Factors influencing the accuracy of biomechanical breast models

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.

Soft-tissue simulation of the breast for intraoperative navigation and fusion of preoperative planning

Computational preoperative planning offers the opportunity to reduce surgery time and patient risk. However, on soft tissues such as the breast, deviations between the preoperative and intraoperative settings largely limit the applicability of preoperative planning. In this work, we propose a high-performance accurate simulation model of the breast, to fuse preoperative information with the intraoperative deformation setting. Our simulation method encompasses three major elements: high-quality finite-element modeling (FEM), efficient handling of anatomical couplings for high-performance computation, and personalized parameter estimation from surface scans. We show the applicability of our method on two problems: 1) transforming high-quality preoperative scans to the intraoperative setting for fusion of preoperative planning data, and 2) real-time tracking of breast tumors for navigation during intraoperative radiotherapy. We have validated our methodology on a test cohort of nine patients who underwent tumor resection surgery and intraoperative radiotherapy, and we have quantitatively compared simulation results to intraoperative scans. The accuracy of our simulation results suggest clinical viability of the proposed methodology.

Quantity versus quality: Age-related differences in muscle volume, intramuscular fat, and mechanical properties in the triceps surae

With aging comes reductions in the quality and size of skeletal muscle. These changes influence the force-generating capacity of skeletal muscle and contribute to movement deficits that accompany aging. Although declines in strength remain a significant barrier to mobility in older adults, the association between age-related changes in muscle structure and function remain unresolved. In this study, we compared age-related differences in (i) muscle volume and architecture, (ii) the quantity and distribution of intramuscular fat, and (iii) muscle shear modulus (an index of stiffness) in the triceps surae in 21 younger (24.6 ± 4.3 years) and 15 older (70.4 ± 2.4 years) healthy adults. Additionally, we explored the relationship between muscle volume, architecture, intramuscular fat and ankle plantar flexion strength in young and older adults. Magnetic resonance imaging was used to determine muscle volume and intramuscular fat content. B-mode ultrasound was used to quantify muscle architecture, shear-wave elastography was used to measure shear modulus, and ankle strength was measured during maximal isometric plantar flexion contractions. We found that older adults displayed higher levels of intramuscular fat yet similar muscle volumes in the medial (MG) and lateral gastrocnemius (LG) and soleus, compared to younger adults. These age-related higher levels of intramuscular fat were associated with lower muscle shear modulus in the LG and MG. We also found that muscle physiological cross-sectional area (PCSA) that accounted for age-associated differences in intramuscular fat showed a modest increase in its association with ankle strength compared to PCSA that did not account for fat content. This highlights that skeletal muscle fat infiltration plays a role in age-related strength deficits, but does not fully explain the age-related loss in muscle strength, suggesting that other factors play a more significant role.

Automatic liver tumor localization using deep learning-based liver boundary motion estimation and biomechanical modeling (DL-Bio)

PURPOSE

Recently, two-dimensional-to-three-dimensional (2D-3D) deformable registration has been applied to deform liver tumor contours from prior reference images onto estimated cone-beam computed tomography (CBCT) target images to automate on-board tumor localizations. Biomechanical modeling has also been introduced to fine-tune the intra-liver deformation-vector-fields (DVFs) solved by 2D-3D deformable registration, especially at low-contrast regions, using tissue elasticity information and liver boundary DVFs. However, the caudal liver boundary shows low contrast from surrounding tissues in the cone-beam projections, which degrades the accuracy of the intensity-based 2D-3D deformable registration there and results in less accurate boundary conditions for biomechanical modeling. We developed a deep-learning (DL)-based method to optimize the liver boundary DVFs after 2D-3D deformable registration to further improve the accuracy of subsequent biomechanical modeling and liver tumor localization.

METHODS

The DL-based network was built based on the U-Net architecture. The network was trained in a supervised fashion to learn motion correlation between cranial and caudal liver boundaries to optimize the liver boundary DVFs. Inputs of the network had three channels, and each channel featured the 3D DVFs estimated by the 2D-3D deformable registration along one Cartesian direction (x, y, z). To incorporate patient-specific liver boundary information into the DVFs, the DVFs were masked by a liver boundary ring structure generated from the liver contour of the prior reference image. The network outputs were the optimized DVFs along the liver boundary with higher accuracy. From these optimized DVFs, boundary conditions were extracted for biomechanical modeling to further optimize the solution of intra-liver tumor motion. We evaluated the method using 34 liver cancer patient cases, with 24 for training and 10 for testing. We evaluated and compared the performance of three methods: 2D-3D deformable registration, 2D-3D-Bio (2D-3D deformable registration with biomechanical modeling), and DL-Bio (DL model prediction with biomechanical modeling). The tumor localization errors were quantified through calculating the center-of-mass-errors (COMEs), DICE coefficients, and Hausdorff distance between deformed liver tumor contours and manually segmented "gold-standard" contours.

RESULTS

The predicted DVFs by the DL model showed improved accuracy at the liver boundary, which translated into more accurate liver tumor localizations through biomechanical modeling. On a total of 90 evaluated images and tumor contours, the average (± sd) liver tumor COMEs of the 2D-3D, 2D-3D-Bio, and DL-Bio techniques were 4.7 ± 1.9 mm, 2.9 ± 1.0 mm, and 1.7 ± 0.4 mm. The corresponding average (± sd) DICE coefficients were 0.60 ± 0.12, 0.71 ± 0.07, and 0.78 ± 0.03; and the average (± sd) Hausdorff distances were 7.0 ± 2.6 mm, 5.4 ± 1.5 mm, and 4.5 ± 1.3 mm, respectively.

CONCLUSION

DL-Bio solves a general correlation model to improve the accuracy of the DVFs at the liver boundary. With improved boundary conditions, the accuracy of biomechanical modeling can be further increased for accurate intra-liver low-contrast tumor localization.

Measurement of the hyperelastic properties of 72 normal homogeneous and heterogeneous ex vivo breast tissue samples

The mechanical properties of normal soft tissues, including breast tissue, have been of interest to the biomedical research community as there are many clinical and industrial applications that can benefit from quantitative information characterizing such properties. For instance, computer assisted surgery planning, elastography for breast cancer diagnosis, and bra design can all involve biomechanical modeling of the breast to predict its deformation or stress distribution. It is known that most biological soft tissues, including breast tissue, exhibit nonlinear mechanical response over large strains. As such, it is necessary to model such tissues as hyperelastic. In this work, we used indentation testing to estimate the hyperelastic parameters of 4 models (3rd order Ogden, 5-term polynomial, Veronda-Westman and Yeoh) estimated from 72 healthy ex vivo breast tissue samples covering adipose, fibroglandular, and mixed tissue. All estimated parameter sets were confirmed to represent stable material using Drucker's stability criterion. We observed that all three tissue types were statistically similar solidifying the use of homogenous breast modelling over large strain simulation.

Multimodal Patient-Specific Registration for Breast Imaging Using Biomechanical Modeling with Reference to AI Evaluation of Breast Tumor Change

Background: The strategy to combat the problem associated with large deformations in the breast due to the difference in the medical imaging of patient posture plays a vital role in multimodal medical image registration with artificial intelligence (AI) initiatives. How to build a breast biomechanical model simulating the large-scale deformation of soft tissue remains a challenge but is highly desirable. Methods: This study proposed a hybrid individual-specific registration model of the breast combining finite element analysis, property optimization, and affine transformation to register breast images. During the registration process, the mechanical properties of the breast tissues were individually assigned using an optimization process, which allowed the model to become patient specific. Evaluation and results: The proposed method has been extensively tested on two datasets collected from two independent institutions, one from America and another from Hong Kong. Conclusions: Our method can accurately predict the deformation of breasts from the supine to prone position for both the Hong Kong and American samples, with a small target registration error of lesions.

The Biomechanics of the Fibrocystic Breasts at Finite Compressive Deformation

The deformation of the human breast, especially that of the female, under variable pressure conditions, has been a recent focus for researchers, both in the computational biomechanics, computational biology and the health sector. When the deformation of the breast is large, it hampers suitable cyst tracing as a mammographic biopsy precontrive data. Finite element methods (FEM) has been instrumental in the currently studied practices to trail nodules dislocation. However, the effect of breast material constitution, especially that of a fibrocystic composition, on the biomechanical response of these nodules has gained less attention. The present study is aimed at developing a finite element fibrocystic breast model within the frame of biosolid mechanics and material hyperelasticity to model the breast deformation at finite strain. The geometry of a healthy stress‐free breast is modelled from a magnetic resonance image (MRI) using tissues deformations measurements and solid modelling technology. Results show that the incompressible Neo-Hookean and Mooney-Rivlin constitutive models can approximate large deformation of a stressed breast. In addition to the areola (i.e. nipple base), the surrounding area of the cyst together with its interface with the breast tissue is the maximum stressed region when the breast is subjected to compressive pressure. This effect can lead to an internal tear of the breast that could degenerate to malignant tissue.

Finite Element Breast Simulation for Sonography Image Registration

In case of female breast cancer, a breast conserving excision is often necessary. For this purpose, information from multiple medical imaging techniques have to be combined. Sonography imaging is essential for dense breast tissue and the only medical imaging technique available during surgery. During sonography of the outer breast quadrants the woman is usually in contralateral posterior oblique position, being in supine orientation while holding her ipsilateral arm over the head. Thus, these images cannot be directly registered with MRI or mammography images because these imaging technologies are performed in other patient positions with hands on the side of the body. Thus, we present a novel Finite Element approach how to enable a sonography image registration by showing the first time how to transfer the supine position with the arm straight on side into a supine position with the ipsilateral arm over the head which can be used to include information from MRI or mammography images. This approach is shown and validated with 3D scanner breast surface data as proof of concept. When comparing the simulation result with a 3D surface scan in supine orientation with the arm over the head, a mean surface distance error of 1.57 mm is achieved.

Deformable Registration for Dose Accumulation

As deformable image registration makes its way into the clinical routine, the summation of doses from fractionated treatment regimens to evaluate cumulative doses to targets and healthy tissues is also becoming a frequently utilized tool in the context of image-guided adaptive radiotherapy. Accounting for daily geometric changes using deformable image registration and dose accumulation potentially enables a better understanding of dose-volume-effect relationships, with the goal of translation of this knowledge to personalization of treatment, to further enhance treatment outcomes. Treatment adaptation involving image deformation requires patient-specific quality assurance of the image registration and dose accumulation processes, to ensure that uncertainties in the 3D dose distributions are identified and appreciated from a clinical relevance perspective. While much research has been devoted to identifying and managing the uncertainties associated with deformable image registration and dose accumulation approaches, there are still many unanswered questions. Here, we provide a review of current deformable image registration and dose accumulation techniques, and related clinical application. We also discuss salient issues that need to be deliberated when applying deformable algorithms for dose mapping and accumulation in the context of adaptive radiotherapy and response assessment.

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.

Optimization method for the determination of Mooney-Rivlin material coefficients of the human breasts in-vivo using static and dynamic finite element models

It has been a long-standing problem in the engineering design of bra for optimal support and shaping due to the difficulty of quantifying the hyper-elastic properties of human breasts. The objective of this study is to determine an optimal approach to obtain the non-linear properties of breast soft tissues and the corresponding deformations during motions. The Mooney-Rivlin material parameters of the breasts in-vivo were verified through an optimization process that involved iteratively changing the material coefficients with the integration of static and dynamic finite element models. Theoretical equations of a rigid-flexible coupled system during the motion of forward-leaning were established with gravitational, centrifugal and Coriolis forces to simulate the dynamic deformation of the flexible breasts. The resultant, optimally generated, coefficients of the Mooney-Rivlin hyperelastic material type for the breast were found. This new set of breast material coefficients was verified by finite element analysis of the breast deformation during forward-leaning and running movement. The method proposed in this study provides an effective way to determine the breast properties for predicting breast deformation and analysis of the bra-breast contact mechanism and thus, improving the design of bras.

A biomechanical breast model evaluated with respect to MRI data collected in three different positions

BACKGROUND

Mammography is a specific type of breast imaging that uses low-dose X-rays to detect cancer in early stage. During the exam, the women breast is compressed between two plates in order to even out the breast thickness and to spread out the soft tissues. This technique improves exam quality but can be uncomfortable for the patient. The perceived discomfort can be assessed by the means of a breast biomechanical model. Alternative breast compression techniques may be computationally investigated trough finite elements simulations.

METHODS

The aim of this work is to develop and evaluate a new biomechanical Finite Element (FE) breast model. The complex breast anatomy is considered including adipose and glandular tissues, muscle, skin, suspensory ligaments and pectoral fascias. Material hyper-elasticity is modeled using the Neo-Hookean material models. The stress-free breast geometry and subject-specific constitutive models are derived using tissues deformations measurements from MR images.

FINDINGS

The breast geometry in three breast configurations were computed using the breast stress-free geometry together with the estimated set of equivalent Young's modulus (E_breast^r = 0.3 kPa, E_breast^l = 0.2 kPa, E_skin = 4 kPa, E_fascia = 120 kPa). The Hausdorff distance between estimated and measured breast geometries for prone, supine and supine tilted configurations is equal to 2.17 mm, 1.72 mm and 5.90 mm respectively.

INTERPRETATION

A subject-specific breast model allows a better characterization of breast mechanics. However, the model presents some limitations when estimating the supine tilted breast configuration. The results show clearly the difficulties to characterize soft tissues mechanics at large strain ranges with Neo-Hookean material models.

Optimizing Design With Extensive Simulation Data: A Case Study of Designing a Vacuum-Assisted Biopsy Tool

Design by Dragging (DBD) [1] is a virtual design tool, which displays three-dimensional (3D) visualizations of many simulation results obtained by sampling a large design space and ties this visual display together with a new user interface. The design space is explored through mouse-based interactions performed directly on top of the 3D data visualizations. Our previous study [1] introduced the realization of DBD with a simplistic example of biopsy needle design under a static bending force. This paper considers a realistic problem of designing a vacuum-assisted biopsy (VAB) needle that brings in more technical challenges to include dynamic tissue reaction forces, nonlinear tissue deformation, and progressive tissue damage in an integrated visualization with design suggestions. The emphasis is placed on the inverse design strategy in DBD, which involves clicking directly on a stress (or other output field parameter) contour and dragging it to a new (usually preferable) position on the contour. Subsequently, the software computes the best fit for the design variables for generating a new output stress field based on the user input. Three cases demonstrated how the inverse design can assist users in intuitively and interactively approaching desired design solutions. This paper illustrates how virtual prototyping may be used to replace (or reduce reliance on) purely experimental trial-and-error methods for achieving optimal designs.

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.

Validation of biomechanical deformable image registration in the abdomen, thorax, and pelvis in a commercial radiotherapy treatment planning system

PURPOSE

The accuracy of deformable image registration tools can vary widely between imaging modalities and specific implementations of the same algorithms. A biomechanical model-based algorithm initially developed in-house at an academic institution was translated into a commercial radiotherapy treatment planning system and validated for multiple imaging modalities and anatomic sites.

METHODS

Biomechanical deformable registration (Morfeus) is a geometry-driven algorithm based on the finite element method. Boundary conditions are derived from the model-based segmentation of controlling structures in each image which establishes a point-to-point surface correspondence. For each controlling structure, material properties and fixed or sliding interfaces are assigned. The displacements of internal volumes for controlling structures and other structures implicitly deformed are solved with finite element analysis. Registration was performed for 74 patients with images (mean vector resolution) of thoracic and abdominal 4DCT (2.8 mm) and MR (5.3 mm), liver CT-MR (4.5 mm), and prostate MR (2.6 mm). Accuracy was quantified between deformed and actual target images using distance-to-agreement (DTA) for structure surfaces and the target registration error (TRE) for internal point landmarks.

RESULTS

The results of the commercial implementation were as follows. The mean DTA was ≤ 1.0 mm for controlling structures and 1.0-3.5 mm for implicitly deformed structures on average. TRE ranged from 2.0 mm on prostate MR to 5.1 mm on lung MR on average, within 0.1 mm or lower than the image voxel sizes. Accuracy was not overly sensitive to changes in the material properties or variability in structure segmentations, as changing these inputs affected DTA and TRE by ≤ 0.8 mm. Maximum DTA > 5 mm occurred for 88% of the structures evaluated although these were within the inherent segmentation uncertainty for 82% of structures. Differences in accuracy between the commercial and in-house research implementations were ≤ 0.5 mm for mean DTA and ≤ 0.7 mm for mean TRE.

CONCLUSIONS

Accuracy of biomechanical deformable registration evaluated on a large cohort of images in the thorax, abdomen and prostate was similar to the image voxel resolution on average across multiple modalities. Validation of this treatment planning system implementation supports biomechanical deformable registration as a versatile clinical tool to enable accurate target delineation at planning and treatment adaptation.

Use of image registration and fusion algorithms and techniques in radiotherapy: Report of the AAPM Radiation Therapy Committee Task Group No. 132

Image registration and fusion algorithms exist in almost every software system that creates or uses images in radiotherapy. Most treatment planning systems support some form of image registration and fusion to allow the use of multimodality and time-series image data and even anatomical atlases to assist in target volume and normal tissue delineation. Treatment delivery systems perform registration and fusion between the planning images and the in-room images acquired during the treatment to assist patient positioning. Advanced applications are beginning to support daily dose assessment and enable adaptive radiotherapy using image registration and fusion to propagate contours and accumulate dose between image data taken over the course of therapy to provide up-to-date estimates of anatomical changes and delivered dose. This information aids in the detection of anatomical and functional changes that might elicit changes in the treatment plan or prescription. As the output of the image registration process is always used as the input of another process for planning or delivery, it is important to understand and communicate the uncertainty associated with the software in general and the result of a specific registration. Unfortunately, there is no standard mathematical formalism to perform this for real-world situations where noise, distortion, and complex anatomical variations can occur. Validation of the software systems performance is also complicated by the lack of documentation available from commercial systems leading to use of these systems in undesirable 'black-box' fashion. In view of this situation and the central role that image registration and fusion play in treatment planning and delivery, the Therapy Physics Committee of the American Association of Physicists in Medicine commissioned Task Group 132 to review current approaches and solutions for image registration (both rigid and deformable) in radiotherapy and to provide recommendations for quality assurance and quality control of these clinical processes.

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.

Population of 224 realistic human subject-based computational breast phantoms

PURPOSE

To create a database of highly realistic and anatomically variable 3D virtual breast phantoms based on dedicated breast computed tomography (bCT) data.

METHODS

A tissue classification and segmentation algorithm was used to create realistic and detailed 3D computational breast phantoms based on 230 + dedicated bCT datasets from normal human subjects. The breast volume was identified using a coarse three-class fuzzy C-means segmentation algorithm which accounted for and removed motion blur at the breast periphery. Noise in the bCT data was reduced through application of a postreconstruction 3D bilateral filter. A 3D adipose nonuniformity (bias field) correction was then applied followed by glandular segmentation using a 3D bias-corrected fuzzy C-means algorithm. Multiple tissue classes were defined including skin, adipose, and several fractional glandular densities. Following segmentation, a skin mask was produced which preserved the interdigitated skin, adipose, and glandular boundaries of the skin interior. Finally, surface modeling was used to produce digital phantoms with methods complementary to the XCAT suite of digital human phantoms.

RESULTS

After rejecting some datasets due to artifacts, 224 virtual breast phantoms were created which emulate the complex breast parenchyma of actual human subjects. The volume breast density (with skin) ranged from 5.5% to 66.3% with a mean value of 25.3% ± 13.2%. Breast volumes ranged from 25.0 to 2099.6 ml with a mean value of 716.3 ± 386.5 ml. Three breast phantoms were selected for imaging with digital compression (using finite element modeling) and simple ray-tracing, and the results show promise in their potential to produce realistic simulated mammograms.

CONCLUSIONS

This work provides a new population of 224 breast phantoms based on in vivo bCT data for imaging research. Compared to previous studies based on only a few prototype cases, this dataset provides a rich source of new cases spanning a wide range of breast types, volumes, densities, and parenchymal patterns.

The effect of intramuscular fat on skeletal muscle mechanics: implications for the elderly and obese

Skeletal muscle accumulates intramuscular fat through age and obesity. Muscle quality, a measure of muscle strength per unit size, decreases in these conditions. It is not clear how fat influences this loss in performance. Changes to structural parameters (e.g. fibre pennation and connective tissue properties) affect the muscle quality. This study investigated the mechanisms that lead to deterioration in muscle performance due to changes in intramuscular fat, pennation and aponeurosis stiffness. A finite-element model of the human gastrocnemius was developed as a fibre-reinforced composite biomaterial containing contractile fibres within the base material. The base-material properties were modified to include intramuscular fat in five different ways. All these models with fat generated lower fibre stress and muscle quality than their lean counterparts. This effect is due to the higher stiffness of the tissue in the fatty models. The fibre deformations influence their interactions with the aponeuroses, and these change with fatty inclusions. Muscles with more compliant aponeuroses generated lower forces. The muscle quality was further reduced for muscles with lower pennation. This study shows that whole-muscle force is dependent on its base-material properties and changes to the base material due to fatty inclusions result in reductions to force and muscle quality.

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.

A review of biomechanically informed breast image registration

Breast radiology encompasses the full range of imaging modalities from routine imaging via x-ray mammography, magnetic resonance imaging and ultrasound (both two- and three-dimensional), to more recent technologies such as digital breast tomosynthesis, and dedicated breast imaging systems for positron emission mammography and ultrasound tomography. In addition new and experimental modalities, such as Photoacoustics, Near Infrared Spectroscopy and Electrical Impedance Tomography etc, are emerging. The breast is a highly deformable structure however, and this greatly complicates visual comparison of imaging modalities for the purposes of breast screening, cancer diagnosis (including image guided biopsy), tumour staging, treatment monitoring, surgical planning and simulation of the effects of surgery and wound healing etc. Due primarily to the challenges posed by these gross, non-rigid deformations, development of automated methods which enable registration, and hence fusion, of information within and across breast imaging modalities, and between the images and the physical space of the breast during interventions, remains an active research field which has yet to translate suitable methods into clinical practice. This review describes current research in the field of breast biomechanical modelling and identifies relevant publications where the resulting models have been incorporated into breast image registration and simulation algorithms. Despite these developments there remain a number of issues that limit clinical application of biomechanical modelling. These include the accuracy of constitutive modelling, implementation of representative boundary conditions, failure to meet clinically acceptable levels of computational cost, challenges associated with automating patient-specific model generation (i.e. robust image segmentation and mesh generation) and the complexity of applying biomechanical modelling methods in routine clinical practice.

A finite element head and neck model as a supportive tool for deformable image registration

PURPOSE

A finite element (FE) head and neck model was developed as a tool to aid investigations and development of deformable image registration and patient modeling in radiation oncology. Useful aspects of a FE model for these purposes include ability to produce realistic deformations (similar to those seen in patients over the course of treatment) and a rational means of generating new configurations, e.g., via the application of force and/or displacement boundary conditions.

METHODS

The model was constructed based on a cone-beam computed tomography image of a head and neck cancer patient. The three-node triangular surface meshes created for the bony elements (skull, mandible, and cervical spine) and joint elements were integrated into a skeletal system and combined with the exterior surface. Nodes were additionally created inside the surface structures which were composed of the three-node triangular surface meshes, so that four-node tetrahedral FE elements were created over the whole region of the model. The bony elements were modeled as a homogeneous linear elastic material connected by intervertebral disks. The surrounding tissues were modeled as a homogeneous linear elastic material. Under force or displacement boundary conditions, FE analysis on the model calculates approximate solutions of the displacement vector field.

RESULTS

A FE head and neck model was constructed that skull, mandible, and cervical vertebrae were mechanically connected by disks. The developed FE model is capable of generating realistic deformations that are strain-free for the bony elements and of creating new configurations of the skeletal system with the surrounding tissues reasonably deformed.

CONCLUSIONS

The FE model can generate realistic deformations for skeletal elements. In addition, the model provides a way of evaluating the accuracy of image alignment methods by producing a ground truth deformation and correspondingly simulated images. The ability to combine force and displacement conditions provides flexibility for simulating realistic anatomic configurations.

Methodology based on genetic heuristics for in-vivo characterizing the patient-specific biomechanical behavior of the breast tissues

This paper presents a novel methodology to in-vivo estimate the elastic constants of a constitutive model proposed to characterize the mechanical behavior of the breast tissues. An iterative search algorithm based on genetic heuristics was constructed to in-vivo estimate these parameters using only medical images, thus avoiding invasive measurements of the mechanical response of the breast tissues. For the first time, a combination of overlap and distance coefficients were used for the evaluation of the similarity between a deformed MRI of the breast and a simulation of that deformation. The methodology was validated using breast software phantoms for virtual clinical trials, compressed to mimic MRI-guided biopsies. The biomechanical model chosen to characterize the breast tissues was an anisotropic neo-Hookean hyperelastic model. Results from this analysis showed that the algorithm is able to find the elastic constants of the constitutive equations of the proposed model with a mean relative error of about 10%. Furthermore, the overlap between the reference deformation and the simulated deformation was of around 95% showing the good performance of the proposed methodology. This methodology can be easily extended to characterize the real biomechanical behavior of the breast tissues, which means a great novelty in the field of the simulation of the breast behavior for applications such as surgical planing, surgical guidance or cancer diagnosis. This reveals the impact and relevance of the presented work.

Symmetric Biomechanically Guided Prone-to-Supine Breast Image Registration

Prone-to-supine breast image registration has potential application in the fields of surgical and radiotherapy planning, image guided interventions, and multi-modal cancer diagnosis, staging, and therapy response prediction. However, breast image registration of three dimensional images acquired in different patient positions is a challenging problem, due to large deformations induced to the soft breast tissue caused by the change in gravity loading. We present a symmetric, biomechanical simulation based registration framework which aligns the images in a central, virtually unloaded configuration. The breast tissue is modelled as a neo-Hookean material and gravity is considered as the main source of deformation in the original images. In addition to gravity, our framework successively applies image derived forces directly into the unloading simulation in place of a subsequent image registration step. This results in a biomechanically constrained deformation. Using a finite difference scheme avoids an explicit meshing step and enables simulations to be performed directly in the image space. The explicit time integration scheme allows the motion at the interface between chest and breast to be constrained along the chest wall. The feasibility and accuracy of the approach presented here was assessed by measuring the target registration error (TRE) using a numerical phantom with known ground truth deformations, nine clinical prone MRI and supine CT image pairs, one clinical prone-supine CT image pair and four prone-supine MRI image pairs. The registration reduced the mean TRE for the numerical phantom experiment from initially 19.3 to 0.9 mm and the combined mean TRE for all fourteen clinical data sets from 69.7 to 5.6 mm.

Simultaneous Estimation of Elasticity for Multiple Deformable Bodies

Material property has great importance in deformable body simulation and medical robotics. The elasticity parameters, such as Young's modulus of the deformable bodies, are important to make realistic animations. Further in medical applications the (recovered) elasticity parameters can assist surgeons to perform better pre-op surgical planning and enable medical robots to carry out personalized surgical procedures. Previous elasticity parameters estimation methods are limited to recover one elasticity parameter of one deformable body at a time. In this paper, we propose a novel elasticity parameter estimation algorithm that can recover the elasticity parameters of multiple deformable bodies or multiple regions of one deformable body simultaneously from (at least two sets of) images. We validate our algorithm with both synthetic test cases and real patient CT images.

Interrogating a multifactorial model of breast conserving therapy with clinical data

Most women with early stage breast cancer do not require removal of the entire breast to treat their cancer; instead, up to 70% of women can be effectively and safely treated by breast conserving therapy (BCT) with surgical removal of the tumor only (lumpectomy) followed by radiation treatment of the remaining breast tissue. Unfortunately, the final contour and cosmesis of the treated breast is suboptimal in approximately 30% of patients. The ability to accurately predict breast contour after BCT for breast cancer could significantly improve patient decision-making regarding the choice of surgery for breast cancer. Our overall hypothesis is that the complex interplay among mechanical forces due to gravity, breast tissue constitutive law distribution, inflammation induced by radiotherapy and internal stress generated by the healing process play a dominant role in determining the success or failure of lumpectomy in preserving the breast contour and cosmesis. We have shown here from a first patient study that even in the idealistic situation of excellent cosmetic outcome this problem requires multiscale modeling. We propose a method to decide which component of the model works best for each phase of healing and what parameters should be considered dominant and patient specific. This patient study is part of a clinical trial registered on ClinicalTrial.gov, identifier NCT02310711.

The Effect of Material Modeling on Finite Element Analysis of Human Breast Biomechanics

Purpose

Finite element analysis has been used extensively in the study of biomechanical modeling of the breast. However, issues regarding the complexity of material models and the influences of geometric boundary conditions on the accuracy of a breast Finite Element (FE) model are still under debate. This work demonstrates the importance of material modeling in FE models of the breast.

Methods

A simple hemispherical geometry is used to model the shape of a human breast. Different material models are being investigated to accurately model changes in terms of displacement, stress, and reaction forces distribution.

Results

The results obtained using nonlinear material models are compared with those obtained employing their linear approximation. Results have shown that differences, in terms of displacement, ranging between 20% and more than 80%, may occur and that large differences are present in terms of maximum principal stresses when the displacement is correctly approximated.

Conclusions

This study clearly shows that, in a FE model, simulating large deformations material modeling strongly influences the accuracy of the solution.

Breast lesion co-localisation between X-ray and MR images using finite element modelling

This paper presents a novel X-ray and MR image registration technique based on individual-specific biomechanical finite element (FE) models of the breasts. Information from 3D magnetic resonance (MR) images was registered to X-ray mammographic images using non-linear FE models subject to contact mechanics constraints to simulate the large compressive deformations between the two imaging modalities. A physics-based perspective ray-casting algorithm was used to generate 2D pseudo-X-ray projections of the FE-warped 3D MR images. Unknown input parameters to the FE models, such as the location and orientation of the compression plates, were optimised to provide the best match between the pseudo and clinical X-ray images. The methods were validated using images taken before and during compression of a breast-shaped phantom, for which 12 inclusions were tracked between imaging modalities. These methods were then applied to X-ray and MR images from six breast cancer patients. Error measures (such as centroid and surface distances) of segmented tumours in simulated and actual X-ray mammograms were used to assess the accuracy of the methods. Sensitivity analysis of the lesion co-localisation accuracy to rotation about the anterior-posterior axis was then performed. For 10 of the 12 X-ray mammograms, lesion localisation accuracies of 14 mm and less were achieved. This analysis on the rotation about the anterior-posterior axis indicated that, in cases where the lesion lies in the plane parallel to the mammographic compression plates, that cuts through the nipple, such rotations have relatively minor effects.This has important implications for clinical applicability of this multi-modality lesion registration technique, which will aid in the diagnosis and treatment of breast cancer.

Breast image analysis for risk assessment, detection, diagnosis, and treatment of cancer

The role of breast image analysis in radiologists' interpretation tasks in cancer risk assessment, detection, diagnosis, and treatment continues to expand. Breast image analysis methods include segmentation, feature extraction techniques, classifier design, biomechanical modeling, image registration, motion correction, and rigorous methods of evaluation. We present a review of the current status of these task-based image analysis methods, which are being developed for the various image acquisition modalities of mammography, tomosynthesis, computed tomography, ultrasound, and magnetic resonance imaging. Depending on the task, image-based biomarkers from such quantitative image analysis may include morphological, textural, and kinetic characteristics and may depend on accurate modeling and registration of the breast images. We conclude with a discussion of future directions.

A study of breast motion using non-linear dynamic FE analysis

This paper presents a new method to simulate non-linear breast motion by using a three-dimensional (3D) dynamic finite element model (FEM). The model consists of a thorax with two breasts and three skin layers with specific mechanical properties. Using free breast vibration, the viscous damping ratios were ascertained to be 0.215 for an 80B size breast. The shear modulus for the breast was derived as the value that gave the minimum difference between the FEM-predicted results and the experimental data. A hyper-elastic neo-Hookean material model simulated the large deformation of breast tissue. The mode shapes of breast motions at different natural frequencies were established. The highest breast displacement amplitude ratio relative to the thorax was at 4 Hz. The study showed that FEM can predict breast displacement with sufficient accuracy and thereby provide the basis by which bras may be engineered more ergonomically in the future.

PRACTITIONER SUMMARY

To facilitate a theoretical analysis of breast motion to enable the design of more supportive bras, a dynamic FEM based on reliable non-linear properties of breast tissues has been developed. The methods and findings have potential widespread benefit for developing new products to promote women's health and comfort.

Simulation-based joint estimation of body deformation and elasticity parameters for medical image analysis

Estimation of tissue stiffness is an important means of noninvasive cancer detection. Existing elasticity reconstruction methods usually depend on a dense displacement field (inferred from ultrasound orMR images) and known external forces.Many imaging modalities, however, cannot provide details within an organ and therefore cannot provide such a displacement field. Furthermore, force exertion and measurement can be difficult for some internal organs, making boundary forces another missing parameter. We propose a general method for estimating elasticity and boundary forces automatically using an iterative optimization framework, given the desired (target) output surface. During the optimization, the input model is deformed by the simulator, and an objective function based on the distance between the deformed surface and the target surface is minimized numerically. The optimization framework does not depend on a particular simulation method and is therefore suitable for different physical models. We show a positive correlation between clinical prostate cancer stage (a clinical measure of severity) and the recovered elasticity of the organ. Since the surface correspondence is established, our method also provides a non-rigid image registration, where the quality of the deformation fields is guaranteed, as they are computed using a physics-based simulation.

Mono- and multimodal registration of optical breast images

Optical breast imaging offers the possibility of noninvasive, low cost, and high sensitivity imaging of breast cancers. Poor spatial resolution and a lack of anatomical landmarks in optical images of the breast make interpretation difficult and motivate registration and fusion of these data with subsequent optical images and other breast imaging modalities. Methods used for registration and fusion of optical breast images are reviewed. Imaging concerns relevant to the registration problem are first highlighted, followed by a focus on both monomodal and multimodal registration of optical breast imaging. Where relevant, methods pertaining to other imaging modalities or imaged anatomies are presented. The multimodal registration discussion concerns digital x-ray mammography, ultrasound, magnetic resonance imaging, and positron emission tomography.

Segmentation of the breast skin and its influence in the simulation of the breast compression during an X-ray mammography

A novel method of skin segmentation is presented aimed to obtain as many pixels belonging to the real skin as possible. This method is validated by experts in radiology. In addition, a biomechanical model of the breast, which considers the skin segmented in this way, is constructed to study the influence of considering real skin in the simulation of the breast compression during an X-ray mammography. The reaction forces of the plates are obtained and compared with the reaction forces obtained using classical methods that model the skin as a 2D membranes that cover all the breast. The results of this work show that, in most of the cases, the method of skin segmentation is accurate and that real skin should be considered in the simulation of the breast compression during the X-ray mammographies.

Image similarity and tissue overlaps as surrogates for image registration accuracy: widely used but unreliable

The accuracy of nonrigid image registrations is commonly approximated using surrogate measures such as tissue label overlap scores, image similarity, image difference, or transformation inverse consistency error. This paper provides experimental evidence that these measures, even when used in combination, cannot distinguish accurate from inaccurate registrations. To this end, we introduce a "registration" algorithm that generates highly inaccurate image transformations, yet performs extremely well in terms of the surrogate measures. Of the tested criteria, only overlap scores of localized anatomical regions reliably distinguish reasonable from inaccurate registrations, whereas image similarity and tissue overlap do not. We conclude that tissue overlap and image similarity, whether used alone or together, do not provide valid evidence for accurate registrations and should thus not be reported or accepted as such.

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.

Modelling prostate motion for data fusion during image-guided interventions

There is growing clinical demand for image registration techniques that allow multimodal data fusion for accurate targeting of needle biopsy and ablative prostate cancer treatments. However, during procedures where transrectal ultrasound (TRUS) guidance is used, substantial gland deformation can occur due to TRUS probe pressure. In this paper, the ability of a statistical shape/motion model, trained using finite element simulations, to predict and compensate for this source of motion is investigated. Three-dimensional ultrasound images acquired on five patient prostates, before and after TRUS-probe-induced deformation, were registered using a nonrigid, surface-based method, and the accuracy of different deformation models compared. Registration using a statistical motion model was found to outperform alternative elastic deformation methods in terms of accuracy and robustness, and required substantially fewer target surface points to achieve a successful registration. The mean final target registration error (based on anatomical landmarks) using this method was 1.8 mm. We conclude that a statistical model of prostate deformation provides an accurate, rapid and robust means of predicting prostate deformation from sparse surface data, and is therefore well-suited to a number of interventional applications where there is a need for deformation compensation.

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.

A reduced order explicit dynamic finite element algorithm for surgical simulation

Reduced order modelling, in which a full system response is projected onto a subspace of lower dimensionality, has been used previously to accelerate finite element solution schemes by reducing the size of the involved linear systems. In the present work we take advantage of a secondary effect of such reduction for explicit analyses, namely that the stable integration time step is increased far beyond that of the full system. This phenomenon alleviates one of the principal drawbacks of explicit methods, compared with implicit schemes. We present an explicit finite element scheme in which time integration is performed in a reduced basis. Futhermore, we present a simple procedure for imposing inhomogeneous essential boundary conditions, thus overcoming one of the principal deficiencies of such approaches. The computational benefits of the procedure within a GPU-based execution framework are examined, and an assessment of the errors introduced is given. It is shown that speedups approaching an order of magnitude are feasible, without introduction of prohibitive errors, and without hardware modifications. The procedure may have applications in interactive simulation and medical image-guidance problems, in which both speed and accuracy are vital.

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.