Magneto-Acoustic Imaging in Biology

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Magneto-acoustic methods can be used to image electrical conductivity in biological samples.

Abstract

This review examines the use of magneto-acoustic methods to measure electrical conductivity. It focuses on two techniques developed in the last two decades: Magneto-Acoustic Tomography with Magnetic Induction (MAT-MI) and Magneto-Acousto-Electrical Tomography (MAET). These developments have the potential to change the way medical doctors image biological tissue.

1. Introduction

Measurement of electrical conductivity has many potential applications in biology and medicine. For instance, tumors often have different electrical properties than the surrounding tissue, so imaging conductivity might be suitable for cancer diagnosis and screening. The distribution of conductivity has been determined using several techniques, including electrical impedance tomography, magnetic resonance electrical impedance tomography, and magnetic induction tomography. This review considers relatively new methods to image conductivity based on magnetic forces, often known as Lorentz forces [1]. Two of these techniques—Magneto-Acoustic Tomography with Magnetic Induction (MAT-MI) and Magneto-Acousto-Electrical Tomography (MAET)—will be analyzed in detail.

2. Lorentz Forces in Biology and Medicine

2.1. Towe and Islam’s Magneto-Acoustic Imaging of Current

In 1988, Bruce Towe and Mohammed Islam, working at Arizona State University, developed a “novel method for the noninvasive measurement of low-level ionically conducted electric currents flowing in electrolytes and tissue” [2]. Of particular interest for this review are their experiments to detect current in hamsters (Figure 1). A few microamps of current, oscillating at a frequency of 3 kHz, were passed through electrodes placed on the neck and near the rectum. At the same time, the hamster was exposed to a 0.2 T magnetic field.

An electric current in a magnetic field experiences a Lorentz force that is directed perpendicular to both the current and field. In Towe and Islam’s experiment, this force caused an acoustic oscillation that was detected with a microphone and a lock-in amplifier. They were able to record currents as low as 7 μA, and concluded that the technique was “a possible basis for a new method of noninvasively measuring bioelectric currents in living organisms.” Their subsequent investigations improved their algorithm for imaging the current distribution [3,4]. From this simple beginning arose all of the results described in this review.

2.2. The Source of the Magneto-Acoustic Signal

Brad Roth, employed at the National Institutes of Health and collaborating with Peter Basser and John Wikswo, calculated the displacement generated by the Lorentz force acting on a current dipole in a conducting sphere [5] (Figure 2). Their analysis of Navier’s equation governing the mechanical behavior of an elastic medium showed that the pressure distribution obeyed the Poisson equation, with a source term equal to the dot product of the magnetic field and the curl of the current density. They confirmed that the displacement is inversely proportional to the shear modulus of the tissue and is not localized around the dipole but instead is distributed widely throughout the sphere. Furthermore, they noted that magneto-acoustic and biomagnetic measurements image the current density in similar ways.

2.3. Wen and Balaban’s Forward and Reverse Methods to Image Conductivity

In 1998, Han Wen, working in Robert Balaban’s laboratory at the National Institutes of Health, was the first to adopt a Lorentz force approach to image conductivity [6]. Like in Towe’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. Wen 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 Wen’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. Wen et al. [6] applied 0.6 MHz ultrasound pulses with a duration of about 150 μs. 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.

Wen and his coworkers named their forward method “Hall Effect Imaging.” In a comment on Wen et al.’s paper, Roth and Wikswo 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 Wen 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, Roth and Wikswo explained why the ultrasound signal in Wen 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 is particularly strong where there is a conductivity discontinuity. In addition, Roth and Wikswo 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. One branch was based on Wen’s reverse method where an electrical signal was injected and an acoustic signal was detected, and the other was based on Wen’s forward method where an acoustic signal was injected and an electrical signal was detected. The reverse method led to MAT-MI.

3. MAT-MI

3.1. Xu and He’s Invention of Magneto-Acoustic Tomography with Magnetic Induction

In 2005, Bin He directed the Biomedical Functional Imaging and Neuroengineering Laboratory at the University of Minnesota, where Yuan Xu was a postdoc. There, Xu and He published their first article on “Magneto-Acoustic Tomography with Magnetic Induction,” which they abbreviated as “MAT-MI” [10]. The novel feature of MAT-MI that distinguished it from Towe’s magneto-acoustic imaging of current and from Wen’s reverse method for conductivity imaging was that Xu and He introduced current into the tissue by electromagnetic induction instead of injecting it through electrodes (Figure 4). The advantage of induction is that the induced current is more uniform. For example, suppose you were measuring the conductivity distribution in the brain. If you passed the current through electrodes on the head, most of the current would shunt through the high conductivity scalp with relatively little passing through the low conductivity skull to enter the brain. This shielding effect is minimized during induction, because the magnetic permeability of the skull, scalp, and brain are all about the same, nearly equal to the permeability of air or a vacuum.

Xu and He’s technique required two magnetic fields: a strong (1 T) static field and a time-varying field. The varying field was applied in brief pulses with a rise time of about a microsecond. This changing magnetic field induced a pulse of eddy current in the sample that interacted with the static field to create a Lorentz force. This force acted as the source of an acoustic wave that was detected by ultrasonic transducers at various locations surrounding the sample. The arrival time of the acoustic signal indicated the distance of the source from the transducer.

Their image reconstruction algorithm consisted of first determining the source of the signal (the dot product between the static magnetic field and the curl of the eddy current density), and then determining the conductivity by dividing the source by the dot product of the static and time-varying magnetic fields [10]. Again, the signal originated primarily from locations where there was a conductivity gradient. As a proof-of-concept, they used MAT-MI to image a coil of wire.

3.2. Development of MAT-MI in Bin He’s Laboratory

Although the 2005 article by Xu and He established MAT-MI as a feasible way to measure conductivity, the nagging question was if it could image biological tissue instead of a loop of wire. Working with graduate student Xu Li, they soon improved the method so it could image saline and gel phantoms having a conductivity comparable to that of tissue [11,12]. Moreover, they performed a detailed theoretical analysis in which they started with a known conductivity distribution, calculated the ultrasound signal that should be produced by it during MAT-MI, added noise, and then ran the results through their conductivity imaging algorithm [12]. This analysis allowed them to determine how sensitive MAT-MI was to noise.

He, collaborating with Li and visiting scientist Rongmin Xia, altered MAT-MI by adding an acoustic lens in front of the ultrasound transducer [13]. In this way, the transducer detected an acoustic signal from a single plane, producing a two-dimensional image that is analogous to a traditional ultrasound B-scan. The sample could then be scanned in the direction perpendicular to that plane, providing a three-dimensional imaging procedure that they called the “focused cylindrical scanning mode.” They used this technique to analyze a block of pork muscle embedded in a layer of fat, which produced the first image of a biological sample using MAT-MI. Graduate student Leo Mariappan and coworkers in He’s lab [14] extended this idea, showing that focusing allowed the transducer to be placed closer to the sample than a nonfocused “point-receiver” transducer, increasing its sensitivity. Qingyu Ma and He further explored the theoretical underpinnings of MAT-MI [15,16].

Xia, Li, and He then formulated a new theory for MAT-MI imaging [17]. They started by noting that the source of the acoustic signal is the divergence of the Lorentz force distribution, which for a uniform magnetic field is equal to the dot product of the magnetic field and the curl of the current density. However, a general vector field is specified by its divergence and curl, and Xia et al. lacked information about the curl of the Lorentz force distribution. They noted that the curl of the force typically produces shear waves rather than pressure waves, and shear waves attenuate rapidly. Therefore, they ignored the curl of the force and analyzed a curl-free vector field whose divergence was the acoustic source. Their theoretical analysis and computer simulations showed that this innovative vectorial approach improved the reconstruction of the conductivity distribution.

One of the most frustrating limitations of most MAT-MI algorithms for imaging conductivity was that they detected a signal arising from where the conductivity changed, but could not image regions having a uniform conductivity. Li and He discovered they could get around this limitation if they utilized multiple coils to induce the eddy currents [18] (Figure 5). Their novel design, which they named “multi-excitation MAT-MI,” provided a better estimation of the conductivity in regions where it is homogeneous. A subsequent paper combined the multi-excitation scheme with acoustic focusing to create a truly three-dimensional imaging technique [19].

By 2010—a mere five years after the introduction of magnetoacoustic tomography with magnetic induction—Bin He’s group was perfecting MAT-MI as a powerful tool for imaging biological tissue [20]. With Gang Hu, He was able to image tissue with a spatial resolution of better than 2 mm [21]. The resolution is ultimately set by the frequency response of the ultrasonic transducer. Their transducers responded to signals with a frequency of about 500 kHz. To further improve the resolution would require detecting higher frequencies, but such high-frequency waves suffer from severe attenuation. He’s team could image conductivity below 1 S/m using single excitation MAT-MI, which is far simpler than the multi-excitation version with multiple coils [22]. They were now in a position to begin studying medically relevant samples. They could detect conductivity differences between normal liver tissue and liver tissue with a tumor [23] and evaluated the system for breast tumor imaging [24]. Working with graduate student Kai Yu, they increased the operating frequency to 1.5 MHz and were able to reach an unprecedented 1 mm spatial resolution, which enabled them to track internal structures within a growing tumor in a mouse cancer model [25].

Most analyses of MAT-MI assumed that the electrical properties of the sample were heterogeneous but the acoustic properties were homogeneous. In an article by Lian Zhou working in He’s group, this assumption was relaxed [26]. They used computer simulations to examine the implications of the speed of sound being inhomogeneous. The speed of sound is important, because it connects the latency of the ultrasonic pulse to the distance from the source of the signal to the transducer. They incorporated known heterogeneities into the MAT-MI imaging algorithm, thereby enhancing the quality of their images. Apparently no analyses of MAT-MI have examined heterogeneities of the acoustic impedance. This parameter may be just as significant as the speed of sound, because traditional ultrasonic imaging is based on waves reflected from boundaries between tissues having different acoustic impedances. If the MAT-MI signal were corrupted by spurious echoes, then reflections off of surfaces separating tissues with unlike acoustic impedances would need to be included in the imaging algorithm. Fortunately, in practice such echoes do not appear to be a problem.

Additional studies from He’s group refined vector source imaging [17], adopted sophisticated concepts such as beamforming and vector imaging point spread functions to improve their imaging algorithm [27], performed finite element calculations of MAT-MI that provide better analysis of irregularly shaped objects [28], and used an exceptionally strong 9.4 T magnetic field associated with a magnetic resonance imaging scanner to further improve the spatial resolution [29]. In 2016, Bin He and his associates summarized their decade of MAT-MI research in a tutorial review [30].

3.3. Recent Advances in MAT-MI

Although Bin He’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 Roth and his student Kaytlin Brinker 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. Brinker and Roth 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].

Xiaodong Sun 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.

Marcin Ziolkowski, Adam Zywica, 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.

Xiao-Heng Yan 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 Han Wen’s “reverse method” proposed in his landmark 1998 article [6]. However, in that paper, Wen 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.

4. MAET

4.1. Montalibet’s Measurement of Current Using the Ultrasonically Induced Lorentz Force

Amalric Montalibet was a graduate student at the National Institute for Health and Medical Research in Lyon, France, when he published—with Jacques Jossinet, Adrien Matias, and Dominique Cathignol—the 2001 article “Electric Current Generated by Ultrasonically Induced Lorentz Force in Biological Media” [50]. Their sample was a volume of pig blood. They applied a brief pulse of ultrasound in the z direction; 5 cycles of a 500 kHz wave with an amplitude of 1.5 MPa. The sample was positioned in a nearly uniform, static, 0.35 T magnetic field oriented in the x direction, which was produced by a permanent magnet. The Lorentz force on the moving ions in the blood separated the negative and positive charge, resulting in an electrical current in the y direction detected by two electrodes that were attached to a current-to-voltage converter (Figure 6). A typical voltage response had an amplitude of about 10 mV.

One of Montalibet’s goals was to confirm that the signal arose from the Lorentz force. He repeated the experiment using an iron “phantom” that had the same shape and size as his permanent magnet but was not magnetized; the response disappeared. He varied the distance between the sample and the ultrasound transducer and observed a time shift in the electric signal that was consistent with the speed of sound. He turned off the ultrasound transducer and the current vanished. He varied the electrical conductivity of his sample and saw a corresponding change in the current. He concluded that “the signal was really created within the medium by Lorentz force: no electrode effect, no signal in the absence of ultrasound or magnetic induction, signal linearly shifted against the distance of the measurement chamber from the transducer, signal proportional to the electric conductivity, as predicted by the theory.” Although he did not use the term “Magneto-Acousto-Electrical Tomography,” his paper nevertheless established the physical basis of MAET.

In a follow-up article, Montalibet and his colleagues applied their method to imaging electrical conductivity [51]. They found that the technique was most sensitive to conductivity gradients, and in particular boundaries between regions of different conductivity. They carried out experiments with agar gel phantoms and everyone’s favorite tissue for studying conductivity: bacon. They could estimate the center of their 10 μs ultrasound pulse to slightly better than one microsecond. These pulses were propagated at a speed of about 1500 m/s, providing a spatial resolution of approximately 1 mm. They contended that “the advantages of this new modality for tissue characterization include the permeability of body tissue to magnetic field and ultrasound, the harmlessness of the applied fields and the improved spatial resolution in the measurement of a tissue’s electric conductivity distribution.”

4.2. Xu and the Development of Magneto-Acousito-Electrical Tomography

Montalibet’s investigations were followed by a pause of several years while the focus of effort shifted from France to Canada. Yuan Xu—the postdoc who helped Bin He conceive of MAT-MI—joined the Department of Physics at Ryerson University (now named the Toronto Metropolitan University) and continued his interest in developing high-spatial-resolution maps of electrical conductivity. Working with Saja Haider, Xu coined the term “Magneto-Acousto-Electrical Tomography” in a 2008 article published in the journal Physiological Measurements [52]. Their theoretical analysis was based on the concept of a “lead field,” the current density distribution that is produced when current is applied through a pair of electrodes. Although they were not applying current through electrodes in their experiment, the lead field was a critical part of their algorithm to image electrical conductivity. In fact, the experiment, which was similar to that conducted earlier by Montalibet, was intended to map the lead field, which could then be used to map conductivity. Haider and her coworkers shared a frustration common among those using MAET: it was great for locating conductivity gradients but was insensitive to regions with uniform conductivity. They speculated that the presence of many microscopic, randomly distributed scatterers (speckles) may improve their sensitivity in macroscopically homogeneous tissue.

Another of Xu’s graduate students, Elena Renzhiglova, further refined MAET [53]. She and her collaborators noted that in a homogeneous tissue the MAET signal is small in part because the spatial oscillations of the short wavelength ultrasonic wave create both positive and negative sources that cancel. To avoid this, they invented a dual-frequency technique, which they called “DF-MAET.” The difference between the two frequencies generates an electric field through a mechanism based on the radiation force of ultrasound. The wavelength of this low-frequency source was long compared to the size of the sample so it did not lead to cancelation of sources and thus provided a stronger signal in a homogeneous medium.

4.3. New Directions in Magneto-Acoustic Tomography

Roth and his students examined two novel ideas related to MAET. Nancy Tseng recognized that ultrasound in the presence of a magnetic field created a unique signature in anisotropic tissue [54]. As in traditional MAET, if the ultrasonic vibration propagates in the z direction and the magnetic field is in the x direction, then the Lorentz force produces a current in the y direction. If, however, the tissue’s electrical conductivity is anisotropic, and the fibers are aligned at an angle to the y-axis, then the Lorentz force and the current it causes will not point in the same direction. The anisotropy rotates the current away from the y-axis, producing a component in the z direction. Because the ultrasonic wave propagates in the z direction, this creates oscillating regions of positive and negative charge and voltage that travel in sync with the wave (Figure 7). In principle, this zebra stripe-like voltage distribution could be observed and would provide information about the anisotropy. Unfortunately, it would probably need to be detected using electrodes within the tissue, instead of electrodes placed around and outside the sample, and therefore may not be practical for noninvasive studies.

Kevin Schalte explored MAET theoretically, but he applied a continuous ultrasonic source rather than a pulsed one [55]. This modification sacrifices one of the main advantages associated with pulsed ultrasound imaging: the delay of a pulse response maps to the distance from the ultrasound detector. The continuous wave instead creates a sinusoidally distributed current source. If, in addition, the conductivity is divided into a background homogeneous part and a spatially varying part, Roth and Schalte showed that the heterogenous part produces a current dipole that creates an electric signal at a distant electrode. They then proposed that measurements on a sample be repeated with ultrasonic waves of different wavelengths and in many directions, and proved that such a procedure would map out the two-dimensional Fourier transform of the heterogeneous part of the conductivity distribution in the spatial frequency domain. Once such an experiment was complete, an inverse Fourier transform would yield the two-dimensional conductivity distribution. “Tomography” is the “T” in MAT-MI and MAET, but of all the conductivity imaging techniques Schalte’s algorithm is the most closely related to true tomography as used in an x-ray computed tomography scan or in MRI. The idea of employing plane waves propagating in a variety of directions during MAET has been extended by several groups [56,57,58,59]. Gözü et al. employed a phased array transducer to provide steerability of the ultrasonic wave [60].

4.4. Grasland-Mongrain and Lorentz Force Electrical Impedance Tomography

Meanwhile back in France, Habib Ammari and an international team of mathematicians analyzed theoretically three techniques: MAT-MI, MAET, and magneto-acoustic current imaging [61]. They did not use the term “MAET” but instead referred to it as “Vibration Potential Tomography.” In each case, they proposed creative algorithms for solving the inverse problem of determining the conductivity distribution from the voltage or pressure. Leonid Kunyansky contributed to the mathematical formulations of these problems too [62].

The next advance in MAET began with the research of graduate student Pol Grasland-Mongrain, who earned his PhD in December, 2013, at the University of Lyon under the direction of Cyril Lafon and Jean-Yves Chapelon. The MAET technique is plagued by many alternative names; Grasland-Mongrain et al. refer to it as “Lorentz Force Electrical Impedance Tomography,” or “LFEIT” [63]. They noted that one limitation of traditional (non-Lorentz) electrical impedance tomography is the ill-posed nature of the inverse problem for calculating conductivity from voltage signals. They explained that LFEIT (or MAET) overcomes this limitation by having a spatial resolution similar to that of ultrasound imaging. Grasland-Mongrain’s approach was like Montalibet’s: an ultrasound transducer, a magnet, and two electrodes to record the voltage. Preferring beef to pork, they acquired a remarkable image of the electrical conductivity of a beef sample containing a complex marbling of fat.

MAET works by causing tissue to vibrate, providing the motion required for the Lorentz force. Could this motion be observed directly (instead of indirectly through the resulting charge separation and electrical current)? In another article arising from his dissertation, Grasland-Mongrain and his coworkers detected displacement in a soft polyvinyl alcohol gel using ultrasound imaging [64]. The experiment was more closely related to Wen’s reverse method; they passed current through the gel in a magnetic field and measured displacement. The gel contained 0.1% graphite powder, which let them use the speckle pattern to image the low-frequency micron-sized displacements. When they repeated the experiment without the magnetic field, the displacements disappeared, ruling out a thermal expansion of the sample brought about by the one hundred milliamps of current. Furthermore, they were able to detect shear waves in the sample. Sound waves have a displacement parallel to the direction of propagation (a longitudinal wave), whereas shear waves have a displacement perpendicular to the direction of propagation (a transverse wave) (Figure 8). They could use their data to estimate the shear modulus. Their later studies created shear waves in tissue with a transcranial magnetic stimulator in a static magnetic field [65] and they believed that these waves might be useful for shear wave elastography [66].

Grasland-Mongrain et al. further probed the speckle pattern and its contribution to MAET [67]. They observed speckle during MAET imaging and suggested that it has spatial characteristics analogous to the speckle common in ultrasonic imaging, but claimed that it arises from a microscopic heterogeneity of electrical conductivity rather than acoustic parameters. They speculate that speckle-based image processing might enhance the image quality of MAET.

Grasland-Mongrain then teamed up with Ammari and collaborators to improve MAET algorithms [68]. They introduced an optimal control method and a modified regularization scheme, and proved that this algorithm “yields the true conductivity distribution as the regularization parameter approaches zero.” Their computations allowed them to evaluate the stability and resolution of the process in the presence of noise.

In 2018, Grasland-Mongrain and Lafon reviewed many techniques for imaging conductivity, including MAT-MI and MAET [69]. They concluded that “electrical conductivity provides potentially a good contrast among biological tissues, with for example a difference from one to ten between adipose tissue and blood at 1 MHz. Although electrical impedance imaging will hardly replace any standard imaging methods (ultrasound imaging, magnetic resonance imaging, CT scan), it could be used as a complement to differentiate tissues.”

4.5. Recent Advances in MAET

The last decade has seen a burst of activity in developing MAET. For example, Liang Guo, Guoqiang Liu, and Hui Xia, of the University of the Chinese Academy of Sciences, proposed a new twist to MAET [70]. They applied an ultrasound pulse to the tissue in a magnetic field, inducing current. They did not record this current with electrodes, however, but instead detected its associated magnetic field with coils. They referred to their technique as “Magneto-Acousto-Electrical Tomography with Magnetic Induction” (MAET-MI), not to be confused with “Magneto-Acoustic Tomography with Magnetic Induction” (MAT-MI). In MAT-MI, the ultrasound transducer detects the acoustic signal, whereas in MAET-MI the transducer generates the acoustic wave. MAET-MI has the advantage over traditional MAET in that it does not require attaching electrodes to the sample; it is non-contact (similar to magnetic resonance imaging). Their computer simulations and gel phantom experiments demonstrated that they could reliably reconstruct the conductivity distribution with MAET-MI. Additionally, other groups have investigated how to implement MAET using coils in place of electrodes [71,72].

Zhishen Sun and associates at the University of the Chinese Academy of Sciences examined another topic linked to MAET, which they called the “secondary process” [73]. An ultrasonic wave in the presence of a magnetic field produces a current. This current, which is in the same magnetic field, creates an acoustic response, as it does during MAT-MI. This secondary process introduces a conductivity-dependent linear damping of the original ultrasonic wave. Sun et al. show, however, that this effect is tiny and should be negligible in biological tissue.

Most measurements of conductivity using MAET are based on the assumption that the electrode is small and makes perfect contact with the sample. Nick Polydorides has carried out finite element model calculations to examine the consequence of large electrodes with a significant contact impedance [74]. He established that electrode area is the dominant artifact compared to a lossy contact, and recommended ways to minimize the electrode effect.

Haoming Lin and his collaborators combined MAET with shear wave elasticity imaging using a single linear array transducer, providing a powerful dual-modal imaging method [75]. With their device, they could make simultaneous measurements of a pork sample’s electrical and mechanical properties.

Much recent research has focused on optimizing the shape for the ultrasound pulse used in MAET. For instance, studies by Zhi-Shen Sun and collaborators [76,77] and by Ming Dai and coworkers [78,79] applied a pulse with a linearly increasing frequency (a “chirp”), somewhat similar to the slice-selection radio-frequency pulses used in magnetic resonance imaging. The pulse sweeps a frequency range, resulting in a central peak with side lobes. Such pulses reduce the peak power by about 25 dB (a factor of over 300), which increases the transducer lifetime. Although pulse compression methods can make the pulse have a longer duration, Sun et al. [77] were able to still obtain 1 mm spatial resolution with such methods.

Another modification of the excitation waveform is to use a coded pulse. Several groups have implemented a Barker coded excitation, which is a digital coding originally developed for pulse compression of radar [80,81,82]. One advantage of such coding is that it increases the signal-to-noise ratio, thereby improving the signal quality. Another advantage is that it can increase the speed of signal processing. In Montalibet et al.’s original MAET experiment, they had to average the signal 2000 times in order to have adequate signal-to-noise ratio [51]. Coded excitation can reduce the need for extensive signal averaging, thereby shortening the imaging time without sacrificing signal quality.

A tremendous amount of additional research on MAET has taken place in the last few years, mainly in China [83,84,85,86,87,88,89,90,91,92,93,94,95].

5. Conclusions

Magneto-Acoustic Tomography with Magnetic Induction and Magneto-Acousto-Electrical Tomography are unique ways to image electrical conductivity in biological tissue. Over the last 35 years, pioneers such as Bruce Towe, Han Wen, Bin He, and Amalric Montalibet, as well as many others, have broke new ground and advanced the field. Research into MAT-MI and MAET appears to be accelerating and these methods hold much promise. One glaring limitation of these studies is the lack of clinical applications: no conductivity maps have been obtained from human patients with the goal of diagnosing disease. Until MAT-MI and MAET prove themselves to be valuable in the clinic, they will remain scientific curiosities of merely academic interest. Nevertheless, the techniques have the potential to revolutionize the way medical doctors image biological tissue.