Optic nerve microcirculation: Fluid flow and electrodiffusion

Zhu, Yi; Xu, Shixin; Eisenberg, Robert S.; Huang, Huaxiong

doi:10.1063/5.0046323

Cited by 11 publications

(29 citation statements)

References 91 publications

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“…I present here the precise specification of the electrical part of the tridomain model 338 lest an important detail be inadvertently omitted. Presenting the precise specification of the flow part of the tridomain would be too much for this paper.…”

Section: Optic Nerve Of the Amphibian Salamandermentioning

confidence: 99%

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Structural analysis of fluid flow in complex biological systems

Eisenberg

2023

MAIO

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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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Section: Optic Nerve Of the Amphibian Salamandermentioning

confidence: 99%

“…It is also not necessary: the material is presented in complete detail in the overlapping publications. 167,302,338,339 The many pages devoted to validation and calibration are of particular importance, although not presented here because of space limitations.…”

Section: Optic Nerve Of the Amphibian Salamandermentioning

confidence: 99%

Structural analysis of fluid flow in complex biological systems

Eisenberg

2023

MAIO

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“…Presenting the precise specification of the flow part of the tridomain would be too much for this paper. It is also not necessary: the material is presented in complete detail in the overlapping publications (167,302,338,339). The many pages devoted to Validation and Calibration are of particular importance although not emphasized here.…”

Section: Optic Nerve Of the Amphibian Salamandermentioning

confidence: 99%

“…For the extracellular space boundary condition, similar boundary conditions are imposed except on the pia matter Γ 7 . The flux across the pia matter is assumed continuous and Ohm's law is used (338) The symbol Δf is used to denote the variation of the variablef from its resting state. Multiplying the equations (23)(24)(25) with 𝑧 𝑖 𝑒 respectively, summing up, and using the charge neutrality condition, we have the following system for the electric fields in 𝑎𝑥, 𝑔𝑙, 𝑒𝑥,…”

Section: Ion Transport We Define the Regionsmentioning

confidence: 99%

“…This concludes the formal presentation of this component of the tridomain model. The rest is found in the original overlapping papers (167,302,338,339) and the entire model, and its components, are validated and calibrated at length in those publications. To repeat: the validation and calibration are at least as important as the derivation.…”

Section: Ion Transport We Define the Regionsmentioning

confidence: 99%

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Structural Analysis of Fluid Flow in Complex Biological Systems

Eisenberg¹

2022

Preprint

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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 their function. 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. 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.

show abstract