Method for detecting free fatty acid in human serum

The method using a triple quadrupole gas chromatography-mass spectrometer with derivatization and selective ion monitoring addresses the inefficiencies of existing methods, enabling rapid and accurate detection of free fatty acids in serum with enhanced sensitivity and specificity.

CN119198995APending Publication Date: 2024-12-27武汉市职业病防治院 +1
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Patent Information

Application Number
CN202411309925.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-19
Publication Date
2024-12-27

AI Technical Summary

Technical Problem

Current methods for detecting free fatty acids in human serum, such as high-performance liquid chromatography, enzymatic colorimetry, and gas chromatography, face challenges with sensitivity, specificity, and efficiency, particularly in large sample volumes, due to issues like environmental sensitivity, long reaction times, and the use of toxic reagents.

Method used

A method utilizing a triple quadrupole gas chromatography-mass spectrometer with a derivatization process involving methanol-acetyl chloride and internal standards, combined with multiple extraction and reaction monitoring, to enhance sensitivity and specificity by selectively monitoring specific parent and daughter ion pairs, reducing nonspecific interference.

Benefits of technology

Enables rapid, sensitive, and accurate detection of multiple free fatty acids in serum, ensuring consistency and repeatability through a standard curve and internal standard method, facilitating comprehensive clinical research.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a method for detecting free fatty acid in human serum. The method comprises the following steps: extracting free fatty acid from a serum sample by using an organic solvent; adding a methanol-acetyl chloride solution for derivatization reaction to generate free fatty acid methyl ester; performing multi-reaction monitoring mode detection on the free fatty acid methyl ester by using a triple quadrupole gas chromatograph-mass spectrometer to obtain the concentration of the free fatty acid methyl ester in the serum sample; and obtaining the concentration of the free fatty acid in the serum sample through a conversion formula of the free fatty acid methyl ester and the free fatty acid. According to the method, the concentration of the free fatty acid in the human serum is detected by adopting a triple quadrupole gas chromatograph-mass spectrometer, so that not only can the detection work of a large number of samples be quickly completed and the trace change of the free fatty acid in the serum be detected with high sensitivity, but also the detection specificity can be enhanced by selectively monitoring specific parent ion and daughter ion pairs; non-specific interference is reduced, and the result is ensured to be accurate.
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Description

Technical Field

[0001] The present invention relates to the field of medical detection technology, and in particular to a method for detecting free fatty acids in human serum. Background Art

[0002] Free fatty acids (FFAs), a class of organic acids present in human lipids, are important components of cell membranes and participate in metabolic activities such as energy storage and cell signal transduction. FFAs in serum usually refer to fatty acids produced during the metabolism of lipid substances. They are important components of the lipid structure of cell membranes, can provide donors for the synthesis of prostaglandins in the human body, and have multiple biological functions. FFAs in serum are mainly intermediate products of fat metabolism and important metabolic substrates for the energy metabolism of body cells. They provide energy for the metabolism of organs such as the heart, liver, and skeletal muscle. A large number of studies have shown that high free fatty acidemia caused by excessive FFAs is associated with the occurrence and development of metabolic syndrome, atherosclerosis, acute coronary syndrome, heart failure and other diseases. Due to the wide variety of FFAs, it is necessary to develop a time-saving, labor-saving and highly specific detection method that can simultaneously detect and identify multiple FFAs.

[0003] At present, the main detection methods of FFAs are high-performance liquid chromatography, enzymatic colorimetry and gas chromatography. The detection of short-chain fatty acids using high-performance liquid chromatography requires a UV detector, but due to the polarity and volatility of FFAs, as well as the lack of suitable chromophores, it is difficult for FFAs to show signals in UV detection. The use of enzymatic colorimetry is easily affected by the environment (such as temperature, humidity, etc.), and the reaction time is long, which is not conducive to large sample volume detection. It is more common to use gas chromatography to detect FFA levels using high-purity nitrogen as a carrier. After the sample is separated by gas chromatography, the mass spectrometer ionizes the substance to be tested and separates it according to the mass-to-charge ratio of the ion, which can effectively determine the level of FFAs. However, due to the low sensitivity of gas chromatography and the long detection process, it is not conducive to the rapid and accurate detection of FFAs levels.

[0004] In addition, sample pretreatment for the determination of FFAs in serum usually includes two steps: after FFAs in plasma are extracted with organic solvents, they react with methanol to form corresponding free fatty acid methyl esters (FAMEs) under the action of derivatization reagents. Common solution systems for fatty acid extraction include chloroform-methanol and methyl tert-butyl alcohol-methanol solutions. Common derivatization methods include acid catalysis and base catalysis. Among them, acid catalysis often uses sulfuric acid, hydrochloric acid, acetyl chloride and boron trifluoride as derivatization reagents, but hydrochloric acid catalysis has a long reaction time and is easy to introduce by-products, which is not suitable for large sample volume detection; while boron trifluoride is highly toxic, has a short shelf life, and is easy to react with oxygen. The base catalysis method is mainly used for the derivatization of animal fats and oils, and is not suitable for the methyl esterification of FFAs. In order to save time and reduce the use of reagents and consumables, a "one-step" reaction method for direct derivatization of samples has been reported, but its recovery rate is lower than that of the "two-step" reaction. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the object of the present invention is to provide a method for detecting free fatty acids in human serum. The method adopts a triple quadrupole gas chromatography-mass spectrometer to detect the concentration of free fatty acids in human serum. It can not only quickly complete the detection of a large number of samples and detect trace changes in free fatty acids in serum with high sensitivity, but also enhance the specificity of detection by selectively monitoring specific parent ion and daughter ion pairs, reduce nonspecific interference, and ensure accurate results.

[0006] To achieve this object, according to a first aspect of the present invention, a method for detecting free fatty acids in human serum is provided, comprising:

[0007] S100, taking the thawed serum sample and placing it in a container, adding a small amount of diluted acidic solution thereto, and then adding an appropriate amount of organic solvent to mix evenly, standing for a period of time, separating and collecting the upper organic phase, repeating the steps at least once, and combining the collected organic phases;

[0008] S200, using an inert gas to blow dry the combined and collected organic phase, adding a specific volume of a methanol-acetyl chloride solution and three internal standard solutions, and performing a derivatization reaction to obtain a first mixed solution;

[0009] S300, performing multiple extraction operations on the first mixed solution, combining the liquids obtained from the multiple extractions, drying with an inert gas, dissolving the residue in a specific volume of an analytical solvent, and performing multiple reaction monitoring detection using a triple quadrupole gas chromatography-mass spectrometer to obtain the concentration of free fatty acid methyl esters in the serum sample;

[0010] S400. Calculating the free fatty acid content in the serum sample using a conversion formula between free fatty acid methyl ester and free fatty acid.

[0011] Furthermore, the diluted acidic solution in step S100 includes an aqueous formic acid solution.

[0012] Furthermore, the organic solution in step S100 includes ethyl acetate solution.

[0013] Furthermore, the internal standard solution in step S200 includes tridecenoic acid-d 9 Isotope internal standard solution, heptadecanoic acid-d 33 Isotope internal standard solution and nonadecanoic acid-d 37 Isotope internal standard solution.

[0014] Furthermore, the inert gas includes nitrogen.

[0015] Furthermore, the analytical solvent in step S300 includes acetonitrile.

[0016] Furthermore, the method also includes constructing a linear regression equation between the concentration of free fatty acid methyl ester and the peak area by analyzing a standard solution with a known concentration.

[0017] Furthermore, the construction of a linear regression equation between the free fatty acid methyl ester concentration and the peak area includes: qualitative analysis based on retention time, the abundance ratio of the auxiliary qualitative ion and the target ion, and quantitative analysis based on the peak area of ​​the quantitative ion.

[0018] Furthermore, the construction of a linear regression equation between the free fatty acid methyl ester concentration and the peak area includes: performing linear fitting with the free fatty acid methyl ester concentration as the horizontal coordinate and the ratio of each free fatty acid methyl ester peak area to the internal standard peak area as the vertical coordinate to obtain a standard curve and construct the linear regression equation.

[0019] Further, step S300 includes calculating the concentration of free fatty acid methyl ester in the serum sample according to the ratio of the free fatty acid methyl ester peak area detected by the multiple reaction monitoring to the internal standard peak area and the linear regression equation; The beneficial effects of the present invention are:

[0020] 1. The present invention uses a triple quadrupole gas chromatography-mass spectrometer to detect the concentration of free fatty acids in human serum. It can not only quickly complete the detection of a large number of samples and detect trace changes in free fatty acids in serum with high sensitivity, but also enhance the specificity of detection by selectively monitoring specific parent ion and daughter ion pairs, reduce nonspecific interference, and ensure accurate results.

[0021] 2. The present invention uses methanol-acetyl chloride solution to carry out methyl esterification and derivatization to produce hydrochloric acid to promote lipid hydrolysis. This method has the advantages of easy preparation of the product, good stability, and high response on the instrument.

[0022] 3. The present invention can simultaneously detect and identify 34 kinds of free fatty acids, providing more comprehensive data support for clinical research and helping to further explore the relationship between free fatty acids and various diseases.

[0023] 4. The present invention ensures the consistency and repeatability of the test results by establishing a standard curve and using the internal standard method for quantitative analysis, which facilitates comparison and communication between clinical laboratories.

[0024] Additional aspects and advantages of the present application will be partially given in the following description, which will become apparent from the following description, or will be understood through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0026] Figure 1 is a flow chart of a method for detecting free fatty acids in human serum according to an embodiment of the present invention;

[0027] Figure 2 This is a peak diagram of a serum sample detected using a triple quadrupole gas chromatography-mass spectrometer in an embodiment of the present invention; DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0029] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present application refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0030] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless specifically defined as in the embodiments of this application.

[0031] like Figure 1 As shown, the present invention provides a method for detecting free fatty acids in human serum, comprising:

[0032] S100, extraction of free fatty acids from serum samples using organic solvents;

[0033] Specifically, the method comprises: placing a thawed serum sample in a container, adding a small amount of diluted acidic solution thereto, adding an appropriate amount of organic solvent and mixing evenly, standing for a period of time, separating and collecting the upper organic phase, repeating the steps at least once, and combining the collected organic phases.

[0034] S200, adding methanol-acetyl chloride solution to carry out derivatization reaction to generate free fatty acid methyl esters;

[0035] Specifically, the method comprises: using an inert gas to blow dry the combined organic phase, then adding a specific volume of a methanol-acetyl chloride solution and three internal standard solutions to the dry residue, and performing a derivatization reaction to obtain a first mixed solution;

[0036] S300, using a triple quadrupole gas chromatography-mass spectrometer to perform multiple reaction monitoring mode detection on the free fatty acid methyl ester to obtain the concentration of free fatty acid methyl ester in the serum sample;

[0037] Specifically, the method comprises: performing multiple extraction operations on the first mixed solution, combining the liquids obtained from the multiple extractions, blowing dry with an inert gas, and finally dissolving the residue in a specific volume of an analytical solvent, performing multiple reaction monitoring detection with a triple quadrupole gas chromatography-mass spectrometer, and obtaining the concentration of free fatty acid methyl esters in the serum sample;

[0038] S400, obtaining the free fatty acid concentration in the serum sample by using a conversion formula between free fatty acid methyl ester and free fatty acid.

[0039] This method uses a triple quadrupole gas chromatography-mass spectrometer to detect the concentration of free fatty acids in human serum. It can not only quickly complete the detection of a large number of samples and detect trace changes in free fatty acids in serum with high sensitivity, but also enhance the specificity of detection by selectively monitoring specific parent ion and daughter ion pairs, reduce nonspecific interference, and ensure that the test results are accurate.

[0040] The instruments and reagents used in the examples of the present invention are shown in Table 1:

[0041] Table 1

[0042]

[0043]

[0044] Embodiment 1:

[0045] This embodiment provides a method for preparing a free fatty acid methyl ester standard curve, comprising:

[0046] 1. Take 25 mg of the mixed standard fatty acid (40 components, C4-C24) CDAA-252604, dissolve it in 1 mL of methanol, store it in a brown volumetric flask at -20°C, and obtain the mixed standard working solution 1.

[0047] 2. In a 2 mL brown volumetric flask, use a microsyringe to add 10 ul of FFAs mixed standard working solution 1 and then add 990 ul of methanol to obtain mixed standard working solution 2.

[0048] 3. Use a microsyringe to dilute the FFAs standard working solution 2 in multiples in sequence. Obtain free fatty acid methyl ester mixed standard working solution 3 at eight concentration points of 15ppm, 10ppm, 5ppm, 2.5ppm, 25ppm, 0.625ppm, 0.3125ppm and 0.15625ppm, as shown in Table 2.

[0049] Table 2

[0050]

[0051] Among them, according to the proportion of substances in the mixed standard quality control certificate, C10 (methyl decanoate), C12 (methyl dodecanoate), C16 (methyl palmitate), C17 (methyl undecanoate), C18 (methyl stearate), C18:1 (methyl oleate), γC18:3 (methyl γ-linolenate), C20 (methyl arachidate), C22 (methyl behenate), and C24 (methyl lignocerate) are 4% standard series substances, and the rest are 2% standard series substances.

[0052] 4. Take 1 mg of tridecenoic acid-d 9 The isotope internal standard was dissolved in 1 mL of methanol to obtain a 1 mg / mL stock solution. 10 μl of the stock solution was dissolved in 5 mL to obtain tridecenoic acid-d 9 Isotope internal standard solution 2ug / mL; take 1mg of heptadecanoic acid-d 33 The isotope internal standard was dissolved in 1 mL of methanol to obtain a 1 mg / mL stock solution. 10 μl of the stock solution was dissolved in 5 mL to obtain heptadecanoic acid-d 33 Isotope internal standard solution 2ug / mL; take 1mg nonadecanoic acid-d 37 The isotope internal standard was dissolved in 1 mL of methanol to obtain a 1 mg / mL stock solution. 30 μl of the stock solution was dissolved in 5 mL to obtain nonadecanoic acid-d 37 Isotope internal standard solution 6ug / mL.

[0053] 5. Take 400ul of mixed standard solution 3 into a test tube, and add 10ul of each of the three internal standard solutions and 6mL of methanol solution, and then add 250ul of acetyl chloride solution. After shaking well, put it into a water bath at 50℃ for 1h. After drying with nitrogen, dissolve it in 200ul of acetonitrile and then re-dissolve it on the machine. When analyzing the sample, the retention time, the abundance ratio of the auxiliary qualitative ion and the target ion are used for qualitative analysis, and the peak area of ​​the quantitative ion is used for quantitative analysis. Linear fitting is performed with the concentration as the horizontal coordinate and the ratio of the peak area to the internal standard peak area as the vertical coordinate to obtain the standard curve. Using the internal standard method, the linear regression equation Y=bX+a (X is the ratio of the peak area of ​​each target substance to the peak area of ​​the internal standard, and Y is the concentration of each target substance) is used to calculate the content of free fatty acid methyl esters and recovery rate indicators in the sample, and R is calculated at the same time. 2 The linearity, sensitivity and determination coefficient R of various free fatty acid methyl esters 2 As shown in Table 3

[0054] Table 3

[0055]

[0056]

[0057]

[0058] As shown in Table 3, it can be understood that the determination coefficients R 2 All of them are greater than 0.995, indicating that the linearity is good within the concentration range set in the experiment. The minimum detection limit of the curve is determined by repeated injection of the lowest curve point of the mixed standard. The detection limit is low, indicating that the sensitivity of this method is good.

[0059] Embodiment 2:

[0060] This embodiment provides a method for detecting free fatty acids in human serum, comprising:

[0061] 1. Take out the blood sample and thaw it in advance.

[0062] 2. Take 100 μL of thawed serum sample in a 2 mL EP tube, add 10 μL of 0.5% formic acid aqueous solution, add 300 μL of ethyl acetate, vortex for 30 seconds, let stand for 1 minute, and take the upper organic phase. Repeat twice and combine the organic phases.

[0063] 3. After drying with nitrogen, redissolve in 6 mL of methanol and add three internal standards, add 250 μL of acetyl chloride, shake manually, and derivatize at 50°C for 1 hour.

[0064] 4. After removing from the water bath, add 2.5 mL of n-hexane and 1 mL of water, vortex for 30 seconds, let stand for 1 minute, and take the upper layer of liquid I.

[0065] 5. Add 2 mL of n-hexane to the lower solution, vortex for 30 seconds, let stand for 1 minute, and take the upper layer of liquid II.

[0066] 6. Add 1 mL of n-hexane to the lower layer of liquid, vortex for 30 seconds, let stand for 1 minute, and take the upper layer of liquid III.

[0067] 7. Liquids I, II, and III were combined, dried with nitrogen, and then redissolved in 200 μL of acetonitrile. Free fatty acid methyl esters were detected using a triple quadrupole gas chromatography-mass spectrometer. The MRM quantitative ions and qualitative ions are shown in Table 4.

[0068] Table 4

[0069]

[0070]

[0071]

[0072] Further, the peak diagram obtained by detection is as follows Figure 2 As shown, according to Figure 2 Calculate the ratio of the peak area of ​​each target substance corresponding to the free fatty acid methyl ester to the peak area of ​​the internal standard, and calculate the corresponding free fatty acid methyl ester content based on the linear equation provided in Table 3 of Example 1; then, the corresponding free fatty acid content can be calculated according to the conversion coefficient between free fatty acid methyl ester and free fatty acid. Among them, according to the published standard for the determination of fatty acids in food (GB 5009.168-2016), the conversion coefficient between free fatty acids and free fatty acid methyl ester can be known, see Table 5.

[0073] Table 5

[0074]

[0075]

[0076] Embodiment 3:

[0077] Serum quality control samples of three concentrations, low, medium and high (4% series substances 0.625, 2.5, 5ug / L, 2% series substances 0.3125, 1.25, 2.5ug / L), were configured. Six parallel experiments were conducted at each concentration level to investigate the spike recovery and relative standard deviation of the method. The samples were measured continuously within 1, 3 and 5 days, and the intra-day and inter-day RSDs were calculated. The intra-day and inter-day precision results of 34 free fatty acid methyl esters are shown in Table 6, and the spike recoveries of 34 free fatty acid methyl esters are shown in Table 7.

[0078] Table 6

[0079]

[0080]

[0081] Table 7

[0082]

[0083]

[0084] From the intra-day and inter-day precision results of 34 free fatty acid methyl esters in Table 6, it can be seen that the intra-day precision and inter-day precision of most fatty acid methyl esters are within a reasonable range, indicating that the detection method has good reproducibility. For example, the inter-day precision of C14:1 (tetradecenoic acid) is as high as 12.61%, while the inter-day precision of C18:1 (oleic acid methyl ester) is only 1.28%, showing the difference in inter-day precision among different fatty acid methyl esters.

[0085] From the spiked recoveries of 34 free fatty acid methyl esters in Table 7, it can be seen that by comparing the recoveries at low, medium and high concentrations, the recoveries of some fatty acids are close to 100%, which means that at different concentration levels, there may be certain deviations in the detection of some fatty acids; by observing the recoveries at different concentrations, it is found that with the increase in concentration, the recoveries of some fatty acids fluctuate, which indicates that the response characteristics of the detection method are different in different concentration ranges; and it can be seen that most of the spiked recoveries are between 80% and 120%, indicating that this method has high accuracy.

[0086] In summary, this method uses a triple quadrupole gas chromatography-mass spectrometer to detect the concentration of free fatty acids in human serum. It can not only quickly complete the detection of a large number of samples and detect trace changes in free fatty acids in serum with high sensitivity, but also enhance the specificity of detection by selectively monitoring specific parent ion and daughter ion pairs, reduce nonspecific interference, and ensure accurate results.

[0087] It should be understood that, although the steps in the flowchart of the accompanying drawings are displayed in sequence as indicated by the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least a part of the steps in the flowchart of the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

[0088] The above description is only a partial implementation method of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for detecting free fatty acids in human serum, characterized in that: include: S100, taking the thawed serum sample and placing it in a container, adding a small amount of diluted acidic solution thereto, and then adding an appropriate amount of organic solvent to mix evenly, standing for a period of time, separating and collecting the upper organic phase, repeating the steps at least once, and combining the collected organic phases; S200, using an inert gas to blow dry the combined and collected organic phase, adding a specific volume of a methanol-acetyl chloride solution and three internal standard solutions, and performing a derivatization reaction to obtain a first mixed solution; S300, performing multiple extraction operations on the first mixed solution, combining the liquids obtained from the multiple extractions, drying with an inert gas, dissolving the residue in a specific volume of an analytical solvent, and performing multiple reaction monitoring detection using a triple quadrupole gas chromatography-mass spectrometer to obtain the concentration of free fatty acid methyl esters in the serum sample; S400. Calculating the free fatty acid content in the serum sample using a conversion formula between free fatty acid methyl ester and free fatty acid.

2. The method for detecting free fatty acids in human serum according to claim 1, characterized in that: The diluted acidic solution in step S100 includes an aqueous formic acid solution.

3. The method for detecting free fatty acids in human serum according to claim 1, characterized in that: The organic solution in step S100 includes ethyl acetate solution.

4. The method for detecting free fatty acids in human serum according to claim 1, characterized in that: The internal standard solution in step S200 includes tridecenoic acid-d9 isotope internal standard solution, heptadecanoic acid-d 33 Isotope internal standard solution and nonadecanoic acid-d 37 Isotope internal standard solution.

5. A method for detecting free fatty acids in human serum according to claim 1, characterized in that: The inert gas includes nitrogen.

6. The method for detecting free fatty acids in human serum according to claim 1, characterized in that: The analytical solvent in step S300 includes acetonitrile.

7. A method for detecting free fatty acids in human serum according to claim 1, characterized in that: It also includes constructing a linear regression equation between the free fatty acid methyl ester concentration and the peak area by analyzing a standard solution of known concentration.

8. The method for detecting free fatty acids in human serum according to claim 7, characterized in that: The construction of the linear regression equation between the free fatty acid methyl ester concentration and the peak area includes: qualitative determination based on the retention time, the abundance ratio of the auxiliary qualitative ion and the target ion, and quantitative determination based on the peak area of ​​the quantitative ion.

9. The method for detecting free fatty acids in human serum according to claim 7, characterized in that: The linear regression equation between the free fatty acid methyl ester concentration and the peak area is constructed by performing linear fitting with the free fatty acid methyl ester concentration as the horizontal coordinate and the ratio of the peak area of ​​each free fatty acid methyl ester to the peak area of ​​the internal standard as the vertical coordinate to obtain a standard curve and construct the linear regression equation.

10. A method for detecting free fatty acids in human serum according to any one of claims 1 to 9, characterized in that: Step S300 includes calculating the concentration of free fatty acid methyl ester in the serum sample according to the ratio of the peak area of ​​free fatty acid methyl ester detected by the multiple reaction monitoring to the peak area of ​​the internal standard and the linear regression equation.