The schematic diagram of TMAS is shown in the lower-right of Fig. 1(a). The action of a focused ultrasonic wave moves charged ions in the nerve tissue. When a magnetostatic field is perpendicular to the movement direction of the charged ions, the Lorentz force on the ions can be induced in the tissue.^[12] The Lorentz force separates the positive and negative ions to opposite directions, thereby forming electric current I_ext to stimulate neurons.

Fig. 1.

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Fig. 1. (a) Schematic diagram of the experiment setup. (C: computer, HSP: headstage probe, MACA: microelectrode AC amplifer, USTC: ultrasonic transmitter card, SMF: static magnetic field, ME: microelectrode, US: ultrasound, UST: ultrasound transducer, PM-N: permanent magnet-N pole, PM-S: permanent magnet-S pole, R: rat, PI: positive ion, NI: negative ion, LF: Lorenz force, and EC: electric current). (b) The photography of the experiment setup (SA: stereotaxic apparatus, GW: ground wire, RW: reference wire, UC: ultrasonic collimator, and PM: permanent magnet).

We assume that the pressure waves are longitudinal and propagate along the z axis and that the magnetostatic field is along the x axis, thereby placing the current density along the y axis in the standard Cartesian coordinate axes.

A longitudinal pressure wave propagating along the z axis obeys the classical wave equation

The relationship between the magnitude of the speed of a fluid element and the magnitude of the instantaneous pressure P can be expressed as

According to Montalibet’s theory,^[13] the current density J_y along the y axis, generated by ultrasound and magnetostatic fields in a biological medium can be expressed as

The relationship between the intensity of the ultrasonic power and the ultrasound pressure satisfies the following equation:

Combining Eqs. (3), (7), and (8), we obtain the following equation:

The electric current field J_y induced by Lorentz force can give rise to a secondary electric current field J_s. The total electric current field J can be expressed as

The value of the total electric current density J, which corresponds to the electric current I_ext, can be used to stimulate the neuron and is used for simulation in the Hodgkin–Huxley neuron model.

The Hodgkin–Huxley neuron model, which successfully describes the dynamic process of the generation of squid axon action potential,^[15,16] is a representative model for studying electrophysiological characteristics of a neuron. The Hodgkin–Huxley neuron model includes the following differential equations^[15]

The fixed parameters used for simulation are listed in Table 1.

Table 1.

Table 1.

Table 1. Fixed parameters for TMAS principle and Hodgkin–Huxley neurons model. . Parameters Values Units σ 0.5 S/m ρ 1120 Kg/m3 c0 1540 m/s Cm 1.0 μF/cm2 ḡNa 120 mS/cm2 ḡK 36 mS/cm2 gL 0.3 mS/cm2 VNa 115 mV VK −12 mV VL 10.59 mV T 6.3 °C

Table 1. Fixed parameters for TMAS principle and Hodgkin–Huxley neurons model. .

A total of fifteen Sprague-Dawley rats (male, 3-month-old) each with body weight of approximately 200 g were used in this electrophysiological study. All efforts were made to minimize animal suffering and the number of animals used. The rat was surgically anesthetized with sodium pentobarbital (3%, 5 mg/100 g, IP), and then fixed on a stereotaxic apparatus (ST-5ND-C, USA) with ear bars and a clamping device. The fur of the rat head was shaven, and the skin was cleaned with 0.9% sodium chloride physiological solution. The skin was cut along the midline of the skull, and the subcutaneous tissue and periosteum were cleaned. The skull was drilled, and the bone was chipped to expose an approximate brain tissue area of 2 mm×2 mm and formed a bone hole.

The scheme of the experimental setup is shown in Fig. 1(a) and the corresponding photograph is shown in Fig. 1(b). Ten permanent magnets (Nd–Fe–B, 100 mm (length) ×100 mm (width) ×20 mm (height)) were inserted in a homemade U-shaped device as shown in the lower-right corner of Fig. 1(b)). The rat head was placed in the middle of the U-shaped device and the rat mouth was fixed by a clamping device. The ultrasonic transducer with a center frequency of 500 kHz, a bandwidth of 50%, a focal length of 30 mm and a diameter of 20 mm (Daping, Hangzhou, China) was placed above the rat head. There was a plastic ultrasonic collimator filled with medical ultrasound gel between the transducer and the rat skull. A single tungsten electrode with a length of 15 cm and diameter of 1 mm (MicroProbes, USA) passed through the bone hole was inserted into the brain tissue below the ultrasonic transducer. The angle between the single electrode and the ultrasonic probe was ∼ 50. The grounded wire and the reference wire are fixed on the scalp by the surgical suture needle. The single tungsten electrode, grounded wire and the reference wire connected with a headstage that was fixed on a stereotaxic apparatus.

An ultrasonic transmitter and receiver card (USB-UT350T, Ultratek, USA) controlled by a computer was used to apply a pulse signal to the focused ultrasonic transducer. Local field potentials (LFPs) from the somatosensory cortex, captured by the single electrode (MicroProbes, USA), were amplified by a microelectrode AC amplifier (Model-1800, A-M system. Inc, USA). The analog signals from AC amplifier were converted into digital signals by a neural signal processor (Cerebus, Cyberknetics, USA) and transmitted to a computer.

The magnetic field intensity measured by Gaussmeter (WT20D, WeiTe, China) at the rat head was approximately 0.35 T. In the experiment, the center frequency, stimulus frequency, and the single stimulus pulse duration were 500 kHz and 100 Hz, 32 μs respectively. The spatial-peak pulse-average intensity (I_SPPA) measured by the ultrasound energy density instrument (YP0511F, Hangzhou, China) was 21.1 W/cm² and the corresponding spatial-peak temporal-average intensity (I_SPTA) was 135.04 mW/cm². The ultrasound intensity was below 190 W/cm², the maximum recommended limit for diagnostic imaging applications.^[7] The LFPs were collected and digitized at a sample rate of 2 kHz, and with a low-pass filter at 125 Hz in the Cerebus system.

First, the LFPs without any stimulation were recorded as a control status (status abbreviation: CTRL). Second, we inserted the permanent magnets on both sides of shaped-U device and recorded the LFPs in the presence of a static magnetic field (status abbreviation: SMF). Third, an ultrasonic wave was transmitted to the rat head and the stimulation lasted 10 min. We recorded the LFPs after stimulation (status abbreviation: TMAS). Finally, the permanent magnets were removed and the rat was only stimulated by ultrasound for 10 min. After FUS, the LFPs were recorded (status abbreviation: FUS).

To test whether TMAS is able to excite action potential of a neuron, the Hodgkin–Huxley neuron model is used to perform CTRL, SMF, TMAS status. In the simulation, the ultrasonic power is 21.1 W/cm² that is lower than that used to stimulate primary somatosensory cortex of human in FUS, and the stimulus frequency is 100 Hz. According to the formula where p₀ is the maximum amplitude of the sound pressure P, ρ is the brain tissue density and c₀ is the speed of ultrasound wave in soft tissue. When I is 21.2 W/cm², the sound pressure p₀ is 0.85 MPa. The intensity of the static magnet is 0.35 T. According to formula (9), the maximum electric current density is 7.9 μA/cm².

The simulation results shown in Fig. 2 indicate that there is no action potential with the statuses of CTRL and SMF (Figs. 2(a) and 2(b)), due to lack of the excitation current when the neuron is not stimulated, or only in the static magnetic field. Figure 2(c) shows that the action potential is generated under TMAS with a current density of 7.9 μA/cm². The above results show that the TMAS can stimulate a neuron and excite action potential in the Hodgkin–Huxley neuron model.

Fig. 2.

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	Fig. 2. Simulation results by using Hodgkin–Huxley neuron model with an electric current density of 7.9 μA/cm2 and a stimulus frequency of 100 Hz for (a) CTRL status, (b) SMF status, and (c) TMAS status.

In order to detect electric current generated by TMAS in brain tissue, an experimental setup is build. The scheme and photograph of the setup are shown in Appendix A: Supplementary Materials (Fig. S1). The rat head moving part of the skull is placed in the middle of the U-shaped device. We use the ionized water to wash the blood to exclude the influence of foreign ions. A sinusoidal signal with a frequency of 500 kHz is generated by arbitrary function generator (33220A, Agilent, USA) and then is separated into two parts by T-type BNC connector. One part is then amplified by a linear power amplifier (240L, ENI Inc., Rochester, NY) to generate ultrasound. The other part is input to the oscilloscope (Two channels, MSO7052B, Agilent, USA). The electric current generated in brain tissue by ultrasound and magnetic field is detected by the custom-designed copper electrodes. The electrodes are linked through two electrical wires to a 1-MV/A current amplifier (HCA-2M-1M, Laser Components, Olching, Germany). The current signal is amplified by the current amplifier and then observed by the oscilloscope (Two channels, MSO7052B, Agilent, USA) with 50-Ω input impedance. The experimental results are shown in Fig. 3. The yellow line represents the electric signal from the function generator, and the green line is for the electric current signal from brain tissue. Both of them have the same frequency (Their numbers of peaks are the same in the same time interval). According to formula (9), the electric current signal has the same frequency as the electric signal (ultrasound signal), therefore, the result is corresponding to formula (9). The above result demonstrates that the ultrasound and magnetic field can induce electric current in brain tissue.

Fig. 3.

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	Fig. 3. Electric signal from function generator, and electric signal from brain tissue.

To quantitatively evaluate the effect of TMAS on brain neuromodulation, the LFPs for four different statuses are recorded and their corresponding mean amplitudes are computed. The LFP signals in CTRL, SMF, TMAS and FUS statuses are shown in Figs. 4(a)–4(d). There is no action potential in CTRL and SMF statuses shown in Figs. 4(a) and 4(b) respectively. When the cortex is stimulated by TMAS and FUS separately, there appear action potentials in LFPs pointed by red arrows shown in Figs. 4(c) and 4(d) respectively. We can also clearly observe that the amplitude of the LFPs with TMAS is higher than those of CTRL, SMF and FUS statuses.

Fig. 4.

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	Fig. 4. LFPs in (a) CTRL status, (b) SMF status, (c) TMAS status, and (d) FUS status. (e) The mean amplitudes of the LFPs (n = 15, mean±s.d., *p < 0.05, paired t-test).

Fig. S1.

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	Fig. S1. The scheme and photograph of the setup.

The mean amplitudes of the LFPs shown in Fig. 4(e) were 0.1095±0.038 mV (CTRL), 0.1103±0.035 mV (SMF), 0.3768±0.075 mV (TMAS), 0.3768±0.075 mV (FUS), respectively (n = 15, mean±s.d., *p < 0.05, paired t-test). The ratio of the mean amplitude between the SMF and CTRL statuses is 1.01 that is close to 1. The results indicate that there is no significant interaction between the static magnetic field and brain tissue. For the TMAS status, the ratios of the mean amplitude between tFUMS and CTRL, and between tFUMS and SMF are 3.44 and 3.42, suggesting that the neuronal activity can be enhanced by TMAS. Meanwhile, the ratios of the mean amplitude between FUS and CTRL, and between FUS SMF are 2.38 and 2.36, which indicate that FUS can also modulate the oscillatory activities of brain, which is consistent with the result of previous FUS study.^[10] To compare mean absolute amplitude between the TMAS and FUS and the increase in the amplitude of LFP is 1.45. Furthermore, the oscillatory activities of brain are significantly increased with TMAS, demonstrating that the TMAS can enhance the effect of FUS on the brain neuron modulation.