This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Under the alternating electrical excitation, biological tissues produce a complex electrical impedance which depends on tissue composition, structures, health status, and applied signal frequency, and hence the bioelectrical impedance methods can be utilized for noninvasive tissue characterization. As the impedance responses of these tissue parameters vary with frequencies of the applied signal, the impedance analysis conducted over a wide frequency band provides more information about the tissue interiors which help us to better understand the biological tissues anatomy, physiology, and pathology. Over past few decades, a number of impedance based noninvasive tissue characterization techniques such as bioelectrical impedance analysis (BIA), electrical impedance spectroscopy (EIS), electrical impedance plethysmography (IPG), impedance cardiography (ICG), and electrical impedance tomography (EIT) have been proposed and a lot of research works have been conducted on these methods for noninvasive tissue characterization and disease diagnosis. In this paper BIA, EIS, IPG, ICG, and EIT techniques and their applications in different fields have been reviewed and technical perspective of these impedance methods has been presented. The working principles, applications, merits, and demerits of these methods has been discussed in detail along with their other technical issues followed by present status and future trends.

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Bioelectrical Impedance Methods for Noninvasive Health Monitoring: A Review.

Visualization of dynamic functional and molecular events in an unperturbed in vivo environment is essential for understanding the complex biology of living organisms and of disease state and progression. To this end, optoacoustic (photoacoustic) sensing and imaging have demonstrated the exclusive capacity to maintain excellent optical contrast and high resolution in deep-tissue observations, far beyond the penetration limits of modern microscopy. Yet, the time domain is paramount for the observation and study of complex biological interactions that may be invisible in single snapshots of living systems. This review focuses on the recent advances in optoacoustic imaging assisted by smart molecular labeling and dynamic contrast enhancement approaches that enable new types of multiscale dynamic observations not attainable with other bio-imaging modalities. A wealth of investigated new research topics and clinical applications is further discussed, including imaging of large-scale brain activity patterns, volumetric visualization of moving organs and contrast agent kinetics, molecular imaging using targeted and genetically expressed labels, as well as three-dimensional handheld diagnostics of human subjects.

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Advanced optoacoustic methods for multiscale imaging of in vivo dynamics

We review the history of photoacoustics from the discovery in 1880 that modulated light produces acoustic waves to the current time, when the pulsed variant of the discovery is fast developing into a powerful biomedical imaging modality. We trace the meandering and fascinating passage of the effect along several conceptual and methodological trajectories to several variants of the method, each with its set of proposed applications. The differences in mechanisms between the intensity modulated effect and the pulsed version are described in detail. We also learn the several names given to the effect, and trace the modern-day divide in nomenclature.

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Photoacoustics: a historical review

Breast cancer is anticipated to be responsible for almost 40,000 deaths in the USA in 2011. The current clinical detection techniques suffer from limitations which motivated researchers to investigate alternative modalities for the early detection of breast cancer. This paper focuses on reviewing the main electromagnetic techniques for breast cancer detection. More specifically, this work reviews the cutting edge research in microwave imaging, electrical impedance tomography, diffuse optical tomography, microwave radiometry, biomagnetic detection, biopotential detection, and magnetic resonance imaging (MRI). The goal of this paper is to provide biomedical researchers with an in-depth review that includes all main electromagnetic techniques in the literature and the latest progress in each of these techniques.

Review of Electromagnetic Techniques for Breast Cancer Detection

We present a photoacoustic computed tomography investigation on a healthy human finger, to image blood vessels with a focus on vascularity across the interphalangeal joints. The cross-sectional images were acquired using an imager specifically developed for this purpose. The images show rich detail of the digital blood vessels with diameters between 100 μm and 1.5 mm in various orientations and at various depths. Different vascular layers in the skin including the subpapillary plexus could also be visualized. Acoustic reflections on the finger bone of photoacoustic signals from skin were visible in sequential slice images along the finger except at the location of the joint gaps. Not unexpectedly, the healthy synovial membrane at the joint gaps was not detected due to its small size and normal vascularization. Future research will concentrate on studying digits afflicted with rheumatoid arthritis to detect the inflamed synovium with its heightened vascularization, whose characteristics are potential markers for disease activity.

Initial results of finger imaging using photoacoustic computed tomography.

A Projection Error Propagation-based Regularization (PEPR) method is proposed and the reconstructed image quality is improved in Electrical Impedance Tomography (EIT). A projection error is produced due to the misfit of the calculated and measured data in the reconstruction process. The variation of the projection error is integrated with response matrix in each iterations and the reconstruction is carried out in EIDORS. The PEPR method is studied with the simulated boundary data for different inhomogeneity geometries. Simulated results demonstrate that the PEPR technique improves image reconstruction precision in EIDORS and hence it can be successfully implemented to increase the reconstruction accuracy in EIT.> doi:10.5617/jeb.158 J Electr Bioimp, vol. 2, pp. 2-12, 2011

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Improving Image Quality in Electrical Impedance Tomography (EIT) Using Projection Error Propagation-Based Regularization (PEPR) Technique: A Simulation Study

A Block Matrix based Multiple Regularization (BMMR) technique is proposed for improving conductivity image quality in EIT. The response matrix (J T J) has been partitioned into several sub-block matrices and the highest eigenvalue of each sub-block matrices has been chosen as regularization parameter for the nodes contained by that sub-block. Simulated boundary data are generated for circular domain with circular inhomogeneity and the conductivity images are reconstructed in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm. Conductivity images are reconstructed with BMMR technique and the results are compared with the Single-step Tikhonov Regularization (STR) and modified Levenberg-Marquardt Regularization (LMR) methods. It is observed that the BMMR technique reduces the projection error and solution error and improves the conductivity reconstruction in EIT. Result show that the BMMR method also improves the image contrast and inhomogeneity conductivity profile and hence the reconstructed image quality is enhanced. ; doi:10.5617/jeb.170 J Electr Bioimp, vol. 2, pp. 33-47, 2011

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Improving Conductivity Image Quality Using Block Matrix-based Multiple Regularization (BMMR) Technique in EIT: A Simulation Study

Conductivity image reconstruction is studied with a Block Matrix based Multiple Regularization (BMMR) technique in Electrical Impedance Tomography (EIT) using practical phantoms. The response matrix (JTJ) is partitioned into several sub-block matrices and the largest element of each sub-block matrices is taken as regularization parameter for the nodes of the FEM mesh contained by that sub-block. Boundary potential data are collected from practical phantoms with different inhomogeneity configurations and the conductivity images are reconstructed in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm. Conductivity images, reconstructed with BMMR technique, are compared with the images obtained with Single-step Tikhonov Regularization (STR) and modified Levenberg-Marquardt Regularization (LMR) methods. Results show that BMMR technique reduces the reconstruction error and reconstruct the better conductivity images by improving the conductivity profile of the domain under test for all the phantoms. Image analysis showed that the BMMR method improves image contrast parameters, conductivity profiles, and spatial resolution of the reconstructed images.

Improving the image reconstruction in Electrical Impedance Tomography (EIT) with block matrix-based Multiple Regularization (BMMR): A practical phantom study

Purpose: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). Methods: DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Results: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. Conclusions: We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data. (C) 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3531572]

Samir Kumar Biswas

Papers

Initial results of finger imaging using photoacoustic computed tomography.

Improving Image Quality in Electrical Impedance Tomography (EIT) Using Projection Error Propagation-Based Regularization (PEPR) Technique: A Simulation Study

Improving Conductivity Image Quality Using Block Matrix-based Multiple Regularization (BMMR) Technique in EIT: A Simulation Study

Improving the image reconstruction in Electrical Impedance Tomography (EIT) with block matrix-based Multiple Regularization (BMMR): A practical phantom study

Accelerated gradient based diffuse optical tomographic image reconstruction.