View attachment 202027
Yeah. Just don't understand that bend.
According to Poiseuille's equation, as the blood vessel radius increases, blood viscosity increases (which, on a side note, I don't understand conceptually). This relation works well in the above graph only after ~ 0.01 mm. However, the graph before the inflection point follows the inverse relationship between viscosity and vessel diameter as in Reynolds' number formula. Why is this? Is an MCAT question gonna tell you the width of the vessel before asking the relationship?
Why are there two different relationships between viscosity and diameter (Poiseuille's and Reynolds')? Shouldn't it be the same, regardless of the flow being laminar or turbulent for the respective equations?
Hi
@OrangeMed ! As far as I understand it, Poiseuille's equation
(Flow = ΔPπr^4/8Lη) does NOT tell us that an increasing radius will increase fluid viscosity. No more than the ideal gas law (PV = nRT) tells us that increasing pressure will increase the # of moles of gas in the system. Viscosity can affect flow sure, and so can radius. Temperature can affect the viscosity of a fluid but AFAIK, and particularly the way the MCAT will expect you to understand fluid dynamics, the other factors will not change viscosity directly.
The resistance to flow of a fluid and the resistance to the movement of an object through a fluid are usually stated in terms of the viscosity of the fluid. Experimentally, under conditions of laminar flow, the force required to move a plate at constant speed against the resistance of a fluid is proportional to the area of the plate and to the velocity gradient perpendicular to the plate. The constant of proportionality is called the viscosity.
Here is appears they are measuring, as listed in the graph title, apparent viscosity of fluid. Technically, the AAMC, and any other test maker, can make up and report experimental results as they see fit, even on experimental, made up molecules. This can allow them to test you on basic concepts for which you are responsible, and then ask you to think critically about this new information and how it relates to what you know already (which is what you will be doing as a physician). Since they are reporting apparent viscosity, they are not really violating any laws of physics, we just need to come up with an explanation for what we are seeing within the laws we know.
Here they mention
hematocrit, which is he proportion of your total blood volume that is composed of red blood cells. the more cells there are in the fluid, the greater the viscosity should be (more particles to interact anf shear against eachother in the fluid, producing more friction). This is borne out in medical studies of Hct vs. viscosity of blood.
The addition of formed elements to the plasma (RBCs, WBCs, platelets) further increases the viscosity. RBCs have the greatest effect on viscosity under normal conditions. Note that the increase is non-linear, so that doubling hematocrit more than doubles the relative viscosity. Therefore, blood viscosity strongly depends on hematocrit. At a normal hematocrit of 40-45%, the relative viscosity of blood is 4-5. Patients with a condition called polycythemia, which is a abnormal elevation in red cell hematocrit, have much higher blood viscosities. This increases the resistance to blood flow and therefore increases the work of the heart and can impair organ perfusion. Some patients with anemia have low hematocrits, and therefore reduced blood viscosities.
Unlike water,
blood is non-Newtonian, meaning that viscosity is not independent of flow at all flow velocities. In fact, during conditions such as circulatory shock where microcirculatory flow in tissues is reduced because of decreased arterial pressure, low flow states can lead to several-fold increases in viscosity.
Low flow states permit increased molecular interactions to occur between red cells and between plasma proteins and red cells. This can cause red cells to stick together and form chains of several cells (rouleau formation) within the microcirculation, which increases the blood viscosity.
As for the dip then upturn in viscosity. My thinking is that it has something do to with the diameter of a RBCs, the cells contributing most to blood viscosity and the measurement that determines Hematocrit. The average RBC is 6-8 micrometers in diameter, or 6-8 x 10^-6 m or 6-8 x 10^-3 mm (the untis on the x axis). When the vessel is below this diameter ( < 6-8 mirometer so small, the cells get stuck and apparent viscosity is high. As the vessel gets larger, the cells can move and the viscosity drops quickly. As the vessels grow larger, the cells have more room to interact with each-other, achieve a flow profile similar to laminar flow and RBCs will raise apparent viscosity of the blood. This dip then upturn is actually
known as the Fahraeus-Lindqvist effect and is due to the fact that blood cells are displaced towards the axis of a narrow vessel as they pass through it thereby creating a cell-depleted region near the wall of the vessel and a relatively fast moving core of cells near the center, which results in a decrease in apparent viscosity. The AAMC would NOT expect you to know of this before the MCAT, but you should be able to reason through, explain it if given a passage detailing it.
We can even see this effect in blood of differing viscosities. though it becomes less pronounced as RBCs become fewer in the blood.
The MCAT no need to give you exact numbers for vessel diameters, but they can give you relative size changes.
Hope this helps, good luck!
