# Haematology: erythrocyte sedimentation rate (ESR)

Draft

###### Definition and measurement method

The erythrocyte sedimentation rate (ESR) $v_{ESR}$ is the sedimentation velocity of individual red blood cells (RBC, erythrocytes, from Ancient Greek $\grave{\epsilon}&space;\varrho&space;\upsilon&space;\theta&space;\rho&space;\grave&space;{o}\sigma$, red, and $\kappa&space;\grave{\upsilon&space;}\tau&space;o\varsigma$, hollow) suspended in anti-coagulated blood plasma. It is a common haematology (from Ancient Greek $\alpha\widetilde{&space;\iota&space;}\mu&space;\alpha&space;,&space;-\tau&space;o&space;\varsigma$, dark blood, and $\lambda&space;\grave{o}\gamma&space;o\varsigma$, word) test which provides non specific indications of inflammation.


In the Westergren method, anti coagulated blood (about 1.6 ml of blood and 0.4 ml of anticoagulant) is left to fall inside a Westergren pipette (see Figure 1) marked from 0 (top) to 200 mm (bottom) during the time interval $\Delta&space;t=1&space;h$ (one hour). The pipette must be left undisturbed.

Figure 1: Westergren pipette, from https://laboratoryinfo.com/esr/.

At the end of one hour, the height $h_{fall}\left&space;(&space;\Delta&space;t&space;\right&space;)$ from the top to the blood level (measured in millimeters) is read on the marked pipette, and provides the tested velocity,

$v_{ESR}=h_{fall}\left&space;(&space;\Delta&space;t&space;\right&space;)/\Delta&space;t,&space;\Delta&space;t=1\,&space;h&space;\left&space;[&space;\textup{mm/h}&space;\right&space;]>0$

Normal ESR values are usually assumed to be less than $15\,&space;\textup{mm/h}$ for women and $10\,&space;\textup{mm/h}$ for males, but the upper limit is significantly age and gender dependent [4]. An adult (>20 year age) screening of about non anemic 27000 patients, found that the following simple aging rule fitted the 98% upper bound $v_{ESR}\left&space;(&space;0.98,&space;a&space;\right&space;)$ of the measured ESR:

$\begin{matrix}&space;\\v_{ESR}\left&space;(&space;0.98,a>20,&space;male&space;\right&space;)\approx&space;a/2&space;\,&space;\:&space;\left&space;[&space;\textup{mm/h}&space;\right&space;]&space;\\&space;v_{ESR}\left&space;(&space;0.98,a>20,&space;female&space;\right&space;)\approx&space;\left&space;(a+10&space;\right&space;)/2&space;\:&space;\left&space;[&space;\textup{mm/h}&space;\right&space;]&space;\end{matrix}$

The ESR histogram is highly skewed, implying that the mean value is much lower than the upper bound $v_{ESR}\left&space;(&space;0.98,&space;a&space;\right&space;)$ and the histogram dispersion increases withe the age [2].

###### Sedimentation

Red blood cell (RBC) membrane contains ionized sialic acid (see Remark 1). This is responsible for the negatively charged surface which creates a repulsive electric zeta potential (ζ) between cells, and consequently prevents coagulation. Blood is thus a stable suspension of red blood cells in the plasma fluid. A suspension distinguishes from colloid due to particle diameter $>1\,&space;\mu&space;m$, which is the case of erythrocytes (see Figure 2). In an undisturbed suspension, particles tend to sediment unlike the smaller colloidal particles.


The erythrocyte membrane electrically behaves like a metal surface being negatively charged (electrons, -). The blood plasma behaves like an electrolyte being a solution of positive and negative ions.

Figure 2: The double layer (Helmholtz and diffuse) of plasma ions surrounding an erythrocyte.

To establish electrical neutrality, positive ions are attracted by the negatively charged erythrocyte and form a stable layer (the so-called Helmholtz layer) at a fixed distance from the membrane. A capacitance sets up around the erythrocyte together with a positive electrical potential difference between the positive ion layer and the cell membrane. A further potential difference sets up between the so-called surface of shear and the blood plasma. Beyond the surface of shear, in the so-called diffusion layer, weaker electrical attraction cannot win ionic Brownian motion and positive ions attracted by the cell membrane randomly move (diffusion).

The zeta potential is an indicator of suspension stability, that is the difficulty of sedimentation. The magnitude of the zeta potential indicates the degree of electrostatic repulsion between adjacent, similarly charged particles. For particles that are small enough, a high zeta potential confers stability, i.e. the suspension will resist aggregation and sedimentation.

###### Utility of ESR (from [5])
The ESR is an inexpensive, simple test of chronic inflammatory activity.
Indications for the ESR have decreased as the sophistication of laboratory testing has increased.
The ESR rises with age, but this increase may simply reflect a higher disease prevalence in the elderly.
The use of the ESR as a screening test in asymptomatic persons is limited by its low sensitivity and specificity.
... omissis
When there is a moderate suspicion of disease, the ESR may have some value as a “sickness index.”
An extremely elevated ESR (>100 mm/hr) will usually have an apparent cause—most commonly infection,...omissis
A mild to moderately elevated ESR without obvious etiology should prompt repeat testing after several months rather than an expensive search for occult disease.
###### Remarks

Remark 1  (from [6]).

Sialic (from Ancient Greek $\sigma&space;{\acute{\iota}}&space;\alpha&space;\lambda&space;o\nu$,  saliva) acid, a nine-carbon sugar, is an acetylated derivative of neur-aminic acid (see Figure 3). Red blood cells (RBCs) have a net negative surface charge and this bulk charge is due to ionized sialic acid. Decreased surface charge and sialic acid content have been reported in older erythrocytes, and it is postulated that the decreased electro-negativity may be related to cell senescence.

Figure 3: 3D projection of the commonest sialic acid (NANA) chemical structure
###### Reference

[1] A. Miller, M. Green and D. Robinson, Simple rule for calculating normal erythrocyte sedimentation rate, British Medical J, vol. 286, 1983, p. 266.

[2] M. B. Andresdottir, N. Sigfusson, H. Sigvaldason and V. Gudnason, Erythrocyte sedimentation rate, and independent predictor of coronary heart disease in men and women. The Reykjavik study, American J. of Epidemiology, Vol. 158, No. 9, 2003, pp. 844-851.

[3] H. Pockel Fernandes, C. Lenz Cesar and M. de L. Barjas-Castro, Electrical properties of the red blood cell membrane and immunohematological investigation, Rev Bras Hematol Hemoter. Vol. 33, No. 4, 2011, pp 297–301.

[4] Editorial team, Erythrocyte Sedimentation Rate (ESR) : Principle, Methods of Determination and Clinical Significance, Laboratory Info, January 2020, from https://laboratoryinfo.com/esr/.

[5] M.L. Brigden, Clinical Utility of the Erythrocyte Sedimentation Rate, American Family Physician, Vol. 60, No.5, October 1999, pp. 1443-1450.

[6] D. Kumar and S.I. Rizvi, Erythrocyte membrane bound and plasma sialic acid during aging, Vol. 68, No. 4, 2013, pp. 762–765