22
WIRE MYOGRAPH SYSTEM - 620M
- USER GUIDE
APPENDIX 2 - NORMALIZATION THEORY
The importance of making a normalization before initiating an experiment with any tubular tissue segment is described in chapter
3.2. In this appendix the mathematical rationale and calculations underlying the normalization procedure are described in detail.
Mathematical calculations
Let (X
i
, Y
i
) be the pair of values representing the micrometer reading (see appendix 3) and force reading respectively character-
izing each step in the normalization procedure. Y
0
is the force reading at the start position of the normalization procedure where
the wires are just separated and the force reading is approximately zero. Then, given that tension on the vessel is equal to force
divided by wall length, the wall tension at the i-th micrometer reading is calculated by:
T
i
=
(Y
i
– Y
0
)
2δ • (a
1
– a
2
)
where δ is the microscope eyepiece reticule calibration factor in mm per division and a
1
and a
2
are the vessel end points when
measuring the length of the mounted vessel segment.
The internal circumference of the mounted vessel at the i-th reading is calculated by:
IC
i
= IC
0
+ (2•(X
i
– X
0
))
where IC
0
is the internal circumference of the mounted vessel when the wires are just separated and is given by:
IC
0
= (2 + ) • d
where d is the wire diameter. For 40 µm wires, IC
0
= 205.6 µm.
Using the Laplace relation, the effective pressure P
i
is calculated for each pair of readings. The effective pressure is an estimate
of the internal pressure, which is necessary to extend the vessel to the measured internal circumference.
P
i
=
T
i
IC
i
2
( )
The stepwise distension is continued until the calculated effective pressure exceeds the target transmural pressure. The target
value needs to be optimized for the individual tissue preparation (optimal active force as determined by the length-tension rela-
tionship for that tissue). For rat mesenteric arteries the target transmural pressure is normally 100 mmHg (13.3 kPa):
T
100 mmHg
= 100 mmHg•
IC
2
( (
An exponential curve is fitted to the internal circumference pressure data as illustrated in figure 3.9. Now the isobar correspond-
ing to 100 mmHg is used to calculate the IC
100
value from the point of interception between the function of the exponential curve
and the function of the 100 mmHg isobar.
The normalised internal circumference IC
1
is calculated by multiplying the internal circumference corresponding to 100 mmHg,
IC
100
, by a factor k. The factor is for rat mesenteric arteries 0.9. Again, this value should be optimized for the particular tissue
preparation being used by a length-tension curve.
IC
1
= k •IC
100
APPENDIX 2
