Selectivity is the ability of a method to determine a particular analyte in a complex matrix without interference from other ingredients of the matrix. Specificity, however, is the ultimate in selectivity, and it means that no interference is expected to occur, but these two terms are used interchangeably in the literature. If a method has specificity for an analyte, it means that either you have it or you do not. Selectivity can be graded as low, high, partial, good or bad,

sion, specificity, selectivity, sensitivity, ME and stability testing.

but the selectivity refers to 100% selectivity (or 0% interference) [19].

*3.6.3. Method of standard addition*

minimise the matrix effect.

*3.7.1. Selectivity and specificity*

**3.7. Validation**

Alternatively, the endogenous concentration of the analyte in the matrix can be subtracted from the added concentrations and uses the subtracted concentrations to build the calibration curve. Using the actual biological matrix for making the calibrators and QCs reduces the recovery and matrix effects between samples and calibrators. Again, the limitation of this method is that the increase in background peak area after spiking with standards has to be at least 15–20% of the background peak area, and the LLOQ is limited by the endogenous background concentration even if much lower concentrations can be detected by the method. Another difficulty is when multiple analytes with different endogenous compounds need to be quantified [15].

Alternatively, the background concentration in the blank matrices can be lowered by dilution of the blank matrices before spiking with standards. However, by diluting the matrix, the composition of the matrices in the study samples versus calibration curve is different leading to different recoveries of the analytes. Therefore, the extraction recoveries of analytes between the matrix and diluted matrix should be determined before using this method [15].

#### *3.6.1. Surrogate matrices*

Surrogate matrices can vary widely from a simplest form, mobile-phase solvents (neat) or pure water to a synthetic polymer-based solution. Some biological matrices, e.g. cerebrospinal fluid or tears, are difficult to obtain. The surrogate matrix should simulate the authentic matrix in terms of composition, salt content, analyte solubility, recovery and ME. For example, phosphate-buffered saline (PBS) or bovine serum albumin (BSA) in PBS (20–80 g/L) has the similar protein and ionic strength as human plasma.

To use neat solutions as surrogate matrices, extraction recovery and ME are required to be com parable with the original matrix. For example, thromboxane B2 and 12(S)-hydroxyeicosatetraenoic acid were quantified in human serum using mixture of water/methanol/acetonitrile (80:10:10, v/v/v) as a surrogate matrix, and the ME and recoveries of the analytes were demonstrated to be comparable.

#### *3.6.2. Stripped matrices*

Biological matrices can be stripped from particular endogenous components to generate analyte-free surrogate matrices. Adding activated charcoal, for example, can adsorb and remove the analyte from the matrix, but the charcoal must effectively remove from the matrix before spiking the analyte. Some analytes, e.g. homocysteine, cannot be removed by the charcoal and also the composition of the matrix may change or cause batch-to-batch variation after adding the charcoal leading to the altered analyte recovery and ME. Some light-sensitive analytes can be decomposed by heat or exposing to the light and therefore removed from the matrix.

#### *3.6.3. Method of standard addition*

One of the approaches for validation of the assay is to determine the accuracy throughout the validation step, using the biological matrix containing the endogenous compound to prepare the standard curves and all pools of six or more assays of each QC sample [3]. The amount of the analyte in the matrix (Cbasal) can be computed using a calibration curve in the substitute matrix, and the concentration of the analyte in the QC can be calculated by subtracting the Cbasal from the calculated one as follows, Creal = Cfound – Cbasal, in which Cfound is the concentration of the analyte in the QCs calculated against a calibration curve in the substitute matrix and Creal is the corrected concentration [3]. When using this approach, the LLOQ of the method cannot be smaller than the endogenous concentrations of the analyte in the matrix, and there-

Alternatively, the endogenous concentration of the analyte in the matrix can be subtracted from the added concentrations and uses the subtracted concentrations to build the calibration curve. Using the actual biological matrix for making the calibrators and QCs reduces the recovery and matrix effects between samples and calibrators. Again, the limitation of this method is that the increase in background peak area after spiking with standards has to be at least 15–20% of the background peak area, and the LLOQ is limited by the endogenous background concentration even if much lower concentrations can be detected by the method. Another difficulty is when

Alternatively, the background concentration in the blank matrices can be lowered by dilution of the blank matrices before spiking with standards. However, by diluting the matrix, the composition of the matrices in the study samples versus calibration curve is different leading to different recoveries of the analytes. Therefore, the extraction recoveries of analytes between

Surrogate matrices can vary widely from a simplest form, mobile-phase solvents (neat) or pure water to a synthetic polymer-based solution. Some biological matrices, e.g. cerebrospinal fluid or tears, are difficult to obtain. The surrogate matrix should simulate the authentic matrix in terms of composition, salt content, analyte solubility, recovery and ME. For example, phosphate-buffered saline (PBS) or bovine serum albumin (BSA) in PBS (20–80 g/L) has

To use neat solutions as surrogate matrices, extraction recovery and ME are required to be com parable with the original matrix. For example, thromboxane B2 and 12(S)-hydroxyeicosatetraenoic acid were quantified in human serum using mixture of water/methanol/acetonitrile (80:10:10, v/v/v) as a surrogate matrix, and the ME and recoveries of the analytes were dem-

Biological matrices can be stripped from particular endogenous components to generate analyte-free surrogate matrices. Adding activated charcoal, for example, can adsorb and remove the analyte from the matrix, but the charcoal must effectively remove from the matrix before

multiple analytes with different endogenous compounds need to be quantified [15].

the matrix and diluted matrix should be determined before using this method [15].

the similar protein and ionic strength as human plasma.

*3.6.1. Surrogate matrices*

onstrated to be comparable.

*3.6.2. Stripped matrices*

fore a lot of blank matrices need to be screened to find the suitable one.

116 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

In the standard addition method, every study sample is divided into aliquots of equal volumes, and the aliquots are spiked with known and varying amounts of the analyte to build the calibration curve. The sample concentration is then calculated as the negative x-intercept of the calibration line. This method is very accurate because it allows direct quantitation of endogenous analytes without manual subtraction of background peak areas. The disadvantage of the method is that it requires a large amount of sample and is very time-consuming and labour intensive. Examples of using this method when the analyte-free matrices are not available include measuring abscisic acid, a phytohormone from plant leaves and the emission of polycyclic aromatic hydrocarbons from petroleum refineries. Standard addition can also be used when some matrix components produce MS signals that interfere with the analytes of interest.

We have used this method by some modifications to measure homocysteine and pyridoxal 5-phosphate in samples of human serum and whole blood, respectively [16, 17]. The matrix was first spiked with different concentrations of the analytes, and the endogenous concentrations of the analytes were estimated using the negative x-intercept of the calibration line. Then, the endogenous concentrations were added to the spiked concentrations, and new calibration curves with real concentrations were constructed (practical example 4). QCs were prepared in both actual and surrogate matrices, and the sample volume reduced to only 20 μL to minimise the matrix effect.

#### **3.7. Validation**

All the developed analytical methods need to be validated to make sure that each measurement of the content of the analyte in the sample in routine analysis is close to the true values [7]. There are international guidelines for validation of the analytical methods including FDA [6], European Medicines Agency (EMA) [14], International Union of the Pure and Applied Chemistry (IUPAC) [18] and Association of Official Analytical Chemists (AOAC) International. The major parameters need to be validated including linearity, accuracy, precision, specificity, selectivity, sensitivity, ME and stability testing.

#### *3.7.1. Selectivity and specificity*

Selectivity is the ability of a method to determine a particular analyte in a complex matrix without interference from other ingredients of the matrix. Specificity, however, is the ultimate in selectivity, and it means that no interference is expected to occur, but these two terms are used interchangeably in the literature. If a method has specificity for an analyte, it means that either you have it or you do not. Selectivity can be graded as low, high, partial, good or bad, but the selectivity refers to 100% selectivity (or 0% interference) [19].

Selectivity can be calculated by comparing the chromatograms obtained after injection of a blank sample with and without the analyte or analytical solutions and with and without the matrix components.

chemicals and in high-performance liquid chromatography (HPLC) are repeatability of peak area, dilutions factors, reference materials and sampling. Sampling, calibration and repeat-

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The LOD is generally defined as the lowest amount of an analyte in a sample that can be detected by a particular analytical method. LOD is usually evaluated using the calculation of the signal/noise relationship considering the assumption that data normality, homoscedasticity and independency of residuals are met. The signal-to-noise ratio is determined by comparing the analytical signals at known low concentrations compared with those of blank sample up to a concentration that produces a signal equivalent to three times the standard deviation of the blank sample [19]. Determination of the LOD is not necessary during the validation,

On the other hand, the lowest concentration of an analyte in a sample, which can be reliably quantified is defined as the LLOQ. The analyte signal at the LLOQ level should be at least five times the signal of blank sample and the accuracy and precision within 20% of the nominal concentrations. The LLOQ should be selected based on the expected concentrations in the study. For example, for bioequivalence studies the LLOQ should not be higher than 5% of the

ME measurement is necessary for validation when the analytical method uses mass spectrometry as the detector due to the ion suppression or induction caused by the matrix components. The ME evaluation required spiking the analyte (at low and high concentrations) in six lots of matrix obtained from individual donors. First, the ratio of the peak area in the presence of matrix to the peak area in the absence of the matrix is calculated to achieve the matrix factor (MF), followed by the calculation of the IS normalised MF by dividing the MF of the analyte of interests by the MF of the IS. The CV of the IS-normalised MF is calculated from the six lots of the matrix and should be ≤15% (practical example 5). In some cases that this method is not practical (e.g. online sample preparation), the variability of the response should be assessed by analysing at least six lots of matrix spiked at low and high levels. The overall CV should not be greater than 15%. The ME is also recommended to be tested in haemolysed, hyperlipidaemic matrices or plasma collected from renally or hepatically impaired patients depending

Stability testing must be planned based on the conditions applied to the samples during processing. The stability is tested using spiked concentrations of the analyte to the matrix at low and high QC levels (six replicates at two levels are generally sufficient). Short-term stability at room temperature (2–8 h depending on the latest period of time required for sample processing), long-term stability at storage temperature (e.g. at −20°C or −80°C), freeze and

ability were the most significant sources, which affect combined uncertainty [20].

because the assay may have high variability in that level.

maximum concentration of the analyte in the samples (Cmax) [14].

*3.7.5. LOD and LLOQ*

*3.7.6. Matrix effect (ME)*

*3.7.7. Stability*

on the target population of the study [14].

#### *3.7.2. Accuracy*

Accuracy (or trueness or bias) is the most important aspect of validation and should be addressed in any analytical method. Accuracy shows the extent of agreement between the experimental value (calculated from replicate measurements) and the nominal (reference) values. Accuracy is a measurement of the systematic errors affecting the method. To estimate the accuracy of a method, the analyte is measured in comparison with a reference material or by spiking known amount of analyte in the blank matrix (QC samples) and calculating the percentage of recovery from the matrix. It can also be estimated using the comparison of the results from the method by a reference method [19].

The guideline for validation of analytical methods by the EMA [14] recommends checking the accuracy within run and between runs by analysing a minimum of five samples per four QC levels (LLOQ, low, medium and high) as a representative of the whole analytical range in at least two different days. The accuracy needs to be reported as the percentage of the nominal concentrations and the mean concentration should be within 15% of the nominal values for all QC levels, except LLOQ, which should be within 20% of the nominal values [14].

#### *3.7.3. Precision*

The term precision is defined as the closeness of repeated individual measurements of an analyte under specified conditions. This term is demonstrating the repeatability and reproducibility of the method and expressed as the coefficient of variation (CV). Precision should be measured for LLOQ, low, medium and high QC samples in the same run that accuracy is testing. The acceptance criteria are also similar to the accuracy evaluation [14, 19].

#### *3.7.4. Uncertainty*

To make sure that a method is correctly fit for the purpose of measurement, "uncertainty" of the method is required to be evaluated [7].

A detailed list of all possible sources of uncertainty needs to be prepared. A preliminary study may identify the most significant sources of uncertainty. Typically, the two sources of uncertainties are Type A or random error and Type B or systematic error. Random error is caused by unpredictable variations and gives rise to variations in repeated observations. The random error can generally be minimised by increasing the number of observations. Systematic error, however, is a type of errors, which remain constant, or its variation is predictable and therefore independent of the number of observations. The result should be corrected for all recognised significant systematic errors. The steps involved in uncertainty estimation are identification of uncertainty sources, quantification of uncertainty components and calculation of combined and expanded uncertainty. The main sources of uncertainity are sampling, environmental conditions, method validation, instruments, weighting and dilutions, reference materials, chemicals and in high-performance liquid chromatography (HPLC) are repeatability of peak area, dilutions factors, reference materials and sampling. Sampling, calibration and repeatability were the most significant sources, which affect combined uncertainty [20].

#### *3.7.5. LOD and LLOQ*

Selectivity can be calculated by comparing the chromatograms obtained after injection of a blank sample with and without the analyte or analytical solutions and with and without the

Accuracy (or trueness or bias) is the most important aspect of validation and should be addressed in any analytical method. Accuracy shows the extent of agreement between the experimental value (calculated from replicate measurements) and the nominal (reference) values. Accuracy is a measurement of the systematic errors affecting the method. To estimate the accuracy of a method, the analyte is measured in comparison with a reference material or by spiking known amount of analyte in the blank matrix (QC samples) and calculating the percentage of recovery from the matrix. It can also be estimated using the comparison of the

The guideline for validation of analytical methods by the EMA [14] recommends checking the accuracy within run and between runs by analysing a minimum of five samples per four QC levels (LLOQ, low, medium and high) as a representative of the whole analytical range in at least two different days. The accuracy needs to be reported as the percentage of the nominal concentrations and the mean concentration should be within 15% of the nominal values for all

The term precision is defined as the closeness of repeated individual measurements of an analyte under specified conditions. This term is demonstrating the repeatability and reproducibility of the method and expressed as the coefficient of variation (CV). Precision should be measured for LLOQ, low, medium and high QC samples in the same run that accuracy is

To make sure that a method is correctly fit for the purpose of measurement, "uncertainty" of

A detailed list of all possible sources of uncertainty needs to be prepared. A preliminary study may identify the most significant sources of uncertainty. Typically, the two sources of uncertainties are Type A or random error and Type B or systematic error. Random error is caused by unpredictable variations and gives rise to variations in repeated observations. The random error can generally be minimised by increasing the number of observations. Systematic error, however, is a type of errors, which remain constant, or its variation is predictable and therefore independent of the number of observations. The result should be corrected for all recognised significant systematic errors. The steps involved in uncertainty estimation are identification of uncertainty sources, quantification of uncertainty components and calculation of combined and expanded uncertainty. The main sources of uncertainity are sampling, environmental conditions, method validation, instruments, weighting and dilutions, reference materials,

QC levels, except LLOQ, which should be within 20% of the nominal values [14].

testing. The acceptance criteria are also similar to the accuracy evaluation [14, 19].

matrix components.

results from the method by a reference method [19].

118 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

*3.7.2. Accuracy*

*3.7.3. Precision*

*3.7.4. Uncertainty*

the method is required to be evaluated [7].

The LOD is generally defined as the lowest amount of an analyte in a sample that can be detected by a particular analytical method. LOD is usually evaluated using the calculation of the signal/noise relationship considering the assumption that data normality, homoscedasticity and independency of residuals are met. The signal-to-noise ratio is determined by comparing the analytical signals at known low concentrations compared with those of blank sample up to a concentration that produces a signal equivalent to three times the standard deviation of the blank sample [19]. Determination of the LOD is not necessary during the validation, because the assay may have high variability in that level.

On the other hand, the lowest concentration of an analyte in a sample, which can be reliably quantified is defined as the LLOQ. The analyte signal at the LLOQ level should be at least five times the signal of blank sample and the accuracy and precision within 20% of the nominal concentrations. The LLOQ should be selected based on the expected concentrations in the study. For example, for bioequivalence studies the LLOQ should not be higher than 5% of the maximum concentration of the analyte in the samples (Cmax) [14].

#### *3.7.6. Matrix effect (ME)*

ME measurement is necessary for validation when the analytical method uses mass spectrometry as the detector due to the ion suppression or induction caused by the matrix components. The ME evaluation required spiking the analyte (at low and high concentrations) in six lots of matrix obtained from individual donors. First, the ratio of the peak area in the presence of matrix to the peak area in the absence of the matrix is calculated to achieve the matrix factor (MF), followed by the calculation of the IS normalised MF by dividing the MF of the analyte of interests by the MF of the IS. The CV of the IS-normalised MF is calculated from the six lots of the matrix and should be ≤15% (practical example 5). In some cases that this method is not practical (e.g. online sample preparation), the variability of the response should be assessed by analysing at least six lots of matrix spiked at low and high levels. The overall CV should not be greater than 15%. The ME is also recommended to be tested in haemolysed, hyperlipidaemic matrices or plasma collected from renally or hepatically impaired patients depending on the target population of the study [14].

#### *3.7.7. Stability*

Stability testing must be planned based on the conditions applied to the samples during processing. The stability is tested using spiked concentrations of the analyte to the matrix at low and high QC levels (six replicates at two levels are generally sufficient). Short-term stability at room temperature (2–8 h depending on the latest period of time required for sample processing), long-term stability at storage temperature (e.g. at −20°C or −80°C), freeze and thaw and stock solution stabilities are the most common tests. The stability of QC samples are analysed against a freshly prepared calibration curve, and the calculated concentrations should be within 15% of the nominal concentrations. The stability of processed samples in the autosampler temperature also determines how long samples can be stored in the autosampler without the analyte been degraded [14]. Any other variation during sample processing which can potentially affect the stability of the analyte of interest needs to be tested during validation.

### **4. Practical examples**

#### **4.1. Practical example 1: impact of weighting**

See **Table 1**.

#### **4.2. Practical example 2: linearity assessment**

In **Table 2,** it shows that the linear regression model (LRM) must systemically be rejected at the 95% confidence level (Fcrit,95% = 4.53) for lack-of-fit test and at 99% confidence level (Fcrit,99% = 10.56) for Mandel's fitting test. Thus, despite the fact that r and quality coefficient (QC) are greater than 0.997 and lower than 5%, respectively, the linearity of the calibration lines was rejected based on the F-tests. So, the r is not a good measure of the linearity assessment. Even with a QC value less than 3%, the LRM is rejected at the 95% confidence level (**Table 2**). Alternatively, the residual plots give useful information to validate the chosen regression model.

The residual plot can be used to check if the principle assumptions, i.e. normality of the residuals and homoscedasticity, are met when evaluating the goodness of fit of the regression model. The U-shaped residual plot usually shows that a curvilinear regression model is a better fit than an LRM. In order to correct the non-linearity, a quadratic curvilinear function (f(x) = a + bx + cx<sup>2</sup> ) can be chosen. The "lack of fit" tests for the quadratic regression model

(QRM) are summarised in **Table 2**. The test for lack of fit indicates that this QRM fits the calibration data at 99% confidence level in all cases except one. To check the suitability of the order of polynomial regression model, the significance of the second-order coefficient needs to be estimated. The P-value on the second-order coefficient, shown in **Table 2**, is systemically smaller than 1%, and therefore a lower order model should not be considered. Moreover, residual plots (**Figure 2**) were constructed for the QRM, and the residuals were randomly scattered within a horizontal band around the centre line. Therefore, the QRM was selected as the reference model. It is noted that an increase of the variance is observed at higher concentra-

**Table 2.** The F-value of the lack-of-fit (LOF) test and Mandel's fitting test is compared with the quality coefficient for

For the quadratic regression model, the F-value of the lack-of-fit test and the P-value for testing significance of the second-order coefficient for the quadratic regression model are represented. The significance value at the 95% confidence

level is underlined (reproduced from Van Loco et al. [8] with permission from Springer-Verlag).

**Linear regression model Quadratic regression model**

11.08 51.46 3.93 0.9982 0.63 0.0000 19.42 56.84 4.23 0.9978 1.58 0.0000 7.13 26.29 3.67 0.9985 0.94 0.0006 6.99 37.73 3.79 0.9984 0.18 0.0002 11.43 58.21 4.03 0.9981 0.31 0.0000 29.91 53.02 3.53 0.9986 4.08 0.0000 49.80 71.07 3.76 0.9984 5.69 0.0000 23.77 73.86 3.19 0.9989 1.66 0.0000 31.95 63.37 3.24 0.9988 3.55 0.0000 7.49 33.50 2.92 0.9991 0.54 0.0003 9.99 55.19 3.95 0.9983 0.15 0.0000 10.71 28.65 4.70 0.9975 1.89 0.0005 25.21 79.60 3.34 0.9987 1.62 0.0000 13.16 35.74 3.37 0.9987 1.93 0.0002

**LOF Mandel's test value QC (%) r LOF P-value on second-order coefficient**

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As a summary, in this example, a linear model with r > 0.997 and QC < 5% but with lack of fit (LOF) yielded predicted values for a mid-scale calibration standard that significantly differ from the nominal ones. The accuracy was overestimated, while the precision on the results

The role of IS concentration on the linearity of the calibration curve has been demonstrated by Tan et al. [13]. They presented a case in which decreasing concentration of the IS from 100%

tions [8].

several linear calibration lines of Cd.

was comparable in both LRM and QRM [8].

**4.3. Practical example 3: IS concentration and the linearity**

**Table 1.** Increasing the accuracy of the lower end of the calibration curve by applying the weighing.

For the quadratic regression model, the F-value of the lack-of-fit test and the P-value for testing significance of the second-order coefficient for the quadratic regression model are represented. The significance value at the 95% confidence level is underlined (reproduced from Van Loco et al. [8] with permission from Springer-Verlag).

**Table 2.** The F-value of the lack-of-fit (LOF) test and Mandel's fitting test is compared with the quality coefficient for several linear calibration lines of Cd.

(QRM) are summarised in **Table 2**. The test for lack of fit indicates that this QRM fits the calibration data at 99% confidence level in all cases except one. To check the suitability of the order of polynomial regression model, the significance of the second-order coefficient needs to be estimated. The P-value on the second-order coefficient, shown in **Table 2**, is systemically smaller than 1%, and therefore a lower order model should not be considered. Moreover, residual plots (**Figure 2**) were constructed for the QRM, and the residuals were randomly scattered within a horizontal band around the centre line. Therefore, the QRM was selected as the reference model. It is noted that an increase of the variance is observed at higher concentrations [8].

As a summary, in this example, a linear model with r > 0.997 and QC < 5% but with lack of fit (LOF) yielded predicted values for a mid-scale calibration standard that significantly differ from the nominal ones. The accuracy was overestimated, while the precision on the results was comparable in both LRM and QRM [8].

#### **4.3. Practical example 3: IS concentration and the linearity**

**Concentration (ng/mL) Area ratio Accuracy**

**4. Practical examples**

See **Table 1**.

(f(x) = a + bx + cx<sup>2</sup>

**4.1. Practical example 1: impact of weighting**

120 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

**4.2. Practical example 2: linearity assessment**

 0.002 0 0 0.006 125 92.3 0.019 104 94.1 37.5 0.400 98.5 94.1 0.836 101 99.3 3.320 98.5 98.9 5.290 97.8 98.5 6.890 102 103

residual plots give useful information to validate the chosen regression model.

**Table 1.** Increasing the accuracy of the lower end of the calibration curve by applying the weighing.

**(no weighting)**

) can be chosen. The "lack of fit" tests for the quadratic regression model

thaw and stock solution stabilities are the most common tests. The stability of QC samples are analysed against a freshly prepared calibration curve, and the calculated concentrations should be within 15% of the nominal concentrations. The stability of processed samples in the autosampler temperature also determines how long samples can be stored in the autosampler without the analyte been degraded [14]. Any other variation during sample processing which can potentially affect the stability of the analyte of interest needs to be tested during validation.

In **Table 2,** it shows that the linear regression model (LRM) must systemically be rejected at the 95% confidence level (Fcrit,95% = 4.53) for lack-of-fit test and at 99% confidence level (Fcrit,99% = 10.56) for Mandel's fitting test. Thus, despite the fact that r and quality coefficient (QC) are greater than 0.997 and lower than 5%, respectively, the linearity of the calibration lines was rejected based on the F-tests. So, the r is not a good measure of the linearity assessment. Even with a QC value less than 3%, the LRM is rejected at the 95% confidence level (**Table 2**). Alternatively, the

The residual plot can be used to check if the principle assumptions, i.e. normality of the residuals and homoscedasticity, are met when evaluating the goodness of fit of the regression model. The U-shaped residual plot usually shows that a curvilinear regression model is a better fit than an LRM. In order to correct the non-linearity, a quadratic curvilinear function

> **Accuracy (1/x weighting)**

> > The role of IS concentration on the linearity of the calibration curve has been demonstrated by Tan et al. [13]. They presented a case in which decreasing concentration of the IS from 100%

**Figure 2.** Plots of residuals for (a) the linear regression model (LRM) and (b) the quadratic regression model (QRM) versus predicted values (adopted from Van Loco et al. [8] with permission from Springer-Verlag).

to 5% ULOQ made the calibration curve non-linear. In that case, the cross-contribution from the analyte to the IS is equivalent to 5% of the concentration of the analyte. The cross-signal contribution from the analyte to the IS is either due to the isotope interference or chemical impurity in reference standard [13].

#### **4.4. Practical example 4: method of standard addition for homocysteine calibration curve**

**Table 3** shows the calculated calibration curve data for homocysteine standard solutions spiked into a pooled human serum.

To estimate the endogenous concentrations of homocysteine in the sample of pooled human serum, the negative x-intercept of the curve is calculated:

 x = \_\_\_\_\_\_\_ −0.262 0.000598 = 438 ng/mL. (4) Then, the nominated concentration is changed to the spiked + endogenous concentrations,

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Now, by comparing the detector response for the unknown samples with the second calibra-

**Table 5** is representing the analyte peak area spiked in six different lots of human plasma. The MF has been calculated by dividing the area of analyte (or IS) in each matrix to the average peak area of the analyte (or IS) in the pure solutions. The IS-normalised MF is the ratio of the MF for the

**Spiked + endogenous concentration (ng/mL) Calculated concentration (ng/mL)**

**Table 4.** Homocysteine calibration curve: The x-axis is representing the spiked + endogenous concentrations.

**Analyte of interest IS IS-normalised MF**

**Spiked Pure (mean of three replicates)**

**Peak area Matrix**

and a new calibration is constructed (**Table 4**).

**4.5. Practical example 5: ME calculations**

Regression equation: y = 0.000598 x – 0.000762.

**three replicates)**

**Table 5.** Calculation of ME.

**Peak area Matrix**

**factor**

**factor Spiked Pure (mean of**

1,095,000 1,210,000 0.905 4,320,000 6,343,333 0.681 1.33 1,050,000 0.868 6,240,000 0.984 0.882 1,110,000 0.917 5,780,000 0.911 1.01 1,120,000 0.926 5,660,000 0.892 1.04 1,100,000 0.909 5,770,000 0.910 0.999 1,130,000 0.934 5,170,000 0.815 1.15 Mean 1.07 SD 0.154 CV% 14.4

tion curve, the unknown sample concentrations can be calculated.

 + 438 = 438 381.51 + 438 = 488 469.28 + 438 = 1038 1071.34 + 438 = 1538 1545.77 + 438 = 2038 2091.35 + 438 = 2538 2606.98 + 438 = 3038 3023.15 + 438 = 3538 3471.01

**Table 3.** Homocysteine calibration curve: the x-axis is representing the spiked concentrations.

Then, the nominated concentration is changed to the spiked + endogenous concentrations, and a new calibration is constructed (**Table 4**).

Now, by comparing the detector response for the unknown samples with the second calibration curve, the unknown sample concentrations can be calculated.

#### **4.5. Practical example 5: ME calculations**

**Table 5** is representing the analyte peak area spiked in six different lots of human plasma. The MF has been calculated by dividing the area of analyte (or IS) in each matrix to the average peak area of the analyte (or IS) in the pure solutions. The IS-normalised MF is the ratio of the MF for the

**Table 4.** Homocysteine calibration curve: The x-axis is representing the spiked + endogenous concentrations.

**Table 5.** Calculation of ME.

to 5% ULOQ made the calibration curve non-linear. In that case, the cross-contribution from the analyte to the IS is equivalent to 5% of the concentration of the analyte. The cross-signal contribution from the analyte to the IS is either due to the isotope interference or chemical

**Figure 2.** Plots of residuals for (a) the linear regression model (LRM) and (b) the quadratic regression model (QRM)

**Table 3** shows the calculated calibration curve data for homocysteine standard solutions

To estimate the endogenous concentrations of homocysteine in the sample of pooled human

0.000598 = 438 ng/mL. (4)

**4.4. Practical example 4: method of standard addition for homocysteine calibration**

**Spiked concentrations (ng/mL) Calculated concentration (ng/mL)**

**Table 3.** Homocysteine calibration curve: the x-axis is representing the spiked concentrations.

versus predicted values (adopted from Van Loco et al. [8] with permission from Springer-Verlag).

122 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

impurity in reference standard [13].

spiked into a pooled human serum.

Regression equation: y = 0.000598 x + 0.262.

serum, the negative x-intercept of the curve is calculated:

0 N/A 50 30.87 600 632.76 1100 1107.05 1600 1652.48 2100 2167.02 2600 2584.02 3100 3031.75

x = \_\_\_\_\_\_\_ −0.262

**curve**

analyte to the MF for the IS. The CV% in this example was 14.4%, which is within the acceptance limit for the matrix effect by the EMA guideline for validation of bioanalytical methods [14].

HPLC High-performance liquid chromatography

IUPAC International Union of Pure and Applied Chemistry LC–MS/MS Liquid chromatography tandem mass spectrometry

Linearity of Calibration Curves for Analytical Methods: A Review of Criteria for Assessment…

http://dx.doi.org/10.5772/intechopen.72932

125

IDMS Isotope dilution mass spectrometry

IS Internal standard

LOD Limit of detection

LOF Lack of fit

ME Matrix effect MF Matrix factor

MS Mass spectrometry

POM Power of the mean

SD Standard deviation SD Standard deviation

SIL Stable isotope labelled SPE Solid-phase extraction

**Author details**

Seyed Mojtaba Moosavi1

ULOQ Upper limit of quantification

WLSLR Weighted least squares linear regression

\*Address all correspondence to<EMAIL_ADDRESS>1 The University of Technology Sydney, Sydney, Australia

2 The University of Queensland, Brisbane, Australia

and Sussan Ghassabian2

\*

QC Quality control

PBS Phosphate buffer saline

QRM Quadratic regression model

LLE Liquid–liquid extraction

LRM Linear regression model

LLOQ Lower limit of quantification

### **5. Key results**

### **Abbreviations**

### **Author details**

analyte to the MF for the IS. The CV% in this example was 14.4%, which is within the acceptance limit for the matrix effect by the EMA guideline for validation of bioanalytical methods [14].

• Calibration curve is a regression model between an known concentration of an analyte and the response from an instrument enabling the estimation of the concentration of the analyte

• Weighted least squares linear regression (WLSLR) is necessary when the standard deviations across the standard range are not consistent. Weighting improves the sensitivity and

• Coefficient of correlation is not a suitable measure for the linearity of the calibration curve,

• Stable isotope-labelled compounds are the most preferable internal standards. However, carefully chosen structural analogues with similar functional groups and physicochemical

• The concentration of the internal standard may affect the linearity of the calibration curve due to the cross signal contribution between the analyte and the internal standards.

• When an analyte-free matrix does not exist, the amount of endogenous analyte in the matrix can be estimated using the negative x-intercept of the regression equation and adding this value to the spiked concentrations of the analyte to calculate the actual concentrations of each standard.

• During validation of an analytical method, selectivity, specificity, accuracy, precision, uncertainty, LLOQ, matrix effect and stability are the minimum criteria to be evaluated.

and the linearity should be evaluated using an appropriate statistical analysis.

properties can contribute to generation of comparable analytical methods.

**5. Key results**

**Abbreviations**

4PL Four-parameter logistic

ANOVA Analysis of variance

BSA Bovine serum albumin

CV Coefficient of variation

CIS-Max Maximum IS concentration CIS-Min Minimum IS concentration

EMA European Medicines Agency

FDA Food and Drug Administration

ELISA Enzyme-linked immunosorbent assay

in an unknown sample.

accuracy of the lower end of the calibration range.

124 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Seyed Mojtaba Moosavi1 and Sussan Ghassabian2 \* \*Address all correspondence to<EMAIL_ADDRESS>1 The University of Technology Sydney, Sydney, Australia 2 The University of Queensland, Brisbane, Australia

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[9] Hayashi Y et al. Detection limit estimated from slope of calibration curve: An application

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**Section 3**

**Validation Approaches**


**7. References**

262 Myocarditis

Treatment for myocarditis mainly involves targeting the symptoms of heart dysfunction. If the disease progresses to dilated cardiomyopathy, heart transplantation is necessitated. Regrettably, for 50% of patients progressing to dilated cardiomyopathy, survival is limited to 5 years. Broad-spectrum antivirals tested in clinical trials with children and adults have been few and mildly successful. Specific therapies designed against viruses (enteroviruses) for prevention and/or management of viral myocarditis are still desperately needed. One challenge in designing specific antivirals or vaccines for viral myocarditis is the range of possible etiologies and immune mechanisms that may be responsible. Although enteroviral infection inducing or exacerbating an autoimmune response is a likely cause for viral myocarditis, supporting data defining a link between viral infection and the onset of acute and/or chronic myocarditis in humans must still be determined. The existence of many viral serotypes for promising etiological agents like coxsackievirus B also poses a problem in

Dampening the Th1 immune response in viral myocarditis is a therapeutic avenue consistently featured in past and recent studies. Many key innate immune players, such as cytokines and chemokines, are targets of potential Th1 skewing therapeutics. Cytokines presenting at the site of viral infection have a significant influence on whether a tolerant or autoimmune response is chosen. Targeting cytokines, chemokines and other immunomodulating factors for myocarditis therapy may depend on the timing and duration of the particular factor and the maintenance of immune balance to prevent the

For quite some time scientists have investigated virus and host cellular and molecular events that underlie the pathogenesis of enteroviral-induced myocarditis. Our lab has demonstrated the significance of many key innate players that contribute to coxsackievirus-B3 induced myocarditis in mouse models. Horwitz et al first revealed the importance of IFN-γ expression in the pancreas for the protection from coxsackievirus B3 infection and the induction of myocarditis (Horwitz et al. 2000). Later on, Horwitz et al again demonstrated a protective role against coxsackievirus B3-induced myocarditis with cytokine expression in the pancreas, this time, with transgenic expression of TGF-β in the beta cells (Horwitz et al. 2006). This work was followed by Richer et al, who provided a role for TLR4 and stimulation by *Salmonella minnesota* lipopolysaccharide in bypassing the protective effect exerted by TGF-β in coxsackievirus B3-induced myocarditis (Richer et al. 2006). Our lab has also investigated the role of IL-6 in disease severity. Poffenberger et al demonstrated that in the absence of IL-6, a greater early immune response occurred, instigating a severe chronic disease pathology (Poffenberger et al. 2009). Recently, Poffenberger et al described susceptibility loci on chromosome 17 that implicate the highly suggested genetic component as a factor dictating viral myocarditis pathogenesis (Poffenberger et al. 2010). Though work from our lab has contributed a great deal to the understanding of coxsackievirus B3-induced myocarditis, there remains many unanswered questions with regards to the true key immune players that dictate disease pathogenesis. It is likely that an interplay of genetic and environmental factors influence the susceptibility and severity of virus-induced myocarditis however, we must not discount the significance of the innate immune response in shaping the outcome of virus-induced disease. It is possible that this early immune response may

**5. Therapeutic challenges and future directions**

designing specific antiviral therapies.

development of autoimmunity.

**6. Conclusion**

The Key Players of Coxsackievirus-Induced Myocarditis 265

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**13**

*Canada*

**Cellular and Immunological**

*St. Paul's Hospital, University of British Columbia*

**Regulation of Viral Myocarditis**

David Marchant, Farshid S. Garmaroudi and Bruce M. McManus

Since the discovery of coxsackievirus type B3 (CVB3) more than 50 years ago there has been considerable progress in the understanding of viral heart disease. Coxsackievirus was first discovered as a filterable agent associated with a paralytic syndrome, so named for its identification in Coxsackie, New York (coxsackievirus type A) (Dalldorf and Sickles, 1948). Coxsackievirus type B (CVB) was isolated the following year from patients with aseptic meningitis and by the mid-1950s an association with acute myocarditis in humans was apparent (Melnick et al., 1949). Many other viruses have since been shown to cause myocarditis and its long term sequelae, arrhythmias, dilated cardiomyopathy (DCM) and heart failure. By example, adenovirus, herpes viruses, and influenza can cause myocarditis in humans and models of heart failure. The viral agent most often reported as being the cause of viral myocarditis is CVB3. For example, CVB3 RNA can be detected in the heart muscle of 10 - 35 % of DCM patients (Feldman and McNamara, 2000; Hosenpud et al., 2001),

Inflammation of the heart muscle can have many causes, not least of which is viral infection. Cocaine [(Jentzen, 1989) reviewed in (Maraj et al., 2010)], virus induced, autoimmune (possibly due to resolved microbial infection), and even vaccine induced myocarditis (Cassimatis et al., 2004) have all been reported with a wide degree of occurrence. Though very rare, the vaccine induced aetiology is classified as idiopathic due to the poorly understood mechanism of inflammation. This manifestation of myocarditis is so rare it is probably very complex in cause and mechanism, requiring both environmental and genetic susceptibility factors of the host to trigger myocardial immune invasion. The subject of this chapter is one of the most common forms of myocarditis, and perhaps the most studied: myocarditis due to viral infection. In such cases, myocyte dropout and provisional matrix fibrosis, focal lesions of immune cell invasion are marked and key observations in the

With an experimental understanding of CVB3 induced myocarditis comes a better understanding of the breadth of symptoms presented by the admitted patient, before,

**1. Introduction**

depending on the study cohort.

**1.1 Myocarditis etiologies**

diagnosis of these cases.

**1.2 Clinical presentation**

*UBC James Hogg Research Centre, Institute for Heart + Lung Health,*


**Author details**

*Environmental Issues and Sustainable Development*

During the early stage of MFC technology, it was considered that this technology could only be used for the treatment of the limited wastewater, but in the recent years, it has been seen that it could be used in the treatment of almost all kinds of industrial, agricultural and municipal wastewater. The most suitable temperature studied for electricity generation via MFC is about 30°C in a regulated climate. Glycerol wastewater, the main source of pollution in the biodiesel industries, has reported a maximum

is an important characteristic for an effective and efficient treatment technology. An earlier study has reported the simultaneous methane and bio-electricity production in the anaerobic digestion process for higher concentrated wastewater at a longer detention time [62]. MFC with certain microbes have the ability for removable of organic matter, sulfides, nitrides, phosphorous, salinity, etc. Do et al. [110] reported

MFC is a wonderful technology in transferring the chemical energy inside the wide varieties of the waste organic matter with the help of the microorganism into bio-electricity. The current MFC technology is capable of producing only low power outputs which are suitable for small telemetry and wireless sensor system with a small power requirement in the remote areas. However, [39] achieved a peak power

With a minor adjustment, MFCs could also be used to generate biohydrogen instead of bio-electricity that could be extracted and processed for later use. The anode potential is improved with an external voltage of 0.23 V for overcoming the thermodynamic barrier which is much lesser than the conventional fermentation process. The electron and hydrogen ion produced by the microbial activities at the anodic chamber combines at an oxygen devoid cathode chamber generating biohydrogen. MFC has a potential of about 8–9 mol H2/mol glucose in comparison to 4 mol H2/mol glucose produced from a conventional fermentation process [52]. In order to produce hydrogen gas in a standard MFC, the anodizing potential for an

The MFC is also utilized as an electrochemical biosensor for pollutant analysis. The metabolic activities of the electrogenic microorganisms are highly affected by the sudden change in the concentration of the targeted analyte in the exposed aquatic environment and are reflected as a change of the output electric signal. MFC sensor is a self-sustained sensor unlike other types of the biosensor which require an external source of power. The biofilm-electrode is used as the sensing

Anaerobic treatment is most commonly used to treat dairy wastewaters, mainly hybrid anaerobic and UASB digesters. Upstream anaerobic sludge blanket reactors

with 81% COD removal using dairy wastewater as a substrate

the maximum of 90% COD removal and 80% columbic efficiency.

with 3D laminated composites as electrodes [39].

additional voltage must be increased roughly 0.23 V or more.

[109]. The low cost and the operational stability

**15.1 Treatment of wastewater**

surface power density 600 mW/m2

**15.2 Bio-electricity**

density of 122 W/m3

**15.3 Biohydrogen**

**15.4 Bio-sensor**

**16. Conclusion**

element in the MFC sensor [67].

**120**

Aman Dongre1 , Monika Sogani2 \*, Kumar Sonu2 , Zainab Syed1 and Gopesh Sharma1

1 Department of Biosciences, Manipal University Jaipur, Jaipur, Rajasthan, India

2 Department of Civil Engineering, Manipal University Jaipur, Jaipur, Rajasthan, India

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**16. Conclusion**

SCI is a relevant health issue because of the impact it has on the patient, his/ her family, and health system. Even though there is active research for treatment development, being surgical or medical, in order to achieve motor recovery, in the present time, there are only treatments to reduce the damage after SCI and prevent future damage so none of this therapies are curative; one of this treatments is rehabilitation, which must be coordinated by a multidisciplinary team to reduce possible complications that may arise.

To achieve better outcomes at clinical level, it is recommended to perform an integral rehabilitation therapy that combines different strategies, for example,

#### *Rehabilitation Therapies in Spinal Cord Injury Patients DOI: http://dx.doi.org/10.5772/intechopen.92825*

functional, transcutaneous, or epidural electrical stimulation in addition to musculoskeletal rehabilitation exercises to decrease complications associated with this pathology. It is important to emphasize that some rehabilitation strategies have not yet been approved by health authorities for commercial use and to date have only shown results in very small populations with very particular characteristics, which impede their general application in patients with SCI, in addition to the heterogeneity of spinal cord injuries due to the level of injury, age, treatments used before, or time since injury.

The ultimate goal of these interventions is to achieve patient's societal reintegration and become independent in most of the activities according to the severity of their condition; therefore improving and updating these strategies create opportunities for novel innovative research, as well as implementing rehabilitation strategies as a complement for regenerative pharmacological and non-pharmacological strategies for the SCI patient.