Each set of calibration solutions is measured using the spectrometric system to be employed recording absorbance readings for key wavelengths. This process should be done with several replicates using multiple different instruments to allow for inter- instrument spectrophotometer variability and lot differences between the calibration materials. Because of the spectrophotometer differences and according to Beer’s Law (A = abc), where path length affects absorbance, interference indices are not transfer- able between different types of instrument.
An important part of developing the index calibration is to account for absorb- ance of other interferences at the selected measurement wavelength(s). Detection of turbidity is simplified because hemoglobin and bilirubin do not absorb at wave- lengths above 700 nm. However, for calibration of the icterus index, absorbance readings should be taken at at least 2 wavelengths because hemoglobin (hemolysis) and turbidity (lipemia or particulate matter) both absorb light across the absorbance spectrum of bilirubin (340–500 nm). There are two main approaches to handling the absorbance of other interferences across the light spectrum. One is to account for the contribution of hemolysis and turbidity by measuring the absorbance of the standards at selected wavelengths and subtracting these from the total absorbance at the wavelength(s) used to measure icterus. Alternatively, indices may be calculated directly from the measurement of absorbance across a continuous spectrum of wave- lengths using derivative spectrometry.
10.2.2.1 Subtraction Using Selected Wavelengths
The selected wavelength subtraction approach relies on measurement of absorb- ance of the 3 sets of standards (hemolysate, bilirubin and Intralipid®) at 2–3 dif- ferent selected wavelengths. If the icterus index method relies on the peak absorb- ance of bilirubin at 454 nm, then additional wavelengths could include 550 nm for hemolysate and 700 nm for turbidity. The absorbance of hemolysate at 550 nm is plotted against the absorbance of hemolysate at 454 nm and a polynomial regression is applied (Fig. 10.2). In this example, a 2nd order polynomial regression is used; H0, H1, H2 are constants determined by the regression and A550 or A454 is the absorbance of the hemolysate at the specified wavelength.
(10.1) HemolysateA454=H0+H1ãA550+H2ãA5502
0.8
0.6
0.4
0.2
0 0
hemolysate absorbance (at 550 nm)
0.5 1.0 1.5 2.0
hemolysate absorbance (at 454 nm)
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 0
turbidity absorbance (at 700 nm)
0.5 1.0 1.5 2.0
turbidity absorbance (at 454 nm)
Fig. 10.2: Hemolysate and turbidity absorbances at peak wavelengths plotted against absorbance at the wavelength used for determination of icterus (454 nm). Polynomial regressions are used to calculate corrections factors.
10.2 Generating Interference Indices 105
Similarly, the absorbance of Intralipid® at 700 nm is plotted against the Intralipid® absorbance at 454 nm again applying a polynomial regression (Fig. 10.2), where T0, T1, T2 are constants determined by the regression.
(10.2)
For detection of icterus at 454 nm, the sum of HemolysateA454+TurbidityA454 is equal to the total absorbance contributions of hemolysate and turbidity at 454 nm. This sum is then subtracted from the absorbance at 454 nm, yielding the concentration of icterus alone. Thus, by measuring samples at these 3 wavelengths (454, 550, 700 nm) the interference index for icterus is corrected for contributions of hemolysis or tur- bidity when present. In the absence of these other interferences, the values of these correction factors are negligible. Note that Equations 1 and 2 are both 2nd order poly- nomials, which were determined to be the best fit for the example data. The best fit for regression data is determined empirically with each experimental dataset and may range from simple 1st order polynomials (y = a0 + a1x) to more complex 3rd order (y = a0
+ a1x + a2x2 + a3x3) equations. These equations are simply a tool to calculate and sub- tract the contribution of a given interferent to the absorbance at another wavelength.
10.2.2.2 Index Calculation Using Derivative Spectrometry
Another option to handle the absorbance contributions of different interferences across the light spectrum is to use derivative spectrometry. Derivative spectrometry refers to transforming the absorbance readings over a range of wavelengths with a 1st derivative. The basis for this approach is that substances with overlapping absorb- ance spectra, such as hemoglobin and bilirubin, can be differentiated by using the derivatives in combination with the extinction coefficients. Thus, measurement of interferences using derivative spectrometry effectively replaces the need for subtrac- tion. Fig. 10.3 shows the absorbance spectra and 1st derivatives for hemolysate, biliru- bin, and turbidity.
With this approach, the absorbance of each standard is recorded across the rel- evant range of wavelengths. For hemolysis and icterus this range is ~400–800 nm.
Again, because hemoglobin and bilirubin do not absorb at >700 nm, turbidity meas- urement is somewhat simplified (discussed below). For icterus absorbance readings, the extinction coefficient (ε) can be calculated according to Beer’s Law for each wave- length where the concentration of interference added is known and the path length (l)=1 using the following equations.
Extinction coefficient at 1st Wavelength:
(10.3) TurbidityA454=T0+T1ãA700+T2ãA7002
"1 =A1/c1
Extinction coefficient at 2nd Wavelength:
(10.4)
Extinction coefficient at nth Wavelength:
(10.5)
Extinction coefficients are thus calculated for interferences at each measured wave- length. With the extinction coefficients computed, the concentration of each interfer- ent can be calculated using the vector dot product of the derivative of the absorbance
"2 =A2/c1
"n =An/c1.
0 앥0.01 앥0.02 앥0.03 앥0.04
absorbance
2.5 2.0 1.5 1.0 0.5 0
400 500 600 turbidity
800 wavelength (nm)
300 700
absorbance
2.0 1.5 1.0 0.5 0 앥0.5
400 500 600 hemoglobin
800 wavelength (nm)
300 700
absorbance
2.0 1.5 1.0 0.5 0
앥0.5 400 500 600 bilirubin
800 wavelength (nm)
300 700
400 500 600 turbidity 1st derivative
800 wavelength (nm)
300 700
dA/dl
0.10 0.08 0.06 0.04 0.02 0 앥0.02 앥0.04
400 500 600 hemoglobin 1st derivative
800 wavelength (nm)
300 700
0.03 0.02 0.01 0 앥0.01 앥0.02 앥0.03 앥0.04
400 500 600 bilirubin 1st derivative
800 wavelength (nm)
300 700
dA/dldA/dl
Fig. 10.3: Hemoglobin, bilirubin, and turbidity absorbance curves and first derivatives.
10.2 Generating Interference Indices 107
and the extinction coefficient. The equation to calculate the vector dot product for icterus is as follows:
Icterus =dA d
ã["]Icterus (10.6)
The vector dot product is summed for all measured wavelengths as follows:
(10.7)
The use of the derivative effectively accounts for the absorbance of other interfer- ences, eliminating the need for subtraction. Currently, few manufacturers employ this creative approach.