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Infusions Redux, DNS And Cerebral Edema

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There’s a book on fluid and electrolyte management that I’ve been reading recently. Called, “Practical Guideline on Fluid Therapy” and authored, as probably evident by the English used in the title, by a very Indian Sanjay Pandya, the book contains many interesting nuggets for day to day practice. Although like most Indian books there is a distinct absence of the emphasis on applying one’s brain, it is nevertheless worth the time to peruse. Today I will be discussing two equations from the book and a question that came up in my mind about the usage of a specific fluid.

Calculating ECF volume deficit (in dehydration, etc.)

  1. If the patient’s previous body weight is known, all you gotta do to obtain ECF deficit is find out the difference between his present and past weight.
  2. Another technique uses changes in the Hematocrit to discern ECF volume deficit. This method is applicable only if there is no hemorrhage, hemolysis or other situations involving loss of blood cells, the idea being that any change in blood volume is caused by plasma volume change. So if there’s dehydration and loss of ECF volume, plasma volume shrinks and causes the hematocrit to rise.

ECF Volume Deficit in liters = 0.2 * lean body weight * [(Current hematocrit/Desired hematocrit) – 1]

Can someone figure out the proof for the above equation and post it here? Like most other stuff, I absolutely hate roting math formulas and prefer remembering their derivations. This equation is taking me some time to prove.

To help get started, here are a couple of possible pointers I’m currently exploring:

Total body water (TBW) when expressed as a percentage of Total body weight (TBwt), varies by gender and age. In young adult men for example

TBW = 60% TBwt

TBW in liters

TBwt in kg

Interestingly enough, TBW when expressed as a percentage of lean body weight (LBwt) is a constant and isn’t conditioned upon gender or age.

TBW = 70% LBwt

LBwt = (100/70) * TBW

= (100/70) * [(x/100) * TBwt]

= (x/70) * TBwt

x is the percentage of TBwt that is TBW

Plasma volume is related to blood volume as follows

Plasma volume = Blood volume * [(100 – Hematocrit)/Hematocrit]

Plasma volume is also 1/4 of ECF volume. ECF is 1/3 of TBW. So plasma volume is 1/12 of TBW.

Calculating Electrolyte Infusion Rates

Change in plasma electrolyte concentration in mEq/L when 1 liter of  infusate is given

= [Infusate electrolyte concentration in mEq/L – Actual electrolyte concentration in mEq/L] / (TBW + 1)

This one’s easy to derive. Taking Na+ as our electrolyte example,

Initial Na+ content = x * TBW

Initial Na+ concentration = (x * TBW)/TBW

Final Na+ content after infusing 1L infusate = (x * TBW) + {y * 1}

Final Na+ concentration = [(x * TBW) + {y}]/(TBW + 1)

Change in Na+ concentration due to infusion = [(x * TBW) + {y}/(TBW + 1)] – [(x * TBW)/TBW]

= (yx)/(TBW+1)

x = mEq/L of Na+ initially in the body

y = mEq/L of Na+ in the infusate

And voila! There you have it!

And now for that promised question:

Given the fact that DNS (Dextrose Normal Saline) only stays in the ECF, would it be right to assume that it’s contraindicated in cerebral edema?

The interesting thing is that on exploring the scientific literature, I found that recent research shows that it isn’t just the shifting of fluid into the brain parenchyma that should be avoided when infusing fluid; hyperglycemia is a real danger as well. How hyperglycemia contributes to cerebral edema and especially in situations of cerebral ischemia is a topic of ongoing research and multiple plausible hypotheses are being investigated.

As per Pandya’s book, by the way, it is best to restrict glucose infusion to ≤ 0.5 grams/kg/hour when infusing any glucose containing fluid to avoid complications of hyperglycemia.

Readability grades for this post:

Kincaid: 11.4
ARI: 12.4
Coleman-Liau: 11.2
Flesch Index: 57.0/100
Fog Index: 14.6
Lix: 46.9 = school year 8
SMOG-Grading: 12.4

Copyright © Firas MR. All rights reserved.

Infusion Confusion – How To Calculate Drug Infusion Rates

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The erosion of math and analytical skills that occurs with medics is truly astounding. Not surprising some might argue, what with it being such a memory oriented field. One area that many medics struggle with is drug dosage calculations. In the ER, one often doesn’t have the luxury of time and instant thinking is absolutely critical. Numbers need to be played out in seconds and optimal drug regimens have to be formulated. I was helping a colleague understand calculations for dopamine infusion the other day and thought like sharing with you folks some of the things we talked about.

Dopamine is used especially in ER settings to increase perfusion/blood pressure by means of its vasopressor, inotropic and chronotropic effects. When re-establishing blood pressure in a patient,  attention not only needs to be paid to drugs that might be used but also fluid replacement for any amount of fluid loss from the body. Two questions need to be asked before starting a dopamine infusion:

  1. How much dopamine?
  2. How much fluid and how fast?

The usual dosage of dopamine is somewhere between 5-10 μg/kg/min. For the following example I’ll use 10 μg/kg/min.

1μg = 0.001mg.

For a patient weighing x kg, the dosage is therefore 0.01x mg/min. Now that you’ve established how much dopamine you need to infuse per minute, here comes the second part.

Suppose you intend to infuse y ml of fluid (as part of the dopamine infusion, i.e. aside from any other fluid infusions already in place). Say also that you’ve added z mg of dopamine to form the infusate. Dopamine is supplied in liquid form, so any amount of dopamine occupies a certain volume in ml, which in most situations is negligible.

y ml of infusate = volume of Normal Saline, etc. + volume of dopamine

If z mg of dopamine is contained in y ml of infusate,

0.01x mg dopamine is contained in [0.01x/z] * y ml of infusate.

Thus you’re interested in giving [0.01x/z] * y ml of infusate every minute and a simple formula is derived where:

rate of dopamine infusion in ml/min = [0.01x/z] * y

and therefore, z = [0.01x/(rate of infusion in ml/min)] * y

x = body weight in kg

z = amount of dopamine added in mg

y = total volume of infusate in ml

For any drug infusion:

rate of infusion in ml/min = [(total drug dose in mg/min)/(amount of drug added in infusate in mg)] * volume of infusate in ml

This infusate is typically given via an infusion set that specifies a unique drops per ml ratio. At our pediatrics ER for example, infusion sets come in two forms – microdrip infusion sets (1 ml = 60 drops) and macrodrip infusion sets (1 ml = 20 drops). Simply multiply the rate of infusion in ml/min with 60 or 20 to get the infusion rate in drops/min for micro and macro IV sets respectively.

As seen from the formula above, when deciding to add a given amount of drug to form the infusate, three things need to be fixed first:-

  1. Dose of drug in the mg/min format (should be appropriate to the clinical condition of the patient).
  2. Total volume of infusate in ml (again, this depends on the clinical condition and hemodynamic stability of the patient).
  3. Speed or rate of fluid replacement in ml/min (this is important as sudden fluid-volume changes in the body can be problematic in certain cases and you want to go for a rate that is optimal, neither too slow nor too fast.)

And with that I end this post. Hope readers find this useful. Comments and corrections are welcome!

Readability grades for this post:

Kincaid: 8.4
ARI: 7.9
Coleman-Liau: 10.2
Flesch Index: 65.7/100 (plain English)
Fog Index: 12.7
Lix: 39.4 = school year 6
SMOG-Grading: 11.6

Copyright © Firas MR. All rights reserved.

Written by Firas MR

June 13, 2008 at 1:41 pm

Comprehending Drug Concentrations and Dilutions

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Good medical practice requires you to make sense of drug concentrations and dilutions!

Bonjour! Every year, an unprecedented number of casualties result from errors made by medical staff in administering drugs based on faulty dilutions. Besides human error, a lack of standardized methods for the representation of drug concentrations, contributes significantly to this preventable morbidity and mortality. Today, I will very briefly be discussing, some of the basic rules for calculating drug concentrations & dilutions.

Drug concentrations, when put as percentages (%), either mean weight/weight (w/w %), weight/volume (w/v %), volume/volume (v/v %) or part/part percentages. Furthermore, the denominator in each of these fractions could either stand for the solvent, or the solution as a whole. So, suppose you see a dilution that says 1:1000 (or 1/1000) of 1% lidocaine, which of these fractions apply? To take the complexity up a notch, consider how many milligrams of epinephrine and lidocaine are contained in 50 mL of a 1:100,000 solution obtained by adding 0.1 mL of 1:1000 epinephrine to 10 mL of 1% lidocaine. Understandably, novices find such questions extremely frustrating enigmas.

The key to understanding (i) concentrations & (ii) dilutions, is to engrave in one’s mind the following conventional rules:

  • Concentrations:- x % of a drug denotes x grams of the drug (or solute) in 100 milliliters of the solution. Eg. 1% lidocaine contains 1g of lidocaine in 100 mL of solution.
  • Dilutions:- Anything represented in an x : y (eg. 1:1000) fashion, is x grams of drug (or solute) divided by y milliliters of solution. Eg. 1:1000 of an epinephrine solution contains 1g of epinephrine in 1000 mL of the solution.

Keeping these cardinal rules in mind, problems such as the above are a piece of cake. With them, you have blissfully attained nirvana! Let us now break down the second sample question:

0.1 mL of 1:1000 epinephrine contains 0.1 mg of epinephrine. 10 mL of 1% lidocaine contains 100 mg of lidocaine. By adding 0.1 mL of 1:1000 of epinephrine to 10 mL of 1% lidocaine, you are in effect adding 0.1 mg of epinephrine to 10 mL of solvent (in this case, lidocaine) with the resultant volume of solution being 10.1 mL. In other words, when you’ve done this, you will have gotten

0.1 mg of epinephrine in 10.1 mL solution

= 0.0001 g of epinephrine in 10.1 mL solution

= 1g of epinephrine in 101000 mL solution

Mathematically, the exact dilution thus obtained would therefore be 1:101000. This is approximately the same as a 1:100000 dilution, that we would’ve obtained had we dropped 0.1 mL from our 10.1 mL final solution volume value. So congratulations, you’ve now successfully made yourself ~ 10 mL of a 1:100000 solution of epinephrine using 1% lidocaine!

Again, because 10 mL of the solution contained 100 mg of lidocaine, 50 mL of such a solution would contain [100 x (50/10)] milligrams of lidocaine = 500 mg lidocaine.

Similarly, because 1:100000 epinephrine solution means 1g of epinephrine in 100000 mL solution, 50 mL such a solution would contain [1 x (50/100000)] grams of epinephrine = [1 x (50/100000) x 1000] milligrams = 0.5 mg of epinephrine.

Seeing how easy this is, you can now dabble around with quirky questions such as:

  • How many milligrams of epinephrine are present in 100 mL of a 1:35000 preparation? (Hint:- 1:35000 means 1g of epinephrine in 35000 mL of solution.)
  • 5 mL of 1:1000 epinephrine is added to 10 mL of anesthetic solution. What is the resultant dilution of the final preparation? (this is a modification of our sample question)
    • Previously, we had a final solution volume of 10.1 mL and neglected the 0.1 mL (arriving at 1:101000 ≈ 1:100000) because it was too minuscule to make a difference. In the present case, the final solution volume comes to (5+10 =) 15 mL, which is significant enough to not ignore. 1:1000 epinephrine contains 1 mg per 1 mL of solution; 5 mL of solution would therefore contain 5 mg of epinephrine. So, this comes to 5 mg of epinephrine in 15 mL of final solution = 1 mg in 3 mL = 0.001 grams per 3 mL = 1:3000. See, it’s peace!

For more on concentrations and dilutions, you might want to look at an article from here.

As you read your textbooks, you’ll come across drug dosages in some of these forms that ought to be remembered for applying to patients. Before you mindlessly swallow such information, take a step back and check to see if everything adds up. Know whether using an approximation in the calculations is likely to significantly alter your results and if that could affect your treatment. I happened to come across numerous errors from a pediatrics textbook that our school prescribes, namely “Essentials of Pediatrics by O.P. Ghai 6ed” with regard to concentrations & dilutions. As an example, Table 7.2 under ‘Neonatal Resuscitation’ says that 1:10000 epinephrine, which is the concentration that’s needed for neonates, can be prepared by adding 0.5 mL of 1:1000 epinephrine in 5 mL of solvent (in this case water or something similar such as saline). Although this might be due to a typographical error in the book, the approach is clearly flawed. In having done so, what you would’ve gotten would be 0.5 mg of epinephrine in a 5.5 mL preparation = 0.0005 mg in 5.5 mL preparation = 1:11000 dilution. Given a neonate’s low body weight and the average listed dosage as 0.2 mL/kg, this doesn’t affect the final dosage the patient receives much, only reducing it by 0.002 mg/kg. Such an error would’ve been unacceptable had the patient been of a considerably larger body weight, as in a massive adult, so as to cause small decimal errors to add up to significantly larger ones. You could easily have obtained a 1:10000 dilution by adding 0.5 mL of 1:1000 epinephrine to 4.5 mL of solvent in your garden-variety 5 mL syringe.

With that, you’ve come to the end of this post. Readers are welcome to send in their comments. Until my next piece, adieu!! 🙂

—— a thought:- Einsteinian physics holds that in the enormous space-time fabric, you, I and everything else in the universe are traveling at the ‘speed’ of light!! Relative to a given frame of reference, that is. Some of this speed goes into our movement in ‘space’ while the rest of it goes into our movement through ‘time’. And because we only have a limited amount of speed (namely ‘c’ or the speed of light), the faster we move through space, the slower our speed through time becomes as seen from that frame of reference and/or observer. If you had to celebrate your birthday with your family in 6 months earth time, but couldn’t physically be with them on earth because you had to attend to a mission on the international space station for the present year, your family would celebrate your birthday later than you would on the station as seen from their frame of reference! To them, your clock ticks slower than theirs. That’s because the ISS & its crew move faster through space than humans on earth. Read more on the time dilation phenomenon here and here.

Copyright © 2006 – 2008 Firas MR. All rights reserved.

Written by Firas MR

July 10, 2007 at 1:57 pm