Introduction: Active fluid circulation and transport are key functions of living organisms, which drive efficient delivery of oxygen and nutrients to various physiological compartments. Because fluid circulation occurs in a network, the systemic flux and pressure are not simple outcomes of any given component. Rather, they are emergent properties of network elements and network topology. Moreover, consistent pressure and osmolarity gradients across compartments such as the kidney, interstitium, and vessels are known. How these gradients and network properties are established and maintained is an unanswered question in systems physiology. Previous studies have shown that epithelial cells are fluid pumps that actively generate pressure and osmolarity gradients. Polarization and activity of ion exchangers that drive fluid flux in epithelial cells are affected by pressure and osmolarity gradients. Therefore, there is an unexplored coupling between the pressure and osmolarity in the circulating network. Here we develop a mathematical theory that integrates the influence of pressure and osmolarity on solute transport and explores both cell fluid transport and systemic circulation. This model naturally generates pressure and osmolarity gradients across physiological compartments, and demonstrates how systemic transport properties can depend on cell properties, and how the cell state can depend on systemic properties. When epithelial and endothelial pumps are considered together, we predict how pressures at various points in the network depend on the overall osmolarity of the system. The model can be improved by including physiological geometries and expanding solute species, and highlights the interplay of fluid properties with cell function in living organisms.
Materials and
Methods: In this paper, we develop a mathematical model of systemic fluid circulation, incorporating active pumping properties of epithelial and endothelial cells and network connectivity. The model is based on convection diffusion equation and continuity of fluxes. It starts with cell transport properties, and incorporates pressure- and osmolarity-dependent solute transport at the single cell level. We then use the cell scale model to derive transport/pumping properties of epithelial and endothelial barriers. The results directly relate phenomenological coefficients of transport equations with cell-level properties. We then incorporate active pumping properties of cells in a circulation network model in analogy to elctrical circuit based on Kirchhoff law, but now include both solute and fluid pumping in the network to study the systemic property of fluid and solute transport.
Results, Conclusions, and Discussions: In this paper, we develop a mathematical model of systemic fluid circulation, incorporating active pumping properties of epithelial and endothelial cells and network connectivity. The model starts with cell transport properties, and incorporates pressure- and osmolarity-dependent solute transport at the single cell level. We then use the cell scale model to derive transport/pumping properties of epithelial and endothelial barriers. The results directly relate phenomenological coefficients of transport equations with cell-level properties. We find that there are two different regimes where the absolute osmolarity has opposite influences on the flux. The boundary is a function of both pressure and osmolarity gradient. We then incorporate active pumping properties of cells in a circulation network model, but now include both solute and fluid pumping in the network. The model predicts overall solute and fluid flux in the network as well as osmolarities and pressures in the various compartments in the network. Gradients of osmolarity and pressure are natural outcomes of the model, and can influence each other. We show that inclusion of active transport or pumping properties of endothelia/epithelia fundamentally changes the overall network circulation properties. Specifically, the model predicts how the total osmolarities of the system can influence network transport properties and pressure/osmolarity gradients across compartments. In analogy to the water pump, we show that there exists a regime of highest efficiency/lowest mechanical stress for kidney epithelial cells. If the operating point is outside of this regime, cells are likely to experience stress, leading to possible diseases. Results on how blood oncotic pressure influences the flux provides some understanding on hypertension and some kidney diseases related to protein filtration. We also point out how the model can be extended to include realistic network geometries and physiology-level feedback control. Mechanical rigidity of the network can be relaxed and growth can be included to allow the network morphology to adapt to pressure/osmolarity changes, leading to a fluid-centric theory of morphogenesis.
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