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Analysis of Solution Exchange in Flow Chambers with Applications to Cell Membrane Permeability Measurement


Cell membrane permeability estimation using flow chamber experiments is susceptible to errors caused by non-negligible solution exchange time after switching of perfusate reservoirs. To prevent such confounding effects, we have undertaken theoretical and experimental analyses of the mass transport of osmotically active solutes. A diffusion-convection model was used to predict the kinetics of solution exchange as a function of Peclet number (Pe) and chamber geometry, yielding guidelines for the design of flow chambers optimized for permeability measurement. Common experimental methods for quantifying solution exchange kinetics (using transmittance or absorbance measurements) were also simulated, and found to be associated with significant error. We therefore used a confocal microscopy technique to validate the dependence of solute exchange kinetics on Pe; the solution exchange time was negligible for flow rates with Pe > 106. A fluorescence quenching method was used to estimate the membrane water permeability (L p) of mouse insulinoma (MIN6) cells in adherent monolayer cultures, yielding L p A/V w0 = (4.4 ± 0.1) × 10−8 Pa−1 s−1 (where A/V w0 is the ratio of cell surface area to isotonic water volume).

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a :

Fluorescence quenching constant

A :

Cell membrane surface area

C :

Solute concentration

\( \tilde{C} \) :

Nondimensional solute concentration

D :

Solute diffusivity

\( \tilde{F} \) :

Nondimensional cell fluorescence

h :

Half-thickness of flow chamber

\( \tilde{h} \) :

Flow chamber aspect ratio

L p :

Cell membrane water permeability

m :


M :

Final node in the discretized \( \tilde{x} \)-domain

N :

Final node in the discretized \( \tilde{y} \)-domain

Pe :

Peclet number

r :

Radial coordinate

\( \tilde{r} \) :

Nondimensional radial coordinate

R :

Tube radius


Ideal gas constant

t :


t rise :

Rise time

\( \tilde{t} \) :

Nondimensional time

T :

Absolute temperature

u max :

Maximum velocity in x-direction

u x :

Velocity in x-direction

V w :

Cell water volume

\( \tilde{V} \) :

Nondimensional change in cell volume

x :

Horizontal distance from channel inlet

x c :

Site where cell response is measured

\( \tilde{x} \) :

Nondimensional x-coordinate

\( \tilde{x}_{\infty } \) :

Nondimensional far-field boundary

y :

Vertical distance from channel midline

\( \tilde{y} \) :

Nondimensional y-coordinate

α :

Coefficient in empirical correlation

β :

Exponent in empirical correlation

γ :

Coefficient in empirical correlation

ε :

Extinction coefficient



\( \tilde{\Uptheta } \) :

Nondimensional absorbance


Osmotic pressure

ρ :

Relative opacity



\( \tilde{\Upomega } \) :

Nondimensional transmittance

i :

Intracellular, or index in the \( \tilde{x} \)-domain

j :

Index in the \( \tilde{y} \)-domain (or \( \tilde{r} \)-domain)


Extracellular, or equilibrium



k :

Index in the \( \tilde{t} \) domain




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This work was supported in part by the National Science Foundation (NSF) under awards CBET-0541530 and CBET-0954587 (to JOMK), as well as the Georgia Tech/Emory Center for the Engineering of Living Tissues, an NSF Engineering Research Center (EEC-9731643). Fellowship support (for AZH) was provided by the NSF, the Howard Hughes Medical Institute, the Medtronic Foundation and the George Family Foundation.

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Correspondence to Jens O. M. Karlsson.

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Associate Editor Edward Guo oversaw the review of this article.

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Higgins, A.Z., Karlsson, J.O.M. Analysis of Solution Exchange in Flow Chambers with Applications to Cell Membrane Permeability Measurement. Cel. Mol. Bioeng. 3, 269–285 (2010).

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  • Parallel-plate flow chamber
  • Fluorescence quenching
  • Osmosis
  • Water transport
  • Hydraulic conductivity
  • Beta cell