Three-dimensional poly(1,8-octanediol–co-citrate) scaffold pore shape and permeability

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拉普拉斯的三维模型分割算法

拉普拉斯的三维模型分割算法

拉普拉斯的三维模型分割算法拉普拉斯的三维模型分割算法(Laplacian-based 3D model segmentation algorithm)是一种常用的计算机图形学算法,用于将三维模型分割成不同的部分,帮助用户更好地理解和操作模型。

本文将综合介绍此算法的原理、步骤及其应用领域,以期给读者一个生动、全面且有指导意义的了解。

首先,我们需要了解拉普拉斯算子(Laplacian operator)。

拉普拉斯算子是一种微分算子,用于描述函数的二阶导数。

在三维模型分割中,我们将使用离散的近似算子来计算模型上的各个点的拉普拉斯算子值。

这些拉普拉斯算子值将作为特征来进行模型的分割。

基于拉普拉斯算子的三维模型分割算法可以被分为以下几个步骤。

1. 数据预处理:首先,需要对三维模型进行预处理,包括去噪、表面重建等操作,以提高模型的质量和准确性。

这一步骤对于获取更好的分割结果至关重要。

2. 建立模型的Graph Laplacian:在这一步骤中,我们将基于三维模型的几何信息建立Graph Laplacian。

Graph Laplacian是一个对称正定矩阵,它可以描述模型的拓扑结构和几何特征。

我们可以使用不同的方法来计算Graph Laplacian,如基于顶点或基于边的方法。

3. 特征向量的计算:通过对Graph Laplacian进行特征值分解,我们可以得到与每个特征值对应的特征向量。

这些特征向量对应于模型的不同部分,具有不同的物理含义。

通过选取前几个特征向量,我们可以得到一组高频和低频的分割特征。

4. 分割标签的生成:在这一步骤中,我们根据特征向量的值对每个点进行分割标签的生成。

常见的方法是使用K-means聚类方法或通过图割(Graph cuts)算法来对特征向量进行聚类操作。

这样,我们便可以将模型的不同部分分配给不同的类别。

5. 后处理:最后,通过一些后处理技术,如形态学运算、区域合并等,对分割结果进行进一步的优化和提升。

生成亚像素光条提取并生成点集进行双目三维重建和圆柱拟合求半径的程序-概述说明以及解释

生成亚像素光条提取并生成点集进行双目三维重建和圆柱拟合求半径的程序-概述说明以及解释

生成亚像素光条提取并生成点集进行双目三维重建和圆柱拟合求半径的程序-概述说明以及解释1.引言概述部分是文章的引言,用于向读者介绍本文的研究背景、目的和重要性。

首先,我们需要简要概括本文要解决的问题和研究内容。

然后,可以介绍相关领域的现状和该问题存在的挑战。

最后,强调本文的研究目的和创新点。

以下是1.1 概述部分的内容参考:"亚像素光条提取、双目三维重建以及圆柱拟合求半径是计算机视觉领域中的研究热点。

本文旨在研究一种新的方法,通过生成亚像素光条提取并生成点集,实现双目三维重建和圆柱拟合求半径的程序。

这一方法具有广泛的应用前景,可在工业制造、机器人导航、虚拟现实等领域中发挥重要作用。

在过去的几十年里,图像处理和计算机视觉技术取得了巨大的进展,但在亚像素光条提取、双目三维重建和圆柱拟合求半径方面仍然存在一些挑战。

传统的方法通常受限于像素级别的精度,难以捕捉到细节信息,而新的亚像素光条提取技术通过子像素级别的精确度,提供更精确的图像信息。

本文的主要目的是通过结合亚像素光条提取、双目三维重建和圆柱拟合求半径的程序,实现对三维场景的精确重建和圆柱体参数的准确测量。

同时,我们将实验验证所提出方法的有效性,并对实验结果进行评估和分析。

本文的创新点在于采用了一种全新的生成亚像素光条提取并生成点集的方法,能够提高重建和测量的准确性和稳定性。

我们认为,本研究的成果将为相关领域的研究和应用提供有益的参考,并为未来的研究工作提供新的思路和方向。

"在编写文章的其他部分时,请注意按照大纲的结构逐步展开,提供详细的介绍、分析和实验验证。

同时,也可根据具体情况自行调整和完善文章的内容。

1.2文章结构文章结构部分的内容如下:文章结构部分旨在介绍本文的整体结构和各个章节的内容安排。

本文分为引言、正文和结论三个部分。

在引言部分,首先对整篇文章进行概述,简要介绍文章研究的背景和意义。

接着对文章的结构进行概括性描述,说明各章节的内容安排和逻辑顺序。

fcc晶体八面体滑移系施密特因子

fcc晶体八面体滑移系施密特因子

FCC晶体八面体滑移系施密特因子1. 引言晶体的滑移是指晶体中原子沿着晶体晶格平面滑动的现象。

滑移是晶体塑性变形的基础,对于材料的力学性能和加工性能具有重要影响。

施密特因子是描述滑移系的指标之一,可以用来预测滑移的可能方向和滑移面。

本文将重点介绍FCC(面心立方)晶体中的八面体滑移系施密特因子。

首先,我们将简要介绍FCC晶体的结构特点,然后详细讨论八面体滑移系的构成和施密特因子的计算方法。

2. FCC晶体的结构特点FCC晶体是一种常见的晶体结构,在许多金属和合金中都存在。

其晶胞由一个立方晶格和一个面心立方晶格组成,每个晶胞中包含4个原子。

FCC晶体的晶胞内部存在6个滑移面和12个滑移方向。

滑移面是晶体中原子沿着滑移方向滑移的平面,滑移方向是指原子在滑移面上滑移的方向。

在FCC晶体中,八面体滑移系是最主要的滑移系。

3. 八面体滑移系的构成八面体滑移系由两个滑移面和一个滑移方向组成。

在FCC晶体中,八面体滑移系的滑移面分别为{111}和{110}面,滑移方向为<110>方向。

八面体滑移系的构成可以用图示来表示,如下所示:/|/ |/ |----| || |----其中,上面的平面表示滑移面{111},下面的平面表示滑移面{110},中间的线表示滑移方向<110>。

4. 施密特因子的计算方法施密特因子是描述滑移系的指标,可以通过计算滑移系中滑移面和滑移方向之间的夹角来得到。

夹角越小,施密特因子越大,滑移的可能性也就越大。

施密特因子的计算公式如下:Schmid factor = cos(φ) * cos(θ)其中,φ表示滑移面法线与滑移方向的夹角,θ表示滑移面法线与晶体轴的夹角。

在八面体滑移系中,滑移面{111}的法线与滑移方向<110>之间的夹角为45度,滑移面{110}的法线与滑移方向<110>之间的夹角为35.26度。

因此,八面体滑移系施密特因子的计算公式为:Schmid factor = cos(45) * cos(35.26)计算得到的施密特因子为0.5。

【高分子专业英语翻译】

【高分子专业英语翻译】

【高分子专业英语翻译】第五课乳液聚合大部分的乳液聚合都是由自由基引发的并且表现出其他自由基体系的很多特点,最主要的反应机理的不同源自小体积元中自由基增长的场所不同。

乳液聚合不仅允许在高反应速率下获得较高分子量,这在本体聚合中是无法实现或效率低下的,,同时还有其他重要的实用优点。

水吸收了大部分聚合热且有利于反应控制,产物在低粘度体系中获得,容易处理,可直接使用或是在凝聚,水洗,干燥之后很快转化成固体聚合物。

在共聚中,尽管共聚原理适用于乳液体系,单体在水相中溶解能力的不同也可能导致其与本体聚合行为不同,从而有重要的实际意义。

乳液聚合的变化很大,从包含单一单体,乳化剂,水和单一引发剂的简单体系到这些包含有2,3个单体,一次或分批添加,,混合乳化剂和助稳定剂以及包括链转移剂的复合引发体系。

单体和水相的比例允许变化范围很大,但是在技术做法上通常限制在30/70到60/40。

单体和水相比更高时则达到了直接聚合允许的极限,只有通过分批添加单体方法来排除聚合产生的大量的热。

更复杂的是随着胶体数的增加粘度也大大增加,尤其是当水溶性的单体和聚合物易容时,反应结束胶乳浓度降低。

这一阶段常常伴随着通过聚集作用或是在热力学不稳定时凝结作用而使胶粒尺寸增大。

第十课高分子的构型和构象本课中我们将使用根据经典有机化学术语而来的构型和构象这两个词。

构型异构是由于分子中存在一个或多个不对称中心,以最简单的C原子为例,每一碳原子的绝对构型为R型和S型,当存在双键时会有顺式和反式几何异构。

以合成聚合物为例,构型异构的典型问题和R.S型不对称碳原子在主链上的排布有关。

这些不对称碳原子要么来自不对称单体,如环氧丙烷,要么来自对称单体,如乙烯单体,,这些物质的聚合,在每个单体单元中形成至少一个不对称碳原子。

大分子中的构型异构源于侧链上存在不对称的碳原子,例如不对称乙烯单体的聚合,也是可能的,现今已经被广泛研究。

和经典有机化学术语一致,构象,旋转体,旋转异构体,构象异构体,指的是由于分子单键的内旋转而形成的空间排布的不同。

7大晶系的弹性模量矩阵元

7大晶系的弹性模量矩阵元

式中C ij就是我们通常所说的弹性模量,可以证明,上述刚度矩阵为对称阵,C ij=C ji,因此,弹性模量的独立张量元数目至多只有21个。

晶系的对称性越高,独立的张量元数目就越少。

需要指出的是,C ij的数目只与晶系有关,而与晶系中具体的对称类型无关。

下面分别讨论七种不同晶系的弹性模量矩阵元:
1.1 三斜晶系(Triclinic system)
三斜晶系是所有七大晶系中对称性最低的晶系,因此拥有最多的独立矩阵元,其形式为:
从上式可以看出,正交晶系拥有相当高的对成性,其独立刚度矩阵元的数目为8
三角晶系(32,3m,32/m)的独立刚度矩阵元的数目为6个。

立方晶系是所有晶系中对称度最高的晶系,其独立的刚度矩阵元数目仅为3个。

至此,我们列出了所有七大晶系的刚度矩阵元,只要求出各晶系对应的所有独立矩阵元,即可得到晶体的刚度矩阵。

2013二元密度黏度(三体作用模型)摩尔折光率

2013二元密度黏度(三体作用模型)摩尔折光率
S. C. Bhatia (B) · J. Sangwan · R. Rani · V. Kiran
Department of Chemistry, Kurukshetra University, Kurukshetra 136 119, Haryana, India e-mail: bhatiasc2@
Abstract Densities, ρ, viscosities, η, speeds of sound, u, and refractive indices, nD, of binary liquid mixtures of 2-ethyl-1-hexanol with benzene, chlorobenzene, and bromobenzene have been measured over the entire range of composition at 298.15 K, 303.15 K, and 308.15 K and at atmospheric pressure. From the experimental data of the density, speed of sound, viscosity, and refractive index, the values of the excess molar volume, V E, isentropic compressibility, κS, and deviations in molar refraction,
Keywords Chlorobenzenes · Density · 2-Ethyl-1-hexanol · Excess molar volume · Molar refraction · Refractive index · Speed of sound · Viscosity

TATB晶体形貌的计算模拟

TATB晶体形貌的计算模拟

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3D重建总是扭曲、空洞、体素化?来看看这个连续场模型吧

3D重建总是扭曲、空洞、体素化?来看看这个连续场模型吧

3D重建总是扭曲、空洞、体素化?来看看这个连续场模型吧作者:Jeong Joon Park等扭曲、空洞、体素化仍然是很多3D重建模型的通病,导致视觉效果很不友好。

Facebook、MIT 等近期提出了新型的基于深度学习的连续场3D 重建模型DeepSDF,可以生成具备复杂拓扑的高质量连续表面。

特别是,由于可以在反向传播过程中顺便求得空间梯度,DeepSDF 能生成非常平滑的表面。

图 1:DeepSDF 通过潜在编码和前馈解码器网络来表征形状的符号距离函数。

以上图像是DeepSDF 在学习到的形状潜在空间中进行两个形状的插值后的光线投射渲染。

深度卷积网络直接用于三维空间时,其时间和空间复杂度会急剧增长,且更经典和紧凑的表面表征(如三角网格或四边形网格)在训练中会出现问题,因为我们可能需要处理未知数量的顶点和任意拓扑。

在尝试用深度学习方法处理输入3D 数据或输出用于目标分割和重建的3D 推理时,这些挑战对深度学习方法的质量、灵活性和保真度带来了限制。

Facebook Reality Lab 的最新研究展示了一种高效、连续的新型生成3D 建模表征和方法。

该方法利用符号距离函数(Signed Distance Function,SDF)的概念,常见的表面重建技术将 SDF 离散化为规则网格用于估计和衡量去噪,而该方法学习一种生成模型来生成连续场。

该研究提出的连续表征可以被直观地理解为学得的形状分类器,其决策边界是形状本身的表面,如图2 所示。

该研究提出的方法与其他研究一样,试图将潜在空间映射到3D 复杂形状分布,但最主要的表征方式是不同的。

尽管在计算机视觉和图形学社区中隐式表面SDF 广为人知,但之前尚未有研究直接学习 SDF 的连续、可泛化 3D 生成模型。

图 2:本研究提出的 DeepSDF 表征应用于 Stanford Bunny:(a) 隐式表面 SDF = 0,SDF < 0 表示表面内的采样点,SDF > 0 表示表面外的采样点;(b) SDF 的 2D 交叉区域;(c) 从 SDF=0 恢复的渲染后的 3D 表面。

三维电催化处理苯并噻唑反应器结构优化

三维电催化处理苯并噻唑反应器结构优化

2017年第36卷第1期 CHEMICAL INDUSTRY AND ENGINEERING PROGRESS·91·化 工 进 展三维电催化处理苯并噻唑反应器结构优化丁杰,宋昭,宋迪慧,刘先树(哈尔滨工业大学市政环境工程学院,黑龙江 哈尔滨 150090)摘要:采用复极性三维电催化反应器降解苯并噻唑,通过考察三维电极反应器的结构参数,从而提高污染物处理效果的同时降低电催化反应体系的能耗。

首先以反应体系的矿化率、矿化电流效率及能耗为评价指标,优化了反应器的电极型式。

然后利用Design-Expert 软件中的Box-Behnken 响应曲面法,以外加电压、电极间距和粒子电极填充比例为自变量,TOC 去除率为响应值,研究了各变量及其相互作用对TOC 去除率的影响,并通过求解回归方程得到多元二次回归方程的预测模型。

结果表明,电极间距和外加电压对TOC 的影响最大,且电极间距和外加电压具有明显的交互性作用。

预测分析最大TOC 去除率为98.18%,相应的最优结构参数为:外加电压9.9V ,电极间距4.2cm ,粒子电极填充比60%,在最优条件下进行试验,实际值与预测值具有良好的一致性,偏差为1.71%。

关键词:电化学;降解;模型;结构参数;苯并噻唑;响应曲面分析法中图分类号:X703.1 文献标志码:A 文章编号:1000–6613(2017)01–0091–09 DOI :10.16085/j.issn.1000-6613.2017.01.012Structural optimization of three-dimensional electrocatalytic reactor forbenzothiazole treatmentDING Jie ,SONG Zhao ,SONG Dihui ,LIU Xianshu(School of Municipal and Environmental Engineering ,Harbin Institute of Technology ,Harbin 150090,Heilongjiang ,China )Abstract :In this study ,bipolar three-dimensional electrocatalytic reactor was applied to benzothiazole degradation and its structural parameters were investigated in order to improve the pollutant removalefficiency and reduce the energy consumption of electrochemistry reactor .Firstly ,the electrode form was improved by comparing the degree of mineralization ,mineralization current efficiency and energy consumption in the reaction system .Then response surface methodology based on Box-Behnken design was successfully applied to analyze the effect of the structural parameters and their interaction on benzothiazole degradation .The effects of three variables ,impressed voltage ,electrode distance and particle electrodes filling ratio upon the total organic carbon removal were evaluated and the prediction model of multivariate quadratic regression equation was acquired .The results showed that electrode distance played the most important role in total organic carbon removal ,followed by impressed voltage and particle electrodes filling ratio ,among which the interaction of electrode distance and the impresses voltage was remarkable .Optimized condition was obtained at 9.9V ,4.2cm and 60% particle electrodes for the reactor .Under the optimal condition ,98.18% of total organic carbon removal was achieved and第一作者及联系人:丁杰(1972—),女,教授,博士生导师,主要从事发酵法生物制氢技术、工业废水处理资源化与综合技术的研究。

三维简单正交晶格伊辛(Ising)模型精确解猜想

三维简单正交晶格伊辛(Ising)模型精确解猜想

三维简单正交晶格伊辛(Ising)模型精确解的猜想伊辛(Ising)模型是一个最简单的模型可以提供非常丰富的物理内容,可以被用来帮助我们发现物理世界的原则。

它不仅可以用来描述晶体的磁性,还可以用来描述非常广泛的现象,如合金中的有序-无序转变、液氦到超流态的转变、液体的冻结和蒸发、晶格气体、玻璃物质的性质、森林火灾、城市交通、蛋白质分子进入它们的活性形式的折叠等。

科学家对伊辛模型的广泛兴趣还源于它是描述相互作用的粒子(或原子或自旋)最简单的模型。

它可以用来测试研究相互作用的粒子在多体系统(特别是理解在临界点及其附近的合作现象和临界行为)任何近似方法的理想工具。

进一步说,三维伊辛模型可以研究从无限大温度到绝对零度相互作用的粒子(或原子或自旋) 系统的演变过程,如果将热力学中的温度作为动力学中时间来考量,它不仅可以理解热力学平衡的无限系统,如一个磁铁,还可以帮助理解我们的宇宙。

另外,平衡相变的理论可以用来研究连续的量子相变、基本粒子的超弦理论、在动力学系统到混沌的转变、系统偏离平衡的长时间行为和动力学临界行为等。

由于伊辛模型中的粒子(或原子或自旋)具有两种可能的状态(自旋向上或向下),它实际上可以对应黑白、上下、左右、前后、是非、正负……原则上,伊辛模型可以描述所有具有两种可能的状态的多体系统,描述两种极端条件间的相互竞争。

尽管伊辛模型是一个最简单的物理模型,目前仅有一维和二维的精确解。

Ising 在1925年解出的精确解表明一维伊辛模型中没有相变发生。

Onsager 于1944年获得二维伊辛模型的配分函数和比热的精确解,为统计物理领域的一个重大进展。

杨振宁于1952年求出二维伊辛模型的自发磁化强度。

二维正方伊辛模型的居里温度精确地存在于122−==−c K c e x 即1/K c = 2.26918531……。

二维伊辛模型的临界指数为α = 0, β = 1/8, γ = 7/4, δ = 15, η = 1/4 和 ν = 1。

3D 生物打印负载转化生长因子 β3 的软骨复合支架说明书

3D 生物打印负载转化生长因子 β3 的软骨复合支架说明书

Chinese Journal of Tissue Engineering Research |Vol 25|No.34|December 2021|54453D 生物打印负载转化生长因子β3的软骨复合支架杨 振1,2,李 浩1,2,付力伟1,2,高仓健1,2,姜双鹏2,王福鑫2,苑志国2,孙志强1,2,查康康1,2,1,22222文题释义:3D 生物打印:通过精准控制生物材料、种子细胞、生长因子在整体3D 结构中的位置、组合与互相作用,使之具有生物活性,并能实现与目标组织或生物器官接近相同,甚至更优越的功能。

转化生长因子β3:作为关节软骨组织形成的重要调节因子,可以促进干细胞迁移和成软骨分化,增强软骨损伤的修复,是一种理想的干细胞招募和促分化因子。

摘要背景:通过募集内源性干细胞原位再生软骨损伤的治疗策略,是未来软骨组织工程研究的新方向。

目的:构建既能募集干细胞又能促进其黏附和增殖,且有利于新生组织成熟的组织工程软骨复合支架。

方法:将脱细胞软骨细胞外基质(extracellular matrix ,ECM)与甲基丙烯酸酯化明胶(methacrylated gelatin ,GelMA)混合配制光敏性生物墨水,利用3D 生物打印技术分别制备单纯聚己内酯[poly(Ɛ-caprolactone),PCL]支架、PCL/GelMA/ECM 支架。

将转化生长因子β3(transforming growth factor β3,TGF-β3)负载于生物墨水中制备PCL/GelMA/ECM/TGF-β3支架,检测其缓释性能。

从形态学、组织学、生物化学、生物力学等角度评价PCL/GelMA/ECM 支架的物理化学性质。

利用CCK-8法检测PCL/GelMA/ECM 支架的细胞毒性。

将脂肪间充质干细胞接种于PCL/GelMA/ECM 支架上,1,4,7 d 后,共聚焦显微镜下观察细胞活性,扫描电镜观察细胞黏附。

卡梅伦液压数据手册(第 20 版)说明书

卡梅伦液压数据手册(第 20 版)说明书
11
iv

CONTENTS OF SECTION 1
☰ Hydraulics
⌂ Cameron Hydraulic Data ☰
Introduction. . . . . . . . . . . . . ................................................................ 1-3 Liquids. . . . . . . . . . . . . . . . . . . ...................................... .......................... 1-3
4
Viscosity etc.
Steam data....................................................................................................................................................................................... 6
1 Liquid Flow.............................................................................. 1-4
Viscosity. . . . . . . . . . . . . . . . . ...................................... .......................... 1-5 Pumping. . . . . . . . . . . . . . . . . ...................................... .......................... 1-6 Volume-System Head Calculations-Suction Head. ........................... 1-6, 1-7 Suction Lift-Total Discharge Head-Velocity Head............................. 1-7, 1-8 Total Sys. Head-Pump Head-Pressure-Spec. Gravity. ...................... 1-9, 1-10 Net Positive Suction Head. .......................................................... 1-11 NPSH-Suction Head-Life; Examples:....................... ............... 1-11 to 1-16 NPSH-Hydrocarbon Corrections.................................................... 1-16 NPSH-Reciprocating Pumps. ....................................................... 1-17 Acceleration Head-Reciprocating Pumps. ........................................ 1-18 Entrance Losses-Specific Speed. .................................................. 1-19 Specific Speed-Impeller. .................................... ........................ 1-19 Specific Speed-Suction...................................... ................. 1-20, 1-21 Submergence.. . . . . . . . . ....................................... ................. 1-21, 1-22 Intake Design-Vertical Wet Pit Pumps....................................... 1-22, 1-27 Work Performed in Pumping. ............................... ........................ 1-27 Temperature Rise. . . . . . . ...................................... ........................ 1-28 Characteristic Curves. . ...................................... ........................ 1-29 Affinity Laws-Stepping Curves. ..................................................... 1-30 System Curves.. . . . . . . . ....................................... ........................ 1-31 Parallel and Series Operation. .............................. ................. 1-32, 1-33 Water Hammer. . . . . . . . . . ...................................... ........................ 1-34 Reciprocating Pumps-Performance. ............................................... 1-35 Recip. Pumps-Pulsation Analysis & System Piping...................... 1-36 to 1-45 Pump Drivers-Speed Torque Curves. ....................................... 1-45, 1-46 Engine Drivers-Impeller Profiles. ................................................... 1-47 Hydraulic Institute Charts.................................... ............... 1-48 to 1-52 Bibliography.. . . . . . . . . . . . ...................................... ........................ 1-53

Regina软件:三维流形拓扑学软件说明书

Regina软件:三维流形拓扑学软件说明书

Introducing Regina,the3-manifold topology softwareBenjamin A.BurtonAuthor’s self-archived versionAvailable from .au/~bab/papers/AbstractAn overview is presented of Regina,a freely available software package for3-manifold topologists.In addition to working with3-manifold triangulations,Regina includes support for normal surfaces and angle structures.The features of the software are described in detail, followed by examples of research projects in which Regina has been used.1IntroductionExperimental work in the study of3-manifold topology has been a historically challenging task.Topological calculations for even simple3-manifold triangulations are often remarkably difficult to perform by hand.Furthermore,triangulations and3-manifolds are difficult to represent and manipulate using standard programming languages.Because of this,relatively little software has been available until recently to assist with these calculations.One prominent exception is SnapPea[Weeks91],under development for over a decade, which provides excellent support for the study of hyperbolic3-manifolds.More recently a number of other tools have become available,many of which are listed at the computational topology website /.Regina is a software package that unites a number of standard3-manifold topology algo-rithms and procedures within a friendly user interface,as well as adding previously unavailable features to the current body of experimental tools.Under development since1999,its growth has to a large extent been guided by its use in a variety of research projects,some of which are noted in Section3.Algorithms that are implemented include triangulation simplification, normal surface enumeration,angle structure analysis and the calculation of algebraic and combinatorial invariants.This software is released under the GNU General Public License and is publicly avail-able from /.Both the user interface and the underlying programmer’s interface are thoroughly documented.Regina continues to grow and currently enjoys a new release every few months.Special thanks must go to David Letscher who assisted with the early phases of development.Thanks also to Marc Culler,Nathan Dunfield,William Jaco,Richard Rannard,J.Hyam Rubinstein and JeffWeeks for many fruitful discussions.In Section2we present a detailed description of the capabilities of Regina.Section3closes with some examples of research projects that have made use of this software.2FeaturesSince its inception,Regina has been carefully designed for rigour and extensibility.The soft-ware is written primarily in the C++programming language and runs under GNU/Linux and related operating systems.A list of the more noteworthy features of Regina is presented below.2.1TriangulationsThe primary objects with which a user interacts when running Regina are3-manifold tri-angulations.As such,a large part of the software is devoted to the creation,analysis and1manipulation of triangulations.2.1.1CreationThe following methods are supported for creating triangulations.•Manual construction of triangulations by entering individual tetrahedron face identifica-tions by hand;•Automatic generation of standard triangulations such as layered solid tori and layered lens spaces[Jaco and Rubinstein03a,Jaco and Rubinstein06];•Automatic construction of Seifertfibred spaces over the2-sphere with up to three ex-ceptionalfibres;•Reconstruction of triangulations from dehydration strings[Callahan et al.99];•Importing triangulations saved from SnapPea[Weeks91].2.1.2AnalysisProperties of a triangulation that the software can compute include the following.•Detailed combinatorial information about the skeleton and boundary components,in-cluding vertex links and the shapes formed by the various triangulation faces;•A variety of homology and homotopy groups;•The quantum invariants of Turaev and Viro[Turaev and Viro92];•3-sphere recognition,as well as a complete connected sum decomposition for closed ori-entable triangulations[Jaco and Rubinstein03a];•Triangulation attributes relating to the existence of particular types of normal surface, such as0-efficiency[Jaco and Rubinstein03a]and the existence of splitting surfaces(de-scribed in Section2.3.3).Pairs of triangulations can be tested for direct isomorphism,or for whether one trian-gulation is isomorphic to a subcomplex of another.In addition the software contains a variety of recognition routines for detecting particular well-formed structures within a tri-angulation.These routines recognise smaller building blocks that often appear within larger triangulations,such as layered solid tori[Jaco and Rubinstein03a,Jaco and Rubinstein06] and thin I-bundles[Burton07].Furthermore,they can detect complete triangulations be-longing to a number of infinite families described in[Burton03],[Martelli and Petronio01] and[Matveev98].As a result Regina can frequently recognise the underlying3-manifolds for well-structured triangulations that it has not previously encountered.2.1.3ManipulationFor the manipulation of a triangulation,the following procedures are available.•Elementary moves(transformations local to a small number of tetrahedra),such as Pach-ner moves and other transformations described in[Burton07],many of which were sug-gested by Letscher;•Automated simplification in which the software attempts to use a combination of these elementary moves to reduce the number of tetrahedra as far as possible,though there is no guarantee that the smallest possible number of tetrahedra will be achieved;•Conversion to a0-efficient triangulation where possible for closed orientable3-manifolds [Jaco and Rubinstein03a];•Barycentric subdivision and the truncation of ideal vertices(vertices whose links are neither2-spheres nor discs);•Conversion of a non-orientable triangulation to an orientable double cover;•Crushing normal surfaces within a triangulation to a point,as described in Section2.3.2.22.2Census CreationRegina can form censuses of all3-manifold triangulations satisfying various sets of constraints.The census algorithm is described in[Burton07]and contains significant optimisations forcensuses of closed minimal P2-irreducible triangulations.In particular the face pairing graphresults of[Burton04]are incorporated into the algorithm,as are the more standard resultsrelating to low degree edges[Burton04,Callahan et al.99,Matveev98].Census creation can require significant amounts of computing time(months or years in some cases).As a result,support is provided for splitting this process into pieces and distributingthese pieces amongst several machines.In addition to forming new censuses,Regina ships with a number of prepackaged cen-suses including closed3-manifolds[Burton03,Burton07],cusped hyperbolic3-manifolds[Callahan et al.99]and knot and link complements(tabulated by Joe Christy).A censuslookup facility for arbitrary triangulations is provided.2.3Normal SurfacesThe theory of normal surfaces is a powerful tool for the study of3-manifolds and for thedevelopment of algorithms for their analysis.Normal surfaces were introduced by Kneser[Kneser29]and further developed by Haken[Haken61,Haken62]who used them to constructan algorithm for recognising the unknot.Haken furthermore began the construction of analgorithm for solving the homeomorphism problem for a certain large class of3-manifolds.Difficulties with the methods of Haken were resolved by Jaco and Oertel and by Hemion[Jaco and Oertel84,Hemion92],leading to afinite time algorithm for determining whethertwo closed irreducible3-manifolds are homeomorphic in the case in which one of these3-manifolds contains an embedded two-sided incompressible surface.Normal surfaces feature in a number of3-manifold decomposition,homeomorphism and recognition algorithms[Jaco et al.02,Jaco and Tollefson95,Rubinstein95,Rubinstein97]as well as in algorithms for the simplification of3-manifold triangulations[Jaco and Rubin-stein03a,Jaco and Rubinstein03b].For a more extensive review of normal surface theory,the reader is referred to[Hemion92].2.3.1CreationProviding a computational tool for the study of normal surfaces was in fact the originalmotivation behind this software.As such,Regina is capable of enumerating all vertex normalsurfaces or almost normal surfaces1within a triangulation,an operation required by mosthigh-level topological algorithms that utilise normal surface theory.Regina can perform this vertex enumeration in a variety of coordinate systems.For an n-tetrahedron triangulation this includes the7n standard triangle and quadrilateral coordi-nates,as well as the smaller set of3n quadrilateral-only coordinates introduced by Tollefsonfor algorithmic efficiency[Tollefson98].The enumeration can be restricted to embedded nor-mal surfaces or can be expanded to include immersed and singular surfaces.Furthermore,elementary support is present for spun normal surfaces,which are non-compact surfaces withinfinitely many discs found in ideal triangulations[Tillmann02].2.3.2AnalysisFor the analysis of normal surfaces,Regina offers the following facilities.•Viewing normal surfaces in a variety of coordinate systems,including the standard andquadrilateral-only coordinates discussed above as well as the edge weight coordinatesintroduced by Casson;•Calculating basic properties of normal surfaces such as Euler characteristic,orientabilityand one-sidedness;•Recognising standard surfaces within a triangulation such as splitting surfaces(see Sec-tion2.3.3below)and vertex and edge links;1Almost normal surfaces are closely related to normal surfaces and are used by Rubinstein in his3-sphere recognition algorithm[Rubinstein95,Rubinstein97].3•Filtering large lists of normal surfaces by various properties such as Euler characteristic, orientability and boundary.In addition the program can crush a normal surface to a point within a triangulation. Crushing is a powerful tool for the analysis of the role played by a surface within a3-manifold, and is used in Jaco and Rubinstein’s0-efficiency algorithm[Jaco and Rubinstein03a].2.3.3Splitting SurfacesSplitting surfaces represent a particular class of normal surfaces whose presence can offer insight into the triangulations containing them.A splitting surface contains precisely one quadrilateral disc within each tetrahedron and no other normal or almost normal discs.These surfaces have a number of interesting combinatorial and topological properties,described in detail in[Burton03].As mentioned earlier,Regina can detect whether splitting surfaces occur within a triangu-lation.It also provides support for splitting surface signatures,which are compact text-based representations from which splitting surfaces and their enclosing3-manifold triangulations can be reconstructed.In addition to performing such reconstructions,the software can form censuses of all possible splitting surface signatures of a given size.2.4Angle StructuresAngle structures,studied originally by Casson and then developed by Lackenby and Rivin [Lackenby00a,Lackenby00b,Rivin94,Rivin03],represent a purely algebraic generalisation of hyperbolic structures.An angle structure on an ideal triangulation is formed by assigning an interior dihedral angle to each edge of every tetrahedron in such a way that a variety of linear equations and inequalities are satisfied.The formation of angle structures is remarkably similar to the formation of normal surfaces, in which a series of triangle and quadrilateral coordinates are assigned to every tetrahedron with a set of linear equations and inequalities similarly imposed upon them.Thus it has been relatively straightforward to extend the normal surface enumeration code used by Regina in such a way that the software can also enumerate vertex angle structures.Included in the requirements of an angle structure is the condition that each dihedral angle θsatisfies0≤θ≤π.In addition to the enumeration of vertex angle structures,Regina can identify whether a triangulation supports any strict angle structures(for which each dihedral angleθsatisfies0<θ<π)or any taut angle structures(for which each dihedral angle is precisely0orπ).2.5ScriptingRegina offers the ability to write and run arbitrary scripts in the Python scripting language. These scripts are essentially high-level programs with immediate access to the mathematical core of Regina,and are ideal for performing repetitive tasks over large sets of data.Such tasks might include performing a sequence of tests upon all triangulations in a census,or testing a prototype for a new algorithm.Regina datafiles can contain embedded scripts,and different files can share code through the use of external libraries of routines.2.6Interfaces and DocumentationThe usual method of running Regina provides a full graphical interface that a user can easily understand and use.Alternatively,for those requiring immediate access to the mathematical core of the software,an interactive command-line interface is offered from which users can con-trol the program using the Python scripting language described above.A variety of specialised utility programs are also available.Significant effort has been spent on documentation for the software.A full reference manual is available for end users to assist them in working with Regina.This reference manual can be read online at /docs/.For users writing Python scripts or for programmers seeking to modify or extend the software,the routines offered by the underlying mathematical core are also fully documented.42.7Data FilesThe datafiles used for saving triangulations and other information adhere to a well-organised hierarchical structure.This structure not only allows multiple triangulations,normal surface lists and other topological structures to be stored together in an organised fashion but it also supports the storing of miscellaneous data such as text notes and Python scripts.Thefile format is well documented in the reference manual and uses compressed XML2,allowing for the simple transfer of native Regina data to and from other programs.3ApplicationsWe close with some examples of research projects in which Regina has been used with success.•In[Burton07]a census is presented of all closed non-orientable minimal P2-irreducible triangulations formed from≤putational support from Regina was required not only for the formation of the census but also for the detailed combinatorial analysis of the resulting triangulations.A similar census of orientable triangulations appears in[Burton03],again relying upon Regina for much computational support.•Various constraints upon the structures of minimal triangulations are proven in[Bur-ton04].For this research Regina was used to obtain and process data that originally motivated the results,as well as to measure the subsequent improvements to the census algorithm.•Research into the existence of taut angle structures on ideal triangulations is described in[Burton et al.03].Here Regina was used to process large bodies of census data to locate and subsequently analyse triangulations that do not support taut structures.•For the studies of0-efficiency and1-efficiency described in[Jaco and Rubinstein03a] and[Jaco and Rubinstein03b],Regina has assisted with the construction and analysis of pathological triangulations.AcknowledgementsThe author would like to acknowledge the support of the American Institute of Mathematics, the Australian Research Council and the Grayce B.Kerr Chair at Oklahoma State University. References[Burton03]Benjamin A.Burton.Minimal Triangulations and Normal Surfaces.PhD thesis, University of Melbourne,2003.Available from /.[Burton04]Benjamin A.Burton.“Face pairing graphs and3-manifold enumeration.”J.Knot Theory Ramifications,13(8):1057–1101,2004.[Burton07]Benjamin A.Burton.“Structures of small closed non-orientable3-manifold tri-angulations.”J.Knot Theory Ramifications,16(5):545–574,2007.[Burton et al.03]Benjamin A.Burton,Ensil Kang,and J.Hyam Rubinstein.“Triangulations of3-manifolds III:Taut structures in low-census manifolds.”In preparation,2003.[Callahan et al.99]Patrick J.Callahan,Martin V.Hildebrand,and Jeffrey R.Weeks.“A census of cusped hyperbolic3-manifolds.”p.,68(225):321–332,1999.[Haken61]Wolfgang Haken.“Theorie der Normalfl¨a chen.”Acta Math.,105:245–375,1961.[Haken62]Wolfgang Haken.“¨Uber das Hom¨o omorphieproblem der3-Mannigfaltigkeiten.I.”Math.Z.,80:89–120,1962.[Hemion92]Geoffrey Hemion.The Classification of Knots and3-Dimensional Spaces.Oxford Science Publications.Oxford University Press,Oxford,1992.2XML is the Extensible Markup Language,an open and widely-supported text-based data format.5[Jaco et al.02]William Jaco,David Letscher,and J.Hyam Rubinstein.“Algorithms for es-sential surfaces in3-manifolds.”In Topology and Geometry:Commemorating SISTAG, number314in Contemporary Mathematics,pages107–124.Amer.Math.Soc.,Provi-dence,RI,2002.[Jaco and Oertel84]William Jaco and Ulrich Oertel.“An algorithm to decide if a3-manifold is a Haken manifold.”Topology,23(2):195–209,1984.[Jaco and Rubinstein03a]William Jaco and J.Hyam Rubinstein.“0-efficient triangulations of3-manifolds.”J.Differential Geom.,65(1):61–168,2003.[Jaco and Rubinstein03b]William Jaco and J.Hyam Rubinstein.“1-efficient triangulations of3-manifolds.”In preparation,2003.[Jaco and Rubinstein06]William Jaco and J.Hyam Rubinstein.“Layered-triangulations of 3-manifolds.”Preprint,arXiv:math/0603601,March2006.[Jaco and Tollefson95]William Jaco and Jeffrey L.Tollefson.“Algorithms for the complete decomposition of a closed3-manifold.”Illinois J.Math.,39(3):358–406,1995. [Kneser29]Hellmuth Kneser.“Geschlossene Fl¨a chen in dreidimensionalen Mannigfaltigkei-ten.”Jahresbericht der Deut.Math.Verein.,38:248–260,1929.[Lackenby00a]Marc Lackenby.“Taut ideal triangulations of3-manifolds.”Geom.Topol.,4: 369–395(electronic),2000.[Lackenby00b]Marc Lackenby.“Word hyperbolic Dehn surgery.”Invent.Math.,140(2): 243–282,2000.[Martelli and Petronio01]Bruno Martelli and Carlo Petronio.“Three-manifolds having com-plexity at most9.”Experiment.Math.,10(2):207–236,2001.[Matveev98]Sergei V.Matveev.“Tables of3-manifolds up to complexity 6.”Max-Planck-Institut f¨u r Mathematik Preprint Series,(67),1998.Available from http://www.mpim-bonn.mpg.de/html/preprints/preprints.html.[Rivin94]Igor Rivin.“Euclidean structures on simplicial surfaces and hyperbolic volume.”Ann.of Math.(2),139(3):553–580,1994.[Rivin03]Igor Rivin.“Combinatorial optimization in geometry.”Adv.in Appl.Math.,31(1): 242–271,2003.[Rubinstein95]J.Hyam Rubinstein.“An algorithm to recognize the3-sphere.”In Proceedings of the International Congress of Mathematicians(Z¨u rich,1994),volume1,pages601–611.Birkh¨a user,Basel,1995.[Rubinstein97]J.Hyam Rubinstein.“Polyhedral minimal surfaces,Heegaard splittings and decision problems for3-dimensional manifolds.”In Geometric Topology(Athens,GA, 1993),volume2of AMS/IP Stud.Adv.Math.,pages1–20.Amer.Math.Soc.,Providence, RI,1997.[Tillmann02]Stephan Tillmann.On character varieties:surfaces associated to mutation& deformation of hyperbolic3-manifolds.PhD thesis,University of Melbourne,2002. [Tollefson98]Jeffrey L.Tollefson.“Normal surface Q-theory.”Pacific J.Math.,183(2):359–374,1998.[Turaev and Viro92]Vladimir G.Turaev and Oleg Y.Viro.“State sum invariants of3-manifolds and quantum6j-symbols.”Topology,31(4):865–902,1992.[Weeks91]Jeffrey R.Weeks.SnapPea.Hyperbolic3-manifold software,1991–2000.Available from /weeks/index/SnapPea.html.Benjamin A.Burton,Department of Mathematics and Statistics,The University of Melbourne, 3010VIC,Australia(**************)6。

计算化学中辅助晶体结构解析

计算化学中辅助晶体结构解析

计算化学中辅助晶体结构解析篇一:标题:计算化学中辅助晶体结构解析正文:随着化学领域的迅速发展,晶体结构解析已经成为化学研究中不可或缺的一部分。

晶体结构解析是指通过计算化学方法来预测分子或原子的晶体结构。

这些方法通常包括分子动力学模拟(MD)、分子轨道理论(MOF)、计算化学蒙特卡罗方法(CCSD)等。

分子动力学模拟(MD)是一种基于分子运动论和统计力学的方法,可以用来预测分子的晶体结构。

MD方法通常使用N-body potential energy function来定义分子的势场,并使用一组数值参数来定义势场的性质。

通过计算分子的N-body 轨道,可以得到分子的晶体结构。

分子轨道理论(MOF)是一种基于分子轨道理论的方法,可以用来预测分子的晶体结构。

MOF方法通常将分子的轨道表示为一组波函数,并通过计算这些波函数之间的相互作用来得到分子的晶体结构。

MOF方法通常需要使用一组数学模型来描述分子的轨道结构,并使用这些模型来计算分子的晶体结构。

计算化学蒙特卡罗方法(CCSD)是一种基于计算化学方法的方法,可以用来预测分子的晶体结构。

CCSD方法通常使用量子化学轨道理论(QCD)来模拟分子的原子轨道,并通过计算这些原子轨道之间的相互作用来得到分子的晶体结构。

CCSD 方法通常需要使用一组数学模型来描述分子的原子轨道,并使用这些模型来计算分子的晶体结构。

在实际应用中,计算化学方法可以用来解决许多化学问题,包括晶体结构解析、分子模拟、分子动力学模拟、药物设计等。

通过使用计算化学方法,我们可以更加精确地预测分子的晶体结构,从而更好地理解分子的性质和行为。

篇二:正文:计算化学是一门以计算机技术为基础的化学学科,它利用数学、物理和化学的理论知识和技能,通过数值计算方法来研究物质的结构和性质。

在计算化学中,晶体结构解析是非常重要的一个领域。

晶体结构是指一个分子或离子在空间中排列的方式,它是理解物质性质和反应机制的基础。

氢气泡动态模板法制备三维多孔金膜

氢气泡动态模板法制备三维多孔金膜

第34 6期2018 6 月无机化 学学报CHINESE JOURNAL OF INORGANIC CHEMISTRYVol.34 No.6 1166-1172氢气泡动态模板法制备三维多孔金膜刘军李容肖洁张渺岚刘绚艳!(湖南化工职业技术学院制药与生物工程学院,株洲 410005)摘要:采用氢气泡阴极沉积法成功制备了具有枝晶结构的三维分级多孔A>膜。

本文详细研究了沉积电位、沉积时间、H!S 〇4浓 度、前驱体浓度等沉积条件对形貌的影响。

由枝晶构成的三维多孔金膜(3DPGF f 0也可以通过方波电位法(SWP0制备。

采用扫描 电(SEM0对泡沫膜的形貌进行了。

研究表明,由纳米簇组成的3DPGFS 对葡萄糖无酶传感具有良好的化活性。

关键词:金泡沫膜&枝晶&电沉积;氢气泡模板;电催化中图分类号! O646.541 文献标识码:A 文章编号! 1001-4861(2018)06-1166-07DOI :10.11862/CJIC.2018.133Three Dimensional Porous Gold Film Prepared by theHydrogen Bubble Dynamic TemplateLIU Jun LI Rong XIAOJie ZHANG Miao-Lan LIU Xuan-Yan!(Department of P harmaceutical and Biological Engineering, Hunan Chemical VocationalTechnology College, Zhuzhou, Hunan 412005, China)Abstract : Au films with three-dimensional (3D) hierarchical pores consisting of interconnected dendrite walls weresuccessfully fabricated by a strategy of cathodic deposition utilizing the hydrogen bubble dynamic template. The deposition conditions like potential, deposition time, H 2SO 4 concentration, precursor concentrations were investigated in detail. Herein, 3D Au porous films (3D PGFs) with dendritic walls could also be prepared by square wave potential (SWP). The morphology of foam films were characterized by scanning electron microscopy (SEM). The 3D PGF s comprised of nanodendrites show good electrocatalytic activities in enzyme-free detection of glucose.Keywords : Au foam film; dendrite; electrodeposition; hydrogen bubble template; electrocatalysis0 IntroductionThree dimensional porous materials have attracted increasing research enthusiasm due to their potential applications in areas such as electrocatalysis[1-2], superhy- drophobicity[2-3], sensors[4], and surface enhanced raman scattering (SERS)[2-5].Considering the preparation methods of porous metals, the template-directed synthesis[6-8] and the dealloying method[9-10] are widely used in the literature.收稿日期:2018-01-04。

Monolithic three dimensional (3D) integrated circu

Monolithic three dimensional (3D) integrated circu

专利名称:Monolithic three dimensional (3D)integrated circuit (IC) (3DIC) cross-tier clockskew management systems, methods andrelated components发明人:Pratyush Kamal,Yang Du申请号:US14159028申请日:20140120公开号:US09213358B2公开日:20151215专利内容由知识产权出版社提供专利附图:摘要:Monolithic three dimensional (3D) integrated circuit (IC) (3DIC) cross-tier clockskew management systems are disclosed. Methods and related components are also disclosed. In an exemplary embodiment, to offset the skew that may result across the tiers in the clock tree, a cross-tier clock balancing scheme makes use of automatic delay adjustment. In particular, a delay sensing circuit detects a difference in delay at comparable points in the clock tree between different tiers and instructs a programmable delay element to delay the clock signals on the faster of the two tiers. In a second exemplary embodiment, a metal mesh is provided to all elements within the clock tree and acts as a signal aggregator that provides clock signals to the clocked elements substantially simultaneously.申请人:QUALCOMM Incorporated地址:San Diego CA US国籍:US代理机构:Withrow & Terranova, PLLC更多信息请下载全文后查看。

3D

3D

Volumetric 3-Dimensions Display (体三维显示技术)最近研究了一下三维立体显示技术(属于较为宽泛的光通信技术外延,我个人觉得),发觉这个领域真的非常“迷人”,特写出来与大家一起分享;)目前的三维立体显示技术共可以分为分光立体眼镜(Glasses-based Stereoscopic)、自动分光立体显示(Autostereoscopi c Displays)、全息术(Hologram)和体三维显示(Volumetric 3-D Display)4大类。

其中的前两类应该都是大家很熟悉的技术了,它们都采用了视差的方式来给人以3D显示的感觉:分别为左眼和右眼显示稍有差别的图像,从而欺骗大脑,令观察者产生3D的感觉。

由于人为制造视差的方式所构造的3D景象并不自然,它加重了观察者的脑力负担,因此看久了会令人头痛。

而全息术则利用的并不是数字化的手段,而是光波的干涉和衍射,它一般只能生成静态的三维光学场景,并且对观察角度还有要求,所以就目前而言,它对于人机交互应用而言还并不适合。

体三维显示则与前三者不同,它是真正能够实现动态效果的3D技术,它可以让你看到科幻电影中一般“悬浮”在半空中的三维透视图像。

体三维显示技术目前大体可分为扫描体显示(Swept-Volume Display)和固态体显示(Solid-Volume Display)两种。

其中,前者的代表作是Felix3D和Perspecta,而后者的代表作则名为DepthCube。

Felix3D拥有一个很直观的结构框架,它是一个基于螺旋面的旋转结构,如下图所示,一个马达带动一个螺旋面高速旋转,然后由R/G/B三束激光会聚成一束色度光线经过光学定位系统打在螺旋面上,产生一个彩色亮点,当旋转速度足够快时,螺旋面看上去变得透明了,而这个亮点则仿佛是悬浮在空中一样,成为了一个体象素(空间象素,Voxel),多个这样的voxel便能构成一个体直线、体面,直到构成一个3D物体,过程很直观,不是么?Perspecta可能是扫描体3D显示领域最令人瞩目的成就了,它采用的是一种柱面轴心旋转外加空间投影的结构,如下图所示,与Felix3D不同,它的旋转结构更简单,就一个由马达带动的直立投影屏,这个屏的旋转频率可高达730rpm,它由很薄的半透明塑料做成。

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Three-dimensional poly(1,8-octanediol–co-citrate)scaffold pore shape and permeability effects on sub-cutaneous in vivo chondrogenesis using primary chondrocytesClaire G.Jeong a ,Huina Zhang a ,Scott J.Hollister a ,b ,c ,⇑aDepartment of Biomedical Engineering,University of Michigan,Ann Arbor,MI 48109-2125,USA bDepartment of Mechanical Engineering,University of Michigan,Ann Arbor,MI 48109-2125,USA cDepartment of Surgery,University of Michigan,Ann Arbor,MI 48109-0329,USAa r t i c l e i n f o Article history:Received 16April 2010Received in revised form 29July 2010Accepted 26August 2010Available online 31August 2010Keywords:Poly(1,8-octanediol–co-citrate)scaffold Pore shape PermeabilityMechanical properties Cartilagea b s t r a c tThe objective of this study was to evaluate the coupled effects of three-dimensional poly(1,8-octanediol–co-citrate)(POC)scaffold pore shape and permeability on chondrogenesis using primary chondrocytes in vivo.Chondrogenesis was characterized as cartilage matrix formation by sulfated glycosaminoglycan (sGAG)quantification,relative mRNA expression of the cartilage-related proteins collagen types I,II and X,aggrecan and matrix metalloproteinases 13and 3and the compressive mechanical properties of the tissue/scaffold construct.A low permeability design with a spherical pore shape showed a significantly greater increase in cartilage matrix formation over 6weeks in vivo than a high permeability design with a cubical pore shape.This increase in cartilage matrix synthesis corresponded with increases in mechan-ical compressive nonlinear elastic properties and histological data demonstrating darker red Safranin-O staining.There was higher mRNA expression for both cartilage-specific proteins and matrix degradation proteins in the high permeability design,resulting in overall less sGAG retained in the high permeability scaffold compared with the low permeability scaffold.Controlled POC scaffolds with a spherical pore shape and low permeability correlated with significantly increased cartilage matrix production using primary seeded chondrocytes.These results indicate that the low permeability design with a spherical pore shape provided a better microenvironment for chondrogenesis than the high permeability design with a cubical pore shape.Thus,scaffold architecture and material design may have a significant impact on the success of matrix-based clinical cartilage repair strategies.Ó2010Published by Elsevier Ltd.on behalf of Acta Materialia Inc.1.IntroductionArticular cartilage has very limited self-repair capability due to its low cellularity and vascularization.Current therapeutic strate-gies,such as microfracture,osteochondral transplantation and autologous chondrocyte implantation,have been applied with rel-ative success for more than a decade,yet are still limited to small defect sizes and suffer from donor site morbidity,restricting their clinical application [1–5].These limitations have increased interest in tissue engineering approaches combining degradable biomate-rial scaffolds with or without cell therapy.While it is widely pos-tulated that scaffolds play a major role in the success or failure of cartilage repair,there is very limited data on how scaffold architecture and materials should be designed to enhance cartilage repair using tissue engineered approaches.Specifically,the mechanical and mass transport environments provided to seeded cells or host cells by implanted scaffolds may significantly affect cell activity,dictating the outcome of cartilage repair.These envi-ronments are determined by scaffold structural parameters,including pore geometry,pore size,porosity,pore interconnectivi-ty,etc.To create scaffolds that enhance chondrogenesis we must first be able to test hypotheses concerning how scaffold design affects chondrogenesis,which requires fabricating scaffolds with controlled architectures.Here we have used a biocompatible,biodegradable elastomer poly(1,8-octanediol–co-citrate)(POC)scaffold and cultured chondrocytes in vivo to examine the coupled effects of designed pore shape and permeability on matrix produc-tion,mRNA gene expression and differentiation of chondrocytes in vivo after sub-cutaneous implantation,as well as the resultant mechanical property changes in scaffold/tissue constructs due to tissue formation and scaffold degradation.POC has been shown to support cell attachment and proliferation of and matrix produc-tion by chondrocytes [6],while our own recent work [7]has dem-onstrated that POC enhances in vitro chondrogenesis over other1742-7061/$-see front matter Ó2010Published by Elsevier Ltd.on behalf of Acta Materialia Inc.doi:10.1016/j.actbio.2010.08.027⇑Corresponding author at:Department of Biomedical Engineering,University ofMichigan,Ann Arbor,MI 48109-2125,USA.Tel.:+17346479962.E-mail address:scottho@ (S.J.Hollister).biodegradable polymers of the same design.Moreover,our previ-ously engineered scaffolds had compressive mechanical properties similar to native articular cartilage(Table2)[8].Our scaffold designs were rigorously fabricated such that only pore shape and scaffold permeability varied in a controlled manner and other factors such as pore size,pore interconnectivity,porosity and scaffold surface area were kept constant between the two dif-ferent designs.Our previous work[7,9–11]demonstrated that a low permeability design with a spherical pore shape promoted chondrogenesis in vitro on different materials using chondrocytes. The purpose of this paper was to investigate whether low perme-ability spherical pore designs also supported enhanced chondro-genesis in vivo.Specifically,we tested the hypothesis that POC scaffolds designed with a spherical pore shape and low permeabil-ity would enhance chondrogenesis in vivo in a sub-cutaneous model.Chondrogenesis in chondrocyte-seeded POC scaffolds was assessed as cartilaginous matrix production,cartilage-specific gene expression and composite tissue/scaffold compressive mechanical properties,including how tissue formation and scaffold degrada-tion interacted in determining thefinal construct mechanics.For this purpose wefirst cultured seeded primary chondrocytes in de-signed POC scaffolds using collagen I(Col I)/hyaluronic acid(HyA) hydrogels as a cell carrier for1week in vitro.These cell/scaffold constructs were then implanted for6weeks in vivo in a sub-cuta-neous nude mouse model[12].2.Materials and methods2.1.Collagen I/hyaluronic acid hydrogelHigh concentration Col I hydrogels and HyA were purchased from BD Bioscience Discovery Labs(San Jose,CA)and Hyalogic LLC(Edwardsville,KS),respectively.High concentration collagen I hydrogels were diluted with0.02N sterile acetic acid to a concen-tration of6mg mlÀ1and5wt.%hyaluronic acid was added based on our previous results showing that a Col I gel with5%HyA en-hanced chondrogenesis[12].2.2.Synthesis of pre-poly(1,8-octanediol–co-citrate)All chemicals were purchased from Sigma–Aldrich(Milwaukee, WI).The pre-polymer(pPOC)was synthesized as previously described[13].Briefly,equimolar amounts of citric acid and 1,8-octanediol were added and the mixture was melted at 160–165°C for15min under aflow of nitrogen gas with stirring and then further lowered to140°C for40min to create the pre-polymer.2.3.Scaffold design and fabricationThe three-dimensional(3D)POC scaffold architecture was de-signed using previous methods and software[12,14–16].Porous POC scaffolds(6.35mm diameter,4.0mm height)with900l m interconnected spherical or cubical pores(porosity spherical50% S50),cubical62%(C62);permeability high(C62)=13.5Âlow (S50))were designed using custom IDL programs(RSI,Boulder, CO).The details of POC scaffold fabrication were as previously re-ported[13,16].In brief,wax molds with a designed architecture were built using a Solidscape Patternmaster™,from which solid free-form fabricated hydroxyapatite(HA)molds were then pre-pared.pPOC was then cured in the HA molds to create the two de-signed scaffold architectures[17].pPOC was poured into the wells of a Teflon container and the HA molds were embedded within the pPOC.The pPOC/HA mold/Teflon container unit was cured at 100°C for1day,followed by curing at100°C for3more days un-der high vacuum(À30in.Hg).The HA mold was removed by incu-bation in a decalcifying reagent(RDO,APEX Engineering Products, Plainfield,IL)for10h,followed by incubation in water(Milli-Q Water Purification System,Billerica,MA)for24h to obtain thefinal porous POC scaffolds,which were dried at room temperature for 24h before autoclaving.2.4.Mechanical testsPorous scaffolds(n=4–6per design per time),gel-filled scaffolds (n=4–6per design per time)or scaffolds with tissue in-growth (after in vitro pre-culture(0week in vivo)or3or6weeks of in vivo sub-cutaneous implantation,n=4–6per design per time) were tested in unconfined compression at a displacement rate of 2mm minÀ1equivalent to a strain rate of0.0063sÀ1using a large strain to applied stretch ratio of E=0.5(k2À1),where k is the stretch ratio(<1for compression)and E is the large strain.(Alliance RT/30 electromechanical test frame,50N load cell with0.5%error range, MTS Systems,Eden Prairie,MN).Data were collected using Test-Works4software.MATLAB(The MathWorks Inc.,Natick,MA)soft-ware(LSQNONLIN)was used tofit a nonlinear elasticity model r=A[e B eÀ1]to the experimental data,where r is thefirst Piola–Kirchoff stress,e is the large strain and A and B are model coefficients. Tangent moduli(=AB e B e)were calculated at10%strain from thefit.2.5.Porosity and permeability measurementsSeven scaffolds per design were scanned using a MS-130high resolution micro-computer tomography(micro-CT)scanner(GE Medical Systems,Toronto,Canada)at19l m voxel resolution be-fore mechanical testing to avoid any compression artifacts.Scaffold permeability(n=6–7)with and without the HyA/Col I(6mg mlÀ1) composite gel and for tissue/scaffold constructs after6week in vivo implantation was measured using a permeability test set-up[9,13].Briefly,a custom permeability chamber was designed to apply a constant hydraulic pressure on a scaffold contained in-side the chamber that forces water toflow through the chamber and into a secondary container placed on top of a scale connected to a computer recording data at3Hz.A customized LabView pro-gram based on an equation derived from Bernoulli’s equation and Darcy’s law[18]was used to compute permeability.The permeability of the scaffolds with the hydrogel was mea-sured to mimic freshly loaded cell conditions in vitro for compari-son with the permeability of scaffolds with tissue in-growth after 6weeks.Primary porcine chondrocytes were seeded into3D scaf-folds byfirst suspending the cells in medium with the composite HyA/Col I gel and then pushing the gel into the3D scaffolds[12]. The gelation procedure was as follows:770l l of Col I(6mg mlÀ1) with77l l of HyA(stock concentration3mg mlÀ1in1.5M sodium chloride,molecular weight 2.4–3MDa)were well mixed,after which the pH of the suspension was increased by the addition of 11l l of0.5N sodium hydroxide with220mg mlÀ1sodium bicar-bonate to initiate gelation,then the hydrogel mixtures were dripped onto pre-prepared sterile scaffolds until the scaffolds were fully soaked andfilled with gel to the top surface,followed by incu-bation at37°C for at least30min to further solidify the gels.The 50%and62%porous scaffolds were seeded with121and150l l of cell/gel mixture,respectively,in order to maintain the same cell density per volume.2.6.In vitro pre-culture and in vivo implantationPorcine chondrocytes(pChon)were isolated from the full depth of the joints of domestic pigs and seeded onto scaffolds following previous methods[12].Cells were resuspended at a density of 30Â106cells mlÀ1in770l l of HyA/Col I composite gel with506 C.G.Jeong et al./Acta Biomaterialia7(2011)505–51450l l of culture medium.The remaining steps were as previously described(see Section2.5).24scaffolds per design(15per design for6weeks in vivo implantation and9per design for1week in vitro pre-culture)seeded with pChon were cultured in chondro-genic medium(Dulbecco’s modified Eagle’s medium(DMEM)sup-plemented with10%fetal bovine serum(FBS),1%penicillin/ streptomycin(Gibco),50mg mlÀ12-phospho-L-ascorbic acid(Sig-ma),0.4mM proline(Sigma),5mg mlÀ1insulin(Gibco),0.1mM non-essential amino acids(Gibco))in12-well plates for1week be-fore in vivo implantation.Chondrocytes were cultured under gen-tle agitation on an orbital shaker and the medium was changed every other day.All POC scaffolds were sterilized in an autoclave and pre-soaked in DMEM for24h,then briefly rinsed with phos-phate-buffered saline(PBS)prior to cell seeding.The cell cultures were maintained in a water-jacketed incubator equilibrated with 5%CO2at37°C.To observe mechanical stiffness changes over time due to degradation,gel-filled scaffolds with no cells(n=4–6per design at each time point)were also subjected to the same in vitro conditions to maintain the same conditions as for the cell/gel-filled scaffolds.After1week of culture30cell-seeded POC scaffolds(15per design)and20gel-filled POC scaffolds(no cells)(n=4per design6weeks)were removed,finely diced and immediately placed in 1ml of pre-prepared papain solution(10U mgÀ1papain(Sigma Aldrich No.P4762),1ÂPBS,5mM cysteine HCl,5mM EDTA,pH 6.0,mixed for2h at37°C and thenfiltered).Scaffolds were di-gested in papain solution for24h at60°C then immediately stored atÀ20°C.The digested tissue/scaffold solution was analyzed by dimethylmethylene blue(DMMB)assay.Briefly,10l of sample was mixed with200l of DMMB reagent and absorbance was read in a plate reader(MultiSkan Spectrum,Thermo,Waltham,MA)at 525nm.A standard curve was established from chondroitin6-sul-fate from shark(Sigma C4384)to determine sample absorbance for [19,20].The total sGAG was normalized to DNA content,which was measured using Hoechst dye33258(Sigma DNA-QF).In brief,10l of digested sample was added to200l of pre-prepared Hoechst solution and read with excitation at355nm and emission at 460nm(Fluoroskan Ascent FL,Thermo,Waltham,MA)in a96-well plate.Readings were compared with standard curves from calf thy-mus DNA(Sigma DNA-QF)[21].2.8.Quantitative polymerase chain reaction(PCR)C.G.Jeong et al./Acta Biomaterialia7(2011)505–514507primer was obtained by qtPCR with serially diluted cDNA sample mixtures.Samples were prepared using a Taqman universal PCR master mix(Applied Biosystems)and custom designed porcine primers.The level of gene expression was calculated with standard samples and normalized to GAPDHfirst and the low permeability design(S50).2.9.HistologyConstructs(n=3per design)at each time point werefixed in 10%buffered formalin overnight,dehydrated in a series of graded ethanol and embedded in paraffin.Tissue sections were stained with hematoxylin and eosin(H&E)for scaffolds without cells or with Safranin-O with Fast Green counterstaining for scaffolds with cells,to assess cell and tissue distribution,cell morphology and sGAG production.The cross-sectional and longitudinal views of eight to ten slides(4sections per slide)were obtained from the center of each scaffold[12].2.10.Statistical analysisData are expressed as means±standard deviation.The statisti-cal significance among different designs or time points was calcu-lated using linear regression and one-way ANOVA with Tukey’s post hoc comparison or Student’s t-test using SPSS software(SPSS for Windows,Release14.0.,SPSS Inc.,Chicago).Data were taken to be significant when a P value of0.05or less was obtained.3.Results3.1.Scaffold design,permeability,and mechanical characterization3D scaffolds were fabricated from POC using solid free-form fabrication methods.The scaffolds were designed with either a spherical or cubical pore shape,with resultant significant differ-ences in permeability.Pore size and regular interconnectivity were maintained between scaffold designs(Fig.1A and Table1).For descriptive purposes the scaffold with a cubical pore design and 62%porosity is designated C62and the scaffold with a spherical pore design and50%porosity is designated S50.By varying the pore shape and porosity scaffolds could be fabricated with signifi-cantly different permeabilities(t-test,P60.05)between designs, with S50having low permeability(3.51±0.95Â10À7m4N sÀ1) and C62having high permeability,13.6times that of S50 (47.4±1.15Â10À7m4N sÀ1)The difference in permeability was far greater than the difference in porosity(C62=S50Â1.2).Sur-face area was also not significantly different between the designs (S50=288±38vs.C62=243±15mm2).Thus,among design parameters permeability and pore shape exhibited the greatest variations between designs.With Col I/HyA hydrogel the scaffold permeability values all de-creased from the original scaffold permeability,as expected,yet con-tinued to exhibit a similar differential trend between designs.Due to collagen gel degradation after1–2weeks the permeability without gel most likely represents the permeability of scaffolds during the 6weeks of in vivo implantation without tissue in-growth,whereas the permeability with the gel represents the scaffolds at0weeks with initial cell seeding.As most of collagen gel was degraded within a week during tissue formation,scaffold permeability changed dynamically during the6week in vivo implantation period with gel and POC degradation,tissue in-growth from seeded chondro-cytes and tissue formation around the scaffold by mouse cells.The permeabilities measured for tissues grown for6weeks after in vivo implantation for both designs were significantly lower than the permeabilities with the gel,indicating extensive growth of tissue into the scaffolds during in vivo implantation.The gel-filled scaffold permeability for the S50low permeability design(1.72±0.45Â10À7m4N sÀ1)was3.3times higher than the permeability of the scaffold with tissue in-growth(0.52±0.01Â10À7m4N sÀ1), whereas that for the C62gel-filled high permeability design (4.14±0.73Â10À7m4N sÀ1)was8.1times higher than the perme-ability of the scaffold with tissue in-growth(0.51±0.01Â10À7m4N sÀ1).However,there was no significant difference in per-meability between tissue/scaffold constructs between designs after 6weeks in vivo implantation.In order to observe mechanical stiffness changes due to scaffold degradation and tissue formation in vivo we implanted gel-filled scaffolds(which were also cultured in vitro for1week before implantation)in mice and measured their stiffness at0,3and 6weeks in vivo to determine changes in effective nonlinear scaf-fold stiffness.Table2summarizes the compressive tangent moduli at10%strain for different scaffold designs after applying the non-linear modelfit for gel-filled or tissue grown scaffolds at each time point.For both designs the tangent modulus increased from0to3 or6weeks when not seeded with cells(Fig.2B).The low perme-ability design demonstrated the greatest increase over the6week implantation period(9times vs.3.4times compared with the high permeability design).There were no significant changes in tangent modulus from3to6weeks for either design(Fig.2B).Unlike the case without cells,both designs with cells showed roughly the same increase(3.8times)in tangent modulus from0to6weeks in vivo.When comparing cases with and without cells,scaffolds with cells showed higher tangent moduli for both designs.In Fig.2A the stress–strain curve for the low permeability de-sign(S50)shifts up from0to3weeks with increased stress at each strain,then shifts down from3to6weeks.The curve for the high permeability design(C62)increased from0to3week and from3 to6weeks.C62(high)showed less nonlinear behavior than S50 (low)at the3week time point,but at the6week time point C62 (high)showed more nonlinear behavior,due to possible increased tissue matrix deposition by host cells within the pores,coupled with slower scaffold degradation.When cells were present both designs increased in nonlinear stiffness over6weeks and showed more nonlinear behavior after implantation,due to tissue formation inside the pores.However, when comparing scaffolds with cells vs.without cells at6weeks, the low permeability design(S50)showed a larger increase in non-linear stiffness than the high permeability design(C62).3.2.Matrix production and mRNA expression before and after in vivo implantationThe low permeability design(S50)showed a significant increase (P60.05)in matrix formation(sGAG/DNA content)over6week in vivo implantation,whereas the high permeability design(C62) did not(Fig.3).An increase in sGAG/DNA content implies that aTable1Scaffold descriptions a.Design(n=8)S50,Low C62,HighPorosity(%)50±1.6262±2.36Permeability without gel(10À7m4N sÀ1)b 3.51±0.9547.4±1.15Permeability with gel(10À7m4N sÀ1)b 1.72±0.45 4.14±0.73Permeability with tissues(in vivo)(10À7m4N sÀ1)c0.52±0.010.51±0.01Surface area(mm2)c288±38243±15Pore shape Spherical CubicalPore diameter900l m900l ma Data are expressed as means±standard deviation.b n=4per design,t-test,P60.05,statistically significant(after6weeks in vivoimplantation).c Not statistically significant(t-test,P60.05).508 C.G.Jeong et al./Acta Biomaterialia7(2011)505–514single cell is more geared towards the chondrocytic phenotype with a higher matrix production/maintenance rate.Even though it was not significantly different,the low permeability design (S50)showed22%higher matrix production than the high perme-ability design(C62)at6weeks,which was the opposite of the re-sults at0weeks(immediately after the1week in vitro pre-culture),where the high permeability design formed35%more ma-trix than the low permeability design.Table2Tangent moduli(MPa)at10%strain(n=4–6)a.In vivo implantation c S50,low b C62,high bWithout cells With cells Without cells With cells0weeks0.059±0.0190.192±0.0470.054±0.0150.122±0.022 3weeks0.531±0.1590.185±0.0266weeks0.525±0.1730.701±0.1310.202±0.0970.467±0.092a Data are expressed as means±standard deviation.b For statistical significance between groups and conditions see Fig.2b and d.c Note that all of the scaffolds were pre-cultured for1week in vitro under the same conditions before in vivo implantation,whether cells were present or not.ACC.G.Jeong et al./Acta Biomaterialia7(2011)505–514509All mRNA expression for the low permeability design except Col X(Fig.4)showed higher ratios than the high permeability design at 0week in vivo(Fig.4A).The ratio of Col II gene expression to Col I gene expression(Col II/Col I),known as the‘‘differentiation index”(DI),and aggrecan expression for the low permeability design(S50) in particular were significantly higher than expression for the high permeability design(C62).A higher DI value indicates a more chondrocytic genotype,while a lower value indicates morefibro-blastic gene expression[22].Type II collagen and aggrecan are typ-ically used as biomarkers of differentiated chondrocytes and cartilaginous tissues[23–25],whereas type I and type X collagen are typically used as markers of dedifferentiated or terminally dif-ferentiated(hypertrophic)chondrocytes,respectively[26,27].In contrast,the high permeability design(C62)showed higher values than the low permeability design(S50)after6weeks in vivo implantation for all expressed genes(Fig.4B).Type I colla-gen and aggrecan expression for C62were significantly higher(4 times)than those for S50.Thus,the results for all gene expression were higher for the C62design after6weeks in vivo,whereas all gene expression was higher for the S50design after1week in vitro culture(Fig.4).Since total sGAG(Fig.3)is a result of not only matrix formation and secretion but also matrix degradation and sGAG leaching out of the scaffold,it is also important to investigate mRNA expression of matrix degradation proteins.MMP-13and MMP-3play critical roles in extracellular matrix(ECM)degradation in cartilage. MMP-13appears to be the primary collagenase of articular carti-lage and is also critical for cartilage turnover and chondrocyte hypertrophy in the growth plate[28,29].In addition to collagen, MMP-13also degrades the proteoglycan molecule aggrecan,giving it a dual role in matrix destruction.[30–32].MMP-3is elevated in arthritis,and degrades non-collagen matrix components of the joints.Both MMP-13and MMP-3mRNA expression for the low permeability design(S50)were significantly higher than for the high permeability design(C62)at0week,which then reversed after6weeks in vivo implantation.Over6weeks the expression of both MMPs greatly increased for the high permeability design, whereas the low permeability design maintained relatively con-stant MMP mRNA expression.In general,mRNA expression levels were high for the low permeability design at0week whereas mRNA expression levels were high for the high permeability design at6week in vivo.3.3.HistologySafranin-O staining(Fig.5)supported the sGAG quantification data(Fig.3)in that more intense and darker sGAG staining inside the scaffolds was observed after6weeks for both designs com-pared with the0week time point.For the0week time point there was no discernible difference in sGAG between scaffold designs. However,after6weeks implantation the low permeability design (S50)showed increased staining over the entire scaffold,with dar-ker sGAG staining particularly near the pore necking area(denoted by arrows),compared with the high permeability design(C62).The innermost parts of the low permeability scaffolds,both cross-sec-tionally and longitudinally,had rich Safranin-O staining,demon-strating that sGAGs were formed and maintained inside the scaffolds.The chondrocytic phenotype was easily observed,with lacunae,for both designs at6weeks.H&E stained images(Fig.6)of scaffolds without seeded cells at 3and6weeks showed that tissue formed outside the scaffold but not in the center pore structures at3weeks.Further infiltration510 C.G.Jeong et al./Acta Biomaterialia7(2011)505–514denote tissues formed at the edge of the scaffolds while the asterisks denote the central parts of the scaffolds.was seen at6weeks.This infiltrated tissue was likelyfibrous tissue resulting from in-growth of surrounding host tissuefibroblasts,as there was no positive staining of Safranin-O/Fast Green for either design at any time point(data not shown).The combination offi-brous tissue formation with scaffold degradation likely dictated the change in mechanical properties of the gel-filled,cell-free pared with S50,C62,High showed deeper cell infiltra-tion into the central part of the pore architecture(asterisks)at 6weeks,likely due to the higher permeability allowing greater and more rapid cell migration.4.DiscussionThe focus of this study was to determine the effects of3D POC controlled scaffold pore shape and permeability on chondrogenesis in vivo.Our previous in vitro studies[7,9]demonstrated that scaf-folds with lower permeability and spherical pore shapes increased cartilage matrix production and gene expression.The question then is whether scaffold permeability and pore shape influence chondrogenesis in vivo.Although the ultimate test of in vivo chondrogenesis would be an articular defect,such a defect would also entail mechanical compression and stimulus effects on chondrogenesis,confounding the investigation of pore shape and permeability influences on chondrogenesis.Thus,we chose a sub-cutaneous mouse model for in vivo chondrogenesis,to better isolate the pore shape and permeability affects on chondrogenesis using scaffolds with different controlled designs manufactured from the same ing the same scaffold material also helps isolate design effects,since we have also shown that the scaf-fold material significantly influences chondrogenesis[7].In order to evaluate the effects of POC scaffold pore architec-tures and the resulting permeability on tissues and the quality of engineered cartilage/scaffold constructs we examined constructs before and after in vivo implantation.Specifically,in this way we would be able to tell how scaffold architecture and the resulting permeability may affect chondrogenesis differently in vitro and in vivo.Some studies have reported that cells are predominantly distributed in the outer or surface zones of scaffolds when cultured in vitro with static seeding[33].Thus we tested pre-cultured POC/ cell constructs in vitro before implantation to ensure that cells were deposited in the scaffold pores and synthesized cartilage ECM(Figs.3and5).Both designs showed an ability to form matrix (Fig.3)and to synthesize articular cartilage-specific proteins (Fig.4)before in vivo implantation.In the in vitro pre-culture period there were no significant dif-ferences between the designs in terms of matrix production (Fig.3).The high permeability design(C62)produced slightly more matrix.However,with respect to relative mRNA expression,the low permeability design(S50)had relatively high mRNA expres-sion for all proteins except Col X.Of note,the differentiation index (Col II/Col I)and aggrecan expression were significantly higher. This can be explained by the relative permeability.With initial cell seeding and with a regular supply of nutrients during1week of in vitro pre-culture cells in both designs were exposed to excessive nutrients,but permeabilities that differed in relative magnitude between the designs,regulated by the permeability and pore shape (Table1).The low permeability design had higher expression of Col II and aggrecan and a higher Col II/Col I ratio,which are indicators of differentiated chondrocytes,closely related to sGAG formation, than the high permeability design(Fig.4).In addition,both MMP-13and MMP-3expression levels for the low permeability design(S50)were almost10times higher than for the high perme-ability design(C62),indicating active matrix remodeling.Hence, the overall sGAG/DNA content at0weeks for the low permeability design showed lower values than that for the high permeability de-sign,since sGAG/DNA would be a product of sGAG secretion/pro-duction inside the scaffolds,matrix degradation and possible sGAG loss by leaching out of the scaffolds.At6weeks after implantation,however,the results were the opposite of the short-term1week in vitro results.At6weeks after implantation the low permeability design(S50)produced more matrix than the high permeability design(C62)and demonstrated a significant increase in matrix production compared with the 1week in vitro data(Fig.3).However,with respect to relative mRNA expression,the high permeability design(C62)had relatively high mRNA expression for all proteins,with Col I and aggrecan expression being significantly higher(Fig.4B).This again can be explained by scaffold permeability.The environment of native articular cartilage is well known for its low permeability, avascularization(thus low nutrient supply)and hypoxic condi-tions.Unlike the in vitro conditions,there is probably limited chondrogenic nutrient supply around sub-cutaneous scaffolds in vivo.The low permeability design with a spherical pore shape likely allows even lower nutrient exchange from the outside.The scaffold permeability differences resulted from a balance between an increase in permeability due to gel and POC degradation and a decrease in permeability due to tissue in-growth.We hypothesize that the permeability difference between designs would be main-tained or possibly increase,allowing increased sGAG retention by the low permeability S50design.In addition,even though mRNA expression of relevant cartilage-like tissue formation proteins such as Col II and aggrecan were lower after6weeks in vivo for the low permeability design,the activities of MMP-13and MMP-3were also lower(2-fold lower for MMP-13and 10-fold lower for MMP-3).Furthermore,mRNA expression of both MMPs remained relatively constant over6weeks after implantation for the low permeability design(Fig.4B).This suggests that the low permeability design may be better at retaining sGAG due to its lim-ited nutrientflux,coupled with lower matrix degradation.These re-sults are in line with the histological data(Fig.5),clearly showing darker staining in the wider area of the middle of the low permeabil-ity scaffolds.There was especially intense sGAG staining near the necks of the spherical pores(Fig.5,arrows),further support for the postulate that the spherical pore shape helps retain cartilage matrix. Regardless of the scaffold pore architecture and permeability,Figs.5 and6show that the pores of the POC scaffold in vivo appeared to be filled with cartilaginous tissue produced by the implanted chondro-cytes,and the scaffold maintained its architecture after6weeks implantation.Along with the biochemical and histological assessments, mechanical assessments,such as changes in the nonlinear mechan-ical properties of entire tissue/scaffold constructs before and after implantation,are important,as mechanical performance is another important factor determining the success of regenerated tissues. Brown et al.[34]recently characterized the nonlinear hyperelastic behavior of20mm discs of bovine patella articular cartilage in unconfined compression at strain rates of0.1and0.025sÀ1.They noted that articular cartilage exhibited nonlinear elastic behavior at both strain rates,although the behavior stiffened at the higher strain rate as a characteristic of poroelastic/biphasic materials like cartilage.Fitting our one-dimensional nonlinear constitutive mod-el to the data of Brown et al.yielded a range of A coefficients from 0.64to1.72,and B coefficients from4.77to6.62.Our scaffold re-sults with cells for the S50designs yielded A=0.145±0.05and B=3.55±0.56,while the C62design yielded A=0.068±0.015 and B=4.44±0.30.With this nonlinear model a higher A value yielded a higher initial tangent stiffness,while a higher B value yielded more nonlinearity and stress paring these results suggests that the engineered cartilage had a nonlinearity similar to the lower range of the bovine results of Brown et al.[34],but the initial tangent stiffness was less.This indicates that512 C.G.Jeong et al./Acta Biomaterialia7(2011)505–514。

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