Modeling tumor growth with variable mass and angiogenesis-driven perfusion through a 3D-1D coupled framework
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arXiv
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| Format: | Preprint |
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2026
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| author | Giverso, Chiara Grappein, Denise Scialò, Stefano |
| author_facet | Giverso, Chiara Grappein, Denise Scialò, Stefano |
| contents | Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling strategy to simulate perfusion in a tumoral tissue with growing mass, interacting with a dynamically evolving capillary network. The tumor is described as a multiphase system including tumor cells and interstitial fluid, governed by a non-linear PDE system for cell volume fraction, pressure, oxygen, and VEGF, and discretized via finite elements. Capillary growth is tackled using a continuous-discrete hybrid tip-tracking approach. The vascular geometry is updated over time according to angiogenic signals, and coupled to the tissue model through a constrained optimization formulation that enforces fluid and nutrient exchange via interface variables. A sensitivity analysis using the Morris elementary effect method identifies key parameters influencing system behavior. Results highlight the critical role of vascular development in regulating tissue perfusion and tumor progression. Overall, the proposed numerical approach provides a versatile tool for investigating tumor-vascular interactions and can support further quantitative analysis of angiogenesis and tumor perfusion dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modeling tumor growth with variable mass and angiogenesis-driven perfusion through a 3D-1D coupled framework Giverso, Chiara Grappein, Denise Scialò, Stefano Numerical Analysis 65N30, 35Q92, 92B05, 92C17 Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling strategy to simulate perfusion in a tumoral tissue with growing mass, interacting with a dynamically evolving capillary network. The tumor is described as a multiphase system including tumor cells and interstitial fluid, governed by a non-linear PDE system for cell volume fraction, pressure, oxygen, and VEGF, and discretized via finite elements. Capillary growth is tackled using a continuous-discrete hybrid tip-tracking approach. The vascular geometry is updated over time according to angiogenic signals, and coupled to the tissue model through a constrained optimization formulation that enforces fluid and nutrient exchange via interface variables. A sensitivity analysis using the Morris elementary effect method identifies key parameters influencing system behavior. Results highlight the critical role of vascular development in regulating tissue perfusion and tumor progression. Overall, the proposed numerical approach provides a versatile tool for investigating tumor-vascular interactions and can support further quantitative analysis of angiogenesis and tumor perfusion dynamics. |
| title | Modeling tumor growth with variable mass and angiogenesis-driven perfusion through a 3D-1D coupled framework |
| topic | Numerical Analysis 65N30, 35Q92, 92B05, 92C17 |
| url | https://arxiv.org/abs/2603.29615 |