# Dimensionless number for blood volume

Comments from the question How is the blood volume of a living organism measured without killing it? by @Nico discussed that the time of blood recirculation scales with the size of the organism. I was curious if there were a series of dimensionless numbers that characterize blood flow, blood volume, and time of blood recirculation?

Such dimensionless numbers exists for stride length and drug penetration.

Edit I like @Nico's comment so much it's going to part of the question. Any description of the circulatory system doesn't necessarily have to be dimensionless. However, I would imagine that one could develop a characteristic time (lets call it Tau) based on blood flow (L/t), cross-sectional area (L^2), and circulation time (t). From that characteristic time Tau, interesting observations and appropriate comparisons about the various ratios and how they vary amongst species.

• Why would it need to be dimensionless? Blood flow is a speed (mm/s), blood volume is a volume (ml) time of blood recirculation is a time (s).
– nico
Commented Apr 16, 2012 at 6:29
• By the way, to further expand my comment, I was considering that the ratio between cardiac output and the volume of the circulatory system would vary between species. I wasn't necessarily implying that it would be higher in smaller animals, although re-reading my comment it looks like I was saying exaclty that!! :)
– nico
Commented Apr 16, 2012 at 6:32
• It is perfectly valid to make normalized comparisons that have dimensions. I think the stride length being dimensionless was coincidental (body length/stride length). An example measurement that normalizes body parameters is the Body Mass Index (BMI) which scales mass:height^2, or the fuel economy of cars express as miles per gallon.
– user560
Commented Apr 16, 2012 at 7:08
• The trouble with miles/gallon is that it has square-cube problems. Motorcycles get far more miles/gallon despite being less aerodynamic, because they are smaller. So if you wanted a measure of how efficient motorcycles as a design independent of their size were, a dimensionless measure would resist scaling problems. It's especially important in biology because nothing is the same size as anything else. Commented Jun 25, 2014 at 15:05
• What blood volume can be normalized to is body volume. Since body volumes is slightly difficult to measure you can assume the density to be equal to that of water and calculate volume from body mass (bad approximation when comparing species with different bone and muscle densities). Commented Nov 21, 2014 at 16:52

Blood volume is not a dimensionless number - it's a volume. Historically we used to measure this in patients or volunteers by giving a large carbohydrate molecule like a starch that is not digestible or harmful to the body. Just like every other body fluid compartment volume (i.e. plasma, interstitial fluid, intracellular and extracellular) that we have, blood volume is estimated by intravenously injecting a known concentration of a particular compound. Once that compound equilibrates you take a blood sample and measure the compound's concentration again.

Initial Concentration * Initial Volume = Final Concentration * Final Volume

When you inject a known volume of a known concentration that only fills the "blood" component, and then you measure a final concentration - you can then solve for the "Final Volume" for "blood volume".

• Great that you dug up this old question and answered it. +1
– AliceD
Commented Jun 19, 2015 at 2:20
• This does not really answer the question. The OP wishes to know if blood volume can be non-dimensionalized. My opinion is that it can be normalized to body size (which seems quite reasonable; larger people would perhaps have higher volume of blood) but I haven't seen any literature on that. Commented Jun 19, 2015 at 5:34
• I see what you are saying - larger individuals would have larger volumes of blood. Similar to energy expenditure, though, that's a nonlinear relationship that you would need a large, diverse sample size to measure empirically (not sure if that's been done yet). The numbers we use clinically, like blood volume being 7% of total body weight, only holds in a 'normal size' or near normal weight individual around 70-80kg. Even though the numbers don't hold at the extremes of weight they remain "close enough" for clinical estimation when needed. Commented Jun 19, 2015 at 13:28
• @VanceAlbaugh So like there is BMI, is there not a blood volume to body weight ratio such that a range of that factor may be considered healthy? Commented Jun 19, 2015 at 15:20
• There is no unit that I am aware of for an index of blood volume for research purposes. Clinically we use the historical values of 7% of total body weight - but realize that is based on 70kg males from 50+ years ago. Obese and morbidly obese individuals have different values because the relationship is nonlinear. Check out this for one model (but definitely not the only one) that has been 'attempted' to model blood volume. ncbi.nlm.nih.gov/pubmed/16756741 Commented Jun 19, 2015 at 22:58