Vijay Rajagopal

Creating Individual-specific Biomechanical Models of the Breast for Medical Image Analysis

RATIONALE AND OBJECTIVES Anatomically realistic biomechanical models of the breast potentially provide a reliable way of mapping tissue locations across medical images, such as mammograms, magnetic resonance imaging (MRI), and ultrasound. This work presents a new modeling framework that enables us to create biomechanical models of the breast that are customized to the individual. We demonstrate the frameworks capabilities by creating models of the left breasts of two volunteers and tracking their deformations across MRIs. MATERIALS AND METHODS We generate customized finite element models by automatically fitting geometrical models to segmented data from breast MRIs, and characterizing the in vivo mechanical properties (assuming homogeneity) of the breast tissues. For each volunteer, we identified the unloaded configuration by acquiring MRIs of the breast under neutral buoyancy (immersed in water). Such imaging is clearly not practical in the clinical setting; however, these previously unavailable data provide us with important data with which to validate models of breast biomechanics. Internal tissue features were identified in the neutral buoyancy images and tracked to the prone gravity-loaded state using the modeling framework. RESULTS The models predicted deformations with root-mean-square errors of 4.2 and 3.6 mm in predicting the skin surface of the gravity-loaded state for each volunteer. Internal tissue features were tracked with a mean error of 3.7 and 4.7 mm for each volunteer. CONCLUSIONS The models capture breast shape and internal deformations across the images with clinically acceptable accuracy. Further refinement of the framework and incorporation of more anatomic detail will make these models useful for breast cancer diagnosis.

Predicting Tumour Location by Simulating Large Deformations of the Breast Using a 3D Finite Element Model and Nonlinear Elasticity

Two of the major imaging modalities used to detect and monitor breast cancer are (contrast enhanced) magnetic resonance (MR) imaging and mammography. Image fusion, including accurate registration between MR images and mammograms, or between CC and MLO mammograms, is increasingly key to patient management (for example in the multidisciplinary meeting), but registration is extremely difficult because the breast shape varies massively between the modalities, due both to the different postures of the patient for the two modalities and to the fact that the breast is forcibly compressed during mammography. In this paper, we develop a 3D, patient-specific, anatomically accurate, finite element model of the breast using MR images, which can be deformed in a physically realistic manner using nonlinear elasticity theory to simulate the breast during mammography.

Modelling Mammographic Compression of the Breast

We have developed a biomechanical model of the breast to simulate compression during mammographic imaging. The modelling framework was applied to a set of MR images of the breasts of a volunteer. Images of the uncompressed breast were segmented into skin and pectoral muscle, from which a finite element (FE) mesh of the left breast was generated using a nonlinear geometric fitting process. The compression plates within the breast MR coil were used to compress the volunteers breasts by 32% in the latero-medial direction and the compressed breasts were subsequently imaged using MRI. The FE geometry of the uncompressed left breast was used to numerically simulate compression based on finite deformation elasticity coupled with contact mechanics, and individual-specific tissue properties. Accuracy of the simulated FE model was analysed by comparing the predicted surface data, and locations of three internal features within the compressed breast, with the equivalent experimental observations. Model predictions of the surface deformation yielded a RMS error of 1.5 mm. The Euclidean errors in predicting the locations of three internal features were 4.1 mm, 4.1 mm and 6.5 mm. Whilst the model reliably reproduced the compressive deformation, further investigations are required in order to test the validity of the underlying modelling assumptions. A reliable biomechanical model will provide a multi-modality imaging registration tool to help identify potential tumours observed between mammograms and other imaging modalities such as MRI or ultrasound.

Modeling of the mechanical function of the human gastroesophageal junction using an anatomically realistic three-dimensional model

The aim of this study was to combine the anatomy and physiology of the human gastroesophageal junction (the junction between the esophagus and the stomach) into a unified computer model. A three-dimensional (3D) computer model of the gastroesophageal junction was created using cross-sectional images from a human cadaver. The governing equations of finite deformation elasticity were incorporated into the 3D model. The model was used to predict the intraluminal pressure values (pressure inside the junction) due to the muscle contraction of the gastroesophageal junction and the effects of the surrounding structures. The intraluminal pressure results obtained from the 3D model were consistent with experimental values available in the literature. The model was also used to examine the independent roles of each muscle layer (circular and longitudinal) of the gastroesophageal junction by contracting them separately. Results showed that the intraluminal pressure values predicted by the model were primarily due to the contraction of the circular muscle layer. If the circular muscle layer was quiescent, the contraction of the longitudinal muscle layer resulted in an expansion of the junction. In conclusion, the model provided reliable predictions of the intraluminal pressure values during the contraction of a normal gastroesophageal junction. The model also provided a framework to examine the role of each muscle layer during the contraction of the gastroesophageal junction.

Breast image registration by combining finite elements and free-form deformations

During breast cancer diagnosis, the breasts undergo large deformations due to gravity or compression loads It is therefore non-trivial to recover the deformation and register medical images of the breast in different orientations (e.g prone versus supine) Free-form deformations and biomechanical finite element models have been used to non-rigidly register breast images from prone to supine, but with limited success In this paper, we demonstrate that the use of a finite element model to predict the deformation of the breast from prone to supine provides a significantly more accurate registration compared to free-form deformation methods We also show that the use of this biomechanical model prediction as a prior to free-form deformation provides a significantly more accurate match than does the use of either method independently.

Towards tracking breast cancer across medical images using subject-specific biomechanical models

Breast cancer detection, diagnosis and treatment increasingly involves images of the breast taken with different degrees of breast deformation. We introduce a new biomechanical modelling framework for predicting breast deformation and thus aiding the combination of information derived from the various images. In this paper, we focus on MR images of the breast under different loading conditions, and consider methods to map information between the images. We generate subject-specific finite element models of the breast by semi-automatically fitting geometrical models to segmented data from breast MR images, and characterizing the subject-specific mechanical properties of the breast tissues. We identified the unloaded reference configuration of the breast by acquiring MR images of the breast under neutral buoyancy (immersed in water). Such imaging is clearly not practical in the clinical setting, however this previously unavailable data provides us with important data with which to validate models of breast biomechanics, and provides a common configuration with which to refer and interpret all breast images. We demonstrate our modelling framework using a pilot study that was conducted to assess the mechanical performance of a subject-specific homogeneous biomechanical model in predicting deformations of the breast of a volunteer in a prone gravity-loaded configuration. The model captured the gross characteristics of the breast deformation with an RMS error of 4.2 mm in predicting the skin surface of the gravity-loaded shape, which included tissue displacements of over 20 mm. Internal tissue features identified from the MR images were tracked from the reference state to the prone gravity-loaded configuration with a mean error of 3.7 mm. We consider the modelling assumptions and discuss how the framework could be refined in order to further improve the tissue tracking accuracy.

Examination of the Effects of Heterogeneous Organization of RyR Clusters, Myofibrils and Mitochondria on Ca2+ Release Patterns in Cardiomyocytes

Spatio-temporal dynamics of intracellular calcium, [Ca2+]i, regulate the contractile function of cardiac muscle cells. Measuring [Ca2+]i flux is central to the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease. However, current imaging techniques are limited in the spatial resolution to which changes in [Ca2+]i can be detected. Using spatial point process statistics techniques we developed a novel method to simulate the spatial distribution of RyR clusters, which act as the major mediators of contractile Ca2+ release, upon a physiologically-realistic cellular landscape composed of tightly-packed mitochondria and myofibrils. We applied this method to computationally combine confocal-scale (~ 200 nm) data of RyR clusters with 3D electron microscopy data (~ 30 nm) of myofibrils and mitochondria, both collected from adult rat left ventricular myocytes. Using this hybrid-scale spatial model, we simulated reaction-diffusion of [Ca2+]i during the rising phase of the transient (first 30 ms after initiation). At 30 ms, the average peak of the simulated [Ca2+]i transient and of the simulated fluorescence intensity signal, F/F0, reached values similar to that found in the literature ([Ca2+]i ≈1 μM; F/F0≈5.5). However, our model predicted the variation in [Ca2+]i to be between 0.3 and 12.7 μM (~3 to 100 fold from resting value of 0.1 μM) and the corresponding F/F0 signal ranging from 3 to 9.5. We demonstrate in this study that: (i) heterogeneities in the [Ca2+]i transient are due not only to heterogeneous distribution and clustering of mitochondria; (ii) but also to heterogeneous local densities of RyR clusters. Further, we show that: (iii) these structure-induced heterogeneities in [Ca2+]i can appear in line scan data. Finally, using our unique method for generating RyR cluster distributions, we demonstrate the robustness in the [Ca2+]i transient to differences in RyR cluster distributions measured between rat and human cardiomyocytes.

The Breast Biomechanics Reference State for Multi-modal Image Analysis

Multi-modality imaging of the breast is becoming increasingly common, and yet combining the information from the different images is difficult due to differences in the basic imaging physics, geometry, and the loading conditions under which the breast is imaged. A key step in moving between these images will be the establishment of a computable and well-understood common reference state. The reference state we use is of the breast in an unloaded configuration, devoid of gravitational and breast compression effects. In this paper we show how breast MR images can be transformed into, and then out of, this reference state to reconstruct configurations associated with other imaging orientations. Finite element models of the breasts of two volunteers were fitted to data derived from MR images of the prone gravity-loaded configurations. These personalized models were used to predict the unloaded and supine gravity-loaded configurations and compared to MR images acquired for these states. The unloaded states were predicted with surface RMS errors of 4.2 mm and 4.1 mm for the two volunteers, whilst the supine gravity-loaded states were predicted with RMS errors of 8.4 mm and 7.7 mm. We demonstrate the transformations into and out of the reference state and discuss clinical applications of these methods.

Development of a three-dimensional finite element model of breast mechanics

A typical breast cancer examination involves the comparison of image patterns in mammograms of craniocaudal (CC) and mediolateral oblique (MLO) views. Obtaining these mammograms requires the compression of the breast in two different directions. During compression, breast tissues undergo large deformations and hence the CC and MLO views do not show exactly the same region of the breast. Nonrigid body registration algorithms typically do not account for the mechanics of the deformation and are thus prone to alignment errors. Finite element model predictions of breast tissue deformation ensure that only physically plausible deformations are used in registration algorithms. A modeling framework has been developed to create anatomically accurate finite element models of the breast. A semi-automatic procedure has been formulated to generate patient specific finite element geometries of breast anatomy. Validation of model predictions has also been conducted on silicon gel samples subjected to gravity loading.

Mapping Microcalcifications Between 2D Mammograms and 3D MRI Using a Biomechanical Model of the Breast

We propose a method to localise the 3D positions of microcalcifications found in X-ray mammograms using the 3D breast modelling framework of Chung et al. [1]. The accuracy of the method was first studied using a phantom embedded with X-ray visible beads. The phantom was subjected to mammographic-like compressions and imaged under X-ray to determine the positions of the beads. Using these data as inputs, the proposed modelling framework was used to predict the bead positions in the uncompressed phantom, which were also determined experimentally using bi-plane X-ray. The bead locations were reconstructed to within 2.8, 3.6 and 2.1 mm. The proposed method was demonstrated on a clinical case by successfully reconstructing the 3D positions of microcalcifications identified in X-ray mammograms and mapping them to a 3D MR data set of the same breast, demonstrating its potential to reliably track such features across different imaging modalities.