Methods for modeling and predicting mechanical deformations of the breast under external perturbations

Abstract

Currently, high field (1.5 T) superconducting MR imaging does not allow live guidance during needle breast procedures. The current procedure allows the physician only to calculate approximately the location and extent of a cancerous tumor in the compressed patient breast before inserting the needle. It can then become relatively uncertain that the tissue specimen removed during the biopsy actually belongs to the lesion of interest. A new method for guiding clinical breast biopsy is presented, based on a deformable finite element model of the breast. The geometry of the model is constructed from MR data, and its mechanical properties are modeled using a non-linear material model. This method allows imaging the breast without or with mild compression before the procedure, then compressing the breast and using the finite element model to predict the tumor’s position during the procedure. A silicon phantom containing a stiff inclusion was imaged uncompressed then compressed. A model of the phantom was constructed and compressed using custom-written software, and also using a commercial FEM simulation package. The displacement of the inclusion’s corners was recorded both in the real phantom and in the two compressed models. A patient’s breast was imaged uncompressed then compressed. A deformable model of the uncompressed breast was constructed, then compressed. The displacement of a cyst and of two vitamin E pills taped to the surface of the breast were recorded both in the real and in the modeled breast. The entire procedure lasted less than a half-hour, making it clinically useful. The results show that it is possible to create a deformable model of the breast based on finite elements with non-linear material properties, capable of modeling and predicting breast deformations in a clinically useful amount of time.

Introduction

The ability to identify a mass in the breast requires that the mass has a different appearance (or a different contrast) from normal tissue. With MRI, the contrast between soft tissues in the breast is 10–100 times greater than that obtained with X-rays (Fischer et al., 1994, Fischer et al., 1995, Orel et al., 1994). A MR image-guided breast localization and biopsy system is needed to help differentiate between the benign enhancing lesions, and carcinomas (Orel et al., 1994). A whole-body MR system at 1.5 T (Signa; GE Medical Systems, Milwaukee, WI) is used for all needle localizations. The technique requires that the patient lies prone with the breast gently compressed between medial and lateral plates. A multicoil array is used, with two coils placed on the medial plate and one coil on the lateral plate. The lateral plate contains a grid of approximately 1000 18-gauge holes placed at 5-mm intervals, which guide the needle in a plane parallel to the tabletop. The correct hole in the plate is identified and a needle is inserted through that hole into the breast with a pre-calculated depth. However the MR imaging-guided localization technique encounters the following problems:

• The appearance, size and shape of the potential cancer lesion greatly depend on the dynamics of the contrast-enhancing agent. The lesion may clearly appear only in the 2 minutes following the contrast agent injection, then the signal intensity may vary arbitrarily, and it is possible that the apparent boundaries of the lesion may change dramatically.

• The needle is not a very sharp object, and cannot be smoothly inserted in the breast. Every time the tip of the needle reaches the interface between two different types of tissue, its further insertion will push the tissue instead of piercing it, causing unwanted deformations until the pressure on the tissue interface is high enough. As soon as the needle pierces the displaced tissue interface, that interface quickly settles back to its original position, or somewhere close to it. The best way to remedy this problem would be to compress the breast as much as possible, which would minimize internal deformations. However doing that would cause blood to be squeezed out of the breast, and would dramatically alter the appearance and shape of the lesion on the MR image, without mentioning the high level of discomfort for the patient who would be very reluctant to feel the pain for the entire duration of the procedure. The best solution would be to mildly compress the breast and obtain MR images clearly showing the position, shape and extent of the lesion. Then the breast would be highly compressed in order to minimize internal deformations during the needle insertion only. However the missing link is to predict the displacement of the lesion from the mildly compressed configuration, to the highly compressed configuration.

The above limitations coupled with the deformable structure of the breast makes needle procedures very sensitive to the initial placement of the needle, and to the amount of breast compression. It thus becomes relatively uncertain that the tissue specimen removed during the biopsy procedure actually belongs to the lesion of interest, due to the added difficulty of accurately locating the tumor’s boundaries inside the breast. It is therefore important to develop techniques, which would solve or bypass the aforementioned problems, increase the level of confidence of a biopsy result (improving the diagnosis), and decrease the cost to society (including health care expenses). The financial savings could be considerable, and the morbidity associated with the biopsy procedure including the lost time from work that occurs as a result of biopsy could be greatly reduced (Stavros et al., 1995).

We present a virtual deformable breast model of the patient whose geometry is constructed from MR data. The elastic properties of the deformable model are based on the use of finite elements with nonlinear material properties capable of modeling the deformation of the breast under external perturbations. A high-field 1.5-Tesla machine Signa Horizon Echospeed (GEMS, Milwaukee, WI) is used to obtain the 3D breast image sets. The image sets are used to construct the geometry of the finite element model. Contours of the breast are extracted, and each breast slice is segmented to locate the different tissue types, using appropriate custom-written software. The model geometry is then created using a custom-written preprocessor, which allows for a variable mesh size. We also developed a software algorithm (BreastView), which models large deformations of the breast model depending on the desired accuracy of the deformation. We hypothesize that the structural complexity of the breast can be simplified to only assign to the model elements, an average value of the mechanical properties of glandular, fatty, and cancerous tissue.

The major novelties in this model include the following:

• Breast plate compression plates results in a large compression, meaning that the total distance between the two plates decreases by more than 10%. In order to model such large deformations, we divide the large deformation compression into a number of much smaller displacement steps. For every displacement step, we make use of small strain theory. Strain is calculated using Cauchy’s infinitesimal strain tensor formula (Fung, 1994). After every small displacement iteration, the tissues’s different material properties are recalculated in all model elements whose maximum principal strain has changed, in order to model the materials’ non-linear behavior. The main advantage of using small strain formulation lies in its simplicity, ease of implementation and fast computation. However, being an incremental formulation, it could lead to an accumulation of discretization errors and in consequence, to a lack of accuracy (Szekely et al., 1998). A way to solve this potential problem would be to use a total Lagrange formulation (as the one we use for estimating the non-linear material properties of tissue from one displacement iteration to the next), in which every state is related to the initial configuration. However that would complicate the formulation and slow down the computation of the solution. We show in a silicon phantom study that the incremental errors introduced by small strain formulation can be neglected for the purpose of this model and overall study.

• We present a new breast fatty tissue material model, which takes into account the effect of fat compartmentalization due to Cooper’s ligaments in the breast. We show through empirical evidence that fat compartmentalization occurs as the breast is being compressed, and that the new updated fatty tissue material model takes that phenomenon into account, and performs better than the original fatty tissue model.

• We apply finite element modeling theory to model the deformation of a human female breast in such a way that the entire process takes less than a half-hour (compared to several hours using a commercial finite element modeling package), which according to the clinicians consulted, is a reasonably short time duration.

This model can be used effectively in several different applications:

• A new method for guiding clinical breast biopsy: This method involves imaging the patient’s breast without any or little compression before a needle procedure, then compressing the breast, and its virtual finite element model (by applying the same pressure to both), and using the displacement of the virtual tumor model to predict the displacement of the real cancer tumor. It is important to note that during the entire procedure (imaging, needle localization, and/or biopsy), the patient remains in the same prone position, and only the equipment ‘moves’ around the patient. Therefore perturbations caused by the patient’s movements are minor. A model like the one presented here is important to this procedure, in which any improvement in confidence for localizing the cancer tumor could become life-saving.

• Other applications: A finite element model of the breast can be a very flexible tool for many applications including registration of different breast MR data sets of the same patient taken under different compression amounts, or registration of different data sets from different imaging modalities. Other possible applications include diagnosis, measurements, surgery planning, simulations of deformation due to inserting a needle, and further away, virtual surgery, and tele-surgery.

The paper is organized as follows.

• In Section 2, the related work is presented and compared to our model. The general flowchart of operation is described.

• Section 3 presents the methods used, going through image acquisition, data extraction, 3D mesh domain creation, model dynamics, and the description of the internal forces due to stiffness.

• Section 4 presents the experimental methods:

  • (a) A deformable silicon gel phantom was built to study the movement of a stiff inclusion inside a deformable environment under plate compression. The phantom was imaged undeformed, then compressed (14%). The performance of our software algorithm was compared to that of a robust commercial FEM software package. A 3D deformable model of the phantom was built from the resulting MR data using our custom-written software and was virtually compressed using BreastView. Another FEM was built using a commercial pre-processor (PATRAN, MSC, CA) from the phantom’s directly measured dimensions, and was virtually compressed using ABAQUS (HKS, RI). The displacement vectors of the 8 corners of the stiff inclusion and its center were measured both from the MR images and from the two finite element models.

  • (b) A patient’s breast was imaged uncompressed and then compressed 26%. The corresponding deformable model was built, and was virtually compressed to match the real compression amount. We tracked the displacement of a small cyst inside the patient’s breast, and used the deformable model to predict the cyst’s position in the real compressed breast. We also tracked the displacement of two vitamin E pills taped to the surface of the patient’s breast.

• Section 5 presents the results and discussion for both experiments. We also present a convergence analysis, and a material properties sensitivity analysis. The results show that it is possible to create a deformable model of the breast based on the use of finite elements with non-linear material properties, capable of modeling the deformation of the breast in a clinically useful amount of time (less than a half-hour for the entire procedure).

• Section 6 deals with additional issues, including the potential sources of error, specific properties of reliability, and summarizes the major novelties in the model.

• Section 7 presents the concluding remarks, and is followed by Appendix A Modeling 8-node hexahedral solid isoparametric elements, Appendix B Modeling linear triangle isoparametric elements, Appendix C Silicon phantom construction which present the finite element modeling theory in detail, as well as details of the silicon phantom construction.