CN106645079B - A kind of human body blood group discrimination method based on red blood cell optical tweezer Raman spectroscopy - Google Patents

Abstract

The invention relates to the technical field of human blood group identification, in particular to a human blood group identification method based on red blood cell optical tweezers Raman spectroscopy technology. Specifically, it includes: using optical tweezers Raman spectroscopy technology to realize real-time Raman spectroscopy detection of red living cells in a physiological environment close to the human body, and obtaining characteristic Raman spectral signals of red blood cells of different blood types; using principal component analysis and linear discriminant analysis The diagnosis algorithm , dig deep into the Raman spectral characteristic fingerprint information of red blood cells of different blood types, and realize the rapid discrimination of different blood types. The advantages of the invention include: non-labeled detection of living cells can maintain the properties of red blood cells to the greatest extent; the detection process is fast; and the discrimination results are objective, reliable and accurate. The invention can provide a new method for rapid identification of clinical human blood type.

Description

A human blood type identification method based on red blood cell optical tweezers Raman spectroscopy

technical field

The invention relates to the field of medical diagnosis application and cell biology of laser spectroscopy technology. More specifically, the present invention relates to the use of optical tweezers Raman spectroscopy technology to perform Raman spectroscopy detection on single active red blood cells of different blood types, which can realize rapid and accurate human blood type identification.

Background technique

Human blood types mainly include four major categories: A, B, AB and O. Different blood types contain different red blood cells. This difference is mainly manifested in the presence of different antigens on the outer surface of red blood cells (RBCs). For example, the outer surface of RBC in type A blood has only antigen A; the outer surface of RBC in type B blood has only antigen B; and the outer surface of RBC in type AB blood has both antigens A and B on the outer surface. In clinical practice, human blood type identification is an extremely important test item. Transfusion errors, where incompatible blood is given, can lead to serious, life-threatening transfusion reactions. In addition, many recent literatures have reported the relationship between blood group and infectious diseases (malaria falciparum, Vibrio cholerae, E. coli), cardiovascular diseases (venous thromboembolism, myocardial infarction, ischemic stroke, peripheral arterial disease), and other neurological diseases. Diseases (Parkinsonian, cognitive impairment) are potentially linked. In particular, some epidemiological studies have shown that there is a certain link between human blood type and the risk of certain cancers. For example, people with blood type A have a higher risk of stomach cancer; people with blood type O have some kind of protective mechanism against pancreatic cancer.

The current clinical blood group identification methods (glass slide method, test tube method, gel micro-column method, etc.) are mainly based on the principle of immunology to determine which antigens exist on the surface of red blood cells. These methods have certain shortcomings, such as: long reaction time and the need to introduce exogenous monoclonal antibody substances, which may affect the original properties of red blood cells; easy to miss diagnosis when testing samples with low antibody titers; relying on the experience of physicians Judging the occurrence of agglutination subjectively can easily lead to missed diagnosis and misdiagnosis. Therefore, the development of a non-labeled, simple, sensitive, accurate and objective method for ABO blood group identification based on RBC analysis has extremely important clinical value.

Raman spectroscopy based on inelastic scattering is a potential non-destructive and sensitive optical detection method, which can provide molecular fingerprint information of biochemical samples, and has been widely used in biomedicine of macromolecules, cells, body fluids and tissue samples detection. Among them, Raman spectroscopy is particularly suitable for the detection and research of living cells, because there is almost no interference signal of water in the spectral band of the Raman fingerprint, which can realize the monitoring of living cells in a liquid environment. However, due to the similar Brownian motion of cells in the culture medium, conventional Raman technology cannot achieve long-term dynamic monitoring of living cells in a physiological environment. It is difficult to detect, but such a treatment method interferes with the normal physiological properties of cells and is also disturbed by strong background signals.

The emergence of optical tweezers Raman spectroscopy (LTRS) technology has greatly overcome the defects of conventional Raman spectroscopy technology, and greatly expanded and promoted the application of this technology in cell detection. LTRS can simultaneously achieve single-cell capture, manipulation, and acquisition of biochemical information, providing a label-free, rapid, and non-destructive method for detection of living cells. There is no report on the detection and analysis of red blood cells by LTRS for blood group identification.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problems existing in the current human blood group differential diagnosis: long reaction time, need to introduce exogenous monoclonal antibody substances, low detection accuracy for detection samples with low antibody titers, and detection results are largely dependent on Based on the subjective judgment of doctors, a method of human blood group identification based on red blood cell optical tweezers Raman spectroscopy is proposed.

In order to achieve the above object, the present invention adopts the following technical solutions:

A human blood type identification method based on red blood cell optical tweezers Raman spectroscopy detection, which is to use optical tweezers Raman spectroscopy technology to perform Raman spectroscopy detection on a single active red blood cell isolated from fresh human blood in a physiological environment to obtain different blood types ( High-quality and characteristic Raman spectral signals of red blood cells of type A, B, AB, O), and multivariate Raman spectral data obtained by principal component analysis (PCA) and linear discriminant analysis (LDA) Statistical analysis, based on the characteristic spectral information of red blood cells of different blood types, realizes non-labeled, rapid, objective and accurate detection and identification of different blood types.

The method for identifying human blood type based on the red blood cell optical tweezers Raman spectroscopy technology of the present invention includes the following steps:

(1) Acquisition of red blood cell samples: Collect fresh blood from people with different blood types, including A, B, AB and O, and mix the collected fresh blood from 4 different blood groups with phosphate buffered saline respectively. Mixing, centrifuging, and repeating at least three times to remove other impurities in blood red blood cells, and finally mixing pure active red blood cells with RPMI1640 cell culture medium to make red blood cell suspension and put it in the sample pool for testing;

(2) Raman spectrum test of red blood cell samples: use the optical potential well generated by laser optical tweezers to move a single red blood cell in the sample cell to a relatively independent area for Raman spectrum detection. The detection conditions are: laser wavelength 785nm, laser power 2-3mW, spectral integration time 40s, spectral test range 420-1700cm-1;

(3) Comparative analysis of the average spectrum of red blood cells of different blood types: The obtained raw red blood cell spectral data is subjected to fluorescence background subtraction and spectral area normalization, and the average spectral comparison analysis is performed to find the characteristic spectral differences of the Raman spectra of red blood cells of different blood types;

(4) Diagnostic recognition model of red blood cells of different blood types: import the preprocessed data into the PCA analysis algorithm for dimensionality reduction processing, and obtain a small amount of principal components (PCs), but these principal components still carry most of the diagnosis in the original data. Use T test to analyze the obtained principal components, and select three PCs with the most diagnostic value; finally, import these three PCs into LDA to perform linear discriminant analysis on different blood type data, and establish 6 discriminant diagnoses with posterior probability Model, calculate the final discrimination accuracy rate of each discriminative diagnosis model, and realize the objective identification of blood type;

The 6 discriminative diagnosis models are respectively a discriminative diagnosis model for distinguishing blood type A and type B;

A discriminative diagnostic model for distinguishing between A and AB blood types;

A discriminative diagnostic model for distinguishing between A and O blood types;

A discriminative diagnostic model for distinguishing between B and AB blood types;

A discriminative diagnostic model for distinguishing between B and O blood types;

A discriminative diagnostic model for distinguishing between AB and O blood types;

(5) Identification of the blood type to be tested: Collect fresh blood of the subject to be tested, obtain the Raman spectrum data of the blood to be tested according to the methods of steps (1) and (2), and import the Raman spectrum data into 6 discriminators respectively. One of the discriminative diagnostic models in the diagnostic model is calculated to obtain the corresponding posterior probability value, that is, the 6 discriminative diagnostic models are calculated at the same time, and the three discriminative diagnostic models with the largest posterior probability belonging to the same blood type are obtained. The blood types identified by the three discriminative diagnosis models should be the same blood type, so that the blood type of the blood sample to be detected can be determined.

Further, the red blood cell suspension of the step (1) is loaded into a petri dish, and the bottom of the petri dish is modified as follows: a small hole with a radius of 1 cm is opened at the bottom of the petri dish, and a high-purity 70-80 μm thick hole is opened at the bottom of the petri dish. The quartz plate seals the above-mentioned small holes, and by adjusting the capture height of the cells, Raman spectroscopy can be performed on red blood cells with different suspension heights, and the signal-to-noise ratio can be improved at the same time.

In the step (2), when performing Raman spectroscopy detection, adjust the objective lens so that the red blood cells are suspended at a height of 20-25 μm at the bottom of the sample cell.

In the present invention, a 100 times oil lens is used as an objective lens, a 785nm laser is concentrated in a sample cell to realize optical tweezers "capture" and Raman spectrum testing of a single red blood cell, and the obtained original measurement spectrum is subjected to fluorescence background subtraction processing to obtain a single red blood cell. The pure Raman spectrum signal is obtained; then the area normalization of the Raman spectrum of a single red blood cell is performed to reduce the spectral difference caused by laser power fluctuation or instrument instability, and ensure the reliability of spectral comparison analysis and multivariate statistical analysis. The obtained Raman spectra of different blood types of red blood cells are compared and analyzed by the average spectrum to find the characteristic differences of the Raman spectra of different red blood cells. Realize objective and accurate human blood type identification.

The present invention adopts the above technical scheme, utilizes optical tweezers Raman spectroscopy technology to realize real-time capture and rapid Raman spectroscopy detection of single active red blood cells, can maintain the survival state of red blood cells during the measurement process, and the detection environment is close to the time when red blood cells circulate in the body The natural physiological state greatly maintains the original biochemical characteristics of red blood cells; since Raman spectroscopy can provide molecular fingerprint information of red blood cells, the Raman spectra of red blood cells in different blood groups will be different; in addition, the multivariate statistical diagnosis algorithm uses To establish a diagnostic model to discriminate and analyze the red blood cell spectral data of different blood types. The invention is a non-marking, rapid, simple, accurate and objective method for identifying human blood type.

The laser optical tweezers red blood cell Raman spectrum blood group discrimination analysis method of the present invention can be extended to be applied to the discrimination analysis of other cancer cells and normal cells.

Description of drawings

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments:

Figure 1A is a schematic diagram of the comparison of the average Raman spectra of red blood cells of type A and type B blood; Figure 1B is a scatter plot of the PCA-LDA discriminant model of red blood cells of type A and type B blood, in which the posterior probability of 0.484 is used as the diagnostic threshold, which can be Obtained 83.9% identification accuracy.

Figure 2A is a schematic diagram of the comparison of the average Raman spectra of red blood cells of type A and type AB blood; Figure 2B is a scatter plot of the PCA-LDA discriminant model of red blood cells of type A and type AB blood, in which the posterior probability of 0.5 is used as the diagnostic threshold, which can be Obtain 100% identification accuracy.

Figure 3A is a schematic diagram of the comparison of the mean Raman spectra of red blood cells of type A and type O blood; Figure 3B is a scatter plot of the PCA-LDA discriminant model of red blood cells of type A and type O blood, in which the posterior probability of 0.395 is used as the diagnostic threshold, which can be Obtained 89.9% identification accuracy.

Figure 4A is a schematic diagram of the comparison of the average Raman spectra of red blood cells of type B and type AB blood; Figure 4B is a scatter plot of the PCA-LDA discriminant model of red blood cells of type B and type AB blood, in which the posterior probability of 0.5 is used as the diagnostic threshold, which can be Obtain 100% identification accuracy.

Figure 5A is a schematic diagram of the comparison of the mean Raman spectra of red blood cells of type B and type O blood; Figure 5B is a scatter plot of the PCA-LDA discriminant model of red blood cells of type B and type O blood, in which the posterior probability of 0.442 is used as the diagnostic threshold, which can be Obtained 98.9% identification accuracy.

Figure 6A is a schematic diagram of the comparison of the average Raman spectra of red blood cells of AB type and O type blood; Figure 6B is a PCA-LDA discriminant model scatter plot of AB type and O type blood red blood cells, in which the posterior probability of 0.061 is used as the diagnostic threshold, which can be Obtain 100% identification accuracy.

Fig. 7A is the Raman spectrum of red blood cells of the blood type to be tested; Fig. 7B is a scatter plot of the PCA-LDA discriminant diagnosis model of red blood cells of type A and B blood, wherein the posterior probability of 0.484 is used as the diagnostic threshold; Fig. C is the type A and O The scatter plot of the PCA-LDA discriminant diagnostic model of red blood cells of type A, in which the posterior probability of 0.395 was used as the diagnostic threshold; Figure 7D is the scatter plot of the PCA-LDA discriminant model of red blood cells of type A and AB, in which the posterior probability of 0.5 was used. The test probability is used as the diagnostic threshold. Solid triangles represent red blood cells of the blood type to be tested and are marked with arrows.

Detailed ways

Example 1

The specific technical details of the present invention are set forth as follows according to the implementation of human ABO blood group identification:

(1) Preparation of red blood cell samples to be tested: 30 fresh blood samples were collected from people with different blood types (A, B, AB, O), and the blood types of the experimental samples were determined by clinical blood type testing. The obtained fresh blood was mixed with PBS buffer, centrifuged, the centrifugation speed was set to 1000r/s, the centrifugation time was 3 minutes, the supernatant was removed after centrifugation, PBS was added again for centrifugation, and the procedure was repeated three times to remove other impurities in the red blood cells. . Finally, the pure active red blood cells and the RPMI1640 cell culture medium are uniformly mixed to prepare a red blood cell suspension for testing in the sample pool. The bottom of the petri dish loaded with red blood cells was modified, specifically, a small hole with a radius of 1 cm was opened at the bottom of the petri dish, and the above-mentioned small hole was sealed with a high-purity quartz piece with a thickness of 70-80 μm, and the bottom of the quartz piece was used as the Cell Raman Spectroscopy Test Window. By adjusting the capture height of cells, Raman spectroscopy can be performed on red blood cells with different suspension heights, and the signal-to-noise ratio can be improved at the same time.

(2) Test red blood cell Raman spectroscopy using optical tweezers Raman spectroscopy: use the optical potential well generated by highly focused laser optical tweezers to move a single red blood cell in the sample cell to a relatively independent area, and adjust the objective lens to suspend the red blood cell in the sample Raman spectrum detection is performed at a height of 20-25 μm at the bottom of the pool to obtain high-quality red blood cell Raman spectrum. During the test, the laser wavelength was 785nm, the laser power was 2 to 3mW, the spectral integration time was 40s, and the spectral test range was 420-1700cm-1.

(3) Compare the average Raman spectra of red blood cells of different blood types: The original spectral signals of red blood cells of different blood types will be preprocessed by fluorescence background subtraction and area normalization, and the final average Raman spectrum is shown in Figure 1-6. The system can obtain high-quality red blood cell Raman spectral signals, which contain many sharp and prominent Raman peaks, such as 490, 567, 621, 676, 753, 791, 827, 857, 898, 937, 1003, 1031, 1082 , 1128, 1173, 1224, 1308, 1337, 1397, 1447, 1547, 1583, 1606 and 1620 cm−1. There are also differences in the Raman peak intensities of red blood cells of different blood types, such as 753, 1003, and 1224 cm−1. In addition, in the 1500-1700cm ^-1 band, there are also differences between different red blood cells.

(4) Blood group identification analysis based on multivariate statistical algorithm PCA-LDA: First, import the preprocessed spectral data into SPSS software for PCA dimensionality reduction processing, reduce the original 635 spectral variables to dozens of PCs, and then use T The test analyzes the obtained PCs, and selects the PCs whose p value is less than 0.05, that is, selects the PCs with the most diagnostic efficacy.

According to the above scheme, PC2, PC3 and PC5 become the most diagnostic PCs for distinguishing between A and B blood types; PC1, PC3 and PC4 become the most diagnostic PCs for distinguishing between A and AB blood types; PC3, PC4 and PC5 became the most diagnostic PCs for distinguishing between A and O blood types; PC1, PC3 and PC4 became the most diagnostic PCs for distinguishing B and AB blood types; PC2, PC4 and PC5 became the most diagnostic PCs for distinguishing B and O blood types The most diagnostic PCs for blood type; PC1, PC2 and PC3 became the most diagnostic PCs for distinguishing AB and O blood types. Afterwards, these selected PCs were subjected to LDA discriminant analysis respectively, and a discriminant diagnosis model was established with posterior probability, which were respectively a discriminative diagnosis model for distinguishing between A and AB blood types; a discriminative diagnosis model for distinguishing between A and O blood types; A discriminative diagnostic model for blood type and AB blood type; a discriminative diagnostic model for distinguishing between B and O blood types; a discriminative diagnostic model for distinguishing between AB and O blood types.

As shown in Figure 1-6, using the posterior probability diagnostic value of 0.484, the accuracy rate of discriminating between type A and type B can reach 83.9%; using the posterior probability diagnostic value of 0.5, the identification of type A and type AB is accurate. The rate of diagnosis can reach 100%; using the posterior probability diagnostic line of 0.395, the identification accuracy rate of type A and type O can reach 89.9%; using the posterior probability diagnostic line of 0.5, the identification accuracy rate of type B and type AB can be Up to 100%; using the posterior probability diagnostic line of 0.442, the identification accuracy rate of B type and O type can reach 98.9%; using the posterior probability diagnostic line of 0.061, the identification accuracy rate of AB type and O type can reach 100% %.

(5) Identification of the blood type to be tested: Collect fresh blood of the subject to be tested, obtain the Raman spectrum data of the blood to be tested according to the methods of steps (1) and (2), and import the Raman spectrum data into 6 discriminators respectively. One of the diagnostic models in the diagnostic model is calculated to obtain the corresponding posterior probability value, that is, the six diagnostic models are calculated at the same time, and the three discriminative diagnostic models with the largest posterior probability belonging to the same blood type are obtained. The blood type determined by the diagnostic model should be the same blood type, so that the blood type of the blood sample to be tested can be determined.

Example 2

(1) Prepare a sample of red blood cells of an unknown blood type to be tested: collect 1 ml of fresh blood from a person of an unknown blood type, mix the obtained fresh blood with PBS buffer, centrifuge, set the centrifugation speed to 1000r/s, and set the centrifugation time to 3 minutes , remove the supernatant after centrifugation, add PBS again for centrifugation, and repeat this procedure three times to remove other impurities in the red blood cells. Finally, the pure active red blood cells and the RPMI1640 cell culture medium were evenly mixed to prepare a red blood cell suspension for testing in the sample pool.

(2) Test red blood cell Raman spectroscopy using optical tweezers Raman spectroscopy: use the optical potential well generated by highly focused laser optical tweezers to move a single red blood cell in the sample cell to a relatively independent area, and adjust the objective lens to suspend the red blood cell in the sample Raman spectrum detection was performed at a height of 20-25 μm at the bottom of the pool to obtain high-quality red blood cell optical tweezers Raman spectrum, as shown in Figure 7(A). During the test, the laser wavelength was 785 nm, the laser power was 2 to 3 mW, the spectral integration time was 40 s, and the spectral test range was 420-1700 cm ^-1 .

(3) Perform principal component dimensionality reduction analysis on the red blood cell optical tweezers Raman spectrum data of the unknown blood type, and select the corresponding principal components with the most diagnostic value for the six diagnostic models and import them into the corresponding diagnostic models and perform discriminant analysis. The specific selection process is as follows: select PC2, PC3 and PC5 to import type A and type B discriminant diagnostic models for discriminant analysis; select PC1, PC3 and PC4 to import type A and AB discriminant diagnostic models for discriminant calculation; select PC3, PC4 and PC5 to import A-type and O-type diagnostic models were selected for discriminant analysis; PC1, PC3 and PC4 were selected and imported into B-type and AB-type discriminant diagnostic models for discriminant analysis; PC2, PC4 and PC5 were selected and imported into B-type and O-type discriminant diagnostic models for discriminant analysis; PC1, PC2 and PC3 were imported into AB-type and O-type diagnostic models for discriminant analysis. The specific calculation results are as follows: 1. In the discriminative diagnosis model of type A and type B, the posterior probability is calculated to be 0.88, and it is discriminated as type A blood; 2. In the discriminative diagnosis model of type A and O, the posterior probability is 0.90, and Blood type A; 3. The posterior probability is calculated as 1.0 in the discriminant diagnosis model of type A and type AB, and it is discriminated as type A blood; the distribution of the posterior probability scatter plots calculated by the three types of diagnosis and diagnosis models are shown in Fig. 7 (B, C, D), where solid triangles represent unknown blood group data points and are marked by arrows. 4. The posterior probability is 0.50 in the B-type and O-type discriminant diagnostic models; 5. The posterior probability is 0.49 in the B-type and O-type discriminant-diagnostic models; 6. The posterior probability in the AB and O-type discriminative diagnostic models The probability is 0.51; in the latter three discriminant diagnosis models, the calculated posterior probabilities are all around 0.5, and it is impossible to accurately discriminate blood types. All models are identified as blood type A, so according to the results, we can objectively conclude that the unknown blood type is type A blood.

The invention uses optical tweezers Raman technology to detect the unique biochemical information of active red blood cells of different blood types, and introduces the multi-diagnostic algorithm PCA-LDA to deeply mine the potential diagnostic information in the spectral data, establishes a high-precision discrimination model, and develops a non-labeled, A new method for rapid, accurate and objective blood type identification.

Claims (3)

1. a kind of human blood type identification method based on red blood cell optical tweezers Raman spectroscopy technology, it is characterized in that: collect the fresh human blood of these 4 kinds of blood group people of A type, B type, AB type and O type, and separate out single active red blood cell , using optical tweezers Raman spectroscopy technology to conduct Raman spectroscopy detection on single active red blood cells isolated from fresh human blood in a physiological environment to obtain red blood cell Raman spectral data of type A, type B, type AB, type O blood, and then Principal component analysis and linear discriminant analysis are used to perform multivariate statistical analysis on the obtained Raman spectral data. According to the characteristic spectral information of red blood cells of four blood types, the detection and identification of blood types A, B, AB and O can be realized, including The following steps: (1) Acquisition of red blood cell samples: Collect fresh blood from people with different blood types, including A, B, AB and O, and mix the collected fresh blood from 4 different blood groups with phosphate buffered saline respectively. Mix and centrifuge to remove impurities in blood red blood cells, and finally mix the pure active red blood cells with the RPMI1640 cell culture medium to make a red blood cell suspension and place it in the sample pool for testing; (2) Raman spectrum test of red blood cell samples: use the optical potential well generated by laser optical tweezers to move a single red blood cell in the sample cell to a relatively independent area for Raman spectrum detection. The detection conditions are: laser wavelength 785nm, laser power 2-3mW, spectrum integration time 40s, spectrum testing range 420-1700cm ^-1 ; (3) Comparative analysis of the average spectrum of red blood cells of different blood types: The obtained raw red blood cell spectral data is subjected to fluorescence background subtraction and spectral area normalization, and the average spectral comparison analysis is performed to find the characteristic spectral differences of the Raman spectra of red blood cells of different blood types; (4) Diagnostic identification model of red blood cells of different blood types: import the processed data into the PCA analysis algorithm for dimensionality reduction processing, and obtain a small amount of principal components; use the T test to analyze the obtained principal components, and select the most diagnostic value. Finally, the three principal components are imported into LDA to perform linear discriminant analysis on different blood type data, and 6 discriminative diagnosis models are established, and the final discrimination accuracy rate of each discriminative diagnosis model is calculated to realize the objective identification of blood types; The 6 discriminative diagnosis models are respectively a discriminative diagnosis model for distinguishing blood type A and type B; A discriminative diagnostic model for distinguishing between A and AB blood types; A discriminative diagnostic model for distinguishing between A and O blood types; A discriminative diagnostic model for distinguishing between B and AB blood types; A discriminative diagnostic model for distinguishing between B and O blood types; A discriminative diagnostic model for distinguishing between AB and O blood types; (5) Identification of the blood type to be tested: Collect fresh blood of the subject to be tested, obtain the Raman spectrum data of the blood to be tested according to the methods of steps (1) and (2), and import the Raman spectrum data into 6 discriminators respectively. A certain discriminative diagnosis model in the diagnosis model is calculated to obtain the corresponding posterior probability value, and the blood type of the blood sample to be detected is determined. 2 . The method for identifying human blood group based on red blood cell optical tweezers Raman spectroscopy technology according to claim 1 , wherein the red blood cell suspension in step (1) is loaded in a petri dish, and the bottom of the petri dish is Carry out the following treatment: open a small hole with a radius of 1 cm at the bottom of the culture dish, seal the above small hole with a high-purity quartz sheet with a thickness of 70-80 μm, and adjust the capture height of the cells to realize the red blood cells with different suspension heights. Raman test. 3 . The method for identifying human blood group based on red blood cell optical tweezers Raman spectroscopy technology according to claim 1 , wherein in the step (2), when performing Raman spectroscopy detection, the objective lens is adjusted to suspend the red blood cells in the sample. 4 . 20-25μm height position at the bottom of the pool.