Disclosure of Invention
The invention aims to provide a method for detecting clopidogrel intermediates and impurities, which adopts specific reversed-phase high performance liquid chromatography analysis conditions to separate and measure the clopidogrel intermediates and 5 related impurities thereof, and can effectively realize separation and quantitative measurement of the clopidogrel intermediates and 5 related substances thereof so as to reduce the influence of the impurities on the quality of a final clopidogrel product.
The method for detecting the clopidogrel intermediate and impurities adopts a high performance liquid chromatography to detect and analyze the clopidogrel intermediate and impurities, wherein a chromatographic column used in the high performance liquid chromatography is a chromatographic column with octadecylsilane chemically bonded silica gel as a filler;
the structural formula of the clopidogrel intermediate is as follows:
the impurities comprise first impurities, second impurities, third impurities, fourth impurities and fifth impurities, and the specific structural formula is as follows:
according to the high performance liquid chromatography, A, B mobile phases are used, the mobile phase A is methanol-phosphate buffer solution-acetonitrile with the volume ratio of 20:50:30-30:65:5, and the mobile phase B is methanol-phosphate buffer solution-acetonitrile with the volume ratio of 10:10:80-20:30:50, and a linear gradient elution mode is adopted.
The method according to the present invention, wherein the column used for high performance liquid chromatography is a column packed with octadecylsilane chemically bonded silica.
The method according to the invention, wherein the high performance liquid chromatography uses a column with a packing size of 4 to 10 μm, preferably a packing size of 5 μm.
The method according to the present invention, wherein the high performance liquid chromatography uses a column having an inner diameter of 3 to 10mm, preferably 4.6mm.
According to the method of the present invention, the column length of the chromatographic column used in the high performance liquid chromatography is 150 to 300mm, preferably 250mm.
According to the method of the present invention, wherein the high performance liquid chromatography uses a column packing size of 5 μm, an inner diameter of 4.6mm and a column length of 250mm. The above model parameters may be abbreviated as 5 μm by 4.6mm by 250mm, or other similar abbreviations.
The method according to the present invention, wherein the chromatographic column used for high performance liquid chromatography is a C18 chromatographic column.
The method according to the present invention, wherein the chromatographic column used for high performance liquid chromatography is a ZORBAX SB-C18 chromatographic column.
The method according to the invention, wherein the chromatographic column used for high performance liquid chromatography is a ZORBAX SB-C18 chromatographic column under the brand name Agilent.
The method according to the invention, wherein the column box temperature of the chromatographic column at the time of separation analysis by high performance liquid chromatography is 25 to 45 ℃, such as 25 to 30 ℃, such as about 30 ℃. The invention finds that the separation effect is quite good within the range of 25-30 ℃ of the column temperature box.
The method according to the invention, wherein the high performance liquid chromatography is using A, B two mobile phases. The mobile phase A is a mixed solution of methanol, acetonitrile and phosphate buffer solution, and the mobile phase B is a mixed solution of methanol, acetonitrile and phosphate buffer solution. The invention finds that mobile phase B has quite good separation effect in the range of methanol-phosphate buffer-acetonitrile (10:10:80) to methanol-phosphate buffer-acetonitrile (20:30:50) in the range of methanol-phosphate buffer-acetonitrile (20:50:30) to methanol-phosphate buffer-acetonitrile (30:65:5).
According to the method of the invention, wherein the high performance liquid chromatography is performed using A, B two mobile phases. Mobile phases A, B are all mixed solutions of methanol-phosphate buffer solution and acetonitrile. The elution mode is gradient elution. The specific linear elution procedure is as follows:
time (minutes)
|
Mobile phase a (%)
|
Mobile phase B (%)
|
0
|
30
|
70
|
10
|
30
|
70
|
25
|
0
|
100
|
65
|
0
|
100
|
66
|
30
|
70
|
80
|
30
|
70 |
The invention discovers that the linear elution is carried out according to the specific elution mode, and all related substances have quite good separation effect. In various embodiments of the present invention, all mobile phase elution is performed according to the linear elution procedure described above, unless otherwise specified.
In one embodiment, the mobile phase phosphate buffer has a pH of 2.0 to 8.0, such as a pH of 6.0 to 7.0, such as a pH of 6.0.+ -. 0.05. The invention has found that the separation effect is quite good in the pH value range of 6.0-7.0. The acid or base for adjusting the pH value includes acetic acid, formic acid, phosphoric acid, hydrochloric acid, ammonia water, etc., preferably phosphoric acid. In the experiments carried out in the following of the present invention, as not specifically described, mobile phases A, B were each methanol-phosphate buffer solution-acetonitrile mixed solution, and the pH values of mobile phases A, B were each 6.0.+ -. 0.05.
In one embodiment, the phosphate buffer is obtained by: about 3.48g to 1000ml of purified water of anhydrous dipotassium hydrogen phosphate is weighed, dissolved and mixed uniformly, and the pH value is regulated to 6.0+/-0.05 by phosphoric acid.
According to the method of the present invention, the flow rate of the mobile phase in the high performance liquid chromatography is 0.8ml/min to 1.2ml/min, and the flow rate of the mobile phase is preferably 1.0ml/min.
The method according to the invention, wherein the detector in high performance liquid chromatography is an ultraviolet detector. In one embodiment, the detection wavelength used is 215 to 225nm, with a preferred detection wavelength of 220nm.
According to the method of the invention, the measured concentration of the clopidogrel intermediate is 1-3 mg/ml, preferably 1.5-2.5 mg/ml, and preferably 2.0mg/ml.
The method according to the invention comprises the following steps:
(1) Preparing a test solution: taking a clopidogrel intermediate sample, adding a mixed solvent of methanol, acetonitrile and water to dissolve the clopidogrel intermediate sample, adding the mixed solvent of methanol, acetonitrile and water to fix the volume and preparing a solution of 1-3 mg/ml of the clopidogrel intermediate in each 1ml, particularly preparing a sample solution of 1.5-2.5 mg/ml, and preferentially preparing a sample concentration of 2.0 mg/ml;
(2) Preparation of control solution: precisely measuring the solution in the step (1), placing the solution in a 500ml volumetric flask, adding a mixed solvent of methanol, acetonitrile and water, diluting to a scale, shaking uniformly, and taking the mixed solvent as a control solution, wherein the concentration of the control solution is equal to 0.2% of that of a sample solution;
(3) Preparing a system applicability solution: dissolving a clopidogrel intermediate, an impurity I, an impurity II, an impurity III, an impurity IV and an impurity V by using a mixed solvent of methanol, acetonitrile and water, diluting and preparing about 2mg of the clopidogrel intermediate in each 1ml, and respectively 0.004mg of the impurity I, the impurity II, the impurity III, the impurity IV and the impurity V as a system applicability solution;
(4) Taking 5-25 mu l, preferably 15 mu l, of the solution in the step (1), the step (2) and the step (3), injecting the solution into a high performance liquid chromatograph, and reading at least one of the following information of impurities: the number of impurities, the types of impurities, the relative amounts of the impurities, the degree of separation between the respective chromatographic peaks, the peak areas of the respective chromatographic peaks;
(5) Reading impurity information according to the step (4), and calculating the contents of the first impurity, the second impurity, the third impurity, the fourth impurity and the fifth impurity according to a main component self-comparison method added with correction factors, wherein the calculation formulas of the contents of the first impurity, the second impurity, the third impurity, the fourth impurity and the fifth impurity are as follows: the peak area of impurity in the sample solution of step (1) is multiplied by the correction factor of impurity/the peak area of the main component of the control solution of step (2) is multiplied by 0.2, wherein the correction factor of impurity one is 0.67, the correction factor of impurity two is 1.0, the correction factor of impurity three is 0.92, the correction factor of impurity four is 0.68, and the correction factor of impurity five is 0.97. It should be noted that when the correction factor is between 0.9 and 1.1, it is considered that there is no significant difference in response, and calculation or determination may be performed without adding the correction factor; when the correction factor is between 0.2 and 5, the correction factor is substituted to calculate the test result or be used as the standard judgment basis; when the correction factor is less than 0.2 or more than 5, the self-control method should not be used for quantification or result judgment.
In the invention, the separation degree of clopidogrel intermediate and 5 impurities thereof is more than 2.
The beneficial effects of the invention are as follows:
according to the method for detecting clopidogrel intermediates and impurities, provided by the invention, the clopidogrel intermediates and 5 related impurities thereof are separated and measured by adopting specific reversed-phase high performance liquid chromatography analysis conditions, so that the separation and quantitative measurement of the clopidogrel intermediates and 5 related substances thereof can be effectively realized, and the influence of the impurities on the quality of the final clopidogrel product is reduced.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1:
instrument and conditions:
agilent 1260Infinity II high performance liquid chromatograph; a column (Agilent ZORBAX SB-C18,5 μm. Times.4.6 mm. Times.250 mm) packed with octadecylsilane chemically bonded silica, methanol-pH 6.0 phosphate buffer-acetonitrile (27:63:10) as mobile phase A, methanol-pH 6.0 phosphate buffer-acetonitrile (12:28:60) as mobile phase B, and linear gradient elution according to the elution gradient table above; the detection wavelength is 235nm; column Wen Xiangzhu temperature is 30 ℃; the flow rate of the mobile phase is 0.9ml/min; the liquid phase analysis sample volume was 15. Mu.l.
The test steps are as follows:
preparing a system applicability solution: the clopidogrel intermediate (shown as LBGL003 in the diagram, the same applies hereinafter), the impurity one (shown as LBGL100 in the diagram, the same applies hereinafter), the impurity two (shown as LBGL200 in the diagram, the same applies hereinafter), the impurity three (shown as LBGL400 in the diagram, the same applies hereinafter), the impurity four (shown as LBGL500 in the diagram, the same applies hereinafter) and the impurity five (shown as LBGL600 in the diagram) are taken in appropriate amounts, and a mixed solvent of methanol, acetonitrile and water is added in appropriate amounts to dissolve, dilute and prepare a solution of about 2mg of the clopidogrel intermediate, 2mg of each 1ml of LBGL100, LBGL200, LBGL400, LBGL500 and LBGL600 as a system applicability solution.
Preparing a test solution: taking about 40mg of the clopidogrel intermediate, precisely weighing, placing into a 20ml measuring flask, adding a mixed solvent of methanol, acetonitrile and water, dissolving, diluting to a scale, and shaking uniformly to obtain the clopidogrel intermediate.
And precisely measuring 15 mu l of each of the system applicability solution and the sample solution, performing chromatographic analysis according to the chromatographic conditions, and recording chromatograms, wherein the results are respectively shown in fig. 1 and fig. 2.
As can be seen from fig. 1, the degree of separation between the known impurities, the unknown impurities and the main component in the system applicability solution is greater than 2.0, so as to achieve effective separation, and the system applicability is good; in addition, the system applicability solution contains 6 specific added substances of clopidogrel intermediates and other 5 impurities, wherein the 6 substances are represented in fig. 1, and 5 impurities can be attributed by preparing a single impurity solution, for example, in fig. 1, RT12.622min is known LBGL100, RT3.596min is known LBGL200, RT13.622min is known LBGL400, RT8.698min is known LBGL500, RT46.753min is known LBGL600, and RT14.470min is clopidogrel intermediates LBGL003. Other examples below may also readily attribute each substance.
As can be seen from FIG. 2, 1 impurity was detected in the sample solution, wherein RT3.644min is the known LBGL200, and the separation degree between each impurity and the main component in the sample solution is greater than 2.
Example 2:
instrument and conditions:
agilent 1260Infinity II high performance liquid chromatograph; a column (Agilent ZORBAX SB-C18,5 μm. Times.4.6 mm. Times.250 mm) packed with octadecylsilane chemically bonded silica, methanol-pH 6.0 phosphate buffer-acetonitrile (25:65:10) as mobile phase A, methanol-pH 6.0 phosphate buffer-acetonitrile (15:30:55) as mobile phase B, and linear gradient elution according to the elution gradient table above; the detection wavelength is 235nm; column Wen Xiangzhu temperature is 30 ℃; the flow rate of the mobile phase is 1.0ml/min; the liquid phase analysis sample volume was 15. Mu.l.
The test steps are as follows:
preparing a system applicability solution: a solution of about 2mg of each of the clopidogrel intermediates, LBGL100, LBGL200, LBGL400, LBGL500 and LBGL600 per 1ml was prepared as a system applicability solution by dissolving a proper amount of each of the clopidogrel intermediates, LBGL100, LBGL400, LBGL500 and LBGL600 in a proper amount of a mixed solvent of methanol, acetonitrile and water, and diluting.
Preparing a test solution: taking about 40mg of the clopidogrel intermediate, precisely weighing, placing into a 20ml measuring flask, adding a mixed solvent of methanol, acetonitrile and water, dissolving, diluting to a scale, and shaking uniformly to obtain the clopidogrel intermediate.
And precisely measuring 15 mu l of each of the system applicability solution and the sample solution, performing chromatographic analysis according to the chromatographic conditions, and recording chromatograms, wherein the results are shown in fig. 3 and 4 respectively.
As can be seen from fig. 3, the degree of separation between the known impurities, the unknown impurities and the main component in the system applicability solution is greater than 2.0, so as to achieve effective separation, and the system applicability is good; in addition, the system-applicable solution contains 6 specific added substances of clopidogrel intermediates and other 5 impurities, wherein the 6 substances are represented in fig. 3, and 5 impurities can be attributed by preparing a single impurity solution, for example, in fig. 3, RT12.630min is known as LBGL100, RT3.594min is known as LBGL200, RT13.630 min is known as LBGL400, RT8.701min is known as LBGL500, RT46.760min is known as LBGL600, and RT14.480min is known as clopidogrel intermediate LBGL003. Other examples below may also readily attribute each substance.
As can be seen from FIG. 4, 1 impurity was detected in the sample solution, wherein RT3.973min is the known LBGL200, and the separation degree between each impurity and the main component in the sample solution is greater than 2.
Example 3:
instrument and conditions:
agilent 1260Infinity II high performance liquid chromatograph; a column (Agilent ZORBAX SB-C18,5 μm. Times.4.6 mm. Times.250 mm) packed with octadecylsilane chemically bonded silica, methanol-pH 6.0 phosphate buffer-acetonitrile (22:60:18) as mobile phase A, methanol-pH 6.0 phosphate buffer-acetonitrile (16:25:59) as mobile phase B, and linear gradient elution according to the elution gradient table above; the detection wavelength is 235nm; column Wen Xiangzhu temperature is 30 ℃; the flow rate of the mobile phase is 1.1ml/min; the liquid phase analysis sample volume was 15. Mu.l.
The test steps are as follows:
preparing a system applicability solution: a solution of about 2mg of each of the clopidogrel intermediates, LBGL100, LBGL200, LBGL400, LBGL500 and LBGL600 per 1ml was prepared as a system applicability solution by dissolving a proper amount of each of the clopidogrel intermediates, LBGL100, LBGL400, LBGL500 and LBGL600 in a proper amount of a mixed solvent of methanol, acetonitrile and water, and diluting.
Preparing a test solution: taking about 40mg of the clopidogrel intermediate, precisely weighing, placing into a 20ml measuring flask, adding a mixed solvent of methanol, acetonitrile and water, dissolving, diluting to a scale, and shaking uniformly to obtain the clopidogrel intermediate.
The system applicability solution and the sample solution were measured precisely and 15. Mu.l each, the chromatographic analysis was performed according to the above chromatographic conditions, and the chromatograms were recorded, and the results were shown in FIG. 5 and FIG. 6, respectively.
As can be seen from fig. 5, the degree of separation between the known impurities, the unknown impurities and the main component in the system applicability solution is greater than 2.0, so as to achieve effective separation, and the system applicability is good; in addition, the system-applicable solution contains 6 specific added substances of clopidogrel intermediates and other 5 impurities, wherein the 6 substances are represented in fig. 5, and 5 impurities can be attributed by preparing a single impurity solution, for example, in fig. 5, RT12.623min is known LBGL100, RT3.594min is known LBGL200, RT13.719 min is known LBGL400, RT8.695min is known LBGL500, RT46.771min is known LBGL600, and RT14.467min is clopidogrel intermediate LBGL003. Other examples below may also readily attribute each substance.
As can be seen from FIG. 6, 1 impurity was detected in the sample solution, wherein RT3.560 min is the known LBGL200, and the degree of separation between each impurity and the main component in the sample solution is greater than 2.
Example 4:
instrument and conditions:
agilent 1260Infinity II high performance liquid chromatograph; a column (Agilent ZORBAX SB-C18,5 μm. Times.4.6 mm. Times.250 mm) packed with octadecylsilane chemically bonded silica, methanol-pH 6.0 phosphate buffer-acetonitrile (20:50:30) as mobile phase A, methanol-pH 6.0 phosphate buffer-acetonitrile (18:30:52) as mobile phase B, and linear gradient elution according to the elution gradient table above; the detection wavelength is 235nm; column Wen Xiangzhu temperature 25 ℃; the flow rate of the mobile phase is 1.0ml/min; the liquid phase analysis sample volume was 15. Mu.l.
The test steps are as follows:
preparing a system applicability solution: a solution of about 2mg of each of the clopidogrel intermediates, LBGL100, LBGL200, LBGL400, LBGL500 and LBGL600 per 1ml was prepared as a system applicability solution by dissolving a proper amount of each of the clopidogrel intermediates, LBGL100, LBGL400, LBGL500 and LBGL600 in a proper amount of a mixed solvent of methanol, acetonitrile and water, and diluting.
Preparing a test solution: taking about 40mg of the clopidogrel intermediate, precisely weighing, placing into a 20ml measuring flask, adding a mixed solvent of methanol, acetonitrile and water, dissolving, diluting to a scale, and shaking uniformly to obtain the clopidogrel intermediate.
The system applicability solution and the sample solution were measured precisely and 15. Mu.l each, and were subjected to chromatographic analysis under the above-mentioned chromatographic conditions, and the chromatograms were recorded, with the results shown in FIG. 7 and FIG. 8, respectively.
As can be seen from fig. 7, the degree of separation between the known impurities, the unknown impurities and the main component in the system applicability solution is greater than 2.0, so as to achieve effective separation, and the system applicability is good; in addition, the system-applicable solution contains 6 specific added substances of clopidogrel intermediates and other 5 impurities, wherein the 6 substances are represented in fig. 7, and 5 impurities can be attributed by preparing a single impurity solution, for example, in fig. 7, RT12.625min is known as LBGL100, RT3.292 min is known as LBGL200, RT13.6271 min is known as LBGL400, RT8.691min is known as LBGL500, RT46.781min is known as LBGL600, and RT14.469min is known as clopidogrel intermediates LBGL003. Other examples below may also readily attribute each substance.
As can be seen from FIG. 8, 1 impurity was detected in the sample solution, wherein RT3.260min is the known LBGL200, and the separation degree between each impurity and the main component in the sample solution is greater than 2.
Example 5:
instrument and conditions:
agilent 1260Infinity II high performance liquid chromatograph; a column (Agilent ZORBAX SB-C18,5 μm. Times.4.6 mm. Times.250 mm) packed with octadecylsilane chemically bonded silica, methanol-pH 6.0 phosphate buffer-acetonitrile (30:65:5) as mobile phase A, methanol-pH 6.0 phosphate buffer-acetonitrile (20:20:60) as mobile phase B, and linear gradient elution according to the elution gradient table above; the detection wavelength is 235nm; column Wen Xiangzhu temperature is 30 ℃; the flow rate of the mobile phase is 1.0ml/min; the liquid phase analysis sample volume was 15. Mu.l.
The test steps are as follows:
preparing a system applicability solution: a solution of about 2mg of each of the clopidogrel intermediates, LBGL100, LBGL200, LBGL400, LBGL500 and LBGL600 per 1ml was prepared as a system applicability solution by dissolving a proper amount of each of the clopidogrel intermediates, LBGL100, LBGL400, LBGL500 and LBGL600 in a proper amount of a mixed solvent of methanol, acetonitrile and water, and diluting.
Preparing a test solution: taking about 40mg of the clopidogrel intermediate, precisely weighing, placing into a 20ml measuring flask, adding a mixed solvent of methanol, acetonitrile and water, dissolving, diluting to a scale, and shaking uniformly to obtain the clopidogrel intermediate.
The system applicability solution and the sample solution were measured precisely and 15. Mu.l each, and were subjected to chromatographic analysis under the above-mentioned chromatographic conditions, and the chromatograms were recorded, with the results shown in FIG. 9 and FIG. 10, respectively.
As can be seen from fig. 9, the degree of separation between the known impurities, the unknown impurities and the main component in the system-applicable solution is greater than 2.0, so as to achieve effective separation, and the system applicability is good; in addition, the system-applicable solution contains 6 specific added substances of clopidogrel intermediates and other 5 impurities, wherein the 6 substances are shown in fig. 9, and 5 impurities can be attributed by preparing a single impurity solution, for example, in fig. 9, RT12.629min is known as LBGL100, RT3.292 min is known as LBGL200, RT13.6271 min is known as LBGL400, RT8.697min is known as LBGL500, RT46.781min is known as LBGL600, and RT14.4638 min is known as clopidogrel intermediates LBGL003. Other examples below may also readily attribute each substance.
As can be seen from FIG. 10, 1 impurity was detected in the sample solution, wherein RT3.553min is the known LBGL200, and the separation degree between each impurity and the main component in the sample solution is greater than 2.
Example 6:
instrument and conditions:
agilent 1260Infinity II high performance liquid chromatograph; a column (Agilent ZORBAX SB-C18,5 μm. Times.4.6 mm. Times.250 mm) packed with octadecylsilane chemically bonded silica, methanol-pH 6.0 phosphate buffer-acetonitrile (28:65:7) as mobile phase A, methanol-pH 6.0 phosphate buffer-acetonitrile (15:22:63) as mobile phase B, and linear gradient elution according to the elution gradient table above; the detection wavelength is 235nm; column Wen Xiangzhu temperature is 35 ℃; the flow rate of the mobile phase is 1.0ml/min; the liquid phase analysis sample volume was 15. Mu.l.
The test steps are as follows:
preparing a system applicability solution: a solution of about 2mg of each of the clopidogrel intermediates, LBGL100, LBGL200, LBGL400, LBGL500 and LBGL600 per 1ml was prepared as a system applicability solution by dissolving a proper amount of each of the clopidogrel intermediates, LBGL100, LBGL400, LBGL500 and LBGL600 in a proper amount of a mixed solvent of methanol, acetonitrile and water, and diluting.
Preparing a test solution: taking about 40mg of the clopidogrel intermediate, precisely weighing, placing into a 20ml measuring flask, adding a mixed solvent of methanol, acetonitrile and water, dissolving, diluting to a scale, and shaking uniformly to obtain the clopidogrel intermediate.
The system applicability solution and the sample solution were measured precisely and 15. Mu.l each, and were subjected to chromatographic analysis under the above-mentioned chromatographic conditions, and the chromatograms were recorded, with the results shown in FIG. 11 and FIG. 12, respectively.
As can be seen from fig. 11, the degree of separation between the known impurities, the unknown impurities and the main component in the system-applicable solution is greater than 2.0, so as to achieve effective separation, and the system applicability is good; in addition, the system applicability solution contains 6 specific added substances of clopidogrel intermediates and other 5 impurities, wherein the 6 substances are represented in fig. 1, and 5 impurities can be attributed by preparing a single impurity solution, for example, in fig. 1, RT12.623min is known LBGL100, RT3.292 min is known LBGL200, RT13.616min is known LBGL400, RT8.697min is known LBGL500, RT46.7825in is known LBGL600, and RT14.463min is known clopidogrel intermediates LBGL003. Other examples below may also readily attribute each substance.
As can be seen from FIG. 12, 1 impurity was detected in the sample solution, wherein RT3.616min is the known LBGL200, and the separation degree between each impurity and the main component in the sample solution is greater than 2.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.