Diffusivity of ions in agarose gels and intervertebral disc: Effect of porosity

Wei Yong Gu, Hai Yao, Adriana L. Vega, Daniel Flagler

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


The effect of tissue porosity on ion (sodium, potassium, and chloride) diffusivity in agarose gels and porcine intervertebral disc tissues was investigated using an electrical conductivity method. An empirical, constitutive model for diffusivity (D) of solutes in porous fibrous media was proposed: D/D o = exp[-α(r s1/2) β] where r s is the Stokes radius of a solute, κ is the Darcy permeability of the porous medium, D o is the diffusivity in free solution, α and β are two positive parameters whose values depend on material structure. It is found that α = 1.25 ± 0.138, β = 0.681 ± 0.059 (95% confidence interval, R 2 = 0.92, n = 72) for agarose gels and α = 1.29 ± 0.171 and β = 0.372 ± 0.088 (95% confidence interval, R 2 = 0.88, n = 86) for porcine annulus fibrosus. The functional relationship between solute diffusivity and tissue deformation was derived. Comparisons of our model prediction with experimental data on diffusion coefficients of macromolecules (proteins, dextrans, polymer beads) in agarose gels in the literature were made. Our results were also compared to the data on ion diffusivity in charged gels and in cartilaginous tissues reported in the literature. There was a good agreement between our model prediction and the data in the literature. The present study provides additional information on solute diffusivity in uncharged gels and charged tissues, and is important for understanding nutritional transport in avascular cartilaginous tissues under different mechanical loading conditions.

Original languageEnglish (US)
Pages (from-to)1710-1717
Number of pages8
JournalAnnals of biomedical engineering
Issue number12
StatePublished - Dec 2004


  • Agarose gel
  • Annulus fibrosus
  • Diffusion coefficient
  • Electrical conductivity
  • Intervertebral disc
  • Ion diffusion
  • Tissue porosity

ASJC Scopus subject areas

  • Biomedical Engineering


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