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## #98 new question

# [FAQ] How to write "mL/min/1.73 m2"?

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### Description

This is a FAQ and has come up at least 3 times now.

How to write "mL/min/1.73 m^{2}"?

This is the conventional writing of units for Glomerular Filtration Rate (GFR) which is "indexed" or "corrected" or "adjusted" for a standard Body Surface Area (BSR) or 1.73 m^{2}.

Syntactically in UCUM we can write `mL/min/((173/100).m2)` as the closest approximation to the exact notation convention, and simplified `mL/min/173.100/m2` or `dL/min/173/m2` or some such. But the question is not the syntax, but is that even semantically correct?

LOINC has recently listed this as "mL/min/m2{1.73}" isn't that wrong because 1.73 is meaningless in the curly braces?

I don't think it is wrong because of 1.73 in curly braces.

But I am not sure it is right. It could be right. I had discussed this with Clem a while ago, and at a rock-bottom level I trust Clem's intuition in quantitative considerations.

There is evidence however that we should leave the unit simply

mL/min

without anything else, and if one wants to put the reminder of 1.73 m2 in, then it should be simply:

mL/min{1.73m2}

Below I review the two positions based on 2 papers:

- The original paper that came up with the whole idea of "correcting" or "indexing" the GFR by BSA McIntosh JF, Moller E, Van Slyke DD. Studies of urea excretion: III. The influence of body size on urea output. J Clin Invest 1928;6:467-483.
- A more recent review of the issue Geddes CC, Woo YM, Brady S. Glomerular filtration rate—what is the rationale and justification of normalizing GFR for body surface area? Nephrol Dial Transplant (2008) 23: 4–6

However neither the 1928 article nor the 2008 article are being conscious about dimensionality and units, both of them use a conventional sloppy notation of either no units at all (1928) or with the conventional dubious units (2008).

So, we can think a few possible dimensionally consistent interpretation of the original 1928 idea.

The original 1928 article describes the matter as follows:

The "standard" clearance *C*_{s} is

C_{s}=U/Bx sqrt(V_{corr})

and the "maximum" clearance *C*_{m} is

C_{m}=U/BxV_{corr}

where

V_{corr}=V_{observed}x 1.73 /A

They say "The corrected urine volume is the observed volume of urine in cubic centimeter per minute multiplied by the factor 1.73, A being the body area in square meters that is normal for the subject's height and age."

This is all very confusing if you stop ignoring dimensionality of quantities as those (and most) authors do. Just imagine the mind-boggling dimensionality of square root of a volume, i.e., *L*^{3/2}. And how can a standard clearance have a different dimensionality from a maximum clearance? And how can the dimensionality of the maximum clearance be that of a volume?

Unfortunately the 1928 paper does not define *U* and *B*, but we shall assume that *U* is the urine creatinine concentration collected in urine over a period of time and *B* is the creatinine concentration in blood plasma (aka "serum creatinine") at some point during that same period. Therefore the quotient *U* / *B* would be dimensionless. To arrive at a clearance volume rate, one must therefore assume that the volume *V* they speak of is the volume of the urine collected during the measurement period, hence it isn't a volume but a volume rate *V*/*T*. This then yields the dimensionality for *C*_{m} of indeed a volume rate, and the authors use "cubic centimeter per minute" or mL/min.

Now the 1928 authors say that V_{corr} is

V_{corr}=V_{observed}x 1.73 /A

which as written would make the dimensionality of *V*_{corr} volume divided by area, i.e., length. That of course makes no sense. So we shall assume that they actually mean

V_{corr}=V_{observed}x 1.73m^{2}/A

So, effectively then the correction that the 1928 authors propose is taking the raw measured GFR and multiplying it with with a dimensionless the factor:

BSA_{standard}/BSA_{patient}

or

1.73 m

^{2}/BSA_{patient}

So, the original 1928 corrected GFR proposal would have maintained the dimensionality of GFR as mL/min whether or not the correction is applied, because all that was done is multiplying the raw measured GFR by dimensionless number.

This gives rise to my claim that GFR corrected for patient BSA in terms of a standard 1.73 m^{2} is still a clearance, still has the same dimensionality as raw GFR and the units stay at mL/min.

To understand the whole point, I like to point out that multiplying with *BSA*_{standard} / *BSA*_{patient} is the same as dividing the raw GFR by

BSA_{patient}/BSA_{standard}

i.e., dividing by

1.73 m

^{2}/BSA_{patient}

This means that a taller and heavier patient will have a smaller corrected GFR because the assumption is that the GFR needs to be higher for a taller and heavier patient to be sufficient for his higher production of excretable metabolic end products. So this would be an "indexed" GFR, or the GFR of the patient if he had the "standard" BSA of 1.73 m^{}2^{}.

However, another way of looking at it would be to say that in fact the reported property is not actually a GFR, it is not a filtration rate relative to a the patient's BSA. But it is the patient's BSA stated not in the SI unit m^{2} but in the odd unit 1.73m^{2}. So if the patient's BSA was indeed 1.73 m^{2}, then his BSA would be 1 (1.73 m^{2}) where the whole term in parenthesis is the unit. If we then use the formula:

C_{m}=U/BxV_{observed}/BSA_{patient}

then the unit would indeed be

mL/min/1.73m

^{2 }

and we can write it in UCUM in one of the forms given at the beginning.

At this point I have given rationale for writing this as a simple volume rate, or as a volume rate per area with area using an oddly scaled unit. I am out of steam here without having found a clear justification of the LOINC recommendation.

However, it all depends how LOINC defines the property. If they claim it is a volume rate (VRAT in LOINC), then the unit they give is wrong. If they claim it is a "length rate" or velocity, then the unit is right. If we call a corrected or adjusted GFR still a GFR, I think we ought to write it as a volume rate mL/min and we may indicate the adjustment in a curly brace annotation of no further semantic value. All the knowledge of correction (and which BSA formula was used!!) should be implied by the citation of the property, i.e., the LOINC code, not the unit.

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McIntosh? 1928 paper