Applied Magnetic Resonance最新文献

Semiclassical Magnetization Dynamics with Combined Landau–Lifshitz and Gilbert Relaxation and Electron Paramagnetic Resonance 结合Landau-Lifshitz和Gilbert弛豫和电子顺磁共振的半经典磁化动力学

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-05-02 DOI: 10.1007/s00723-026-01839-7

A. V. Popov, S. V. Demishev

{"title":"Semiclassical Magnetization Dynamics with Combined Landau–Lifshitz and Gilbert Relaxation and Electron Paramagnetic Resonance","authors":"A. V. Popov, S. V. Demishev","doi":"10.1007/s00723-026-01839-7","DOIUrl":"10.1007/s00723-026-01839-7","url":null,"abstract":"<div><p>A semiclassical model of magnetization dynamics with a combined relaxation term, including Landau–Lifshitz and Gilbert contributions, is considered and applied for the computation of the electron paramagnetic resonance (EPR) spectra. It is shown that when both contributions have comparable amplitudes, varying the relaxation parameter leads to a restructuring of the EPR spectrum, emulating a magnetic transition with an abrupt change in the resonance field and splitting of the absorption line into several spectral components. These effects occur in a system describing single magnetic oscillator with a constant gyromagnetic ratio and are caused exclusively by the peculiarities of magnetic relaxation in systems with significant damping, i.e., with broad EPR absorption lines. Such lines are characteristic of various strongly correlated electron systems, where magnetic fluctuations additionally contribute to line broadening. The simulation results show that the complex structure of EPR spectra in strongly correlated electron systems may be due to magnetic relaxation processes and, in general, may not be associated with the presence of several types of oscillating magnetic dipoles.</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 5","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147802095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploiting Fast-Field-Cycling NMR Relaxometry to Differentiate Sickle Cell Hemoglobin from Hemoglobin A 利用快速场循环核磁共振弛豫法区分镰状细胞血红蛋白和血红蛋白A

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-04-10 DOI: 10.1007/s00723-026-01837-9

Kirsten Buniak, Manuel Arsenio Lores Guevara, Rémi Kogon, Nestor Juan Rodríguez de la Cruz, David Faux

{"title":"Exploiting Fast-Field-Cycling NMR Relaxometry to Differentiate Sickle Cell Hemoglobin from Hemoglobin A","authors":"Kirsten Buniak, Manuel Arsenio Lores Guevara, Rémi Kogon, Nestor Juan Rodríguez de la Cruz, David Faux","doi":"10.1007/s00723-026-01837-9","DOIUrl":"10.1007/s00723-026-01837-9","url":null,"abstract":"<div><p>Hemoglobin S (HbS) is the primary protein within the red blood cells of patients suffering from sickle cell anemia (SCA). SCA is a serious blood disorder that can lead to widespread organ damage and even death. Current diagnostic tests have their limits, whether it is due to cost, reliability, time constraints, staffing, or ability to distinguish between different cell types. In the search for better alternatives, many new techniques are being explored. This study investigates fast-field-cycling NMR (FFC NMR) relaxometry as a low magnetic field alternative for distinguishing HbS from healthy hemoglobin A (HbA). Five blood samples from healthy individuals and two samples from patients with sickle cell disease (SCD) were processed by classical methods. Each HbA and HbS sample was subjected to repeated measurements of the frequency-dependent relaxation rate <span>({R}_{1}left(fright))</span>. Each NMR dispersion (NMRD) profile was analyzed using the 3-Tau Model (3TM) providing seven physically meaningful fit parameters per sample. The 3TM analysis of NMRD profiles allows HbA and HbS to be clearly distinguished. The surface water dynamic time constant <span>({tau }_{l})</span> and desorption time constant <span>({tau }_{d})</span> for HbS were found to be approximately half those for HbA. The bulk water dynamic correlation time <span>({tau }_{b})</span> was found to be linked to HbS polymerization and directly related to viscosity. The Fe(III) content was important for defining the shape and form of the NMRD profiles. Protein dynamics do not contribute significantly to NMRD profiles. The FFC NMR approach with 3TM analysis shows promise as a diagnostic technique for SCD.</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 3-4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00723-026-01837-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147643161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimizing Diffusion Tensor Imaging (DTI) via Deep Learning with Minimal Number of Diffusion Encoding Gradient Directions (NDGD) 基于最小数量扩散编码梯度方向的深度学习优化扩散张量成像（DTI）

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-04-09 DOI: 10.1007/s00723-026-01836-w

Sarah Saeed Khan, Irfan Ullah, Faisal Najeeb, Hammad Omer

{"title":"Optimizing Diffusion Tensor Imaging (DTI) via Deep Learning with Minimal Number of Diffusion Encoding Gradient Directions (NDGD)","authors":"Sarah Saeed Khan, Irfan Ullah, Faisal Najeeb, Hammad Omer","doi":"10.1007/s00723-026-01836-w","DOIUrl":"10.1007/s00723-026-01836-w","url":null,"abstract":"<div><p>Diffusion tensor imaging (DTI) provides valuable microstructural information through 3D diffusion measurements, with its accuracy largely dependent on the number of diffusion-encoding gradient directions (NDGD). While higher NDGD improves estimates of metrics such as mean diffusivity (MD) and Fractional Anisotropy (FA), it also increases scan time and computational burden. To address this, we propose a U-Net-based model that integrates Inception modules for multiscale feature extraction and Convolutional Block Attention Modules (CBAM) for refining spatial and channel information. The model generates high-quality, increased NDGD-equivalent data from reduced NDGD, thereby preserving critical microstructural details while significantly reducing scan time. The experimental results demonstrate strong performance, with an SSIM of 99.75%, PSNR of 55.9 dB, and low Artifact Power (0.14). Furthermore, FA and MD maps derived from the model closely matched those from full NDGD, confirming its robustness. These findings highlight the potential of the proposed approach to make DTI more efficient and clinically practical by shortening scans without compromising diagnostic accuracy or patient comfort.</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 3-4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Radiation-Induced Free Radicals in Sodium Alginate for Possible Use as a Radiation Dosimeter 辐射诱导的海藻酸钠自由基可能用作辐射剂量计

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-04-07 DOI: 10.1007/s00723-026-01834-y

El-Saeid Ramadan El-Shawadfy, Sameh Mohammed Gafar

引用次数: 0

Monitoring Oxidative Stability of Edible Oils During Heating via Low-Field NMR Relaxation and Diffusion Coefficient 利用低场核磁共振弛豫和扩散系数监测食用油加热过程中的氧化稳定性

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-04-06 DOI: 10.1007/s00723-026-01838-8

Le Liu, Zijian Jia, Jingwen Yue

{"title":"Monitoring Oxidative Stability of Edible Oils During Heating via Low-Field NMR Relaxation and Diffusion Coefficient","authors":"Le Liu, Zijian Jia, Jingwen Yue","doi":"10.1007/s00723-026-01838-8","DOIUrl":"10.1007/s00723-026-01838-8","url":null,"abstract":"<div><p>This study investigates the oxidative behavior and molecular structural evolution of edible oils during thermal treatment using a comprehensive analytical framework based on low-field nuclear magnetic resonance (LF-NMR). Ten representative edible oils were subjected to controlled heating, and transverse relaxation and diffusion signals were acquired using CPMG and PGSE pulse sequences. Characteristic decay times were extracted from time-domain relaxation attenuation curves, while inverse Laplace transformation was applied to obtain T<sub>2</sub> distributions and associated structural parameters. Self-diffusion coefficients (D) were further determined to characterize translational molecular mobility. The results show that prolonged heating induces systematic changes in LF-NMR parameters. The decay time and T<sub>2</sub> values derived from both attenuation and inversion analyses decrease progressively with heating time for most oils, indicating enhanced spin–spin interactions and restricted local molecular motion caused by oxidation. I In contrast, D exhibits oil-dependent trends, reflecting the competition between molecular fragmentation and aggregation, as well as viscosity-related effects. These findings demonstrate that T<sub>2</sub> and D provide complementary information on oxidation-induced structural evolution. Overall, LF-NMR is shown to be a rapid, non-destructive, and sensitive technique for monitoring molecular transformations and assessing oxidative stability of edible oils during thermal processing.</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 3-4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Metabolic Characterization of Methanolic Extract of Indian Mustard Microgreens Using High-Resolution 800 MHz NMR Spectroscopy and LC–MS 利用高分辨率800 MHz核磁共振光谱和LC-MS分析印度芥菜微绿叶甲醇提取物的代谢特征

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-03-24 DOI: 10.1007/s00723-026-01835-x

Anamta Rizvi, Sailendra Kumar, Gurvinder Singh, Dinesh Kumar, Sangeeta Saxena

{"title":"Metabolic Characterization of Methanolic Extract of Indian Mustard Microgreens Using High-Resolution 800 MHz NMR Spectroscopy and LC–MS","authors":"Anamta Rizvi, Sailendra Kumar, Gurvinder Singh, Dinesh Kumar, Sangeeta Saxena","doi":"10.1007/s00723-026-01835-x","DOIUrl":"10.1007/s00723-026-01835-x","url":null,"abstract":"<div><p>Indian mustard microgreens are recognized for their high nutritional value, being rich sources of vitamins, minerals, amino acids, and various bioactive compounds such as glucosinolates, phenolic compounds, and flavonoids, which have been linked to a variety of health advantages including antiinflammatory, antioxidant, and anticancer properties. Characterizing the metabolites present in mustard microgreens can help elucidate their potential health-promoting effects, thus aiding in dietary recommendations as well as guiding culinary practices for optimizing nutrient content and flavor. In the present study, we aimed to characterize the metabolites present in the methanolic extracts of mustard microgreens using high-field 800 MHz NMR spectroscopy and liquid chromatography-mass spectrometry (LC-MS) based analysis. The composite use of 1D <sup>1</sup>H and 2D <sup>1</sup>H-<sup>13</sup>C HSQC, <sup>1</sup>H-<sup>1</sup>H TOCSY and J-resolved NMR spectral analysis employing commercial software CHENOMX led to the identification of 40 metabolites, including amino acids, organic acids, sugar molecules, γ-aminobutyric acid (GABA), and some phenolic compounds. LC–MS analysis provided complementary information, confirming the presence of key metabolites identified by NMR and revealing additional compounds not detected by NMR alone. The integrated analysis of NMR and LC–MS data enabled the comprehensive characterization of the metabolic profile of mustard microgreens, shedding light on their nutritional and medicinal properties.</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 3-4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

NMR and MRI Relaxation Effects Induced by Bio-Synthesized Magnetic Quantum Dots in Serum: Comparative Analysis with Carbon Quantum Dots 生物合成磁量子点在血清中诱导的核磁共振和磁共振弛豫效应：与碳量子点的比较分析

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-03-19 DOI: 10.1007/s00723-026-01833-z

Ayush Shukla, Gurvinder Singh, Mayur Mohan Ghate, Krishna Mohan Poluri, Poonam Tandon, Dinesh Kumar

{"title":"NMR and MRI Relaxation Effects Induced by Bio-Synthesized Magnetic Quantum Dots in Serum: Comparative Analysis with Carbon Quantum Dots","authors":"Ayush Shukla, Gurvinder Singh, Mayur Mohan Ghate, Krishna Mohan Poluri, Poonam Tandon, Dinesh Kumar","doi":"10.1007/s00723-026-01833-z","DOIUrl":"10.1007/s00723-026-01833-z","url":null,"abstract":"<div><p>Magnetic quantum dots (MQDs) combining optical fluorescence with magnetic responsiveness are of growing interest for magnetic resonance-based applications; however, their relaxation behavior in complex biological environments is not fully understood. In this work, MQDs were synthesized via a green, plant-mediated hydrothermal route using <i>Punica granatum</i> peel extract as a natural reducing and stabilizing agent, followed by controlled incorporation of Fe<sup>3</sup>⁺ ions to impart magnetic functionality. The resulting MQDs are quasi-spherical, nanoscale particles exhibiting good colloidal stability and preserved surface functionalization. High-field <sup>1</sup>H NMR studies in human serum revealed concentration-dependent modulation of spectral features and relaxation behavior induced by MQDs, arising from localized magnetic field inhomogeneities. Comparative analysis with carbon quantum dots and free Fe<sup>3</sup>⁺ ions demonstrated that MQDs exhibit controlled transverse relaxation effects in a biological environment. NMR relaxation measurements and MRI phantom experiments further confirmed the ability of MQDs to enhance T₂-weighted contrast, with a non-monotonic T₂ response reflecting the interplay between interfacial shielding at low concentrations and susceptibility-driven dephasing at higher concentrations. Overall, this study provides a systematic assessment of the magnetic relaxation behavior of green-synthesized MQDs in a biologically relevant medium and highlights their potential utility as magnetically responsive nanomaterials for magnetic resonance-based imaging and sensing applications.</p><h3>Graphic abstract</h3>\u0000<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 3-4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Ruthenium nanoparticles loaded Gd-DTPA with self-purification capacity for acute kidney injury 具有自净化能力的钌纳米颗粒负载Gd-DTPA治疗急性肾损伤

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-02-27 DOI: 10.1007/s00723-026-01832-0

Guangyang Xiang, Meiying Wan, Yang Qiu, Xi Ye, Bo Huang

引用次数: 0

Ionic Mobility in the N-Octyl-N,N-diethylammonium Tetra-fluoroborate ([N228][BF4]) Protic Ionic Liquid in Solid and Liquid States Probed by Solid-State 2H NMR 固态2H核磁共振探测n -辛基- n， n -二乙基四氟硼酸铵（[N228][BF4]）质子液体的固态和液态离子迁移率

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-02-24 DOI: 10.1007/s00723-026-01830-2

Iana Denisova, Tatiana V. Zhalnina, Ekaterina V. Tatarintseva, Sergey A. Prikhod’ko, Alexander E. Khudozhitkov, Alexander G. Stepanov, Ralf Ludwig, Daniil I. Kolokolov

{"title":"Ionic Mobility in the N-Octyl-N,N-diethylammonium Tetra-fluoroborate ([N228][BF4]) Protic Ionic Liquid in Solid and Liquid States Probed by Solid-State 2H NMR","authors":"Iana Denisova, Tatiana V. Zhalnina, Ekaterina V. Tatarintseva, Sergey A. Prikhod’ko, Alexander E. Khudozhitkov, Alexander G. Stepanov, Ralf Ludwig, Daniil I. Kolokolov","doi":"10.1007/s00723-026-01830-2","DOIUrl":"10.1007/s00723-026-01830-2","url":null,"abstract":"<div><p>The cation structure plays a crucial role in determining the properties and consequently the potential applications of ionic liquids. Understanding how cation structure can govern ionic mobility is essential for optimizing their performance in a wide range of fields. In this work, we study the ionic mobility of a tri-alkyl-ammonium-based protic ionic liquid (PIL) featuring an asymmetric cation paired with tetra-fluoroborate anion by means of <sup>2</sup>H NMR spectroscopy. By applying solid-state <sup>2</sup>H NMR spectroscopy on the perdeuterated N–H(N–D) group of the ammonium cation over a wide temperature range from 123 to 463 K, we have monitored the cations’ dynamics in both solid and liquid states. The molecular dynamics of the PIL were quantified through the analysis of spin–lattice (<i>T</i><sub>1</sub>) and spin–spin (<i>T</i><sub>2</sub>) relaxation times. <sup>2</sup>H NMR spectra line shape analysis was additionally used to quantify the un-averaged deuterons quadrupolar coupling constant (DQCC = 177 kHz at 123 K) of the N–D deuteron in this PIL. The spin relaxation analysis yielded the activation barriers and pre-exponential factors for isotropic and anisotropic motion, providing detailed insights into the dynamical behavior of [N<sub>228</sub>][BF<sub>4</sub>]. Our findings demonstrate that cation asymmetry benefits ionic mobility, suggesting that [N<sub>228</sub>][BF<sub>4</sub>] is a promising candidate for electrolyte applications.</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Motion Artifact Correction in MRI with a Gibbs Sampling Residual Diffusion Model 基于Gibbs采样残差扩散模型的MRI运动伪影校正

IF 1.1 4区物理与天体物理

Applied Magnetic Resonance Pub Date : 2026-02-24 DOI: 10.1007/s00723-026-01831-1

Jingwen Yue, Rui Chen, Zijian Jia, Le Liu

{"title":"Motion Artifact Correction in MRI with a Gibbs Sampling Residual Diffusion Model","authors":"Jingwen Yue, Rui Chen, Zijian Jia, Le Liu","doi":"10.1007/s00723-026-01831-1","DOIUrl":"10.1007/s00723-026-01831-1","url":null,"abstract":"<div><p>Motion artifacts in magnetic resonance imaging (MRI) substantially degrade image quality and compromise subsequent image analysis and clinical interpretation. To address this challenge, we propose Gibbs Sampling Residual Diffusion Motion Correction (GRDMoCo), a novel retrospective motion correction framework based on a deep generative diffusion model. GRDMoCo decouples the conventional diffusion process into two sub-processes—residual diffusion and noise diffusion—enhancing the model’s capacity to capture the underlying mechanisms of motion artifact generation. Furthermore, it integrates a Gibbs sampling strategy to effectively tackle the non-convex optimization problem inherent in motion parameter estimation, enabling progressive artifact suppression through a residual-guided diffusion process. Extensive experiments demonstrate that GRDMoCo consistently outperforms state-of-the-art methods in both qualitative and quantitative evaluations, achieving superior anatomical boundary preservation and accurate morphological restoration, particularly in abnormal brain tissues. On real motion-corrupted datasets, GRDMoCo achieves an average structural similarity index (SSIM) of 0.9734 and a peak signal-to-noise ratio (PSNR) of 36.7 dB, significantly exceeding all benchmark approaches. In conclusion, GRDMoCo offers an effective deep learning-based solution for MRI motion artifact correction with strong clinical potential, especially for motion-prone populations such as infants and patients with Alzheimer’s disease, and also holds promise for extension to other motion-sensitive imaging modalities, including functional MRI (fMRI) and diffusion-weighted imaging (DWI).</p></div>","PeriodicalId":469,"journal":{"name":"Applied Magnetic Resonance","volume":"57 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0