Method of determining calibration curve and analysis method and apparatus using the same

• US 5,948,368 A
• Filed: 10/09/1997
• Issued: 09/07/1999
• Est. Priority Date: 01/09/1996
• Status: Expired due to Fees

• Current Assignee: Fuji Photo Film Co Limited (Fujifilm Holdings Corporation)
• Original Assignee: Fuji Photo Film Co Limited (Fujifilm Holdings Corporation)
• Inventors: Makino, Yoshihiko, Hirai, Kikuo
• Primary Examiner(s): Budens, Robert D.
• Application Number:
  US08/947,658
• Time in Patent Office: 698 Days
• Field of Search: 422/50, 422/62, 422/67, 422/68.1, 422/119, 436/50
• US Class Current: 422/119
• CPC Class Codes: G01N 33/48 Biological material, e.g. blood, urine G01N33/02, G01N33/26, G01N33/44, G01N33/46 take precedence; Haemocytometers counting blood corpuscules distributed over a surface by scanning the surface G06M11/02
• CPC Class Codes: G01N 33/96 involving blood or serum control standard
• CPC Class Codes: Y10S 435/967 Standards, controls, materials, e.g. validation studies, buffer systems

Abstract

One sigmoid calibration curve is split into three parts of low concentration region represented by a high degree function, intermediate concentration region represented by an exponential function and high concentration region represented by a high degree function according to the present invention. The boundary condition of the adjacent two functions is set so that the two functions have an equal slope at the boundary point; thereby, regression functions of the calibration curves in respective regions are found. The number of standard samples for finding a calibration curve can be reduced while the calibration curve found is of high accuracy.

Claims

1. An apparatus for quantitative analysis of an analyte in a sample by referring to a calibration curve prepared by using the interrelation between the known concentrations of the analyte in standard samples and analytical measured values of the standard samples, said apparatus comprising:

1) input means for inputting the known concentrations (p_i) of the analytes contained in plural standard samples and their analytical measured values (q_i);

2) a processor for receiving the data input from said input means and processing the operations mentioned below to determine a regression function of the calibration curve on the basis of the input (p_i) and (q_i), said operations including steps of;

(a) expressing the part of calibration curve of an intermediate concentration region (p₁ -p₂), which is defined as the region of linear portion in a semi-logarithmic graph in which respective concentrations (p_i) of the standard sample and the logarithmic values (log q_i) of the corresponding analytical measured values (q_i) are plotted on a rectangular coordinate system, said linear portion having the most proximate concentrations p₁ and p₂ at both ends, as

space="preserve" listing-type="equation">Y=exp (b·

X+d)

which means

space="preserve" listing-type="equation">X=(ln Y-d)/b (1)

wherein Y is the analytical measured value (q_i),

X is the concentration of the analyte in the standard sample (p_i), and

b and d are coefficients;

(b) expressing the part of calibration curve of the low concentration region (from the minimum concentration p₀ in the standard sample to concentration p₁) as

space="preserve" listing-type="equation">X=e·

Y.sup.2 +f·

Y+g (2)

wherein e, f and g are coefficients;

(c) expressing the part of calibration curve of the high concentration region (from concentration p₂ to the maximum concentration p₃ in the standard sample) as

space="preserve" listing-type="equation">X=l·

Y.sup.2 +m·

Y+n (3)

wherein l, m and n are coefficients;

(d) setting boundary conditions where the differentiated value (dX/dY) of Equation (1) at the coordinate (p₁, q₁) is equal to the differentiated value (dX/dY) of Equation (2) at the coordinate (p₁, q₁) and the differentiated value (dX/dY) of Equation (2) at the coordinate (p₂, q₂) is equal to the differentiated value (dX/dY) of Equation (3) at the coordinate (p₂, q₂); and

(e) calculating respective coefficients in Equations (1), (2) and (3) and finding therefrom the continuous regression function of the calibration curve for the whole concentration region covering from p₀ to p₃ ;

3) a calibration curve generator for generating the calibration curve to be used for quantitative analysis of the analyte contained in a test sample, the calibration curve being prepared from the regression function determined by said processor;

4) a measurement means for measuring an analytical value of the sample containing an unknown concentration of the analyte to obtain an analytical measured value; and

5) an output means for calculating and outputting the concentration of the analyte in the sample by comparing the analytical measured value of the sample and the calibration curve.

2. The apparatus of claim 1, further comprising alarm means which is activated in the event that the standard deviation of the set of measured analytical values for a known concentration of analyte exceeds a predetermined value.

3. The apparatus of claim 1, further comprising alarm means which is activated in the event that the average of the measured analytical values (qi) for one of the standard samples, excluding the standard samples having the minimum and maximum analyte concentrations, is not between the averages of the measured analytical values for the immediately preceding (qi-1) and immediately following (qi+1) standard samples, as ranked by known analyte concentration.

4. The apparatus of claim 1, further comprising alarm means which is activated in the event that, for the calculated coefficients, q₀ >

-f/(2·

e)>

q₁ or q₂ >

-m/(2·

l)>

q₃.

5. An apparatus for quantitative analysis of an analyte in a sample by referring to a calibration curve prepared by using the interrelation between the known concentrations of the analyte in standard samples and analytical measured values of the standard samples, said apparatus comprising:

1) input means for inputting the known concentrations (p_i) of the analytes contained in plural standard samples and their analytical measured values (q_i);

2) a processor for receiving the data input from said input means and processing operations to determine a regression function of the calibration curve on the basis of the input (p_i) and (q_i), said operations comprising;

(a) expressing the part of calibration curve of an intermediate concentration region (p₁ -p₂) as an exponential function, said intermediate concentration region being defined as the linear portion of a semi-logarithmic plot of respective concentrations (p_i) of the standard sample and the logarithmic values (log q_i) of the corresponding analytical measured values (q_i) on a rectangular coordinate system;

(b) expressing the part of calibration curve of a low concentration region as a multi-degree function, said low concentration region being defined as that portion of the semi-logarithmic plot from the minimum concentration (p₀) to the lower concentration end (p₁) of the intermediate region;

(c) expressing the part of calibration curve of the high concentration region as a multi-degree function, said high concentration region being defined as that portion of the semi-logarithmic plot from the higher concentration end (p₂) of the intermediate concentration region to the maximum concentration (p₃);

(d) setting boundary conditions that at the boundary points between the multi-degree functions and the exponential function, the values of the first derivative of the multi-degree function and the first derivative of the exponential function are identical; and

(e) calculating the continuous regression function by determining the identity of the functions for the intermediate, low and high concentration regions which correspond to requirements (a) through (d);

3) a calibration curve generator for generating the calibration curve to be used for quantitative analysis of the analyte contained in a test sample, the calibration curve being prepared from the regression function determined by said processor;

4) a measurement means for measuring an analytical value of the sample containing an unknown concentration of the analyte to obtain an analytical measured value; and

5) an output means for calculating and outputting the concentration of the analyte in the sample by comparing the analytical measured value of the sample and the calibration curve.

6. The apparatus of claim 5, further comprising alarm means which is activated in the event that the standard deviation of the set of measured analytical values for a known concentration of analyte exceeds a predetermined value.

7. The apparatus of claim 5, further comprising alarm means which is activated in the event that the average of the measured analytical values (q_i) for one of the standard samples, excluding the standard samples having the minimum and maximum analyte concentrations, is not between the averages of the measured analytical values for the immediately preceding (q_i-1) and immediately following (q_i+1) standard samples, as ranked by known analyte concentration.

8. The apparatus of claim 5, further comprising alarm means which is activated in the event that the continuous regression function determined in step (e) has a local minimum value or local maximum value between the values of q₀ and q₃.