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Updated: Jan 13, 2026

In Vitro 3D Cell-Cultured Arterial Models for Studying Vascular Drug Targeting Under Flow
Published on: March 14, 2021
Bidirectional Endothelial Feedback Drives Turing-Vascular Patterning and Drug-Resistance Niches: A Hybrid
Zonghao Liu1, Louis Shuo Wang2, Jiguang Yu3,4
1Innovation Center for Cancer Research, Clinical Oncology School, Fujian Medical University, Fuzhou 350014, China.
This study introduces a hybrid model linking partial differential equations and agent-based modeling to simulate tumor angiogenesis. The findings reveal how endothelial cell feedback creates vascular patterns, leading to drug resistance.
Area of Science:
- Computational Biology
- Mathematical Oncology
- Biophysics
Background:
- Tumor growth and treatment efficacy are significantly impacted by tumor microenvironment heterogeneity, particularly vascularization.
- Perfusion heterogeneity in tumors leads to variable oxygen and drug distribution, fostering treatment resistance.
- Understanding the interplay between tumor angiogenic factor (TAF) and endothelial cell behavior is crucial for developing effective therapies.
Purpose of the Study:
- To develop and analyze a multiscale hybrid partial differential equation-agent-based model (PDE-ABM) integrating tumor cells, endothelial cells, and molecular signaling.
- To investigate how endothelial cell feedback mechanisms, specifically TAF secretion and chemotaxis, drive vascular pattern formation.
- To identify key parameters that influence vascular heterogeneity and drug penetration, and to propose strategies for mitigating treatment resistance.
Main Methods:
- Development of a coupled PDE-ABM framework simulating TAF, oxygen, and drug dynamics alongside discrete endothelial and tumor cell behaviors.
- Linear stability analysis of a reduced endothelial-TAF reaction-diffusion subsystem to identify conditions for Turing instability.
- Simulation of emergent vascular patterns and assessment of their impact on drug penetration and hypoxic region formation.
Main Results:
- Bidirectional coupling between endothelial cell migration along TAF gradients and TAF secretion is necessary and sufficient for generating spatially periodic vascular clusters.
- These emergent vascular patterns create inter-cluster hypoxic regions, resulting in heterogeneous drug penetration and the development of resistant cell niches.
- TAF clearance, chemotactic sensitivity, and endothelial motility were identified as critical parameters for homogenizing tumor perfusion.
Conclusions:
- The hybrid PDE-ABM effectively captures multiscale dynamics driving tumor vascularization and heterogeneity.
- Targeting the endothelial-TAF feedback loop offers a potential strategy to improve drug delivery and overcome treatment resistance.
- The study provides a foundation for future extensions to 3D and saturable kinetics for quantitative clinical applications.
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