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  • CHAPTER 15

    Breast Imaging using Electrical ImpedanceTomography (EIT)

    Gary A. Ybarra, Qing H. Liu, Gang Ye, Kim H. Lim, Joon-Ho Lee, William T. Joines, andRhett T. GeorgeDepartment of Electrical and Computer Engineering, Duke University, Box 90291 Durham, NC 27708-0291

    CONTENTS

    1. Introduction ................................................................................................... 002. 3D Electrical Impedance Tomography System at Duke University ............................ 003. The EIT Inversion Problem and Image Reconstruction ........................................... 00

    3.1. Problem Formulation............................................................................... 003.1.1. Electrodes Modeling .................................................................... 00

    3.2. The Inverse Problem................................................................................ 003.3. Discretization......................................................................................... 00

    3.3.1. Validation with Measured Data....................................................... 003.4. Inversion of Synthetic Data....................................................................... 003.5. Inversion of Measured Data ...................................................................... 00

    4. Conclusion..................................................................................................... 00References........................................................................................................... 00

    1. INTRODUCTION

    X-ray mammography is the standard imaging method used forearly detection of breast cancer. Unfortunately, the procedureis uncomfortable or even painful for many women, the highcost of the system forbids its widespread use in developingcountries, the ionizing radiation exposure is damaging to thebreast tissue, and the harmful effects are cumulative. Further-more, the method suffers from high percentages of missed de-tections and false alarms resulting in fatalities and unneces-sary mastectomies.

    Electrical impedance tomography (EIT) is an attractive al-ternative modality for breast imaging. The procedure is com-fortable, the clinical system cost is a small fraction of thecost of an X-ray system, making it affordable for widespread

    ISBN:1-58883-090-XCopyright c 2007 American Scientific PublishersAll rights of free production any former reserved.

    screening. The procedure poses no safety hazards, and the po-tential is significant for detecting very small tumors in earlystages of development.

    This chapter begins with an historical account of researchand development of EIT systems. The Duke system is thendescribed in detail, including our inversion algorithm basedon a distorted Born iterative method [1, 2] (Section 2).

    The first impedance imaging system was the impedancecamera constructed by Henderson and Webster [3]. The sys-tem used a rectangular array of 100 electrodes placed on thechest with a single large electrode placed on the back. Elec-trodes were driven sequentially with a 100 kHz voltage signal,while the resulting current flowing into each driven electrodewas measured. A conductivity contour map was producedbased on the assumption that currents flowed in straight lines

    Emerging Technology in Breast Imaging and MammographyEdited by Jasjit Suri, Rangaraj M. Rangayyan, and Swamy Laxminarayan

    Pages:116

  • 2 Breast Imaging using Electrical Impedance Tomography (EIT)

    through the subject. The image showed relatively low conduc-tivity regions corresponding to the locations of the lungs witha maximum to minimum contrast ratio of approximately 2.5:1.

    In the early eighties, Barber and Brown [4] constructed arelatively simple EIT system using 16 electrodes and applieda constant amplitude current at 50 kHz between two electrodesat a time [5]. Differential voltages were recorded from adja-cent electrodes. Data were recorded at a rate sufficient to gen-erate 10 images per second. The images were computed usinga method known as back-projection, a method that had beenused with great success in the field of X-ray tomography. Theimage appeared to show bones, muscle tissue, and blood ves-sels. However, the resolution of the image was very low. Thisimage is generally regarded as the first successful in vivo im-age generated by an EIT system.

    EIT images of the lungs and gastrointestinal system werepublished in 1985 [6]. These images showed the passageof tap water through the esophagus as well as conductivitychanges in the lung regions during respiration. The images,scaled in units of log resistivity change, were of low resolu-tion. Studies were undertaken to assess the accuracy of thegastric function images and good correlation with other meth-ods was obtained [7]. Experiments were also undertaken toassess the systems use for monitoring respiration [8], cardiacfunctions [9], hyperthermia [10], and intraventricular hemor-rhage in low-birth weight neonates [11]. Although the exper-iments produced images of the required function, the reso-lution remained low at 10% of the diameter of the observedregion.

    At the same time, work progressed on alternative recon-struction algorithms such as the perturbation method [12] andthe Newton-Raphson method. Yorkey and Webster [13] con-cluded that the Newton-Raphson method was the best of theexisting iterative EIT reconstruction techniques in one-stepcorrection and in image accuracy for a given number of it-erations.

    Since the mid-1980s, interest in EIT has grown consider-ably. A number of European research groups have adopted theback-projection algorithm. A recent trend is the use of back-projection at multiple frequencies and the use of data fromone frequency as the reference against which data at other fre-quencies may be imaged [14, 15, 16]. In 1989, this methodwas used to produce a frequency-based differential image ofthe abdomen, and, in 1990, of the forearm [17]. The forearmimage demonstrated that the significant change in muscle con-ductivity with frequency between 40 kHz and 80 kHz allowsmuscle tissue to be clearly imaged. The feasibility of imagingbased on the change in conductivity phase angle was demon-strated in 1991 using both a resistive phantom and an in vivomeasurement of the thorax [18].

    In 1987 in vitro and in vivo studies were carried out to de-termine the feasibility of imaging local temperature changesusing EIT to monitor hyperthermia therapy [14]. EIT may beused for temperature monitoring because tissue conductivityis known to change with temperature.

    Since 1987, Holder and others [19, 20, 21] have researchedthe use of back-projection-based EIT system for imaging thebrain. In 1990, Smith introduced the Sheffield (mark 2) system[22]. The images produced were of conductivity change ratherthan absolute conductivity and of low resolution. In 1992, Bar-ber and Brown began work on a multi-frequency tomograph(mark 3), which operated at seven frequencies between 9.6kHz and 614 kHz. Results published in 1994 showed EIT im-ages of the lungs based on conductivity variation with fre-quency [23]. The images were similar to those obtained usingconductivity change.

    Gisser, Newell, and Isaacson at Rensselaer Polytechnic In-stitute (RPI) were the first to adopt an adaptive, multiple-driveapproach to EIT. In 1987, the term distinguishability was in-troduced [24] to describe how different current distributionpatterns generate different boundary voltages for a given con-ductivity distribution. The optimum current distribution pat-tern produces the largest change in boundary voltages for agiven conductivity distribution when compared to those pro-duced from a uniform current distribution. The generationof optimum current distributions requires an EIT instrumentcapable of applying currents with independently controllableamplitudes to all electrodes simultaneously.

    Hartov et al. [25] at Dartmouth built and tested a 32-channel, multifrequency (DC to 1 MHz) 2D EIT system.The resolution of the A/D converter was 16-bits with a 200kHz sampling frequency. The system simultaneously applieda voltage signal and measured currents at all electrodes. Mag-nitudes and phases of impedance were calculated using thereference voltage and the response current signals. Image re-construction was based on the Newton method. In their fi-nite element modeling, they used a dual mesh approach: afine mesh for voltage calculation in the forward problem; acoarse mesh for calculating conductivity and permittivity inthe inverse problem. Osterman et al. [26] modified the Dart-mouth EIT system to investigate its feasibility for routinebreast examinations. In their in vivo test, 16 electrodes formedan electrode array and were in direct contact with the breastthrough a radially translating interface. The electrode arraywas located below an examination table, on which a partici-pant would lie prone with the breast to be imaged pendant inthe array. Multi-channel measurements were conducted at 10frequencies on both breasts. Thirteen women were tested. Theexamination of each breast took about 10 minutes. The resultsshowed that structural features in the EIT images correlatedwith limited clinical information available on the participants.However, near-surface electrode artifacts were evident in thereconstructed images. They concluded that their system wassensitive, but not very specific. An initial study on the consis-tency of the exam has been performed with an improved breastinterface [27]. With increasing levels of electrode placementuncertainty, they imaged 25 breasts in four separate substud-ies. Their results suggest that their EIT breast exams are con-sistent provided the electrode placement is well controlled,typically with better than 1 cm accuracy. The major limitation

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