Breast elastography has been proposed as a new screening modality. The idea behind is to use the stiffness of tissues as the contrast agent, as pathologies change stiffness of tissue significantly. However, the advantage of elastography over other imaging modalities (MRI, US) is that it can provide mechanical parameters which precisely describe stiffness distribution within the breast tissue. Therefore, in addition to the ability of detecting the presence of abnormalities, elastography is capable of classifying them as well. These parameters are useful for several purposes including in vivo tumor classification, real-time surgery assistance, training surgeons, VR systems, etc.
In this work, we use nonlinear (hyperelastic) models that are valid for large amounts of deformation. The goal is to find the corresponding numbers, called hyperelastic parameters, which represent the stiffness of a detected tumor. The approach is to solve an inverse problem in which the unknown hyperelastic parameters are reconstructed iteratively. For this purpose, we use two well-known hyperelastic models: Yeoh and Veronda-Westman. While the Yeoh model can be solved easily using inverse matrix techniques, the Veronda-Westman model requires a different approach due to its nonlinear form. Accordingly, we have developed a novel technique for this purpose.
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To validate the work, we use numerical and experimental phantoms mimicking a cancerous breast tissue. The experimental phantom is made up of PVA, which demonstrates nonlinear mechanical behavior. Also, displacement data is acquired using an ultrasound imaging system.
Keywords: soft tissues, breast elastography, hyperelasticity, inverse problem, phantom study
It is an astonishing fact that cancer is the second leading cause of death worldwide. There are a variety of types of cancer one can develop among which breast cancer is the second most common type (after lung cancer). It is the most common cancer in women worldwide, and the leading cause of death in women between 40 and 50 years of age. Men are also susceptible to breast cancer, but it is 100 times more frequent in women. Statistics show that one in nine women will develop breast cancer, and one-third of these will die from the disease. Although mortality from breast cancer has been declining in developed countries over the last two decades due to improved diagnosis and improved treatment, globally the prevalence of breast cancer has increased and become the second most common cause of cancer deaths in 2008 , while it had the fifth ranking only a few years before, in 2003 . Even in Canada, it is estimated that ???? women will be diagnosed with breast cancer in 2010, and ??? of them will die of it.
These devastating statistics clearly highlight the importance of early diagnosis of cancers. If the tumor is detected in early stages, there is high chance to remove it with minimum risk to patient's health.
1.1. What is cancer?
The term cancer is used for diseases in which abnormal cells divide without control and are able to invade other tissues. There are more than 100 different types of cancer. Most cancers are named based on the organ or type of cell in which they start; however, cancer cells can spread to other parts of the body through the blood and lymph systems. All cancers begin in cells, where normal cells become cancer cells. When cells become old or damaged, they die and are replaced with new cells, but sometimes this orderly process goes wrong due to damage or change in the DNA of a cell. This affects normal cell growth and division, and other cells as well. When this happens, it means cells do not die when they should, and new cells form when the body does not need them. These extra cells, then, may form a mass of tissue called a tumor. [cancer.gov]
Image from http://www.cancer.gov
There are two types of tumors in terms of malignancy: benign (non-cancerous) or malignant (cancerous). The big difference is that cells in benign tumors do not spread to other parts of the body. They can often be removed and in most cases they do not come back. On the other hand, however, cells in the malignant tumors can invade nearby tissues and spread to other parts of the body. This process, spreading cancer cells from one part of the body to another, is called metastasis. [cancer.ca]
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1.2. Anatomy of breast
Breasts are attached by connective tissue to the underlying pectoralis major muscles. Each breast is made of glands, ducts (thin tubes) and fatty tissue. The internal structure of the breast consists of a compound tubuloalveolar gland composed of about 20 lobes, which radiate from the nipple. The lobes are supported by dense connective tissue and surrounded by adipose tissue. Lobules are groups of glands that can produce milk. Fatty tissue fills the spaces between the lobules and ducts and protects them. Breast tissue in younger women is mostly made of glands and milk ducts, but older women's breasts are made up mostly of fatty tissue. [Lurie]
Image from http://www.cancer.ca
1.3. Breast Cancer
The breasts (mammary glands) of females are highly susceptible to cysts and tumors. Lumps in the breast are very common, but most lumps are not breast cancer. Non-malignant cysts are the most frequent diseases of the breast. [Anatomy and physiology, Eva Lurie Weinreb, pp. 793-795]
Breast cancer starts in the cells of the breast, and most often is first noticed as a painless lump in the breast or armpit. Fibroadenoma is a benign tumor of the breast that frequently occurs in women under the age of 35. Carcinoma of the breast is the most common malignancy in women. In the earliest stages of carcinoma, cancer cells are found only in the milk ducts or lobules. If it starts within the ducts, this is called ductal carcinoma, whereas lobular carcinoma, which begins in the lobules.
If cancer is diagnosed before the cells have spread to the surrounding tissue, there is no risk of them spreading after they have been removed. When breast cancer spreads out of the duct or lobule, it is called invasive cancer. It can still be treated effectively if diagnosed early. [Human anatomy, Kent Van De Graaff, pp.720-730]
The causes of breast cancer are not known, but women who are most susceptible are those who are over age 35, who have a family history of breast cancer, and who never having given birth. Meanwhile, many women with breast cancer do not have a family history of the disease. [wcr 2008].
1.4. Breast screening
The most important factor in the treatment of all types of cancers is early detection; because, the prognosis worsens as the disease progresses. If the cancerous tissue is detected in early stages, there is a greater chance of removing it with little risk to the patient's health.
For breast cancer, one diagnostic procedure that should be routinely performed by a woman is breast self-examination (BSE). The importance of a BSE is not to prevent disease of the breast, but to detect any problems before they become life-threatening. Therefore, women are advised to do the manual-palpation test monthly from the age of twenty to check for any abnormalities in their breasts. [cancer.ca]
1.5. Clinical Exams for Breast Cancer Diagnosis
Although BSE is a simple test that any woman can do easily, relying just on the manual-palpation is not safe, as there may be tiny lumps or even lumps deep inside the tissue that one cannot sense from merely doing the palpation. Today, there are several medical imaging modalities (mammography, MRI, ultrasound, etc) by which breast tissue is imaged, and a skilled physician looks for any potential tumors in the tissue. Also, research is being done on a variety of breast imaging techniques that can contribute to the early detection of breast cancer and improve the accuracy in distinguishing non-cancerous breast conditions from breast cancers.
Here we briefly describe conventional imaging modalities that are used for detecting breast tumors.
Mammography is a specific type of imaging that uses a low-dose x-ray system to examine breasts. X-rays are the oldest and most frequently used form of medical imaging which involve exposing a part of the body to a small dose of ionizing radiation to produce pictures of the inside of the body. A mammography exam, called a mammogram, is used to aid in the early detection and diagnosis of breast diseases in women. Two recent advances in mammography include digital mammography (FFDM) and computer-aided detection (CAD).
Mammograms are used to detect either early breast cancer in women experiencing no symptoms (Screening Mammography), or diagnose breast disease in women experiencing symptoms (Diagnostic Mammography). Diagnostic mammography is used to evaluate a patient with abnormal clinical findings such as a lump, pain or nipple discharge. It may also be done after an abnormal screening mammography in order to evaluate the area of concern on the screening exam.
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There is always a slight chance of cancer from excessive exposure to radiation. However, the benefit of an accurate diagnosis (even for small tumors) far outweighs the risk.
One limitation of initial mammograms is that they are not usually enough to determine the existence of a benign or malignant disease with certainty. If a finding or spot seems suspicious, the radiologist may recommend further diagnostic studies. Interpretations of mammograms can be difficult because a normal breast can appear differently for each woman. Because some breast cancers are hard to visualize, a radiologist may want to compare the image to views from previous examinations. Not all cancers of the breast can be seen on mammography.
Although mammography is the best screening tool for breast cancer available today and women are encouraged to take it every two years, it does not detect all breast cancers. Also, a small portion of mammograms indicate that a cancer could possibly be present when it is not (called a false-positive result).
1.7. Magnetic Resonance Imaging
Magnetic resonance imaging (MRI) is a noninvasive medical test that helps physicians diagnose and treat medical conditions. MRI uses a powerful magnetic field, radio frequency pulses and a computer to produce detailed pictures of organs, soft tissues, bone and virtually all other internal body structures. Detailed MR images allow physicians to better evaluate various parts of the body and certain diseases that may not be assessed adequately with other imaging methods such as x-ray, ultrasound or CT. MRI of the breast offers valuable information about many breast conditions that cannot be obtained by other imaging modalities, such as mammography or ultrasound. However, it is not a replacement for mammography or ultrasound imaging, but rather a supplemental tool for detecting and staging breast cancer and other breast abnormalities.
Image from http://www.radiologyinfo.org
Unlike mammography, MRI does not depend on ionizing radiation. Instead, while in the magnet, radio waves redirect the axes of spinning protons, which are the nuclei of hydrogen atoms, in a strong magnetic field. The magnetic field is produced by passing an electric current through wire coils in most MRI units. Other coils, located in the machine and in some cases, placed around the part of the body being imaged, send and receive radio waves, producing signals that are detected by the coils. A computer then processes the signals and generates a series of images each of which shows a thin slice of the body. The images can then be studied from different angles by the interpreting physician.
Overall, the differentiation of abnormal (diseased) tissue from normal tissues is often better with MRI than with other imaging modalities such as x-ray, CT and ultrasound.
Benefits of MRI include ability to detect small breast lesions that are sometimes missed by mammography, and ability to fully image the dense breast common in younger women, as well as breast implants, both of which are difficult to image using traditional mammography. More importantly, MRI poses almost no risk to the average patient. Limitations of MRI are that typically it costs more and may take more time to perform than other imaging modalities. It also cannot always distinguish between cancer and benign breast disease (such as fibroadenomas or fibrocystic change), leading to a false positive result.
1.8. Breast Ultrasound
Ultrasound imaging, also called ultrasound scanning or sonography, involves exposing part of the body to high-frequency sound waves to produce pictures of the inside of the body. Because ultrasound images are captured in real-time, they can show the structure and movement of the body's internal organs.
Ultrasound imaging is based on the same principles involved in the sonar used by bats, ships and fishermen. When a sound wave strikes an object, it bounces back, or echoes. By measuring these echo waves it is possible to determine how far away the object is, as well as its size, shape, and consistency (whether the object is solid, filled with fluid, or both).
In medicine, ultrasound is used to detect changes in appearance of organs, tissues, and vessels or detect abnormal masses, such as tumors.
In an ultrasound examination, a transducer both sends the sound waves and records the echoing waves. When the transducer is pressed against the skin, it directs small pulses of inaudible, high-frequency sound waves into the body. As the sound waves bounce off of internal organs, fluids and tissues, the sensitive microphone in the transducer records tiny changes in the sound's pitch and direction. These signature waves are instantly measured and displayed by a computer, which in turn creates a real-time picture on the monitor. One or more frames of the moving pictures are typically captured as still images.
Image from http://www.radiologyinfo.org
The primary use of breast ultrasound today is to help diagnose breast abnormalities, and to characterize potential abnormalities seen on mammography. Ultrasound imaging can help to determine if an abnormality is solid (which may be a non-cancerous lump of tissue, or a cancerous tumor), or fluid-filled (such as a benign cyst), or both cystic and solid. Today, ultrasound is being investigated for use as a screening tool for women who are at high risk for breast cancer and unable to tolerate an MRI examinations, have dense breasts, have silicone breast implants and very little tissue can be included on the mammogram, or are pregnant or should not to be exposed to x-rays (which is necessary for a mammogram). Also, as ultrasound provides real-time images, it is often used to guide biopsy procedures.
The advantages of using ultrasound are being noninvasive, real-time imaging, widely available, easy-to-use and less expensive than other imaging methods. On the other hand, it has its own limitations: Many cancers are not visible on ultrasound, as the quality of images is poorer than other modalities. [http://www.radiologyinfo.org]
1.9. Summary of conventional screening modalities
As we explained, mammography is the only screening tool for breast cancer that is known to reduce deaths due to breast cancer through early detection. Even though, mammograms do not detect all breast cancers. Some breast lesions and abnormalities are not visible or are difficult to interpret on mammograms. In breasts that are dense (there is a lot of glandular tissue and less fat) many cancers can be hard to see on mammography. Besides, many studies have shown that ultrasound and MRI can help supplement mammography by detecting small breast cancers that may not be visible with mammography. Supplemental screening ultrasound is usually only considered for women at high risk for breast cancer when the breast tissue is dense.
By the way, medical studies are currently being conducted to determine whether MRI and other imaging methods can contribute to the early detection and prevention of deaths from breast cancer.
Clinical diagnosis of breast disease is based on clinical history, physical examination, and diagnostic tests, such as mammography, ultrasonic scanning, MRI, etc. If the test suggests breast cancer, definitive diagnosis is determined by biopsy (microscopic examination of tissue sample). Then, if the tumor is found to be malignant, surgery is performed, the extent of which depends on the size of tumor and whether metastasis has occurred.
Other than surgery, there are also a variety of other treatments to breast cancer that can be applied if needed. They include Radiation therapy, Chemotherapy, Biological therapy, etc.
A common weakness of most conventional imaging modalities, referred to as low specificity, is that although they can detect the presence of pathological tissues, they are incapable of classifying tumors and determining whether they are malignant. To address this major issue, elastography has been developed. Elastography is an imaging technique that provides the spatial distribution of tissue stiffness which is then used to detect or classify tumors. It has been known for a very long time that many cancers (breast, prostate, liver metastases, etc.) appear as hard nodules. Manual palpation is a standard practice to detect them, but many nodules elude palpation by virtue of their small size or of their deep location within the body. Elastography, then, is expected to overcome most of these difficulties because it combines the penetration depth and resolution of imaging modalities (MR, US) with high sensitivity to stiffness contrast.
The core of elastography techniques is their inverse problem of stiffness parameter reconstruction. In other words, the spatial distribution of hyperelastic parameters is reconstructed by solving a set of equations inversely. Reconstruction techniques are based on elasticity constitutive models that are selected to model the forward problem. These are divided into linear and nonlinear (hyperelastic) models. Linear elasticity assumes that the relationship between stress and strain is linear, and uses two parameters, Young's modulus and Poison's ratio, to describe the mechanical behavior of tissue. However, given that most soft tissues exhibit nonlinear characteristics under the mechanical stimulation of elastography procedures, we employ a hyperelastic formulation. Moreover, tissue hyperelastic parameters can be used for cancer diagnosis.
In this work, we use two well-known hyperelastic models: Yeoh and Veronda-Westman. For Yeoh model, the system of equations can be solved easily using matrix-based inversion techniques. However, in the case of Veronda-Westman model, due to its exponential form, the system of equations becomes nonlinear. This makes using matrix-based inversion techniques not possible as well as introducing convergence and excessive computation time issues. Previous works established optimization and/or regularization approaches, which were time-demanding. We have developed a novel efficient technique to reconstruct the unknown Veronda-Westman model parameters, in which no optimization or regularization is involved. The main idea of the proposed technique is to use approximations to the exponential term of the Veronda-Westman function. Having the approximation, we define intermediate variables, and change the system of equations into an equivalent linear system in terms of these variables. Hence, we solve this linear system for the intermediate variables, and finally, we determine the hyperelastic parameters using the intermediate variables.
1.12. Research Objectives
In this work, we focus on the classification capability of elastography, as the presence of tumor can be ascertained using other conventional imaging modalities. This means that we know the geometry (segmentation) and structure of the cancerous breast tissue as a priori. Consequently, we create a proper Finite Element (FE) mesh to model the breast tissue based on its known geometry. We use ABAQUS, a commercial FE solver, to model the compression we apply while performing elastography. To reduce the duration of reconstruction procedure, we use a novel technique called Statistical FEM (SFEM) which has been recently developed in our lab.
To summarize, our goal is to find hyperelastic parameters that represent the stiffness of tissues. To do this, we have developed a reconstruction algorithm that iteratively solves for the unknown hyperelastic parameters of the detected tumor. These parameters are useful in determining the type of tumor (benign or malignant.) in vivo. This is a great achievement since this way many of cases will not be sent unnecessarily for a biopsy. There are some other benefits in having these parameters such as implementing VR systems for training surgeons or real-time guided surgeory, etc.
To validate our work, we use numerical and experimental breast-mimicking phantoms. Each phantom has three tissue types (tumor, glandular and adipose tissues) resembling a real cancerous tissue. For the numerical phantoms, we use simulated displacement data, whereas for the experimental phantom displacement data is acquired using an ultrasound imaging system. The phantom is constructed using PVA-C, which has been used widely in modeling soft tissues because of its nonlinear behavior.