JP2018096850A - Quantitative and correction method by polynomial calibration curve - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simplify a quantitative operation by a polynomial calibration curve in chromatography, and enlarge the quantitative range while keeping the quantitative accuracy and reliability.SOLUTION: A creation method of a polynomial calibration curve in chromatography includes: a process of approximating calibration points plotted using a concentration x and an output value y in a quadratic equation or cubic equation, and plotting the calibration points until the approximation equation becomes a simple increasing function; and a process of determining the upper limit of an output value by multiplying a maximum value of the simple increasing function by a constant number less than one or by multiplying a maximum output value of the calibration points by a constant number of one or more.SELECTED DRAWING: None

Description

  The present invention relates to a method of correcting a chromatographic polynomial calibration curve, and relates to a method for simplifying daily quantitative operations and improving accuracy.

  Chromatography is a technique for qualitative analysis and quantitative analysis of a plurality of target components. The qualitative analysis is generally performed by measuring a standard sample in advance and checking whether or not the elution time matches the standard sample. In quantitative analysis, standard samples with different concentrations are prepared, chromatographed, a calibration curve is created based on the detector output (peak height, area, etc.) against the concentration, and the concentration of the unknown sample is determined based on it. To do. The calibration curve is formulated by creating an approximate expression for the output (peak height, area, etc.) with respect to the concentration using the least square method or the like.

  When the concentration range of the quantitative target component is wide, a phenomenon in which the slope of the calibration curve slightly decreases on the high concentration side is often observed. In addition, on the low concentration side, the recovery rate of the target component is lowered, and similarly, a phenomenon that the slope of the calibration curve is slightly reduced is often observed. In such a case, since the error becomes large in the approximation by the linear expression, a calibration curve approximated by a polynomial such as a quadratic expression or a cubic expression is used. When a polynomial is used, the calibration curve becomes a curve, and naturally it cannot be created with a standard sample of one concentration. It is indispensable to create a calibration curve using a plurality of standard samples having different concentrations, and there is a problem that a lot of work is required.

  In the case of the primary expression, since the concentration and the output (peak height, area, etc.) are in a completely proportional relationship, the calibration value for the output (peak height, area, etc.) of the unknown sample is always one. When a polynomial is used, the calibration value for the output (peak height, area, etc.) of the unknown sample is not necessarily one. If there are two or more calibration values for the output (peak height, area, etc.) of an unknown sample, it is difficult to determine which is a true quantitative value. Further, in the vicinity of the extreme value, the amount of change in the output (peak height, area, etc.) with respect to the concentration becomes extremely small (the primary differential value approaches 0), making it difficult to ensure quantitative accuracy and reliability.

  An object of the present invention is to simplify a quantitative operation using a polynomial calibration curve in chromatography, and to extend a quantitative range while ensuring quantitative accuracy and reliability.

The present invention is a method for creating a polynomial calibration curve in chromatography,
A step of approximating a calibration point plotted with concentration x and output value y as a quadratic or cubic equation, and plotting the calibration point until the approximate equation becomes a simple increase function;
Multiplying the maximum value of the simple increase function by a constant less than 1 or multiplying the maximum output value of the calibration point by a constant of 1 or more to determine the upper limit of the output value;
It is characterized by comprising.

In the present invention, a standard sample having a specific concentration x ₀ is measured by chromatography, and a ratio between the obtained output value y ₀ and the output value with respect to the concentration x ₀ calculated by the approximate expression is calculated, The method may further include a step of approximating a correction output value obtained by multiplying the output value of the calibration point by the ratio by a quadratic expression or a cubic expression.

  Then, the approximate expression that approximates the corrected output value is multiplied by a constant less than 1 to the maximum value of the simple increase function, or the maximum output value of the corrected output value is multiplied by a constant of 1 or more, and the upper limit of the output value. May be further included.

  Details of the present invention will be described for each procedure. In addition, the flowchart showing the procedure of fixed_quantity | assay using a calibration curve is shown in FIG.

(Step 1)
First, a standard sample having a plurality of concentrations is measured, and output values (peak height, area, etc.) with respect to the concentration are obtained. Polynomial approximation is performed by the least square method, and a standard calibration curve (hereinafter sometimes simply referred to as a calibration curve) is created.

(Step 2)
Next, the shape of the approximate expression is specified from the coefficient a of the polynomial, the coordinates of the extreme values (p, q), and the value of the discriminant D, and the upper limit of quantification is determined. When the polynomial is a quadratic expression, if the coefficient a <0, the shape having the maximum value is taken (see FIG. 1). If the coordinates of the local maxima are not positive (p, q), the created calibration curve is not a simple increase function, so it is judged abnormal and an instruction is given to prompt remeasurement, etc., and the calibration point plot is increased or abnormal. Correct the plot of the calibration point that seems to be a value (hereinafter, the response when it is determined to be abnormal is the same). When the coordinates of the maximum value are both positive (p, q), it is determined that the created calibration curve is normal, and the upper limit of quantification is determined. The upper limit of quantification is calculated by multiplying the q coordinate of the maximum value by the coefficient f1. The coefficient f1 may be less than 1, and is not particularly specified. However, as the coefficient f1 is closer to 1, the quantification accuracy becomes worse, and when the value is decreased, the quantification range is narrowed. Therefore, a value of about 0.6 to 0.95 is obtained. Desirable (see FIG. 3a).

  If the coefficient a> 0, a shape having a minimum value is taken (see FIG. 2). When the minimum value coordinate p is not negative, the created calibration curve is determined to be abnormal. When the coordinate p of the minimum value is negative, it is determined that the created calibration curve is normal, and the quantitative upper limit value is determined. The upper limit of quantification is calculated by multiplying the y value of the calibration point of the maximum concentration by the coefficient f2. The coefficient f2 may be 1 or more, and is not particularly specified. However, the larger the value, the lower the reliability of quantification, and the smaller the value, the narrower the quantification range. A value is desirable (see FIG. 3b).

  Table 1 is a table showing a list of the shape of the secondary equation and the upper limit of quantification obtained by the above means.

多項式が３次式の場合、係数ａ＞０であれば極値はあるものの単純増加関数の形状をとる（図４参照）。係数ａ＜０であれば減少関数の形態をとることから、作成された検量線は異常と判断する。判別式Ｄ＞０の場合、定量上限値は、極大値のｑ座標に係数ｆ３を乗じて算出する。係数ｆ３は１未満であればよく、特に指定するものではないが、１に近いほど定量精度が悪くなり、値を小さくすると定量範囲が狭くなるため、０．６〜０．９５程度の値が望ましい。判別式Ｄ≦０の場合、極大、極小値は存在しないことから、定量上限値は、最大濃度の検量点のｙ値に係数ｆ４を乗じて算出する。係数ｆ４は１未満であればよく、特に指定するものではないが、１に近いほど定量精度が悪くなり、値を小さくすると定量範囲が狭くなるため、０．６〜０．９５程度の値が望ましい（図５参照）。

In the case where the polynomial is a cubic expression, if the coefficient a> 0, there is an extreme value but the shape of a simple increasing function is taken (see FIG. 4). If the coefficient a <0, it takes the form of a decreasing function, so that the created calibration curve is determined to be abnormal. When discriminant D> 0, the quantitative upper limit value is calculated by multiplying the q coordinate of the maximum value by the coefficient f3. The coefficient f3 need only be less than 1, and is not particularly specified. However, the closer to 1, the lower the accuracy of quantification, and the smaller the value, the narrower the quantitation range. desirable. In the case of discriminant D ≦ 0, there is no maximum or minimum value, so the upper limit of quantification is calculated by multiplying the y value of the calibration point of the maximum concentration by the coefficient f4. The coefficient f4 need only be less than 1, and is not particularly specified. However, the closer to 1, the lower the quantitative accuracy, and the smaller the value, the narrower the quantitative range. Desirable (see FIG. 5).

  Table 2 is a table showing a list of the shape of the cubic formula and the upper limit of quantification obtained by the above means.

（ステップ３）
未知試料を測定し、出力値（ピーク高さ、面積等）を得る。

(Step 3)
An unknown sample is measured, and an output value (peak height, area, etc.) is obtained.

(Step 4)
It is determined whether the output value (peak height, area, etc.) of the unknown sample is within the upper limit of quantification obtained in step 2, and if it is less than the upper limit of quantification, the quantitative calculation is performed according to the approximate expression. However, if the output value (peak height, area, etc.) is between the upper limit of quantification and the extreme value, quantitative calculation may be performed according to the approximate expression, but there may be an error in quantification accuracy. It is preferable to add a warning flag indicating this.

(Step 5)
The measurement is repeated from step 3 for the unknown samples, and the measurement of the unknown sample group is completed.

(Step 6)
When further measurement of different unknown sample groups is performed, the calibration curve is corrected. FIG. 6 shows the flow of correction.

  One sample among a plurality of standard samples used in creating the reference calibration curve is used to correct the reference calibration curve. The correction standard sample is measured, and output values (peak height, area, etc.) are obtained (FIG. 6b). A ratio F (AF / AR) between the output value (AF) of the obtained correction standard sample and the output value (AR) obtained at the time of creating the corresponding reference sample is calculated.

  All the output values (AR1 to ARn) obtained at the time of creating the calibration curve are multiplied by the ratio F to calculate a corrected output point (FIG. 6c).

濃度に対する補正出力値（ピーク高さ、面積等）から最小二乗法により多項式近似を再度行い、補正検量線を作成する（図６ｄ）。なお、比率Ｆが一定値以上または以下の場合、検量線の形態が大きく変化していることを意味することから、検量線の補正ではなく、新しい検量線を再作成する指示を出す、または、測定を中止するなどのアクションを行うことが好ましい。一般的に比率Ｆは０．９から１．１の範囲が好ましいが、定量結果への影響を個々に判断し指定することが望ましく、この値に限定するものではない。ここでは、基準検量線を補正するために１濃度の試料を用いることを前提に説明したが、複数濃度の標準試料を用いて補正を実施しても良い。この場合、面積比率Ｆが複数得られるが、平均値で補正を実施すれば、より補正の精度が高まることになる。また、基準検量線作成時に使用していない濃度の標準試料で補正を行っても問題ない。基準検量線の対応する濃度の出力値（ピーク高さ、面積等）を近似関数（基準検量線の近似式）により求め、比率Ｆを算出し、前述の通り補正計算に用いれば良い。

Polynomial approximation is performed again by the least square method from the corrected output values (peak height, area, etc.) for the concentration, and a corrected calibration curve is created (FIG. 6d). If the ratio F is greater than or less than a certain value, it means that the form of the calibration curve has changed significantly, so that an instruction to recreate a new calibration curve is issued instead of correction of the calibration curve, or It is preferable to perform an action such as stopping the measurement. In general, the ratio F is preferably in the range of 0.9 to 1.1. However, it is desirable to individually determine and specify the influence on the quantitative result, and is not limited to this value. Here, the description has been made on the assumption that a sample of one concentration is used to correct the reference calibration curve, but the correction may be performed using a standard sample of a plurality of concentrations. In this case, a plurality of area ratios F can be obtained. However, if correction is performed with an average value, the accuracy of correction is further increased. In addition, there is no problem even if correction is performed with a standard sample having a concentration not used when creating a standard calibration curve. The output value (peak height, area, etc.) of the corresponding concentration of the reference calibration curve is obtained by an approximate function (approximate expression of the reference calibration curve), the ratio F is calculated, and used for the correction calculation as described above.

(Step 7)
Similar to step 2, the shape of the approximate expression is specified by the coefficient of the newly obtained polynomial, etc., and the quantitative upper limit corresponding to each is determined again.

  Thereafter, the process returns to step 3 to measure an unknown sample and perform quantitative calculation.

  As described above, in the method of the present invention, even when a polynomial such as a quadratic equation or a cubic equation is used for the calibration curve, a standard sample of one concentration is used in the daily analytical operation, and a standard calibration curve is used. In addition, the unknown sample can be quantified and the man-hours can be greatly reduced. In addition, the reliability of the quantitative value can be improved by calculating the upper limit of quantification from the coefficient of the approximate expression and using it as a criterion.

It is the figure which classified the form of the quadratic equation (when coefficient a <0). It is the figure which classified the form of the quadratic equation (when coefficient a> 0). It is the figure which showed the fixed quantity upper limit at the time of using the secondary type | formula for a calibration curve in this invention. It is the figure which classified the form of the cubic equation. It is the figure which showed the upper limit of fixed_quantity | quantitative_assay at the time of using the cubic equation for a calibration curve in this invention. It is the figure which showed an example of the procedure of correction | amendment of a calibration curve in this invention. It is the figure shown in the flowchart which showed the procedure of fixed_quantity | assay using a calibration curve in this invention (in the case of a quadratic formula). It is the figure shown in the flowchart which showed the procedure of fixed_quantity | assay using a calibration curve in this invention (in the case of a cubic formula). It is the figure which showed the system configuration used in the Example. 2 is a diagram showing a standard calibration curve obtained in Example 1. FIG. It is the figure which expanded the peak 3 of the reference | standard calibration curve of FIG. 6 is a diagram showing a standard calibration curve obtained in Example 2. FIG. It is the figure which showed typically the quantitative upper limit in Example 2. FIG. A shows a shape having a maximum value, and FIG. B shows a shape having a minimum value. 6 is a chromatogram of the standard sample 1 when the flow rate is changed in Example 2. 6 is a diagram showing a part of the quantitative result of peak 5 in Example 2. FIG. The horizontal axis is the result of quantification when creating a standard calibration curve.

Example 1
The effect of the present invention was verified by performing actual chromatography. FIG. 9 shows the system used for verification. Solvent deaerator (SD-8020) 2, liquid feed pump (DP-8020) 3, sample injector (AS-8020) 4, column oven (CO-8020) 6, UV-visible detector (UV-8020) 7 And a data processing device (LC-8020II) 9 (both manufactured by Tosoh Corporation). As the analytical column 5, TSKgel ODS-100Z (5 μm, 4.6 mm ID × 15 cm) manufactured by Tosoh Corporation was used, and p-hydroxybenzoic acids were separated. Other conditions are as follows.
Injection volume: 80 uL, column temperature: 40 ° C., flow rate: 1.0 mL / min
Eluent: CH ₃ CN / H ₂ O (60/40), detection: 280 nm
Standard samples: Methyl p-Hydroxybenzoate (0.1 mg / 1 mL), Propyl p-Hydroxybenzoate (0.2 mg / 1 mL), Butyl p-Hydroxybenzoate (0.3 mg / 1 mL), Hexyl p-Hydrooxybene 0.4 mg / mL , Heptyl p-Hydroxybenzoate (0.5 mg / 1 mL)
The above mixture is the standard sample 1, the sample diluted 1/2 is the standard sample 2, the sample diluted 1/4 is the standard sample 3, the sample diluted 1/8 is the standard sample 4, the sample diluted 1/16 is the standard sample The sample diluted 5 or 1/32 was designated as standard sample 6, and the sample diluted 1/64 was designated as standard sample 7.
Unknown sample:
Mixture A; , Heptyl p-Hydroxybenzoate (0.100 mg / 1 mL) Mixture mixture B; ), Hexyl p-Hydroxybenzoate (0. 133 mg / 1 mL), Heptyl p-Hydroxybenzoate (0.278 mg / 1 mL) Mixture The above-mentioned two unknown samples were converted into 1/2, 1/4, 1/8, 1/16, 1/32, The sample was diluted 1/64 to obtain unknown samples A1 to 7 and unknown samples B1 to B7. A total of 14 types were adjusted and used for verification.

  FIG. 10 is a standard calibration curve prepared using seven standard samples with different concentrations adjusted in the above procedure. Taking the concentration (dilution ratio) on the horizontal axis and the area of each component on the vertical axis, it is approximated by a quadratic equation passing through the origin by the least square method (y = ax ^ 2 + bx + c, c = 0). Table 4 shows the coefficients of the approximate formulas of each component, the maximum concentration, the maximum area, and the upper limit of quantification.

いずれのピークに対しても、係数ａは負の値を示すことから、標準検量線は極大値を持つ形状であることが分かる。定量上限面積は、係数ｆ１＝０．８５として計算を行った。つまり、極大面積の８５％までを正確に定量できる範囲としたものである。

Since coefficient a shows a negative value for any peak, it can be seen that the standard calibration curve has a maximum value. The upper limit area for quantification was calculated with a coefficient f1 = 0.85. In other words, up to 85% of the maximum area can be accurately quantified.

  Immediately after creating the standard calibration curve, the unknown samples A1 to A7, B1 to B7, a total of 14 types, were measured, and the results quantified by the standard calibration curve are shown in Tables 5 and 6.

得られた面積値は、ぼぼ全ての試料、全ての成分で、定量最大面積を下回っているが、未知試料Ａ１のピーク３のみ、定量最大面積をわずかに上回っている。図１１はピーク３に対する検量線を拡大して、極大と定量上限面積の範囲を示した図である。これからも分かるように、未知試料Ａ１のピーク３は検量線の極大と定量上限面積の範囲に入っていることが分かる。すなわち、この成分は検量線の極大値にかなり近寄っており、定量の信頼性が低いと判定される。

The obtained area value is below the maximum fixed area for almost all samples and all components, but only the peak 3 of the unknown sample A1 is slightly higher than the maximum fixed area. FIG. 11 is an enlarged view of the calibration curve with respect to peak 3, showing the range of the maximum and the upper limit area of quantification. As can be seen, it can be seen that peak 3 of unknown sample A1 falls within the range of the maximum of the calibration curve and the upper limit area of quantification. That is, this component is very close to the maximum value of the calibration curve, and it is determined that the reliability of quantification is low.

(Example 2)
The system and measurement conditions used for verification are the same as in Example 1 except for the following.
Detection wavelength: 254 nm
Standard sample: Standard sample 7 of Example 1 was diluted 1/2, 1/4, 1/8, 1/16, 1/32, 1/64 to obtain standard samples 8-14.
Unknown sample: Unknown sample A7 and unknown sample B7 of Example 1 were diluted 1/4, 1/16, and 1/64, respectively, to obtain unknown samples A8 to 10 and unknown samples B8 to 10.

  FIG. 12 is a calibration curve created using standard samples 7 to 14 having different concentrations adjusted by the above procedure. Taking the concentration (dilution ratio) on the horizontal axis and the area of each component on the vertical axis, it is approximated by a quadratic equation passing through the origin by the least square method (y = ax ^ 2 + bx + c, c = 0). FIG. 12a is positive in both concentration (x-axis) and area (y-axis), near the calibration area, and FIG. 12b is a wide area so that the existence of extreme values is clear.

  Table 7 shows the coefficient of the approximate expression of each component, the shape of the function, the maximum concentration, the maximum area, and the upper limit area for quantification.

ピーク５に対しては、係数ａは負の値を示すことから、標準検量線は極大値を持つ形状であることが分かる。また、ピーク１から４に対しては、係数ａは正の値を示すことから、標準検量線は極小値を持つ形状であることが分かる。

For the peak 5, since the coefficient a shows a negative value, it can be seen that the standard calibration curve has a maximum value. In addition, for the peaks 1 to 4, since the coefficient a shows a positive value, it can be seen that the standard calibration curve has a minimum value.

  The calculation was performed with the coefficient f1 = 0.85 for the upper limit area of quantification for peak 5 and the coefficient f2 = 1.20 for the y coordinate ARn of the largest measurement point (calibration point) for peaks 1 to 4 (FIG. 13).

  Immediately after creating the standard calibration curve, eight types of unknown samples A7 to A10 and B7 to B10 were measured, and the results quantified by the standard calibration curve are shown in Table 8. The obtained area values are below the maximum fixed area for all samples and all components, and it can be seen that the quantitative value is within a reliable range mathematically.

次に、流速を０．９５、０．９９、１．０１、１．０５ｍＬ／ｍｉｎと僅かに変化させ、上記検量線を１濃度の標準試料にて補正し、その補正検量線を基に未知試料Ａ７〜Ａ１０、Ｂ７〜Ｂ１０、計８種を測定し、同様に定量を実施した。検量線を補正するための基準点として、最も高い濃度である標準試料１で定量計算を試みた。

Next, the flow rate is slightly changed to 0.95, 0.99, 1.01, 1.05 mL / min, the calibration curve is corrected with a standard sample of one concentration, and the unknown is based on the corrected calibration curve. Samples A7 to A10 and B7 to B10, a total of 8 types, were measured and quantified in the same manner. As a reference point for correcting the calibration curve, quantitative calculation was attempted with the standard sample 1 having the highest concentration.

  FIG. 14 shows the chromatograms of standard sample 1 and standard sample 4 at a flow rate of 1.00 mL / min at which the original calibration curve (reference calibration curve) was measured, and flow rates of 0.95, 0.99 for which correction calculation was performed. It is the chromatogram of the standard sample 1 in 1.01 and 1.05 mL / min. As can be seen from this, the elution time of each peak changes greatly, and it can be easily estimated that in an ordinary analysis, accurate quantification cannot be performed unless the calibration curve is remeasured. It was verified whether the present invention functions effectively even in such a state.

  FIG. 15 is a diagram showing a part of the quantification results of peaks 1 to 5. FIG. 5 is a graph plotting the results of quantification at the time of creating a standard calibration curve on the horizontal axis and the results of quantifying unknown samples by correcting the calibration curve by changing the flow velocity on the vertical axis. If the quantitative value is accurate, both will show the same value. That is, the data point comes to be on a straight line of y = ax (a = 1).

  Under any condition and peak, the area of all unknown samples is below the upper limit of quantification, so the quantification results are guaranteed. In addition, it can be seen that the difference from the quantification result performed at the time of creating the standard calibration curve is also very small in all regions and is on a straight line y = x, and the absolute value of the quantification value is secured.

1. 1. Eluent 2. Deaeration device Liquid feed pump (sample side)
4). 4. Sample injection valve Analysis column 6. 6. Column constant temperature bath UV-visible detector 8. Waste liquid9. System control and data processing equipment

Claims (4)

A method for preparing a polynomial calibration curve in chromatography,
A step of approximating a calibration point plotted with concentration x and output value y as a quadratic or cubic equation, and plotting the calibration point until the approximate equation becomes a simple increase function;
Multiplying the maximum value of the simple increase function by a constant less than 1 or multiplying the maximum output value of the calibration point by a constant of 1 or more to determine the upper limit of the output value;
A creation method comprising. A standard sample having a specific concentration x ₀ is measured by chromatography, and the ratio between the obtained output value y ₀ and the output value with respect to the concentration x ₀ calculated by the approximate expression is calculated, and the output value of the calibration point is calculated. The creation method according to claim 1, further comprising a step of approximating a correction output value obtained by multiplying each of the ratios by a quadratic expression or a cubic expression.   For the approximate expression approximating the corrected output value, multiply the local maximum value of the simple increase function by a constant less than 1 or multiply the maximum output value of the corrected output value by a constant of 1 or more to re-set the upper limit of the output value. The production method according to claim 2, further comprising a determining step.   4. A method for determining that a calibration curve created by the method according to claim 2 or 3 is not reliable when the ratio is a certain value or more.

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