A Unified Model for Blood and Lymph Flow with Coupled Nonsmooth Biochemical Dynamics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918363488321536 |
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| author | Jaszczak-Dyka, Bogna Płociniczak, Łukasz |
| author_facet | Jaszczak-Dyka, Bogna Płociniczak, Łukasz |
| contents | We present a unified mathematical framework for modeling blood and lymph flow in biological vessels, with a particular focus on lymph transport through lymphangions. Starting from first principles, we rigorously derive a system of partial differential equations (PDEs) that govern the fluid dynamics using perturbative methods. To capture the active regulation of lymphangion valves, we couple these PDEs with a system of two nonlinear ordinary non-smooth differential equations (ODEs) describing the chemical kinetics of calcium ions and nitric oxide. These biochemical species play a critical role in valve opening and closing, influencing lymph propulsion. We further analyze a reduced model consisting of two non-smooth ODEs, identifying parameter regimes that guarantee the existence of a stable limit cycle. This oscillatory behavior aligns with experimental observations of lymphatic pumping, providing theoretical validation and new insights into lymphatic physiology. Our results offer a comprehensive mathematical description of lymph flow regulation and open possibilities for future studies on pathological conditions and therapeutic interventions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00779 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Model for Blood and Lymph Flow with Coupled Nonsmooth Biochemical Dynamics Jaszczak-Dyka, Bogna Płociniczak, Łukasz Analysis of PDEs Classical Analysis and ODEs 35Q92, 34A36, 92C35 We present a unified mathematical framework for modeling blood and lymph flow in biological vessels, with a particular focus on lymph transport through lymphangions. Starting from first principles, we rigorously derive a system of partial differential equations (PDEs) that govern the fluid dynamics using perturbative methods. To capture the active regulation of lymphangion valves, we couple these PDEs with a system of two nonlinear ordinary non-smooth differential equations (ODEs) describing the chemical kinetics of calcium ions and nitric oxide. These biochemical species play a critical role in valve opening and closing, influencing lymph propulsion. We further analyze a reduced model consisting of two non-smooth ODEs, identifying parameter regimes that guarantee the existence of a stable limit cycle. This oscillatory behavior aligns with experimental observations of lymphatic pumping, providing theoretical validation and new insights into lymphatic physiology. Our results offer a comprehensive mathematical description of lymph flow regulation and open possibilities for future studies on pathological conditions and therapeutic interventions. |
| title | A Unified Model for Blood and Lymph Flow with Coupled Nonsmooth Biochemical Dynamics |
| topic | Analysis of PDEs Classical Analysis and ODEs 35Q92, 34A36, 92C35 |
| url | https://arxiv.org/abs/2603.00779 |