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.

The dilute suspension properties, including the intrinsic viscosity, intrinsic solvent diffusivity, intrinsic conductivities of perfect conductors and perfect insulators, for a family of particles that smoothly interpolate between spheres and cubes were determined using three different simulation techniques in order to explore the role of particle shape.

The Coulomb energy E_C is defined by the energy required to charge a conductive object and scales inversely to the self–capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number 〈m〉, a natural measure of knot complexity and, correspondingly, we find E_C to be directly related to 〈m〉 of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute E_C for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈E_C〉 is directly proportional to 〈m〉. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi–flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path-integral, and finite-element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi-conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self-avoiding worm-like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex-shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (α_E, α_M) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient $\left[\sigma \right]$ in the conductive and insulating particle limits, which are required to estimate $\left[\sigma \right]$ in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for α_E and α_M that should be useful in materials design and characterization applications.

In composites, carbon nanotubes (CNTs) are rarely perfectly straight and they usually exhibit complex shapes. In this paper, we employ the method-of-moments formulation for arbitrary thin wires to study the electromagnetic scattering characteristics of CNTs with realistic shapes. More than 800 different CNT shapes were simulated in this work. These shapes were generated using a coarse-grained molecular dynamics model calibrated using realistic CNT shapes encountered experimentally. The analysis shows that the shape and orientation of CNTs has a strong effect on the scattered electromagnetic response. We used the theory of characteristic modes (TCM) to explain this dependence of the scattered electromagnetic waves on the shape of the CNT. Using TCM, we developed simplified but highly accurate formulas that link the shapes of the CNTs to the resonances in their total extinction coefficient spectrum. These formulations have the potential to be the basis for advancing the nondestructive evaluation of CNT composites using electromagnetic waves as well as the development of novel CNT electromagnetic systems and devices.

The capability of the level set method is illustrated for shape and location reconstruction using real measurement data in the range of 3-8 GHz. An experimental setup is utilized to measure the S-parameters using two Vivaldi antennas revolving around metallic pipes of different cross-sections. A two-dimensional reconstruction of the pipe's cross section is retrieved using the level set algorithm combined with the method of moments and the frequency hopping technique. The results show good agreement between the reconstructed cross section and the true configuration. This indicates to the strength of the level set method and its ability to cope with the noise in real measurements.