# Magneto-Acoustic Imaging in Biology
## 2 Lorentz Forces in Biology and Medicine
### [PERSON] and [PERSON]'s Forward and Reverse Methods to Image Conductivity  
In 1998, [PERSON], working in [PERSON]'s laboratory at the National Institutes of Health, was the first to adopt a Lorentz force approach to image conductivity [6]. Like in [PERSON]'s experiment, he applied current pulses to a tissue sample using two electrodes. The sample was in a static magnetic field and the resulting pressure was detected with an ultrasound transducer. [PERSON] and his collaborators used this technique to image a block of bacon, whose alternating layers of fat and muscle had markedly different conductivities. The axial position of each layer could be determined from the arrival time of the acoustic signal produced by the Lorentz force. A later arrival time corresponded to a deeper layer because the acoustic signal needed more time to propagate to the transducer. They found that the acoustic signal emanated from regions where the conductivity was changing, which in their case meant the boundaries between fat and muscle. In [PERSON]'s nomenclature, this design--in which current was injected through electrodes and an acoustic signal was recorded with a transducer--was termed the \"reverse method\" of conductivity imaging. The \"forward method\" is the opposite process: an acoustic signal is injected through a transducer and the resulting electrical signal is recorded using electrodes [6; 7; 8] (Figure 3). The forward method also operates through the Lorentz force. The ultrasonic wave causes the tissue to oscillate back and forth. The charged ions in the conducting fluid move with the tissue. If a static magnetic field is present, these moving ions experience a Lorentz force: the cations in one direction and the anions in the opposite direction. This separation of positive and negative charge acts as a source of the electrical potential detected by the electrodes. [PERSON] et al. [6] applied 0.6 MHz ultrasound pulses with a duration of about 150 \(\upmu\)s. Again, the origin of the signal was localized to where the conductivity was changing. A typical voltage difference recorded by the electrodes was a few microvolts. [PERSON] and his coworkers named their forward method \"Hall Effect Imaging.\" In a comment on [PERSON] et al. 's paper, [PERSON] and [PERSON] pointed out that the term \"Hall effect\" is misleading [9]. In traditional Hall effect studies, a current makes the positive and negative charge carriers move in _opposite_ directions, so their magnetic deflections are in the same direction. A voltage appears only if the positive and negative charges have different mobilities or concentrations. In [PERSON] et al. 's technique, the acoustic oscillation makes the positive and negative charge carriers move in the _same_ direction, so their magnetic deflections are in opposite directions. A voltage is induced even if the mobilities and concentrations of the positive and negative charges are identical. Thus, this review will not use the term \"Hall Effect Imaging.\"  
In their comment, [PERSON] and [PERSON] explained why the ultrasound signal in [PERSON] et al. 's reverse method arises where the conductivity changes [9]. Its source is the curl of the current. In a homogeneous region, the current is proportional to the electric field, and in a static magnetic field the curl of the electric field is zero, so there is no source. The curl of the current is nonzero only in regions where there is a conductivity gradient and  
Figure 3: The forward and reverse methods to perform magneto-acoustic imaging. is particularly strong where there is a conductivity discontinuity. In addition, [PERSON] and [PERSON] mentioned that in anisotropic tissue the curl of the current density does not vanish even if the tissue is homogeneous. At the start of the twenty-first century, the path leading toward the development of a Lorentz force technique to measure electrical conductivity forked.