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During inflammation, cytokines and histamine cause vasodilation to increase blood flow to the inflamed area. However, it is also said that vasodilation slows blood flow which facilitates the adhesion and movement of leucocytes through the blood vessels and into extravascular tissue. My question is how does it slow blood flow? To me it would seem that there would be less drag force for a given volume of blood which would increase the speed of flow. There would also be less resistance.

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The measurement that decreases during vasodilation is flow velocity, $v$, or a change in distance over change in time $\frac{\Delta x}{\Delta t}$. Prior to a reflex response, the same rate of flow, $Q$, or $\frac{\Delta V}{\Delta t}$ enters the capillary bed (here we use a capital V to represent volume, where $\Delta V$ is a change in volume, and $\frac{\Delta V}{\Delta t}$ is the change in volume over change in time. Because volume is area times a third distance dimension (e.g., if we say area is height times width, then volume is area times depth or thickness), we can describe flow as flow velocity times cross sectional area ($Q = A \cdot v$, or $Q = A \cdot \frac{\Delta x}{\Delta t}$). If you increase the cross sectional area, $A$, and maintain the same flow, $Q$, then flow velocity, $v$, has to decrease.

A more intuitive explanation would involve turning on a garden hose and covering part of the end with your thumb. The smaller the opening you allow, the greater the flow velocity through the end of the garden hose. The same volume of water leaves the hose per unit time. It's just moving at a faster flow velocity if you decrease the cross sectional area (and at a slower flow velocity if you increase the cross sectional area).

This is discussed in Chapter 4 of Costanzo Physiology, in the section on hemodynamics.

The actual physical measurements end up being more difficult to predict in a situation with parallel capillary beds and reflex responses. $Q$ does not stay constant, for both the specific capillary bed, and for the entire circulatory system. However, you can say that, as a general rule flow velocity, or $v$, will decrease when cross sectional area, $A$, increases. As @BryanKrause points out in particular, provided the series resistance for a capillary bed doesn't change, the initial $Q$ for the capillary bed won't change, which means this caveat isn't relevant.

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  • $\begingroup$ You might improve the answer by considering an entire branch of the vascular tree from artery to capillary. Because resistance does not occur in one cross-section, local vasodilation has a bigger effect on velocity than flow, even when the overall pressure is distributed in a parallel configuration with other branches of the tree. $\endgroup$ – Bryan Krause Nov 13 '18 at 23:38
  • $\begingroup$ @BryanKrause could you be more specific with your suggestion? This is textbook level material, and I'm honestly not certain if in a local (vs. systemic) inflammatory response there are good measurements that show resistance clamped upstream of a dilating arteriole, enforcing a constant $Q$. $\endgroup$ – De Novo Nov 13 '18 at 23:55
  • $\begingroup$ It doesn't have to be upstream or downstream specifically, if there is any part of the vascular tree that is not affected (or less affected) the effect on velocity in the affected area will be bigger than the effect on flow, because flow is dependent on the series resistance whereas velocity depends on the local cross-sectional area. $\endgroup$ – Bryan Krause Nov 14 '18 at 0:13
  • $\begingroup$ I don't have time to grab a reference but I think the important vasodilation for leukocyte infiltration is on the venous side. $\endgroup$ – Bryan Krause Nov 14 '18 at 0:19
  • $\begingroup$ @BryanKrause local mediators of inflammation have different actions on venules than on arterioles, but the question is about the relationship between dilation (i.e., increased cross sectional area) and flow velocity. If you have a specific suggestion for how to change the answer, I'd be happy to incorporate it, or you can feel free to edit. I trust your physiology knowledge. $\endgroup$ – De Novo Nov 14 '18 at 2:22

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