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Stiffness-tunable biomaterials provide a good extracellular matrix environment for axon growth and regeneration

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Neural Regeneration Research 2025年第5期20卷 1364-1376页

作者： Ronglin Han Lanxin Luo Caiyan Wei Yaru Qiao Jiming Xie Xianchao Pan Juan Xing Department of Pathophysiology School of Basic Medical SciencesSouthwest Medical UniversityLuzhouSichuan ProvinceChina Department of Medicinal Chemistry School of PharmacySouthwest Medical UniversityLuzhouSichuan ProvinceChina

Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to providing physical support for cells, the extracellular matrix also conveys critical mechanical stiffness cues. During the development of the nervous system, extracellular matrix stiffness plays a central role in guiding neuronal growth, particularly in the context of axonal extension, which is crucial for the formation of neural networks. In neural tissue engineering, manipulation of biomaterial stiffness is a promising strategy to provide a permissive environment for the repair and regeneration of injured nervous tissue. Recent research has fine-tuned synthetic biomaterials to fabricate scaffolds that closely replicate the stiffness profiles observed in the nervous system. In this review, we highlight the molecular mechanisms by which extracellular matrix stiffness regulates axonal growth and regeneration. We highlight the progress made in the development of stiffness-tunable biomaterials to emulate in vivo extracellular matrix environments, with an emphasis on their application in neural repair and regeneration, along with a discussion of the current limitations and future prospects. The exploration and optimization of the stiffness-tunable biomaterials has the potential to markedly advance the development of neural tissue engineering.

关键词： alginate axon growth biomaterials extracellular matrix neural repair neurons neuroregeneration polyacrylamide polydimethylsiloxane stiffness

THE GENERATING SET OF THE DIFFERENTIAL INVARIANT ALGEBRA AND MAURER-CARTAN EQUATIONS OF A(2+1)-DIMENSIONAL BURGERS EQUATION

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Journal of Systems Science & Complexity 2013年第2期26卷 281-290页

作者： MEI Jianqin WANG Haiyan school of mathematical sciences Dalian University of Technology

The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a （2＋1）-dimensional Burgers equation, based on the theory of equi... 详细信息

关键词： (2+1)-dimensional Burgers equation differential invariants Lie pseudo-groups MaurerCaftan equation moving frame method.

Scale-aware shape manipulation

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Journal of Zhejiang University-Science C(Computers and Electronics) 2014年第9期15卷 764-775页

作者： Zheng LIU Wei-ming WANG Xiu-ping LIU Li-gang LIU school of mathematical sciences University of Science and Technology of China school of mathematical sciences Dalian University of Technology

A novel representation of a triangular mesh surface using a set of scale-invariant measures is *** measures consist of angles of the triangles(triangle angles) and dihedral angles along the edges(edge angles)which are scale and rigidity independent. The vertex coordinates for a mesh give its scale-invariant measures, unique up to scale, rotation, and translation. Based on the representation of mesh using scale-invariant measures, a two-step iterative deformation algorithm is proposed, which can arbitrarily edit the mesh through simple handles *** algorithm can explicitly preserve the local geometric details as much as possible in different scales even under severe editing operations including rotation, scaling, and shearing. The efficiency and robustness of the proposed algorithm are demonstrated by examples.

关键词： Differential coordinates Scale-invariant measures Surface deformation

Block basis property of a class of 2×2 operator matrices and its application to elasticity

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Chinese Physics B 2013年第9期22卷 474-479页

作者：宋宽侯国林阿拉坦仓 school of mathematical sciences Inner Mongolia University

A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2 ×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of solving symplectic elasticity problems by using the method of separation of variables. Moreover, the theoretical result is applied to two plane elasticity problems via the separable Hamiltonian systems.

关键词： symplectic elasticity block Schauder basis separable Hamiltonian system operator matrices

An H^m-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues

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Science China Mathematics 2017年第8期60卷 1529-1542页

作者： HAN JiaYu YANG YiDu school of mathematical sciences Guizhou Normal University

We develop an Hm-conforming(m 1) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval [-1, 1] that are made up of the generalized Jacobi polynomials(GJPs) and the nodal basis *** the basis functions on multi-dimensional rectangles consist of the tensorial product of the basis functions on the interval [-1, 1]. Then we construct the spectral element interpolation operator and prove the associated interpolation error estimates. Finally, we apply the H2-conforming spectral element method to the Helmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics.

关键词： spectral element method multi-dimensional domain interpolation error estimates transmission eigenvalues

Robust mesh deformation with salient features preservation

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Science China(Information sciences) 2016年第5期59卷 96-104页

作者： Yong ZHAO Shengjie LU Hailong QIAN Pengcheng YAO school of mathematical sciences Ocean University of China

Triangular meshes often contain a few salient features. Traditional deformation algorithms mainly preserve the local details and volume, thus producing unnatural results. This paper proposes a robust and effective algorithm to prevent the distortion of salient features. Firstly, the salient features can be automatically extracted through saliency-based clustering and aggregation. A nonlinear energy function is then minimized to make the salient features behave rigidly to retain the shape. Finally, for the robustness of the minimization, we generate a coarse solid subspace around the input mesh, and carry out the energy minimization in this *** show that our algorithm can preserve the salient features and obtain visual-pleasing results.

关键词： mesh deformation salient features rigid deformation coarse solid subspace nonlinear energy minimization

Continuous solutions for fractional integral inclusion in locally convex topological space

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Applied Mathematics(A Journal of Chinese Universities) 2009年第2期24卷 175-183页

作者： Rabha W.Ibrahim school of mathematical sciences Faculty of Sciences and Technology

The existence of continuous solutions for fractional integral inclusion via its singlevalued problem and fixed point theorem for set-valued function in locally convex topological spaces is discussed. The proof of the single-valued problem will be based on the Leray- Schauder fixed point theorem. Moreover, the controllability of this solution is studied.

关键词： Riemann-Liouville integral operator integral inclusion set-valued function

Existence of Periodic Solutions of Sublinear Hamiltonian Systems

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Acta Mathematica Sinica,English Series 2016年第5期32卷 621-632页

作者： Wei DING Ding Bian QIAN Chao WANG Zhi Guo WANG school of sciences Nantong University school of mathematical sciences Soochow University school of mathematical Science Yancheng Teachers University

The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need ... 详细信息

关键词： Periodic solutions critical points impacts bouncing solutions nonsmooth saddle point theorem

Graph Theory Methods for Decomposition w.r.t. Outputs of Boolean Control Networks

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Journal of Systems Science & Complexity 2017年第3期30卷 519-534页

作者： ZOU Yunlei ZHU Jiandong College of mathematical sciences Yangzhou University Institute of Mathematics School of Mathematical Sciences Nanjing Normal University

This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.

关键词： Boolean control network decomposition w.r.t outputs semi-tensor product.