All four of the modalities being investigated by our group work by iteratively optimizing a two- or three-dimensional finite element (FE) model of specific material properties throughout some portion of the breast. An optimization algorithm compares actual measurements made outside the breast—light intensities, electromagnetic (EM) fields, or mechanical displacements—to data predicted using the FE model. The model is then iteratively adjusted to make its predictions approximately match observation, and the property distribution corresponding to the best available convergence is used to generate an image. It is because of FE modeling's essential role in this process that we refer to all four techniques as model-based alternative breast-imaging modalities.
Below, we briefly indicate the physical basis of each imaging modality. We then describe how we integrate our research on all four modalities into a single initiative centered on two shared-resource "cores," one clinical and one computational.
2.1 Magnetic Resonance Elastography (MRE)
In this technique, mechanical vibrations are applied to the breast's surface that propagate through the breast as a three-dimensional, time-harmonic spatial displacement field varying locally with the mechanical properties of each tissue region. Magnetic resonance (MR) techniques are used to image this displacement field. These data are used to optimize an FE model of the breast's three-dimensional mechanical property distribution by iteratively refining an initial estimate of that distribution until the model predicts the observed displacements as closely as possible. MRE is distinguished from the other three methods discussed in this book by the fact that a very large, three-dimensional data set is supplied to its FE modeling algorithm. This mandates special "subzone" techniques to reduce the computational challenge, as discussed in Chapter 3. MRE is also the only nontomographic technique in this set of alternative modalities.
The principal hypothesis underpinning our MRE project is that the mechanical properties of breast tissue provide unique information for the detection, characterization, and monitoring of pathology. There is much evidence to suggest that tissue hardness is strongly associated with cancer. The effectiveness of clinical palpation for hard tissue in discovering larger tumors is well-established; in the Breast Cancer Demonstration Project, approximately one-third of malignancies were discovered by physical examination rather than by x-ray mammography . Although little quantitative work has appeared on the mechanical properties or behavior of breast tissue, measurements of the sonoelasticity of masses in rodent prostatectomy specimens have shown good correlations with elasticity [13-15].
As detailed in Chapter 4, our MRE team has recovered images based on time-harmonic, steady-state mechanical wave generation, MR measurement, and numerical inversion to form images of mechanical properties at or near the acquisition resolution of MRI. Further, a number of clinical exams have been completed that have demonstrated feasibility, provided preliminary estimates of the elastic properties of the normal breast, and highlighted areas where further investigation is warranted.
2.2 Electrical Impedance Spectroscopy (EIS)
EIS passes small AC currents through the pendant breast by means of a ring of electrodes placed in contact with the skin. Magnitude and phase measurements of both voltage and current are made simultaneously at all electrodes.
The observed patterns of voltage and current are a function both of the signals applied and of the interior structure of the breast. EIS seeks to optimize an FE model of the spatial distribution of conductivity and permittivity in the breast's interior, using the applied signals as known inputs and the observed signals as known outputs. EIS is referred to as electrical impedance spectroscopy because AC currents can be applied to the breast at a wide range of frequencies.
In the frequency range of interest for this modality, the so-called j3 dispersion is sensitive to cellular morphology and tissue microarchitecture, particularly membrane structures (both intra- and extracellular). At the low end of the spectrum, charging and discharging of membranes occurs, which introduces capacitance and forces electric current to pass through the extracellular medium. As frequency is increased, cellular capacitive reactance decreases, which causes an increase in current flow through the intracellular space. This makes higher-frequency signals more sensitive to intracellular influences. Also at higher frequencies, dipolar reorientation of proteins and tissue organelles can occur. Hence, the ¡3 dispersion electrical-property spectrum contains information about both the extra- and intracellular environments.
A study by Cuzick et al.  supports this view. The authors measured the electrical depolarization index of breasts in vivo for 661 women scheduled for open biopsy. Comparison of abnormalities detected from the electrical depolarization data to biopsy results yielded 70% specificity at 80% sensitivity and 55% specificity at 90% sensitivity for palpable masses. The authors hypothesize that the measured effect results from a loss of transepi-thelial potential during the carcinogenesis of normally polarized epithelial cells, and further surmise that abnormal proliferation extending around the borders of the malignancy into the surrounding regions of the affected site (which has been shown to occur in breast and other epithelial cancers) causes the electrical differences sensed at the surface. If these intrinsic electrical polarization-depolarization phenomena do occur, they will perturb the actively induced electric fields associated with EIS imaging and may produce a detectable, larger-than-tumor signature.
Further, there are significant differences between the electrical impedances of histologically-confirmed diseased breast tissue and normal breast [17-20]. These impedance heterogeneities within and around a tumor can be discriminated with EIS. Further, the dispersion characteristics of normal and cancerous tissues differ. This last fact is of particular interest; it means that it may be possible to create a clinical tool that spatially resolves spectroscopic information in such a way as to distinguish tumor from normal tissue.
The goal of our EIS team has been to develop an ultrafast, multidimensional (i.e., spatio-spectral) EIS imaging system complete with data acquisition electronics, breast positioning interface, and exam-control and image-reconstruction software. We have constructed three generations of such systems, the first of which has been operational for the majority of exam sessions described in Ch. 6 of this book and the latest of which represents a large step forward in capability and speed and is now operational for clinical use. This advanced instrument is a considerable asset in addressing fundamental questions surrounding the potential role of EIS in breast-imaging applications. It has yet to be optimized for clinical use from both the hardware and software perspectives (see Ch. 6).
2.3 Microwave Imaging Spectroscopy (MIS)
Like EIS, MIS interrogates the breast using EM fields. It differs in using much higher frequencies (300-3000 MHz). In this range it is appropriate to treat EM phenomena in the breast in terms of wave propagation rather than voltages and currents. The technologies and mathematics used in EIS and MIS are, therefore, somewhat divergent, despite the fact the both exploit EM interactions in tissue.
Like EIS and NIS, MIS surrounds the breast with a circular array of transducers. In this case, these are antennas capable of acting either as transmitters or receivers. Unlike the transducers used in EIS and NIS, these antennas are not in direct contact with the breast but are coupled to it through a liquid medium (i.e., the breast is pendant in a liquid-filled tank). Sinusoidal microwave radiation at a fixed frequency is emitted by one antenna and measured at the other antennas. Each antenna takes its turn as the transmitter until the entire array has been so utilized. A wide range of frequencies may be employed, hence the term "microwave imaging spectroscopy." As in the other modalities, an FE model of either a two-dimensional slice or a three-dimensional subvolume of the breast is iteratively adjusted so that the magnitude and phase measurements predicted using the transmitted waveforms as known inputs converge as closely as possible with those actually observed. The breast properties imaged are permittivity and conductivity, as in EIS, but because of the disjoint frequency ranges employed these properties may serve as proxies for different physiological variables in the two techniques.
Electromagnetic fields interact with tissues through three basic mechanisms: (1) the displacement of conduction (free) electrons and ions in tissue as a result of the force exerted on them by the applied EM field; (2) polariza tion of atoms and molecules to produce dipoles; and (3) orientation of permanently dipolar molecules in the direction of the applied field. The number of free electrons and ions that are available to create a conduction current within the tissue in response to an applied field is proportional to the tissue's intrinsic electrical conductivity. The degree to which it can be polarized, either by the creation of new dipoles or by the co-orientation of permanently dipolar molecules, is a measure of its permittivity.
Ex vivo data show that electrical property values can differ by a factor of 5 to 10 between normal and malignant human breast tissues over the microwave frequency range [21, 22]. Malignant mammary tumors apparently have electrical properties which mimic those typically found in high-water-content tissues such as muscle, whereas normal breast has properties typical of low-water-content, fatty tissues. The increased blood volume associated with the neovascularization of the rapidly proliferating tumor periphery may be responsible for increased water content, a variable to which microwave illumination is particularly sensitive. In fact, one study has found that for normal and malignant human tissues of the same histological type, greater differences in electrical properties occur in mammary than in colon, kidney, liver, lung, and muscle .
In short, EM properties in the microwave band offer high intrinsic contrast for pathology, especially in the breast. Exploiting this contrast for imaging has been challenging because of the difficulties associated with inducing and measuring a response noninvasively that can be used to discriminate local variations in EM properties. However, our MIS effort has met a number of these challenges and is poised to complete the first critical evaluation of the potential of microwave breast imaging. A clinical imaging system has been realized that transceives broadband, high-fidelity propagating fields through a noncontacting antenna array translated axially under computer control; this system will deliver MIS exams to pendant breasts immersed in a fluid that promotes signal coupling.
2.4 Near Infrared Spectroscopic Imaging (NIS)
In NIS, a circular array of optodes (in this case, optical fibers transceiving infrared laser light) is placed in contact with the pendant breast. Each optode in turn is used to illuminate the interior of the breast, serving as a detector when nonactive. A two- or three-dimensional FE model of the breast's optical properties is iteratively optimized until simulated observations based on the model converge with observation.
Published data have long supported the notion that near infrared spectroscopy and imaging offer excellent contrast potential. Studies have shown 2:1 contrast between excised tumor and normal breast at certain near infrared wavelengths [23, 24]. Correlations with increase in blood vessel number and size (which is characteristic of neovascularization in the tumor periphery and may lead to a fourfold increase in blood volume) have been reported  and have been estimated to translate into 4:1 contrast in optical absorption coefficients  (see Sec. 3, "Correlation With Pathology").
In addition to the absorption contrast afforded by blood-concentration changes in tumorigenic regions of the breast, contrast specificity provided by light scattering resulting from calcifications involving matrix accumulation of insoluble phosphates, often associated with tumors, may also be exploitable for imaging purposes . The detailed forms of microcalcifications would not be visible due to spatial resolution limits, but the aggregate optical signature of calcification clusters may be detectable. Another potential contrast mechanism is provided by the lipid content of the tissue, the spectral peaks of which occur at 750 nm and 940 nm; these peaks would presumably be reduced in breast cancers as compared to surrounding, normal, fattier tissue. It is furthermore notable that the optical properties imaged spectrally with NIS—absorption and scatter—can be used to deduce certain physiological variables, such as total hemoglobin concentration and oxygen saturation. These are being investigated as possible means to differentiate benign from malignant breast disease (see Ch. 10).
Our NIS initiative has been the first of our modality initiatives to regularly employ three-dimensional data acquisition and image reconstruction during clinical breast exams. Further, it has led the way in terms of analyzing its imaging data in both the normal and abnormal breast in relation to clinical factors and histological indicators in order to explore and explain the biological/physiological basis of image contrast. It has also pioneered the overall movement within our program toward image assessment by both quantitative methods (contrast-to-noise metrics) and qualitative methods (observer experiments) in order to characterize how nonlinear image reconstruction influences traditional contrast-detail and region-of-interest curves.
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