A finite element model to accurately predict real deformations of the breast

Preoperative three-dimensional simulation of the breast appearance after wide local excision or level one oncoplastic techniques for breast-conserving treatment does not set unrealistic expectations for aesthetic outcome: One-year follow-up of a randomised controlled trial

INTRODUCTION

Simulation of aesthetic outcomes of wide local excision and level one oncoplastic breast conserving treatment (BCT) using 3-dimensional surface imaging (3D-SI) prepares women for their aesthetic outcome. It remains unknown whether women's memory of this information at the one-year follow-up matches their perception of reality or affects the quality of life.

METHODS

With ethical approval, a prospective 3-arm RCT was conducted and it included 3D-simulation, viewing post-operative 2D photographs of other women and standard care. At one-year post-surgery, the participants completed a visual analogue scale (VAS) for the question "How well do you think the information about how your breasts are likely to look after surgery reflects how they actually look today?" and the BCT BREAST-Q module. The Kruskal-Wallis test was used to examine between-group differences at a 5% significance level.

RESULTS

From 2017 to 2019, 117 women completed the primary endpoint of being informed about the aesthetic outcome via verbal description, photographs or simulation. Seventy-eight (74%) of the 106 women who remained eligible attended the one-year follow-up. The standardised preoperative 3D-SI simulation did not affect the patient's perception of the aesthetic outcome compared to standard care or viewing 2D photographs as measured using the VAS (p = 0.40) or BREAST-Q scores for satisfaction with information (p = 0.76), satisfaction with breasts (p = 0.70), and psychosocial wellbeing domains (p = 0.81).

DISCUSSION

Viewing their own 3D-SI standardised simulation did not significantly affect how the participants perceived their aesthetic outcome. In addition, it did not alter the patient-reported satisfaction. These results demonstrated that simulation for wide local excision or level one oncoplastic surgery does not set unrealistic expectations of the aesthetic outcome when used in a preoperative setting.

SYNOPSIS

The use of a non-bespoke three-dimensional simulation of the aesthetic outcome for breast conserving treatment in the preoperative setting does not over-inflate expectations compared to standard care.

Identifiability of soft tissue constitutive parameters from in-vivo macro-indentation

Reliable identification of soft tissue material parameters is frequently required in a variety of applications, particularly for biomechanical simulations using finite element analysis (FEA). However, determining representative constitutive laws and material parameters is challenging and often comprises a bottleneck that hinders the successful implementation of FEA. Soft tissues exhibit a nonlinear response and are commonly modeled using hyperelastic constitutive laws. In-vivo material parameter identification, for which standard mechanical tests (e.g., uniaxial tension and compression) are inapplicable, is commonly achieved using finite macro-indentation test. Due to the lack of analytical solutions, the parameters are commonly identified using inverse FEA (iFEA), in which simulated results and experimental data are iteratively compared. However, determining what data must be collected to accurately identify a unique parameter set remains unclear. This work investigates the sensitivities of two types of measurements: indentation force-depth data (e.g., measured using an instrumented indenter) and full-field surface displacements (e.g., using digital image correlation). To eliminate model fidelity and measurement-related errors, we employed an axisymmetric indentation FE model to produce synthetic data for four 2-parameter hyperelastic constitutive laws: compressible Neo-Hookean, and nearly incompressible Mooney-Rivlin, Ogden, and Ogden-Moerman models. For each constitutive law, we computed the objective functions representing the discrepancies in the reaction force, the surface displacement, and their combination, and visualized them for hundreds of parameter sets, spanning a representative range as found in the literature for the bulk soft tissue complex in human lower limbs. Moreover, we quantified three identifiability metrics, which provided insights into the uniqueness (or lack thereof) and the sensitivities. This approach provides a clear and systematic evaluation of the parameter identifiability, which is independent of the selection of the optimization algorithm and initial guesses required in iFEA. Our analysis indicated that the indenter's force-depth data, despite being commonly used for parameter identification, was insufficient for reliably and accurately identifying both parameters for all the investigated material models and that the surface displacement data improved the parameter identifiability in all cases, although the Mooney-Rivlin parameters remained poorly identifiable. Informed by the results, we then discuss several identification strategies for each constitutive model. Finally, we openly provide the codes used in this study, to allow others to further investigate the indentation problem according to their specifications (e.g., by modifying the geometries, dimensions, mesh, material models, boundary conditions, contact parameters, or objective functions).

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.

Experimental characterisation and modelling of breast Cooper's ligaments

The aim of this study was to characterise the mechanical behaviour of Cooper's ligaments. Such ligaments are collagenous breast tissue that create a three-dimensional structure over the entire breast volume. Ten ligaments were extracted from a human cadaver, from which 28 samples were cut and used to perform uniaxial tensile tests. Histological analysis showed that the main direction of the fibres visible to the naked eye corresponds to the orientation of the fibres on a microscopic scale. The specimens were cut according to this orientation, which allowed the sample to be stretched in the main fibre direction. From these experimental stretch/stress curves, an original anisotropic hyperelastic constitutive law is proposed to model the behaviour of Cooper's ligaments and the material parameter validity is discussed.

Three-dimensional simulation of aesthetic outcome from breast-conserving surgery compared with viewing photographs or standard care: randomized clinical trial

INTRODUCTION

Over half of women with surgically managed breast cancer in the UK undergo breast-conserving treatment (BCT). While photographs are shown prior to reconstructive surgery or complex oncoplastic procedures, standard practice prior to breast conservation is to simply describe the likely aesthetic changes. Patients have expressed the desire for more personalized information about likely appearance after surgery. The hypothesis was that viewing a three-dimensional (3D) simulation improves patients' confidence in knowing their likely aesthetic outcome after surgery.

METHODS

A randomized, controlled trial of 117 women planning unilateral BCT was undertaken. The randomization was three-way: standard of care (verbal description alone, control group), viewing two-dimensional (2D) photographs, or viewing a 3D simulation before surgery. The primary endpoint was the comparison between groups' median answer on a visual analogue scale (VAS) for the question administered before surgery: 'How confident are you that you know how your breasts are likely to look after treatment?'

RESULTS

The median VAS in the control group was 5.2 (i.q.r. 2.6-7.8); 8.0 (i.q.r. 5.7-8.7) for 2D photography, and 8.9 (i.q.r. 8.2-9.5) for 3D simulation. There was a significant difference between groups (P < 0.010) with post-hoc pairwise comparisons demonstrating a statistically significant difference between 3D simulation and both standard care and viewing 2D photographs (P < 0.010 and P = 0.012, respectively).

CONCLUSION

This RCT has demonstrated that women who viewed an individualized 3D simulation of likely aesthetic outcome for BCT were more confident going into surgery than those who received standard care or who were shown 2D photographs of other women. The impact on longer-term satisfaction with outcome remains to be determined.Registration number: NCT03250260 (http://www.clinicaltrials.gov).

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.

Deep learning reconstruction of digital breast tomosynthesis images for accurate breast density and patient-specific radiation dose estimation

The two-dimensional nature of mammography makes estimation of the overall breast density challenging, and estimation of the true patient-specific radiation dose impossible. Digital breast tomosynthesis (DBT), a pseudo-3D technique, is now commonly used in breast cancer screening and diagnostics. Still, the severely limited 3rd dimension information in DBT has not been used, until now, to estimate the true breast density or the patient-specific dose. This study proposes a reconstruction algorithm for DBT based on deep learning specifically optimized for these tasks. The algorithm, which we name DBToR, is based on unrolling a proximal-dual optimization method. The proximal operators are replaced with convolutional neural networks and prior knowledge is included in the model. This extends previous work on a deep learning-based reconstruction model by providing both the primal and the dual blocks with breast thickness information, which is available in DBT. Training and testing of the model were performed using virtual patient phantoms from two different sources. Reconstruction performance, and accuracy in estimation of breast density and radiation dose, were estimated, showing high accuracy (density <±3%; dose <±20%) without bias, significantly improving on the current state-of-the-art. This work also lays the groundwork for developing a deep learning-based reconstruction algorithm for the task of image interpretation by radiologists.

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.

The identification of the unloaded configuration of breast tissue with unknown non-homogenous stiffness parameters using surface measured data in deformed configuration

Large deformation analysis of the breast is known as a useful approach for locating the tumor and treatment strategies of breast cancer, for which knowing the breast stiffness parameters and unloaded configuration is crucial to obtain reliable results. In this study, an iterative inverse finite element algorithm is developed to identify the unloaded configuration of the breast while its stiffness constants are unknown and its internal structure is assumed to be non-homogeneous. The position vector of surface points in the deformed configuration of the breast is employed to obtain the unknowns of the inverse problem. An objective function based on the difference between the position vector of the calculated and measured deformed configurations is defined. Thereafter, the objective function is minimized using a gradient-based method. The sensitivity analysis for material parameters is performed using an analytic direct differentiation approach. Through several numerical examples, the effectiveness of the proposed inverse method for identifying the unloaded configuration of a uniform, a computational breast phantom with a single inclusion as well as a computational breast phantom with randomly distributed stiffness, is demonstrated. The effects of the number of load cases, measurement error, and initial guesses on the results of the inverse problem are investigated, as well. It is observed that the unloaded configuration of the computational breast phantom with a single inclusion or heterogeneous breast tissues can be accurately found by considering an equivalent homogenous material for the tissue.

Feasibility, Image Quality and Clinical Evaluation of Contrast-Enhanced Breast MRI Performed in a Supine Position Compared to the Standard Prone Position

Background: To assess the feasibility, image quality and diagnostic value of contrast-enhanced breast magnetic resonance imaging (MRI) performed in a supine compared to a prone position. Methods: One hundred and fifty-one patients who had undergone a breast MRI in both the standard prone and supine position were evaluated retrospectively. Two 1.5 T MR scanners were used with the same image resolution, sequences and contrast medium in all examinations. The image quality and the number and dimensions of lesions were assessed by two expert radiologists in an independent and randomized fashion. Two different classification systems were used. Histopathology was the standard of reference. Results: Two hundred and forty MRIs from 120 patients were compared. The analysis revealed 134 MRIs with monofocal (U), 68 with multifocal (M) and 38 with multicentric (C) lesions. There was no difference between the image quality and number of lesions in the prone and supine examinations. A significant difference in the lesion extension was observed between the prone and supine position. No significant differences emerged in the classification of the lesions detected in the prone compared to the supine position. Conclusions: It is possible to perform breast MRI in a supine position with the same image quality, resolution and diagnostic value as in a prone position. In the prone position, the lesion dimensions are overestimated with a higher wash-in peak than in the supine position.

Characterization of human female breast and abdominal skin elasticity using a bulge test

Characterization of material properties of human skin is required to develop a physics-based biomechanical model that can predict deformation of female breast after cosmetic and reconstructive surgery. In this paper, we have adopted an experimental approach to characterize the biaxial response of human skin using bulge tests. Skin specimens were harvested from breast and abdominal skin of female subjects who underwent mastectomy and/or reconstruction at The University of Texas MD Anderson Cancer Center and who provided informed consent. The specimens were tested within 2 h of harvest, and after freezing for different time periods but not exceeding 6 months. Our experimental results show that storage in a freezer at -20 °C for up to about 40 days does not lead to changes in the mechanical response of the skin beyond statistical variation. Moreover, displacement at the apex of the bulged specimen versus applied pressure varies significantly between different specimens from the same subject and from different subjects. The bulge test results were used in an inverse optimization procedure in order to calibrate two different constitutive material models - the angular integration model proposed by Lanir (1983) and the generalized structure tensor formulation of Gasser et al. (2006). The material parameters were estimated through a cost function that penalized deviations of the displacement and principal curvatures at the apex. Generally, acceptable fits were obtained with both models, although the angular integration model was able to fit the curvatures slightly better than the Gasser et al. model. The range of the model parameters has been extracted for use in physics-based biomechanical models of the breast.

An automated computational biomechanics workflow for improving breast cancer diagnosis and treatment

Clinicians face many challenges when diagnosing and treating breast cancer. These challenges include interpreting and co-locating information between different medical imaging modalities that are used to identify tumours and predicting where these tumours move to during different treatment procedures. We have developed a novel automated breast image analysis workflow that integrates state-of-the-art image processing and machine learning techniques, personalized three-dimensional biomechanical modelling and population-based statistical analysis to assist clinicians during breast cancer detection and treatment procedures. This paper summarizes our recent research to address the various technical and implementation challenges associated with creating a fully automated system. The workflow is applied to predict the repositioning of tumours from the prone position, where diagnostic magnetic resonance imaging is performed, to the supine position where treatment procedures are performed. We discuss our recent advances towards addressing challenges in identifying the mechanical properties of the breast and evaluating the accuracy of the biomechanical models. We also describe our progress in implementing a prototype of this workflow in clinical practice. Clinical adoption of these state-of-the-art modelling techniques has significant potential for reducing the number of misdiagnosed breast cancers, while also helping to improve the treatment of patients.

Monte Carlo study on optimal breast voxel resolution for dosimetry estimates in digital breast tomosynthesis

Digital breast tomosynthesis (DBT) is currently used as an adjunct technique to digital mammography (DM) for breast cancer imaging. Being a quasi-3D image, DBT is capable of providing depth information on the internal breast glandular tissue distribution, which may be enough to obtain an accurate patient-specific radiation dose estimate. However, for this, information regarding the location of the glandular tissue, especially in the vertical direction (i.e. x-ray source to detector), is needed. Therefore, a dedicated reconstruction algorithm designed to localize the amount of glandular tissue, rather than for optimal diagnostic value, could be desirable. Such a reconstruction algorithm, or, alternatively, a reconstructed DBT image classification algorithm, could benefit from the use of larger voxels, rather than the small sizes typically used for the diagnostic task. In addition, the Monte Carlo (MC) based dose estimates would be accelerated by the representation of the breast tissue with fewer and larger voxels. Therefore, in this study we investigate the optimal DBT reconstructed voxel size that allows accurate dose evaluations (i.e. within 5%) using a validated Geant4-based MC code. For this, sixty patient-based breast models, previously acquired using dedicated breast computed tomography (BCT) images, were deformed to reproduce the breast during compression under a given DBT scenario. Two re-binning approaches were applied to the compressed phantoms, leading to isotropic and anisotropic voxels of different volumes. MC DBT simulations were performed reproducing the acquisition geometry of a SIEMENS Mammomat Inspiration system. Results show that isotropic cubic voxels of 2.73 mm size provide a dose estimate accurate to within 5% for 51/60 patients, while a comparable accuracy is obtained with anisotropic voxels of dimension 5.46  ×  5.46  ×  2.73 mm³. In addition, the MC simulation time is reduced by more than half in respect to the original voxel dimension of 0.273  ×  0.273  ×  0.273 mm³ when either of the proposed re-binning approaches is used. No significant differences in the effect of binning on the dose estimates are observed (Wilcoxon-Mann-Whitney test, p-value  >  0.4) between the 0° the 23° (i.e. the widest angular range) exposure.

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.

Anthropomorphic breast model repository for research and development of microwave breast imaging technologies

A repository of anthropomorphic numerical breast models is made available for the scientific community to support research and development of microwave imaging technologies for diagnostic and therapeutic applications. These models are constructed from magnetic resonance imaging (MRI) scans acquired at our university hospital. Our 3D breast modelling method is used to translate the MRI scans into 3D models representing the geometry and microwave-frequency properties of tissues in the breast. The reconstructed models demonstrate anatomical realism, reconfigurable complexity, and flexibility to adapt to simulations of various microwave imaging techniques and prototype systems. With these models, realistic and rigorous test scenarios can be defined in simulations to support feasibility analysis, performance verification and design improvements of developing microwave imaging techniques, prior to testing on experimental systems. A repository of breast models is created which includes breasts of varying classification - fatty, scattered, heterogeneous, and dense. In addition, the models include brief documentation to facilitate researchers in selecting a model by matching its features with their requirements.

A momentum-based diffeomorphic demons framework for deformable MR-CT image registration

Neuro-navigated procedures require a high degree of geometric accuracy but are subject to geometric error from complex deformation in the deep brain-e.g. regions about the ventricles due to egress of cerebrospinal fluid (CSF) upon neuroendoscopic approach or placement of a ventricular shunt. We report a multi-modality, diffeomorphic, deformable registration method using momentum-based acceleration of the Demons algorithm to solve the transformation relating preoperative MRI and intraoperative CT as a basis for high-precision guidance. The registration method (pMI-Demons) extends the mono-modality, diffeomorphic form of the Demons algorithm to multi-modality registration using pointwise mutual information (pMI) as a similarity metric. The method incorporates a preprocessing step to nonlinearly stretch CT image values and incorporates a momentum-based approach to accelerate convergence. Registration performance was evaluated in phantom and patient images: first, the sensitivity of performance to algorithm parameter selection (including update and displacement field smoothing, histogram stretch, and the momentum term) was analyzed in a phantom study over a range of simulated deformations; and second, the algorithm was applied to registration of MR and CT images for four patients undergoing minimally invasive neurosurgery. Performance was compared to two previously reported methods (free-form deformation using mutual information (MI-FFD) and symmetric normalization using mutual information (MI-SyN)) in terms of target registration error (TRE), Jacobian determinant (J), and runtime. The phantom study identified optimal or nominal settings of algorithm parameters for translation to clinical studies. In the phantom study, the pMI-Demons method achieved comparable registration accuracy to the reference methods and strongly reduced outliers in TRE (p [Formula: see text] 0.001 in Kolmogorov-Smirnov test). Similarly, in the clinical study: median TRE  =  1.54 mm (0.83-1.66 mm interquartile range, IQR) for pMI-Demons compared to 1.40 mm (1.02-1.67 mm IQR) for MI-FFD and 1.64 mm (0.90-1.92 mm IQR) for MI-SyN. The pMI-Demons and MI-SyN methods yielded diffeomorphic transformations (J  >  0) that preserved topology, whereas MI-FFD yielded unrealistic (J  <  0) deformations subject to tissue folding and tearing. Momentum-based acceleration gave a ~35% speedup of the pMI-Demons method, providing registration runtime of 10.5 min (reduced to 2.2 min on GPU), compared to 15.5 min for MI-FFD and 34.7 min for MI-SyN. The pMI-Demons method achieved registration accuracy comparable to MI-FFD and MI-SyN, maintained diffeomorphic transformation similar to MI-SyN, and accelerated runtime in a manner that facilitates translation to image-guided neurosurgery.

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.

Multimodal Breast Parenchymal Patterns Correlation Using a Patient-Specific Biomechanical Model

In this paper, we aim to produce a realistic 2-D projection of the breast parenchymal distribution from a 3-D breast magnetic resonance image (MRI). To evaluate the accuracy of our simulation, we compare our results with the local breast density (i.e., density map) obtained from the complementary full-field digital mammogram. To achieve this goal, we have developed a fully automatic framework, which registers MRI volumes to X-ray mammograms using a subject-specific biomechanical model of the breast. The optimization step modifies the position, orientation, and elastic parameters of the breast model to perform the alignment between the images. When the model reaches an optimal solution, the MRI glandular tissue is projected and compared with the one obtained from the corresponding mammograms. To reduce the loss of information during the ray-casting, we introduce a new approach that avoids resampling the MRI volume. In the results, we focus our efforts on evaluating the agreement of the distributions of glandular tissue, the degree of structural similarity, and the correlation between the real and synthetic density maps. Our approach obtained a high-structural agreement regardless the glandularity of the breast, whilst the similarity of the glandular tissue distributions and correlation between both images increase in denser breasts. Furthermore, the synthetic images show continuity with respect to large structures in the density maps.

A Regression Model for Predicting Shape Deformation after Breast Conserving Surgery

Breast cancer treatments can have a negative impact on breast aesthetics, in case when surgery is intended to intersect tumor. For many years mastectomy was the only surgical option, but more recently breast conserving surgery (BCS) has been promoted as a liable alternative to treat cancer while preserving most part of the breast. However, there is still a significant number of BCS intervened patients who are unpleasant with the result of the treatment, which leads to self-image issues and emotional overloads. Surgeons recognize the value of a tool to predict the breast shape after BCS to facilitate surgeon/patient communication and allow more educated decisions; however, no such tool is available that is suited for clinical usage. These tools could serve as a way of visually sensing the aesthetic consequences of the treatment. In this research, it is intended to propose a methodology for predict the deformation after BCS by using machine learning techniques. Nonetheless, there is no appropriate dataset containing breast data before and after surgery in order to train a learning model. Therefore, an in-house semi-synthetic dataset is proposed to fulfill the requirement of this research. Using the proposed dataset, several learning methodologies were investigated, and promising outcomes are obtained.

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.

Numerical simulation of breast reduction with a new knitting condition

Breast reduction is one of the most common procedures in breast surgery. The aim of this work is to develop a computational model allowing one to forecast the final breast geometry according to the incision marking parameters. This model can be used in surgery simulators that provide preoperative planning and training, allowing the study of the origin of the errors in breast reduction. From the mathematical point of view, this is a problem of calculus of variations with unusual boundary conditions, known as knitting conditions. The breast tissue is considered as a hyperelastic material, discretized with three-dimensional finite elements for the body, whereas the skin is modelled with two-dimensional finite elements on the curved surface. Although the model is of low precision, we show that it is sufficient for a satisfactory prediction of breast reduction surgery results, allowing an analysis of errors frequently performed during the surgery and giving an understanding of how to avoid or correct them. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Stealthy role of size-driven stresses in biomechanics of breast implants capsular contracture

Breast Capsular Contracture (BCC) is one of the adverse complications occurring with greater incidence in breast augmentation surgical procedures. Its formation can be interpreted as the conclusive result of the physiological process known as response to a foreign body. From a biochemical standpoint, the formation of the peri-prosthetic capsule is certainly a multifactorial process: many hypotheses concerning its etiology have been suggested in the literature and a number of related pharmacological protocols have been consequently proposed to clinically treat this pathology with the aim to prevent further complications and avoid future re-interventions. However, the vast majority of these theories seems to be only partially supported by clinical outcomes and thus a shared opinion on this matter is still absent among specialists. Within this framework, by starting from clinical observations which highlighted an unexpected correlation between histo-morphological features of fibrotic capsules and overall size of breast implants, the present study investigates the hypothesis that the biomechanical interaction between prosthesis and host tissue may play a crucial role in the biological processes governing the pathological phenomenon at hand. Therefore, to shed light on the underlying mechanisms which could trigger the breast capsular contracture, both simple analytical solutions, in which elasticity and growth are simultaneously taken into account, and more accurate geometrically faithful Finite Element-based numerical simulations have been exploited. The theoretical findings demonstrate that somehow counter-intuitive radial and hoop stress fields occur at the capsula-implant interface in a way such that their combined action, independently from other possible concurrent factors, results significantly amplified for small-size breast prostheses, localized stress peaks in these cases promoting detaching and rippling phenomena actually observed in BCC clinical complications.

Multiscale Mechano-Biological Finite Element Modelling of Oncoplastic Breast Surgery-Numerical Study towards Surgical Planning and Cosmetic Outcome Prediction

Surgical treatment for early-stage breast carcinoma primarily necessitates breast conserving therapy (BCT), where the tumour is removed while preserving the breast shape. To date, there have been very few attempts to develop accurate and efficient computational tools that could be used in the clinical environment for pre-operative planning and oncoplastic breast surgery assessment. Moreover, from the breast cancer research perspective, there has been very little effort to model complex mechano-biological processes involved in wound healing. We address this by providing an integrated numerical framework that can simulate the therapeutic effects of BCT over the extended period of treatment and recovery. A validated, three-dimensional, multiscale finite element procedure that simulates breast tissue deformations and physiological wound healing is presented. In the proposed methodology, a partitioned, continuum-based mathematical model for tissue recovery and angiogenesis, and breast tissue deformation is considered. The effectiveness and accuracy of the proposed numerical scheme is illustrated through patient-specific representative examples. Wound repair and contraction numerical analyses of real MRI-derived breast geometries are investigated, and the final predictions of the breast shape are validated against post-operative follow-up optical surface scans from four patients. Mean (standard deviation) breast surface distance errors in millimetres of 3.1 (±3.1), 3.2 (±2.4), 2.8 (±2.7) and 4.1 (±3.3) were obtained, demonstrating the ability of the surgical simulation tool to predict, pre-operatively, the outcome of BCT to clinically useful accuracy.

Breast Reduction in the Burned Breast

Mammary hypertrophy can occur in the postburn breast. Patients with burned breasts exhibit the same symptoms of symptomatic macromastia as patients with unburned breasts. The extent of the deformity, the location of the deformity, and the status of the surrounding soft tissue are all assessed before embarking on any surgical plan, which then proceeds in a conservative stepwise fashion. Although many plastic surgeons are reluctant to operate on burned breasts for fear of devascularizing the skin graft or nipple areolar complex, reduction mammaplasty in this group of patients is safe and carries minimal risk if key concepts are followed.

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.

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.

3D surface imaging of the human female torso in upright to supine positions

Three-dimensional (3D) surface imaging of breasts is usually done with the patient in an upright position, which does not permit comparison of changes in breast morphology with changes in position of the torso. In theory, these limitations may be eliminated if the 3D camera system could remain fixed relative to the woman’s torso as she is tilted from 0 to 90 degrees. We mounted a 3dMDtorso imaging system onto a bariatric tilt table to image breasts at different tilt angles. The images were validated using a rigid plastic mannequin and the metrics compared to breast metrics obtained from 5 subjects with diverse morphology. The differences between distances between the same fiducial marks differed between the supine and upright positions by less than one percent for the mannequin, whereas the differences for distances between the same fiducial marks on the breasts of the 5 subjects differed significantly and could be correlated with body mass index and brassiere cup size for each position change. We show that a tilt table - 3D imaging system can be used to determine quantitative changes in the morphology of ptotic breasts when the subject is tilted to various angles.

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.

In-vivo quantification of human breast deformation associated with the position change from supine to upright

Stereophotographic imaging and digital image correlation are used to determine the variation of breast skin deformation as the subject orientation is altered from supine to upright. A change in subject's position from supine to upright can result in significant stretches in some parts of the breast skin. The maximum of the major principal stretch ratio of the skin is different in different subjects and varies in the range of 1.25-1.60. It is also found that the boundaries of the breast move significantly relative to the skeletal structure and other fixed points such as the sternal notch. Such measurements are crucial since they provide basic data for validation of biomechanical breast models based on finite element formulations.

A nonlinear biomechanical model based registration method for aligning prone and supine MR breast images

Preoperative diagnostic magnetic resonance (MR) breast images can provide good contrast between different tissues and 3-D information about suspicious tissues. Aligning preoperative diagnostic MR images with a patient in the theatre during breast conserving surgery could assist surgeons in achieving the complete excision of cancer with sufficient margins. Typically, preoperative diagnostic MR breast images of a patient are obtained in the prone position, while surgery is performed in the supine position. The significant shape change of breasts between these two positions due to gravity loading, external forces and related constraints makes the alignment task extremely difficult. Our previous studies have shown that either nonrigid intensity-based image registration or biomechanical modelling alone are limited in their ability to capture such a large deformation. To tackle this problem, we proposed in this paper a nonlinear biomechanical model-based image registration method with a simultaneous optimization procedure for both the material parameters of breast tissues and the direction of the gravitational force. First, finite element (FE) based biomechanical modelling is used to estimate a physically plausible deformation of the pectoral muscle and the major deformation of breast tissues due to gravity loading. Then, nonrigid intensity-based image registration is employed to recover the remaining deformation that FE analyses do not capture due to the simplifications and approximations of biomechanical models and the uncertainties of external forces and constraints. We assess the registration performance of the proposed method using the target registration error of skin fiducial markers and the Dice similarity coefficient (DSC) of fibroglandular tissues. The registration results on prone and supine MR image pairs are compared with those from two alternative nonrigid registration methods for five breasts. Overall, the proposed algorithm achieved the best registration performance on fiducial markers (target registration error, 8.44 ±5.5 mm for 45 fiducial markers) and higher overlap rates on segmentation propagation of fibroglandular tissues (DSC value > 82%).

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.