Obtaining the concentration-dependent diffusion coefficient from ultrafiltration experiments: Application to hyaluronate

Abstract

A method for determining the concentration‐dependent mutual diffusion coefficient D(C) of a macromolecule‐solvent combination over a wide macromolecular concentration range is presented. All necessary data are gathered from a single experiment, in which polymer concentration profiles are measured during one‐dimensional dead‐end ultrafiltration. Based on these profiles, the convection‐diffusion equation is used to deduce the dependence of D on C. To demonstrate the utility of the approach, studies using sodium hyaluronate dissolved in either 10 mM NaCl or a phosphate buffer were carried out. For hyaluronate (HA) in 10 mM NaCl, the mutual diffusion coefficient varies approximately linearly with concentration according to D(C) = 4.1 × 10−6 C0.96 cm2/s in the range 0 ≤ C ≤ 0.6 mass %, for C expressed in mass %. However, transition points (slope changes) in the D(C) curve are present at C ≅ 0.7 mass % and C ≅ 1.4 mass %. For HA in the phosphate buffer, the mutual diffusion coefficient is well described by D(C) = 1.9 × 10−6 C0.825, for 0 ≤ C ≤ 1.8 mass %. These values agree well with previously published data. The technique is robust, and permits reasonably high polymer concentrations to be easily studied. © 1996 John Wiley & Sons, Inc.

Concentration polarization of hyaluronan on the surface of the synovial lining of infused joints

“…The adsorption of HA onto the synovial surface and clogging of synovial pores are a likely accompaniment to the ultrafiltration process, as noted in vitro (Barry et al 1996; Peppin & Elliott, 2001). In support of this in vivo , the outflow buffering curve for 2–4 mg ml −1 HA, i.e.…”

“…We then calculated the effect of an increase in the membrane reflection coefficient due to membrane fouling by HA, i.e. pore obstruction (Barry et al 1996; Peppin & Elliott, 2001). If membrane fouling raises σ to 0.98, the thickness of the HA layer increases at any given filtration rate, but the increase is minor – just a few micrometres.…”

“…Bhattacharjee et al 2001; Geraldes et al 2003). During HA ultrafiltration from an unstirred, ‘dead‐end’ compartment in vitro at low filtration velocities (∼10 −5 cm s −1 ), however, measurements showed that the steady state was not approached until ∼20–40 h (Barry et al 1996; Zhang & Ethier, 2001). In infused joints the steady state appeared to be approached over just a few hours (Coleman et al 1999; Sabaratnam et al 2003), but the accuracy of assessment of the steady state in vivo was limited by the wide standard error bars associated with biological variation (see later).…”

“…(1 − filtrate concentration)/(infusate concentration), underestimates σ, so we have assumed σ= 0.95–0.98 for the present modelling, in line with Coleman et al (1999). During HA ultrafiltration σ may change and approach even closer to 1 due to membrane fouling and pore clogging (Barry et al 1996; Peppin & Elliott, 2001).…”

“…Diffusion coefficient, D The HA diffusion coefficient changes as a function of HA concentration (Laurent et al 1960; Barry et al 1996; Gribbon et al 1999) and takes the form D = (3.93 + 4.26 C ) × 10 −8 cm 2 s −1 for HA of ∼10 6 Da, where C is in mg ml −1 (Wik & Comper, 1982). We used this relation for the HA diffusion coefficient in the concentration polarization layer.…”