CN112560274B - Photoacoustic effect simulation and emulation method based on acoustic wave superposition - Google Patents
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Abstract
The invention discloses a photoacoustic effect simulation and emulation method based on acoustic wave superposition. The invention provides a method for calculating the photoacoustic signal of the whole body by dividing an initial pressure distribution grid into a plurality of pixel points, respectively calculating the photoacoustic signal independently generated by each pixel point and then calculating the photoacoustic signal according to the superposition principle of waves. The method provided by the invention converts solving of a complex photoacoustic equation into simple cyclic superposition operation, and greatly reduces the operation time. In most cases, the running time of the method provided by the invention is far less than the calculation time of k-Wave.
Description
Technical Field
The invention relates to a photoacoustic effect simulation and emulation method, belonging to the technical field of development of photoacoustic effects, photoacoustic forward models and emulation models.
Background
The photoacoustic effect refers to a physical phenomenon in which an object generates an acoustic signal under excitation of laser light. Based on the photoacoustic effect, photoacoustic imaging technology has gained wide attention and has been rapidly developed in recent years. At present, the photoacoustic imaging technology has achieved certain success in small animal imaging, blood oxygen saturation quantification and tumor benign and malignant diagnosis.
The development of photoacoustic imaging has benefited to some extent from the development and maturation of photoacoustic simulation software. The k-Wave is relatively mature photoacoustic simulation software and is widely applied to various work related to photoacoustic. The most important function in k-Wave is photoacoustic forward model simulation, and photoacoustic effects are simulated by solving a photoacoustic equation through a numerical method and generating photoacoustic signals from initial pressure distribution. However, the numerical method is complex in calculation and long in operation time, and particularly under the conditions of high sampling rate and large initial pressure distribution grid. The shortcoming of low operation speed in the K-Wave greatly reduces the application range of the tool kit.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the numerical method for solving the photoacoustic equation in the photoacoustic simulation software is complex in calculation and long in operation time.
In order to solve the technical problem, the technical scheme of the invention is to provide a photoacoustic effect simulation and emulation method based on acoustic wave superposition, which is characterized by comprising the following steps of:
step 4, only the p-th pixel point in the initial pressure distribution grid is enabled to act through setting the pixel values of the n multiplied by m pixel points;
step 5, under the set sampling rate, using photoacoustic simulation software to obtain an ultrasonic signal output by a jth ultrasonic probe, wherein the ultrasonic signal is a standard signal S, and obtaining the distance d from the center of a pth pixel point in an initial pressure distribution grid to the center of the jth ultrasonic probe;
step 6, calculating a phase operator of the p pixel point for generating the photoacoustic signal according to the position of the j ultrasonic probe and the distance from the p pixel point to the j ultrasonic probe in the obtained standard signal S and the distance d;
step 7, calculating an amplitude operator of the photoacoustic signal generated by the p-th pixel point according to the pixel value of the p-th pixel point in the standard signal S and the distance from the p-th pixel point to the j-th ultrasonic probe;
step 8, changing the phase and amplitude of the standard signal S through a phase operator and an amplitude operator to obtain a photoacoustic signal generated by the p pixel point at the j ultrasonic probe;
step 9, p = p +1, if p > n × m, entering step 10, otherwise, returning to step 4;
and 11, obtaining photoacoustic signals of the integral initial pressure distribution of J ultrasonic probes at different positions.
Preferably, in step 6, the two-dimensional coordinates of the jth ultrasonic probe are (x, y), and the two-dimensional coordinates of the pth pixel point are (x, y) p ,y p ) Then, the calculation process of the phase operator for generating the photoacoustic signal by the p-th pixel point includes the following steps:
calculating the distance d from the p-th pixel point to the j-th ultrasonic probe in the standard signal S p ：
Obtaining a phase operator tau (d) of the photoacoustic signal generated by the p-th pixel point through the propagation velocity v and the sampling rate f of the ultrasonic wave in the medium p ,d)：
When phase operator tau (d) p ,d)>When 0, the phase is shifted to the right; when phase operator tau (d) p ,d)<When 0, the phase is shifted to the left.
Preferably, in step 7, the calculation process of the amplitude operator for generating the photoacoustic signal at the p-th pixel point includes the following steps:
the process of energy dissipation is approximated using a power exponential function of the negative second order, as shown in equation (3) below:
in the formula (3), g (d) p ) Representing the amplitude decay function resulting from energy dissipation; k is an adjustable hyper-parameter, and within the same diffusion distance, the larger k is, the larger energy diffusion is;
obtaining an amplitude operator A (d) of the photoacoustic signal generated by the p-th pixel point p (ii) a p) as shown in the following formula (4):
in the formula (4), P represents the pixel value of the P-th pixel in the standard signal S.
Preferably, in step 8, the photoacoustic signal generated by the p-th pixel point at the j-th ultrasonic probe is represented as S p ：
S p ＝A(d p ；P)g〈S|τ(d p ,d)> (5)
In the formula (5), g<S|τ(d p ,d)>Representation using the phase operator τ (d) p And d) performing a cyclic shift operation on the standard signal S.
The invention provides a method for calculating the photoacoustic signal of the whole body by dividing an initial pressure distribution grid into a plurality of pixel points, respectively calculating the photoacoustic signal independently generated by each pixel point and then calculating the photoacoustic signal of the whole body according to the wave superposition principle. The method provided by the invention converts the solving of the complex photoacoustic equation into simple cyclic superposition operation, thereby greatly reducing the operation time. In most cases, the running time of the method provided by the invention is far less than the calculation time of k-Wave.
Drawings
Fig. 1 is photoacoustic signals generated by three samples by using k-Wave and our method and photoacoustic images reconstructed by using a delay superposition algorithm;
FIG. 2 is a comparison of the running speed (unit: sec) of experiment 3.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The invention provides a photoacoustic effect simulation and emulation method based on sound wave superposition, which comprises the following steps of:
step 4, setting the pixel values of n multiplied by m pixel points to enable only the pth pixel point in the initial pressure distribution grid to act;
step 5, under the set sampling rate, using photoacoustic simulation software to obtain an ultrasonic signal output by a jth ultrasonic probe, wherein the ultrasonic signal is a standard signal S, and obtaining the distance d from the center of a pth pixel point in an initial pressure distribution grid to the center of the jth ultrasonic probe;
taking k-Wave as an example, the pixel value of the p-th pixel point is set to 1 in a fixed grid, and the pixel values of other pixel points are set to 0, so that only the p-th pixel point in the whole initial pressure distribution is ensured to be acted. Under the set sampling rate, arranging an ultrasonic probe around the pixel point to acquire an ultrasonic signal (standard signal S); obtaining distance information d by calculating the distance between the center of the p pixel point and the center of the j ultrasonic probe;
step 6, according to the position of the jth ultrasonic probe, calculating a phase operator of the photoacoustic signal generated by the pth pixel point through the distance from the pth pixel point to the jth ultrasonic probe in the obtained standard signal S and the distance d;
let the two-dimensional coordinate of the jth ultrasonic probe be (x, y), and the two-dimensional coordinate of the pth pixel point be (x) p ,y p ) Then, the calculation process of the phase operator for generating the photoacoustic signal by the p-th pixel point includes the following steps:
calculating the distance d from the p-th pixel point to the j-th ultrasonic probe in the standard signal S p ：
Obtaining a phase operator tau (d) of the photoacoustic signal generated by the p-th pixel point through the propagation velocity v and the sampling rate f of the ultrasonic wave in the medium p ,d)：
When phase operator tau (d) p ,d)>When 0, the phase is shifted to the right; when phase operator tau (d) p ,d)<When 0, the phase is shifted to the left;
step 7, calculating an amplitude operator of the photoacoustic signal generated by the p-th pixel point according to the pixel value of the p-th pixel point in the standard signal S and the distance from the p-th pixel point to the j-th ultrasonic probe;
there are three factors that affect the magnitude of the photoacoustic signal: (1) The size of the pixel value is in direct proportion to the signal amplitude. (2) The signal decays, often in a power exponential fashion in the medium. (3) The spread of signal energy, plane wave energy dissipation, tends to spread in power exponentiation. Because the simulation method of the present invention is based on an ideal environment, the present invention ignores the attenuation of the signal in the medium, only considers the spread of pixel values and energy, and then:
the calculation process of the amplitude operator for generating the photoacoustic signal by the p-th pixel point comprises the following steps:
the process of energy dissipation is approximated using a power exponential function of the negative second order, as shown in equation (3) below:
in the formula (3), g (d) p ) Representing the amplitude decay function resulting from energy dissipation; k is an adjustable hyper-parameter, and within the same diffusion distance, the larger k is, the larger energy diffusion is;
obtaining an amplitude operator A (d) of the photoacoustic signal generated by the p-th pixel point p (ii) a p) as shown in the following formula (4):
in the formula (4), P represents the pixel value of the P-th pixel point in the standard signal S;
step 8Changing the phase and amplitude of the standard signal S through a phase operator and an amplitude operator to obtain the photoacoustic signal S generated by the p pixel point at the j ultrasonic probe p ：
S p ＝A(d p ；P)g<S|τ(d p ,d)> (5)
In the formula (5), g<S|τ(d p ,d)>Representation using the phase operator tau (d) p D) performing a cyclic shift operation on the standard signal S;
step 9, p = p +1, if p > n × m, entering step 10, otherwise, returning to step 4;
and 11, obtaining photoacoustic signals of the overall initial pressure distribution of the J ultrasonic probes at different positions.
To illustrate the effectiveness of the invention, three pictures were used as the initial pressure distribution of the photo-acoustic, respectively a simple object, a simple blood vessel and a complex blood vessel. The first two pictures are the example pictures taken in k-Wave.
The present invention first shows the results generated by k-Wave and our method, as shown in FIG. 1.
The first column of fig. 1 shows three samples, the second and third columns show the photoacoustic signals generated by k-Wave and the method provided by the present invention. The fourth and fifth columns show photoacoustic images in which the generated photoacoustic signals are reconstructed by a delay-and-overlap algorithm. It can be seen that the method provided by the invention can almost achieve the same effect as k-Wave.
The speed advantage of the method provided by the invention over k-Wave under different conditions was then tested. The experiments are summarized in table 1:
table 1 parameter settings in different experiments
Experiment 1: the resolution of the initial pressure profile picture was changed from 64 to 256, the speed of operation of which is shown in table 2. It can be found that the method provided by the invention has obvious advantages under the condition of different resolutions of three samples.
TABLE 2 run speed comparison of experiment 1 (seconds)
Experiment 2: the sampling rate test running speed is changed. The larger the sampling rate, the longer the run time, but the impact of the high sampling rate on k-Wave is much larger than the method provided by the present invention. The method provided by the present invention still has advantages, with the run times shown in table 3.
TABLE 3 run speed comparison of experiment 2 (seconds)
Experiment 3: the probe number was varied to test the operating speed. The number of probes does not change the speed of operation of k-Wave, but since steps 3-9 need to be repeated, the number of probes greatly affects the operation time of our method. A run-time comparison is shown in fig. 2. For samples 1 and 2, the method provided by the present invention has advantages even with a number of probes as high as 512. For sample 3, when the number of probes exceeded 384, k-Wave was faster than the speed of the present invention. Overall, however, the present invention provides a method that has speed advantages in most cases.
Experiment 4: the distance from the probe to the sample was varied to measure the run speed. In k-Wave, the fact that the probe is farther means that a larger grid is needed to contain the probe, and the operation speed of the k-Wave is greatly influenced by the larger number of grids. In contrast, the method provided by the invention is not greatly influenced by the distance of the probe. The run time results are shown in table 4.
TABLE 4 run speed comparison of experiment 4 (seconds)
Claims (4)
1. A photoacoustic effect simulation and emulation method based on acoustic wave superposition is characterized by comprising the following steps:
step 1, dividing an initial pressure distribution grid provided by photoacoustic simulation software into n multiplied by m pixel points, wherein J ultrasonic probes in different positions are in total;
step 2, setting j =1;
step 3, setting p =1;
step 4, only the p-th pixel point in the initial pressure distribution grid is enabled to act through setting the pixel values of the n multiplied by m pixel points;
step 5, under the set sampling rate, using photoacoustic simulation software to obtain an ultrasonic signal output by a jth ultrasonic probe, wherein the ultrasonic signal is a standard signal S, and obtaining the distance d from the center of a pth pixel point in an initial pressure distribution grid to the center of the jth ultrasonic probe;
step 6, calculating a phase operator of the p pixel point for generating the photoacoustic signal according to the position of the j ultrasonic probe and the distance from the p pixel point to the j ultrasonic probe in the obtained standard signal S and the distance d;
step 7, calculating an amplitude operator of the photoacoustic signal generated by the p-th pixel point according to the pixel value of the p-th pixel point in the standard signal S and the distance from the p-th pixel point to the j-th ultrasonic probe;
step 8, changing the phase and amplitude of the standard signal S through a phase operator and an amplitude operator to obtain a photoacoustic signal generated by the pth pixel point at the jth ultrasonic probe;
step 9, p = p +1, if p > n × m, step 10 is entered, otherwise, step 4 is returned;
step 10, J = J +1, if J > J, step 11 is entered, otherwise, step 3 is returned;
and 11, obtaining photoacoustic signals of the integral initial pressure distribution of J ultrasonic probes at different positions.
2. The photoacoustic effect of claim 1 based on superposition of acoustic wavesThe simulation method is characterized in that in the step 6, the two-dimensional coordinates of the jth ultrasonic probe are set as (x, y), and the two-dimensional coordinates of the pth pixel point are set as (x) p ，y p ) Then, the calculation process of the phase operator for generating the photoacoustic signal by the p-th pixel point includes the following steps:
calculating the distance d from the p-th pixel point to the j-th ultrasonic probe in the standard signal S p ：
Obtaining a phase operator tau (d) of the photoacoustic signal generated by the p-th pixel point through the propagation velocity v and the sampling rate f of the ultrasonic wave in the medium p ，d)：
When phase operator tau (d) p And d) > 0, performing phase right shift; when phase operator tau (d) p And d) < 0, the phase is shifted to the left.
3. The photoacoustic effect simulation and emulation method based on acoustic wave superposition as claimed in claim 2, wherein in step 7, the calculation process of the amplitude operator for generating the photoacoustic signal at the p-th pixel point comprises the following steps:
the process of energy dissipation is approximated using a negative quadratic power exponent function, as shown in equation (3) below:
in the formula (3), g (d) p ) Representing an amplitude decay function resulting from energy dissipation; k is an adjustable hyper-parameter, and within the same diffusion distance, the larger k is, the larger energy diffusion is;
obtaining an amplitude operator A (d) of the photoacoustic signal generated by the p-th pixel point p (ii) a p) represented by the following formula (4):
in the formula (4), P represents the pixel value of the P-th pixel in the standard signal S.
4. The photoacoustic effect simulation and emulation method based on acoustic wave superposition as claimed in claim 3, wherein in step 8, the photoacoustic signal generated by the p-th pixel point at the j-th ultrasonic probe is represented as S p ：
S p ＝A(d p ；P)g<S|τ(d p ，d)> (5)
In the formula (5), g<S|τ(d p ，d)>Representation using the phase operator tau (d) p And d) performing a cyclic shift operation on the standard signal S.
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| CN104586363A (en) * | 2015-01-14 | 2015-05-06 | 复旦大学 | Fast photoacoustic imaging image reconstruction method based on image block sparse coefficient |
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