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Qingdong Zhang

Publications and source records attributed to Qingdong Zhang.

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Label-free Prediction of Vascular Connectivity in Perfused Microvascular Networks in vitro

Continuous monitoring and in-situ assessment of microvascular connectivity have significant implications for culturing vascularized organoids and optimizing the therapeutic strategies. However, commonly used methods for vascular connectivity assessment heavily rely on fluorescent labels that may either raise biocompatibility concerns or interrupt the normal cell growth process. To address this issue, a Vessel Connectivity Network (VC-Net) was developed for label-free assessment of vascular connectivity. To validate the VC-Net, microvascular networks (MVNs) were cultured in vitro and their microscopic images were acquired at different culturing conditions as a training dataset. The VC-Net employs a Vessel Queue Contrastive Learning (VQCL) method and a class imbalance algorithm to address the issues of limited sample size, indistinctive class features and imbalanced class distribution in the dataset. The VC-Net successfully evaluated the vascular connectivity with no significant deviation from that by fluorescence imaging. In addition, the proposed VC-Net successfully differentiated the connectivity characteristics between normal and tumor-related MVNs. In comparison with those cultured in the regular microenvironment, the averaged connectivity of MVNs cultured in the tumor-related microenvironment decreased by 30.8%, whereas the non-connected area increased by 37.3%. This study provides a new avenue for label-free and continuous assessment of organoid or tumor vascularization in vitro.

eess.IV

Variable step-size BDF3 method for Allen-Cahn equation

In this work, we analyze the three-step backward differentiation formula (BDF3) method for solving the Allen-Cahn equation on variable grids. For BDF2 method, the discrete orthogonal convolution (DOC) kernels are positive, the stability and convergence analysis are well established in [Liao and Zhang, \newblock Math. Comp., \textbf{90} (2021) 1207--1226; Chen, Yu, and Zhang, \newblock SIAM J. Numer. Anal., Major Revised]. However, the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial, since the DOC kernels are not always positive. By developing a novel spectral norm inequality, the unconditional stability and convergence are rigorously proved under the updated step ratio restriction $r_k:=τ_k/τ_{k-1}\leq 1.405$ (compared with $r_k\leq 1.199$ in [Calvo and Grigorieff, \newblock BIT. \textbf{42} (2002) 689--701]) for BDF3 method. Finally, numerical experiments are performed to illustrate the theoretical results. To the best of our knowledge, this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.

math.NA

Weighted and shifted BDF2 methods on variable grids

Variable steps implicit-explicit multistep methods for PDEs have been presented in [17], where the zero-stability is studied for ODEs; however, the stability analysis still remains an open question for PDEs. Based on the idea of linear multistep methods, we present a simple weighted and shifted BDF2 methods with variable steps for the parabolic problems, which serve as a bridge between BDF2 and Crank-Nicolson scheme. The contributions of this paper are as follows: we first prove that the optimal adjacent time-step ratios for the weighted and shifted BDF2, which greatly improve the maximum time-step ratios for BDF2 in [11,15]. Moreover, the unconditional stability and optimal convergence are rigorous proved, which make up for the vacancy of the theory for PDEs in [17]. Finally, numerical experiments are given to illustrate theoretical results.

math.NA