provides sufficient accuracy (with contact constraints suitably enforced), and may thus be useful for tracking breast tumours between clinical images.