Hitachi F 2500 Manual

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(2)  Remeasurement of Standards 
 
The standards can be remeasured after once preparing a 
calibration curve.    The curve prepared in such case will 
appear as in Fig. A-4. 
 
 
Fig. A-4    Calibration Curve when Standards are Remeasured 
 
 
STD5 Redrawn 
calibration curve
STD6
STD4
STD3
STD2
STD1
Data 
Initially 
measured STD1
CONC
 
Remeasured 
STD1
  
						

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APPENDIX B    DETAILS OF RATE ANALYSIS FUNCTION 
 
 
B.1 Foreword 
 
Rate analysis is used in the analysis of enzyme reactions.    It is 
utilized for clinical and biochemical tests by reagent 
manufacturers, hospitals and so on.    A computer is used to 
calculate the concentration from the variation in data per unit 
time, and the result is displayed and printed out. 
 
B.2 Calculation Method 
 
A timing chart for rate analysis is shown in Fig. B-1.    Data is 
acquired when the initial delay time has elapsed after pressing 
the Measure button.    A regression line is determined from this 
data via the least squares method, and the gradient and activity 
value are calculated.    The calculation formula is as follows. 
 
 
Data :    A0, A1, A2, A3, A4… 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. B-1 
 
Td  :  Initial delay time 
Tm  :  Measurement time 
Tc  :  Sampling interval 
Tt  :  Calculation time
 
Data
Time
 
Td Tc 
Tt
Tm 
Start of 
measurement
 
A1 
A5 
A4 
A3 
A2 
A6
A7 
A0  
						

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Prepare a regression line via least squares method from the 
measured data, and obtain a determination coefficient. 
y = ax + b 
where, 
a = 
()
xyxy
n
xx
niiii
ii−∑ ∑
∑
−∑
∑
22
 b = ()yax
nii−∑
∑* 
x
i :    Time (sec) of each data 
y
i :    Value of each data 
n :    Number of samples 
 
The determination coefficient CD becomes as follows : 
CD = 
()
()
}()} { {∑∑∑−
∑ −∑∑∑−2
i 2
i 2
i 2
i2
i i i iy y n x x ny x y x n
 
 
  Gradient (variation per minute) 
D
i = a
Tk  = 60a (/min) 
 
 Activity 
C
i = k · Di 
 
  R (determination coefficient) 
R = 
CD = ()
()
}()}{
nxy x y
nx x ny yii i i
ii ii−
∑ ∑ ∑
−
∑−
∑ ∑ ∑ 

2
22
22
 
 
 R2 
R2 = (R)
2 = ()
()
}()}{
nxy x y
nx x ny yii i i
ii ii−
∑ ∑ ∑
−
∑−
∑ ∑ ∑ 

2
22
22
 
 
NOTE : If the range for rate calculation does not coincide with 
the actual measured data range, then use only the 
measured data within that range for the calculation. 
  
						

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APPENDIX C  DETERMINATION COEFFICIENT OF   
CALIBRATION CURVE 
 
C.1  Calculation of Determination Coefficient 
 
The determination coefficient and other factors are calculated via 
the following formula. 
 
 
 
 
 
 
 
 
 
 
 
 
An  :  Photometric or average value of standards 
Cn  :  Concentration on approximation curve 
versus A 
Cstdn :  Concentration of standard (input value) 
N  :  Number of standards 
 
DIFF  :  DIFFn = Cn - Cstdn 
RD  :  RD
n = DIFF
A×100 
     
AA
Nn=∑ 
t  :  t
n = DIFF
DIFF
Nn
2
1 ∑
−
 
Determination coefficient  :  R = 
()()
()
CC CC
CCnnstdn
n−− −
∑ ∑
−
∑2
2
2
, 
     R
2 = (R)2 
 
 
 
A3A2
A1
Data
   C1 C2 C3 
  Cstd1  Cstd2   Cstd3Conc  
						

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C.2  Usage of Determination Coefficient 
 
The determination coefficient indicates the goodness of fit of the 
measured standards and the prepared calibration curve.     
The closer this value is to “1”, the better the fit of the measured 
values and calibration curve.    If the value is far from “1”, then 
the standards must be remeasured or the calibration curve mode 
must be changed.    Examples of determination coefficients upon 
changing the calibration curve mode are given below. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
With the above standard data, it can be seen that a quadratic 
curve provides a better result.    A calibration curve, which was 
formerly judged through skill or experience, can thus be judged 
more easily through numerical means. 
 
Data
x :  standard measurement 
points 
When calibration curve type is 
set to linear, 
determination coefficient < 1 
Conc
Data
Conc
When calibration curve type is 
set to quadratic, 
determination coefficient ≒ 1  
						

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APPENDIX D  INTEGRATION METHOD 
 
D.1 Foreword 
 
The integration methods used in the FL Solutions program are 
explained next. 
 
D.2 Integration Methods 
 
The following three methods are available in the FL Solutions 
program. 
 
 Rectangular 
 Trapezoid 
 Romberg 
 
The rectangular method is the simplest one among the above 
three.    Since one sampling cycle is equivalent to the width of 
each sectional area, the total of all data points including peaks 
approximates the area to be obtained. 
The object area shown in Fig. D-1 is the total of the rectangular 
sections obtained from linear approximation of the curve drawn 
via the data points.    If a peak has few data points, the 
approximation will be a rough estimate. 
 
 
Fig. D-1 
 
 
D.2.1 Rectangular 
Method
  
						

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This method is a further improvement on peak area calculation.   
The section of each sampling cycle is indicated by a rectangle on 
which a triangle is formed.    The object area is the sum of all 
these areas. 
 
 
Fig. D-2 
 
By taking just one rectangle, the area of the rectangular part I
r is 
expressed by the following formula. 
 
Fig. D-3 
 
A triangular part is added to this rectangle.    Assuming the area 
of this component is I
T and the area of the triangular part is It, we 
obtain the following : 
I
T = It + Ir = ff
xfxff
x21
112
22−
+=+

 
  
Considering this with respect to the whole area, we obtain : 
D.2.2 Trapezoid 
Method
 
x
f2
f1 
Ir = f1x 
where,  x  :  Sampling interval
f
1  :    Height on left side
of rectangle
  
						

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IT = f
fff
xnn 1
2122+++ + 
 
 K  
						

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The Romberg method is the most accurate of the three methods 
discussed here.    The trapezoid method provides different step 
sizes (sampling intervals) for area determination with high 
accuracy.    In this method based on the sum of errors, two 
different step sizes for individual cases are available.     
However, unlike the conventional (classic) method of continuous 
approximation, an arbitrary decrease in step size is not allowed 
(as in case of an increase in the X-axis direction) for the purpose 
of accurate integration.      This is because the data points that 
define the spectrum are handled as average data.    Still, an 
increase in step size can be made using two or four factors if this 
is necessary for applying the Romberg method.    The Romberg 
method will take the following form. 
 
(1)  Integration is made via trapezoid method per data point. 
 
(2)  Integration is made via trapezoid method per two data 
points. 
 
(3)  By combining the above two results, the following formula is 
obtained. 
 
 I
R = In + IInn2
3 
where, I
R = Integration by Romberg method 
I
n = Trapezoid integration per data point 
I
2n = Trapezoid integration per 2 data points 
 
 
D.2.3 Romberg 
Method
  
						

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APPENDIX E    DESCRIPTION OF FLUOROMETRY 
 
E.1  Description of Fluorometry 
 
 
 
 
 
 
Fig. E-1    Typical Organic Molecular Energy Level 
 
Figure E-1 illustrates the energy level transitions in an organic 
molecule in processes of light absorption and emission. 
When light strikes an organic molecule in the ground state, it 
absorbs radiation of certain specific wavelengths to jump to an 
excited state.    A part of the excitation (absorbed) energy is lost 
on vibration relaxation, i.e., radiationless transition to the lowest 
vibrational level takes place in the excited state. 
 
Excitation
Fluorescence/ 
phosphorescence
Stable stage 
(Ground state)Unstable stage 
(Excited state)
 
Excited triplet state
3
2
1
Ground state V = 0
PhosphorescenceAbsorptionFluorescence
LightLight
3
2
1
Excited state V = 0
Radiationless 
transition
 
Radiationless 
transition
 
Excitation light