磁共振IDEAL-IQ序列定量分析腹腔内脏脂肪含量与2型糖尿病的关系

目的探讨腹腔内脏脂肪含量与糖尿病发生的关系,进而探讨其预测T2DM发病的可行性。方法收集行腹部3.0T MRI检查并有T2DM患者45例(T2DM组),对照组80例,应用IDEAL软件进行图像自动重组,获得脂肪分数(FF图)、弛豫率(R2*)、脂相、水相、同反相位图像。将FF图传至AW 4.6工作站,由两名观察者采用双盲法对FF图进行测量。应用ITK-SNAP软件采用阈值分割法半自动勾画腹腔内脏脂肪(VAT)及皮下脂肪组织(SAT),并计算体积。采用SPSS 26.0软件对数据进行统计学分析。结果(1)T2DM组的腹腔内脏脂肪组织体积(VATV)、肝脏脂肪分数(HFF)、胰腺脂肪分数(PFF)、甘油三酯(TG)及空腹血糖(FBG)均高于对照组,高密度脂蛋白(HDL)低于对照组,差异有统计学意义(P<0.05);(2)ROC曲线分析示:PFF判断是否患T2DM的曲线下面积(AUC)为0.656(P<0.01,95%CI:0.534~0.777),截断值为8.44%,敏感度为50%,特异度为82.5%;HFF判断是否患T2DM的AUC为0.744(P<0.05,95%CI:0.637~0.851),截断值、敏感度、特异度分别为2.99%、97.5%、42.5%。男性患者VATV判断T2DM的最佳阈值为3466 cm^(3),敏感度为63.2%,特异度为89.5%,AUC为0.78(P<0.01),联合SATV、PFF及HFF时,敏感度为78.9%,特异度为84.2%,AUC为0.839(P<0.01);女性患者利用VATV诊断T2DM的最佳阈值为2103 cm^(3),利用该阈值判断T2DM的敏感度为66.7%,特异度为66.7%,AUC为0.68(P<0.05),联合SATV、PFF及HFF时,敏感度为90.5%,特异度为76.2%,AUC为0.909(P<0.01)。(3)TG和FBG每增加1个单位,患T2DM的风险就分别提升了3986.3%及417.1%,即TG和FBG是T2DM发病的独立预测因子。结论PFF、HFF及VATV单独在预测T2DM发病方面,检验效能较低。VATV联合SATV、PFF、HFF预测T2DM发生的检验效能显著提高,其敏感度及特异度亦均明显提高。IDEAL-IQ技术是评估T2DM患者腹腔内异位脂肪组织沉积定量的便捷的方法,具有简单、稳定性好及重复性高的优势。

磁共振IDEAL-IQ序列测量肝脏脂肪含量的可行性研究

目的 探究IDEAL-IQ序列测量肝脏脂肪含量的准确性,以及影响测量准确性的因素。方法 利用GE DISCOVERY MR750 3.0T的单通道头线圈、八通道头线圈以及八通道腹部线圈,对配置的不同浓度的水脂混合溶液模体进行高参数扫描。在GE AW4.6工作站上进行多次脂肪含量测量,并对测量数值进行线性回归分析,讨论测量值与已知配置值的相关性,分析配置水脂混合模体在不同线圈中测量的准确性。结果 对于已知浓度的水脂混合溶液模型,IDEAL-IQ序列在三个线圈测量数据的一元线性回归讨论中,三个回归模型的P<0.0001,测量模型均在α=0.0001的水平上显著性明显,拟合较好,置信度达到99.99%。不同线圈在同参数扫描的情况下,由于信噪比不同,在图像中出现明显噪点,在使用小ROI测量时,会使得同一层面测量结果出现较大偏差。结论 IDEAL-IQ序列运用于脂肪含量的定量测量是可行可靠的,并且精准性较高。但扫描图像的质量对于测量稳定性以及准确性有影响,图像噪声越大则测量结果越不稳定,测量值的偏差越大。在临床扫描条件下,临床医师的测量应该采用适当ROI多点测量取平均值的方式进行肝脏脂肪含量的测量,同时还应该避开肝脏扫描层中的初始层及末端层。如果选取区域落于初始层及末端层,则可能会导致脂肪含量的过估计。

On the Optimal Initial Inner-Core Size for Tropical Cyclone Intensification: An Idealized Numerical Study

Recent observational and numerical studies have revealed the dependence of the intensification rate on the inner-core size of tropical cyclones(TCs). In this study, with the initial inner-core size(i.e., the radius of maximum wind—RMW)varied from 20–180 km in idealized simulations using two different numerical models, we found a nonmonotonic dependence of the lifetime maximum intensification rate(LMIR) on the inner-core size. Namely, there is an optimal innercore size for the LMIR of a TC. Tangential wind budget analysis shows that, compared to large TCs, small TCs have large inward flux of absolute vorticity due to large absolute vorticity inside the RMW. However, small TCs also suffer from strong lateral diffusion across the eyewall, which partly offsets the positive contribution from large inward flux of absolute vorticity. These two competing processes ultimately lead to the TC with an intermediate initial inner-core size having the largest LMIR. Results from sensitivity experiments show that the optimal size varies in the range of 40–120 km and increases with higher sea surface temperature, lower latitude, larger horizontal mixing length, and weaker initial TC intensity. The 40–120 km RMW corresponds to the inner-core size most commonly found for intensifying TCs in observations, suggesting the natural selection of initial TC size for intensification. This study highlights the importance of accurate representation of TC inner-core size to TC intensity forecasts by numerical weather prediction models.

INCOMPRESSIBLE LIMIT OF IDEAL MAGNETOHYDRODYNAMICS IN A DOMAIN WITH BOUNDARIES

We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.

基于“IDEAL”模式的物理问题解决能力培养研究

学生“物理问题解决能力弱”是长期困扰物理教学的问题,认知心理学关于问题解决的“IDEAL”模式为该问题的研究提供了新的视角。以2022年全国乙卷理综第25题为例,借助“IDEAL”模式可以清晰地梳理问题解决的过程,明确各阶段学生遇到的困难及成因。研究发现,借助“读思达”教学法,通过粗读、精读等过程,可以有效帮助学生建构物理模型、理清物理过程,从而提高物理问题解决能力。

基于磁共振IDEAL-IQ分析胰腺脂肪含量及其影响因素

目的:运用磁共振脂肪定量最小二乘估计和不对称回波迭代分解水和脂肪成像(IDEAL-IQ)测量胰腺脂肪分数(PFF),并分析其相关影响因素。方法:选取2021年6月—2023年3月扬州大学附属医院收治的169例患者为研究对象,收集患者住院期间年龄,身高、体质量、空腹血糖(FBG)、总胆固醇(TC)、三酰甘油(TG)、低密度脂蛋白胆固醇(LDL-C)、高密度脂蛋白胆固醇(HDL-C)以及IDEAL-IQ相关参数PFF、肝脏脂肪分数(HFF)、内脏脂肪面积(VFA)等资料,根据PFF结果将受检者分为高脂肪组(PFF≥4.17%)和低脂肪组(PFF<4.17%),比较高脂肪组与低脂肪组间各指标差异,并采用Pearson线性相关分析评价各指标与PFF的相关性。结果:169例受检者85例PFF≥4.17%,设为高脂肪组;84例PFF<4.17%,设为低脂肪组。高脂肪组患者年龄、HFF、BMI、FPC、TC、TG、VFA均高于胰腺低脂肪组,而HDL-C低于胰腺低脂肪组,差异有统计学意义(P<0.05)。PFF与年龄、HFF、BMI、FBG、TG、TC、VFA呈正相关性,与HDL-C呈负相关性(P<0.05)。结论:磁共振IDEAL-IQ技术可用于PFF的测量,PFF与HFF、BMI、FPC、TC、TG、VFA及HDL-C具有一定相关性。

Yeats’s Ideals:Women Old and Young

William Butler Yeats ranks among the most widely admired and intensively studied poets of the 20th century.This paper intends to explore the women who have exerted the most critical influences upon Yeats,namely Gonne,Lady Gregory,and Georgie Hyde-Lees.Even in Yeats’s poetry involved with symbolism,it is worth noting that his employment of symbols has used these women as the archetypes,and that the historical context rendered Yeats’s representations of them in his poetry all the more interesting.

For the Ideal Homeland

A town planner combines British experience with Chinese concept of harmony to build green,low-carbon,and sustainable cities.YANG Wei is a woman who wears many hats.An internationally renowned town planner and urban designer,she is held in high esteem in the academic and planning communities in the U.K.and is a fellow of the U.K.Academy of Social Sciences and former president of the Royal Town Planning Institute(RTPI)based in London.She is also chief executive and co-founder of the Digital Task Force for Planning(DTFP),a non-profit social enterprise,and founding director of London-based planning and urban design firm Wei Yang&Partners.

iDEAL-CIO: Instant Digital Express Advocated “Magic Lamp” for Cloud Intelligence Outlet

Instant Digital Express iDEAL-CIO The “Magic Lamp” for Cloud Intelligence Outlet, which has been recommended, combines innovations to satisfy modern users’ needs and efficiently sift through the ever-expanding amount of intelligent content stored in the cloud. One such innovation introduces a ground-breaking concept to remove superfluous and outdated sequential search patterns that overwhelm the user and computer in order to better serve the user in an eclectic & elastic and multidimensional approach to finding, grouping, assimilation, organizing, and delivering archival content. The cloud intelligence outlet (CIO) is presented in this article as the perfect magic lamp option for quick digital express advocacy. The grouping, indexing, folding, and targeting (GIFT) method of multidimensional online synthetic/analytical intelligent content (MOSAIC) for adaptive intelligence is the fundamental intelligent aggregation and automated process of the Magic Lamp. Three perspectives above this new ideal framework are available to observe: The Magic Lamp proposes contextual and multiple analytical tracks to improve cloud intelligence services conceptually. Technically speaking, MOSAIC combines domain-specific services for a wide range of international users, and through the usage of Cloud Intelligence Outlet, GIFT operationally activates grouping, indexing, folding, and targeting to promote decent experience and in-depth research on target for users’ wants. Because of this, iDEAL-CIO works in tandem with cloud extraction, digital transformation, and archival loading to provide improved service through the readily accessible cloud intelligence outlet.

An Empirical Evaluation of the Impact of Moral and Law Course Teaching on the Effectiveness of University Students’Ideals and Beliefs Education

The Moral and Law course serves as a critical platform for educating university students about ideals and beliefs,and it has a significant impact on the effectiveness of ideals and beliefs education.This paper establishes a mechanism through which Moral and Law course teaching influences the effectiveness of ideals and beliefs education and conducts an empirical evaluation.The results reveal that factors such as the relevance and applicability of the teaching content,the integration of theory and practice,the innovation,interactivity,and participation of teaching methods,as well as classroom atmosphere,teaching facilities,and campus culture,all have a significant positive impact on the effectiveness of ideals and beliefs education for university students.

磁共振脂肪定量技术IDEAL-IQ评价腰椎骨质疏松严重程度的价值

目的 探讨基于MRI迭代最小二乘法水脂分离定量技术(IDEAL-IQ)的椎体骨髓脂肪分数(FF)值在评估腰椎骨质疏松严重程度中的价值。方法 收集88例同时接受双能X线骨密度测量(DXA)和腰椎IDEAL-IQ序列检查的患者,根据DXA结果分为正常骨量组(36例)、低骨量组(23例)和骨质疏松组(29例),并在IDEAL-IQ序列脂肪分数图中测量椎体的脂肪分数;应用单因素方差分析比较3组椎体的FF值,ROC曲线评估诊断效能;FF值与年龄、身高、体重、BMI指数以及BMD值进行Pearson相关分析。结果 正常骨量组、低骨量组、骨质疏松组FF值分别为(38.84±6.75)%、(51.96±7.65)%、(58.39±12.81)%,总体及组间比较差异显著(P<0.05);FF值识别正常组、低骨量组的AUC为0.797,以46.85%为阈值,敏感度、特异度分别为73.91%、80.56%;FF值识低骨量组、骨质疏松组的AUC为0.691,以57.12%为阈值,敏感度、特异度分别为79.31%、69.57%。FF值与年龄呈正相关(P<0.001,r=0.6059);FF与身高(P<0.001,r=-0.3783)、体重(P<0.001,r=-0.4686)、BMI(P<0.001,r=-0.3649)、BMD(p=0.01,r=-0.2738)呈负相关;与性别无明确相关性。结论 IDEAL-IQ能够精准量化椎体的骨髓脂肪含量,对评估骨质疏松症严重程度有一定价值,有助于从骨质量层面反映骨质疏松状态。

Implicative and Fuzzy Implicative Ideals of Lattice Implication Algebras

In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.

磁共振3D-IDEAL-IQ技术定量评估2型糖尿病大腿肌肉脂肪浸润

目的:采用MRI定量技术3D-IDEAL-IQ分析2型糖尿病(T2DM)患者与健康志愿者之间的大腿肌间、肌内脂肪浸润含量差异,并分析其分布情况。方法:搜集确诊为T2DM的男性患者23例,女性患者20例(T2DM组),招募年龄、性别相匹配的健康志愿者40例(对照组,男20例,女20例)。对所有受试者进行大腿中段的MRI检查,分别测量皮下脂肪面积和肌肉区域间脂肪面积,通过各肌肉脂肪分数计算肌肉内的脂肪面积及单纯肌肉面积。再根据人体解剖学分区将肌肉分群,分别计算各肌群的肌肉内脂肪面积及纯肌肉面积。结果:T2DM组的皮下脂肪面积(P=0.004)、肌肉区域间的脂肪面积(P<0.001)、肌内脂肪面积(P<0.001)绝对值均大于对照组;T2DM组的肌内脂肪面积相对值较对照组大(P<0.001),单纯肌肉面积相对值较对照组小(P=0.044),并且大腿前外侧群肌肉减少更为显著(P=0.003)。结论:3D-IDEAL-IQ定量技术可以用于评价T2DM患者大腿肌间和肌内脂肪浸润含量和分布;T2DM患者大腿骨骼肌的脂肪及肌肉的比率较健康人群产生变化,脂肪沉积更明显,肌肉含量更少,且前外侧群的肌肉受累较严重。

3.0 T磁共振T_(2)WI IDEAL及DTI在腰椎间盘退行性变中应用

目的 探讨3.0 T磁共振T_(2)加权成像(T_(2)WI)、三点法非对称回波水脂分离(IDEAL)成像及扩散张量成像(DTI)在腰椎间盘退行性变评估中的应用价值。方法 选择100例腰椎间盘退行性变患者,其中男性51例,女性49例;年龄14~85岁,平均年龄49.4岁;病程1天~3年,平均病程(65.0±16.2)天;发生椎间盘突出部位L_(1/2)椎间盘2例,L_(2/3)椎间盘7例,L_(3/4)椎间盘23例,L_(4/5)椎间盘56例,L5/S1椎间盘48例。采用T_(2)WI IDEAL水相位图根据Pfirrmann分级标准对椎间盘进行分级,并测量各椎间盘T_(2)信号强度(T_(2)SI)。采用矢状位DTI图测量各椎间盘部分各向异性系数(FA)及表观扩散系数(ADC)。比较椎间盘不同Pfirrmann分级间FA、ADC值及T_(2)SI,并统计分析FA、ADC值及T_(2)SI与Pfirrmann分级间的相关性。结果 腰腿痛患者中,Ⅰ级椎间盘19个,Ⅱ级椎间盘126个,Ⅲ级椎间盘178个,Ⅳ级椎间盘144个,Ⅴ级椎间盘33个。椎间盘不同Pfirrmann分级间FA、ADC值及T_(2)SI总体差异均具有统计学意义(P<0.05)。组间多重比较显示,椎间盘ADC值在Ⅳ级与Ⅴ级之间差异无统计学意义(P>0.05),Ⅰ~Ⅲ级组间差异有统计学意义(P<0.05);FA及T_(2)SI组间比较,除Ⅰ级与Ⅱ级间差异无统计学意义(P>0.05)外,其余Ⅲ~Ⅴ级组间差异均有统计学意义(P<0.05)。椎间盘FA值与Pfirrmann分级呈中度正相关(r=0.626,P<0.05);ADC值与Pfirrmann分级呈高度负相关(r=-0.752,P<0.05);T_(2)SI与Pfirrmann分级呈高度负相关(r=-0.712,P<0.05);T_(2)SI与ADC值呈中度正相关(r=0.505,P<0.05);T_(2)SI与FA值呈弱负相关(r=-0.319,P<0.05)。结论 结合T_(2)WI IDEAL和DTI进行分析,可以为腰椎间盘退行性变的临床诊断及疗效评估提供参考依据。

Exploration and optimization of surgical techniques for laparoscopic transhiatal lower mediastinal lymph node dissection for adenocarcinoma of esophagogastric junction: A prospective IDEAL 2a study with qualitative design

Objective: To explore the change and feasibility of surgical techniques of laparoscopic transhiatal(TH)-lower mediastinal lymph node dissection(LMLND) for adenocarcinoma of the esophagogastric junction(AEG)according to Idea, Development, Exploration, Assessment, and Long-term follow-up(IDEAL) 2a standards.Methods: Patients diagnosed with AEG who underwent laparoscopic TH-LMLND were prospectively included from April 14, 2020, to March 26, 2021. Clinical and pathological information as well as surgical outcomes were quantitatively analyzed. Semistructured interviews with the surgeon after each operation were qualitatively analyzed.Results: Thirty-five patients were included. There were no cases of transition to open surgery, but three cases involved combination with transthoracic surgery. In qualitative analysis, 108 items under three main themes were detected: explosion, dissection, and reconstruction. Revised instruction was subsequently designed according to the change in surgical technique and the cognitive process behind it. Three patients had anastomotic leaks postoperatively, with one classified as Clavien-Dindo Ⅲa.Conclusions: The surgical technique of laparoscopic TH-LMLND is stable and feasible;further IDEAL 2b research is warranted.

IDEAL-IQ联合Micro-CT定量评估兔1型糖尿病骨髓脂肪含量和骨小梁微结构相关性的研究

目的 采用定量非对称回波的最小二乘估算法迭代水脂分离序列(iterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation sequence, IDEAL-IQ)联合计算机显微断层扫描(micro computed tomography, Micro-CT)技术评估兔1型糖尿病腰椎骨髓脂肪含量和骨小梁微结构相关性。材料与方法 将16只雄性日本大耳白兔随机分为糖尿病组(n=8)和对照组(n=8),糖尿病组采用四氧嘧啶造模。在造模成功后第0、4、8、12、16周通过IDEAL-IQ定量评估兔腰椎骨髓脂肪含量。在第16周采用Micro-CT及组织病理学检查对兔腰椎骨小梁微结构进行定量评估。不同时间点腰椎IDEAL-IQ脂肪分数差异比较采用重复测量方差分析;同一时间点组间脂肪分数、Micro-CT骨小梁形态计量学参数、组织病理学参数差异比较采用独立样t检验或Mann-Whitney U检验;采用Pearson相关系数评估骨髓脂肪分数与骨小梁形态计量学参数、组织病理学参数相关性。结果 糖尿病组骨髓脂肪含量随时间变化呈上升趋势,且差异存在统计学意义(P<0.05),而对照组各时间点脂肪含量差异无统计学意义(P>0.05);糖尿病组与对照组腰椎骨髓脂肪分数在第16周差异有统计学意义(59.987±4.859 vs. 51.015±8.469,P<0.05);第16周糖尿病组骨体积、总表面积、骨表面积、骨表面积总体积比、骨小梁数量均低于对照组,而骨小梁分离度高于对照组,差异有统计学意义(P<0.05);组织病理学结果显示,与对照组相比,第16周糖尿病兔腰椎骨髓脂肪细胞数量(32.875±11.051 vs. 71.667±13.125, P<0.01)增加,而骨小梁数量(11.375±1.506vs.4.333±1.211, P<0.01)与骨小梁面积(0.927±0.071vs.0.312±0.100, P<0.01)明显减少;IDEAL-IQ脂肪分数与组织病理学脂肪细胞计数呈正相关关系(r=0.539 95%CI:0.012~0.832),与骨小梁模式因子、骨小梁结构模型指数、骨小梁分离度呈轻中度正相关关系,与骨矿物质密度、总体积、骨体积、骨体积分数、总表面积、骨表面积、骨表面积体积比、骨表面积总体积比、骨小梁数量呈轻至中度负相关关系。结论 1型糖尿病腰椎骨髓脂肪含量与骨小梁微结构变化存在相关性,IDEAL-IQ联合Micro-CT的多模态定量影像技术有望为1型糖尿病提供全面的骨髓微环境评估策略。

基于IDEAL-CT试验评价后掺法温拌环氧沥青混合料抗裂性能

薄层环氧沥青在相对经济的条件下可实现路表长寿命,且后掺法工艺克服了其施工要求苛刻而导致应用受限的难题,可实现规模化应用,具有广阔的应用前景。为评价室内模拟后掺法工艺制备的环氧沥青混合料抗裂性能,采用沥青间接拉伸开裂(IDEAL-CT)试验,以最大荷载、最大位移、荷载-位移曲线75%最大荷载处斜率绝对值(∣m_(75)∣)和抗裂指数(CT)为评价指标,研究了纤维和沥青种类、公称最大粒径、沥青用量和空隙率对混合料抗裂性能的影响规律,并探究其抗裂性能评价指标的合理性。结果表明,在环氧沥青混合料中添加纤维、增加油量可延缓裂纹的发展,提高其抗裂性能,其中玄武岩纤维抗裂性能表现最优;环氧沥青混合料抗裂性能与集料公称最大粒径呈负相关,同时其骨架密实型混合料的抗裂性能优于悬浮密实型;混合料变密实,抗变形能力下降,裂纹扩展速度加快,抗裂性能降低;与SBS改性沥青相比,环氧沥青抵抗荷载开裂的能力较强,但抗裂缝延展能力较差,在可能出现变形大或不均匀沉降的结构上应用,应注意防止裂缝发生。评价指标上,最大位移对环氧沥青混合料抗裂性能评价敏感性差,不适合用于评价热固性沥青材料的抗裂性能。

National Hypertension Day: Healthy Living, Ideal Blood Pressure

According to the “Report on Cardiovascular Health and Diseases in China 2022” released by the National Center for Cardiovascular Diseases, the prevalence of cardiovascular diseases in China is on the rise, with approximately 245 million people suffering from hypertension. October 8, 2023.

Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

An Unbounded Fully Homomorphic Encryption Scheme Based on Ideal Lattices and Chinese Remainder Theorem

We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.