Determination of the erythrocyte sedimentation rate using the hematocrit‐corrected aggregation index and mean corpuscular volume

Abstract Background Determination of the erythrocyte sedimentation rate (ESR) by measurement of erythrocyte aggregation is an alternative to the Westergren method and can be performed rapidly. However, its principle is opaque and the ESR values obtained can deviate from Westergren method values (WG ESR) due to hematocrit. Furthermore, WG ESR is affected by particle size, but no studies have examined the effect of individual mean corpuscular volumes (MCVs). Methods Simultaneous measurement of the erythrocyte aggregation index (AI) over a 5‐s interval and determination of the complete blood count in 80 μL blood from 203 patients were performed (hematocrit, 21.4%–52.3%; MCV, 62.7–114.1 fL). ESR values were calculated with the hematocrit‐corrected AI (HAI) for comparison with WG ESR. We improved the calculation formula by using MCV. Results The sedimentation velocity of a single erythrocyte in the samples agreed well with an exponential function of HAI. ESR values calculated using HAI showed excellent correlation with WG ESR (r = 0.899, p < 0.001; Bland–Altman analysis: bias 2.76, limits of agreement (LOA) −24.5 to 30.0), but the difference between the calculated ESR and WG ESR increased with decreasing MCV. Calculation of ESR considering both HAI and MCV eliminated the MCV‐dependent deviation and improved the correlation with WG ESR (r = 0.920, p < 0.001, bias −2.17, LOA −24.6 to 20.3). Conclusion Calculation using HAI and MCV can rapidly provide ESR values that are highly correlated with WG ESR in clinical specimens over a wide range of hematocrit and MCV values.


| INTRODUC TI ON
The erythrocyte sedimentation rate (ESR) is a hematological test for measuring inflammatory activity in the body. 1 The sedimentation curve is sigmoidal and comprises three phases: the lag phase, sedimentation phase, and packing phase. 2 Under low shear flow, erythrocytes dispersed in plasma form rouleaux through interactions with inflammatory proteins such as fibrinogen and immunoglobulins and grow as aggregates over time, increasing the sedimentation rate. 3 Because the Westergren method, the international reference method for ESR measurement, 4 is manual and has a long test duration of 1 h, various methods and automated analyzers have been developed to shorten the measurement time and improve usability. [5][6][7][8][9] In particular, a method for the rapid optical measurement of erythrocyte aggregation, called syllectometry or capillary photometry, can estimate ESR in a very short time. 10,11 Syllectometry provides aggregation parameters calculated from a syllectogram, which is the transmitted or reflected light-intensity waveform caused by the formation of erythrocyte aggregates. 12 However, ESR values obtained from this rapid measurement method have been reported to deviate from the ESR obtained by the Westergren method (WG ESR) due to the hematocrit (Ht), 13,14

and the International Council for
Standardization in Hematology (ICSH) recommends that attention be paid to the differences in the methods. 15 One of the reasons for the discrepancy is that the erythrocyte aggregation parameters are Ht dependent 16,17 and analysis is time dependent. 6,18 The other is that ESR is Ht dependently decreased due to the effect of hindered settling. 19,20 In our previous report, 18 we investigated the effect of Ht and analysis time on an aggregation parameter, namely the aggregation index (AI) determined from the syllectogram, and demonstrated that the effect of Ht on the AI measured over a 5-s interval could be corrected as the Ht-corrected AI (HAI) for samples with added fibrinogen. The sedimentation velocity obtained by eliminating the effect of hindered settling could be expressed by the exponential function of the HAI obtained from the 5-s syllectogram. Moreover, an accurate sedimentation curve could be obtained by calculation based on the modified Stokes' law and HAI. 18

| Sedimentation theory
The sedimentation velocity of a single particle V s is given by Stokes' Equation (1) and increases with the square of the particle diameter. 22 Here, ρ e is the erythrocyte density [kg/m 3 ], ρ p is the plasma density A hindered settling coefficient was reported by Richardson and Zaki, shown in Equation (5). 24 For low Reynolds number conditions, such as ESR, n = 4.65.
The Ht-corrected HAI of the erythrocyte aggregation parameter AI obtained from the 5-s syllectogram measured by our instrument was defined by Equation (6). 18 (1) We reported that V s , obtained by dividing the observed V e by the hindered settling coefficient, agrees well with the value expressed in the following regression equation (Equation (7)) using HAI.
Here, a and b are coefficients and c is the settling velocity in the absence of aggregation, that is, V s . V e was obtained from a previously reported empirical formula (V e = 0.778 × WG ESR/3600/1000 [m/s]). 18 The coefficients a and b were determined by data fitting using V e and HAI obtained from 203 samples (a = 0.0102, b = 0.380).
As previously reported, the settling distance in the packing phase after a constant sedimentation rate was obtained using Mayer's equation. Details of the ESR calculations are as reported in our previous study. 18

| Correction of the sedimentation rate using MCV
To improve the accuracy of ESR estimation, we attempted to determine R ef from the MCV of individuals. Because erythrocytes have a biconcave shape, MCV can be described by the long-axis radius R L , as shown in Equation (8).
Here, β is the ratio of the volume of biconcave erythrocytes to the sphere, which was set to 0.295 based on the volume and long-axis radius of the erythrocyte model reported previously. 25 Oka reported that the effective radius of a biconcave shape was equal to 0.71R L . 15 Therefore, an effective radius from the MCV (R MCV ) is given by The modified velocity V m using R MCV is as in Equation (10). After medical treatment, patients' residual blood in K2-EDTA tubes was used with an opt-out method. A total of 203 blood samples were used for data analysis. Their WG ESR values ranged from 2 to 120 mm, which was required to test the new technology. 26

| Erythrocyte aggregation and complete blood count measurements
A flowchart illustrating the process before the acquisition of ESR values is shown in Figure 1. The analyzer (MEK-1305; Nihon Kohden Corporation) aspirated 80 μL blood and dispensed 60 μL of the sample into the reservoir connected to the syllectogram measuring unit.
The blood sample was withdrawn into a glass cell for optical measurement, and the syllectogram was analyzed to obtain AI, as in the previous report. 18 At the same time, the total blood count, including Ht and MCV (= Ht [%]/red blood cell count [10 6 /μL]), was measured using the remaining 20-μL sample through the built-in complete blood count (CBC) unit, which was similar to the performance-evaluated product. 27 All measurements from sample aspiration were performed in

| Data analysis
Calculation of Pearson's correlation coefficient and data fitting were performed using Microsoft Excel (Microsoft Corporation).
Passing-Bablok linear regression analysis and Bland-Altman analysis were performed using XLSTAT (Addinsoft). Student's t-test was used to compare the means between two groups. All p values <0.05 were considered statistically significant. Figure  Before Ht correction of AI, the correlation between V e and AI was not strong (r = 0.645, p < 0.001) due to the Ht difference. In contrast, the relationship after Ht correction showed a narrowed distribution in the horizontal direction, as shown in Figure 2B. Furthermore, as shown in Figure 2C, the relationship between HAI and the sedimentation velocity of a single erythrocyte V s , obtained by dividing V e by the hindered settling coefficient, exhibited a narrowed distribution in the vertical direction. These results agreed with the previously reported findings obtained with fibrinogen-added healthy blood. 18   Figure 3B shows the Bland-Altman plots: the difference was relatively small for an ESR below 20 mm/h but tended to increase in both positive and negative directions from 30 to 120 mm/h. Figure 4 shows the mean dif-   Figure 5B, the difference was reduced at ESRs below 90 mm compared to the case without MCV correction. As shown in Figure 6, there was no difference in the mean differences for each MCV range, indicating that the MCV dependence was effectively reduced by the correction for MCV.

| DISCUSS ION
In this study, we demonstrated that the ESR calculated using HAI, the AI corrected for the influence of Ht, correlated well with the value obtained by the Westergren method in clinical specimens.
Similar to previous work, 6 a comparison of ESR and AI without Ht correction showed a poor correlation, which was obviously due to Ht ( Figure 2A). We showed that Ht correction of AI and consideration of the influence of the hindered settling occurring in concentrated blood cells effectively improved the ESR calculation in a variety of clinical specimens ( Figure 2B,C). We then confirmed in clinical specimens that the sedimentation velocity of a single erythrocyte could be calculated as an exponential function of HAI. These results demonstrate that the values obtained by our erythrocyte aggregation measurement conform to Stokes' law, which has been widely used to explain the principle of ESR. 19,20,30 Table S1 and Figure S1, and in such cases, a non-parametric method such as Spearman's correlation coefficient is appropriate. The values of Spearman's correlation coefficient were higher than those of Pearson's correlation coefficient (Table S2), but this was because Spearman's correlation coefficient is not affected by outliers or monotonic changes, which can be a problem in a clinical laboratory. Therefore, we believe that the use of Pearson's correlation coefficient, as in previous reports, 11,13 is appropriate for the accurate comparative evaluation of clinical instruments.
Another limitation is that the sample size selection and clinical performance evaluation recommended by the ICSH 15 were not fully performed.
In conclusion, we successfully demonstrated that the simultaneous measurement of CBC, including Ht and MCV measurements, and erythrocyte aggregation in as little as 5 s provides a better correlation with WG ESR than previously reported rapid ESR assays. 13,14 In hematology tests, where ESR and CBC are frequently ordered simultaneously, our method, which can obtain ESR and CBC within 3 min with a single aspiration of only an 80 μL EDTA blood sample, will greatly contribute to improving the efficiency of hematology tests and diagnosis.