# Magneto-Acoustic Imaging in Biology
## 3 Mat-Mi
### Recent Advances in MAT-MI  
Although [PERSON]'s laboratory dominated the early development of magneto-acoustic tomography with magnetic induction, several other groups began to independently examine the procedure. One of the earliest was in 2008, when [PERSON] and his student [PERSON] examined how MAT-MI is affected by anisotropy [31]. Anisotropy means that the conductivity depends on direction. It changes the relationship between the current density and electric field by rotating the current density toward the direction of highest conductivity. Therefore, in anisotropic tissue the current density may have a nonzero curl even if the electric field has zero curl. [PERSON] and [PERSON] analyzed MAT-MI in a homogenous but anisotropic tissue and found that the acoustic wave had an amplitude that was about three times larger in the direction perpendicular to the tissue's fibers. If MAT-MI is used to image conductivity in muscle, or any other fibrous tissue, anisotropy must be accounted for to get accurate results [31; 32].  
[PERSON] and collaborators at the Nanjing Normal University in China devised a better way to analyze MAT-MI data based on acoustic dipole radiation as opposed to monopole radiation [33; 34; 35; 36]. Computer simulations and gel phantom experiments indicated that the technique not only detected conductivity boundaries, but also could reconstruct the entire conductivity distribution, including homogeneous regions, with excellent spatial resolution.  
[PERSON], [PERSON], and their coworkers at the West Pomeranian University of Technology in Poland have derived analytical solutions to idealized examples of MAT-MI [37; 38; 39]. Although analytical solutions always have limiting assumptions, such analytical expressions provide valuable insight into how the system depends on parameters and are useful when testing numerical algorithms for computer simulations.  
[PERSON] and colleagues from the Liaoning Technical University in China have employed magnetic nanoparticles as a contrast agent for MAT-MI [40; 41; 42]. Contrast agents are common in imaging modalities: magnetic resonance imaging uses drugs containing gadolinium and X-ray imaging uses high atomic number elements such as barium and iodine. The use of contrast agents always raises safety concerns (a substance is being injected into the tissue), but it can improve the image quality depending on the specificity of the agent. In MAT-MI, the presence of nanoparticles increased the Lorentz force and the acoustic signal. Furthermore, the nonlinear magnetoacoustic properties of magnetic nanoparticles may allow second harmonic responses that could improve the quality and spatial resolution of the image [43].  
The development of MAT-MI continues to this day as an ingenious technology for measuring electrical conductivity in biological tissue, taking advantage of sophisticated techniques such as the finite element method [44], singular value decomposition [45], ring transducer arrays [46], and others [47; 48; 49].  
The dozens of publications about this technique all trace their origin to [PERSON]'s \"reverse method\" proposed in his landmark 1998 article [6]. However, in that paper, [PERSON] additionally proposed a \"forward method\" that has likewise generated intense interest among biomedical engineers. We must now return to the turn of the century to follow the evolution of this forward method: MAET.