A colleague was recently lamenting to DTs his lack of real-world experience with algebra, which he had not used since high school.
Normally, this is not an issue, but there are circumstances where we in EMS need it. One such is the Parkland formula, which determines the fluid resuscitation requirements of a burn victim.
For those whose algebra is dusty, as is mine, it can look more daunting than it should. The DTs solution is (as usual) to CHEAT. Since it's hard to cheat mathematically, we can instead make the Damned Thing less frightening. Same crap, basically, but off comes the mask, turning the Scooby-Doo ghost into Old Man Jenkins.
In Stepehn J. Rahm's Paramedic Review Manual for National Certification - a highly recommended resource for anyone seeking to refresh and review - we find the following, shamelessly reprinted example:
"A 39-year-old man, who weighs approximately 160 pounds, was trapped inside his burning house and sustained full-thickness burns to approximately 40% of his body. On the basis of the Parkland formula, how much IV crystalloid solution should he receive within the first hour?
a. 620 mL
b. 700 mL
c. 730 mL
d. 815 mL"
Notice that you are not given the Parkland formula. If you are in an NREMT testing situation, you won't have any handy-dandy reference guides either. So how do we work this?
The Answers section of the book reminds us that the Parkland formula is: 4 mL x patient's weight in kilograms x percentage body surface burned. This gives us the total volume of fluid to be delivered in a 24-hour period. We are further reminded that 1/2 of the total should be given over 8 hours, and the remaining fluid delivered over 16 hours.
THIS I gotta REMEMBER? And this STILL doesn't answer the above question. How much should we be giving in the FIRST hour?
THE HARD, TRADITIONAL WAY
160 pounds needs to be turned into kilograms, but we do this all the time for meds and know to divide by 2.2, giving us 73 kg (actually 72.7; we round up.) Plugging in the numbers, the Parkland formula looks like this:
4 mL x 73 (kg) x 40 (% BSA) = TOTAL FLUID.
Not to muddy the water, but the formula only wants the "40" of 40%. In other words, multiplying 4ml x 73 kg x 40% (which is 0.40) is incorrect.
We do the math and get 11,680 mL as the total fluid the patient needs. He needs 1/2 of that, though, over the first 8 hours. So we divide 11,680 by 2 = 5,840.
The Question, though, is how much he should receive in the FIRST hour. The FIRST hour is part of the FIRST EIGHT hours, isn't it? So we just need to divide the 5,840 by eight to find out how much fluid per hour. 5,840 / 8 = 730.
IF we remember the Parkland formula and IF we have a scratch pad and pencil, or calculator, we can easily (albeit, "eventually") figure the answer is C, 730 mL.
THE HARD EXPLANATION OF THE EASY WAY
Algebra, as we in EMS use it, has three main components: Constants, Variables, and Operators.
Operators are the mathematic symbols - "+" (plus), "-" (minus), "/" (divide by), that sort of thing. We can flip-flop these sometimes to make problems more understandable. 8 x 1/2 = 8 x 0.5 = 8 / 2.
Variables are, as the name implies, variable. This is the bit that changes from problem to problem in the test. The patient's weight, for example, won't always be the same, nor will the percentage of BSA burned.
And then there are the Constants. Constants are the actual numbers. A "1" or a "2" or a "27".
In the Parkland formula:
4 mL x patient's weight in kg x BSA burned %
we have one constant, 4 mL. But is that true? We actually have a couple of invisible constants. The answer to the above math gives us the 24-hour fluid volume. It should REALLY read:
24 HOURS OF FLUID = (4 mL x Kg x BSA%)
and we know that we give half of that volume over the first eight hours. To express that algebraically, we can multiply by 1/2 or (my personal preference) divide by 2:
FIRST 8 HOURS = (4 mL x Kg x BSA%) / 2
One of the neat things we can sometimes do with algebra is simplify things. Notice that there are two numbers in the above example: 2 and 4. These are constants; they won't change. As such, we can go ahead and "do the math" with those two numbers. We can lose the 2 by dividing by 2. That changes the 4 as well (4 / 2 = 2). The following is the EXACT SAME FORMULA:
FIRST 8 HOURS = (2 mL x Kg x BSA%)
But we want the amount to give in the first hour. "8 hours" is too much. We can turn that "8 hours" into "1 hour" by dividing by 8, but we have to do so on both sides of the equal sign:
8 HOURS / 8 = (2 mL x Kg x BSA%) / 8
1 HOUR = (2 mL x Kg x BSA%) / 8
Again, to the right of the equal sign, both the "8" and the "2" are constants. We can do the math on those guys to get (2 / 8) = 0.25
1 HOUR = (0.25 mL x Kg x BSA%)
To me, though, dividing by a whole number seems easier than multiplying by a decimal, so we're going to switch the above around a bit:
1 HOUR = (Kg x BSA%) / 4
Whether you want the 24-hour value, the 8-hour, or a single hour, the patient's weight and BSA% don't change. To make the formula even less intimidating, we can multiple those two together, turn them into a single number and be done with it.
JUST THE EASY WAY - SYNOPSIS
When testing, especially when you aren't allowed to reference the formula, just remember that "PARKLAND IS 4".
Figure out your patient weight and burn area - sorry, you need to do this with each problem. But once that is out of the way, remember: Times 4 is the total fluid. Divided by 4 is the amount for each hour, for the first eight hours.
A 39-year-old man, who weighs approximately 160 pounds, was trapped inside his burning house and sustained full-thickness burns to approximately 40% of his body. On the basis of the Parkland formula, how much IV crystalloid solution should he receive within the first hour?
a. 620 mL
b. 700 mL
c. 730 mL
d. 815 mL
Weight has to be in Kg, not pounds, so 160 / 2.2 = 72.7 or 73 kg. We multiply that by the BSA%, 40, to get a number we'll call THISPATIENT. For this question, THISPATIENT is (73 x 40) or 2920.
Parkland volume to give each hour for first eight hours, in mL = THISPATIENT / 4 (example: 2920 / 4 = 730)
Total Parkland volume to give a burn patient, over 24 hours, in mL = THISPATIENT x 4 (example: 2920 x 4 = 11680)
Remember that for the first 8 hours you give HALF THE TOTAL, and HALF OF FOUR IS 2:
Parkland volume to give over first eight hours, in mL = THISPATIENT x 2 (example: 2920 x 2 = 5840)