An algorithm for predicting the electromagnetic field focusing area of ​​a 4×4 array micromagnetic stimulator

Abstract

The present invention discloses an algorithm for predicting the electromagnetic field focusing region of a 4×4 array structure micro-magnetic stimulator, belonging to the field of biomedical engineering, which realizes the prediction of the focusing regions of the magnetic field and the electric field when different-direction currents are applied to the array structure micro-magnetic stimulator, so as to achieve the directional stimulation of nerve cells. The steps are as follows: study the theoretical model of the array structure magnetic stimulator, perform theoretical calculations of the electric field and magnetic field intensities based on the theoretical model, and use numerical analysis and finite element method to verify the electromagnetic field intensities and spatial distributions at a single point; study the electromagnetic field spatial distribution characteristics when four multi-direction current combinations are applied to the coils S 21 , S 22 , S 11 and S 12 in the 4×4 array micro-magnetic stimulator; predict the electromagnetic field focusing region when multi-direction currents are applied to the 4×4 array structure micro-magnetic stimulator according to the distribution law.

Description

Technical Field

[0001] The invention belongs to the technical field of biomedical engineering, and in particular relates to an algorithm for predicting an electromagnetic field focusing area of ​​a 4×4 array structure micromagnetic stimulator. Background Art

[0002] Mental illness is a type of disease in which abnormal brain function leads to cognitive, emotional, volitional and behavioral disorders, including Alzheimer's disease, schizophrenia, autism and depression. Electromagnetic stimulation technology is currently a major means of diagnosing, treating and studying neuropsychiatric diseases. The main technologies currently include electrical stimulation (ES) and transcranial magnetic stimulation (TMS); electrical stimulation includes deep brain stimulation (DBS) and transcranial direct current stimulation (tDCS). Clinical trials have shown that TMS has therapeutic benefits for treating many neurological diseases, such as major depression and Alzheimer's disease. Although there is a certain understanding of the effects of DBS and TMS on brain activity and how these effects change corresponding behaviors, there are still some technical and biological limitations in the application of the two. Magnetic resonance imaging examinations of patients treated with DBS may cause excessive heating at the end of the stimulating electrode, resulting in nerve damage. The DBS stimulating electrode directly contacts biological tissues, and the inflammation and immune response of the tissues may change the treatment effect. The TMS coil is relatively large (size: 10-20 cm), and the magnetic field strength decreases with the square of the distance from the field source, making it difficult to locate target areas deep in the brain and having a low spatial resolution.

[0003] Micro-magnetic stimulation (μMS) has been gaining more and more attention as a new method of neural regulation in recent years. In 2012, Bonmassar et al. first used a sub-millimeter spiral inductor (RF0402 inductor) to activate neuronal tissue, with a stimulation current density of 6.6×10 -9 A / m 2; In 2016, Lee et al used 500μm×500μm square coils and 100μm×50μm trapezoidal coils and proved that they could activate cortical neurons; In 2017, Bonmassar first proposed a 0.316mm×0.316mm planar square spiral coil structure for brain neuron stimulation; In 2017, Bonmassar proved that 1.5mm×1.5mm planar square spiral coils were more efficient than 1.5mm×1.27mm spiral inductor coils in inducing neural activation, and could generate up to 5 times the electric field in tissues, and the energy was better focused; In 2018, Bonmassar et al studied the micromachining process of 300μm×300μm, 100μm thick reinforced planar square spiral coils. There are many microcoil structures for single-coil magnetic stimulation systems, but the magnetic fields generated generally have problems such as poor focusing and inaccurate spatial positioning.

[0004] As early as 1998, Ruohonen et al studied 6×6 square coils and hexagonal cap coils based on circular coils (2 cm in diameter), which improved the focusing and targeting of magnetic stimulation. In 1999, Ruohonen et al theoretically analyzed 6×6 planar square arrays based on circular coils (different diameters), and the study showed that the use of relatively small array coils (less than 5 cm in diameter) can improve the selectivity and controllability of stimulation. In 2015, Cline et al studied a multi-channel transcranial magnetic stimulation system using a circular coil and proposed a spatially distributed stimulation strategy to improve the focusing of TMS. In 2018, Dalie et al proposed a multi-electrode stimulation model without prior knowledge of neural structure, achieving the purpose of selectively stimulating peripheral nerve areas. In 2019, Minusa et al studied a multi-channel magnetic stimulation system using a submillimeter coil (ELJ-RFR10JFB), and conducted experiments in rodents to prove that the multi-channel μMS device produces more effective stimulation than the single-channel device. Array-structured micro-magnetic stimulation systems can reduce power consumption, improve the effectiveness and focus of magnetic stimulation, and improve spatial positioning, but research on multi-channel magnetic stimulation theory is based on circular coils and commercial spiral inductors.

[0005] In 2016, Rizou et al. first proposed a 6×6 array micro-magnetic stimulation platform based on a planar square spiral coil, but did not study the spatial distribution characteristics of the electromagnetic field of the platform. In 2020, Tian et al. proposed an improved F / C structure magnetic stimulation system based on a 100μm×100μm planar square spiral coil, which is superior to the existing single-coil micro-magnetic stimulation system in terms of magnetic field uniformity, magnetic field intensity and inductance. In response to the above problems, this paper proposes a 4×4 array structure multi-channel magnetic stimulator based on a sub-millimeter planar square spiral coil, which has high sensitivity and high spatial resolution, and can complete the directional activation of the direction of neuronal axons, which is of great significance for the treatment of mental illnesses such as epilepsy and depression. Summary of the invention

[0006] The purpose of the present invention is to solve the problem of directional magnetic stimulation of nerve cells and achieve strong focusing and high spatial resolution, and to propose a new method for predicting the spatial focusing area of ​​the electromagnetic field of a 4×4 array structure micromagnetic stimulator.

[0007] The technical solution of the invention is:

[0008] The 4×4 array structure micromagnetic stimulator consists of 16 planar square spiral coils numbered from 00 to 33, each coil numbered S mn , the size is 100μm×100μm, the material is Cu, the wire dimension of the coil is 2μm, the number of turns is 8, the wire spacing is 4μm, the coil thickness is 1.7μm, and the spacing between single coils is 2μm. The method is as follows:

[0009] (1) Electromagnetic field calculation method

[0010] A. Calculation of Magnetic Field

[0011] The magnetic field B generated by the m×n array structure micromagnetic stimulator at a certain point in space r=(x, y, z) is a single coil S mn The magnetic field B generated at point r mn The vector sum of :

[0012] B(r)=∑ mn B mn (rr mn ), m, n=1, 2, 3... (1)

[0013] Single flat square spiral coil S mn The electric field B mn The electric field B generated by the planar square coils with different side lengths at point r S1 , B S2 , B S3 ……B sn Vector sum:

[0014] B mn (rr mn )=B s1 (rr mn )+B s2 (rr mn )+B s3 (rr mn )+……+B sn (rr mn )m,n=1,2,3……(2)

[0015] Among them, the magnetic field B of a plane square coil with a side length a at point r in space s for:

[0016]

[0017]

[0018]

[0019]

[0020] B Bc , B AB , B DA , B CD They represent the magnetic induction intensity generated by the BC, DA, CD and AB sides of a planar square coil with a side length of a at point r.

[0021] B. Calculation of the Induced Electric Field

[0022] The electric field E of the m×n array structure micromagnetic stimulator at a certain point r=(x, y, z) in space is mn The electric field E generated at point r mn The sum is:

[0023] E(r)=∑ m，n E mn (rr mn ), m, n=1, 2, 3... (4)

[0024] Single flat square spiral coil S mn The electric field E mn The electric field E generated by the planar square coils with different side lengths at point r S1 、E S2 、E S3 ……E sn Vector sum:

[0025]

[0026] Among them, the magnetic field E of a plane square coil with a side length a at point r in space s for:

[0027]

[0028]

[0029]

[0030] Among them, vacuum magnetic permeability μ0=4π×10 -7 H / m, dI / dt is the rate of change of input current.

[0031] (2) Analysis of the spatial distribution characteristics of the electromagnetic field

[0032] Current was fed into a single coil S30 in the array structure micromagnetic stimulator (clockwise direction) and current was fed into all 16 planar square spiral coils from 00 to 33 in the same direction (clockwise direction) to study the intensity and uniformity of the electric and magnetic fields and the spatial distribution characteristics of the electromagnetic field. The excitation source was selected as a 25mA, 70kHz sinusoidal signal.

[0033] The S in the 4×4 array micromagnetic stimulator 30 When the coil is fed with clockwise current, the focus area of ​​the magnetic field is concentrated in the center of the coil, and the focus area of ​​the electric field is concentrated around the coil. The maximum electric field strength is 183.64mV / m, the average electric field strength is 84.95mV / m, and the data exceeding 73mV / m accounts for 71.79%;

[0034] When clockwise current was simultaneously passed through the 16 coils in the 4×4 array structure micromagnetic stimulator, the focusing area of ​​the magnetic field was concentrated at the center of the coil and the adjacent areas of the single coils; the focusing area of ​​the electric field was concentrated around the single coils and the adjacent areas of the single coils; the maximum electric field strength was 614.7mV / m, the average electric field strength was 122.82mV / m, and the data exceeding 73mV / m accounted for 84.39%.

[0035] (3) Prediction of electromagnetic field spatial distribution

[0036] The S 21 , S 22 , S 11 and S 12 The coils were respectively supplied with currents in directions I, II, III|, and IV to study the spatial distribution law of the electromagnetic field of the array structure micromagnetic stimulation. On this basis, the electromagnetic field distribution characteristics were predicted when multi-directional currents were supplied to the 4×4 array structure micromagnetic stimulator.

[0037] The currents in directions I, II, III|, and IV are: I combination: S 21 , S 22 , S 11 and S 12 Apply clockwise current; II combination: S 21 and S 12 A clockwise current is applied, S 11 and S 22 Pass counterclockwise current; III combination: S 21 and S 11 A clockwise current is applied, S 22 and S 12 Pass counterclockwise current; IV combination: S 21 , S 22 , S 12 A clockwise current is applied, S 11 Apply counterclockwise current;

[0038] The distribution pattern is as follows: Direction I: When the currents of adjacent coils are in the same direction, the magnetic field strength at the adjacent coils is significantly enhanced, and a magnetic field focusing area appears. The electric field strength in the area around the outermost layer of each single coil is significantly enhanced, and at the same time, an induced electric field also exists at the edge of the adjacent coil where no current is passed. Direction II: When the currents of adjacent coils are in opposite directions, the magnetic field lines at the adjacent coils are in opposite directions and cancel each other out, the magnetic field strength is significantly weakened, and there is no magnetic field focusing area at the adjacent coils; the electric field strength in the area around the outermost layer of each single coil is also significantly weakened, but S 21 Above, S 21 and S 22 , S 21 and S 11 The electric field is enhanced at adjacent locations. III Direction: S 21 and S 11 , S 22 and S 12 The current direction is the same, and the magnetic field strength increases where the two coils are adjacent; S 21 and S 22 , S 11 and S 12 The currents are in opposite directions, and the magnetic field strength weakens where the two coils are adjacent, but S 11 and S 12 The electric field is enhanced where the two coils are adjacent. IV direction: The magnetic field distribution satisfies the above law, but S 11 and S 21The electric field at adjacent locations is significantly enhanced. The study shows that: (i) when the array structure micromagnetic stimulator is fed with multidirectional current, the maximum value of the electric field strength changes significantly, while the maximum value of the magnetic field strength does not change much; (ii) the spatial distribution of the magnetic field and the newly added magnetic field focus area show regular changes; (iii) only when the current direction is I (the currents of adjacent coils are in the same direction), the newly added electric field focus area shows regular changes. In the case of other multidirectional current combinations, no regular changes can be seen in the newly added focus area of ​​the electric field.

[0039] According to the above rules, a multi-directional current (S 03 , S 12 , S 22 , S 23 , S 30 A clockwise current is applied, S 00 , S 01 , S 10 , S 11 , S 31 The electromagnetic field distribution characteristics are predicted by passing a counterclockwise current. Within the area of ​​the energized coil, the area of ​​the magnetic field focus is about 21160um. 2 , which is basically consistent with the predicted magnetic field focusing area position and area; the focusing area of ​​the induced electric field is 9010um 2 , failed to accurately predict the area of ​​610um 2 , the prediction accuracy of the electric field focusing area is 93.22%.

[0040] The advantages and positive effects of the present invention are:

[0041] The algorithm for predicting the electromagnetic field focusing area of ​​a 4×4 array structure micromagnetic stimulator described in the present invention can predict the focusing area of ​​the electromagnetic field when a multi-directional current is passed through the array structure micromagnetic stimulator, thereby achieving directional magnetic stimulation of nerve cells. The array-type multi-channel magnetic stimulator based on a planar square spiral coil proposed in this paper is smaller in size (412×412×1.7μm), improves the effectiveness and focusing of the spatial distribution of magnetic stimulation, and provides a new method for the design of a multi-channel micromagnetic stimulation device. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a schematic diagram of the structure of a 4×4 array structure micromagnetic stimulator. DETAILED DESCRIPTION

[0043] The present invention is further described below with reference to the accompanying drawings and embodiments.

[0044] Implementation method 1:

[0045] Step 1: Through Comsol software modeling and simulation, determine the line width, number of turns, thickness, spacing and other parameters of the planar square microcoil with a fixed size of 100μm×100μm;

[0046] Step 2: Theoretically derive the calculation formulas for the electric field and magnetic field of a single planar square spiral coil, and use numerical analysis and finite element simulation to verify the correctness of the formulas;

[0047] Step 3: Theoretically derive the calculation formulas for the electric field E and magnetic field B of the 4×4 array structure micromagnetic stimulator;

[0048] Step 4: Coil S 21 , S 22 , S 11 and S 12 Pass 25mA, 70kHz, clockwise current to summarize the spatial distribution of electromagnetic field;

[0049] Step 5: Coil S 21 and S 12 25mA, 70kHz, clockwise current is applied to coil S 11 and S 22 Pass 25mA, 70kHz, counterclockwise current to summarize the spatial distribution of electromagnetic field;

[0050] Step 6: Coil S 21 and S 11 25mA, 70kHz, clockwise current is applied to coil S 22 and S 12 Pass 25mA, 70kHz, counterclockwise current to summarize the spatial distribution of electromagnetic field;

[0051] Step 7: Coil S 21 , S 22 , S 12 25mA, 70kHz, clockwise current is applied to coil S 11 Pass 25mA, 70kHz, counterclockwise current to summarize the spatial distribution of electromagnetic field;

[0052] Step 8: Based on the spatial distribution law of the electromagnetic field summarized in the fourth, fifth, sixth and seventh steps above, when multi-directional current is passed through the 4×4 array structure micromagnetic stimulator, the focal area of ​​the electromagnetic field space is predicted.

Claims

1. A method for predicting the electromagnetic field focusing area of ​​a 4×4 array structure micromagnetic stimulator, characterized in that: include The 4×4 array structure micromagnetic stimulator is composed of 16 planar square spiral coils numbered from 00 to 33, each planar square spiral coil is numbered S mn , the size is 100μm×100μm, the material is Cu, the wire dimension of the coil is 2μm, the number of turns is 8, the wire spacing is 4μm, the coil thickness is 1.7μm, and the spacing between single coils is 2μm. The method is as follows: (1) Electromagnetic field calculation method The electromagnetic field theory formula is derived for the 4×4 array structure micro-magnetic stimulator, including the formula derivation of the magnetic field and the induced electric field, wherein: The calculation formula of magnetic field B is: Among them, r = (x, y, z) is the coordinate of a point in space, r mn For coil S mn Coordinates in 3D space, B mn For coil S mn Current I mn The electric field generated; The calculation formula of the induced electric field E is: Among them, r = (x, y, z) is the coordinate of a point in space, r mn For coil S mn Coordinates in 3D space, E mn For coil S mn Current I mn The induced electric field generated; (2) Analysis of the spatial distribution characteristics of the electromagnetic field The electromagnetic field distribution characteristics of the 4×4 array structure micromagnetic stimulator were studied, including the electromagnetic field distribution characteristics of the same-direction current. The input current was 25mA and a 70kHz sinusoidal signal, where: The S in the 4×4 array micromagnetic stimulator 30 When the coil is fed with clockwise current, the focus area of ​​the magnetic field is concentrated in the center of the coil, and the focus area of ​​the electric field is concentrated around the coil. The maximum electric field strength is 183.64mV / m, the average electric field strength is 84.95mV / m, and the data exceeding 73mV / m accounts for 71.79%; When clockwise current was simultaneously applied to the 16 coils in the 4×4 array micromagnetic stimulator, the focus area of ​​the magnetic field was concentrated at the center of the coil and the adjacent areas of the single coils; the focus area of ​​the electric field was concentrated around the single coils and the adjacent areas of the single coils; the maximum electric field strength was 614.7mV / m, the average electric field strength was 122.82mV / m, and the data exceeding 73mV / m accounted for 84.39%; (3) Prediction of electromagnetic field spatial distribution The electromagnetic field spatial distribution characteristics of the 4×4 array structure micromagnetic stimulator were predicted by passing a multi-directional current, and the current size was 25mA, a 70kHz sinusoidal signal, and the method was as follows: The 4×4 array structure micromagnetic stimulator is respectively supplied with currents in directions I, II, III|, and IV, wherein ① When the current direction is I, the electromagnetic field distribution law is as follows: the magnetic field intensity is significantly enhanced at the adjacent parts of the coil, and the electric field intensity is significantly enhanced in the area around the outermost layer of the single coil; ② When the current direction is II, the electromagnetic field distribution law is as follows: the magnetic field intensity is significantly weakened at the adjacent parts of the coil, and the electric field intensity is significantly weakened in the area around the outermost layer of the single coil; ③ When the current direction is III or IV, the electromagnetic field distribution law is: when the current direction of the two adjacent coils is the same, the magnetic field intensity and electric field intensity of the adjacent coils are enhanced; when the current direction of the two adjacent coils is opposite, the magnetic field intensity and electric field intensity of the adjacent coils are weakened; According to the above rules, the electromagnetic field distribution characteristics of the 4×4 array structure micromagnetic stimulator are predicted by passing multi-directional current. Within the area of ​​the energized coil, the focus area of ​​the magnetic field is 21160um. 2 , which is consistent with the predicted magnetic field focusing area position and area; the focusing area of ​​the induced electric field is 9010um 2 , failed to accurately predict the area of ​​610um 2 , the prediction accuracy of the electric field focusing area is 93.22%.

2. The method for predicting the electromagnetic field focusing area of ​​a 4×4 array structure micromagnetic stimulator according to claim 1, characterized in that: The 4×4 array structure micromagnetic stimulator respectively passes currents in directions I, II, III, and IV, specifically: (1) I combination: S 21 , S 22 , S 11 and S 12 Apply clockwise current; (2) II combination: S 21 and S 12 A clockwise current is applied, S 11 and S 22 Apply counterclockwise current; (3) III combination: S 21 and S 11 A clockwise current is applied, S 22 and S 12 Apply counterclockwise current; (4)IV combination: S 21 , S 22 , S 12 A clockwise current is applied, S 11 Apply counterclockwise current.

3. The method for predicting the electromagnetic field focusing area of ​​a 4×4 array structure micromagnetic stimulator according to claim 1, characterized in that: The 4×4 array structure micromagnetic stimulator passes a multi-directional current to predict the electromagnetic field distribution characteristics. The multi-directional current is specifically: S 03 , S 12 , S 22 , S 23 , S 30 A clockwise current is applied, S 00 , S 01 , S 10 , S 11 , S 31 Apply current in counterclockwise direction.

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