Fourier Analysis

傅里叶分析
  • 文章类型: Journal Article
    在过去的几十年里,使用超声骨质量评估进行早期骨质疏松检测已得到重视。具体来说,各种研究集中在使用超声导波的轴向传输,并强调了这种技术对长皮质骨的内在特性的敏感性。这项工作旨在证明低频超声导波的潜力,以推断它们在其中传播的骨骼的特性。专有的超声波换能器,适合在500kHz以下发射超声导波,用于数据收集。收集的数据经过二维快速傅里叶变换处理,以提取实验色散曲线。所提出的反演方案将实验色散曲线与通过半解析等几何分析(SAIGA)方法计算的模拟色散曲线进行了比较。数值模型集成了一个骨模板,其顶部表面上有一个软组织层,模仿实验骨模板。随后,通过减少实验和模拟色散曲线之间的失配来估计骨模型板的机械性能。这种反演严重依赖于超声导波模式的色散轨迹和振幅。结果表明,使用基于SAIGA的反演确定的机械性能与使用体波脉冲回波测量测得的机械性能之间存在5%以下的边际差异。
    Over the past few decades, early osteoporosis detection using ultrasonic bone quality evaluation has gained prominence. Specifically, various studies focused on axial transmission using ultrasonic guided waves and have highlighted this technique\'s sensitivity to intrinsic properties of long cortical bones. This work aims to demonstrate the potential of low-frequency ultrasonic guided waves to infer the properties of the bone inside which they are propagating. A proprietary ultrasonic transducer, tailored to transmit ultrasonic guided waves under 500 kHz, was used for the data collection. The gathered data underwent two-dimensional fast Fourier transform processing to extract experimental dispersion curves. The proposed inversion scheme compares experimental dispersion curves with simulated dispersion curves calculated through the semi-analytical iso-geometric analysis (SAIGA) method. The numerical model integrates a bone phantom plate coupled with a soft tissue layer on its top surface, mimicking the experimental bone phantom plates. Subsequently, the mechanical properties of the bone phantom plates were estimated by reducing the misfit between the experimental and simulated dispersion curves. This inversion leaned heavily on the dispersive trajectories and amplitudes of ultrasonic guided wave modes. Results indicate a marginal discrepancy under 5% between the mechanical properties ascertained using the SAIGA-based inversion and those measured using bulk wave pulse-echo measurements.
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  • 文章类型: Journal Article
    脑灌注不足与认知障碍有关。较高的脑血管阻抗模量(Z)可能导致脑灌注不足。我们测试了遗忘型轻度认知障碍(aMCI)患者(即,患阿尔茨海默病的风险较高的人)的Z高于年龄匹配的认知正常个体,高Z与脑灌注不足有关。58例aMCI患者(67±7年)和25例认知正常受试者(CN,65±6年)同时测量颈动脉压(CAP,通过压平眼压法)和大脑中动脉血流速度(CBV,通过经颅多普勒)。使用CBV和CAP的动态变化之间的交叉光谱和传递函数分析来量化Z。aMCI患者的Z高于NC(1.18±0.34vs.1.01±0.35mmHg/cm/s,P=0.044),频率范围为0.78至4.29Hz。高相干性(>0.9)的频率范围(0.78-3.13Hz)中的平均Z与aMCI和NC患者通过脑组织质量(通过结构MRI)归一化的2D多普勒超声检查测得的总脑血流量呈负相关(r=-0.311,P=0.007),和单独患有aMCI的患者(r=-0.306,P=0.007)。我们的发现表明,aMCI患者的脑血管阻抗高于认知正常的老年人,并且脑血管阻抗的增加与脑灌注不足有关。
    Brain hypoperfusion is associated with cognitive impairment. Higher cerebrovascular impedance modulus (Z) may contribute to brain hypoperfusion. We tested hypotheses that patients with amnestic mild cognitive impairment (aMCI) (i.e., those who have high risk of developing Alzheimer\'s disease) have higher Z than age-matched cognitively normal individuals, and that high Z is correlated with brain hypoperfusion. Fifty-eight patients with aMCI (67±7 years) and 25 cognitively normal subjects (CN, 65±6 years) underwent simultaneous measurements of carotid artery pressure (CAP, via applanation tonometry) and middle cerebral arterial blood velocity (CBV, via transcranial Doppler). Z was quantified using cross-spectral and transfer function analyses between dynamic changes in CBV and CAP. Patients with aMCI exhibited higher Z than NC (1.18±0.34 vs. 1.01±0.35 mmHg/cm/s, P=0.044) in the frequency range from 0.78 to 4.29 Hz. The averaged Z in the frequency range (0.78-3.13 Hz) of high coherence (>0.9) was inversely correlated with total cerebral blood flow measured with 2D Doppler ultrasonography normalized by the brain tissue mass (via structural MRI) across both patients with aMCI and NC (r=-0.311, P=0.007), and in patients with aMCI alone (r=-0.306, P=0.007). Our findings suggest that patients with aMCI have higher cerebrovascular impedance than cognitively normal older adults and that increased cerebrovascular impedance is associated with brain hypoperfusion.
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  • 文章类型: Journal Article
    准确预测沿海水域中的叶绿素a(chl-a)浓度对于沿海经济和生态系统至关重要,因为它是有害藻华的关键指标。尽管强大的机器学习方法在预测chl-a浓度方面取得了长足的进步,在有效建模动态时间模式和处理数据噪声和不可靠性方面仍然存在差距。为了摆脱泥潭,我们引入了一种创新的深度学习预测模型(称为ChloroFormer),将变压器网络与傅立叶分析集成在一个分解架构中,利用来自两个不同研究区域的沿海现场数据。我们提出的模型在捕获chl-a浓度中的短期和中期依赖模式方面表现出卓越的能力,超越其他六个深度学习模型在多步预测准确性方面的性能。特别是在涉及极端和频繁开花的场景中,我们提出的模型显示出卓越的预测性能,特别是在准确预测峰值chl-a浓度方面。通过Kolmogorov-Smirnov检验的进一步验证证明,我们的模型不仅复制了chl-a浓度的实际动态,而且保留了观测数据的分布,展示其鲁棒性和可靠性。提出的深度学习模型解决了准确预测chl-a浓度的关键需求,促进具有复杂动态时间模式的海洋观测探索,从而支持沿海地区的海洋保护和决策。
    The accurate prediction of chlorophyll-a (chl-a) concentration in coastal waters is essential to coastal economies and ecosystems as it serves as the key indicator of harmful algal blooms. Although powerful machine learning methods have made strides in forecasting chl-a concentrations, there remains a gap in effectively modeling the dynamic temporal patterns and dealing with data noise and unreliability. To wiggle out of quagmires, we introduce an innovative deep learning prediction model (termed ChloroFormer) by integrating Transformer networks with Fourier analysis within a decomposition architecture, utilizing coastal in-situ data from two distinct study areas. Our proposed model exhibits superior capabilities in capturing both short-term and middle-term dependency patterns in chl-a concentrations, surpassing the performance of six other deep learning models in multistep-ahead predictive accuracy. Particularly in scenarios involving extreme and frequent blooms, our proposed model shows exceptional predictive performance, especially in accurately forecasting peak chl-a concentrations. Further validation through Kolmogorov-Smirnov tests attests that our model not only replicates the actual dynamics of chl-a concentrations but also preserves the distribution of observation data, showcasing its robustness and reliability. The presented deep learning model addresses the critical need for accurate prediction on chl-a concentrations, facilitating the exploration of marine observations with complex dynamic temporal patterns, thereby supporting marine conservation and policy-making in coastal areas.
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  • 文章类型: Journal Article
    背景:在机器人辅助的微创手术中,外科医生操纵主操纵器时的手震颤会导致从属手术器械的振动。
    方法:这封信通过提出一种改进的增强型带限多线性傅立叶组合器(E-BMFLC)算法来解决这个问题,该算法用于过滤外科医生手的生理震颤信号。所提出的方法使用输入信号的幅度来适应学习速率和针对震颤信号的较高幅度频带的组合器频带的密集划分。
    结果:通过使用提出的改进的E-BMFLC算法,补偿精度可提高4.5%-8.9%,以及小于1毫米的空间位置误差。
    结论:结果表明,在所有过滤方法中,改进的E-BMFLC滤波方法实验成功次数最多,实验时间最少。
    BACKGROUND: During a robot-assisted minimally invasive surgery, hand tremors in a surgeon\'s manipulation of the master manipulator can cause vibrations of the slave surgical instruments.
    METHODS: This letter addresses this problem by proposing an improved Enhanced Band-Limited Multiple Linear Fourier Combiner (E-BMFLC) algorithm for filtering the physiological tremor signals of a surgeon\'s hand. The proposed method uses the amplitude of the input signal to adapt the learning rate and a dense division of the combiner bands for the higher amplitude bands of the tremor signals.
    RESULTS: By using the proposed improved E-BMFLC algorithm, the compensation accuracy can be improved by 4.5%-8.9%, as well as a spatial position error of less than 1 mm.
    CONCLUSIONS: The results show that among all filtering methods, the improved E-BMFLC filtering method has the highest number of successful experiments and the lowest experimental time.
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  • 文章类型: Journal Article
    在电动修复(EKR)中,沉积的溶解有机物(DOM)可能会通过清除反应性物种并产生意外的副产物来阻碍修复。然而,它的转变和机制在很大程度上仍然未知。本研究使用负离子电喷雾电离耦合21特斯拉傅里叶变换离子回旋共振质谱(21TFT-ICRMS)对EKR中的水可萃取DOM(WEOM)进行了分子水平表征。结果表明,在鉴定的7000种WEOM化合物中,55%是反应性的,EKR降低了它们的多样性,分子量分布,和双键当量(DBE)通过电化学和微生物氧化还原反应的组合。含杂原子的WEOM(CHON和CHOS)含量丰富(约占WEOM总量的35%),CHOS通常比CHON更具反应性。低电位(1V/cm)促进脱烷基化和脱硫菌的生长,导致了阳极二氧化碳矿化,-SO和-SO3的阳极裂解,-SH2的阴极裂解;高电势(2V/cm)仅富集脱硫细菌,不同的是,导致不饱和和酚类化合物的阳极氧化和阴极氢化,除了-SH2的阴极裂解。可能需要研究这些变化对土壤质量和氮-硫-碳通量的长期影响,以确定EKR的未知风险和新应用。
    In electrokinetic remediation (EKR), the sedimentary dissolved organic matter (DOM) could impede remediation by scavenging reactive species and generating unintended byproducts. Yet its transformation and mechanisms remained largely unknown. This study conducted molecular-level characterization of the water-extractable DOM (WEOM) in EKR using negative-ion electrospray ionization coupled to 21 tesla Fourier transform ion cyclotron resonance mass spectrometry (21 T FT-ICR MS). The results suggested that ∼55 % of the ∼7,000 WEOM compounds identified were reactive, and EKR lowered their diversity, molecular weight distribution, and double-bond equivalent (DBE) through a combination of electrochemical and microbial redox reactions. Heteroatom-containing WEOM (CHON and CHOS) were abundant (∼ 35% of the total WEOM), with CHOS generally being more reactive than CHON. Low electric potential (1 V/cm) promoted the growth of dealkylation and desulfurization bacteria, and led to anodic CO2 mineralization, anodic cleavage of -SO and -SO3, and cathodic cleavage of -SH2; high electric potential (2 V/cm) only enriched desulfurization bacteria, and differently, led to anodic oxygenation and cathodic hydrogenation of unsaturated and phenolic compounds, in addition to cathodic cleavage of -SH2. The long-term impact of these changes on soil quality and nitrogen-sulfur-carbon flux may be need to studied to identify unknown risks and new applications of EKR.
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  • 文章类型: Journal Article
    在这项研究中,我们提出了一种多路彩色照明策略,以提高傅立叶重叠成像显微镜(FPM)的数据采集效率。而不是顺序点亮一个单通道LED,我们的方法通过彩色相机为每个图像采集打开多个白光LED。因此,每个原始图像包含多路复用的光谱信息。开发了FPM原型,它配备了一个4×/0.13NA物镜,以实现相当于20×/0.4NA物镜的空间分辨率。在实验过程中设计并应用了两个和四个LED照明模式。美国空军1951分辨率目标首先在这些照明条件下成像,在此基础上生成MTF曲线以评估相应的成像性能。接下来,使用H&E组织样品和可分析的中期染色体细胞来评估我们策略的临床效用。结果表明,单个和多路复用(两个或四个LED)照明结果在MTF曲线的所有三个通道上实现了相当的成像性能。同时,与常规显微镜的结果相比,重建的组织或细胞图像成功地保留了细胞核和细胞质的定义,并且可以更好地保留细胞边缘。这项研究最初验证了多路彩色照明对于未来开发高通量FPM扫描系统的可行性。
    In this study, we proposed a multiplexed color illumination strategy to improve the data acquisition efficiency of Fourier ptychography microscopy (FPM). Instead of sequentially lighting up one single channel LED, our method turns on multiple white light LEDs for each image acquisition via a color camera. Thus, each raw image contains multiplexed spectral information. An FPM prototype was developed, which was equipped with a 4×/0.13 NA objective lens to achieve a spatial resolution equivalent to that of a 20×/0.4 NA objective lens. Both two- and four-LED illumination patterns were designed and applied during the experiments. A USAF 1951 resolution target was first imaged under these illumination conditions, based on which MTF curves were generated to assess the corresponding imaging performance. Next, H&E tissue samples and analyzable metaphase chromosome cells were used to evaluate the clinical utility of our strategy. The results show that the single and multiplexed (two- or four-LED) illumination results achieved comparable imaging performance on all the three channels of the MTF curves. Meanwhile, the reconstructed tissue or cell images successfully retain the definition of cell nuclei and cytoplasm and can better preserve the cell edges as compared to the results from the conventional microscopes. This study initially validates the feasibility of multiplexed color illumination for the future development of high-throughput FPM scanning systems.
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  • 文章类型: Journal Article
    当低温EM数据集不完整时,低温电子显微镜(cryo-EM)的重建图表现出畸变,通常由不均匀分布的方向引起。先前已尝试使用倾斜收集策略和对网格或空气-水界面的修改来解决此首选方向问题。然而,这些方法通常需要耗时的实验,效果总是依赖于蛋白质。这里,我们开发了一种包含去除未对齐粒子的程序,以及一种基于傅立叶分量信噪比的迭代重建方法,通过使用纯计算算法恢复丢失的数据来纠正这种失真。此过程称为信噪比迭代重建方法(SIRM),适用于各种蛋白质的不完整数据集,以修复低温EM图中的失真并获得更各向同性的分辨率。此外,SIRM为进一步的重建改进提供了更好的参考图,导致改进的对齐,这最终提高了地图质量和效益模型构建。
    Reconstruction maps of cryo-electron microscopy (cryo-EM) exhibit distortion when the cryo-EM dataset is incomplete, usually caused by unevenly distributed orientations. Prior efforts had been attempted to address this preferred orientation problem using tilt-collection strategy and modifications to grids or to air-water interfaces. However, these approaches often require time-consuming experiments, and the effect was always protein dependent. Here, we developed a procedure containing removing misaligned particles and an iterative reconstruction method based on signal-to-noise ratio of Fourier component to correct this distortion by recovering missing data using a purely computational algorithm. This procedure called signal-to-noise ratio iterative reconstruction method (SIRM) was applied on incomplete datasets of various proteins to fix distortion in cryo-EM maps and to a more isotropic resolution. In addition, SIRM provides a better reference map for further reconstruction refinements, resulting in an improved alignment, which ultimately improves map quality and benefits model building.
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  • 文章类型: Journal Article
    图像相位一致性(IPC)的概念深深植根于人类视觉系统解释和处理空间频率信息的方式。它在视觉感知中起着重要的作用,影响我们识别物体的能力,识别纹理,破译我们环境中的空间关系。IPC对照明的变化是强大的,对比,以及其他可能改变光波振幅的变量,但它们的相对相位不变。此特性对于感知任务至关重要,因为它可以确保对特征的一致检测,而无需考虑照明或其他环境因素的波动。它还可以影响认知和情绪反应;跨元素的内聚阶段信息促进了对统一或和谐的感知,而不一致会产生不和谐或紧张感。在这次调查中,我们首先研究了生物视觉研究的证据,这些证据表明IPC被人类感知系统所采用。我们继续概述IPC的典型数学表示和不同计算方法。然后,我们总结了IPC在计算机视觉中的广泛应用,包括去噪,图像质量评估,特征检测和描述,图像分割,图像配准,图像融合,和物体检测,在其他用途中,并用一些例子说明它的优点。最后,我们讨论了当前与IPC的实际应用相关的挑战以及潜在的增强途径。
    The concept of Image Phase Congruency (IPC) is deeply rooted in the way the human visual system interprets and processes spatial frequency information. It plays an important role in visual perception, influencing our capacity to identify objects, recognize textures, and decipher spatial relationships in our environments. IPC is robust to changes in lighting, contrast, and other variables that might modify the amplitude of light waves yet leave their relative phase unchanged. This characteristic is vital for perceptual tasks as it ensures the consistent detection of features regardless of fluctuations in illumination or other environmental factors. It can also impact cognitive and emotional responses; cohesive phase information across elements fosters a perception of unity or harmony, while inconsistencies can engender a sense of discord or tension. In this survey, we begin by examining the evidence from biological vision studies suggesting that IPC is employed by the human perceptual system. We proceed to outline the typical mathematical representation and different computational approaches to IPC. We then summarize the extensive applications of IPC in computer vision, including denoise, image quality assessment, feature detection and description, image segmentation, image registration, image fusion, and object detection, among other uses, and illustrate its advantages with a number of examples. Finally, we discuss the current challenges associated with the practical applications of IPC and potential avenues for enhancement.
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  • 文章类型: Journal Article
    目的:体积各向同性同时交错的亮血和黑血检查(VISIBLE)可以同时获取血管信号抑制的图像(黑血图像)和无抑制的图像(亮血图像)。我们旨在通过调整k空间填充和使用启动回波来改善明亮的血液图像。
    方法:常规可见中的亮血图像的k空间排列遵循从低到高频率的顺序,而在提议的可见序列中,顺序相反,并添加了启动回声。使用体模评估了启动回波对信噪比(SNR)的影响,考虑白质(WM)和对比后的血液。使用两个VISIBLE序列的常规方法和建议方法,以一维傅立叶变换模式从硫酸铜体模中获取数据。评价每个序列的信号行为。该研究包括14例患者,总共21例转移。对于每个病人来说,在施用造影剂后连续获得常规方法和建议方法的可见图像。使用临床图像,我们对肿瘤的信噪比和对比噪声比(CNR)进行了比较,正常WM,和血管之间的常规和建议的可见序列。
    结果:传统序列和具有不同启动回波数量的拟议序列之间的黑血和亮血图像的SNR没有显着差异,然而,所提出的序列的SNR随着黑色和明亮图像中启动回波数量的增加而降低。当启动回波超过20时,亮血图像的信号行为达到“稳定状态”。亮血图像中血管的SNR在常规和提议的可见序列之间没有显着差异。在传统序列中,亮血图像中WM的SNR明显大于所提出的序列。在所提出的序列中,明亮血液图像中肿瘤的SNR明显大于常规序列。肿瘤和WM之间的CNR,在建议的序列中,明亮血液图像中的血管和WM明显高于常规序列。
    结论:启动回波与高低频k空间排序方法的结合使用导致VISIBLE序列中明亮血液图像的CNR得到改善。
    OBJECTIVE: A volume isotropic simultaneous interleaved bright- and black-blood examination (VISIBLE) can simultaneously acquire images with suppressed vascular signals (black-blood images) and images without suppression (bright-blood images). We aimed to improve of the bright-blood images by adjusting the k-space filling and using startup echo.
    METHODS: The k-space arrangement of bright-blood images in the conventional VISIBLE followed a low-to-high frequency order, whereas that in the proposed VISIBLE sequence was in the reversed order, and a startup echo was added. The effects of startup echo on the signal-to-noise ratio (SNR) were evaluated using phantoms, considering both white matter (WM) and post-contrast blood. Data from copper sulfate phantoms were acquired in 1D Fourier transform mode using both the conventional and proposed methods of the two VISIBLE sequences. The signal behavior with each sequence was evaluated. Fourteen patients with a total of 21 metastases were included in the study. For each patient, VISIBLE images of both conventional and proposed methods were obtained consecutively after the contrast agent administration. Using clinical images, we conducted a comparison of the SNR and contrast-to-noise ratio (CNR) for tumors, normal WM, and blood vessels between the conventional and proposed VISIBLE sequences.
    RESULTS: There was no significant difference in SNRs for both black- and bright-blood images between the conventional sequence and the proposed sequence with different number of startup echoes, however, the SNR of the proposed sequence decreased with increasing number of startup echoes in both black- and bright-images. The signal behavior of the bright-blood image reached a \"steady state\" when the startup echo exceeded 20. The SNRs of blood vessels in the bright-blood images did not differ significantly between conventional and proposed VISIBLE sequences. The SNRs of WM in the bright-blood images was significantly larger in the conventional sequence than in the proposed sequence. The SNRs of tumors in bright blood images was significantly larger in the proposed sequence than in the conventional sequence. The CNRs between tumors and WM, vessels and WM in the bright-blood images were significantly higher in the proposed sequence than in the conventional sequence.
    CONCLUSIONS: The use of the startup echo in combination with the high-to-low frequency k-space ordering method resulted in improved CNR of the bright-blood images in the VISIBLE sequence.
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  • 文章类型: Journal Article
    微阵列基因表达数据由于其维度问题的诅咒而提出了巨大的挑战。功能的绝对数量远远超过可用的样品,导致过拟合和降低分类精度。因此,必须通过有效的特征提取方法来降低微阵列基因表达数据的维数,以减少数据量并提取有意义的信息,以提高分类准确性和可解释性。在这项研究中,我们发现了应用STFT(短期傅里叶变换)的唯一性,LASSO(最小绝对收缩和选择运算符),和EHO(大象放群优化),用于从肺癌中提取重要特征并降低微阵列基因表达数据库的维度。肺癌的分类使用以下分类器进行:高斯混合模型(GMM),基于GMM的粒子群优化算法(PSO),去趋势波动分析(DFA)朴素贝叶斯分类器(NBC),带GMM的萤火虫,径向基核支持向量机(SVM-RBF)和基于GMM的花授粉优化(FPO).使用FPO-GMM分类器的EHO特征提取在96.77的范围内获得了最高的准确性,F1得分为97.5,MCC为0.92,Kappa为0.92。报告的结果强调了利用STFT的重要性,拉索,和EHO用于特征提取,以降低微阵列基因表达数据的维数。这些方法还有助于改善和早期诊断肺癌,并提高分类准确性和可解释性。
    The microarray gene expression data poses a tremendous challenge due to their curse of dimensionality problem. The sheer volume of features far surpasses available samples, leading to overfitting and reduced classification accuracy. Thus the dimensionality of microarray gene expression data must be reduced with efficient feature extraction methods to reduce the volume of data and extract meaningful information to enhance the classification accuracy and interpretability. In this research, we discover the uniqueness of applying STFT (Short Term Fourier Transform), LASSO (Least Absolute Shrinkage and Selection Operator), and EHO (Elephant Herding Optimisation) for extracting significant features from lung cancer and reducing the dimensionality of the microarray gene expression database. The classification of lung cancer is performed using the following classifiers: Gaussian Mixture Model (GMM), Particle Swarm Optimization (PSO) with GMM, Detrended Fluctuation Analysis (DFA), Naive Bayes classifier (NBC), Firefly with GMM, Support Vector Machine with Radial Basis Kernel (SVM-RBF) and Flower Pollination Optimization (FPO) with GMM. The EHO feature extraction with the FPO-GMM classifier attained the highest accuracy in the range of 96.77, with an F1 score of 97.5, MCC of 0.92 and Kappa of 0.92. The reported results underline the significance of utilizing STFT, LASSO, and EHO for feature extraction in reducing the dimensionality of microarray gene expression data. These methodologies also help in improved and early diagnosis of lung cancer with enhanced classification accuracy and interpretability.
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