WPI EVOM - Appendix D: Resistance Calculations; Resistance; Unit Area Resistance

46 World Precision Instruments
APPENDIX D: RESISTANCE CALCULATIONS
Resistance
The value of the blank (control well) always adds to the total resistance measured
across a tissue culture membrane. The blank resistance must be measured and then
subtracted from the resistance reading across the tissue in order to obtain the true
tissue resistance. For example, suppose the resistance through a 0.15 M KCl solution
and across the membrane support (with no tissue present) of a 12-well cell culture
insert measures 130 Ω. This is the blank or control reading for that cell culture insert.
(Resistance may vary for culture cups made by other manufacturers.) In this example,
using 800 Ω as the sample measurement, the calculated resistance for the tissue itself
(R tissue) is:
R
Total
= 800 Ω
R
blank
= 130 Ω
R
blank
+ R
true tissue
= R
Total
R
true tissue
= R
Total
- R
blank
R
true tissue
= 800 Ω - 130 Ω = 670 Ω
Unit Area Resistance
As the resistance is inversely proportional to the area of the tissue, instead of
reporting resistance, typically the product of the resistance and the area is calculated
and reported. The unit area resistance is independent of the area of the membrane
used and may be used to compare data obtained from inserts of dierent sizes.
The unit area resistance is obtained by multiplying the meter readings by the eective
surface area of the lter membrane. The dimension is Ω-cm
2
. The resistance is
inversely proportional to the surface area. Thus, the larger the membrane, the lower
the resistance.
Resistance of a unit area = Resistance (Ω) x Eective Membrane Area* (cm
2
)
* See manufacturing specications for the particular insert
Unit Area = 1 cm
2
The unit area resistance is independent of the area of the membrane used and may
be used to compare data obtained from inserts of dierent sizes.
Continuing with the previous example, in which the R
true tissue
= 670 Ω, if an eective
membrane diameter (d) was 6.5 mm, the unit area resistance would be:
Resistance x Eective Membrane Area = 670 Ω * π r
2
= 670 Ω * 3.14* 3.25* 3.25 / 100