The application of practical Kedem-Katchalsky equations in membrane transport

Jarzyńska, Maria

doi:10.2478/s11534-006-0034-x

Cited by 7 publications

(10 citation statements)

References 13 publications

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“…These two effects are modelled by the transfer functions (see e.g. [ 37 ]) where this time in which P i , j is the permeability of the membrane separating the i −th and j −th compartments to the solute and σ reflect reflects the solvent-drag reflection coefficient.…”

Section: Methodsmentioning

confidence: 99%

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

Poulain

Riseth²,

Vinje³

2023

PLoS ONE

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The glymphatic system is the subject of numerous pieces of research in biology. Mathematical modelling plays a considerable role in this field since it can indicate the possible physical effects of this system and validate the biologists’ hypotheses. The available mathematical models that describe the system at the scale of the brain (i.e. the macroscopic scale) are often solely based on the diffusion equation and do not consider the fine structures formed by the perivascular spaces. We therefore propose a mathematical model representing the time and space evolution of a mixture flowing through multiple compartments of the brain. We adopt a macroscopic point of view in which the compartments are all present at any point in space. The equations system is composed of two coupled equations for each compartment: One equation for the pressure of a fluid and one for the mass concentration of a solute. The fluid and solute can move from one compartment to another according to certain membrane conditions modelled by transfer functions. We propose to apply this new modelling framework to the clearance of 14C-inulin from the rat brain.

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Section: Methodsmentioning

confidence: 99%

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

Poulain

Riseth²,

Vinje³

2023

PLoS ONE

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“…The oxygen exchanges include diffusion and advection through the microvascular wall, as a semi-permeable membrane [55]: where is the microvascular wall permeability.…”

Section: Methodsmentioning

confidence: 99%

Microvascular morphology affects radiotherapy outcomes: a computational study

Possenti,

Vitullo,

Cicchetti

et al. 2023

Preprint

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Radiotherapy (RT) is the most common cancer treatment, and hypoxia is one of the main causes of resistance to RT. We investigate how microvascular morphology affects radiation therapy results, exploring the role of the microvasculature. Several computational models have been developed to analyze microvascular oxygen delivery. However, few of these models have been applied to study RT and the microenvironment. We generated 27 different networks, covering 9 scenarios defined by the vascular density and the network regularity. Leveraging these networks, we solved a computational mixed-dimensional model for fluid flow, red blood cell distribution, and oxygen delivery in the microenvironment. Then, we simulated a fractionated RT treatment (30 × 2GyRBE) using the Linear Quadratic model, accounting for oxygen-related (OER) modifications by two different models from the literature. First, the analysis of the hypoxic volume fraction and its distribution reveals a correlation between hypoxia and treatment outcome. The study also shows how vascular density and regularity are essential in determining the success of treatment. Indeed, in our computational dataset, an insufficient vascular density or regularity is sufficient to decrease the success probability for photon-based RT. We also applied our quantitative analysis to hadron therapy and different oxygenation states to assess the consistency of the microvasculature’s role in various treatments and conditions. While proton RT provides a Tumor Control Probability similar to photons, carbon ions mark a clear difference, especially with bad vascular scenarios, i.e., where strong hypoxia is present. These data also suggest a scenario where carbon-based hadron therapy can help overcome hypoxia-mediated resistance to RT. As a final remark, we discuss the significance of these data with reference to clinical data and the possible identification of subvoxel hypoxia, given the size similarity between the computational domain and the imaging voxel.

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“…To describe how the oxygen is delivered to the tissue, the flux φ O2 has to be detailed. We model the vascular wall as a semipermeable membrane, see for example, [25]. As a result, the total oxygen flux across the membrane can be split into the sum of diffusive flux, φ dif f O2 , and convective flux, φ adv O2 , namely…”

Section: Oxygen Transfermentioning

confidence: 99%

A Mesoscale Computational Model for Microvascular Oxygen Transfer

et al. 2021

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We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneity of oxygenation in the tissue microenvironment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy.

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The application of practical Kedem-Katchalsky equations in membrane transport

Cited by 7 publications

References 13 publications

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

Microvascular morphology affects radiotherapy outcomes: a computational study

A Mesoscale Computational Model for Microvascular Oxygen Transfer

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