Edited by: Xiaoli Li, Beijing Normal University, China
Reviewed by: Yi Yuan, Yanshan University, China; Thomas Tarnaud, Ghent University, Belgium
This article was submitted to Neural Technology, a section of the journal Frontiers in Neuroscience
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Parkinson’s disease (PD) is a common degenerative neurological disease of the nervous system in middle-aged and elderly people. Its incidence is the second highest among neurodegenerative diseases affecting the elderly. Its prevalence among people over 65 is approximately 1.7%. Its incidence and prevalence both increase with age (
In 2003, Norton et al. proposed the transcranial magnetoacoustic stimulation (TMAS) method and conducted a theoretical derivation. This technology combines magnetic and focused ultrasound based on the Hall effect, and uses the induced current generated by the coupling of transcranial focused ultrasound and static magnetic field to excite or inhibit neurons in the target area (
Transcranial magnetic acoustic stimulation is a method of neuromodulation based on Hall effect coupling TMS and FUS to generate induced currents, which may be accompanied by the stimulating effect of ultrasound during TMAS treatment.
Based on CT images of volunteer’s skull, this paper establishes a TMAS numerical simulation model comprised of human skull, 128-element phase-controlled transducer and permanent magnet. Numerical simulations transcranial sound pressure field, and then coupled with the static magnetic field to obtain the TMAS induction electric field distribution. It stimulates the STN in the BG-Th neural network in the PD state by using the induced currents at the focal point and the acoustic axis, and explored the parameters of the sound pressure field by changing the waveform, duty cycle, and repetition frequency of the transcranial focused ultrasound when fundamental frequency is fixed at 500 kHz. The effect on various neurons in the BG-Th neural network was evaluated, and screening of effective parameters that can make Th respond normally to cortical control motor behavior signals was conducted.
The numerical simulations were all performed on a Lenovo Think Station D30 workstation (Lenovo Group Ltd., Beijing, China) with an Nvidia TitanX GPU (NVIDIA Corporation, Santa Clara, CA, United States). Simulations were performed based on computer programming using CUDA C on the platform of Visual Studio Community 2013 (Microsoft Corporation, Redmond, Washington, United States). The simulation of the BG-Th model was carried out in MATLAB (The Mathworks Inc., Natick, MA, United States).
Volunteer’s head CT data (49-year-old male, scanning parameters were 120 kV and 100 mA, scanning thickness was 3 mm) was used to establish a human head, 128-element concave spherical phase-controlled transducer. The numerical simulation model of TMAS transcranial focusing comprised of water and permanent magnets is shown in
Numerical simulation model of transcranial focusing of a concave spherical phased transducer with 128 elements.
The Westervelt acoustic wave nonlinear propagation equation is (
where ∇^{2} is the Laplacian,
In this paper, the parameters of the skull and brain tissue such as density (ρ), sound speed (c) and attenuation coefficient (α) were obtained from the bone porosity (φ) converted from the Hounsfield unit (H) of the CT images and the calculation method was as follows (
where the
Numerical simulation constant parameters.
ρ (kg⋅m^{–3}) | α (dB⋅mm^{–1}) | β | ||
Water | 998 | 1,500 | 0.2 | 3.50 |
Cortical skull | 1,600 | 3,200 | 8 | 4.40 |
Based on the time reversal (TR) method (
Schematic of
where
The bias parameter b and the pulse signal
Relationship between the parameters and the ultrasonic shape.
Name | ||||
Upper half of sine | 0 | 1 | 0 | |
Lower half of sine | 0 | 0 | 1 | |
Sine wave | 0 | 1 | 1 | |
Offset sine wave | 1 | 1 | 1 | |
The temperature distribution was calculated through the Pennes bioheat conduction equation written as (
where C_{r} [J⋅(kg°C)^{–1}] and r [W⋅(m°C)^{–1}] are the specific heat and the thermal conductivity of the medium, respectively, T is the transient temperature of the acoustic medium, T_{0} is the initial temperature and set as 37°C in the simulation, Q is the volumetric energy loss which is equal to 2αI, where
Constant parameters for the temperature field simulation.
T_{0} (°C) | |||
Water | 0.54 | 4,180 | 22 |
Cortical skull | 1.30 | 1,840 | 37 |
Brain | 0.52 | 3,700 | 37 |
The Montalibet theoretical equation is (
where
Establish single neuron models of the STN, GPe, GPi and Th based on the H-H model. The BG-Th neural network model is constructed as shown in
BG-Th neural network model.
where
where
where
where
where
By counting the number of spikes for each neuron in a nucleus, we can obtain an average rate,
where
The reliability index (
where
In healthy BG-Th, optimum performance of the Th neural network can be achieved, and the
This paper first simulates the condition that the input sound intensity of pulsed sinusoidal ultrasonication is 0.3 W⋅cm^{–2}, the fundamental frequency is 0.5 MHz, the repetition frequency is 10 Hz, the duty cycle is 50%, and the static magnetic field is 0.3 T.
The influence of input sound intensity on TMAS,
In this paper, the effect of ultrasound parameters on TMAS treatment was investigated by numerical simulation while keeping the pulsed sinusoidal ultrasound fundamental frequency of 0.5 MHz and the magnetic induction strength of static magnetic field is 0.3 T. Take the TMAS-induced current at the focal point to stimulate a single STN neuron as an example. When the duty cycle is 50%, the repetition frequency is 10 Hz, and the STN neuron membrane potential and firing rate with different TMAS input sound intensities are shown in
The influence of TMAS input sound intensity on a single STN membrane firing. Columns 1–3 ultrasonic input sound intensity
Under the condition that the ultrasound duty cycle is 50% and the input sound intensity is 0.1 W⋅cm^{–2}, the STN neuron membrane potential changes with the ultrasound pulse repetition frequency of the TMAS stimulation as shown in
The effect of TMAS repetition frequencies on a single STN discharge. Columns 1–3 ultrasonic pulse repetition frequencies
When the ultrasonic pulse repetition frequency is 10 Hz and the input sound intensity is 0.1 W⋅cm^{–2}, the STN neuron membrane potential changes with the ultrasonic duty cycle of TMAS stimulation as shown in
The effect of TMAS duty cycle on the discharge of a single STN. Columns 1–3 Ultrasonic Duty Cycle,
The BG-Th neural network is constructed based on the H-H model and the structured sparse connection method. Each nucleus contains 10 neurons and the duration is 1,000 ms. The membrane potential of the 1st neuron in the STN, GPe and GPi nuclei and ten neurons of Th membrane potentials in the BG-Th neural network in healthy and PD states changes with time as shown in
The curve of neuron membrane potential over time, single neuron of STN, GPe, GPi and ten neurons of Th membrane potentials under
Under the conditions of a pulse repetition frequency of 10 Hz and an input sound intensity of 0.1 W⋅cm^{–2}, the random function rand is used to determine the initial value of the neuron membrane potential and the position of the synaptic connection, and the
0% (PD) | 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% |
0.350 | 0.333 | 0.35 | 0.333 | 0.300 | 0.350 | 0.350 | 0.333 | 0.333 | 0.333 | 0.333 |
0.467 | 0.467 | 0.467 | 0.450 | 0.467 | 0.450 | 0.433 | 0.467 | 0.467 | 0.450 | 0.467 |
0.500 | 0.483 | 0.500 | 0.467 | 0.467 | 0.467 | 0.416 | 0.433 | 0.433 | 0.417 | 0.400 |
0.567 | 0.517 | 0.533 | 0.517 | 0.533 | 0.567 | 0.450 | 0.567 | 0.483 | ||
0.633 | 0.617 | 0.517 | 0.533 | 0.567 | 0.417 | 0.417 | 0.400 | 0.433 | ||
0.667 | 0.617 | 0.550 | 0.650 | 0.567 | 0.617 | 0.650 | 0.550 | |||
0.683 | 0.683 | 0.683 | 0.667 | |||||||
0.716 | 0.450 | 0.516 | 0.650 | 0.483 | 0.567 | 0.567 | 0.167 | 0.533 | ||
0.767 | 0.750 | 0.750 | 0.750 | 0.633 | 0.717 | 0.767 | 0.733 | 0.750 | 0.750 | |
0.883 | 0.817 | 0.783 | 0.750 | 0.850 | 0.833 |
Under the condition that the duty cycle of the bias pulse sinusoidal ultrasound is 50% and the repetition frequency is 10 Hz, uniform TMAS with different ultrasonic input sound intensities at the geometric focus stimulates the STN nucleus in the BG-Th neural network, and the Th discharge result is shown in
The influence of the input sound intensity of the biased ultrasound TMAS on the abnormal discharge of the Th nerve nucleus in the BG-Th neural network.
When the bias pulse sinusoidal ultrasonic input sound intensity is 0.2 W⋅cm^{–2}, the duty cycle is 50%, and the repetition frequency is 10 Hz, the acoustic axis sound pressure or induced current density distribution area is as shown in
The influence of the biased ultrasound distribution on the abnormal discharge of the Th nerve nucleus in the BG-Th neural network.
When the fundamental frequency of the bias pulse sinusoidal ultrasound is 0.5 MHz, the duty cycle is 50%, the input sound intensity is 0.2 W⋅cm^{–2}, the repetition frequency is 10 Hz, the maximum density of the TMAS-induced current is 22.3 μA⋅cm^{–2}, and the current density distributions with different static magnetic field strengths are as shown in
The distribution of induced current density under different static magnetic field strengths,
The results of this paper show that the TMAS induced current can effectively suppress the PD state under the conditions of magnetic induction strength of 0.3 T and ultrasonic output sound intensity of 0.2 W⋅cm^{–2}. The ultrasound focal I_{SPTA} under this condition is 2.41 W⋅cm^{–2}, which is much smaller than the 5.63 W⋅cm^{–2} with ultrasound stimulation in the literature (
In this study, when performing ultrasonic waveform analysis in TMAS, it was found that at a fundamental frequency of 0.5 MHz, the upper half-sine and lower half-sine of sinusoidal ultrasound TMAS had excitatory and inhibitory effects on neurons, respectively, which would result in a weak stimulation effect on neurons. Since half-sine is difficult to implement in the actual transducer, and bias sine can be generated by superimposing a pulsed square wave signal on the pulsed sine signal, only half-sine is used for the principal analysis of the smaller sine wave effect, and bias sine wave ultrasound TMAS is chosen to explore the effect of stimulation parameters on the BG-TH neural network in the PD state.
The BG mainly includes the striatum, STN, GPe, GPi, substantia nigra pars compacta (SNc) and substantia nigra reticulata (SNr) nuclei. In this study, we simulated the STN, GPe, and GPi nuclei in BG based on the H-H neuron model. The sensory-motor cortex input was considered as pulsed electrical input and the signals from other brain regions were considered as direct current input, and the enhancement and weakening of synaptic connectivity signals due to the absence of dopaminergic neurons in the SNc in the PD state were simulated by changing this direct current input. Each nucleus pulposus is composed of 10 H-H neurons. Although it was shown by
In this study, a non-homogeneous head model is constructed based on real human head CT, and the Westervelt acoustic nonlinear propagation equation be used to simulate the sound pressure field, and the Pennes biological heat conduction equation is sampled to simulate the temperature field. Since vascularity and blood flow are not the focus of attention in this paper, these two factors are not considered in the above model, which may have some effect on the distribution of sound pressure/temperature in the acoustic pressure field/temperature field. In this paper, TMAS modeling simulation was performed based on the cranial CT data of only one volunteer, and the next step will be to investigate the effect of cranial parameters on TMAS PD for the cranial CT data of multiple volunteers.
Based on the Westervelt acoustic wave nonlinear equation, this paper constructs the ultrasonic transcranial focused sound pressure field, superimposes the uniform static magnetic field, and obtains the TMAS-induced current distribution according to the Montalibet theory. The construction of the PD state BG-Th neural network model is based on the H-H neuron model. The TMAS-induced current is used to stimulate a single STN neuron and the STN nucleus in a neural network, and parameters such as the ultrasonic waveform, sound strength, duty cycle, and repetition frequency are changed according to the firing state and relay reliability judgment stimulus effect. The results show that when the duty cycle of the ultrasonic wave is approximately 50%, the sound pressure field is −1 dB, the static magnetic field strength is 0.3 T and the ultrasonic input sound strength is 0.2 W⋅cm^{–2}, The magnitude of magnetic induction strength was changed to 0.2 and 0.4 T. The induced current was the same when the sound intensity was 0.4 and 0.1 W⋅cm^{–2}. The TMAS-induced current in the focal range can modulate the PD state with an
This paper refers to an existing TMAS experiment in rats and mice, and simulates the sound pressure field based on sinusoidal ultrasound before and after modulation and the establishment of the TMAS induction electric field. We propose that when the input sound intensity is between 0.1–0.3 W⋅cm^{–2}, TMAS has a modulation effect on PD, which is consistent with the TMAS mouse experiment results of
The original contributions presented in the study are included in the article/
This study was reviewed and approved by the Ethics Committee of Tianjin Medical University, China. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.
YZ designed the study and wrote the manuscript. MZ and ZL collected the relevant literatures. PW provided the CT data. XJ reviewed and edited the manuscript. All authors read and approved the submitted manuscript.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
This work was partially funded by National Natural Science Foundation of China (Grant No. 81272495) and the Natural Science Foundation of Tianjin (Grant No. 16JC2DJC32200).
Numerical simulations were all performed on a Lenovo Think Station D30 workstation (Lenovo Group Ltd., Beijing, China) with an Nvidia TitanX GPU (NVIDIA Corporation, Santa Clara, CA, United States).
The Supplementary Material for this article can be found online at: