This research draws upon several fields, including: mathematics, image processing, computer vision, pattern recognition and biomedical engineering. In Chapter 1, breast MRI was introduced and its advantages and disadvantages relative to other imaging modalities were discussed. In this chapter, a general background in a variety of relevant topics is provided. The first part of the chapter describes the basic principles in MRI physics. It then describes the anatomy of the human breast and breast mammography. This material is required for understanding the material in the later chapters of this thesis. The last section of the chapter provides a basic background of statistical pattern recognition, including basic classifier types and methods for evaluating classification performance, which is needed for understanding the methods that are described in Chapter 6.
This section acquaints the reader with the underlying physics of MRI and of its clinical application, particularly to DCE MRI of the breast. This section provides the reader with basic knowledge of the imaging method (DCE-MRI) that is later used as the primary source of clinical data for this research. The majority of the material in this section is primarily based on (Warren and Coulthard, 2002, Haacke et al., 1999).
Subatomic particles, such as protons, have the quantum property of spin. Magnetic Resonance signals are a result of the interaction between a magnetic field and the spin angular momentum of atomic nuclei (Leggett, 2004). More specifically, the precession of the hydrogen protons yields changes in the flux in the nearby coils. These changes in flux are used to create an MR image. Hydrogen nuclei are most commonly used, mainly because they are more abundant in the human body than any other nucleus capable of undergoing nuclear magnetic resonance (NMR) and thus give a denser signal for a given period of time.
In the absence of a magnetic field, nuclear spins do not have any preferred direction of alignment. Each nucleus spins around an axis called the magnetic moment. Once placed in a strong magnetic field, B0, producing bulk (averaged) nuclear magnetization, M, the magnetic moments of the bulk magnetisation (i.e. the average magnetic moment) will tend to align with the direction of the magnetic field (Figure 2.1).
The magnetization, M, has a naturally-preferred alignment in the direction of B0. Nuclei with such a property are called nuclear spins, where the Z axis denotes the initial alignment of the top. The bulk magnetisation of the protons is then tipped away from the external field direction to produce a magnetic field that yields changes in the flux in any nearby coil (Haacke et al., 1999).
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Y |
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Z |
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X |
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Magnetic moment |
Figure 2.1:� Larmor precessing of a nuclear spin around an applied magnetic field, B0
In NMR the precession frequency ω0 is called the Larmor frequency and is given by:
��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� ,������ (2.1)
where γ is a scalar called the gyromagnetic ratio and is measured in radians per second per Tesla (unit of magnetic flux density). The values of γ are different for different nuclei. From equation (2.1) it can be seen that the precession frequency is directly proportional to the static field strength. A typical field strength used in clinical MRI is 1.5 Tesla in which the Larmor frequency for hydrogen is 63.9 MHz.
To measure the bulk magnetization, M has to be disturbed by an oscillating magnetic field applied at right angles to B0. The field has to be applied at precisely the Larmor frequency to produce the effect because resonant absorption of energy by the protons due to an external oscillating magnetic field occurring exactly at the Larmor frequency. The oscillating field is usually referred to as the Radio Frequency (RF) magnetic pulse, because it is applied for only a few milliseconds. An RF pulse that rotates M through 90○ from its initial position aligned with Z is called a 90○ pulse. If the amplitude of the RF pulse is doubled or, alternatively, if it is applied for twice as long, then M is rotated by 180○. The strength of the magnetic field, B1, of the RF pulse is typically in the order of 10-5 B0.
After the nuclear magnetization M is moved away from its initial alignment by an RF pulse, it will begin to realign itself as soon as the RF pulse is switched off. The z component of the magnetization Mz recovers exponentially with time constant T1, toward its equilibrium value M0, the value at which M is aligned with B0. The MR signal is produced by the transverse magnetisation of the precessing spins in the measured volume of the body. This signal decays in amplitude and is detected externally, often by the same coil that produces the RF pulse (Poole, 2007). T1 is called the longitudinal relaxation time or spin-lattice relaxation time. The actual meaning of T1 is that the difference between Mz and M0 is decreased by 63% of its value in each T1 period, provided that no additional RF pulses are applied. The relaxation process can be described as follows:
������������������������������������������������������������������������������������������������������������������������������������ ,��������� (2.2)
where �is the longitudinal magnetisation (in the direction of B0) and M0 is its equilibrium value.�
In a similar way, the amount of any magnetization rotated into the transverse plane, , declines during the recovery to equilibrium. As with longitudinal relaxation, the decay to the final value of �is exponential. This process can be described as follows:
����������������������������������������������������������������������������������������������������������������������������������������������������������� , ����� (2.3)
where Mxy(t) is the transverse component of the magnetisation and T2 is the time constant of the exponential decay of the transverse magnetisation. It is often called �transverse relaxation time� or the �spin-spin� relaxation time.
�is always less than or equal to . The meaning of is that �decreases by 63% of its value in each �period in the absence of any RF pulses. MR imaging has been developed to show the differences in these relaxation time constants.
The underlying principal in MR imaging is that the Larmor precession frequency is used to mark the position of the encoded volume. The precession frequency, ω0, of an NMR signal is directly proportional to the strength of the static magnetic field �(Equation 2.1). A magnetic field gradient coil can change the strength of �as a function of the position within the scanner. Thus, the Larmor frequency varies along the direction of the gradient coil (Figure 2.2).
Given that only one dimension can be encoded at a time, three separate gradient magnetic coils are used in an MRI scanner, , �and , one for each axis. The imaging process therefore encodes each one of the directions sequentially by alternately turning on each one of the gradient fields.
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Figure 2.2: The magnetic fields in a single slice MR imaging
A magnetic field gradient, , is applied at the same time of an �RF pulse. The frequency of the RF pulse, , matches exactly the Larmor frequency, , at the position of the imaged slice.
Once the gradient has been switched on, a 90� (flip angle) RF pulse is applied. A 90� RF pulse is considered to be the simplest and the signal resulting from it is called the free induction decay (FID). Nuclei with a Larmor frequency that matches the RF pulse frequency are then rotated through 90� and precess to yield an NMR signal. The position of the selected slice is changed by changing the frequency of the RF pulse. This frequency depends on the position along the z axis:
������������������������������������������������������������������������������������������������������������������������������������������������������������������ ������ (2.4)
To excite a slice, a range of frequencies ω1< ω <ω2 have to be produced, corresponding to the range of frequencies inside the excited slice. To do that, an RF pulse is used. The RF pulse�s shape is selected to be a sinc shape that creates a �top hat� shape response that is 1 inside the frequency interval of the slice, and 0 outside of this interval. This happens because the Fourier transform of the sinc function is a rectangular function.
The slice thickness is typically a few millimetres and is controlled by the frequency spread contained within the 90○ RF pulse.
To spatially encode the NMR signal, a frequency-encoding gradient is switched on at the moment the slice selection gradient has been switched off. Protons at different positions along the frequency encoding direction will therefore precess at different frequencies and will generate different frequency signals in the receiving coil. To separate the signals and create a readable image, an inverse Fourier transform is then performed.
The raw data, received by the RF receiver coil of a MR scan is known as k-space. The inverse 2D Fourier transform of the k-space is the MR image that will be interpreted by a clinician.
Various pulse sequences are used in MRI. Two of the most common ones are the spin echo (SE) and gradient echo (GE) pulse sequences. The GE is especially important for dynamic contrast-enhanced (DCE) MRI acquisition.
In the case of an SE sequence, a 90○ RF pulse is applied. After half of the echo time (TE) has passed, a 180○ RF pulse is applied, which re-phases the precessing spins at time TE. This pulse compensates for signal loss caused by inhomogeneities in the magnetic field and maximises the signal emission. The SE sequence will result at TE. The whole sequence is repeated with a repetition time (TR), depending on the desired image (i.e. T1-weighted, T2-weighted or proton-weighted).
In the case of GE sequences the echo is produced by reversing the gradient field, which causes a re-phased RF echo (i.e. gradient echo). In addition, the initial 90○ RF pulse may be substituted with a pulse with a (RF pulse) flip angle smaller than 90○, which does not use the entire longitudinal magnetisation. This allows faster image acquisition at the expense of decreased signal intensity. GE sequences suffer from higher susceptibility to image artefacts than SE sequences owing to a greater sensitivity to field inhomogeneities (Fischer and Brinck, 2004).���
In 2D MR imaging, a single slice is excited at a time. The slices are adjacent and, ideally, have no gaps between them. The field of view (FOV) of each slice is rectangular and approximately 2�3 mm in thickness. In 3D MR imaging, the entire breast is excited as a volume. The TR values for 2D imaging are usually between 200 and 300 ms. The ideal flip angle is between 70○ and 90○.
The 3D acquisition technique allows thin slices to be acquired with no gaps (typically 2 mm thick). Another advantage of the 3D acquisition technique is a shorter acquisition time. This is the result of the shorter repetition time (TR) that is usually in the order of 10 ms. The flip angle for 3D imaging is typically 25○. However, 3D MRI acquisition suffers from a higher susceptibility to artefacts and requires a higher dose of contrast agent (see Section 2.1.8 for further details about contrast agents) (Fischer and Brinck, 2004).��
Although most of the tissues in the human body have a similar water or proton density, in MRI the NMR signal strength is greatly influenced by the T1 and T2 relaxation times. This, in turn, influences the intensity of the different tissues in the displayed image. Disease can also considerably alter the signal strength of a tissue.�
The longest T1 relaxation times usually appear in body fluids. Body fluids also have long T2 values. However, relaxation times are greatly decreased by the presence of blood. In practice, the differences between T1 and T2 are used to produce T1 and T2-weighted images (Warren and Coulthard, 2002), as demonstrated in Table 2.1. By altering the acquisition parameters, different tissue types can be highlighted in the image.
Table 2.1: Proton T1 relaxation times for some types of tissue at 0.5, 1.0 and 1.5 T
T2 does not vary greatly with Larmor frequency (Warren and Coulthard, 2002).
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Tissue |
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Grey matter |
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1040 |
1140 |
100 |
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White matter |
450 |
660 |
720 |
90 |
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Muscle |
560 |
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1160 |
35 |
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Cerebral Spinal Fluid (CSF) |
4000 |
4000 |
4000 |
2000 |
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Liver |
360 |
- |
720 |
60 |
The bias field is a phenomenon that causes the same type tissue in different locations in the MR image to have different levels of intensity. It is identified as a low spatial frequency signal that increases the average intensity in some parts of the image and reduces it in others. The bias field originates in non-uniformity in the �excitation field owing to non-uniformity in the interaction between the RF field and the tissue of the patient being imaged. This non-uniformity results in different amounts of signal being received from tissue in different spatial locations (Hayton, 1998).
Fat usually has high intensity on T1- and T2-weighted images unless suppressed. Bright fat can sometimes obscure adjacent tissue and can introduce artefacts. Two main methods are used to suppress the fat signal:
1. The short Tau Inversion Recovery (STIR) sequence
2. Chemical shift saturation
In the first method, a �RF pulse is used to invert the spin alignment from �to . No signal is produced by this process because no magnetization is introduced in the transverse plane. At a time (TI) later, a �RF pulse, or a ( �RF pulse pair, is used to tip the magnetization into the transverse plane to generate a gradient-echo or spin-echo signal, respectively. The amount of z-magnetization ( ) presented immediately before the �pulse determines the signal obtained. The �of fat is shorter than most other tissues. Therefore, TI is chosen such that the �RF pulse is applied at exactly the time that the fat �has recovered to zero (Figure 2.3). Note that other tissues with longer �values will have a negative �value at that point. However, in the resulting image, only the magnitude of �is important and the sign is ignored.
In the second method, the fat signal is suppressed, based on the small difference in the Larmor frequency of fat protons compared to water protons. The difference in the resonant frequency ω0 is called a chemical shift, because it arises from the different magnetic environment of the hydrogen protons. It is therefore possible to apply a �RF pulse tuned to the fat molecules, but not to the water molecules, provided that the field gradients have been switched off. The z-magnetization of the fat molecules will be zero after the pulse, thus it can be followed by a conventional gradient or spin echo sequence, which will yield a very low fat signal and thus a low SNR that results in a �fat free� noisy image.
Figure 2.3:� STIR sequence fat suppression
TI is chosen such that the magnetization in the Z direction is zero for fat, but not zero for most other tissues. Thus fat will yield no signal in the image� (reproduced from (Warren and Coulthard, 2002)).
When imaging breast implants, the silicone filling material produces a high signal, which can mask enhancing tissue. However, because silicone protons are chemically shifted from water and fat protons, a selective saturation process can be applied, just as in the chemical shift suppression of fat.
MR breast imaging often uses �and -weighted images pre- and post-contrast (i.e. before and after the injection of a contrast agent into the bloodstream) to identify suspicious lesions, because many cannot be detected in conventional / -weighted (non-contrast) images. Malignant lesions, as well as some benign conditions, show contrast enhancement after the injection of a contrast agent. The contrast enhancement is primarily due to angiogenesis (growth of new blood vessels) around the malignant tissue, which accelerates the blood inflow, and hence the flow of contrast agent around the tissue. Also, malignancy-related angiogenesis creates vessels with �leaky endothelial linings� (Morris and Liberman, 2005), which increase the flow of contrast agent in the extracellular compartment at the site of the tumor. This allows the creation of contrast-enhanced MR images that are created by subtracting the pre-contrast from each post-contrast image and thereby providing a better contrast for malignant lesions.
Most malignant tissues enhance in contrast-enhanced MRI (i.e. 1 pre-contrast, 1 post-contrast), which makes it sensitive to breast cancer (Morris and Liberman, 2005, Warren and Coulthard, 2002). However, it can be difficult to distinguish benign from malignant disease, because some benign conditions also exhibit contrast enhancement. This limitation can be diminished by using dynamic contrast-enhanced (DCE) MRI. DCE MRI involves taking a series of sequential -weighted images every few seconds, or tens of seconds (typically 60�90), following a bolus injection of Gd-DTPA (gadolinium-diethylene-triamine pentaacetic acid; gadopentetate dimeglumine). The result of the acquisition is a series of volumes resulting from the �acquisitions at the different time points, as demonstrated in Figure 1.2. In this case, both the rate of signal change in addition to the characteristic shape of the signal versus time is used to interpret the image and identify suspicious lesions (Figure 1.1).
The characteristic behaviour of enhancement curves in DCE-MRI is related to excessive angiogenesis, the growth of new blood vessels, around many types of malignant tissues. Angiogenesis is a natural process, occurring both in healthy and diseased tissues in the body. In some malignant conditions, the body loses control of the angiogenesis process and excessive angiogenesis develops. Tumours cannot enlarge beyond 1 to 2 mm unless they are vascularised; thus, angiogenesis is a requisite for continued tumour growth, in addition to metastasis (secondary growth of malignant tissues around the body). Hence, angiogenesis is a necessary biologic condition of malignancy (and some benign disease as well) (Morris and Liberman, 2005).
In DCE MRI, angiogenesis facilitates contrast enhancement in two ways, increased vascularity leads to an increased contrast agent inflow, and increased vessel permeability leads to an accelerated contrast extravasation at the tumour site (Morris and Liberman, 2005), which enhances the exchange of the contrast agent between the tissue compartments. The molecular weight of the Gd-DTPA contrast agent allows it to diffuse outside the blood vessels into the extra-cellular compartment, but not to penetrate the cell membrane. Figure 2.4 shows the major tissue compartments involved in the distribution of contrast agent (represented by stars).
Contrast enhancement in DCE-MRI is related both to malignant and benign disease. However, contrast enhancement is also related to some healthy tissue such as the liver. To properly interpret DCE-MRI and to be able differentiate between malignant and benign lesions, a deep knowledge of breast and human anatomy is required. This knowledge provides contextual information that can easily be used by humans, but, to date, can hardly be automated for use in CAE tools.
Figure 2.4: Major compartments and functional variables involved in the distribution of a contrast agent
This section focuses on breast MRI and its interpretation. It describes the anatomy of the human breast, the types of breast cancer and their characteristics of appearance in breast MRI.
The human breast is actually a skin gland, enveloped in a fibrous fascia (Morris and Liberman, 2005). The breast content is bounded by the skin on the outside and by the pectoralis major muscle on the back side (which marks the beginning of the chest wall). There are many layers between the breast and the pectoralis major muscle. However, the breast is not completely separated from the pectoralis major muscle and there are lymphatic and blood vessels that penetrate the breast. Breast tissue is divided into parenchyma (glandular tissue) and stroma (connective/fibrous tissue). The parenchyma consists of 15 to 20 lobes (milk glands) that converge toward the nipple. Ducts from the lobes converge into 6 to 10 major ducts that hold a ductal ampulla, beneath the nipple and connect to the outside through the nipple (Figure 2.5). The lobes are arranged in segments of glandular tissue that are connected by stromal tissue (Morris and Liberman, 2005). A segment of lobular tissue, connected to a duct, is called Terminal Duct Lobular Units or TDLU (Figure 2.5). The stromal tissue is mainly fatty tissue and ligaments that surround the lobes and ducts in the breast.
Breast cancer can develop in each of the breast tissue types. Different tissue types may develop different types of cancer that may have different characteristics in DCE-MR images, thus making the description of malignant lesions more complicated.
Breast cancer is a heterogeneous disease which has several subtypes (Claus et al., 1993).� In general, breast cancer can be divided into two types:
1. Carcinoma in situ � when the malignant mass stays confined inside the tissue in which it has developed
2. Invasive carcinoma � when the malignant mass invades surrounding tissue.
Several histological subtypes of breast cancer are known.� Of these, the most common ones are (Claus et al., 1993):
1. Invasive ductal carcinoma (IDC). Starts in a duct, then breaks through the basement membrane (i.e. the wall of the duct) and invades the stromal tissue.
2. Ductal carcinoma in situ (DCIS). Cancerous cells develop inside a duct, but do not penetrate the basement membrane.
3. Invasive lobular carcinoma (ILC). Starts in a lobular gland and invades the surrounding tissue.
4. Lobular carcinoma in situ (LCIS). Also called lobular neoplasia, begins in a lobular gland, but does not penetrate the gland�s wall.
5. Medullary carcinoma.� This is an invasive breast cancer that has a well-defined boundary between the cancerous tissue and the surrounding tissue.
Some of the less common breast cancer types include the colloid carcinoma, tubular carcinoma and adenoid cystic carcinoma.
Figure 2.5: The anatomy of human breast
Adapted with changes from (Hayton, 1998).
In DCE-MRI, ductal carcinoma tends to show a linear enhancement similar to that of a blood vessel. Mass enhancement, on the other hand, is usually easier to spot and analyse if the lesion size is sufficient. Improving the specificity of DCE-MRI may thus improve both detection and categorisation of breast cancer and may help differentiate between enhancing normal tissue (e.g. blood vessels) and enhancing malignant tissue (e.g. DCIS).
The prevention of breast cancer is still impossible and thus the main treatment strategy relies on early detection, using mammography. Owing to its relatively high cost, DCE-MRI of the breast is usually reserved for cases with high probability or known malignancy and for cases where other imaging techniques (e.g. ultrasound, mammography) cannot provide a definitive answer. In most cases, X-ray mammography is performed first and only high risk patients are referred to DCE-MRI (Morris and Liberman, 2005). Other imaging methods include Computed Tomography (CT), Single Photon Emission Tomography (SPECT), Positron Emission Tomography (PET) and Tomosynthesis. These include a relatively high level of exposure to ionizing radiation, both on the patient�s side and on the technologist�s side. In SPECT and PET, a radio-isotope is injected into the patient blood stream and the photons that are emitted from the patient�s body, during the radioactive decay process, are then received by a detector to create the image.
In -weighted images, both normal breast tissue and fibrous tissue (i.e. connective tissue that is not muscles) show a low signal intensity and fat shows an intermediate to high signal intensity. Most benign and malignant lesions also show a low signal intensity on -weighted sequences and cannot be differentiated from normal breast tissue on non-enhanced -weighted images. In -weighted images, fat is of an intermediate signal intensity. The signal intensity of the breast tissue depends on the water content, varying from a low signal intensity in fibrosis to a high or very high signal intensity in the majority of cysts. In contrast-enhanced images, normal breast tissue demonstrates only a slight increase in signal intensity, with some exceptions (such as blood vessels). Malignant lesions enhance, but there are also benign lesions that may enhance in a similar fashion.
Patients with benign breast changes may show delayed and diffuse patchy enhancement in 25�30% of cases (Figure 2.6). However, in 5�10% of cases, there may be focal enhancement, which may be rapid and simulate malignancy (Figure 2.7).
Although tumours can be identified within fatty tissue, the differentiation of benign and malignant tumours cannot be undertaken with certainty using signal characteristics on -weighted or -weighted sequences, except in the case of a cyst. The use of intravenous gadolinium has increased both the sensitivity and specificity of breast MRI, because most malignant tumours enhance markedly (Warren and Coulthard, 2002).
Following the injection of a contrast agent, most cancers show an early steep rise in enhancement within the first 5 minutes, typically by 70�100% (a threshold that gives high sensitivity, but low specificity). If a lesion enhances by less than 60% or does not enhance at all, it is most likely to be benign, although up to 10% of cancers will also enhance slowly (Warren and Coulthard, 2002).
Time/intensity enhancement curves have been studied by many, including