3.1. Method Optimization
Three simple chemometric methods CLS, PLS and PCR have been used for simultaneous determination of PAR & ORP in their pharmaceutical dosage form. Absorption spectra in its raw form and in its manipulated forms (First derivative, Second derivative, Ratio spectra, First derivative of ratio spectra and Second derivative of ratio spectra) as different sets of data (Fig. 3) were used to build CLS, PLS and PCR models in the range of 215-275 nm.
Figure 4 displays the absorption spectra of Zero, First derivative, Second derivative, Ratio spectra, First derivative of ratio spectra and Second derivative of ratio spectra of PAR, ORP and their mixture. CLS, PLS and PCR models were constructed by using a calibration set consisting different ratios of PAR & ORP as shown in Table 1.
Table 1 Chemometric design for calibration and validation sets for PAR & ORP.
Set
|
Calibration set
|
Set
|
Calibration set
|
Set
|
Validation set
|
Mix No.
|
PAR
|
ORP
|
Mix No.
|
PAR
|
ORP
|
Mix No.
|
PAR
|
ORP
|
C1
|
7
|
7
|
C10
|
9
|
9
|
C1
|
7
|
5
|
C 2
|
9
|
9
|
C11
|
9
|
5
|
C 2
|
5
|
5
|
C 3
|
9
|
7
|
C12
|
5
|
8
|
C 3
|
9
|
6
|
C 4
|
7
|
6
|
C13
|
5
|
7
|
C 4
|
6
|
9
|
C 5
|
6
|
6
|
C14
|
7
|
8
|
C 5
|
9
|
8
|
C 6
|
6
|
8
|
C15
|
8
|
8
|
C 6
|
8
|
5
|
C 7
|
8
|
9
|
C16
|
6
|
5
|
C 7
|
8
|
6
|
C 8
|
8
|
7
|
C17
|
6
|
7
|
C 8
|
5
|
6
|
C 9
|
7
|
9
|
|
|
|
|
|
|
Cross-validation and Scaling were carried out on the calibration set through leaving out one at a time cross-validation and mean center scaling for PLS and PCR models. The number of latent variables is varied from one model to another. Wavelength range from 215 to 275 nm with Δλ = 0.1 nm for Zero, First and Second derivative and with Δλ = 1 nm for Ratio spectra and its derivatives was used in all measurements as it was found to give more precise and more accurate results. Parameters used in the construction of PLS and PCR models were demonstrated in Table 2.
Table 2
Set
|
Calibration set
|
Set
|
Calibration set
|
Set
|
Validation set
|
Mix No.
|
PAR
|
ORP
|
Mix No.
|
PAR
|
ORP
|
Mix No.
|
PAR
|
ORP
|
C1
|
7
|
7
|
C10
|
9
|
9
|
C1
|
7
|
5
|
C 2
|
9
|
9
|
C11
|
9
|
5
|
C 2
|
5
|
5
|
C 3
|
9
|
7
|
C12
|
5
|
8
|
C 3
|
9
|
6
|
C 4
|
7
|
6
|
C13
|
5
|
7
|
C 4
|
6
|
9
|
C 5
|
6
|
6
|
C14
|
7
|
8
|
C 5
|
9
|
8
|
C 6
|
6
|
8
|
C15
|
8
|
8
|
C 6
|
8
|
5
|
C 7
|
8
|
9
|
C16
|
6
|
5
|
C 7
|
8
|
6
|
C 8
|
8
|
7
|
C17
|
6
|
7
|
C 8
|
5
|
6
|
C 9
|
7
|
9
|
|
|
|
|
|
|
Chemometric parameters used for construction of PLS & PCR models. |
The optimal number of latent variables is different from one model to another and is demonstrated for PLS in Fig. 5 and for PCR in Fig. 6.
3.2. Method validation
The Validation of CLS, PLS and PCR models were calculated by the analysis of their predictive ability on the validation (prediction) set for assessment of the accuracy and precision. The predicted values and actual values of both calibration and validation sets were compared then predicted residual error sum of squares (PRESS) and root mean square error of prediction (RMSEP) were calculated for various models as follow:
PRESS = Calculate the difference between expected values and predicted values for all the samples and square them then sum them together.
RMSEP = Divide PRESS by number of mixtures and calculate the root of the resulted value.
Results for different chemometric methods are shown in Tables 3,4,5.
Table 3
Method
|
Range (nm)
|
Interval (nm)
|
Scaling
|
Cross Validation
|
Zero
|
215-275
|
0.1
|
Mean center
|
Leave one out
|
First derivative
|
215-275
|
0.1
|
Mean center
|
Leave one out
|
Second derivative
|
215-275
|
0.1
|
Mean center
|
Leave one out
|
Ratio spectra
|
215-275
|
1
|
Mean center
|
Leave one out
|
Ratio derivative
|
215-275
|
1
|
Mean center
|
Leave one out
|
Ratio second derivative
|
215-275
|
1
|
Mean center
|
Leave one out
|
Results obtained From CLS models for determination of PAR & ORP in calibration and validation sets. |
Table 4
Spectra order
|
Zero
|
First derivative
|
Second derivative
|
Ratio spectra
|
Ratio derivative
|
Ratio 2nd derivative
|
CLS
|
Parameter
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
Calibration set
|
Mean
|
99.39
|
99.67
|
99.74
|
100.18
|
102.90
|
102.90
|
99.27
|
99.82
|
103.05
|
100.14
|
102.47
|
100.83
|
PRESS
|
1.9331
|
10.0823
|
0.2146
|
1.0009
|
10.9490
|
15.1091
|
3.1221
|
6.9166
|
140.6719
|
1.8254
|
56.6871
|
3.6026
|
|
RMSE
|
0.3372
|
0.7701
|
0.1123
|
0.2426
|
0.8025
|
0.9427
|
0.4285
|
0.6379
|
2.8766
|
0.3277
|
1.8261
|
0.4603
|
Validation set
|
Mean
|
99.03
|
100.55
|
99.89
|
104.32
|
96.94
|
117.86
|
98.67
|
100.93
|
108.78
|
101.45
|
105.83
|
102.75
|
PRESS
|
0.3072
|
2.5266
|
0.1291
|
1.3856
|
22.5319
|
34.0142
|
0.5022
|
2.0533
|
33.8073
|
1.3540
|
18.8684
|
2.0020
|
RMSE
|
0.1960
|
0.5620
|
0.1270
|
0.4162
|
1.6782
|
2.0620
|
0.2505
|
0.5066
|
2.0557
|
0.4114
|
1.5358
|
0.5002
|
Results obtained From PLS models for determination of PAR & ORP in calibration and validation sets. |
Table 5
Spectra order
|
Zero
|
First derivative
|
Second derivative
|
Ratio spectra
|
Ratio derivative
|
Ratio 2nd derivative
|
PLS
|
Parameter
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
Calibration set
|
Mean
|
100.02
|
100.02
|
100.03
|
100.01
|
100.08
|
100.03
|
100.01
|
100.01
|
100.06
|
100.00
|
100.17
|
100.10
|
PRESS
|
0.0920
|
0.1342
|
0.1016
|
0.1080
|
0.4750
|
0.2267
|
0.0852
|
0.1398
|
0.9250
|
0.1590
|
1.5352
|
0.5594
|
RMSEP
|
0.0736
|
0.0888
|
0.0773
|
0.0797
|
0.1671
|
0.1155
|
0.0708
|
0.0907
|
0.2333
|
0.0967
|
0.3005
|
0.1814
|
Validation set
|
Mean
|
100.70
|
100.58
|
101.10
|
105.96
|
101.55
|
123.01
|
100.75
|
101.10
|
100.93
|
100.83
|
113.28
|
103.68
|
PRESS
|
0.1524
|
1.0837
|
0.2410
|
1.9214
|
19.8164
|
25.2057
|
0.1778
|
1.3162
|
0.8381
|
1.5144
|
12.5025
|
2.4698
|
RMSEP
|
0.1380
|
0.3681
|
0.1735
|
0.4901
|
1.5739
|
1.7750
|
0.1491
|
0.4056
|
0.3237
|
0.4351
|
1.2501
|
0.5556
|
Results obtained From PCR models for determination of PAR & ORP in calibration and validation sets. |
3.2.1. For CLS
Zero absorption spectra and Ratio spectra can be used for determination of PAR only and not applicable for ORP. First derivative spectra can be used for determination of both PAR & ORP with the most powerful prediction for both drugs (least RMSEP for both calibration and validation sets). On the other hand, Ratio derivative and Ratio second derivative spectra may be used for determination of ORP only and can’t be used for determination of PAR. However, Second derivative spectra can’t be beneficial for determination of both drugs.
3.2.2. For PLS
Zero absorption spectra, First derivative spectra, Ratio spectra and Ratio derivative spectra can be used for determination of both PAR & ORP in which First derivative has the most powerful prediction for ORP while Zero & Ratio spectra have the most powerful prediction for PAR (It is better to use Zero absorption spectra as there is no need for extra processing). On the other hand, Second derivative spectra and Ratio second derivative spectra can’t be used for determination of both drugs at all.
3.2.3. For PCR
Zero absorption spectra, Ratio spectra and Ratio derivative spectra can be applicable for determination of both drugs in which Zero absorption spectra has the most powerful prediction for both PAR & ORP. Also, First derivative spectra may be used for determination of PAR only and can’t be used for determination of ORP. On the other hand, Second derivative spectra and Ratio second derivative can’t be used for determination of both PAR & ORP.
Although the Raw data set (Zero spectra) is the simplest method but manipulation of the spectra to give different sets of data makes a great differences and may improves the results. Although the ratio spectra set of data requires an extra-processing before carrying out the measurements, First and Second derivative of ratio spectra sets of data requires more manipulation as it needs more extra process than the ratio spectra.
3.3. Application to Pharmaceutical Tablets
The proposed chemometric methods were successfully applied for simultaneous determination of PAR and ORP in Orphenadrine plus® tablets. The results were acceptable with a great agreement in respect with labeled concentrations. The standard addition technique was carried out for accuracy and demonstrated that excipients interference was not observed (Tables 6,7, 8).
Table 6
Spectra order
|
Zero
|
First derivative
|
Second derivative
|
Ratio spectra
|
Ratio derivative
|
Ratio 2nd derivative
|
PLS
|
Parameter
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
Calibration set
|
Mean
|
100.02
|
100.02
|
100.02
|
100.16
|
102.12
|
102.00
|
100.02
|
100.03
|
100.31
|
100.08
|
100.34
|
100.04
|
PRESS
|
0.0924
|
0.1371
|
0.0948
|
1.3985
|
15.6814
|
16.6506
|
0.0898
|
0.1647
|
3.7990
|
0.5882
|
3.4579
|
0.3150
|
RMSEP
|
0.0737
|
0.0898
|
0.0747
|
0.2868
|
0.9604
|
0.9897
|
0.0727
|
0.0984
|
0.4727
|
0.1860
|
0.4510
|
0.1361
|
Validation set
|
Mean
|
100.70
|
100.58
|
101.17
|
106.82
|
103.87
|
121.31
|
100.76
|
101.12
|
100.34
|
101.37
|
116.35
|
104.22
|
PRESS
|
0.1526
|
1.0827
|
0.2431
|
2.5506
|
19.4536
|
24.8743
|
0.1783
|
1.2955
|
1.3670
|
1.1259
|
14.8215
|
2.2239
|
RMSEP
|
0.1381
|
0.3679
|
0.1743
|
0.5646
|
1.5594
|
1.7633
|
0.1493
|
0.4024
|
0.4134
|
0.3752
|
1.3611
|
0.5272
|
Pharmaceutical preparation (Orphenadrine Plus® tablets) and standard addition results from using CLS chemometric models. |
Table 7
Spectra order
|
Zero
|
First derivative
|
Second derivative
|
Ratio spectra
|
Ratio derivative
|
Ratio 2nd derivative
|
CLS
|
Parameter
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
Pharmaceutical formulation
|
Mean
|
100.07
|
102.13
|
99.79
|
100.11
|
104.83
|
109.00
|
99.44
|
105.77
|
83.69
|
101.50
|
109.96
|
100.33
|
SD
|
0.91
|
1.88
|
0.50
|
0.51
|
8.62
|
3.00
|
1.11
|
5.18
|
35.02
|
1.29
|
7.59
|
1.94
|
Standard addition technique
|
Mean
|
100.34
|
102.42
|
99.03
|
99.94
|
102.20
|
110.30
|
98.71
|
109.00
|
76.34
|
101.24
|
109.82
|
100.59
|
SD
|
0.82
|
1.20
|
0.50
|
0.86
|
10.68
|
4.28
|
0.51
|
8.95
|
27.91
|
1.51
|
9.38
|
1.72
|
Pharmaceutical preparation (Orphenadrine Plus® tablets) and standard addition results from using PLS chemometric models. |
Table 8
Spectra order
|
Zero
|
First derivative
|
Second derivative
|
Ratio spectra
|
Ratio derivative
|
Ratio 2nd derivative
|
CLS
|
Parameter
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
Pharmaceutical formulation
|
Mean
|
100.01
|
100.67
|
98.90
|
100.12
|
104.14
|
136.36
|
100.29
|
99.73
|
100.41
|
99.62
|
116.33
|
106.43
|
SD
|
0.06
|
1.88
|
0.40
|
0.15
|
21.59
|
12.56
|
0.30
|
1.59
|
0.29
|
1.97
|
18.46
|
3.99
|
Standard addition technique
|
Mean
|
100.53
|
100.25
|
99.40
|
100.47
|
107.68
|
110.18
|
100.52
|
99.89
|
99.46
|
99.85
|
107.97
|
104.85
|
SD
|
0.47
|
1.95
|
0.66
|
0.16
|
11.29
|
38.42
|
0.44
|
1.97
|
1.38
|
1.98
|
10.28
|
8.31
|
Pharmaceutical preparation (Orphenadrine Plus® tablets) and standard addition results from using PLS chemometric models. |
3.4. Statistical Analysis
Statistical analysis of these proposed methods has been done out by One-way ANOVA method where calculated F values were calculated to be lower in value than the theoretical ones showing that there was not significant difference between the proposed methods with exception of determination of ORP by using CLS and PLS models (Table 9, Tables S1 & S2). The results of determination of ORP in PLS models demonstrated that there is a significant difference between Second derivative absorption spectra and all other absorption spectra while there is no significant difference between all other absorption spectra. Also, the results of determination of ORP in CLS models demonstrated that:
Table 9
Spectra order
|
Zero
|
First derivative
|
Second derivative
|
Ratio spectra
|
Ratio derivative
|
Ratio 2nd derivative
|
CLS
|
Parameter
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
PAR
|
ORP
|
Pharmaceutical formulation
|
Mean
|
100.07
|
101.38
|
98.90
|
103.91
|
116.24
|
114.08
|
100.11
|
100.68
|
99.66
|
100.74
|
110.60
|
105.42
|
SD
|
0.07
|
0.27
|
0.40
|
1.52
|
31.10
|
31.78
|
0.11
|
1.96
|
1.32
|
1.91
|
11.96
|
3.00
|
Standard addition technique
|
Mean
|
100.16
|
100.50
|
99.40
|
104.14
|
102.65
|
109.53
|
100.31
|
100.60
|
100.63
|
100.40
|
110.48
|
102.63
|
SD
|
0.17
|
1.13
|
0.66
|
2.86
|
10.90
|
4.08
|
0.32
|
1.94
|
1.66
|
1.87
|
11.79
|
7.33
|
Statistical comparison of the results obtained by the proposed methods using One-way ANOVA. |
For Zero order absorption: There is no significant difference between Zero absorption spectra & all other absorption spectra except second derivative absorption.
For First derivative absorption: There is no significant difference between First derivative absorption spectra & all other absorption spectra except Second derivative and Ratio spectra absorption.
For Second derivative absorption: There is significant difference between Second derivative absorption spectra & all other absorption spectra except Ratio spectra absorption.
For Ratio spectra absorption: There is no significant difference between Ratio spectra absorption spectra & all other absorption spectra except First derivative absorption and Ratio second derivative absorption.
For Ratio derivative absorption: There is no significant difference between Ratio derivative absorption spectra & all other absorption spectra except Second derivative absorption.
For Ratio second derivative absorption: There is no significant difference between Ratio second derivative absorption spectra & all other absorption spectra except Ratio spectra absorption and Second derivative absorption.