Induced Current Electro-Thermal Imaging for Breast Tumor Detection: A Numerical and Experimental Study

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.

On the utilization of the adjoint method in microwave tomography

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.

Harmonic Motion Microwave Doppler Imaging method for breast tumor detection

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.

Harmonic motion microwave Doppler imaging: a simulation study using a simple breast model

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.

Use of the isolated problem approach for multi-compartment BEM models of electro-magnetic source imaging

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.

An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging

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.

Sensitivity of EEG and MEG measurements to tissue conductivity

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.

Electrical conductivity imaging via contactless measurements: an experimental study

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.

Forward problem solution of electromagnetic source imaging using a new BEM formulation with high-order elements

Representations of the active cell populations on the cortical surface via electric and magnetic measurements are known as electromagnetic source images (EMSIs) of the human brain. Numerical solution of the potential and magnetic fields for a given electrical source distribution in the human brain is an essential part of electromagnetic source imaging. In this study, the performance of the boundary element method (BEM) is explored with different surface element types. A new BEM formulation is derived that makes use of isoparametric linear, quadratic or cubic elements. The surface integration is performed with Gauss quadrature. The potential fields are solved assuming a concentric three-shell model of the human head for a tangential dipole at different locations. In order to achieve 2% accuracy in potential solutions, the number of quadratic elements is of the order of hundreds. However, with linear elements, this number is of the order of ten thousand. The relative difference measures (RDMs) are obtained for the numerical models that use different element types. The numerical models that employ quadratic and cubic element types provide superior performance over linear elements in terms of accuracy in solutions. Assuming a homogeneous sphere model of the head, the RDMs are also obtained for the three components (radial and tangential) of the magnetic fields. The RDMs obtained for the tangential fields are, in general, much higher than those obtained for the radial fields. Both quadratic and cubic elements provide superior performance compared with linear elements for a wide range of dipole locations.

Electrical conductivity imaging via contactless measurements

A new imaging modality is introduced to image electrical conductivity of biological tissues via contactless measurements. This modality uses magnetic excitation to induce currents inside the body and measures the magnetic fields of the induced currents. In this study, the mathematical basis of the methodology is analyzed and numerical models are developed to simulate the imaging system. The induced currents are expressed using the A-phi formulation of the electric field where A is the magnetic vector potential and phi is the scalar potential function. It is assumed that A describes the primary magnetic vector potential that exists in the absence of the body. This assumption considerably simplifies the solution of the secondary magnetic fields caused by induced currents. In order to solve phi for objects of arbitrary conductivity distribution a three-dimensional (3-D) finite-element method (FEM) formulation is employed. A specific 7 x 7-coil system is assumed nearby the upper surface of a 10 x 10 x 5-cm conductive body. A sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular-value decomposition of the sensitivity matrix shows various characteristics of the imaging system. Images are reconstructed using 500 voxels in the image domain, with truncated pseudoinverse. The noise level is assumed to produce a representative signal-to-noise ratio (SNR) of 80 dB. It is observed that it is possible to identify voxel perturbations (of volume 1 cm3) at 2 cm depth. However, resolution gradually decreases for deeper conductivity perturbations.

Forward problem solution for electrical conductivity imaging via contactless measurements

The forward problem of a new medical imaging system is analysed in this study. This system uses magnetic excitation to induce currents inside a conductive body and measures the magnetic fields of the induced currents. The forward problem, that is determining induced currents in the conductive body and their magnetic fields, is formulated. For a general solution of the forward problem, the finite element method (FEM) is employed to evaluate the scalar potential distribution. Thus, inhomogeneity and anisotropy of conductivity is taken into account for the FEM solutions. An analytical solution for the scalar potential is derived for homogeneous conductive spherical objects in order to test FEM solutions. It is observed that the peak error in FEM solutions is less than 2%. The numerical system is used to reveal the characteristics of the measurement system via simulations. Currents are induced in a 9x9x5 cm body of conductivity 0.2 S m(-1) by circular coils driven sinusoidally. It is found that a 1 cm shift in the perturbation depth reduces the field magnitudes to approximately one-tenth. In addition, the distance between extrema increases. Further simulations carried out using different coil configurations revealed the performance of the method and provided a design perspective for a possible data acquisition system.

Differential characterization of neural sources with the bimodal truncated SVD pseudo-inverse for EEG and MEG measurements

A method for obtaining a practical inverse for the distribution of neural activity in the human cerebral cortex is developed for electric, magnetic, and bimodal data to exploit their complementary aspects. Intracellular current is represented by current dipoles uniformly distributed on two parallel sulci joined by a gyrus. Linear systems of equations relate electric, magnetic, and bimodal data to unknown dipole moments. The corresponding lead-field matrices are characterized by singular value decomposition (SVD). The optimal reference electrode location for electric data is chosen on the basis of the decay behavior of the singular values. The singular values of these matrices show better decay behavior with increasing number of measurements, however, that property is useful depending on the noise in the measurements. The truncated SVD pseudo-inverse is used to control noise artifacts in the reconstructed images. Simulations for single-dipole sources at different depths reveal the relative contributions of electric and magnetic measures. For realistic noise levels the performance of both unimodal and bimodal systems do not improve with an increase in the number of measurements beyond approximately 100. Bimodal image reconstructions are generally superior to unimodal ones in finding the center of activity.

Optimal reference electrode selection for electric source imaging

One goal of recording voltages on the scalp is to form images of electrical sources across the cerebral cortex (electric source imaging). In this study, an objective criterion is introduced for selecting the optimal location for the reference electrode to attain the maximum spatial resolution of the source image, for example as provided here by the truncated singular value decomposition pseudo-inverse solution. The head model features a realistic cortex within a 3-shell conductive sphere, and pyramidal cell activity is represented by 9104 normal current elements distributed across the cortical area. On the scalp, 234 electrodes provide the measurements with respect to a chosen reference electrode. The effects of the reference electrode when located at the mastoid, occipital pole, vertex or center of the head are analyzed by a singular value decomposition of the lead field matrices. Sensitivity to noise, and hence the spatial resolution, is found to depend on characteristics of the lead field matrix that are determined by the choice of the image source surface, electrode array and location of the reference electrode. Using a reference close to a source surface increases the sensitivity of the measurement system in identifying the nearby activity of low spatial frequency content. However, this feature is compromised by a reduction in spatial resolution for distant cortical areas due to noise in the measurements. A new performance measure, the image sensitivity map, is introduced to identify the cortical regions that provide peak image sensitivity. This measure may be exploited in designing the geometry of an electrode array and selecting the location of the reference electrode to follow the activity on a specific area of the cortical surface.

Electrical impedance tomography: induced-current imaging achieved with a multiple coil system

An experimental study of induced-current electrical impedance tomography verifies that image quality is enhanced by employing six rather than three induction coils by increasing the number of independent measurements. However, with an increasing number of coils, the inverse problem becomes more sensitive to measurement noise. Using 16 electrodes to measure surface voltages, it is possible to collect 6 x 15 = 90 independent measurements. For comparison purposes, images of two-dimensional conductivity perturbations are reconstructed by using the data for three and six coils with the truncated pseudoinverse algorithm. By searching for the optimal truncation index that minimizes the noise error plus the resolution error, the signal-to-noise ratio of the data acquisition system was established as 58 db. Images obtained with this six-coil system reveal the sizes and locations of the conductivity perturbations. This system also provides images within the central region of the object space, a capability not achieved in previous experimental studies using only three circular coils. Nevertheless, the three-coil system can identify the conductivity perturbations near the periphery. However, it displays shifts in the locations and spread in the sizes of perturbations near the center of the object.

A comparative study of several exciting magnetic fields for induced current EIT

In this study, the selection of coil configuration parameters (coil radius and coil centre shift) for induced current EIT using circular coils is investigated. An alternative coil configuration is suggested, which produces approximately linear (spatially) magnetic fields in order to strengthen the currents in the central region. Injected current EIT, with Sheffield data collection protocol, and induced current EIT, with two different coil configurations, are compared with respect to singular-value patterns, sensitivity distributions and imaging performances. It is observed that for the proposed alternative coil configuration the measurements are more sensitive to inner region conductivity perturbations when compared to injected current EIT and induced current EIT using circular coils. The images obtained by induced current EIT are comparable to that obtained by injected current EIT.

Electrical impedance tomography. Determination of the boundary of an object inserted into a water-filled cylinder

In order to circumvent the electrode position determination problem in static electrical impedance tomography, it is possible to insert the object to be imaged into a water-filled cylinder on which the electrodes are at fixed and known positions. It has previously been shown that if the boundary of the internally placed object and the conductivity of the salty water in the cylinder are known, then a significant improvement in the conductivity image of the object is obtained. An algorithm for finding the boundary of an internally placed object is developed based on the finite element method (FEM). The boundary is assumed to obey a parametric model and the parameters are estimated by inverting a matrix representing the sensitivity of the boundary voltage measurements to parameter variations. The algorithm assumes that the object's internal conductivity is uniform and known. Simulation studies show that if the internal conductivity is not uniform to the extent found in the arm cross-sections, up to 9% error in the boundary, as measured from a centrally placed reference point, may result. It is also shown that if previous knowledge about the boundary shape is used to model the boundary with fewer numbers of parameters, then the boundary may be found with less error.

Electrical impedance tomography using induced and injected currents

A two-dimensional forward problem formulation is introduced for electrical impedance tomography (EIT) using induced currents. The forward problem is linearised around a certain resistivity distribution and the inverse problem is formulated as a solution of a linear system of equations. Sensitivity of boundary measurements to resistivity variations are analysed for spatially uniform, linear and quadratic fields. The formulation, however, is suitable for studying the effects of a general magnetic field applied to induce the currents in the conductive object. A similar inverse problem formulation is also developed for EIT using injected currents. Simulation studies are performed by reconstructing images of a simulation distribution using both methods separately with generalised inversion. It is also shown that the derived formulations for the inverse problems of the two methods can be combined to solve a larger set of equations with a greater number of independent measurements.