The transport of oxygen within red blood cells (RBCs) is governed by the interplay between molecular diffusion, membrane permeability, and reversible binding to hemoglobin. In this work, authors develop a theoretical framework for modeling oxygen diffusion and hemoglobin reactions, progressively incorporating three cases of increasing complexity: (i) diffusion with constant coefficients, (ii) diffusion with concentration-dependent coefficients, and (iii) diffusion under the influence of static magnetic fields. In the first case, oxygen transport is described by Fickian diffusion coupled with the reversible binding and unbinding of oxygen to hemoglobin, assuming a constant diffusion coefficient. In the second case, experimentally validated concentration-dependent diffusion coefficients are introduced, capturing the effects of macromolecular crowding within the RBC interior. In the third case, the potential influence of static magnetic fields is considered via an effective diffusion coefficient, , distinguishing between diamagnetic oxyhemoglobin and paramagnetic deoxyhemoglobin; however, under fields below ∼10 T, these effects are negligible. The resulting system of coupled partial differential equations is solved using finite-difference discretization schemes, allowing numerical analysis of concentration fields in space and time. Initial and boundary conditions reflect physiological venous to artery transitions and realistic membrane permeabilities. Results highlight the predominant role of concentration-dependent diffusion in modulating oxygen and hemoglobin distributions, while magnetic contributions are only under ultra-high fields. This framework establishes a generalizable basis for further quantitative studies on hemoglobin-mediated oxygen transport and may serve as a foundation for integrating more complex biophysical interactions relevant to red cell physiology.
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