A Focus Gain Simulation Method for Planar Phased Array HIFU Therapy System

Abstract

The present invention discloses a focusing gain simulation method for a planar phased array high-intensity ultrasonography (HIFU) treatment system. The method relates to the field of focused ultrasound technology and includes the following steps: S1: establishing a planar phased array far-field axial sound pressure focusing gain formula based on the Rayleigh integral formula of a rectangular piston sound source and the principle of all-electronic focusing phase control; S2: utilizing the planar phased array far-field axial sound pressure focusing gain formula to simulate any one or all of the variations in the axial sound pressure focusing gain with transmission frequency, array element spacing, array element size, and array element number. Based on the Rayleigh integral formula of a rectangular piston sound source, the present invention first calculates and derives the radiation sound field of a single rectangular piston array element, then superimposes the radiation sound pressures of n rectangular array elements at an observation point to obtain the total radiation sound pressure of the planar phased array, and deduces the far-field ultrasound focusing gain of the planar phased array by normalizing the total radiation sound pressure of the planar phased array. The method also specifically provides a planar phased array far-field axial sound pressure focusing gain formula.

Description

Technical Field

[0001] The present invention relates to the field of focused ultrasound technology, and more particularly to a focusing gain simulation method for a planar phased array HIFU treatment system. Background Art

[0002] High-intensity focused ultrasound (HIFU) is a rapidly developing minimally / non-invasive treatment technology. It has been used to treat a variety of diseases, including uterine fibroids, prostate cancer, breast cancer, liver cancer, kidney cancer, pancreatic cancer, thyroid cancer, bone metastases, brain tumors, essential tremor, and Parkinson's disease. HIFU uses an external ultrasound transducer to focus low-intensity ultrasound waves onto the target lesion tissue in the body, generating high-intensity focused ultrasound. The high-intensity focused ultrasound generates temperature rise, cavitation, and mechanical effects at the target lesion tissue, causing coagulative necrosis of the target lesion tissue without damaging surrounding normal biological tissue, thereby achieving the goal of non-invasive treatment of the lesion tissue [Kennedy, J E. High intensity focused ultrasound: surgery of the future? [J]. Br J Radiol, 2003, 76(909): 590-599.].

[0003] At present, the typical HIFU system mainly uses a spherically curved concave ultrasonic transducer as the treatment head [Ellens N, Lucht B, Gunaseelan ST, et al. A novel, flat, electronically-steered phased array transducer for tissue ablation: preliminary results [J]. Physics in Medicine & Biology, 2015, 60(6): 2195-215]. This treatment head generally contains a single, dozens, hundreds or thousands of array elements. Since this treatment head has an inherent focusing center (i.e., the center of the sphere), it is easy and convenient to achieve high-intensity ultrasonic energy convergence and deposition near its center of the sphere (i.e., the geometric focus). However, this treatment head cannot achieve a good ultrasonic focusing effect at a position relatively far from its geometric focus. If you want to achieve a relatively good ultrasonic focusing effect in a larger spatial range, you must use a mechanical moving system to complete the switching and regulation of the focus spatial position, which results in a relatively long HIFU treatment time.

[0004] To minimize HIFU treatment time and alleviate patient pain, a fully electronic focus control method can be used to switch the focal point's spatial position. The time required for a single fully electronic focus control depends on the electronic drive system and the transducer's electrical excitation response, typically in the millisecond range. Compared to the seconds required for mechanical focus control, this significantly reduces focus control time, thereby shortening HIFU treatment time.

[0005] However, the all-electronic focus control method can only be realized by relying on a phased array ultrasonic transducer. Although the spherically curved concave phased array ultrasonic transducer can achieve a good ultrasonic focusing effect in a small space around the geometric focus through the all-electronic focus control method, it is difficult to achieve a good ultrasonic focusing effect in a large space away from its geometric focus through the all-electronic focus control method. In this case, it is necessary to combine the assistance of a mechanical movement system to achieve a good ultrasonic focusing effect in a large space. A series of studies by Ellens and Hynynen et al. verified the feasibility of achieving all-electronic focus control in a large space in HIFU treatment by using a planar phased array ultrasonic transducer [

[24] Ellens N, Hynynen K.Frequency considerations for deep ablation with high-intensity focused ultrasound: A simulation study [J]. Medical Physics, 2015, 42(8)].

[0006] However, planar phased array ultrasonic transducers do not have an inherent geometric focus. When the focus position is switched and controlled within a large range of space in an all-electronic manner, the focused ultrasonic field distribution corresponding to different focuses is also different, and is more complex than the spatial focused ultrasonic field distribution of a spherically curved concave single element / phased array ultrasonic transducer with a fixed geometric focus.

[0007] Therefore, it is of great significance to explore the focusing performance of the HIFU treatment system equipped with a planar phased array, which will help accelerate the planar phased array HIFU treatment system into the practical application stage. Summary of the Invention

[0008] In order to solve the above problems and defects in the prior art, the present invention provides a method for simulating the focusing performance of a planar phased array HIFU treatment system.

[0009] In order to achieve the above-mentioned purpose of the present invention, the technical solutions adopted are as follows:

[0010] A method for simulating the focus gain of a planar phased array HIFU treatment system, the method comprising the following steps:

[0011] S1: Based on the Rayleigh integral formula of the rectangular piston sound source and the axis sound pressure focusing gain formula of the planar phased array in the far field based on the principle of all-electronic focusing phase control;

[0012] S2: Using the formula for the axial sound pressure focusing gain in the far field of the planar phased array, simulate any or all of the variations in the axial sound pressure focusing gain with the transmission frequency, array element spacing, array element size, and number of array elements.

[0013] Preferably, in step S1, the specific steps of establishing the axis sound pressure focusing gain formula of the planar phased array far field are as follows:

[0014] S101: First, derive the radiation sound field of a single rectangular piston array element. The center of the rectangular piston array element is located at the coordinate origin, the radiation surface of the rectangular piston array element is located in the xOy plane, and the surface of the rectangular piston array element vibrates along the z direction.

[0015] S102: For any observation point in the space corresponding to the z direction of the rectangular piston array element, the surface of the rectangular piston array element is divided into an infinite number of small rectangular surface elements, each small rectangular surface element is used as a point source, and the sound pressure generated by each small rectangular surface element at the observation point is calculated;

[0016] S103: Superimposing the sound pressures radiated by all the small rectangular surface elements, thus obtaining the radiated sound pressure generated by a rectangular piston array element at the observation point;

[0017] S104: Calculate the phase compensation θ based on the radiated sound pressure obtained in step S3 0n , array element center coordinates (x n ,y n , 0) the radiation sound pressure of the n-th rectangular array element at the observation point, n = 1, 2, ... N;

[0018] S105: Superimposing the radiation sound pressures obtained in step S4 to obtain the total radiation sound pressure of the planar phased array;

[0019] S106: Normalizing the total radiated sound pressure of the planar phased array to obtain an ultrasonic focusing gain formula for the planar phased array.

[0020] Furthermore, in step S102, specifically, the position vector of the observation point is r, the angle between r and the z axis is θ, and the rotation angle is According to the Rayleigh integral principle, the rectangular piston array element surface is divided into an infinite number of small rectangular surface elements;

[0021] The point source intensity of the small rectangular surface element dS, whose center is located at the polar radius ρ and the polar angle σ, is dQ = v a dS, where v a represents the amplitude of the vibration velocity on the surface of the array element; then the sound pressure generated by the small rectangular surface element at the observation point is:

[0022]

[0023] Among them, ρ m is the density of the ultrasound propagation medium; k = ω0 / c m is the wave number, ω0=2πf0 is the angular frequency, f0 represents the frequency; g is the distance from the center of the small rectangular surface element to the observation point; c m is the sound velocity of the ultrasonic propagation medium; j represents the imaginary unit, ω represents the angular frequency, θ0 represents the initial phase, k represents the wave number, and t represents the time.

[0024] Furthermore, in step S103, the sound pressures radiated by all the small rectangular surface elements are superimposed, and the calculation formula is as follows:

[0025]

[0026] Where,

[0027] S represents the integrated area, and (x, y) represents the Cartesian coordinates. When r is much larger than the size of the rectangular array element, that is, in the far field:

[0028] g≈r-ρcos(r,ρ) (6)

[0029] in, r represents the distance from the center of the rectangular array element to the observation point;

[0030] The calculated p is the radiated sound pressure generated by a rectangular array element at the observation point.

[0031] Furthermore, the radiated sound pressure generated by a rectangular array element at the observation point is optimized as follows: the g in the amplitude in equation (5) is replaced by the distance r from the center of the rectangular array element to the observation point; and the g in the phase is replaced by equation (6), thus obtaining:

[0032]

[0033] According to the geometric relationship:

[0034]

[0035] Substitute (8) into (7) and integrate to obtain:

[0036]

[0037] Furthermore, according to equation (9), the phase compensation θ of each array element is 0n , array element center coordinates (x n ,y n , 0) the radiation sound pressure of the nth rectangular array element at the observation point is:

[0038]

[0039] Among them, r n ,θ n 、 They correspond to the center offset of the nth rectangular array element (x n ,y n ,0), the distance and angle coordinates corresponding to the coordinates of the observation point in the offset spherical coordinate system; b n 、a n is the size of the nth rectangular array element;

[0040] Furthermore, the phase compensation θ 0n , which is calculated as follows:

[0041] For the focus F(x F ,y F , z F ), to ensure that the phase of the ultrasonic wave emitted by each array element is consistent when it propagates to the focus F; according to the sound ray theory, the phase compensation of each array element can be calculated as:

[0042]

[0043] Among them, (x n ,y n ,0) is the coordinate of the center point of the nth array element, c m is the speed of sound in the medium in which ultrasound propagates.

[0044] Furthermore, the total radiated sound pressure of the planar phased array is:

[0045]

[0046] Since the phase part in formula (11) are equal, so:

[0047]

[0048] Where, ρ m c m v a is regarded as the sound pressure p0 radiated from the surface of the array element.

[0049] Furthermore, in step S106, the equation (12) is calculated with respect to ρ m c m v a After normalization, the ultrasonic focusing gain of the planar phased array can be obtained as:

[0050]

[0051] Specifically speaking about the focusing gain on the axis, if the coordinates of the observation point are F(0, 0, z F ), formula (13) can be further expressed as:

[0052]

[0053] in,

[0054] Furthermore, in step S2, the ultrasonic focusing performance of the planar array is simulated using the hydrophone method.

[0055] In S t Under the premise of keeping the same, the simulation of different array element spacing E space The influence of the transmitting frequency f0 on the axis sound pressure focusing gain under the condition of

[0056] In S t Under the premise of keeping the same, the array element spacing E under different transmission frequencies is simulated space Impact on the axis sound pressure focusing gain;

[0057] While maintaining the number of array elements and the array element spacing E space Under the premise of no change, the array element size E is simulated under different transmission frequencies. size Impact on the axis sound pressure focusing gain;

[0058] While maintaining the array element size E size and array element spacing E space Under the premise of no change, the simulation simulates the influence of the number of array elements N on the axis sound pressure focusing gain under different transmission frequencies.

[0059] The beneficial effects of the present invention are as follows:

[0060] Based on the Rayleigh integral formula for a rectangular piston sound source, this paper first calculates and derives the radiated sound field of a single rectangular piston array element. The radiated sound pressure of n rectangular array elements at the observation point is then superimposed to obtain the total radiated sound pressure of the planar phased array. By normalizing the total radiated sound pressure of the planar phased array, the far-field ultrasonic focusing gain of the planar phased array is derived. The paper also specifically provides a formula for the axial sound pressure focusing gain of the planar phased array in the far field. Using this formula, the paper simulates and studies how the axial sound pressure focusing gain varies with transmission frequency, element spacing, element size, and number of elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Schematic diagram of the planar ultrasonic phased array in Example 1.

[0062] Figure 2 1 is a flowchart of the steps of the simulation method described in Example 1.

[0063] Figure 3 Schematic diagram of the calculation of the sound pressure radiated by the rectangular piston sound source in Example 1.

[0064] Figure 4 Schematic diagram of the 6144-element planar phased array under test in Example 1.

[0065] Figure 5 Schematic diagram of a device for testing the ultrasonic focusing performance of a planar array using the hydrophone method according to Example 1.

[0066] Figure 6 This is a three-dimensional distribution diagram of the selected focus in Example 1.

[0067] Figure 7 This is a two-dimensional top view of the selected focus in Example 1.

[0068] Figure 8 It is a planar phased array model with 10×10 elements.

[0069] Figure 9 It is a planar phased array model with 20×20 elements.

[0070] Figure 10 It is a planar phased array model with 40×40 elements.

[0071] Figure 11 It is a planar phased array model with 80×80 elements.

[0072] Figure 12 It is a planar phased array model with 160×160 elements.

[0073] Figure 13 It is a planar phased array model with 320×320 elements.

[0074] Figure 14 It is a planar phased array model with 640×640 elements.

[0075] Figure 15 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 9.6mm and 12.0mm on the axis sound pressure focusing gain.

[0076] Figure 16 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 4.8mm and 6.0mm on the axis sound pressure focusing gain.

[0077] Figure 17 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 2.4mm and 3.0mm on the axis sound pressure focusing gain.

[0078] Figure 18 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 1.2mm and 1.5mm on the axis sound pressure focusing gain.

[0079] Figure 19 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 0.6mm and 0.75mm on the axis sound pressure focusing gain.

[0080] Figure 20 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 0.3mm and 0.375mm on the axis sound pressure focusing gain.

[0081] Figure 21 This is the effect of the transmitting frequency f0 of the planar phased array with array element parameters of 0.15mm and 0.1875mm on the axis sound pressure focusing gain.

[0082] Figure 22 It is the effect of the element spacing of a planar phased array with a transmission frequency of f0 = 200KHz on the axis sound pressure focusing gain.

[0083] Figure 23 It is the effect of the element spacing of a planar phased array with a transmission frequency of f0 = 400KHz on the axis sound pressure focusing gain.

[0084] Figure 24 It is the effect of the element spacing of a planar phased array with a transmission frequency of f0 = 600KHz on the axis sound pressure focusing gain.

[0085] Figure 25 It is the effect of the element spacing of a planar phased array with a transmission frequency of f0 = 800KHz on the axis sound pressure focusing gain.

[0086] Figure 26It is the effect of the element spacing of a planar phased array with a transmitting frequency of f0 = 1.0 MHz on the axis sound pressure focusing gain.

[0087] Figure 27 It is the effect of the element spacing of a planar phased array with a transmitting frequency of f0 = 1.2 MHz on the axis sound pressure focusing gain.

[0088] Figure 28 It is the effect of the element spacing of a planar phased array with a transmitting frequency of f0 = 1.4 MHz on the axis sound pressure focusing gain.

[0089] Figure 29 It is the effect of the element spacing of a planar phased array with a transmitting frequency of f0 = 1.6 MHz on the axis sound pressure focusing gain.

[0090] Figure 30 It is the effect of the element spacing of a planar phased array with a transmitting frequency of f0 = 1.8 MHz on the axis sound pressure focusing gain.

[0091] Figure 31 It is the effect of the element spacing of a planar phased array with a transmitting frequency of f0 = 2.0 MHz on the axis sound pressure focusing gain.

[0092] Figure 32 It is a planar phased array model with 10×10 elements.

[0093] Figure 33 It is a planar phased array model with 20×20 elements.

[0094] Figure 34 It is a planar phased array model with 30×30 elements.

[0095] Figure 35 It is a planar phased array model with 40×40 elements.

[0096] Figure 36 It is a planar phased array model with 50×50 elements.

[0097] Figure 37 It is a planar phased array model with 60×60 elements.

[0098] Figure 38 It is a planar phased array model with 70×70 elements.

[0099] Figure 39 It is a planar phased array model with 80×80 elements.

[0100] Figure 40 It is the effect of the number of array elements of a planar phased array with a transmission frequency of f0 = 200 kHz on the axis sound pressure focusing gain.

[0101] Figure 41 It is the effect of the number of array elements of a planar phased array with a transmission frequency of f0 = 400 kHz on the axis sound pressure focusing gain.

[0102] Figure 42 It is the effect of the number of array elements of a planar phased array with a transmission frequency of f0 = 600 kHz on the axis sound pressure focusing gain.

[0103] Figure 43 It is the effect of the number of array elements of a planar phased array with a transmission frequency of f0 = 800 kHz on the axis sound pressure focusing gain.

[0104] Figure 44 It is the effect of the number of array elements of a planar phased array with a transmitting frequency of f0 = 1.0 MHz on the axis sound pressure focusing gain.

[0105] Figure 45 It is the effect of the number of array elements of a planar phased array with a transmitting frequency of f0 = 1.2 MHz on the axis sound pressure focusing gain.

[0106] Figure 46 It is the effect of the number of array elements of a planar phased array with a transmitting frequency of f0 = 1.4 MHz on the axis sound pressure focusing gain.

[0107] Figure 47 It is the effect of the number of array elements of a planar phased array with a transmitting frequency of f0 = 1.6 MHz on the axis sound pressure focusing gain.

[0108] Figure 48 It is the effect of the number of array elements of a planar phased array with a transmitting frequency of f0 = 1.8 MHz on the axis sound pressure focusing gain.

[0109] Figure 49 This is the effect of the number of array elements of a planar phased array with a transmission frequency of f0 = 2.0 MHz on the axis sound pressure focusing gain.

[0110] Figure 50 is the maximum peak-to-peak voltage distribution at the actual focus.

[0111] Figure 51 is the total focus deviation distribution between the actual focus and the selected focus.

[0112] Figure 52 is the radial focus deviation distribution between the actual focus and the selected focus.

[0113] Figure 53 is the distribution of axial focus deviation between the actual focus and the selected focus.

[0114] Figure 54 This is a -6dB focus control area without strict constraints.

[0115] Figure 55 It is a strictly constrained -6dB focus control area.

[0116] Figure 56 It is the total focus deviation within the -6dB focus control area under strict constraints.

[0117] Figure 57 It is the radial focus deviation within the -6dB focus control area under strict constraints.

[0118] Figure 58 It is the axial focus deviation within the -6dB focus control area under strict constraints.

[0119] Figure 59 It is the axis sound pressure focusing gain of the 6144-element planar phased array.

[0120] Figure 60 It is the maximum peak-to-peak value of the axis voltage of the 6144-element planar phased array and its fitting. DETAILED DESCRIPTION

[0121] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0122] Example 1

[0123] The planar phased array involved in this embodiment is composed of multiple square array elements, and its sound field is naturally formed by the superposition of the radiation sound fields of each square array element. Figure 1 .

[0124] like Figure 2 As shown, a method for simulating the focus gain of a planar phased array HIFU treatment system is provided, wherein the method comprises the following steps:

[0125] S1: Based on the Rayleigh integral formula of the rectangular piston sound source and the axis sound pressure focusing gain formula of the planar phased array in the far field based on the principle of all-electronic focusing phase control;

[0126] S2: Using the formula for the axial sound pressure focusing gain in the far field of the planar phased array, simulate any or all of the variations in the axial sound pressure focusing gain with the transmission frequency, array element spacing, array element size, and number of array elements.

[0127] S101: First, derive the radiation sound field of a single rectangular piston array element, such as Figure 3 The figure shows a rectangular piston sound source with a width of a and a length of b. The center of the rectangular piston array element is located at the origin of the coordinate system, the radiation surface of the rectangular piston array element is located in the xOy plane, and the surface of the rectangular piston array element vibrates along the z direction with a vibration velocity of:

[0128]

[0129] Among them, v a is the amplitude of the vibration velocity of the array element surface, ω0=2πf0 is the angular frequency, f0 represents the frequency, and θ0 represents the initial phase.

[0130] S102: For any observation point in the space corresponding to the z direction of the rectangular piston array element, the position vector of the observation point is r, the angle between r and the z axis is θ, and the rotation angle is According to the Rayleigh integral principle, the surface of the rectangular piston array element is divided into an infinite number of small rectangular surface elements. Each small rectangular surface element is regarded as a point source, and the sound pressure generated by each small rectangular surface element at the observation point is calculated.

[0131] The point source intensity of the small rectangular surface element dS, whose center is located at the polar radius ρ and the polar angle σ, is dQ = v a dS, where v a represents the amplitude of the vibration velocity on the surface of the array element; then the sound pressure generated by the small rectangular surface element at the observation point is:

[0132]

[0133] Among them, ρ m is the density of the ultrasonic propagation medium. The medium used in this embodiment is water, and its density is ρ m =1000kg / m 3 ; k = ω0 / c m is the wave number, ω0=2πf0 is the angular frequency, f0 represents the frequency; g is the distance from the center of the small rectangular surface element to the observation point; c m is the sound velocity of the ultrasonic propagation medium; j represents the imaginary unit, ω represents the angular frequency, θ0 represents the initial phase, k represents the wave number, and t represents the time.

[0134] S103: According to formula (2), the sound pressure radiated by all small rectangular surface elements is superimposed, that is, dS is integrated to obtain the radiated sound pressure generated by a rectangular array element at the observation point. The calculation formula is as follows:

[0135]

[0136] Where,

[0137] S represents the integrated area, (x, y) represents the Cartesian coordinates;

[0138] When r is much larger than the size of the rectangular array element, that is, in the far field:

[0139] g≈r-ρcos(r,ρ) (4)

[0140] in, r represents the distance from the center of the rectangular array element to the observation point; the calculated p is the radiated sound pressure generated by a rectangular array element at the observation point.

[0141] In the far field, the amplitudes of the sound waves emitted by the small rectangular elements on the rectangular piston array element are not much different when they reach the observation point. The radiated sound pressure generated by a rectangular array element at the observation point is optimized as follows: replace the g in the amplitude in equation (3) with the distance r from the center of the rectangular array element to the observation point; and replace the g in the phase with equation (4), thus obtaining:

[0142]

[0143] According to the geometric relationship:

[0144]

[0145] Substitute (8) into (7) and integrate to obtain:

[0146]

[0147] For a similar Figure 3 For the planar phased array shown in FIG, its radiated sound field is the superposition of the radiated sound fields of all rectangular array elements at the observation point.

[0148] S104: Calculate the phase compensation θ based on the radiated sound pressure obtained in step S3 0n , array element center coordinates (x n ,y n , 0) the radiation sound pressure of the n-th rectangular array element at the observation point, n = 1, 2, ... N;

[0149] According to formula (4), the phase compensation θ of each array element is 0n , array element center coordinates (x n ,y n ,0) at the observation point is:

[0150]

[0151] Among them, r n ,θ n 、 is the center offset of the nth rectangular array element (x n ,y n ,0), the distance and angle coordinates corresponding to the coordinates of the observation point in the offset spherical coordinate system; b n 、a n is the size of the nth rectangular array element.

[0152] The core principle of focusing ultrasound waves emitted by a phased array ultrasonic transducer at a target location is that the phases of the ultrasound waves emitted by each array element are consistent upon reaching the target location, creating a linear superposition effect and achieving superposition and focusing enhancement of the ultrasound. Therefore, in order to fully electronically focus the ultrasound waves excited by a planar phased array at a selected focal point, it is necessary to control the ultrasonic emission phase of each array element. The focusing scheme adopted in this embodiment uses acoustic ray theory to perform phase compensation on each array element of the planar phased array.

[0153] Specifically, for each element in the planar phased array, its emitted sound pressure is:

[0154] p n =p0sin(ω0t+θ 0n ) (9)

[0155] Among them, the emission sound pressure amplitude of each transducer unit is uniformly p0, θ 0n represents the phase compensation of each array element, ω0 = 2πf0 is the angular frequency, and the subscript n represents the nth array element of the planar phased array.

[0156] like Figure 3 As shown, the planar phased array radiation surface is located on the xOy plane, the center of the phased array is located at the origin of coordinates, and the z axis is perpendicular to the array surface and passes through the center of the array. For the focus F(x F ,y F , z F ), in order to ensure that the phase of the ultrasonic wave emitted by each array element is consistent when it propagates to the focus F, according to the sound ray theory, the phase compensation of each array element can be calculated as:

[0157]

[0158] Among them, (x n ,y n ,0) is the coordinate of the center point of the nth array element, c m is the sound velocity of the ultrasonic propagation medium. The medium used in this embodiment is water, and its sound velocity c m =1500m / s.

[0159] S105: Superimpose the radiation sound pressures obtained in step S4 to obtain the total radiation sound pressure of the planar phased array, which is expressed as follows:

[0160]

[0161] Since the phase part in formula (11) are equal, so:

[0162]

[0163] Where, ρ m c m v a is regarded as the sound pressure p0 radiated from the surface of the array element.

[0164] S106: Normalize the total radiated sound pressure of the planar phased array to obtain the ultrasonic focusing gain of the planar phased array, specifically by comparing equation (12) with respect to ρ m c m v a After normalization, the ultrasonic focusing gain of the planar phased array can be obtained as:

[0165]

[0166] Specifically speaking about the focusing gain on the axis, if the coordinates of the observation point are F(0, 0, z F ), formula (13) can be further expressed as:

[0167]

[0168] in,

[0169] The planar phased array elements used in the simulation of this embodiment are square elements with the same size, i.e. n =b n =a. Therefore, formula (14) can be further expressed as:

[0170]

[0171] S2: Simulate the variation of ultrasonic focusing gain with transmission frequency, array element spacing, array element size, and number of array elements. The specific simulation model experiment is as follows:

[0172] The hydrophone method is used to test the ultrasonic focusing performance of the 6144-element planar phased array. Figure 4 shown. Figure 4 The phased array is clearly shown to consist of 96 planar modules, each containing 8×8=64 square array elements. The radiating surface of the phased array lies in the xOy plane, with the array center at the origin. The z-axis is perpendicular to the array surface and passes through the center of the array. The phased array transmits at a frequency of f0=516kHz, with a center-to-center spacing of 14.1mm between adjacent modules and 1.5mm between adjacent array elements. Each element measures approximately 1.35×1.35mm. 2 The experimental device for hydrophone test is as follows: Figure 5As shown in Figure 2, the planar ultrasonic phased array is controlled by the treatment planning system (TPS) installed in computer 2 through a control system for phase and amplitude regulation. The planar array is coupled via degassed water. Computer 1 controls the movement of the needle hydrophone via a stepper motor, enabling ultrasonic field pickup and measurement at various locations. The signals received by the hydrophone are transmitted to computer 1 via an oscilloscope for recording and storage for subsequent data processing.

[0173] The ultrasonic focus area to be measured is a cylinder with a radius of 90mm and a height of 170mm directly above the plane phased array, and the central axis of the cylinder coincides with the z-axis of the array, and its bottom is 30.0mm above the array. In the measured area, starting from the bottom of the cylinder, a measured plane is set every 10mm in the height direction. On each measured plane, the center of the circle is used as the starting point: the azimuth angle starts from 0°, and a radius line is drawn every 45°, and the radial direction is divided into circles with radii of 30, 60, 70, 80, and 90mm respectively. The intersection of all the measuring lines is the selected ultrasonic focus to be measured, such as Figure 6 、 7 As shown in Figure 2, a planar array is set up on the TPS to transmit ultrasound waves at a uniform acoustic power of 1 W, electronically focused at a selected focal position. A needle hydrophone captures the ultrasonic signal around the selected focal point. For each selected focal point, the maximum peak-to-peak voltage around the focal point is determined by the hydrophone, and the corresponding actual focal coordinate position is recorded for subsequent data analysis.

[0174] The total acoustic radiation area S of the planar phased array t =S e ×N, where S e =a 2 is the area of ​​each square element. t Under the premise of keeping the same, the different array element spacing E space (or different element sizes E size , or the influence of the transmitting frequency f0 on the axis sound pressure focusing gain under different array element numbers N).

[0175] Table 1 lists the model parameters of the planar phased array used in the simulation. The total acoustic radiation area S of each planar phased array is t =9216mm 2 , remains unchanged. The schematic diagram corresponding to each planar phased array model can be found in Figures 8 to 14 .

[0176] Table 1. Model parameters of planar phased array (S t =9216mm 2 remain unchanged)

[0177]

[0178] The commonly used HIFU transmission frequency is generally between 200kHz and 2.0MHz, and the commonly used axial treatment range (or focal length) is generally greater than 30mm. Given the array element size used in this embodiment, this essentially satisfies the far-field conditions required for equation (15) to hold. Both the frequency and axial position in this embodiment are within this range.

[0179] Figures 15-21 Different array element spacing E is given space (or different element sizes E size , or different array element numbers N), the axis sound pressure focusing gain changes with the transmission frequency f0. Figures 15-21 It can be seen that:

[0180] (1) When the wavelength λ corresponding to the emission frequency f0 is c m / f0 is greater than the array element spacing E space When , within the set z-axis range, the axis sound pressure focusing gain decreases monotonically without an extreme value, and the decreasing trend intensifies with increasing frequency. The axis sound pressure focusing gain increases with increasing frequency, but the increasing trend decreases.

[0181] (2) When the wavelength λ corresponding to the emission frequency f0 is c m / f0 is less than the array element spacing E space When the axis sound pressure focusing gain is set in the z-axis range, it generally increases first and then decreases, and the increasing trend is stronger than the decreasing trend. There is a maximum point, but the wavelength λ = c m / f0 compared to the array element spacing E space If there are many small ones. The aforementioned maximum value has a slight downward trend with the increase of frequency. The reduction of the array element spacing seems to aggravate this slight downward trend, and the coordinate position corresponding to the maximum value gradually shifts toward the +z direction (i.e., the direction away from the phased array) with the increase of frequency; on the right side of the maximum point, the decreasing trend of the axis sound pressure focusing gain weakens with the increase of frequency; on the right side far from the maximum point, the axis sound pressure focusing gain increases with the increase of frequency, but the increasing trend decreases; on the left side far from the maximum point, that is, close to the axis range of the planar phased array, ignoring the small fluctuations of the axis sound pressure focusing gain in the region, the axis sound pressure focusing gain decreases with the increase of frequency.

[0182] (3) The wavelength λ corresponding to the emission frequency f0 is c m / f0 is equal to the array element spacing E spaceThis is a significant turning point. At this point, the axial sound pressure focus gain begins to reach its maximum value within the set z-axis range. The initial starting value of the axial sound pressure focus gain increases with frequency, then decreases for the first time at this transmission frequency. Later, the axial sound pressure focus gain maximum value begins to decrease slightly with increasing frequency.

[0183] (4) Array element spacing E space If it is larger, under the premise that the total sound radiation area remains unchanged, it means that the number of array elements is small. At this time, no matter how the transmission frequency changes, the axial sound pressure focusing gain of the planar phased array is not very high, which is difficult to meet the actual HIFU treatment needs. Moreover, the higher the transmission frequency, the farther the maximum point is from the planar phased array, and it can even reach a position close to 1.0m, which is also difficult to use in actual HIFU treatment.

[0184] (5) Array element spacing E space The reduction has an enhancing effect on the axis sound pressure focusing gain, and the higher the emission frequency, the better the enhancement effect appears.

[0185] Analyze the array element spacing E space Impact on the peak sound pressure at the axial focus

[0186] The model parameters of the planar phased array are consistent with those in Table 1. The difference is that in this embodiment: t Under the premise of keeping the same, the array element spacing E under different transmission frequencies space (or different element sizes E size , or the influence of different array element numbers N) on the axis sound pressure focusing gain. Figures 8 to 14 The effect of the transmitting frequency f0 on the axis sound pressure focusing gain can be reflected in the figure. Therefore, in order to highlight the array element spacing E space (or different element sizes E size , or the influence of different array element numbers N) on the axis sound pressure focusing gain, especially Figures 15-21 The curve is reintegrated and the axis sound pressure focusing gain is given as the array element spacing E when the transmission frequency is f0 = 200kHz: 200kHz: 2.0MHz. space (or element size E size , or the number of array elements N) of the curve, such as Figures 15-21 As shown. Figures 15-21 Yes Figures 8 to 14 After reprocessing the data, Figures 8 to 14 The results also apply to Figures 15-21 Even so, we can still Figures 15-21 The following results were obtained from the analysis:

[0187] (1) The increase of the transmission frequency f0 has an enhanced effect on the axis sound pressure focusing gain, and the array element spacing E space The smaller the value, the better the enhancement effect. The larger the array element spacing, the less obvious the enhancement effect.

[0188] (2) For any transmitting frequency f0, the axis sound pressure focusing gain generally increases with the decrease of the array element spacing, especially in the axis section relatively close to the planar phased array, where this increase is very obvious; however, as the axis position gradually moves away from the planar phased array, this increase gradually weakens and eventually approaches 0.

[0189] (3) The reduction in the array element spacing will cause the maximum point of the axis sound pressure focusing gain to shift toward the +z direction.

[0190] (4) The smaller the array element spacing, the closer the axis sound pressure focusing gain is, but the increase in the transmission frequency will weaken this approach phenomenon.

[0191] Array element size E size Impact on the axis sound pressure focusing gain

[0192] This section no longer keeps the total acoustic radiation area of ​​the planar phased array unchanged, but keeps the number of array elements N = 80 × 80 = 6400 and the array element spacing E space =1.5mm remains unchanged, and the array element size E is studied under different transmission frequencies. size Impact on the on-axis sound pressure focusing gain.

[0193] Table 2 lists the model parameters of the planar phased array used in the simulation. The schematic diagram corresponding to each planar phased array model is shown in Figures 22-31 .

[0194] Table 2. Model parameters of planar phased array (N = 80 × 80 = 6400 and E space =1.5mm remains unchanged)

[0195]

[0196]

[0197] Figures 22-31 The axis sound pressure focusing gain is given as the array element size E when the transmission frequency is f0 = 200kHz: 200kHz: 2.0MHz. size The change curve of Figures 22-31 It can be seen that:

[0198] (1) Array element size E size The increase in has an enhancing effect on the axis sound pressure focusing gain.

[0199] (2) When the transmission frequency is relatively low, especially when the wavelength corresponding to the transmission frequency is greater than the array element spacing, as the transmission frequency increases, the axial sound pressure focusing gain corresponding to the same array element size also increases significantly.

[0200] (3) When the wavelength corresponding to the transmission frequency is not greater than the array element spacing, as the transmission frequency increases, the axial sound pressure focusing gain peak corresponding to the same array element size tends to slowly decrease, but the axial sound pressure focusing gain uniformity improves.

[0201] (4) The wavelength λ = 1.5 mm corresponding to the transmitting frequency f0 = 1.0 MHz is equal to the array element spacing used in this part of the study. When the transmitting frequency f0 ≥ 1.0 MHz, the axis sound pressure focusing gain should reach a maximum point, but Figures 22-31 However, the actual result is not like this; only when the array element size is close to the array element spacing, the axis sound pressure focusing gain will have a maximum point; and the closer the array element size is to the array element spacing, the more obvious the axis sound pressure focusing gain will be. Therefore, according to the inference, the prerequisite for its establishment is that the array element size is close to the array element spacing. It is further speculated that if the array element size is basically consistent with the array element spacing, the emission frequency of the aforementioned landmark turning point will be reduced.

[0202] (5) If the array element size is small, under the premise that the number of array elements and the array element spacing remain unchanged, it means that the total sound radiation area is small and the array element distribution appears to be relatively more dispersed. At this time, regardless of how the transmission frequency changes, the axial sound pressure focusing gain of the planar phased array is not very high, which is difficult to meet the actual HIFU treatment needs.

[0203] The influence of the number of array elements N on the axis sound pressure focusing gain

[0204] This section does not keep the total acoustic radiation area of ​​the planar phased array unchanged, but keeps the array element size E size =1.2×1.2mm 2 and array element spacing E space =1.5mm remains unchanged, and the influence of the number of array elements N on the axis sound pressure focusing gain under different transmitting frequencies is studied.

[0205] Table 3 lists the model parameters of the planar phased array used in the simulation. The schematic diagram corresponding to each planar phased array model is shown in Figures 32-39 .

[0206] Table 3. Model parameters of planar phased array (E size =1.2×1.2mm 2 and E space =1.5mm remains unchanged)

[0207]

[0208]

[0209] Figures 40-49 The curve of axis sound pressure focusing gain changing with the number of array elements N is given when the transmission frequency is f0 = 200kHz: 200kHz: 2.0MHz. Figures 40-49 It can be seen that:

[0210] (1) Increasing the number of array elements N has an enhanced effect on the axial sound pressure focusing gain.

[0211] (2) When the transmission frequency is relatively low, especially when the wavelength corresponding to the transmission frequency is greater than the array element spacing, as the transmission frequency increases, the axial sound pressure focusing gain corresponding to the same number of array elements also increases significantly.

[0212] (3) When the wavelength corresponding to the transmission frequency is not greater than the array element spacing, as the transmission frequency increases, the axial sound pressure focusing gain peak corresponding to the same number of array elements tends to slowly decrease, but the axial sound pressure focusing gain uniformity improves.

[0213] (4) The wavelength λ = 1.5 mm corresponding to the transmitting frequency f0 = 1.0 MHz is equal to the array element spacing used in this part of the study. When the transmitting frequency f0 ≥ 1.0 MHz, the axis sound pressure focusing gain should reach a maximum point, but Figures 40-49 However, the actual result is not the case; the greater the number of array elements, the more likely it is that the axis sound pressure focusing gain will have a maximum point; therefore, for the previous inference, another prerequisite for its validity is that the number of array elements is as large as possible. It is further speculated that if the number of array elements continues to increase, the emission frequency of the aforementioned landmark turning point will decrease.

[0214] (5) If the number of array elements is small, under the premise that the array element size and array element spacing remain unchanged, it means that the total sound radiation area is small and the size of the planar phased array is also small. At this time, no matter how the transmission frequency changes, the axial sound pressure focusing gain of the planar phased array is not very high, which is difficult to meet the actual HIFU treatment needs.

[0215] Hydrophone measurement results of the focused acoustic field of a 6144-element planar phased array

[0216] Figure 50 shows the maximum peak-to-peak voltage V measured by the hydrophone around the selected focus. m，pp The three-dimensional distribution of the maximum voltage peak-to-peak value at the actual focus. The maximum value is V m，pp，max =2.59 V, the minimum value is V m，pp，min =0.78V. Overall, Figure 50The results show that the focused ultrasound intensity of the 6144-element planar phased array is higher near the center of the measurement area, and the closer to the boundary of the measurement area, the lower the focused ultrasound intensity.

[0217] Figure 51 Given Figure 50 Medium V m，pp The actual focus corresponds to Figure 7 、 8 The total focus deviation between the selected focus points in the image. The maximum total focus deviation is approximately FD max =4.41mm. Overall, Figure 51 This shows that the focus deviation of the phased array is small near the center of the measurement area, and the closer to the boundary of the measurement area, the larger the focus deviation. In addition, the maximum focus deviations in the radial direction (on the xy plane) and the axial direction (parallel to the z axis) are approximately 3.71 mm and 3.60 mm, respectively. Figures 52-53 shown.

[0218] Furthermore, considering the maximum peak-to-peak voltage of all focal points relative to the maximum value V m，pp，max = 2.59 V drops no more than 6dB (i.e. V m，pp ≥0.5V m，pp，max ), the circled ultrasound focus area (i.e. -6dB focus control area) is as follows Figure 54 As shown. It can be seen that only a small number of focuses near the upper and lower circumferences of the measured cylindrical area are excluded from the -6dB focus control area. In order to describe the -6dB focus control area more clearly and conveniently, we want to limit the -6dB focus control area to a cylinder. Even under the most stringent constraints, we use the minimum radius corresponding to the outermost focus on all measured planes in the -6dB focus control area as the radius of the cylinder in the -6dB focus control area. This area is at least a cylinder with a radius of 70mm and a height of 170mm, as shown in the figure. Figure 55 As shown. Figure 55 Among all the maximum peak-to-peak voltages, the minimum is 1.33V. Figures 56-58 It shows that the maximum values ​​of the total focus deviation, radial focus deviation and axial focus deviation within the -6dB focus control area of ​​the cylinder are approximately 3.62mm, 3.06mm and 3.60mm, respectively, indicating that the 6144-element HIFU phased array has strong all-electronic ultrasonic focusing capability.

[0219] In addition, we also used Equation (15) to simulate the axis sound pressure focusing gain of the 6144-element planar phased array. The results are as follows: Figure 59 As a comparison, we plot the maximum peak-to-peak voltage measurement value on the axis of the measured area on Figure 60The fitting curves are presented in Figure 2. Clearly, the two trends do not match. Simulation results show that the axial acoustic pressure focusing gain of the 6144-element planar phased array exhibits a monotonically decreasing trend within the selected axial range z = [30mm, 200mm]. Measurement results, however, show that the axial maximum peak-to-peak voltage of the 6144-element planar phased array first increases and then decreases. In other words, the axial ultrasonic focusing parameters of the two devices vary in a similar manner in the far field, but in starkly different ways in the near field. We analyze that the primary reason for this discrepancy is that the near-field axial position is too close to the 6144-element planar phased array. This creates a large angle of incidence between the ultrasonic waves emitted by each element and the hydrophone. Since the hydrophone has limited directivity, the closer the axial position is to the phased array, the closer the hydrophone is to the array, and the larger the angle of incidence becomes. Consequently, the ultrasonic signal picked up by the hydrophone becomes increasingly weaker than the actual ultrasonic signal. The discrepancy between the two also suggests that the -6dB focus control range described above may require more accurate measurement. Further measurement and verification requires the use of a wide-angle directivity sound field measurement system.

[0220] This example uses the Rayleigh integral formula for a rectangular piston sound source, combined with a fully electronic focusing phase control method based on ray theory, to derive a formula for the far-field ultrasonic focusing gain of a planar phased array. Specifically, a formula for the axial sound pressure focusing gain of a planar phased array in the far field is given. Using this formula, this example simulates how the axial sound pressure focusing gain varies with transmission frequency, array element spacing, array element size, and number of array elements. The results demonstrate that:

[0221] (1) Under the premise of keeping the total acoustic radiation area of ​​the planar phased array unchanged, the wavelength corresponding to the emission frequency is equal to the array element spacing, which is a landmark turning point. When the wavelength corresponding to the emission frequency is greater than the array element spacing, the axis sound pressure focusing gain decreases monotonically; when the wavelength corresponding to the emission frequency is less than the array element spacing, the axis sound pressure focusing gain generally increases first and then decreases, and there is a maximum point. The reduction in the array element spacing has an enhancement effect on the axis sound pressure focusing gain, and the higher the emission frequency, the better the enhancement effect. If the array element spacing is large, the number of array elements is small, and the axis sound pressure focusing gain at any emission frequency is not high, and the higher the emission frequency, the farther the maximum point is, which is difficult to meet the actual HIFU treatment needs. The axis sound pressure focusing gain increases as the array element spacing decreases. The reduction in the array element spacing will cause the axis sound pressure focusing gain maximum point to shift toward the +z direction.

[0222] (2) Under the premise of keeping the number of array elements and the array element spacing unchanged, increasing the array element size has an enhancing effect on the axial sound pressure focusing gain. The closer the array element size is to the array element spacing, the more likely the axial sound pressure focusing gain will have a more obvious maximum point. It is speculated that the closer the array element size is to the array element spacing, the smaller the signature turning point emission frequency will be. The smaller the array element size, the smaller the total sound radiation area, and the axial sound pressure focusing gain at any emission frequency is not high, which is difficult to meet the actual HIFU treatment needs.

[0223] (3) Under the premise of keeping the array element size and array element spacing unchanged, increasing the number of array elements has an enhancing effect on the axial sound pressure focusing gain. The more array elements there are, the more likely it is that the axial sound pressure focusing gain will have a maximum value point. It is speculated that the more array elements there are, the lower the frequency of the landmark turning point will be. With fewer array elements, the total sound radiation area is smaller, and the axial sound pressure focusing gain at any transmission frequency is not high, which is difficult to meet the actual HIFU treatment needs.

[0224] However, it should be noted that for a few planar phased array models with larger element sizes, the compliance with near-field conditions may be worse, but this should not affect the overall general rules.

[0225] On the other hand, the measurement results of the focused ultrasonic field of the 6144-element planar HIFU phased array using the hydrophone method show that the -6dB focus control area of ​​the planar phased array is at least a cylinder with a radius of 70mm and a height of 170mm. The maximum values ​​of the total focus deviation, radial focus deviation and axial focus deviation in this area are 3.62mm, 3.06mm and 3.60mm, respectively. In general, whether from the perspective of the -6dB focus control area or from the perspective of focusing accuracy, the planar phased array has good all-electronic ultrasonic focusing performance. However, the change trends of the simulation results of the axis sound pressure focusing gain and the measurement results of the axis maximum voltage peak-to-peak value of the phased array are different in the near field. This is mainly due to the limited directivity of the hydrophone, which causes the ultrasonic signal picked up by it in the near field to be weaker than the real ultrasonic signal.

[0226] Obviously, the above embodiments of the present invention are merely examples for the purpose of illustrating the present invention, and are not intended to limit the embodiments of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A method for simulating the focus gain of a planar phased array HIFU treatment system, characterized by: The method comprises the following steps: S1: Based on the Rayleigh integral formula of the rectangular piston sound source and the axis sound pressure focusing gain formula of the planar phased array in the far field based on the principle of all-electronic focusing phase control; S2: Using the far-field axial sound pressure focusing gain formula of the planar phased array, simulate any or all of the variations of the axial sound pressure focusing gain with the transmission frequency, array element spacing, array element size, and array element number; Step S1: Establishing the axis sound pressure focusing gain formula of the planar phased array in the far field. The specific steps are as follows: S101: First, derive the radiation sound field of a single rectangular piston array element. The center of the rectangular piston array element is located at the coordinate origin, and the radiation surface of the rectangular piston array element is located at x O y Plane, rectangular piston element surface along z Directional vibration; S102: For rectangular piston array elements z Any observation point in the space corresponding to the direction; divide the surface of the rectangular piston array element into an infinite number of small rectangular surface elements, take each small rectangular surface element as a point source, and calculate the sound pressure generated by each small rectangular surface element at the observation point; S103: Superimposing the sound pressures radiated by all the small rectangular surface elements, thus obtaining the radiated sound pressure generated by a rectangular piston array element at the observation point; S104: Calculate phase compensation based on the radiated sound pressure obtained in step S3 θ 0n , array element center coordinates ( x n , y n , 0) n The radiated sound pressure of the rectangular array element at the observation point is: n =1, 2, ...N; S105: Superimposing the radiation sound pressures obtained in step S4 to obtain the total radiation sound pressure of the planar phased array; S106: normalizing the total radiated sound pressure of the planar phased array to obtain an ultrasonic focusing gain formula for the planar phased array; Step S102, specifically, the position vector of the observation point is r , r and z The angle between the axes is θ , the rotation angle is φ ; According to the Rayleigh integral principle, the rectangular piston array element surface is divided into an infinite number of small rectangular surface elements; The center is located at the polar radius ρ , the polar angle is σ Small rectangular surface element at dS , and its point source intensity is dQ = v a dS ,in, v a represents the amplitude of the vibration velocity on the surface of the array element; then the sound pressure generated by the small rectangular surface element at the observation point is: (4) in, is the density of the ultrasound propagation medium; k = ω 0 / c m is the wave number, ω 0=2 πf 0 is the angular frequency, f 0 represents frequency; g is the distance from the center of the small rectangular surface element to the observation point; c m is the speed of sound in the ultrasonic propagation medium; Represents an imaginary unit, Indicates angular frequency, Indicates the initial phase, Indicates the wave number, Indicates time.

2. The method for simulating the focus gain of a planar phased array HIFU treatment system according to claim 1, wherein: Step S103: The sound pressures radiated by all the small rectangular surface elements are added together. The calculation formula is as follows: (5) Where, , ; represents the integral area, ( x 、 y ) represents Cartesian coordinates; When r is much larger than the size of the rectangular array element, that is, in the far field: (6) in, ; Represents the distance from the center of the rectangular array element to the observation point; Calculated It is the radiated sound pressure generated by a rectangular array element at the observation point.

3. The method for simulating the focus gain of a planar phased array HIFU treatment system according to claim 2, wherein: The radiated sound pressure generated by a rectangular array element at the observation point is optimized as follows: g The distance from the center of the rectangular array element to the observation point Instead, g Then use formula (6) to replace it, and then get: (7) According to the geometric relationship: (8) Substitute (8) into (7) and integrate to obtain: (9)。 4. The method for simulating the focus gain of a planar phased array HIFU treatment system according to claim 3, wherein: According to formula (9), the phase compensation of each array element is θ 0n , array element center coordinates ( x n , y n , 0) n The radiated sound pressure of a rectangular array element at the observation point is: (10) in, r n 、 θ n 、 φ n Respectively represent the n The center offset of the rectangular array element ( x n , y n , 0), the distance and angle coordinates corresponding to the coordinates of the observation point in the offset spherical coordinate system; b n 、 a n It is n The size of a rectangular array element.

5. The method for simulating the focus gain of a planar phased array HIFU treatment system according to claim 4, wherein: The phase compensation θ 0n , which is calculated as follows: For arrays z Direction corresponding to the selected focus in space F ( x F , y F , z F ), to ensure that the ultrasonic wave emitted by each array element propagates to the focus F The phase is consistent at the time; according to the sound ray theory, the phase compensation of each array element can be calculated as: (2) in,( x n , y n , 0) is the n The coordinates of the center point of each array element, c m is the speed of sound in the medium in which ultrasound propagates.

6. The method for simulating the focus gain of a planar phased array HIFU treatment system according to claim 5, wherein: The total radiated sound pressure of the planar phased array is: （11） Since the phase part in formula (11) are equal, so: (12) Where, Considered as the sound pressure radiated from the surface of the array element p 0.

7. The method for simulating the focus gain of a planar phased array HIFU treatment system according to claim 6, wherein: Step S106, Equation (12) relative to After normalization, the ultrasonic focusing gain of the planar phased array can be obtained as: (13) Specifically for the focusing gain on the axis, if the coordinates of the observation point are F (0, 0, z F ), formula (13) can be further expressed as: in, .

8. The method for simulating focus gain of a planar phased array HIFU treatment system according to claim 7, wherein: Step S2, using the hydrophone method to simulate the ultrasonic focusing performance of the planar array, exist S t Under the premise of keeping the same, simulate different array element spacing E space The transmission frequency in the case f 0 on the axis sound pressure focusing gain; exist S t Under the premise of keeping the same, simulate the array element spacing under different transmission frequencies E space Impact on the axis sound pressure focusing gain; While maintaining the number of array elements and the spacing between array elements E space Under the premise of no change, the array element size is simulated under different transmission frequencies E size Impact on the axis sound pressure focusing gain; While maintaining the array element size E size and element spacing E space Under the premise of no change, the number of array elements under different transmission frequencies is simulated N Impact on the on-axis sound pressure focusing gain.

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