Structural analysis of fluid flow in complex biological systems

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Eisenberg R. Structural analysis of fluid flow in complex biological systems. MAIO [Internet]. 2023 Feb. 7 [cited 2023 Mar. 24];4(1). Available from:

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Copyright (c) 2022 Robert Eisenberg


bidomain model; conservation laws; fluid flow; glymphatic system


Biology is about structure. Structures within structures. Organs within animals, tissues within organs, cells within tissues, and molecules, often proteins within cells. The structures are so complex that they can only be described by numbers. No numbers are of more importance than those that describe proteins. The numbers that describe coordinates of its atoms, often determined by Patterson functions (which are inverse Fourier Transforms of intensities) of crystal diffraction. Without these numbers, structural biology would hardly exist. Without numbers, engineering would not exist. Numbers are surely needed by the engineers who produce the x-rays diffracting from atoms of protein crystals. Devices of engineering have function. They are built to implement equations. Engineering devices use structures to implement equations, when power is supplied at the right places, that produces appropriate flows. Flows are the essence of life. Equilibrium means death in most living systems. Flows in biological structures are hard to analyze because we do not know input output equations in advance. Sometimes we do not know the function of the structures. Flows, forces, and structures of life (like those of engineering) are related by field equations of conservation laws, partial differential equations, constrained by location and properties of structures. Constraints are boundary conditions located on the complicated domain of biological structure. The hierarchy of structures allows a handful of atoms (in proteins and nucleic acids) to control macroscopic function. Dealing with this complexity is simplified if one systematically analyzes structure using the most general field theory known, electricity described by the Maxwell equations, without significant known error. Currents are involved because flows of biology usually involve migration of charges, convection of water and solutes, diffusion of ions that form the plasma of life, and their interactions. Interactions can dominate function. Here I show how a few complex structures can be understood in engineering detail. This approach may be useful in dealing with biological and medical issues in many other cases. In one limited case—the clearance of a toxic waste (potassium ions) from the optic nerve—this approach seems to have succeeded.


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