LUMAT LB 9507 - A.1 Mathematical Basis

Appendix LB 9507
2
A.1 Mathematical Basis
A.1.1 Overview of the Mathematical Data Reduction
This chapter provides an overview of the LIA data reduction which
is performed after the measurement of a full standard curve. The
following steps take place one after another:
1. The ZERO concentration factor ”f” is calculated if the first
standard concentration = 0. This factor represents part of the
2nd, non-zero standard, so that the entire curve forms a
nearly straight line in the transformed area (see below).
Thus, one gets a correct linear curve at the low end. See the
formula for calculation of the factor on page 5, A.1.3).
2. Calculation of the optimum B
max
for logit-log transformation, if
defined in the protocol. It is optimized in accordance with the
requirement of having no saturation at the high RLU end of
the curve, for both LIA and ILMA types.
The logit-log transformation typically results in a raising of the
curve when B
max
is very close to the highest B
n
or B
0
value,
respectively. This is counterbalanced according to the
equation for the variable B
max
value on page 7, A.1.5.
3. All standard RLU mean values B
i
and entered concentration
values are now transformed in the logit-log range with the
usual normalization of
(B
i
- NSB) / (B
max
- NSB)
where NSB could also be = 0, i.e. for all concentrations C
i
in
c
i
and B
i
in b
i
as:
c
i
= log (f * C
1
+ C
i
)
and
b
i
= logit (B
x
- NSB) / (B
max
- NSB)