非局部灌注门控血管生成系统：全局弱解、快信号极限与侵袭前沿
A Nonlocal Perfusion-Gated Angiogenesis System: Global Weak Solutions, Fast-Signal Limits, and Invasion Fronts
- College of Engineering, Boston University（波士顿大学工程学院）
- Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出一个二维非局部灌注门控血管生成模型，证明压力-灌注映射的Lipschitz稳定性与全局有界弱解存在性，推导快信号极限收敛，并确定侵袭前沿的阈值条件，通过有限体积实验验证机制。
AI中文摘要：
连续介质血管生成系统通常使用局部内皮或血管密度作为氧输送的代理指标，而不区分结构形成的血管与压力支持的血管功能。我们构建了一个二维模型，其中管腔化密度决定归一化的非局部电导率、全局求解的压力场以及一个门控氧输送和血管退化的血流功能密度。对于固定的正正则化参数和信号弛豫时间，我们证明了压力-灌注映射的Lipschitz稳定性以及全局有界弱可解性；强血管紧致性来自非局部常微分方程稳定性估计而非空间平滑。当氧气和血管内皮生长因子时间尺度同时消失时，弱解沿子序列收敛到一个抛物-椭圆-常微分方程系统，两个快场在\\(L^2(0,T;H^1)\\)中强收敛。一个局部冻结的一维约化允许在阈值\\(B+2\sqrt{DR}\\)（当\\(B\geq-\sqrt{DR}\\)时）或\\(-DR/B\\)（否则）处或之上恰好存在单调侵袭前沿。有限体积实验验证了分析机制，并表明等质量血管场可以产生不同的功能质量和氧合水平。
英文摘要：
Continuum angiogenesis systems often use local endothelial or vessel density as an oxygen-delivery proxy without distinguishing structurally formed vessels from pressure-supported vascular function. We formulate a two-dimensional model in which lumenized density determines a normalized nonlocal conductivity, a globally solved pressure field, and a flow-functional density that gates oxygen delivery and vessel regression. For fixed positive regularization parameters and signal relaxation times, we prove Lipschitz stability of the pressure--perfusion map and global bounded weak solvability; strong vessel compactness follows from a nonlocal ordinary differential equation stability estimate rather than spatial smoothing. As the oxygen and vascular endothelial growth factor timescales vanish simultaneously, weak solutions converge along a subsequence to a parabolic--elliptic--ordinary differential equation system, with both fast fields converging strongly in \(L^2(0,T;H^1)\). A locally frozen one-dimensional reduction admits monotone fronts precisely at or above the threshold \(B+2\sqrt{DR}\) for \(B\geq-\sqrt{DR}\) and \(-DR/B\) otherwise. Finite-volume experiments verify the analytical mechanisms and show that equal-mass vessel fields can generate distinct functional masses and oxygenation levels.
