## Science!

Blinded Enlightened by Science!

In the post, Reading a Map, we found our hero DTs attempting to yet again simplify EMS math, as he has done so successfully in the past.  And lo! it seemed he had again succeeded!

Indeed.  Behold the hideous formula for mean arterial pressure,

((Diastolic BP * 2) + Systolic BP) / 3

Too horrible for words!  Too grotesque for thought!  And too much damned work for 2 am.  With parry and jab, the plucky DTs vanquished the offending formula with a simple,

(Systolic / 10) + Diastolic

Yes, as flash bulbs popped, our hero stood proudly upon the podium and explained his conquest, with concrete examples – and even a table!  Yet even as he spoke, the silhouette of the beastly equation (quite undead) rose stealthily in the background to the horrified gasps of the press…

In other words, it seems that simplistic equation don’t work so well.

The two methods agree completely when (Systolic / Diastolic) = 1.43.  For instance, 120/84 results in MAP=96 using either formula.  80/56 results in MAP=64, again using either formula.

The examples in the original post, plucked randomly from mine own head, all just happened to work out to within a few mmHg, making it an attractive theory.  Without peer review, my team published (I count my hands as two separate co-workers, while typing, to help spread the blame).

Further field research blew the thing apart.  A simple 120/61 provides traditional MAP=81, DTsMAP=73 – too much error to ignore.  As did 137/76, MAP=96 and DTsMAP=90.

A random number generator was quickly pressed into service – with rules (eg Systolic must always be greater than diastolic, etc.)  The results did not bear out the usefulness of the formula.

And THIS, folks, is why we have to relearn CPR every couple of years, always with new rules; and why ET tubes in the field are losing support, and a host of other data-driven changes we see all the time in the field.

Cuz it’s Science!

I’ve figured a 2-am cheat for the MAP, which doesn’t work half-bad.  Not the linesy-roadsy MAP, the other kind.

Blood pressure is one of the more important measurements we can take, we all know that and I won’t belabor the point.  If we’ve been in the business long enough, we get a feel for a blood pressure that’s “not right”, in the overall picture of patient age, habitus, etc.

The real golden nugget of the BP is, of course, the mean arterial pressure or MAP.  This is the number which some studies suggest must be maintained over 60 (other sources state 65), and failure to do so results in poor organ perfusion or even organ ischemia.  We’re talking kidney failure, liver problems, the works.

So, what is the mean arterial pressure or MAP?

Wikipedia defines it as “… a term used in medicine to describe an average blood pressure in an individual.  It is defined as the average arterial pressure during a single cardiac cycle.”  Great.  Okay.

The article proceeds to inform us that to find the MAP, all we need to do is multiply the cardiac output by the systemic vascular resistance, and add the central venous pressure.  Wiki tells us that the CVP “is usually small enough to be neglected in this formula”.

So the MAP is (CO x SVR).

And cardiac output is…?  Along with systemic vascular resistance, it is hard to measure in the field, that’s what it is mes amis.

Wiki goes on to state that there are several ways to estimate the map, using the systolic blood pressure (SBP) and diastolic blood pressure (DBP).  This is more my speed – I got those numbers.  There are a few ways to use them to figure out MAP, to whit:

MAP = DBP + (0.33 x (SBP – DBP))

(English translation:  Subtract diastolic from systolic, multiply that number by 0.33, then add diastolic back in.)

-OR-

MAP = 2/3 DBP + 1/3 SBP

(English: multiply diastolic by 0.66, multiply systolic by 0.33, add those products)

-OR-

MAP = ((2 * DBP) + SBP ) / 3

(multiply diastolic by 2, add in systolic, divide this number by three)

Yeah, right.  This is just uno poquito mas math than I like doing.

Now, I’ve noticed a lot of ambulance folk are equipped with PDAs and the like, which is wonderful if you don’t mind whipping it out to calculate all this – with blood or vomit or worse on your gloves.  Better and easier to do it in your head, if you need it.

Here’s how:

For comparison purposes we’re going to use the third MAP equivalency formula, 2 times the Diastolic, plus Systolic, then divide the whole shebang by three.  That’s the formula I’ve most seen touted in books and such for us field grunts.  Using that formula, we see that for a patient with a BP of 80/40, this equals ((2 x 40) + 80 / 3), or (80 + 80)/3, or a MAP of 53.33.

Again, this is too much work.

The DTs 2-am MAP formula is:  Systolic / 10 + Diastolic.  Easy-peasy.  This yields, from a BP of 80/40:  80/10 = 8, plus 40 is 48.

Like any good 2am rule, this is fast, easy, and wrong.  Notice we’re a full five mmHg off the “official” estimated MAP.

Notice also that you wouldn’t probably bother figuring this out in this example, anyway – 80/40 is Not a Good BP, and you already know that.   But if you’re wondering about the mean arterial pressure for a patient with a better-sounding BP, the formula works very nicely:

 BP MAP DTs MAP 100/65 77 75 108/75 86 86 144/100 115 114 136/90 105 104 192/160 171 179

… and so on.  Again, not many systems ask “What is the patient’s mean arterial pressure?”  If you want to ballpark it, though, Systolic/10 + Diastolic is probably an easier way to go.

So, there it is.

## MedMath: Parkland Formula Trick

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 Stephen 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?

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

or

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)

## MedMath: Dopamine Trick

(Note: Originally posted with a typo, “800 mg” instead of the correct “400 mg” – but now corrected!  Thanks everybody!)

Last week DTs began to brush up on med math, in preparation of precepting a rising medic with Major Transport Company.

“Brush up on medmath, DTs?” you say. “Shouldn’t you know this stuff?”

Well, yes. But as any medic will tell you, med math is one of those facets of EMS where everyone has their own method. My preceptee-to-be has already expressed an interest in learning more in this fascinating area.

So I was re-familiarizing meself with all the available methods, e.g. Ratio and Proportion method, Formula method, Cross-multiplication, Three-Step, Rule-of-Fours, and so-on, when I came to Dopamine, and the Neat Thing.

Dopamine: the bugaboo of 2-am drips. Here is a sample word problem: You have a patient who weighs 220 lbs, and the doctor orders you to start a 5 mcg/kg/min dopamine drip. You have 400mg dopamine and a 250ml bag of D5w. What is the drip rate?

Lessee here, this guy weighs 220lbs, which times 2.2 is 100kg, and we need 5 mikes/kg so that’s 100 kg * 5 is 500 micrograms per minute, and there’s 400 milligrams of medicine in 250 milliliters of D5w so that makes 1600 micrograms per milliliter…

At 2am medics have been known to run screaming into the night.

Now, dopamine is especially atrocious because different dosages seem to have different properties. For instance, 2mcg/kg/min is a “renal” dose, appropriate for maintaining renal function, while 5mcg/kg/min is considered an inotropic or “cardiac” dose, and 15+mcg/kg/min is the alpha agonist or “vasopressor” dosage, useful for maintaining blood pressure. So, yeah, somebody somewhere is at some point gonna make the medic start a dopamine drip.

So here’s the Neat Thing:

In all this reading, and now of course I can’t find exactly where, but props to the Brady company and Dr. Bryan Bledsoe – I’m pretty sure it was in one of their Tomes – DTs came across something called the Colorado Down and Dirty Dopamine Ditty. At least, I think that’s what it was called.

Easy-peasy dopamine calculation for when you want the cardiac dose of 5mcg/kg/min: When your concentration is 1600 micrograms/milliliter, take the patient’s weight IN POUNDS, divide by 10, and subtract 2. That’s your drip in milliliters per hour.

(220 POUNDS / 10) = 22, subtract 2 = 20 milliliters/hour.

As long, that is, as you want the 5 mcg/kg/min rate.

Now, as the “down and dirty” implies, this is not exactly right. For instance, a patient weighting 160 pounds gets, by the Colorado method, (160/10)-2 = 14 ml/hour. The actual calculation, where (milliliters per hour) = (weight kg) * (dose mcg/kg/min) * (60 min/hour) / (concentration mcg/ml)

(deep breath)

would be ((160/2.2) * 5 * 60)/1600, or (72.73 * 300)/1600, or 13.64 ml/hr. The Colorado method is therefore 0.36 ml/hr off! This is a 2.67% error! BFD. At 2 am, this is great.

But

The DTs Cheat is even easier, and has a more consistant error rate.

The DTs Cheat: Weight (kilograms) / 5.

Done.

A 220 lb patient is (as we all know from endless classes) the Perfect Weight Drug Patient (not so much for lifting). 220 lb = 100 kg.

100 kg / 5 = 20 ml/hr.

“DTs, this is all fine,” you say, gently, “But you do realize that your simplistic, and simple-minded method, may not always apply? I mean, come on, it works for a 100 kg patient, but…”

That’s what I thought, too, so I built a model (simple spreadsheet did for it) and ran the formulas head-to-head from a 50 lb patient through a 380 lb patient. At 50 lbs, the Colorado method was 29.6% off; the DTs method was 6.67%; at 380 lbs, Colorado was 11.16% while DTs was 6.67%.

 Weight lbs Weight kg (lbs / 2.2) Dopamine Dose 5mcg/kg Pump ml/hr = (kg*dose*60) /1600 Colorado ( lbs / 10) – 2 Error Error % DTS Cheat (kgs/ 5) Error Error % 50 22.73 113.64 4.26 3 1.26 29.60% 4.5 0.28 6.67% 60 27.27 136.36 5.11 4 1.11 21.78% 5.5 0.34 6.67% 70 31.82 159.09 5.97 5 0.97 16.19% 6.4 0.40 6.67% 80 36.36 181.82 6.82 6 0.82 12.00% 7.3 0.45 6.67% 90 40.91 204.55 7.67 7 0.67 8.74% 8.2 0.51 6.67% 100 45.45 227.27 8.52 8 0.52 6.13% 9.1 0.57 6.67% 110 50.00 250.00 9.38 9 0.37 4.00% 10.0 0.63 6.67% 120 54.55 272.73 10.23 10 0.23 2.22% 10.9 0.68 6.67% 130 59.09 295.45 11.08 11 0.08 0.72% 11.8 0.74 6.67% 140 63.64 318.18 11.93 12 0.07 0.57% 12.7 0.80 6.67% 150 68.18 340.91 12.78 13 0.22 1.69% 13.6 0.85 6.67% 160 72.73 363.64 13.64 14 0.36 2.67% 14.5 0.91 6.67% 170 77.27 386.36 14.49 15 0.51 3.53% 15.5 0.97 6.67% 180 81.82 409.09 15.34 16 0.66 4.30% 16.4 1.02 6.67% 190 86.36 431.82 16.19 17 0.81 4.98% 17.3 1.08 6.67% 200 90.91 454.55 17.05 18 0.95 5.60% 18.2 1.14 6.67% 210 95.45 477.27 17.90 19 1.10 6.16% 19.1 1.19 6.67% 220 100.00 500.00 18.75 20 1.25 6.67% 20.0 1.25 6.67% 230 104.55 522.73 19.60 21 1.40 7.13% 20.9 1.31 6.67% 240 109.09 545.45 20.45 22 1.55 7.56% 21.8 1.36 6.67% 250 113.64 568.18 21.31 23 1.69 7.95% 22.7 1.42 6.67% 260 118.18 590.91 22.16 24 1.84 8.31% 23.6 1.48 6.67% 270 122.73 613.64 23.01 25 1.99 8.64% 24.5 1.53 6.67% 280 127.27 636.36 23.86 26 2.14 8.95% 25.5 1.59 6.67% 290 131.82 659.09 24.72 27 2.28 9.24% 26.4 1.65 6.67% 300 136.36 681.82 25.57 28 2.43 9.51% 27.3 1.70 6.67% 310 140.91 704.55 26.42 29 2.58 9.76% 28.2 1.76 6.67% 320 145.45 727.27 27.27 30 2.73 10.00% 29.1 1.82 6.67% 330 150.00 750.00 28.13 31 2.88 10.22% 30.0 1.88 6.67% 340 154.55 772.73 28.98 32 3.02 10.43% 30.9 1.93 6.67% 350 159.09 795.45 29.83 33 3.17 10.63% 31.8 1.99 6.67% 360 163.64 818.18 30.68 34 3.32 10.81% 32.7 2.05 6.67% 370 168.18 840.91 31.53 35 3.47 10.99% 33.6 2.10 6.67% 380 172.73 863.64 32.39 36 3.61 11.16% 34.5 2.16 6.67%

So anyway, there’s that for what it’s worth. 400mg of dopamine in 250ml D5w, kgs/5, set your drip.

Of course, if you have a pump, by all means do it the long way – makes it much easier to modify during transport.

And, if anyone can figure out a neat little math trick to get rid of that constant 6.67% (I am certain there must be one!) please let me know, as that would be very cool indeed.