Mechanical model of the breast for the prediction of deformation during imaging

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.

Do static and dynamic activities induce potentially damaging breast skin strain?

Background/Aim

This study aimed to quantify breast skin strain and strain rate and the effect of support garments at reducing strain and to determine characteristics that correlate with strain during static and dynamic activity.

Methods

39 women (UK size 32C to 36G) had electromagnetic sensors applied to their breast skin. Sensor coordinates were recorded while standing, walking, running, in no, low and high breast support conditions, plus bare-breasted in the estimated neutral position to calculate strain. Relative breast coordinates and 35 inter-sensor distances identified peak breast skin strain (%) and strain rate (%·s^-1), which were then correlated with nipple kinematics, breast pain and participant characteristics.

Results

Mean peak breast skin strain was generally <60% during standing, walking and running; however, some individuals exhibited 93% strain in bare-breasted running. Compared with low support, high support did not further reduce strain during standing and walking. Peak breast skin strain/strain rate location was longitudinal, in lateral and medial breast regions and displayed strong correlations with breast volume, body mass index and bust circumference.

Conclusion

Static and dynamic activity did not result in excessive breast skin strain, suggesting low risk of skin damage. However, during running, some individuals experienced excessive skin strains (up to 93%) and strain rates (up to 1258%·s^-1). Breast skin strain/strain rate location suggests lift is required in the lateral and medial bra cup to reduce strain, particularly in larger breast volumes due to increased skin strain risk.

Phenomenological tissue fracture modeling for an Endoscopic Sinus and Skull Base Surgery training system based on experimental data

The ideal simulator for Endoscopic Sinus and Skull Base Surgery (ESSS) training must be supported by a physical model and provide repetitive behavior in a controlled environment. Development of realistic tissue models is a key part of ESSS virtual reality (VR)-based surgical simulation. Considerable research has been conducted to address haptic or force feedback and propose a phenomenological tissue fracture model for sino-nasal tissue during surgical tool indentation. Mechanical properties of specific sino-nasal regions of the sheep head have been studied in various indentation and relaxation experiments. Tool insertion at different indentation rates into coronal orbital floor (COF) tissue is modeled as a sequence of three events: deformation, fracture, and cutting. The behavior in the deformation phase can be characterized using a non-linear, rate-dependent modified Kelvin-Voigt model. A non-linear model for tissue behavior prior to the fracture point is presented. The overall model shows a non-positive dependency of maximum force on tool indentation rate, which indicates faster tool insertion velocity decreases the maximum final fracture force. The tissue cutting phase has been modeled to characterize the force necessary to slice through the COF. The proposed model in this study can help develop VR-based ESSS base simulators in otolaryngology and ophthalmology surgeries. Such simulators are useful in preoperative planning, accurate surgical simulation, intelligent robotic assistance, and treatment applications.

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.

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.

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 polynomial hyperelastic model for the mixture of fat and glandular tissue in female breast

In the breast of adult women, glandular and fat tissues are intermingled and cannot be clearly distinguished. This work studies if this mixture can be treated as a homogenized tissue. A mechanical model is proposed for the mixture of tissues as a function of the fat content. Different distributions of individual tissues and geometries have been tried to verify the validity of the mixture model. A multiscale modelling approach was applied in a finite element model of a representative volume element (RVE) of tissue, formed by randomly assigning fat or glandular elements to the mesh. Both types of tissues have been assumed as isotropic, quasi-incompressible hyperelastic materials, modelled with a polynomial strain energy function, like the homogenized model. The RVE was subjected to several load cases from which the constants of the polynomial function of the homogenized tissue were fitted in the least squares sense. The results confirm that the fat volume ratio is a key factor in determining the properties of the homogenized tissue, but the spatial distribution of fat is not so important. Finally, a simplified model of a breast was developed to check the validity of the homogenized model in a geometry similar to the actual one.

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.

Prediction of prone-to-supine tumor displacement in the breast using patient position change: investigation with prone MRI and supine CT

BACKGROUND

One of the challenges for clinical use of preoperative breast magnetic resonance imaging (MRI) is how to transfer prone MRI information to the operating theater with a supine surgical position. The aim of this study was to retrospectively evaluate tumor displacement in the breast by changing the patient position from prone to supine (prone-to-supine tumor displacement), using preoperative prone MRI and supine computed tomography (CT).

METHODS

Preoperatively, 55 Japanese women with 57 breast cancer lesions underwent breast MRI in the prone position and breast CT in the supine position. Tumor positions in both the prone and supine positions were measured on X-, Y-, and Z-coordinates by fixing the nipple to the origin (0, 0, 0). As an indicator of the mobility of the breast, the ratio of the breast projection between the prone MRI and supine CT (prone-to-supine projection ratio) was calculated. The direction and distance of prone-to-supine tumor displacement was analyzed by dividing the breast into four quadrants according to the tumor position.

RESULTS

When changing the patient position from prone to supine, tumors located in the inner-upper and inner-lower quadrants tended to move radially toward the center of the nipple. The movement distance of the tumors in the inner-lower and outer-lower quadrants was very strongly correlated with the prone-to-supine breast projection ratio (r ≥ 0.8, p < 0.05). Conversely, in the outer-upper quadrant, the direction of tumor displacement was variable, and the distance of tumor displacement did not correlate with the prone-to-supine projection ratio.

CONCLUSIONS

The present study showed that prone-to-supine tumor displacement in the breast differs depending on tumor location. The inner-lower quadrant of the breast may be the most predictable area for prone-to-supine tumor displacement.