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An Inverse Approach to Determine Solute and Solvent Permeability Parameters in Artificial Tissues

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Abstract

This study presents a generic numerical model to simulate the coupled solute and solvent transport in tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA; dimethylsulfoxide or DMSO). Osmotic responses of various tissue cells within the artificial tissue are predicted by the numerical model with three model parameters: Permeability of the tissue cell membrane to water (Lp), permeability of the tissue cell membrane to the solute or CPA (ω), and the diffusion coefficient of the solute or CPA in the extracellular space (D). By fitting the model results with published experimental data on solute/water concentrations at various locations within an artificial tissue, we were able to determine the permeability parameters of artificial tissue cells in the presence of 1.538 M DMSO. Lp and ω were determined at three different locations within the artificial tissue assuming a constant value of solute diffusivity (D = 1.0×10−9 m2/s). The best fit values of Lp ranged from 0.59×10−14 to 4.22×10−14 m3/N-s while ω ranged from 0 to 6.6×10−13 mol/N-s. Based on these values of Lp and ω, the solute reflection coefficient, σ = 1 − ω \(\bar v_{{\rm CPA}}\)/L p ranged from 0.9923 to 1.0. The relative values of ω and σ suggest that the artificial tissue cells are relatively impermeable to DMSO (or ω≈0 and σ≈1.0). This observation was used to modify our model to predict the values of Lp and D assuming ω = 0 and σ = 1.0. The best fit values of Lp ranged from 640×10−14 to 2.1×10−14 m3/N-s while D ranged from 0.63×10−9 to 1.52×10−9 m2/s. The permeability parameters obtained in the present study represent the first such effort for artificial tissues.

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Authors and Affiliations

  1. Bioengineering Laboratory, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, 70803

    Yimeng He & Ram V. Devireddy

  2. Department of Mechanical Engineering, 2508 CEBA Bldg., Louisiana State University, Baton Rouge, LA, 70803

    Ram V. Devireddy

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  1. Yimeng He
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  2. Ram V. Devireddy
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Correspondence to Ram V. Devireddy.

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He, Y., Devireddy, R.V. An Inverse Approach to Determine Solute and Solvent Permeability Parameters in Artificial Tissues. Ann Biomed Eng 33, 709–718 (2005). https://doi.org/10.1007/s10439-005-1511-x

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  • DOI: https://doi.org/10.1007/s10439-005-1511-x

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