asymmetry

不对称
  • 文章类型: Journal Article
    反铁磁体由于其在小规模和低功耗设备中的优势而成为下一代自旋电子器件的竞争性候选者。在铁磁(FM)/反铁磁(AFM)系统中,由自旋轨道转矩(SOT)驱动的磁化和交换偏置(EB)的电操纵已成为自旋电子学的重点。这里,报道了在Co/IrMn中实现大的垂直EB场,以及在Pt/Co/IrMn系统中SOT对磁性Co层和EB场的磁矩的有效操纵。在SOT驱动的开关过程中,观察到非对称操纵状态。具有相同振幅但方向相反的电流脉冲引起不同的磁化状态。磁光克尔测量表明,这是由于AFM中稳定和亚稳态的反铁磁畴共存。利用这些FM/AFM结构的不对称特性,五个自旋逻辑门,即AND,OR,NOR,NAND,而不是,通过SOT在单个单元中实现。这项研究提供了对SOT在AFM上的特殊能力的见解,也为基于AFM自旋电子系统构建内存逻辑和神经形态计算细胞铺平了道路。
    Antiferromagnets are competitive candidates for the next generation of spintronic devices owing to their superiority in small-scale and low-power-consumption devices. The electrical manipulation of the magnetization and exchange bias (EB) driven by spin-orbit torque (SOT) in ferromagnetic (FM)/antiferromagnetic (AFM) systems has become focused in spintronics. Here, the realization of a large perpendicular EB field in Co/IrMn and the effective manipulation of the magnetic moments of the magnetic Co layer and EB field by SOT in Pt/Co/IrMn system is reported. During the SOT-driven switching process, an asymmetrically manipulated state is observed. Current pulses with the same amplitude but opposite directions induce different magnetization states. Magneto-optical Kerr measurements reveal that this is due to the coexistence of stable and metastable antiferromagnetic domains in the AFM. Exploiting the asymmetric properties of these FM/AFM structures, five spin logic gates, namely AND, OR, NOR, NAND, and NOT, are realized in a single cell via SOT. This study provides an insight into the special ability of SOT on AFMs and also paves an avenue to construct the logic-in-memory and neuromorphic computing cells based on the AFM spintronic system.
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  • 文章类型: Journal Article
    步行的自适应控制通常在分体式跑步机上进行研究,在那里,人们通过调整脚的位置和时间逐渐减少他们的步长不对称(SLA)。尽管有人提出这种适应可能部分地由减少不稳定性的愿望驱动,不对称的变化是否会影响人们在应对不稳定扰动时保持平衡的能力,这是未知的。这里,我们使用间歇性扰动来确定SLA的变化是否会影响通过矢状面和额面中的全身角动量(WBAM)测量的反应平衡控制。16名神经典型的老年人(70.0±5.3岁;6名男性)以2:1的皮带速度比在跑步机上行走,并实时视觉反馈其已达到的步长和目标步长。我们使用混合效应模型来确定在施加扰动期间SLA或足部放置与WBAM之间是否存在关联。在扰动过程中,使用更多积极的SLA行走与前向WBAM的少量减少有关(快带和慢带的p<0.001),但横向WBAM增加(快带的p=0.045;慢带的p=0.003)。当参与者以更积极的SLA行走时,他们缩短了脚在慢腰带上的位置,在慢带扰动期间,这种缩短与正向WBAM的适度减少(p<0.001)和横向WBAM的小幅增加(p=0.008)有关。我们的发现表明,在分裂皮带跑步机行走过程中发生的时空变化可以通过降低人们对失平衡的敏感性来改善矢状面稳定性。但这可能是以牺牲正面稳定为代价的。
    The adaptive control of walking is often studied on a split-belt treadmill, where people gradually reduce their step length asymmetries (SLAs) by modulating foot placement and timing. Although it is proposed that this adaptation may be driven in part by a desire to reduce instability, it is unknown if changes in asymmetry impact people\'s ability to maintain balance in response to destabilizing perturbations. Here, we used intermittent perturbations to determine if changes in SLA affect reactive balance control as measured by whole-body angular momentum (WBAM) in the sagittal and frontal planes. Sixteen neurotypical older adults (70.0 ± 5.3 years old; 6 males) walked on a treadmill at a 2:1 belt speed ratio with real-time visual feedback of their achieved and target step lengths. We used mixed-effects models to determine if there were associations between SLA or foot placement and WBAM during the applied perturbations. Walking with more positive SLAs was associated with small reductions in forward WBAM (p < 0.001 for fast and slow belts) but increased lateral WBAM (p = 0.045 for fast belt; p = 0.003 for slow belt) during perturbations. When participants walked with more positive SLAs, they shortened their foot placement on the slow belt, and this shortening was associated with moderate reductions in forward WBAM (p < 0.001) and small increases in lateral WBAM (p = 0.008) during slow-belt perturbations. Our findings suggest that spatiotemporal changes that occur during split-belt treadmill walking may improve sagittal-plane stability by reducing people\'s susceptibility to losses of balance, but this may come at the expense of frontal-plane stability.
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  • 文章类型: Journal Article
    虚拟现实疾病(VRMS)的存在是制约VR产业进一步发展的关键因素,而解决这个问题的前提是能够准确有效地检测到它的发生。针对目前缺乏高精度、有效的检测方法,提出了一种基于熵不对称性和交叉频率耦合值不对称性的脑电信号VRMS检测方法。首先,分别对所选的4对双侧大脑电极的EEG进行多变量变分模态分解(MVMD),并计算了低频和高频分量上的三种熵值,即近似熵,模糊熵和排列熵,以及低频和高频分量之间的三种相幅耦合特征,即平均值,标准差和相关系数;其次,计算了左电极和右电极之间的熵差和交叉频率耦合特征;最后,通过t检验选择最终的特征集,并将其输入SVM进行分类,从而实现了VRMS的自动检测。结果表明,该方法下的三个分类指标,即,准确度,敏感性和特异性,达到99.5%,99.3%和99.7%,分别,ROC曲线下面积值达到1,证明该方法可作为检测VRMS发生的有效指标。
    The existence of Virtual Reality Motion Sickness (VRMS) is a key factor restricting the further development of the VR industry, and the premise to solve this problem is to be able to accurately and effectively detect its occurrence. In view of the current lack of high-accuracy and effective detection methods, this paper proposes a VRMS detection method based on entropy asymmetry and cross-frequency coupling value asymmetry of EEG. First of all, the EEG of the four selected pairs of electrodes on the bilateral brain are subjected to Multivariate Variational Mode Decomposition (MVMD) respectively, and three types of entropy values on the low-frequency and high-frequency components are calculated, namely approximate entropy, fuzzy entropy and permutation entropy, as well as three types of phase-amplitude coupling features between the low-frequency and high-frequency components, namely the mean value, standard deviation and correlation coefficient; Secondly, the difference of the entropies and the cross-frequency coupling features between the left electrodes and the right electrodes are calculated; Finally, the final feature set are selected via t-test and fed into the SVM for classification, thus realizing the automatic detection of VRMS. The results show that the three classification indexes under this method, i.e., accuracy, sensitivity and specificity, reach 99.5 %, 99.3 % and 99.7 %, respectively, and the value of the area under the ROC curve reached 1, which proves that this method can be an effective indicator for detecting the occurrence of VRMS.
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  • 文章类型: Journal Article
    了解和预测人口对气候变化的反应是一项至关重要的挑战。人口对气候变化的反应的一个关键组成部分是局灶性生物率(例如,人口增长率)由于潜在组成部分变化的非补偿效应而对气候变化的响应变化(例如,出生率和死亡率)确定病灶率。我们将这些反应称为非补偿性气候变化效应。由于生物速率对气候变化的不同反应已记录在各种系统中,并出现在物种内部和物种之间的多个组织级别,非补偿性效应可能几乎无处不在。然而,非补偿性气候变化应对措施如何结合和规模影响人口的人口统计通常不清楚,需要将它们映射到人口变化的出生率和死亡率。我们提供了一个灵活的框架,用于将物种内部和物种之间的上游汇率的非补偿性变化纳入其中,并绘制其对跨尺度的额外下游汇率的影响,以最终影响人口增长率。在整个过程中,我们提供了该框架的具体示例和潜在应用。我们希望这一框架有助于加强我们对人口应对气候变化的理解和统一研究。
    Understanding and predicting population responses to climate change is a crucial challenge. A key component of population responses to climate change are cases in which focal biological rates (e.g., population growth rates) change in response to climate change due to non-compensatory effects of changes in the underlying components (e.g., birth and death rates) determining the focal rates. We refer to these responses as non-compensatory climate change effects. As differential responses of biological rates to climate change have been documented in a variety of systems and arise at multiple levels of organization within and across species, non-compensatory effects may be nearly ubiquitous. Yet, how non-compensatory climate change responses combine and scale to influence the demographics of populations is often unclear and requires mapping them to the birth and death rates underlying population change. We provide a flexible framework for incorporating non-compensatory changes in upstream rates within and among species and mapping their consequences for additional downstream rates across scales to their eventual effects on population growth rates. Throughout, we provide specific examples and potential applications of the framework. We hope this framework helps to enhance our understanding of and unify research on population responses to climate change.
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  • 文章类型: Journal Article
    在这项探索性研究中,我们比较和对比了两种从功能磁共振成像(fMRI)数据中得出侧向指数(LI)的方法:LI工具箱中的加权自举平均值(工具箱方法),以及一种新颖的方法,该方法使用从左半球和右半球的同源区域中减去激活来给出一系列差异分数(镜像方法)。数据来自31个人,这些人在接受功能性经颅多普勒超声(fTCD)测试时被选中,其中包括高比例的非典型偏侧人群。在两个任务上,单词生成和语义匹配,与工具箱法相比,镜像法通常与FTCD侧向性具有更好的一致性,无论是针对单个感兴趣的区域,和对应于大脑中动脉的大区域。这种方法的LI估计的置信区间(CI)比工具箱方法的置信区间小得多;使用镜像方法,大多数参与者被可靠地侧向向左或向右,而使用工具箱方法,较高的比例被归类为双边(即,LI的CI跨越零)。讨论了fMRI方法之间差异的原因:一个问题是工具箱方法在广泛的阈值范围内平均LI。此外,对来自两个半球的任务相关t统计图的检查表明,语言偏侧化在以失活为特征的区域中是明显的,所以关键信息可能会因为忽略零以下的体素激活而丢失,正如传统的LI估计所做的那样。
    In this exploratory study we compare and contrast two methods for deriving a laterality index (LI) from functional magnetic resonance imaging (fMRI) data: the weighted bootstrapped mean from the LI Toolbox (toolbox method), and a novel method that uses subtraction of activations from homologous regions in left and right hemispheres to give an array of difference scores (mirror method). Data came from 31 individuals who had been selected to include a high proportion of people with atypical laterality when tested with functional transcranial Doppler ultrasound (fTCD). On two tasks, word generation and semantic matching, the mirror method generally gave better agreement with fTCD laterality than the toolbox method, both for individual regions of interest, and for a large region corresponding to the middle cerebral artery. LI estimates from this method had much smaller confidence intervals (CIs) than those from the toolbox method; with the mirror method, most participants were reliably lateralised to left or right, whereas with the toolbox method, a higher proportion were categorised as bilateral (i.e., the CI for the LI spanned zero). Reasons for discrepancies between fMRI methods are discussed: one issue is that the toolbox method averages the LI across a wide range of thresholds. Furthermore, examination of task-related t-statistic maps from the two hemispheres showed that language lateralisation is evident in regions characterised by deactivation, and so key information may be lost by ignoring voxel activations below zero, as is done with conventional estimates of the LI.
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  • 文章类型: Journal Article
    目的:当前的握力(HGS)协议采用了多种标准,影响不对称HGS的评估。研究了这些不同标准对跌倒预测的影响。本研究旨在比较平均和最大HGS不对称标准的相对表现,作为预测中国中年或老年人跌倒发生率的工具。
    方法:9627名50岁以上的中国成年人参加了中国健康与退休纵向研究(2013-2015波)。HGS的测量基于最大记录值(HGSmax)或平均值(HGSave)来实现。这些值用于计算HGS不对称性。根据自我报告的数据评估了2年内的跌倒发生率。当测量2年跌倒风险时,使用Logistic回归分析来确定HGSmax不对称性或HGSave不对称性的预测性能。
    结果:当比较HGSmax和HGSave标准时,观察到HGS不对称的总体比率及其细分比率的显着差异,具有中等稠度(κ=0.599,p<0.001)。在2年的随访期间,记录了1743起坠落事件。调整后的逻辑回归模型表明,只有HGSmax不对称>30.0%与跌倒风险显着相关(p=0.034,比值比=1.36,95%置信区间:1.02-1.81)。
    结论:这些发现强调了HGS标准在检测HGS不对称性中的重要性,并表明HGSmax是预测50岁以上中国成年人跌倒风险的更可靠标准。
    OBJECTIVE: Current handgrip strength (HGS) protocols employ a variety of criteria, affecting the assessment of asymmetric HGS. The impact of these different criteria on fall prediction is understudied. This study was devised to compare the relative performance of average and maximum HGS asymmetry criteria as tools to predict fall incidence among middle-aged or older adults in China.
    METHODS: 9627 Chinese adults 50 + years of age who were participants in the China Health and Retirement Longitudinal Study (2013-2015 waves) were evaluated. The measurement of HGS was achieved based on either the maximum recorded value (HGSmax) or the average (HGSave), and these values were employed for the calculation of HGS asymmetry. Fall incidence over a 2-year period was evaluated based on self-reported data. Logistic regression analyses were utilized to determine the predictive performance of HGSmax asymmetry or HGSave asymmetry when gaging 2-year fall risk.
    RESULTS: Significant differences in overall rates of HGS asymmetry and the rates of subdivisions thereof were observed when comparing the HGSmax and HGSave criteria, with moderate consistency (kappa = 0.599, p < 0.001). Over the 2-year follow-up period, 1743 fall incidents were recorded. Adjusted logistic regression models indicated that only HGSmax asymmetry > 30.0% was significantly related to fall risk (p = 0.034, odds ratio = 1.36, 95% confidence interval: 1.02-1.81).
    CONCLUSIONS: These findings highlight the importance of HGS criteria in detecting HGS asymmetry, and suggest that HGSmax is a more robust criterion for predicting fall risk among Chinese adults 50 + years of age.
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  • 文章类型: Journal Article
    多巴胺能神经元的脑不对称性在帕金森病运动症状中的作用尚不明确。来自丘脑底核的局部现场记录揭示了该疾病的一些神经生理学生物标志物:增加的β活性,增加了低频活动和高频振荡。相位-振幅耦合协调神经元活动的定时,并允许确定大脑不同区域内的通信机制。在这项研究中,我们讨论了使用相位-振幅耦合评估左旋多巴给药前后24例帕金森病患者的两个半球之间的差异。将丘脑低(12-20Hz)和高β(20-30Hz)振荡与低(30-45Hz)振荡进行了比较,中(70-100赫兹)和高频(260-360赫兹)频段。我们发现左右之间存在明显的β相位-振幅耦合不对称性,并且药物治疗具有相反的依赖性作用,这与运动症状的减少有关。特别是,当评估右下丘脑时,在OFF条件(P<0.01)和ON状态(P<0.0001)期间发现高频和高β振荡之间的高耦合,而在分析中考虑左下丘脑时,情况正好相反,在OFF条件下,高频和高β振荡之间的耦合较低(P<0.01),其次是较高的一个在ON状态(P<0.01)。有趣的是,这些不对称性独立于运动开始侧,左或右。这些发现对神经信号具有重要意义,这些神经信号可用于在帕金森氏症中触发自适应深部脑刺激,并可以提供对丘脑下动力学的更详尽的见解。
    The role of brain asymmetries of dopaminergic neurons in motor symptoms of Parkinson\'s disease is still undefined. Local field recordings from the subthalamic nucleus revealed some neurophysiological biomarkers of the disease: increased beta activity, increased low-frequency activity and high-frequency oscillations. Phase-amplitude coupling coordinates the timing of neuronal activity and allows determining the mechanism for communication within distinct regions of the brain. In this study, we discuss the use of phase-amplitude coupling to assess the differences between the two hemispheres in a cohort of 24 patients with Parkinson\'s disease before and after levodopa administration. Subthalamic low- (12-20 Hz) and high-beta (20-30 Hz) oscillations were compared with low- (30-45 Hz), medium- (70-100 Hz) and high-frequency (260-360 Hz) bands. We found a significant beta-phase-amplitude coupling asymmetry between left and right and an opposite-side-dependent effect of the pharmacological treatment, which is associated with the reduction of motor symptoms. In particular, high coupling between high frequencies and high-beta oscillations was found during the OFF condition (P < 0.01) and a low coupling during the ON state (P < 0.0001) when the right subthalamus was assessed; exactly the opposite happened when the left subthalamus was considered in the analysis, showing a lower coupling between high frequencies and high-beta oscillations during the OFF condition (P < 0.01), followed by a higher one during the ON state (P < 0.01). Interestingly, these asymmetries are independent of the motor onset side, either left or right. These findings have important implications for neural signals that may be used to trigger adaptive deep brain stimulation in Parkinson\'s and could provide more exhaustive insights into subthalamic dynamics.
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  • 文章类型: Journal Article
    有不同的理论被引用为运动病的原因。不对称耳石器官功能是晕动病的病因学理论之一。在我们的研究中,目的是揭示在晕船的病理生理学中是否存在起源于囊性反射途径的原因。在我们的研究中,患者组包括15名诊断为晕船的男子水手,对照组包括15名没有晕船的男子水手。比较两组之间的颈诱发肌源性前庭电位(cVEMP)发现。在水手们晕船的左右耳朵里,发现在100、95和90dB正常听力水平(nHL)水平下,p13和n23波的平均潜伏期明显短于对照组(全部p<0.05)。在晕船组,发现100nHL水平的cVEMP耳间波振幅不对称率明显高于对照组(p=0.001)。我们的研究结果表明,在晕船的病理生理学中,可能存在从糖反射途径引起的原因。
    There are different theories cited as the cause of Motion Sickness. Asymmetrical otolithic organ function is one of the etiology theories of motion sickness. In our study, the aim was to reveal whether there is a cause originating from the sacculocolic reflex pathway in the physiopathology of seasickness. The patient group included 15 man sailors with diagnosis of seasickness and the control group included 15 man sailors without seasickness in our study. Cervical evoked myogenic vestibular potential (cVEMP) findings were compared between the groups. In the right and left ears of sailors with seasickness, the mean latencies of the p13 and n23 waves at 100, 95, and 90 dB normal hearing level (nHL) levels were found significantly shorter than in the control group (p < 0.05, for all). In the seasickness group, cVEMP interaural wave amplitude asymmetry ratio at 100 nHL level were found significantly higher than the control group (p = 0.001). The findings of our study indicated that there may be reasons arising rom the sacculocolic reflex pathway in the pathophysiology of seasickness.
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  • 文章类型: Journal Article
    鼻中隔对颅面结构的发育至关重要。鼻中隔偏离是口腔呼吸的解剖学原因之一,进而导致咬合不正。
    为了评估鼻中隔偏曲引起的鼻呼吸阻塞的患者的颌面和头颅特征,以及这些缺陷与各种错牙合之间的关系以及面部不对称程度。
    对选定的患者采用两点评估,一个在耳鼻喉科使用临床检查和CT-PNS和根据Mladina分类分类的严重程度,另一个在牙科部门,使用临床检查,PA脑电图,外侧脑电图,和面部照片。
    咬合不正与各种等级的间隔偏离之间的关联具有统计学意义,P值为0.006。结果显示13例患者具有I类骨骼模式,20名II类患者,和7例III类骨骼模式患者。7级鼻中隔偏曲患者均无I类错合,2级鼻中隔偏曲患者均无III类错合。II类I类错牙合是鼻中隔偏曲患者中最常见的类型。7级鼻中隔偏曲与最大ANS量相关,上述偏曲表明面部不对称。
    II类1类错牙合畸形是最常见的类型,而III类错牙合畸形在较高等级的鼻中隔偏曲中更为常见。上颌和下颌不对称性随鼻中隔偏曲程度的增加而显着恶化,是引起面部不对称性的重要因素之一。
    UNASSIGNED: The nasal septum is crucial in the development of the craniofacial structures. Deviated nasal septum is one of the anatomical causes of mouth breathing which in turn lead to malocclusion.
    UNASSIGNED: To evaluate the dentofacial and cephalometric characteristics in individuals with nasal breathing obstruction brought on by nasal septal deviation, as well as the relationship between these defects and various malocclusions and the degree of facial asymmetry.
    UNASSIGNED: A two-point evaluation was adopted for the selected patients, one at the ENT department using clinical examination and CT-PNS and the severity classified according to the Mladina classification and another at the dental department, using clinical examinations, PA cephalograms, lateral cephalograms, and facial photographs.
    UNASSIGNED: The association between malocclusion and various grades of septal deviation was statistically significant with a P value of 0.006. Results showed that 13 patients are with Class I skeletal pattern, 20 patients with Class II, and 7 patients with Class III skeletal pattern. None of the grade 7 nasal septal deviation patients had class I malocclusion and none of the grade 2 nasal septal deviation patients had class III malocclusion. Class II division I malocclusion was the most common type noted in patients with nasal septal deviation. Grade 7 nasal septal deviation was associated with the maximum amount of ANS and mentioned deviation indicating significant facial asymmetry.
    UNASSIGNED: Class-II Division-1 malocclusion was the most common type noted and Class III malocclusion was more common in higher grades of nasal septal deviation. Maxillary and mandibular asymmetry worsens significantly with an increase in the grade of nasal septal deviation and is one of the significant factors in causing facial asymmetry.
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  • 文章类型: Journal Article
    目的:探讨帕金森病(PD)患者与正常对照(NC)眼间视网膜结构和血管密度的不对称性(IA)。
    方法:78名受试者,包括40名PD患者和38名NC,完成了光学相干断层扫描血管造影(OCTA)和神经系统检查的三个等级量表(UPDRS-III,MMSE和MoCA)。IA是通过右眼和左眼差异的绝对值计算的。黄斑神经节细胞内丛状层(GCIPL)的厚度IA,乳头周围视网膜神经纤维层(pRNFL),和浅表毛细血管丛(SCP)的血管密度,深毛细血管丛(DCP),从OCTA获得放射状乳头周围毛细血管(RPC)。
    结果:眼睛的运动症状发作侧显示SCP的旁瓣内血管密度较低(51.09±3.46vs49.81±4.16,P=0.03),而DCP的中央凹上半部分(49.55±5.81vs47.33±5.71,=0.04)。PD患者表现出上半pRNFL厚度较大的IA(5.27[2.67,10.87]vs3.08[1.62,5.61],P=0.02)和侧腹GCIPL(2.40[1.25,6.35]vs1.40[0.50,2.45],P=0.02)。PD和NC之间的血管密度未发现明显的眼间不对称性。较高的UPDRS-III量表与GCIPL中IA较大(β=0.093,P=0.001)和DCP中IA较小(β=-0.065,P=0.037)相关。
    结论:眼睛的运动症状发作侧显示比眼睛另一侧更严重的黄斑血管密度损失。PD患者GCIPL和pRNFL结构不对称改变,显示了作为PD诊断生物标志物的潜力。
    OBJECTIVE: To investigate interocular asymmetry (IA) of retinal structure and vessel density in patients with Parkinson\'s disease (PD) and normal controls (NC).
    METHODS: Seventy-eight subjects including 40 PD patients and 38 NC had completed optical coherence tomography angiography (OCTA) and neurological examinations for three rating scales (UPDRS-III, MMSE and MoCA). The IA was calculated by the absolute value of difference in right and left eyes. The IA of thickness in macular ganglion cell inner-plexiform layer (GCIPL), peripapillary retinal nerve fiber layer (pRNFL), and vessel density of superficial capillary plexus (SCP), deep capillary plexus (DCP), radial peripapillary capillary (RPC) were obtained from OCTA.
    RESULTS: The motor-symptom-onset side of eyes showed lower vessel density in parafovea of SCP (51.09 ± 3.46 vs 49.81 ± 4.16, P = 0.03) and superior hemi of perifovea DCP (49.55 ± 5.81 vs 47.33 ± 5.71, = 0.04). The PD patients showed larger IA in thickness of superior half of pRNFL (5.27 [2.67, 10.87] vs 3.08 [1.62, 5.61], P = 0.02) and parafovea GCIPL (2.40[1.25, 6.35] vs 1.40[0.50, 2.45], P = 0.02). No significant interocular asymmetry was found in vessel density between PD and NC. A higher UPDRS-III scale was associated with larger IA in GCIPL (β = 0.093, P = 0.001) and smaller IA in DCP (β = -0.065, P = 0.037).
    CONCLUSIONS: The motor-symptom-onset side of eyes showed more severe loss of macular vessel density than the other side of eyes. The PD patients showed asymmetrical structural change in GCIPL and pRNFL, which showed the potential as the diagnostic biomarker for PD.
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