CN109938701A - It is a kind of for levying the optoacoustic Nakagami statistical analysis technique of microcosmic random structure number density surely - Google Patents

Abstract

The invention discloses a photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures. The Nakagami is used to analyze a probability density function that approximates the photoacoustic signal amplitude envelope to obtain optimal model parameters. The technology can determine Characterizing the number density of microscopic random structures. Photoacoustic spectroscopy can quantitatively characterize the size information of sub-wavelength microstructures in deep tissues, but only size properties cannot accurately and completely represent microstructure properties. The present invention combines the power spectrum analysis method and the photoacoustic signal envelope Nakagami statistical method, and by integrating them, a more comprehensive microstructure characterization, including feature size and number density, can be achieved. Since many diseases are closely associated with microstructural changes, this work facilitates the diagnosis and staging of these diseases with high ease of use and safety.

Description

A photoacoustic Nakagami statistical analysis for characterizing the number density of microscopic random structures Analysis method

technical field

The invention relates to a photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures, which is used to quantify the number density of random microstructures to achieve a more comprehensive description of the random microstructures.

Background technique

Photoacoustic imaging is a new type of biomedical imaging technology based on the photoacoustic effect, which combines the advantages of rich optical contrast of optical imaging and deep imaging depth of acoustic imaging. Also, non-ionizing radiation (eg, lasers or microwaves) used in photoacoustic imaging is more biosafe than ionizing radiation (eg, X-rays). These advantages make photoacoustic imaging show great application prospects in many fields of biomedicine.

The properties of random microstructures, including their feature size and number density, are useful indicators for differentiating different types of tissues. The development of some diseases is also accompanied by changes in tissue microstructure. For example, liver cirrhosis and chronic kidney disease may lead to deepening of tissue fibrosis, and tumor and normal tissue also have different microstructures. Therefore, it has important biomedical value for the non-invasive characterization of random microstructure of tissues.

The resolution of conventional photoacoustic imaging mainly depends on the frequency and bandwidth of the detected photoacoustic signal. Imaging microstructures in tissue must detect high-frequency and broadband photoacoustic signals. However, these random microstructures in deep tissue often appear as unrecognizable speckle noise in images due to factors such as the strong attenuation properties of high-frequency signals and medium inhomogeneity. Therefore, traditional photoacoustic imaging techniques are difficult to apply to the assessment of random microstructure of tissues. It was recently found that the photoacoustic spectral slope parameter can only quantify the characteristic size of random microstructures, but not their number density.

SUMMARY OF THE INVENTION

Purpose of the invention: In order to overcome the shortcomings of the existing photoacoustic imaging technology in the evaluation of the random surrounding structure of the organization, the present invention provides a photoacoustic Nakagami statistical analysis method for characterizing the number density of the microscopic random structure, which uses the Nakagami statistical model to approximate the light. The probability density function of the acoustic signal amplitude envelope to obtain the optimal model parameters. The shape parameter of the optimized Nakagami model only has a monotonically increasing relationship with the number density of microscopic random structures, but has nothing to do with factors such as signal intensity and random microstructure feature scale; therefore, the number density of microscopic random structures can be characterized by Nakagami statistical analysis; At the same time, using the shape parameters of the Nakagami model as imaging parameters, photoacoustic imaging can characterize and classify different tissues according to the number density characteristics of random microstructures of tissues; further, the method of the present invention is compared with methods such as photoacoustic spectrum slope parameters. Combined, a more comprehensive description of the random microstructure of tissues, including feature size and number density, can be achieved.

Technical scheme: In order to realize the above-mentioned purpose, the technical scheme adopted in the present invention is:

A photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures, comprising the following steps:

(1) Measurement of acousto-optic signals;

(2) The amplitude envelope of the photoacoustic signal is described by the data histogram, and the probability density function of the amplitude of the photoacoustic signal is calculated;

(3) The probability density function is approximated by the Nakagami distribution, and the optimal parameters of the Nakagami distribution are obtained;

(4) the photoacoustic signal is divided into several consecutive frames, and every two frames have the same overlap, and the method of steps (2) and (3) is used to calculate the optimal parameter of the Nakagami distribution of each frame;

(5) changing the position of the ultrasonic transducer, and repeating steps (1) to (4) to obtain the time series of the shape parameters corresponding to the photoacoustic signals collected at different positions;

(6) The optimal shape parameter time series of Nakagami distribution is used as the imaging parameter, and the delay sum algorithm is used to calculate the average value of the shape parameters of the Nakagami distribution corresponding to the microscopic random structure with the coordinate r in the sample, so as to obtain the light of the sample. sound image S(r);

(7) Characterizing the number density of microscopic random structures by the contrast of the photoacoustic image S(r).

The shape parameter of the Nakagami distribution is only related to the number density of the microscopic random structures that generate the photoacoustic signal samples, and the shape parameter m increases monotonically with the number density of the random microstructures. Therefore, photoacoustic images are obtained using the shape parameters of the Nakagami distribution as imaging parameters, and the contrast of the photoacoustic images reflects the number density distribution of microscopic random structures. In the field of biomedicine, many changes in tissue physiology and pathology are accompanied by changes in tissue microstructure, such as cancer cells, microthrombi, red blood cell aggregation, liver cirrhosis, and fatty liver. Using photoacoustic images with the shape parameters of Nakagami distribution as imaging parameters can effectively reflect the number density distribution and changes of these microscopic forms, thereby providing valuable imaging data for the diagnosis and staging of related lesions.

The step (1) is specifically as follows: irradiating the sample (biological tissue) with the pulsed laser generated by the pulsed laser, the sample absorbs the energy of the pulsed laser and generates ultrasonic waves (photoacoustic effect); the ultrasonic transducer located at position i receives the ultrasonic waves. , after being amplified and sampled by the circuit system, it is stored in the computer, and the stored signal is recorded as the photoacoustic signal p(t, ri ), ri represents the coordinates of the ultrasonic transducer at the _i position, _i =1,2, 3,...,I,t represents the time of occurrence.

The step (2) is specifically as follows: first, perform Hilbert transform on the photoacoustic signal p(t, _ri ) to obtain P(t, _ri )=|H[p(t, _ri )]|, H represents the Hilbert transform; then, statistical analysis of the histogram is performed on P(t, _ri ) to calculate the probability density function F(R) of the amplitude R of the photoacoustic signal.

The step (3) is specifically: adopting the Nakagami distribution f(R; m, Ω) to approximate the probability density function F(R), where f(R; m, Ω) is:

Where: Γ( ) and U( ) represent the Gamma function and the unit step function, respectively, m and Ω are two undetermined parameters of the Nakagami distribution, the shape parameter m determines the shape of the Nakagami distribution, and the amplitude parameter Ω determines the amplitude of the Nakagami distribution ;

Search m and Ω so that f(R; m, Ω) best fits F(R) under the least squares criterion, that is, it satisfies the following formula:

||f(R;m,Ω)-F(R)||→min

At this time, m and Ω are the optimal shape parameter m and amplitude parameter Ω.

In the Nakagami distribution, the magnitude parameter is only related to the overall magnitude of the probability density function, while the shape parameter determines the shape of the probability density function, which is related to the characteristics of the microscopic random structure; the shape parameter increases monotonically with the number density of the microscopic random structure ; and, for microscopic random structures with different microscopic feature scales, such as particles of different diameters, the shape parameter is only related to the number density of the microscopic random structures, and not dependent on the microscopic scales of the microscopic random structures; therefore, the maximum value of the Nakagami distribution is The optimal shape parameters can be used to characterize the number density of microscopic random structures.

The step (4) is specifically: dividing the photoacoustic signal p(t, r _i ) into several consecutive frames, and the jth frame is denoted as p(t _j , r _i ), j=1, 2, 3, ..., T is the time interval between two adjacent frames, W is the time window width of each frame, t _j is the occurrence time of the jth frame; adopt the methods of steps (2) and (3) Calculate the optimal shape parameter m(jT, r _i ) and amplitude parameter Ω(jT, r _i ) of the jth frame, so as to obtain the shape parameter time series corresponding to the photoacoustic signal collected at the position r _i .

In the step (6), the photoacoustic image S(r) of the sample:

in: round( ) means rounding, and c means the speed of sound.

Beneficial effects: The photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures provided by the present invention has the following advantages compared to the prior art: 1. The method of the present invention can identify random microscopic particles in deep tissues. structure, and evaluate the random microstructure, quantify the number density of the random microstructure, and facilitate a more comprehensive description of the random microstructure (including feature size and number density); 2. The method of the present invention can be combined with the photoacoustic spectrum parameter analysis method. combined to achieve a more comprehensive description of random microstructures, including feature size and number density; for microstructures in deep tissues that cannot be identified by traditional photoacoustic imaging, the present invention can be used for better statistical identification; due to many Diseases are closely related to microstructural changes, and the use of the methods of the present invention can therefore aid in the diagnosis and staging of these diseases.

Description of drawings

Figure 1 is a schematic diagram of the photoacoustic excitation and detection principle of the microscopic random structure;

Fig. 2 is the process of approximating the probability density function of the photoacoustic signal amplitude using Nakagami distribution: (a) is the photoacoustic signal radiated from 100μm microspheres, the number density is 4 spheres/mm ³ ; (b) is the pair of (a) in (c) is the data histogram of the amplitude network of the photoacoustic signals of three number densities; (d) is the sum of the shape parameter m of Nakagami distribution and the number density of microspheres of different sizes relationship between;

Figure 3 shows the results of the experimental setup and phantom experiments: (a) is the structural block diagram of the experimental device; (b) is the relationship between the shape parameter m and the concentration of the microspheres for 100 μm microspheres; (c) is for the 200 μm microspheres sphere, the relationship between the shape parameter m and the concentration of microspheres;

Figure 4 shows the hybrid model photoacoustic imaging: (a) is a schematic diagram of the signal detection and structure segmentation method; (b) is the reconstructed image based on the photoacoustic signal amplitude; (c) is the reconstruction based on the photoacoustic signal energy Image; (d) is the reconstructed image based on the slope of the photoacoustic signal; (e) is the reconstructed image based on the shape parameter m of the Nakagami distribution of the photoacoustic signal.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

The photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures includes the following steps:

(1) Measurement of acousto-optic signals

The sample (biological tissue) is irradiated with the pulsed laser generated by the pulsed laser, and the sample absorbs the energy of the pulsed laser and generates ultrasonic waves (photoacoustic effect); the ultrasonic transducer located at position i receives the ultrasonic waves, which are amplified and sampled by the circuit system. Stored in the computer, the stored signal is recorded as the photoacoustic signal p(t, ri ), ri represents the coordinates of the ultrasonic transducer at the _i position, _i =1, 2, 3, ..., I, t represents the time ;

(2) The amplitude envelope of the photoacoustic signal is described by the data histogram, and the probability density function of the amplitude of the photoacoustic signal is calculated.

First, perform Hilbert transform on the photoacoustic signal p(t, _ri ) to obtain P(t, _ri )=|H[p(t, _ri )]|, where H represents the Hilbert transform; then , perform statistical analysis on the histogram of P(t, _ri ), and calculate the probability density function F(R) of the amplitude R of the photoacoustic signal;

(3) The probability density function is approximated by the Nakagami distribution, and the optimal parameters of the Nakagami distribution are obtained

Using the Nakagami distribution f(R; m, Ω) to approximate the probability density function F(R), f(R; m, Ω) is:

Where: Γ( ) and U( ) represent the Gamma function and the unit step function, respectively, m and Ω are two undetermined parameters of the Nakagami distribution, the shape parameter m determines the shape of the Nakagami distribution, and the amplitude parameter Ω determines the amplitude of the Nakagami distribution ;

Search m and Ω so that f(R; m, Ω) best fits F(R) under the least squares criterion, that is, it satisfies the following formula:

||f(R;m,Ω)-F(R)||→min

At this time, m and Ω are the optimal shape parameter m and amplitude parameter Ω;

(4) The photoacoustic signal is divided into several consecutive frames, and every two frames have the same overlap. Therefore, the method of steps (2) and (3) can be used to calculate the optimal parameters of Nakagami distribution for each frame

Divide the photoacoustic signal p(t, r _i ) into several consecutive frames, the jth frame is denoted as p(t _j , r _i ), j=1, 2, 3, ..., T is the time interval between two adjacent frames, W is the time window width of each frame, t _j is the occurrence time of the jth frame; adopt the methods of steps (2) and (3) Calculate the optimal shape parameter m(jT, r _i ) and amplitude parameter Ω(jT, r _i ) of the jth frame, so as to obtain the shape parameter time series corresponding to the photoacoustic signal collected at the position r _i ;

(5) changing the position of the ultrasonic transducer, i.e. changing i, and repeating steps (1) to (4) to obtain the time series of the shape parameters corresponding to the photoacoustic signals collected at different positions;

(6) The optimal shape parameter time series of Nakagami distribution is used as the imaging parameter, and the delay sum algorithm is used to calculate the average value of the shape parameters of the Nakagami distribution corresponding to the microscopic random structure with the coordinate r in the sample, so as to obtain the light of the sample. Acoustic image S(r):

in: round( ) means rounding, and c means the speed of sound;

(7) Characterizing the number density of microscopic random structures by the contrast of the photoacoustic image S(r).

The present invention will be further described below with reference to a specific embodiment.

Two sets of agar phantoms with a height and diameter of about 4 cm were prepared. Polystyrene divinylbenzene (PSDVB) microspheres with diameters of 100 μm and 200 μm were randomly embedded in different phantom groups. Each set included three samples with number densities of 0.05, 0.25 and 2 balls/mm ³ , respectively. The transducer scans around each sample in a ring-like fashion and detects the photoacoustic signal at 140 evenly spaced locations and averages the measured signals 40 times to reduce noise at each location. Furthermore, comparing (b) and (c) in Fig. 3, we note that at the same particle concentration, the value of the shape parameter m is approximated for different particle sizes. Experiments confirm that the shape parameter m of the Nakagami distribution extracted from the statistical distribution of the photoacoustic signal envelope is capable of quantitatively discriminating microsphere aggregates with different particle concentrations.

Based on the above analysis, we propose a novel photoacoustic imaging modality based on the shape parameter m of the Nakagami distribution to differentiate tissues according to their microstructural features. As shown in Fig. 4(a), the sample is a mixed agar model, which consists of three equal-sized sector segments. The diameter and number density of microspheres in each sector were (100 μm, 0.05 spheres/mm ³ ), (100 μm, 0.25 spheres/mm ³ ) and (200 μm, 0.05 spheres/mm ³ ), respectively. Scan around the sample and detect the signal at 180 equally spaced locations.

Figure 4(b) shows the conventional photoacoustic image of the sample reconstructed by using the delayed sum algorithm. Because the microspheres are so small compared to the signal wavelength, the microsphere aggregates look like many random blobs and it is difficult to distinguish the difference between each sector. Then, the received signal is divided into consecutive frames. Every two frames have the same overlap. Therefore, the signal energy, spectral slope, shape parameter m of the Nakagami distribution can be calculated for each frame and imaged as parameters. (c), (d), and (e) in Fig. 4 plot the distribution of the signal energy, spectral slope, and shape parameter m of the Nakagami distribution in the sample, respectively. As shown in (c) of Fig. 4, the signal energy also cannot indicate the difference between the three regions.

As shown in (d) of Fig. 4, the slope of the photoacoustic spectrum clearly distinguishes regions containing particles of different diameters. The slope of the photoacoustic spectrum was lower in regions containing large microspheres than in regions containing small microspheres. However, the slope of the photoacoustic spectrum still cannot distinguish each sector because the particles in it, although with different concentrations, are the same size. In the distribution image of the shape parameter m of the Nakagami distribution shown in (e) of FIG. 4 , high-density regions correspond to large values of shape parameter m, while low-density regions all have small values of shape parameter m. The Nakagami distribution successfully classifies different regions based on differences in particle concentration. Photoacoustic spectroscopy combined with envelope statistics allowed the classification of the three regions on the basis of a more comprehensive characterization of the stochastic microstructure.

The above is only the preferred embodiment of the present invention, it should be pointed out that: for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can also be made, and these improvements and modifications are also It should be regarded as the protection scope of the present invention.

Claims (6)

1. a photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures, is characterized in that: comprise the steps: (1) Measurement of acousto-optic signals; (2) The amplitude envelope of the photoacoustic signal is described by the data histogram, and the probability density function of the amplitude of the photoacoustic signal is calculated; (3) The probability density function is approximated by the Nakagami distribution, and the optimal parameters of the Nakagami distribution are obtained; (4) the photoacoustic signal is divided into several consecutive frames, and the method of steps (2) and (3) is used to calculate the optimal parameter of the Nakagami distribution of each frame; (5) changing the position of the ultrasonic transducer, and repeating steps (1) to (4) to obtain the time series of the shape parameters corresponding to the photoacoustic signals collected at different positions; (6) The optimal shape parameter time series of Nakagami distribution is used as the imaging parameter, and the delay sum algorithm is used to calculate the average value of the shape parameters of the Nakagami distribution corresponding to the microscopic random structure with the coordinate r in the sample, so as to obtain the light of the sample. sound image S(r); (7) Characterizing the number density of microscopic random structures by the contrast of the photoacoustic image S(r). 2. the photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures according to claim 1, is characterized in that: described step (1) is specially: utilize the pulsed laser light that pulsed laser produces to irradiate sample, sample Absorb the energy of the pulsed laser and generate ultrasonic waves; the ultrasonic transducer located at the position i receives the ultrasonic waves, which are amplified and sampled by the circuit system and stored in the computer, and the stored signal is recorded as the photoacoustic signal p(t, r _i ), ri represents the coordinates of the ultrasonic transducer at the _i position, i=1, 2, 3, . . . , I, and t represents the occurrence time. 3. The photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures according to claim 1, characterized in that: the step (2) is specifically: first, for the photoacoustic signal p(t,r _{i )} perform Hilbert transform to obtain P(t, _ri )=|H[p(t, _ri )]|, where H represents the Hilbert transform; Statistical analysis of the graph to calculate the probability density function F(R) of the amplitude R of the photoacoustic signal. 4. the photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures according to claim 1, is characterized in that: described step (3) is specifically: adopt Nakagami distribution f (R; m, Ω) The approximate probability density function F(R), f(R; m,Ω) is: Where: Γ( ) and U( ) represent the Gamma function and the unit step function, respectively, m and Ω are two undetermined parameters of the Nakagami distribution, the shape parameter m determines the shape of the Nakagami distribution, and the amplitude parameter Ω determines the amplitude of the Nakagami distribution ; Search m and Ω so that f(R; m,Ω) best fits F(R) under the least squares criterion, that is, it satisfies the following formula: ||f(R;m,Ω)F(R)||→min At this time, m and Ω are the optimal shape parameter m and amplitude parameter Ω. 5. The photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures according to claim 1, wherein the step (4) is specifically: the photoacoustic signal p(t, r _i ) It is divided into several consecutive frames, and the jth frame is denoted as p(t _j , r _i ), T is the time interval between two adjacent frames, W is the time window width of each frame, and t _j is the occurrence time of the jth frame; adopt the methods of steps (2) and (3) to calculate the optimal shape parameter m of the jth frame (jT, r _i ) and the amplitude parameter Ω(jT, r _i ) to obtain the shape parameter time series corresponding to the photoacoustic signal collected at the position r _i . 6. The photoacoustic Nakagami statistical analysis method for characterizing the number density of microscopic random structures according to claim 1, characterized in that: in the step (6), the photoacoustic image S(r) of the sample: in: round( ) means rounding, and c means the speed of sound.