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In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

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This study proposes using magnetically induced currents in medical infrared imaging to increase the temperature contrast due to the electrical conductivity differences between tumors and healthy tissues. There are two objectives: (1) to investigate the feasibility of this active method for surface and deep tumors using numerical simulations, and (2) to demonstrate the use of this method through different experiments conducted with phantoms that mimic breast tissues. Tumorous breasts were numerically modeled and simulated in active and passive modes. At 750 kHz, the applied current was limited for breast tissue-tumor conductivities (0.3 S/m and 0.75 S/m) according to the local specific absorption rate limit of 10 W/kg. Gelatin-based and mashed potato phantoms were produced to mimic tumorous breast tissues. In the simulation studies, the induced current changed the temperature contrast on the imaging surface, and the tumor detection sensitivity increased by 4 mm. An 11-turn 70-mm-long solenoid coil was constructed, 20 A current was applied for deep tumors, and a difference of up to 0.4  ∘ C was observed in the tumor location compared with the temperature in the absence of the tumor. Similarly, a 23-turn multi-layer coil was constructed, and a temperature difference of 0.4  ∘ C was observed. The temperature contrast on the body surface changed, and the tumor detection depth increased with the induced currents in breast IR imaging. The proposed active thermal imaging method was validated using numerical simulations and in vitro experiments.

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A hybrid method for tissue imaging using dielectric and elastic properties is proposed and investigated with simple bi-layered breast model. In this method, local harmonic motion is generated in the tissue using a focused ultrasound probe. A narrow-band microwave signal is transmitted to the tissue. The Doppler component of the scattered signal, which depends on the dielectric and elastic properties of the vibrating region, is sensed. A plane-wave spectrum technique is used together with reciprocity theorem for calculating the response of a vibrating electrically small spherical tumor in breast tissue. The effects of operating frequency, antenna alignment and distance, and tumor depth on the received signal are presented. The effect of harmonic motion frequency on the vibration amplitude and displacement distribution is investigated with mechanical simulations using the finite element method. The safety of the method is analyzed in terms of microwave and ultrasound exposure of the breast tissue. The results show that the method has a potential in detecting tumors inside fibro-glandular breast tissue.

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Harmonic Motion Microwave Doppler Imaging (HMMDI) method is recently proposed as a non-invasive hybrid breast imaging technique for tumor detection. The acquired data depend on acoustic, elastic and electromagnetic properties of the tissue. The potential of the method is analyzed with simulation studies and phantom experiments. In this paper, the results of these studies are summarized. It is shown that HMMDI method has a potential to detect malignancies inside fibro-glandular tissue.

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Tissues have different electrical conductivity and metabolic energy consumption values depending on their state of health and species. Since metabolic heat generation values show differences from tissue to tissue, thermal imaging has started to play an important role in medical diagnoses. Temperature differences of healthy and cancerous tissue may be changed by means of frequency dependent current stimulation within medical safety limits, and thus, depth dependent imaging performance can be increased. In this study, a three-dimensional realistic model of a woman breast and malignant tissue is generated and frequency dependent feasibility work for the proposed method is implemented. Temperature distributions are obtained by solving Pennes Bio Heat Equation (using finite element method). Temporal and spatial temperature distribution images are obtained at desired depths for two cases; with and without current application. Different temperature distributions are imaged by altering the frequency of the applied current and the corresponding conductivity value. Improvement in the imaging performance can be provided by current stimulation, and the temperature difference generated by 40 mm(3) tumor at 1.5 cm depth can be detected on breast surface with the state-of-the-art thermal imagers.

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We present the four key areas of research-preprocessing, the volume conductor, the forward problem, and the inverse problem-that affect the performance of EEG and MEG source imaging. In each key area we identify prominent approaches and methodologies that have open issues warranting further investigation within the community, challenges associated with certain techniques, and algorithms necessitating clarification of their implications. More than providing definitive answers we aim to identify important open issues in the quest of source localization.

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A new data acquisition system has been developed. This system measures the external magnetic fields due to induced currents in the body at a relatively low operation frequency of 50 kHz . Data is obtained by scanning a 2-D area on the body surface. For each transmitter position, a single sample (averaged) of the field distribution is used for image reconstruction. The Steepest Descent Algorithm is used to solve the inverse problem related to the field profiles. High-resolution images of agar blocks and an anesthetized leech are presented. The system sensitivity is measured as 13.2 mV/(S/m) using saline solution phantoms and as 155 V/S using resistors. The signal to noise ratio in the measurements is calculated to be 35.44 dB. The linearity in the measurements is explored using saline solutions in the biological conductivity range. The nonlinearity is measured to be 3.96% of the full scale. The nonlinearity is found to be 0.12% when resistor phantoms are used. The spatial resolution in the conductivity images is measured as 9.36 mm for a 7.5-mm-diameter cylindrical agar object. The results show that it is possible to distinguish two bars separated 14.4 mm from each other.

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The isolated problem approach (IPA) is a method used in the boundary element method (BEM) to overcome numerical inaccuracies caused by the high-conductivity difference in the skull and the brain tissues in the head. Hämäläinen and Sarvas (1989 IEEE Trans. Biomed. Eng. 36 165-71) described how the source terms can be updated to overcome these inaccuracies for a three-layer head model. Meijs et al (1989 IEEE Trans. Biomed. Eng. 36 1038-49) derived the integral equations for the general case where there are an arbitrary number of layers inside the skull. However, the IPA is used in the literature only for three-layer head models. Studies that use complex boundary element head models that investigate the inhomogeneities in the brain or model the cerebrospinal fluid (CSF) do not make use of the IPA. In this study, the generalized formulation of the IPA for multi-layer models is presented in terms of integral equations. The discretized version of these equations are presented in two different forms. In a previous study (Akalin-Acar and Gençer 2004 Phys. Med. Biol. 49 5011-28), we derived formulations to calculate the electroencephalography and magnetoencephalography transfer matrices assuming a single layer in the skull. In this study, the transfer matrix formulations are updated to incorporate the generalized IPA. The effects of the IPA are investigated on the accuracy of spherical and realistic models when the CSF layer and a tumour tissue are included in the model. It is observed that, in the spherical model, for a radial dipole 1 mm close to the brain surface, the relative difference measure (RDM*) drops from 1.88 to 0.03 when IPA is used. For the realistic model, the inclusion of the CSF layer does not change the field pattern significantly. However, the inclusion of an inhomogeneity changes the field pattern by 25% for a dipole oriented towards the inhomogeneity. The effect of the IPA is also investigated when there is an inhomogeneity in the brain. In addition to a considerable change in the scale of the potentials, the field pattern also changes by 15%. The computation times are presented for the multi-layer realistic head model.

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The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obtain the potential and magnetic field patterns using realistic head models. The formulations incorporate the use of the isolated problem approach for increased accuracy in solutions. If a personal computer is used for computations, each transfer matrix is calculated in 2.2 h. After this pre-computation period, solutions for arbitrary source configurations can be obtained in milliseconds for a realistic head model. A hybrid algorithm that uses snakes, morphological operations, region growing and thresholding is used for segmentation. The scalp, skull, grey matter, white matter and eyes are segmented from the multimodal magnetic resonance images and meshes for the corresponding surfaces are created. A mesh generation algorithm is developed for modelling the intersecting tissue compartments, such as eyes. To obtain more accurate results quadratic elements are used in the realistic meshes. The resultant BEM implementation provides more accurate forward problem solutions and more efficient calculations. Thus it can be the firm basis of the future inverse problem solutions.

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Monitoring the electrical activity inside the human brain using electrical and magnetic field measurements requires a mathematical head model. Using this model the potential distribution in the head and magnetic fields outside the head are computed for a given source distribution. This is called the forward problem of the electro-magnetic source imaging. Accurate representation of the source distribution requires a realistic geometry and an accurate conductivity model. Deviation from the actual head is one of the reasons for the localization errors. In this study, the mathematical basis for the sensitivity of voltage and magnetic field measurements to perturbations from the actual conductivity model is investigated. Two mathematical expressions are derived relating the changes in the potentials and magnetic fields to conductivity perturbations. These equations show that measurements change due to secondary sources at the perturbation points. A finite element method (FEM) based formulation is developed for computing the sensitivity of measurements to tissue conductivities efficiently. The sensitivity matrices are calculated for both a concentric spheres model of the head and a realistic head model. The rows of the sensitivity matrix show that the sensitivity of a voltage measurement is greater to conductivity perturbations on the brain tissue in the vicinity of the dipole, the skull and the scalp beneath the electrodes. The sensitivity values for perturbations in the skull and brain conductivity are comparable and they are, in general, greater than the sensitivity for the scalp conductivity. The effects of the perturbations on the skull are more pronounced for shallow dipoles, whereas, for deep dipoles, the measurements are more sensitive to the conductivity of the brain tissue near the dipole. The magnetic measurements are found to be more sensitive to perturbations near the dipole location. The sensitivity to perturbations in the brain tissue is much greater when the primary source is tangential and it decreases as the dipole depth increases. The resultant linear system of equations can be used to update the initially assumed conductivity distribution for the head. They may be further exploited to image the conductivity distribution of the head from EEG and/or MEG measurements. This may be a fast and promising new imaging modality.

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A data-acquisition system has been developed to image electrical conductivity of biological tissues via contactless measurements. This system uses magnetic excitation to induce currents inside the body and measures the resulting magnetic fields. The data-acquisition system is constructed using a PC-controlled lock-in amplifier instrument. A magnetically coupled differential coil is used to scan conducting phantoms by a computer controlled scanning system. A 10000-turn differential coil system with circular receiver coils of radii 15 mm is used as a magnetic sensor. The transmitter coil is a 100-turn circular coil of radius 15 mm and is driven by a sinusoidal current of 200 mA (peak). The linearity of the system is 7.2% full scale. The sensitivity of the system to conducting tubes when the sensor-body distance is 0.3 cm is 21.47 mV/(S/m). It is observed that it is possible to detect a conducting tube of average conductivity (0.2 S/m) when the body is 6 cm from the sensor. The system has a signal-to-noise ratio of 34 dB and thermal stability of 33.4 mV/degrees C. Conductivity images are reconstructed using the steepest-descent algorithm. Images obtained from isolated conducting tubes show that it is possible to distinguish two tubes separated 17 mm from each other. The images of different phantoms are found to be a good representation of the actual conductivity distribution. The field profiles obtained by scanning a biological tissue show the potential of this methodology for clinical applications.

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