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Old 04-29-2012
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Question Osmolarity, Serum Sodium, and Water Intake!

A previously well 18-year-old girl is admitted to the ICU because of altered mental status. She does not respond to instructions and her arms are postured in a flexor position. Laboratory data reveal a serum sodium concentration of 125 mmol/L. Her friends indicate that the patient had taken ecstasy at a party the night before, and because she was extremely thirsty the next morning, she had consumed a lot of water in a short period of time. Assuming that the reduction in osmolarity is entirely due to water consumption, that her initial weight was 60 kg, and that her initial osmolarity was 300 mOsm/L, which of the following is approximately how much water she would have had to drink to produce the observed hyponatremia?

2.5 L
3.5 L
5 L
6 L
7 L
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this one gets off-guard

so let's see. 60kg is her weight, so than how much water she has? 4/5 should be water - 48L is TBW

than 1/3 should be extracellular water - 16 L

from this 1/3 is blood - 5.3.

so if 5.3 L is 300mOsm/L in a normal state... but I assume that to dilute these 300 more than by half she would need to drink more than her blood water than? like 7 Litters...
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I just wanted to point out that we have her initial osmolaroty 300 and her serum Na level 125. It is confusing, but to compare we have calculate her osmolarityHer osmolarity was apr 260 (2 x125 + 10).
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Serum sodium initially300=2 x +10
X =145


TBNa/TBW=serum Na
TBNa=TBH2O x Serum Na
TBNa= 48 x 145 = 6960=const


TBW after drinking = TBNa/125=6960/125=55.6


55.6-48>7
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Default 7

7 it is

my calculations are the same as Teresa's
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Quote:
Originally Posted by Teresa View Post
Serum sodium initially300=2 x +10
X =145


TBNa/TBW=serum Na
TBNa=TBH2O x Serum Na
TBNa= 48 x 145 = 6960=const


TBW after drinking = TBNa/125=6960/125=55.6


55.6-48>7
TBW is 60 % of BWt that makes it 36 l not 48 ?
How you get to that ?
Also what is the 10 for ?


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Quote:
Originally Posted by Kabutar111 View Post
Also what is the 10 for ?
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approximately 10 = serum glucose/18 + BUN/2.8 - given they're both within normal range
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Default correction

Quote:
Originally Posted by Kabutar111 View Post
TBW is 60 % of BWt that makes it 36 l not 48 ?
@Kabutar111 - you're absolutely right!!!! oooops!

only the first part of calculations was wrong.

@Teresa hope you don't mind me using your notes

so it should be:

Serum sodium before drinking water was 300 = 2 x Na +10
so Na=145

TBNa/TBW=serum NaTBNa=TBH2O x Serum Na
TBNa= 36 x 145 = 5220 =const


TBW after drinking = TBNa/125=5220/125=41,76

41,76 - 36 = 5,76

So the answer should be 6L

@Kabutar111 - what's the right answer?
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Quote:
Originally Posted by Casandra View Post
approximately 10 = serum glucose/18 + BUN/2.8 - given they're both within normal range
Did you noticed any question where it make any difference ?
B/c all I noticed it makes calc complicated
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Quote:
Originally Posted by Casandra View Post
@Kabutar111 - you're absolutely right!!!! oooops!

only the first part of calculations was wrong.

@Teresa hope you don't mind me using your notes

so it should be:

Serum sodium before drinking water was 300 = 2 x Na +10
so Na=145

TBNa/TBW=serum NaTBNa=TBH2O x Serum Na
TBNa= 36 x 145 = 5220 =const


TBW after drinking = TBNa/125=5220/125=41,76

41,76 - 36 = 5,76

So the answer should be 6L

@Kabutar111 - what's the right answer?
Why you think TBNa will give you serum Na coc
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Quote:
Originally Posted by Kabutar111 View Post
Why you think TBNa will give you serum Na coc
it won't give me serum Na concentration - we already have it both before drinking water (145) and afterwards (125).
do you mean where is this formula (serum Na=approximately TBNa/TBW) from?
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Quote:
Originally Posted by Casandra View Post
it won't give me serum Na concentration - we already have it both before drinking water (145) and afterwards (125).
do you mean where is this formula (serum Na=approximately TBNa/TBW) from?
Yes
Also can you please tell me the diff b/w osmolarity and mosm/l
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This formula comes from Goljan RR - Water, electrolytes... chapter.

about osmolarity you wrote here: Osmolality of Zero!
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Quote:
Originally Posted by Casandra View Post
@Kabutar111 - you're absolutely right!!!! oooops!

only the first part of calculations was wrong.

@Teresa hope you don't mind me using your notes

so it should be:

Serum sodium before drinking water was 300 = 2 x Na +10
so Na=145

TBNa/TBW=serum NaTBNa=TBH2O x Serum Na
TBNa= 36 x 145 = 5220 =const

TBW after drinking = TBNa/125=5220/125=41,76

41,76 - 36 = 5,76

So the answer should be 6L

@Kabutar111 - what's the right answer?
I don't mind at all. Sorry for the error. I actually didn't calculate. I took a shortcut and used drSikorski calculation. I also assumed that everybody is familiar with dr.Goljan Fluids and hemodynamics chapter.

If it is unclear how I got the answer here is the explanation.
You will need 3 formulas:

1/ TBW=60% Body weight

2/ Posm=2xserum NA+ glucose/18 + BUN/2.8
if glucose and BUN is normal then you can simplify the formula

Posm=2 x serum Na + 10
If glucose was very high like 1000 mg/dL it would not work

so serum Na= (Posm - 10)/2

3/
serum Na= TBNa/TBW so


TBW=TB Na/ serum Na and

TB Na = serum Na x TBW


TB Na will not change as she is drinking pure water, so TB Na1 (before) = TB Na 2 (after drinking)

TBW1 (before) =60% body weight = 60% x 60 =36
Serum Na 1 (before) = serum Na1= (Posm1 - 10)/2 = (300-10)/2= 145

TWNa1= serum Na1 x TBW1=145 x 36= 5220

because TBW 1 (before) = TBW 2 (after) = 5220

now we can calculate TBW2 =TBNa2 / serum Na 2
serum na 2 was given and = 125

So TBW 2 = 5220/125 =41.76

so the TBW change, which is the water she was drinking is
TBW2-TBW1= 41.76-36= 5.5.76
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TB Na = serum Na * TBW

I can't get this in my head ,how is this true
Why TBNa can be calculated just from serum when it is distributed all over the body ?

Second why would think Na coc will stay constant as she is in ecstasy and sweating like crazy ??
I really appreciate your response
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Default .

Quote:
Originally Posted by Kabutar111 View Post
TB Na = serum Na * TBW

I can't get this in my head ,how is this true
Why TBNa can be calculated just from serum when it is distributed all over the body ?
sorry can't help you here. it's just a formula someone worked on and Goljan confirms it in his book and lectures... but maybe someone here will be able to explain it...

Quote:
Originally Posted by Kabutar111 View Post
Second why would think Na coc will stay constant as she is in ecstasy and sweating like crazy ??
I really appreciate your response
Even if she was sweating like crazy she would be loosing more water than Na (sweat is hypotonic). But that's not the most important issue here in this question. In the stem they clearly say that "Assuming that the reduction in osmolarity is entirely due to water consumption (...)" so they say that it's not that she lost Na (anyhow), it's just that she "diluted" herself.

I hope that helps
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The answer is 7 ,
Anyone ???


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Default hmmm...

Quote:
Originally Posted by Kabutar111 View Post
The answer is 7 ,
Anyone ???


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hmm....
I still stick by the calculations above... maybe they just assumed that TBW is 4/5 of the pt's weight - there are different schools on that...
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Quote:
Originally Posted by Casandra View Post
hmm....
I still stick by the calculations above... maybe they just assumed that TBW is 4/5 of the pt's weight - there are different schools on that...
tbw is 4/5 or 80% of total weight
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Assuming that she had a normal osmolarity of 300 mOsmol/L initially, at her initial body weight of 60 kg, with 60% of body weight being water, her initial volume was 36 L. A sodium concen- tration of 125 mM is equivalent to an osmolarity of 250 mOsmol/L. Assum- ing that her normal osmolarity of 300 mOsm was reduced to 250 mOsm by the ingestion of water, she drank approximately 7 L.
Osmolarity= mOsmol/Volume
300 mOsm/L = 60 kg 60% 300/Initial Volume
Initial Volume =10,800 mOsmol/300 mOsm/L = 36 L

250 mOsm/L = 60 kg 60% 300/New Volume
New Volume=10,800 mOsmol/250 mOsmol/L ≅ 43L

Volume Consumed= New Volume Initial Volume
= 43 L 36 L = 7 L

now someone enlighten me please

The amount of water ingested by the patient was not likely this high because she probably lost significant amount of salt as sweat while under the influence of ecstasy. Her signs and symptoms are due to the brain swelling caused by hypotonicity.
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Quote:
Originally Posted by Kabutar111 View Post
Osmolarity= mOsmol/Volume
300 mOsm/L = 60 kg 60% 300/Initial Volume
Initial Volume =10,800 mOsmol/300 mOsm/L = 36 L
I don't know this formula :/
actually, are those 2 separate formulas?
because I have no idea where did that number I bolded come from. do you?
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Quote:
Originally Posted by Kabutar111 View Post
Assuming that she had a normal osmolarity of 300 mOsmol/L initially, at her initial body weight of 60 kg, with 60% of body weight being water, her initial volume was 36 L. A sodium concen- tration of 125 mM is equivalent to an osmolarity of 250 mOsmol/L. Assum- ing that her normal osmolarity of 300 mOsm was reduced to 250 mOsm by the ingestion of water, she drank approximately 7 L.
Osmolarity= mOsmol/Volume
300 mOsm/L = 60 kg 60% 300/Initial Volume
Initial Volume =10,800 mOsmol/300 mOsm/L = 36 L

250 mOsm/L = 60 kg 60% 300/New Volume
New Volume=10,800 mOsmol/250 mOsmol/L ≅ 43L

Volume Consumed= New Volume Initial Volume
= 43 L 36 L = 7 L

now someone enlighten me please

The amount of water ingested by the patient was not likely this high because she probably lost significant amount of salt as sweat while under the influence of ecstasy. Her signs and symptoms are due to the brain swelling caused by hypotonicity.
The answer really depends on which formula we use:
TBW =60% (Goljan) or TBD 4/5 (not sure?)
also
Posm= 2x serum Na+10
or
Posm= 2x serum Na (that you used to get the 250 osm from 125 Na)

If I follow your calculations and use this formula: Posm= 2x serum Na+10
my Posm would be 240

Now using your calculation
New Volume=10,800 mOsmol/250 mOsmol/L ≅ 43L

I would substitute 250 with 240 using Posm= 2x serum Na+10 formula, and get New voulme 41.5
41.5-36=5.5

So the question is which formula to use???
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Quote:
Originally Posted by Teresa View Post
The answer really depends on which formula we use:
TBW =60% (Goljan) or TBD 4/5 (not sure?)
also
Posm= 2x serum Na+10
or
Posm= 2x serum Na (that you used to get the 250 osm from 125 Na)

If I follow your calculations and use this formula: Posm= 2x serum Na+10
my Posm would be 240

Now using your calculation
New Volume=10,800 mOsmol/250 mOsmol/L ≅ 43L

I would substitute 250 with 240 using Posm= 2x serum Na+10 formula, and get New voulme 41.5
41.5-36=5.5

So the question is which formula to use???

Sorry 260 not 240 as 2x250 + 10 = 260
the rest is correct, I hope
Getting confused
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Quote:
Originally Posted by Casandra View Post
I don't know this formula :/
actually, are those 2 separate formulas?
because I have no idea where did that number I bolded come from. do you?
the number is just the result of values in line above ??
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Quote:
Originally Posted by DocSikorski View Post
tbw is 4/5 or 80% of total weight
if this is it than our calculations will be ok! could you provide the source?
Teresa is saying that in Goljan it's 60%...
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Quote:
Originally Posted by Casandra View Post
if this is it than our calculations will be ok! could you provide the source?
Teresa is saying that in Goljan it's 60%...
it is 60
mr Fischer is screaming the same in physio vids.

the value is out of the question .
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Quote:
Originally Posted by Kabutar111 View Post
the number is just the result of values in line above ??
No, it's not.

First formula is: 300 mOsm/L = 60 kg 60% 300/Initial Volume

so after transformation: Initial Volume = 60 kg 60% 300/300 mOsm/L = 36 x 1 = 36 L

In the second formula you gave it's
Initial Volume =10,800 mOsmol/300 mOsm/L = 36 L

So those are 2 separate formulas. I didn't know any of them.

Where's this explanation from anyway?
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Quote:
Originally Posted by Kabutar111 View Post
TB Na = serum Na * TBW

I can't get this in my head ,how is this true
Why TBNa can be calculated just from serum when it is distributed all over the body
?

Second why would think Na coc will stay constant as she is in ecstasy and sweating like crazy ??
I really appreciate your response
It because 95% TBNa is in ECF and it moves between Vascular and ISF compatments antill it reaches equilibrium.
we assume that:
1/ Na is the main factor that determines Posm,
2/ Na is limited to ECF
3 Na is in equilibrium between intravascular and interstitial compartments

This my understanding based on Goljan notes
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Quote:
Originally Posted by Casandra View Post
No, it's not.

First formula is: 300 mOsm/L = 60 kg 60% 300/Initial Volume

so after transformation: Initial Volume = 60 kg 60% 300/300 mOsm/L = 36 x 1 = 36 L

In the second formula you gave it's
Initial Volume =10,800 mOsmol/300 mOsm/L = 36 L

So those are 2 separate formulas. I didn't know any of them.

Where's this explanation from anyway?
let me help you here.
300 is not used in first line its just kept there .
and you calculated all the way.

second formula is nothing but multiplicationof numerator by 300
which you mentioned first formula.

more detail tomorrow i m little intoxicated right now.
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Quote:
Originally Posted by Teresa View Post
It because 95% TBNa is in ECF and it moves between Vascular and ISF compatments antill it reaches equilibrium.
we assume that:
1/ Na is the main factor that determines Posm,
2/ Na is limited to ECF
3 Na is in equilibrium between intravascular and interstitial compartments

This my understanding based on Goljan notes
than it should be equally distributed between the two.
according to it we should multiply the right side by 2 to get it TB
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Quote:
Originally Posted by Kabutar111 View Post
let me help you here.
300 is not used in first line its just kept there .
and you calculated all the way.

second formula is nothing but multiplicationof numerator by 300
which you mentioned first formula.

more detail tomorrow i m little intoxicated right now.
it's a transformation of this formula: 300 mOsm/L = 60 kg 60% 300/Initial
Volume. period

how was the number 10,800 calculated (the one in the second formula)? is it some kind of fixed number?

ok ok, I'll wait till tomorrow ;P
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it's a transformation of this formula: 300 mOsm/L = 60 kg 60% 300/Initial
Volume. period

how was the number 10,800 calculated (the one in the second formula)? is it some kind of fixed number?

ok ok, I'll wait till tomorrow ;P
It's really the same thing, what we did
10800=60x06x300
The difference is how he calculated ser Na from 125 to 250. Based on the formula we used it would be 260
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Old 05-02-2012
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if this is it than our calculations will be ok! could you provide the source?
Teresa is saying that in Goljan it's 60%...
I was wrong.
80% is the TBW for Peds.

60% for adults

http://en.wikipedia.org/wiki/Body_water
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than it should be equally distributed between the two.
according to it we should multiply the right side by 2 to get it TB
And it is. If it wasn't we couldn't use the formula

Not sure what sides you are referring to?

We don't measure the amount of Na either in intravascular nor ISF, but it's concentrations. It should be equal in both compartments due to water movement.
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It's really the same thing, what we did
10800=60x06x300
The difference is how he calculated ser Na from 125 to 250. Based on the formula we used it would be 260
Thanks Teresa - it's official - I AM BLIND

I'm still waiting for Kabutar111 to reveal the source of the question/explanation but anyways I stick to our calculations because I rely on Goljan and I understand the concept that stands behind those calculations.

I'll re-read the question tomorrow - maybe I'll get enlightened
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than it should be equally distributed between the two.
according to it we should multiply the right side by 2 to get it TB
on the right side of the formula (TB Na = serum Na * TBW) we have Na concentration (not an absolute amount!) so it's equal in vascular and interstitial part of ECF, hence we don't need to multiply it by 2.
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Thanks Teresa - it's official - I AM BLIND

I'm still waiting for Kabutar111 to reveal the source of the question/explanation but anyways I stick to our calculations because I rely on Goljan and I understand the concept that stands behind those calculations.

I'll re-read the question tomorrow - maybe I'll get enlightened
It doesn't work for me. I get more and more confused
I don't mind giving it a rest, especially that I am not sure what the issue is?
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It doesn't work for me. I get more and more confused
I don't mind giving it a rest, especially that I am not sure what the issue is?
i will give it rest, as i understood the whole problem is extra 10.

@tersa - what to do if we see same type Q next time , w/ 10 or w/o

@casandra its pretest question and explanation too.
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i will give it rest, as i understood the whole problem is extra 10.

@tersa - what to do if we see same type Q next time , w/ 10 or w/o

@casandra its pretest question and explanation too.
I would definitely go with the 10 as it accounts for
glucose/18+BUN/2.8 (assuming normal values of glucose, and BUN)
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