This work was supported by the research unit FOR 2688 - Wa1336/12 of the German Research Foundation and by the Marie Sk&#322;odowska-Curie grant agreement No. 860436-EVIDENCE. T. J. and C. W. acknowledge funding from French German University (DFH/UFA). A. D. acknowledges funding by the Young Investigator Grant of Saarland University.

Blood sample collection and experiments were approved by the &#34;&#196;rztekammer des Saarlandes&#34;, ethics votum 51/18, and performed after informed consent was obtained according to the Declaration of Helsinki. Standard measurements should be performed with ethylenediaminetetraacetic acid (EDTA)-anticoagulated blood (standard EDTA concentration of 1.6 mg/mL blood, European norm NF EN ISO 6710), in Westergren tubes. The volume required to fill the Westergren tube depends on the manufacturer (as lower parts sometimes contain a wider reservoir); The volume should be about 1 mL of full blood, and 800 &#181;L for the tubes indicated in the Table of Materials. The method described below is however valid no matter the specific suspension and container shape, as long as the hematocrit of the probed samples is higher than 25%16. Volumes, containers, suspending medium, and additives should therefore be selected according to the specific objectives of the performed research.
1. Experiments and measurements
NOTE: Record the sedimentation rate of the sample every minute.
<ol>
	<li>Sample preparation (if required): If a control hematocrit or suspending liquid is required, start by washing the cells and preparing the samples (as an example, we show how to prepare samples with various fibrinogen levels, by mixing autologous serum and plasma). Serum can indeed be approximated as fibrinogen-free plasma26,27, and can be used in order to decrease the aggregation of RBCs, in otherwise physiological conditions. In order to prepare several samples, collect the blood in standard EDTA tubes of 9 mL and the serum in standard serum tubes (with silica beads as clotting activators) of 9 mL.
	<ol>
		<li>Centrifuge the blood samples (i.e., 9 mL of standard EDTA and serum tubes in the chosen example) at 3,000 x g for at least 7 min, for optimal compaction of the packed erythrocytes. Replace the supernatant with PBS or the desired suspending liquid, if a sufficient quantity is available. If it is simply required to control the hematocrit in autologous plasma, proceed directly to step 1.1.3. Otherwise, gently mix after inclusion of the supernatant for washing.</li>
		<li>Repeat three times. Perform the last wash with the desired suspending liquid in any case.
		<ol>
			<li>In the chosen example, prepare mixtures of autologous plasma and serum with determined proportions (e.g., 25%/75%, 50%/50%, or 75%/25% of plasma-serum volume fraction). For example, when preparing 2.5 mL of the 25%/75% plasma-serum mixture, add 0.625 mL of plasma to 1.875 mL of serum.</li>
		</ol>
		</li>
		<li>Extract the required volume of packed cells and suspend it in the desired liquid. Process the packed cells as a highly viscous liquid (using standard pre-pipetting and/or reverse-pipetting or a positive displacement pipette28). In the chosen example, for a 4 mL sample at a hematocrit of 45%, suspend 1.8 mL of packed cells within 2.2 mL of the plasma-serum mixture.</li>
	</ol>
	</li>
	<li>If the hematocrit of the sample is not controlled, determine it by high-speed microcentrifugation (other standard methods are also suitable).
	<ol>
		<li>Extract the required amount of sample for hematocrit determination: fill the micro-hematocrit capillaries by immersing its lower tip in the liquid. Stop it by covering the top opening when the required amount of sample rises in the tube by capillary suction.</li>
		<li>Seal the capillaries with sealing wax. Place them in the micro-hematocrit centrifuge and run it at 15,000 x g(12,000 rpm) for 5 min, or according to the manufacturer&#39;s instructions.</li>
		<li>Read the hematocrit level on the capillary and write it down for reference.</li>
	</ol>
	</li>
	<li>Set up a camera for recording the samples&#39; sedimentation. To avoid overloading the memory or draining the battery, power the device from the mains and save the pictures directly to a computer or external hard drive.
	<ol>
		<li>Set up a steady camera in front of the holder where the ESR tubes will be left at rest. Use a white, illuminated background (white sheets of paper in the background work perfectly).</li>
		<li>Using empty Westergren tubes, preferably without markings, set the focus and the field of view of the camera to obtain the highest resolution where the samples will be placed. Preferably, ensure that the borders of the pictures are aligned in the vertical and horizontal direction.</li>
		<li>Take a picture of a scaled tube to extract the pixel resolution. The use of RGB pictures is recommended.</li>
		<li>Set the light and the exposure time of the camera to have a white background, but no saturation. The example in Figure 1 has been obtained using a Canon EOS M50, with an exposure time of 1/15s, an aperture of F8.0, Tungsten white balance, in single shot mode with manual focus, and an ISO speed of 1,000.</li>
	</ol>
	</li>
	<li>Prepare and place the ESR tubes.
	<ol>
		<li>Fill the bottom container of the Westergren tube with the volume corresponding to the manufacturer&#39;s instructions. Insert the Westergren tube in the bottom container as indicated by the manufacturer.</li>
		<li>As soon as the first tube is ready, place it in the holder and start the camera recording. Recording one picture every minute usually gives a good resolution of the ESR kinetic curve.</li>
		<li>Prepare and place the next samples. Make sure not to stand in front of any sample when a picture is taken.</li>
		<li>Let the measurements run for at least 2 h, in order to compare with standard measurements at 30 min, 1 h, and 2 h. However, it is also better to see the saturation and arrest of the sedimentation. For healthy samples, or in case of inflammation, recording the samples overnight, between 12 h and 24 h, is more than sufficient since the curvature of the fastest samples is visible within 3 h13,19. However, if a condition decreases the sedimentation velocity, as a decrease in fibrinogen concentration does (i.e., in the chosen example, high serum volume fraction), recordings of 50 h or more might be required to obtain the most accurate information16,19.</li>
	</ol>
	</li>
</ol>
2. Image analysis
NOTE: Once the images are recorded, extract the ESR curve. An example of Matlab code is provided as Supplementary File 1 (MatlabCodeImageAnalysisSampled.m).
<ol>
	<li>Select or identify a region of interest (ROI) where only one tube is visible, the lower border being located under the lowest position of the erythrocyte cell-free plasma interface but within the sample (see&#160;Figure 1A, B). If required, rotate the picture so that the vertical direction is aligned along the first component of the picture.</li>
	<li>Convert the ROI of the RGB picture into a gray-scale picture or matrix Gr. Usually, combining the three-color channels (red [R], green [G] and blue [B]) as Gr = 2 * R - B - G&#160;is very efficient with a clear background (see Figure 1C and MatlabCodeImageAnalysisSampled.m lines 121-128).</li>
	<li>Binarize the picture. For a healthy sample, using the Otsu threshold29 usually gives a consistent result (see Figure 1D and line 133 of MatlabCodeImageAnalysisSampled.m). For samples with a high hematocrit or with some hemolysis, it might be better to adjust it manually or use another automatic method (as done in lines 129-131 of MatlabCodeImageAnalysisSampled.m), depending on the exact contrast obtained between the various phases inside the tube.</li>
	<li>Obtain the average of the pixel (or elements) values of Gr along the horizontal direction. This step minimizes the noise and efficiently averages the possible interface irregularities (see Figure 1E and MatlabCodeImageAnalysisSampled.m line 137).</li>
	<li>Before computing the variations, smooth the curve with a moving average, especially if the tubes contain some horizontal markings (see Figure 1F). For the provided examples, a moving window of ~2.5 mm (50 pixels) was used for this process (see line 138 of MatlabCodeImageAnalysisSampled.m). Then, identify the interface position as the point with the highest intensity variation (see Figure 1G).</li>
	<li>Repeat for each picture and each sample. For each sample, save the positions of the interface along time in an appropriate format to fit the physical model with any suitably fit software.</li>
</ol>
3. Fitting of the physical model
<ol>
	<li>Using any suitably fit software, knowing the hematocrit and the initial height of the blood column h0, find the values of the delay time t0, the dimensionless time &#947;, and the final packed volume fraction &#934;m of the erythrocytes that minimizes the sum of squared residual deviations for the physical model17. A Matlab code (ShapeAnalyzerIntegrated.m) is provided as Supplementary File 2 as an example of how to perform such a fit. See Supplementary File 2 for further instructions. As described elsewhere16,17, erythrocytes at physiological hematocrit sediment as a soft particle gel, where the important physical parameters are the difference in density between the plasma and RBCs of the donor &#916;&#961;, the RBC characteristic diameter rRBC, the plasma viscosity at room temperature &#951;, and the donor&#39;s hematocrit &#934;. Using these parameters, and assuming that the gravitational stress is the main driving process for the plasma to flow upward through the porous network formed by the erythrocytes after a delay time t0, one obtains the temporal evolution16,17: 
	<img alt="Equation 1" src="/files/ftp_upload/64502/64502eq1v6.png" style="margin: auto;" /> 
	with <img alt="Equation 2" src="/files/ftp_upload/64502/64502eq2v6.png" style="margin: auto;" />, <img alt="Equation 3" src="/files/ftp_upload/64502/64502eq3v6.png" style="opacity: 0.9; margin: auto;" />, and <img alt="Equation 4" src="/files/ftp_upload/64502/64502eq4v6.png" style="margin: auto;" />&#160;being the average disk radius of an erythrocyte. An example of a Matlab code performing this is provided as an attachment (ShapeAnalyzerIntegrated.m fits the function defined in SedimFit.m [Supplementary File 3]). Alternatively, G/&#947; can also be used directly as a fit parameter with units of 1/t.</li>
	<li>Once the quantitative curve is extracted from the picture, save the physical parameters of the sample. Traditional ESR values at 30 min, 1 h, or 2 h can still be extracted from the curve for reference (see ShapeAnalyzerIntegrated.m lines 123-132).</li>
</ol>

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The authors have no conflicts of interest to declare relevant to the content of this article.

For the automated protocol to work efficiently, it is important to have a clear background and proper illumination. A dark background might prevent the existence of an efficient binarization threshold. For samples with some hemolysis, which usually occurs (increases) over time, it is important to verify first that the chosen binarization threshold is relevant for both the initial and final pictures.
When it comes to the binarization process of the picture, the choice of the ROI and binarization threshold is the most sensitive step. It might be useful to manually test different threshold values on three different pictures (at the beginning, middle, and end of the sedimentation process) to ensure that the choice of the threshold indeed provides the relevant binarization for the whole process. If the sample experiences strong hemolysis, it might be necessary to restrict the analysis of the sample to the beginning of the process, when a clear interface can still be observed. As for any ESR measurement, it is also essential to avoid the presence of any bubbles in the tube. However, if some small bubbles are observed at the top of the tube, a ROI starting below the bubbles and right on top of the initial interface might still provide the relevant measurement. In this case, however, it is important to include some background space on the right and left of the tube so that the Otsu threshold can be determined while always considering a significant amount of pixels with the grey level of the background.
The method, as with all ESR measurements, relies on the assumption that a clear interface between packed erythrocytes and cell-free plasma can be seen. If the sample experiences some significant amount of hemolysis, or if the hematocrit of the sample is too diluted (under 25%17), such an interface will not be observed anymore. An ESR measurement in these conditions is then impossible to perform.
As stated earlier, this method ensures to provide the relevant speed of the gel collapse Um, which can be corrected according to the initial hematocrit of the patient17. Figure 3A, along with the raw measurements of Um, also shows the corrected values for a normalized hematocrit of &#934;0 = 0.45. It can be seen that the correction removes the overall dependency on &#934;0, as well as most of the data dispersion. Determining Um based directly on the relevant physical model also implies that the technique is more objective than an arbitrary curve smoothing, with arbitrary choices of smoothing parameters. Amongst others, this method has been shown to be more robust in medical contexts where abnormally low ESR values are observed19,20.
Another intrinsic interest of this measurement is that it gives more robust and physically interpretable data. For instance, in the case of a lowered ESR, it allows distinguishing whether the delay time t0 of the collapse is prolonged, if the network of RBCs is unusually disordered through &#947;, or if the final compaction&#160;&#934;m of the cells is somehow hindered16,19,20.
Interestingly, the measurement of the maximum sedimentation velocity is also more robust and sensitive to fibrinogen levels, as already highlighted in previous studies13,14,15. This is an important feature, as the ESR is often used to monitor inflammation, which is associated with elevated levels of fibrinogen. This sensitivity essentially arises from uncoupling Um from the time of gel collapse, which is known to have an important random component34,35,36. More accurately, as highlighted in Figure 4D16, for higher concentrations of fibrinogen, the intrinsic random variation of the delay time (in which measurements above 150 mg/mL are between 12 min and 30 min, even among a single donor) has the same order of magnitude as its underlying dependency on this parameter (between 150 mg/dL and 300 mg/dL; the average trend of the measurements only decrease from 0.45 h to 0.4 h [i.e., 27 min to 24 min]). Since this delay time is actually included in the traditional height measurement at 30 min or 1 h (durations that this delay time can sometimes reach or exceed), extracting the maximum velocity Um (presenting a systematic and significant trend for each donor) then provides a more robust and meaningful parameter13,14,15,34,35,36.
Moreover, the parameter Um can efficiently be corrected for the initial hematocrit, according to the practical result <img alt="Equation 11" src="/files/ftp_upload/64502/64502eq11v6.png" style="opacity: 0.9; margin: auto;" />&#160;described earlier17. When combining data for all the healthy donors in a previous study17, values of &#947; = 0.50 &#177; 0.06 and&#160;&#934;m&#160;= 0.86 &#177; 0.04 are obtained, which nicely reproduce the trend of Um as a function of the donor hematocrit &#934;, as shown in Figure 3. However, in practical cases, it might be more rigorous to correct the ESR with the&#160;&#947; and&#160;&#934;m values obtained for a specific donor, since fibrinogen levels can also significantly change between donors and have a significant influence on these parameters (Figure 4).
Considering the points discussed and including them in routine medical procedures, the accuracy and versatility of the ESR as an in vitro clinical tool will further improve.

The erythrocyte sedimentation rate (ESR) is a medical in vitro clinical tool, formally introduced in evidenced-based medicine during the twentieth century1,2,3,4. It is currently used worldwide as a nonspecific inflammatory test, or to monitor the evolution of some specific conditions5,6,7,8. This is mainly due to an increase in the fibrinogen concentration, but also in other plasma components such as IgM1,9,10,11. According to the current Westergren standard protocol, ESR values are reported as the measurement of the cell-free plasma layer at a given time point (30 min or 1 h) after leaving a vertical tube of a typical size of 20 cm vertically at rest12. However, this measurement method has been criticized since qualitatively different stages in the sedimentation process have been reported, including a delay before reaching the maximum settling velocity13. This delay lasts more than 1 h in approximately half of healthy samples14. The velocity during this phase obeys a different scaling than during the second, faster phase of the sedimentation15. Restricting the readout to the average settling velocity during the first hour then compares a different mix of various blood properties between different individuals.
Moreover, it has recently been demonstrated that the usual theoretical considerations behind this protocol were erroneous16,17,18. At physiological hematocrit (above approximately 25%), red blood cells (RBCs) do not sediment as separate aggregates, but rather as a continuous, so-called percolating, network of RBCs17,18, obeying a different set of physical equations than the usually mentioned Stokes sedimentation16,17. It has been shown that considering a physical description based on the time-resolved measurements of the sedimentation (whole curve) was more robust in some novel medical contexts19,20. Moreover, these measurements could be used to shed light on the physical mechanisms altering the ESR in pathologies in which cell shapes are altered19,20. Additionally, a slow ESR can have a useful medical interpretation, as indicated in the measurements of a cohort of neuroacanthocytosis syndrome patients19,20. This article reviews how to practically implement the measurement of physically-meaningful parameters, based on the whole ESR kinetics. More accurately, the method presented here extracts the maximum sedimentation speed Um, the value of which can be corrected to consider the effect of the hematocrit of the donor16,17. This parameter is more accurate and thus more reliable than the traditional measurement16,17,19,20.
In addition, in some fundamental research, instead of monitoring the inflammation state of a given patient, it is interesting to exclude the effect of hematocrit on the ESR21,22,23, or to investigate the role of RBCs in a modified ESR19,20,24,25 between different donors. It might be useful to compare samples which are not directly full blood samples from patients. Therefore, resuspending RBCs with a controlled hematocrit in the autologous plasma, or in a plasma-substituent, might be used as the first step of ESR measurement. For instance, solutions of Dextran 70 kDa with a concentration of 55 mg/mL in phosphate buffered saline (PBS) produces a sedimentation range within the control range for healthy cells19. This manuscript also shows how such steps should be conducted, and that the presented analysis is also relevant in these cases.

<table><tbody><tr><td>Anticoagulant (EDTA or Heparin) tube (for blood sample)</td><td>SARSTEDT</td><td>267001 or 265</td><td>Anticoagulated blood sample to characterize</td></tr><tr><td>Camera EOS M50</td><td>Canon</td><td>Kit EF-M18-150 IS STM</td><td>Any camera should work, provided that sector alimentation, connection to computer for automated shooting and adapted objective are available</td></tr><tr><td>Centrifuge</td><td>HERMLE</td><td>302.00 V03 - Z 36 HK</td><td>Requirements: at least 3000 x g ofr 7 min.</td></tr><tr><td>Micro-centrifuge</td><td>MLW</td><td>TH21</td><td>or any other way to determine the hematocrit</td></tr><tr><td>Micro-hematocrit capilaries</td><td>Fisher scientific</td><td>11884040</td><td>or other capillaries/containers for hematocrit determination</td></tr><tr><td>Phosphate Buffered Saline (PBS)</td><td>ThermoFisher</td><td>10010023</td><td>1x PBS, pH 7.4, 298 Osm</td></tr><tr><td>Pipettes (e.g. positive displacement pipette)</td><td>Gilson</td><td>FD10006</td><td>Pipette required to manipulate blood and/or packed cells.Other models are of course suitable, but be careful to treat blood and pakced cells as highly viscous fluids.</td></tr><tr><td>Wax sealing plate</td><td>Hirschmann</td><td>9120101</td><td>Sealing wax for the micro-hematocrit capillaries</td></tr><tr><td>Westergren tubes</td><td>Praxindo</td><td>A9244560</td><td>Any other standard Wetsergren tube should work too</td></tr><tr><td>White background with illumination</td><td>/</td><td>/</td><td>White sheet(s) of paper behind the samples, with usual room light is perfcetly sufficient.</td></tr></tbody></table>

erythrocyte sedimentation rate: a physics-driven characterization in a medical context

Erythrocyte (or red blood cell) sedimentation rate (ESR) is a physical derived parameter of blood which is often used in routine health checks and medical diagnosis. For instance, in the case of inflammation, a higher ESR is observed due to the associated increase in fibrinogen and other plasma proteins. It was believed that this increase was due to the formation of larger aggregates of red blood cells (RBCs) caused by the increase in fibrinogen. Indeed, fibrinogen is an agent-fostering aggregation of RBCs and in the Stokes regime-assumed to be observed in blood-larger aggregates sediment faster. However, all models of ESR measurements based on this hypothesis require further specific physical assumptions, not required in any other system. Besides, modern studies in the field of colloidal suspensions have established that attractive particles form percolating aggregates (i.e. aggregates as wide as the container). The sedimentation of these colloids then follows a so-called &#34;colloidal gel collapse&#34;. Recently, it has been shown that RBCs actually follow the same behavior. This hypothesis also allows to efficiently and analytically model the sedimentation curve of RBCs, from which robust and physically-meaningful descriptors can be extracted. This manuscript describes how to perform such an analysis, and discusses the benefits of this approach.

An example of an image sequence correctly acquired is provided as Supplementary Movie 1 (MovieS1.avi). A series of characteristic fits of the model is shown for various conditions in Figure 2. Fibrinogen concentration was determined from the fibrinogen concentration in the plasma Fib0, assuming that the serum does not have any fibrinogen at all. Hence, Fib = C Fib0, where C is the plasma volume fraction in the plasma-serum mixture. In previous studies16, Fib0 was determined by standard methods in the Clinical Chemistry Laboratory of Saarland University Hospital (Homburg, Germany). If it is necessary to measure such a quantity independently, a convenient method to determine fibrinogen concentration includes (semi-)automated ball coagulometers, which might also require obtaining a citrate-anticoagulated sample of blood from the donor30. The ESR curves from the studies which generated these curves could be fitted with a Pearson coefficient R2 <img alt="Equation 11" src="/files/ftp_upload/64502/64502eq11.jpg" style="margin: auto;" /> [0.974, 0.9996], with an average of 0.996 and a standard deviation of 0.004 (only one curve out of 35 gave a R2 &#60; 0.99). The parameters eventually extracted are the final hematocrit in the RBC phase &#934;m, the delay time t0-required for the gel to fracture and start to collapse-and the maximum instantaneous velocity <img alt="Equation 6" src="/files/ftp_upload/64502/64502eq6v6.png" style="opacity: 0.9; margin: auto;" />, reached at the start of the collapse. The dimensionless parameter &#947; is associated with the inverse of the pore area in the compacting network of RBCs (expressed in multiples of particle radius),&#160;&#916;&#961; is the difference in density between the plasma and RBCs of the donor, a&#160;is the RBC characteristic diameter,&#160;&#951; is the plasma viscosity at room temperature, and&#160;&#934; is the donor&#39;s hematocrit. The fit is actually performed by fixing&#160;&#916;&#961;,a,&#951;&#160;and&#160;&#934; and then determining the best &#947;,&#160;&#934;m&#160;and t0. The hematocrit should be determined independently via another standard method, while the other can be fixed at standard values (&#916;&#961;<img alt="Equation 100" src="/files/ftp_upload/64502/64502eq100.png" style="margin: auto;" />80kg/m3&#160;31,32, &#951;<img alt="Equation 100" src="/files/ftp_upload/64502/64502eq100.png" style="font-size: 14px; margin: auto;" />1.5 mPa s&#160;33, and a<img alt="Equation 100" src="/files/ftp_upload/64502/64502eq100.png" style="font-size: 14px; margin: auto;" />4 &#956;m). Any deviation of the other parameters would simply modify the determined value of&#160;&#947; by a corresponding factor, but would not change the final determination of Um, which is then a robust parameter in that regard.
Collections of parameter values collected in previous fundamental studies, showing the trends of the parameters as a function of the hematocrit and fibrinogen levels, are shown in Figure 3 and Figure 4.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/64502/64502fig01.jpg" /> 
Figure 1: Image processing. (A) Ideal view of several samples, with relevant ROIs, highlighted for one sample. (B) Zoom on the selected ROI. (C) Conversion of the colored ROI into grey-level. (D) Binarized picture obtained with the Otsu threshold. (E) The horizontally-averaged intensity of the binary picture as a function of the height (per the usual convention in image processing, the origin is considered to be on the top of the picture; see also step 2.4 of the protocol.) (F) Smoothed intensity by performing a moving average on a 50 pixel vertical neighborhood (see also step 2.5 of the protocol). (G) Variations of the smoothed intensity along the vertical direction. The position of the absolute maximal value is taken as the position of the interface (see also step 2.5 of the protocol). <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/64502fig01large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/64502/64502fig02.jpg" /> 
Figure 2: Characteristic fits. (A) Curves and fits obtained for a healthy donor, with various adjusted hematocrits. The curves are adapted from a previous study17. (B) Curves and fits obtained for a healthy donor, with various fibrinogen concentrations. Various fibrinogen concentrations were obtained by mixing autologous plasma and serum in various proportions. The curves and data are from a previous study16. Error bars (obtained from pixel resolution or fit statistics) are smaller than the symbol size. The figures have been reprinted with permission from Dasanna et al.16 (18 samples from four independent blood drawings) and Darras et al.17(16 samples from seven independent blood drawings). <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/64502fig02large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/64502/64502fig3v3.jpg" /> 
Figure 3: Characteristic values of the extracted parameters for various hematocrits. (A) Variation of the extracted maximal sedimentation velocity Um as a function of the sample hematocrit &#934;. Circles are individual measurements; different colors are related to different healthy donors. The continuous red line is the trend predicted by the model, obtained with the average values of &#934;m and &#947;. The corrected value of Um for a hematocrit of&#160;&#934; = 0.45 is also shown, both as triangles for individual values and as a straight line for the predicted constant of the model. This corrected value has been computed according to the model as <img alt="Equation 10" src="/files/ftp_upload/64502/64502eq10v6.png" style="margin: auto;" />. (B) Values obtained for the parameter &#947;. (C) Values obtained for the parameter &#934;m. (D) Values obtained for the parameter t0. Error bars for individual data obtained from fit statistics are smaller than the symbol size. This figure has been adapted with permission from Darras et al.17. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/64502fig3v2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/64502/64502fig4v3.jpg" /> 
Figure 4: Characteristic values of the extracted parameters for various fibrinogen concentrations. (A) Variation of the extracted maximal sedimentation velocity Um as a function of the sample fibrinogen concentration. Different colors are related to different healthy donors. (B) Values obtained for the parameter &#947;. (C) Values obtained for the parameter &#934;m. (D) Values obtained for the parameter t0. Error bars for individual data obtained from fit statistics are smaller than the symbol size. This figure has been reprinted with permission from Dasanna et al.16. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/64502fig4v2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Supplementary Movie 1: Example of a properly acquired image sequence. Various sample types are shown in these pictures from two different donors (same blood group). From left to right, all samples having duplicates: full blood from donor 1, suspension of RBCs from donor 1 in Dextran 70 kDa (55 mg/mL PBS) with controlled hematocrit at 45%, full blood from donor 2, suspension of RBCs from donor 2 in Dextran (45% hematocrit), suspension of RBCs from donor 1 in plasma of donor 2 (45% hematocrit), and suspension of RBCs from donor 2 in plasma of donor 1 (45% hematocrit). The samples have a wide range of sedimentation speeds, and the suspensions in Dextran also show some hemolysis. However, the provided code MatlabCodeImageAnalysisSampled.m efficiently analyzes all of them. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/MovieS1.avi" target="_blank">Please click here to download this Movie.</a>
Supplementary File 1: MatlabCodeImageAnalysisSampled.m. Main code used for the image analysis (step 2 of the protocol). In order to run the code on a specific device, line 8 should be modified. It should contain the path to the folder containing the pictures of the Westergren tubes to analyze, ending with the prefix of the pictures, if any. A set of compressed pictures is available for open-access download on Zenodo (DOI: 10.5281/zenodo.7290177). The code, and in particular the properties of each sample (defined in lines 14-61), has already been adapted to analyze these pictures. For this picture set, the prefix used was &#39;IMG_&#39;. Therefore, the string line 8 should end with &#39;\IMG_&#39; (or &#39;/IMG_&#39; on Linux systems). The last part of the code (lines 166-179) also automatically plots the extracted sedimentation curves for each sample. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/MatlabCodeImageAnalysisSampled.zip" target="_blank">Please click here to download this File.</a>
Supplementary File 2: ShapeAnalyzerIntegrated.m. Main code used to fit the physical model (step 3 of the protocol). To run this code, simply copy and paste it into the folder containing the output text files from MatlabCodeImageAnalysisSampled.m, along with SedimFit.m. The names of the files to analyze (without the .txt extension) should be listed in line 9. The initial hematocrit and height of the tube should also be contained in lines 12 and 15, respectively. This code is already prepared to analyze the curves extracted from the open-access pictures on Zenodo (DOI: 10.5281/zenodo.7290177). Once the aforementioned line codes have been modified, simply click on the &#39;Run&#39; button in the Matlab Editor toolbar. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/ShapeAnalyzerIntegratedv2.zip" target="_blank">Please click here to download this File.</a>
Supplementary File 3: SedimFit.m. Physical model adjusted by ShapeAnalyzerIntegrated.m. This file is a Matlab function, defining the functions that are fitted to the experimental curves to extract the physical parameters. It should be in the same folder as ShapeAnalyzerIntegrated.m when the analysis is run. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/64502/SedimFit.zip" target="_blank">Please click here to download this File.</a>

Watch this Scientific Journal Video about Erythrocyte Sedimentation Rate: A Physics-Driven Characterization in a Medical Context at JoVE.com

Erythrocyte Sedimentation Rate: A Physics-Driven Characterization in a Medical Context

Erythrocyte sedimentation rate (ESR) is a physical parameter, often used in routine health checks and medical diagnosis. A theoretical model that allows to extract physically-meaningful parameters from the whole sedimentation curve, based on modern colloidal knowledge, has recently been developed. Here, we present a protocol to automatically collect the ESR over time, and extract the parameters of this recent model from this automated data collection. These refined parameters are also likely to improve the medical testimony.

Erythrocyte (or red blood cell) sedimentation rate (ESR) is a physical derived parameter of blood which is often used in routine health checks and medical ...

erythrocyte-sedimentation-rate-physics-driven-characterization

Nanyang Technological University

Research

JoVE Journal

Medicine

3.2K Views.  Saarland University. Dit protocol stemt de metingen van de bezinkingssnelheid van erytrocyten af op het nieuwste fysieke model en biedt een robuustere analyse van de test. Dit protocol maakt een nauwkeuriger en systematischer gebruik van de bezinkingssnelheid van erytrocyten mogelijk, maar biedt ook de conventionele waarden. We hebben eerder aangetoond dat deze techniek bijzonder relevant is voor aandoeningen met een lage bezinkingssnelheid van erytrocyten.Het kan worden gebruikt voor diagnostische screeni...

Video: Erythrocyte Sedimentation Rate: A Physics-Driven Characterization in a Medical Context

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability

Analytical ultracentrifugation (AUC) can be used to study reversible interactions between macromolecules over a wide range of interaction strengths and under physiological conditions. This makes AUC a method of choice to quantitatively assess stoichiometry and thermodynamics of homo- and hetero-association that are transient and reversible in biochemical processes. In the modality of sedimentation equilibrium (SE), a balance between diffusion and sedimentation provides a profile as a function of radial distance that depends on a specific association model. Herein, a detailed SE protocol is described to determine the size and monomer-monomer association energy of a small membrane protein oligomer using an analytical ultracentrifuge. AUC-ES is label-free, only based on physical principles, and can be used on both water soluble and membrane proteins. An example is shown of the latter, the small hydrophobic (SH) protein in the human respiratory syncytial virus (hRSV), a 65-amino acid polypeptide with a single &#945;-helical transmembrane (TM) domain that forms pentameric ion channels. NMR-based structural data shows that SH protein has two protonatable His residues in its transmembrane domain that are oriented facing the lumen of the channel. SE experiments have been designed to determine how pH affects association constant and the oligomeric size of SH protein. While the pentameric form was preserved in all cases, its association constant was reduced at low pH. These data are in agreement with a similar pH dependency observed for SH channel activity, consistent with a lumenal orientation of the two His residues in SH protein. The latter may experience electrostatic repulsion and reduced oligomer stability at low pH. In summary, this method is applicable whenever quantitative information on subtle protein-protein association changes in physiological conditions have to be measured.&#160;&#160;

Sedimentation equilibrium (SE) can be used to study protein-protein interactions in a physiological environment. This manuscript describes the use of this technique to determine the effect of pH on the stability of a homo-pentamer formed by the small hydrophobic (SH) protein encoded by the human syncytial respiratory virus (hRSV).

Analytical ultracentrifugation (AUC) can be used to study reversible interactions between macromolecules over a wide range of interaction strengths and ...

Chemistry

Endothelialized Microfluidics for Studying Microvascular Interactions in Hematologic Diseases

Advances in microfabrication techniques have enabled the production of inexpensive and reproducible microfluidic systems for conducting biological and biochemical experiments at the micro- and nanoscales 1,2. In addition, microfluidics have also been specifically used to quantitatively analyze hematologic and microvascular processes, because of their ability to easily control the dynamic fluidic environment and biological conditions3-6. As such, researchers have more recently used microfluidic systems to study blood cell deformability, blood cell aggregation, microvascular blood flow, and blood cell-endothelial cell interactions6-13.However, these microfluidic systems either did not include cultured endothelial cells or were larger than the sizescale relevant to microvascular pathologic processes. A microfluidic platform with cultured endothelial cells that accurately recapitulates the cellular, physical, and hemodynamic environment of the microcirculation is needed to further our understanding of the underlying biophysical pathophysiology of hematologic diseases that involve the microvasculature.
Here, we report a method to create an "endothelialized" in vitro model of the microvasculature, using a simple, single mask microfabrication process in conjunction with standard endothelial cell culture techniques, to study pathologic biophysical microvascular interactions that occur in hematologic disease. This "microvasculature-on-a-chip" provides the researcher with a robust assay that tightly controls biological as well as biophysical conditions and is operated using a standard syringe pump and brightfield/fluorescence microscopy. Parameters such as microcirculatory hemodynamic conditions, endothelial cell type, blood cell type(s) and concentration(s), drug/inhibitory concentration etc., can all be easily controlled. As such, our microsystem provides a method to quantitatively investigate disease processes in which microvascular flow is impaired due to alterations in cell adhesion, aggregation, and deformability, a capability unavailable with existing assays.

A method to culture an endothelial cell monolayer throughout the entire inner 3D surface of a microfluidic device with microvascular-sized channels (&lt;30 &mu;m) is described. This in vitro microvasculature model enables the study of biophysical interactions between blood cells, endothelial cells, and soluble factors in hematologic diseases.

Advances in  microfabrication techniques have enabled the production of inexpensive and  reproducible microfluidic systems for conducting biological and ...

Bioengineering

Micro-particle Image Velocimetry for Velocity Profile Measurements of Micro Blood Flows

Micro-particle image velocimetry (&mu;PIV) is used to visualize paired images of micro particles seeded in blood flows. The images are cross-correlated to give an accurate velocity profile. A protocol is presented for &mu;PIV measurements of blood flows in microchannels. At the scale of the microcirculation, blood cannot be considered a homogeneous fluid, as it is a suspension of flexible particles suspended in plasma, a Newtonian fluid. Shear rate, maximum velocity, velocity profile shape, and flow rate can be derived from these measurements. Several key parameters such as focal depth, particle concentration, and system compliance, are presented in order to ensure accurate, useful data along with examples and representative results for various hematocrits and flow conditions.

Micro-particle image velocimetry (&mu;PIV) is used to visualize paired images of micro particles seeded in blood flows which are cross-correlated to give an accurate velocity profile. Shear rate, maximum velocity, velocity profile shape, and flow rate, each of which has clinical applications, can be derived from these measurements.

Micro-particle image velocimetry (&mu;PIV) is used to visualize paired images of micro particles seeded in blood flows. The images are cross-correlated to ...

Controlled Microfluidic Environment for Dynamic Investigation of Red Blood Cell Aggregation

Blood, as a non-Newtonian biofluid, represents the focus of numerous studies in the hemorheology field. Blood constituents include red blood cells, white blood cells and platelets that are suspended in blood plasma. Due to the abundance of the RBCs (40% to 45% of the blood volume), their behavior dictates the rheological behavior of blood especially in the microcirculation. At very low shear rates, RBCs are seen to assemble and form entities called aggregates, which causes the non-Newtonian behavior of blood. It is important to understand the conditions of the aggregates formation to comprehend the blood rheology in microcirculation. The protocol described here details the experimental procedure to determine quantitatively the RBC aggregates in microcirculation under constant shear rate, based on image processing. For this purpose, RBC-suspensions are tested and analyzed in 120 x 60 &#181;m poly-dimethyl-siloxane (PDMS) microchannels. The RBC-suspensions are entrained using a second fluid in order to obtain a linear velocity profile within the blood layer and thus achieve a wide range of constant shear rates. The shear rate is determined using a micro Particle Image Velocimetry (&#181;PIV) system, while RBC aggregates are visualized using a high speed camera. The videos captured of the RBC aggregates are analyzed using image processing techniques in order to determine the aggregate sizes based on the images intensities.

The protocol described details an experimental procedure to quantify Red Blood Cell (RBC) aggregates under a controlled and constant shear rate, based on image processing techniques. The goal of this protocol is to relate RBC aggregate sizes to the corresponding shear rate in a controlled microfluidic environment.

Blood, as a non-Newtonian biofluid, represents the focus of numerous studies in the hemorheology field. Blood constituents include red blood cells, white ...

A Rapid and Chemical-free Hemoglobin Assay with Photothermal Angular Light Scattering

Photo-thermal angular light scattering (PT-AS) is a novel optical method for measuring the hemoglobin concentration ([Hb]) of blood samples. On the basis of the intrinsic photothermal response of hemoglobin molecules, the sensor enables high-sensitivity, chemical-free measurement of [Hb]. [Hb] detection capability with a limit of 0.12 g/dl over the range of 0.35 - 17.9 g/dl has been demonstrated previously. The method can be readily implemented using inexpensive consumer electronic devices such as a laser pointer and a webcam. The use of a micro-capillary tube as a blood container also enables the hemoglobin assay with a nanoliter-scale blood volume and a low operating cost. Here, detailed instructions for the PT-AS optical setup and signal processing procedures are presented. Experimental protocols and representative results for blood samples in anemic conditions ([Hb] = 5.3, 7.5, and 9.9 g/dl) are also provided, and the measurements are compared with those from a hematology analyzer. Its simplicity in implementation and operation should enable its wide adoption in clinical laboratories and resource-limited settings.

A photo-thermal angular light scattering (PT-AS) sensor enables the rapid and chemical-free hemoglobin assay of nanoliter-scale blood samples. Here, details of the PT-AS setup and a measurement protocol for the hemoglobin concentration in blood are provided. Representative results for anemic blood samples are also presented.

Photo-thermal angular light scattering (PT-AS) is a novel optical method for measuring the hemoglobin concentration ([Hb]) of blood samples. On the basis ...

Magnetic Levitation Coupled with Portable Imaging and Analysis for Disease Diagnostics

Currently, many clinical diagnostic procedures are complex, costly, inefficient, and inaccessible to a large population in the world. The requirements for specialized equipment and trained personnel require that many diagnostic tests be performed at remote, centralized clinical laboratories. Magnetic levitation is a simple yet powerful technique and can be applied to levitate cells, which are suspended in a paramagnetic solution and placed in a magnetic field, at a position determined by equilibrium between a magnetic force and a buoyancy force. Here, we present a versatile platform technology designed for point-of-care diagnostics which uses magnetic levitation coupled to microscopic imaging and automated analysis to determine the density distribution of a patient's cells as a useful diagnostic indicator. We present two platforms operating on this principle: (i) a smartphone-compatible version of the technology, where the built-in smartphone camera is used to image cells in the magnetic field and a smartphone application processes the images and to measures the density distribution of the cells and (ii) a self-contained version where a camera board is used to capture images and an embedded processing unit with attached thin-film-transistor (TFT) screen measures and displays the results. Demonstrated applications include: (i) measuring the altered distribution of a cell population with a disease phenotype compared to a healthy phenotype, which is applied to sickle cell disease diagnosis, and (ii) separation of different cell types based on their characteristic densities, which is applied to separate white blood cells from red blood cells for white blood cell cytometry. These applications, as well as future extensions of the essential density-based measurements enabled by this portable, user-friendly platform technology, will significantly enhance disease diagnostic capabilities at the point of care.

We present a magnetic levitation technique coupled with automated imaging and analysis in both a smartphone-compatible device and a device with embedded imaging and processing. This is applied to measure the density distribution of cells with two demonstrated biomedical applications: sickle cell disease diagnosis and separating white and red blood cells.

Currently, many clinical diagnostic procedures are complex, costly, inefficient, and inaccessible to a large population in the world. The requirements for ...

Measuring Deformability and Red Cell Heterogeneity in Blood by Ektacytometry

Decreased red cell deformability is characteristic of several disorders. In some cases, the extent of defective deformability can predict severity of disease or occurrence of serious complications. Ektacytometry uses laser diffraction viscometry to measure the deformability of red blood cells subject to either increasing shear stress or an osmotic gradient at a constant value of applied shear stress. However, direct deformability measurements are difficult to interpret when measuring heterogenous blood that is characterized by the presence of both rigid and deformable red cells. This is due to the inability of rigid cells to properly align in response to shear stress and results in a distorted diffraction pattern marked by an exaggerated decrease in apparent deformability. Measurement of the degree of distortion provides an indicator of the heterogeneity of the erythrocytes in blood. In sickle cell anemia, this is correlated with the percentage of rigid cells, which reflects the hemoglobin concentration and hemoglobin composition of the erythrocytes. In addition to measuring deformability, osmotic gradient ektacytometry provides information about the osmotic fragility and hydration status of erythrocytes. These parameters also reflect the hemoglobin composition of red blood cells from sickle cell patients. Ektacytometry measures deformability in populations of red cells and does not, therefore, provide information on the deformability or mechanical properties of individual erythrocytes. Regardless, the goal of the techniques described herein is to provide a convenient and reliable method for measuring the deformability and cellular heterogeneity of blood. These techniques may be useful for monitoring temporal changes, as well as disease progression and response to therapeutic intervention in several disorders. Sickle cell anemia is one well-characterized example. Other potential disorders where measurements of red cell deformability and/or heterogeneity are of interest include blood storage, diabetes, Plasmodium infection, iron deficiency, and the hemolytic anemias due to membrane defects.

Here we present techniques to measure red cell deformability and cellular heterogeneity by ektacytometry. These techniques are applicable to general investigations of red cell deformability and specific investigations of blood diseases characterized by the presence of both rigid and deformable red cells in circulation, such as sickle cell anemia.

Decreased red cell deformability is characteristic of several disorders. In some cases, the extent of defective deformability can predict severity of ...

Immunology and Infection

A Precision Medicine Tool for Measurement and Monitoring of Hemoglobin S in Sickle Cell Disease Patients Receiving Transfusion Therapy

Sickle cell disease (SCD) causes many severe health complications, including anemia, stroke, and acute chest syndrome. Red blood cell transfusion is the most commonly used therapy to treat or prevent these devastating complications. Other therapies include hydroxyurea therapy as well as bone marrow transplantation. Chronic intermittent transfusion is especially indicated to prevent recurrent strokes. However, transfusion therapy is associated with significant adverse effects (e.g., alloimmunization and iron overload). The point-of-care (POC) lateral flow immunoassay used here quantifies the %HbS in 15 min using a small patient blood sample. Utilizing this information, the healthcare provider is able to adjust blood transfusion volume for SCD patients to achieve the desired target HbS (most often &#60;30%), while reducing the risk of transfusion-related complications. When compared to laboratory hemoglobin electrophoresis data for 38 whole blood samples, the POC test performed with very high correlation and linear fit (slope = 0.9949, R2 = 0.9751). The strong agreement between the two hemoglobin S percentage (%HbS) quantifying methods shows that 89.5% of samples fall within &#177;5.2% HbS bias. The calibration for quantifying %HbS is built into the device to allow for an automated quantification of %HbS. This time- and cost-effective POC test thus allows the healthcare provider to make timely informed decisions when treating SCD patients, using accurate and updated data.

We have developed a point-of-care immunoassay to rapidly quantify hemoglobin S (HbS) levels during transfusion therapy for sickle cell disease (SCD) patients. By applying a small amount of treated blood to the device, the healthcare provider can determine the %HbS in a SCD patient to immediately inform clinical decisions.

Sickle cell disease (SCD) causes many severe health complications, including anemia, stroke, and acute chest syndrome. Red blood cell transfusion is the ...

Characterization of Sickling During Controlled Automated Deoxygenation with Oxygen Gradient Ektacytometry

In sickle cell disease (SCD), a single point mutation in the gene coding for beta-globin causes the production of abnormal hemoglobin S (HbS). When deoxygenated, HbS can polymerize, forming rigid rods of hemoglobin, resulting in the sickling of red blood cells (RBCs). These sickled RBCs have significantly reduced deformability, causing vaso-occlusion, which leads to numerous SCD-related clinical complications, including pain, stroke, and organ damage. RBC deformability is also reduced by RBC dehydration, resulting in dense red blood cells that are more likely to sickle. To date, there is not a single widely available, rapid, and reproducible laboratory assay capable of predicting the disease severity or directly monitoring the treatment effects for novel, non-fetal hemoglobin inducing therapies. In this study, we describe a protocol to measure RBC deformability as a function of pO2 that allows for the quantitation of sickling behavior in SCD patients. Oxygen gradient ektacytometry measures RBC deformability, expressed as the elongation index (EI), as a function of pO2. RBCs are exposed to a fixed shear stress of 30 Pa during one round of deoxygenation and reoxygenation. Six readout parameters are produced. Of these, the point of sickling (PoS), defined as the pO2 at which maximum EI (EImax) shows a 5% decrease, and minimum EI during deoxygenation (EImin) are the most informative, reflecting an individual patient&#8217;s pO2 at which sickling starts and the minimal deformability of a patient&#8217;s red blood cells, respectively. PoS is associated with an individual patient&#8217;s hemoglobin affinity for oxygen, whereas EImin shows a strong correlation with fetal hemoglobin levels. We conclude that oxygen gradient ektacytometry is a promising technique to monitor the treatment of patients with SCD, as a biomarker for anti-sickling agents in clinical and preclinical trials, and an important tool to study sickling behavior of RBCs from individuals with SCD and sickle cell traits.

Here, we present oxygen gradient ektacytometry, a rapid and reproducible method to measure red blood cell deformability in samples from patients with sickle cell disease under controlled deoxygenation and reoxygenation. This technique provides a way to study red blood cell sickling and to monitor sickle cell disease treatment efficacy.

In sickle cell disease (SCD), a single point mutation in the gene coding for beta-globin causes the production of abnormal hemoglobin S (HbS). When ...

Quantitative Analysis of Viscoelastic Properties of Red Blood Cells Using Optical Tweezers and Defocusing Microscopy

The viscoelastic properties of erythrocytes have been investigated by a range of techniques. However, the reported experimental data vary. This is not only attributed to the normal variability of cells, but also to the differences in methods and models of cell response. Here, an integrated protocol using optical tweezers and defocusing microscopy is employed to obtain the rheological features of red blood cells in the frequency range of 1 Hz to 35 Hz. While optical tweezers are utilized to measure the erythrocyte-complex elastic constant, defocusing microscopy is able to obtain the cell height profile, volume, and its form factor a parameter that allows conversion of complex elastic constant into complex shear modulus. Moreover, applying a soft glassy rheology model, the scaling exponent for both moduli can be obtained. The developed methodology allows to explore the mechanical behavior of red blood cells, characterizing their viscoelastic parameters, obtained under well-defined experimental conditions, for several physiological and pathological conditions.

Here, an integrated protocol based on optical tweezers and defocusing microscopy is described to measure the rheological properties of cells. This protocol has wide applicability in studying the viscoelastic properties of erythrocytes under variable physio-pathological conditions.

The viscoelastic properties of erythrocytes have been investigated by a range of techniques. However, the reported experimental data vary. This is not ...

Erythrocyte Sedimentation Rate: A Physics-Driven Characterization in a Medical Context

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