| JOURNAL HOME | CME HOME | THIS MONTH | PAST ISSUES | ETOC | COLLECTIONS |
| AUTHORS | REVIEWERS | EDITORIAL BOARD | FEEDBACK | RSS | HELP |
| ||||||||||||||
| ||||||||||||||
|
|
|
|
||||||||||||
|
||||||||||||||
Department of Biophysics of Cerrahpasa Medical Faculty, Istanbul University, Istanbul, Turkey Sureyyapasa Thoracic and Cardiovascular Disease Hospital, Cardiovascular Surgery Clinic, Istanbul, Turkey
To the Editor:
In the study published by Eckmann et al. (1) there are interesting data about the alterations of blood viscosity under various conditions during surgery. However, the information concerning the relation between shear rate and vessel diameter is confusing, especially to the readers who are interested in hemorheology.
It is well known that hemorheology is the science dealing with flow and deformation of blood and blood vessels (2). Its major field of interest is blood viscosity (BV). BV is determined by plasma viscosity, hematocrit, erythrocyte deformability, and aggregability. These factors are interrelated in a complex manner. Because of the erythrocytes ability to deform and aggregate, blood is a fluid with non-Newtonian behavior. That is to say, blood viscosity varies with the force applied to it. BV is dependent on shear rate. This means viscosity decreases when shear rate increases. The rheological term "shear rate" is almost synonymous with velocity gradient. Shear rate is determined by the diameter of vessels. The high shear rate is present when flow is fast and the vessel diameter small, and low shear rate is present when flow is slow and the vessel has a large diameter. The non-Newtonian behavior of blood is due to the tendency of erythrocytes to aggregate at low shear rates. Furthermore, when shear rate is high, the erythrocytes are deformed to optimally adapt to flow conditions. In normal circumstances, in capillaries, high shear rates occur and blood viscosity is low (2–4).
Although in their introduction the relation between shear rate and vessel diameter correlated positively, the low flow is reported to result in low shear rates, which is evidence of the inverse relation between shear rate and the vessel diameter shown in the discussion section of their study. This paradox can cause confusion for the readers. We think that basic information should be used carefully in scientific investigations.
References
Department of Anesthesia, University of Pennsylvania, Philadelphia, Pennsylvania
In Response:
We appreciate the concern that some basic information conveyed in our article (1) may have confused some readers. As we stated in the introduction of the original manuscript, "The shear rate is determined by the velocity of bloodflow and by the size of the blood vessel." Drs. Ercan and Koskal are correct that shear rate and the velocity gradient of the flowing fluid are nearly synonymous, but they are incorrect to state that shear rate is determined by the vessel diameter alone. Any interpretation of a relationship between vessel diameter and shear rate must a priori include knowledge of the instantaneous volume flow rate of blood through that vessel. As an example, a vessel’s diameter may remain fixed over time while the bloodflow rate through the vessel may change over time. The velocity gradient (and hence, the shear rate) is also time dependent, yet the vessel diameter is not. In this case, there is no direct relationship between shear rate and vessel diameter. The physiology is a deterministic system, whereas the experiments we performed were not. We did not perform in vivo measures using blood vessels; rather, we used a viscometer to impose a shear rate using a fixed geometry in vitro. This technique allows the measurement of shear stress (the product of viscosity and shear rate) from which the viscosity can be extracted, which was our experimental goal. The paradox the correspondents illustrate as having been presented in our manuscript refers to both positive and inverse correlations between shear rate and vessel diameter. No such experiments were performed, and one cannot directly correlate shear rate with vessel diameter unless the velocity field is known. We wrote in the introduction, ". . .the viscosity of blood within the circulation at any instant or location varies depending on the shear rate within the particular vessel." As a parallel, the reader should be aware that the shear rate within the circulation at any instant or location varies depending on the volume flow rate of the blood and the vessel diameter.
Reference
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
