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.

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5 Responses

  1. I think your medmath is incorrect. I apologize, i know I’m only a lowly EMT-B but shouldn’t it be

    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 800 milligrams of medicine in 250 milliliters of D5w so that makes 1600 micrograms per milliliter…

    2400 mcg per ml? How did you get 1600?
    I thought you would have to multiply 800 mg by four? and 250 ml by four in order to convert it properly?

  2. I apologize again my math was incorrect, 3200 mcg not 2400 mcg

    • Mostafa,

      Thanks so much for reading – and correcting! And might I point out, there is no such thing as a “lowly EMT-B”; as the saying goes, “Paramedics save lives; EMT-Bs save Paramedics”.

      The major problem (which I’ll try to address today, if I can find a way) in switching from a wholly by-hand blog such as I ran for almost six years, vs. WordPress, is there seems no quick way to import all the neat comments folks have left me. Yesterday, doing the initial move, I took every post verbatim, as-it-was-originally-posted, even if as in this case it meant including errors. I’ve cut-and-pasted the comments from this post, from the old site, where others also stepped up and corrected me. Should have been 400mg in 250ml for 1600 mcg/ml.

      Hey awesome stories – I love it!!

      That constant error of 6.67% is because you’re dividing by 5, which is also multiplying by 0.2, instead of 0.1875. The 6.67 comes from the % difference between these.

      The 0.1875 comes from 5*60/1600 = 0.1875 which comes from (5mcg/kg) x (1ml/1600mcg) x (60min/hour).

      0.1875 = 3/16…. so you could multiply the pt’s weight (kg) by 3, then divide by 16, that’ll give you the EXACT amount.. but easy at 2am? maybe not..

      but i’m confused if 800mg in 250ml is 1600mcg/L ?

      but I think your trick is good enough for me!
      cheers
      james | 08.03.08 – 9:19 am | #

      Yikes! James, thanks so much! I’m certain I’d never have found that error (nor have been able to explain it so succinctly). And you’re quite right about the typo – I should have written 400mg dopamine for a 250mg bag. That’s just the sort of error that will get someone in trouble one of these days – and I suspect my next post will be about just that, big time errors in textbooks. Thanks for your illuminating comment!
      DTs | 08.11.08 – 7:35 am | #

      Can you change it on the page to the correct mix of 400 mg in 250 mL please? I wanted to use your page to show somone this method, but that error is too big for me to use, plus anyone who doesn’t do the math could make the mistake if they tried to use the method. . .I did the math (to make sure I was right) others might not.
      Crystal | 09.12.08 – 6:19 pm | #

      You guys use the ‘Dopamine clock’ down there?
      Anonymous | Homepage | 10.26.08 – 5:13 am | #

      So I have a way to correct your numbers, but first a note, as pointed out above, you gave the right number for the standard concentration, but the wrong numbers for the standard admixture, all these numbers are predicated on 400mg/250ml (1600mcg/ml). (And, I can’t fault you, when I reread this prior to posting, I noticed I had put the numbers in backwards.)

      So, for cardiac dosing, again, as noted above, if you reduce the equation, you wind up with 3*kg/16=ml/hr, thus kg*(3/16)=mg/hr, but if you take that 3/16 and get the inverse, 16/3=5.33 repeating, thus kg/5.33 repeating=ml/hr. If you shave that down to just kg/5.33~mg/hr, you wind up with a very small margin of error (It increases as the weight increases, but for a 300lb pt, you are less than 1 gtt/hr off, assuming a 60 drop set.) I don’t think the most anal retentive person in the world can fault that, not to mention set a drip set that finely. (And if you have a pump in your ambulance, I hate you.)

      Alright, well that’s great and all, but what about renal dosing? Seems like there ought to be an easy way to figure that as well, and sure enough, there is. Doing the math again, it reduces to 3*kg/40=ml/hr=kh*(3/40)=kg/13.33 repeating~kg/13.33. Now using kg/13.33 gives you an even better error rate, less than .16 gtts/hr for a 300lb pt!

      For vasopressor dosing, the math runs (9*kg)/16=ml/hr=kg*(9/16)=kg/1.77 repeating~lg/1.77. Unfortunately, this gives a much larger error rate…all the way up to a bit over 20 gtts/hr for our 300lb pt. I still don’t think that on my best day I ever set a drip set that accurately.

      All of these numbers are put together in a fancy shmancy table available in both html and
      Marcus Prieskop | 11.01.08 – 6:12 am | #

      Bah, I was too verbose, it cut me off.

      In any case, you can also get the table as an Excel document.

      Finally, I just thought that I would note that I was most of the way through some engineering degrees before I found EMS.

      EMS geeks unite!

      Marcus
      Marcus Prieskop | 11.01.08 – 6:17 am | #

  3. Actually your method results in errors ranging from 6.67% at the lowest to 9.51% at the highest; always giving more dopamine than necessary. The Colorado Down-n-Dirty ranges from -29.6% to 11.16% as you note, but more importantly it produces less error than yours from 100lbs to 240lbs.

    When calculating the % error you should do (x’-x)/x as we need to know the difference from the true value. Your formula could subtract 1 mL/hr for every 150 lbs and be more accurate. Shoot me an email and I’ll send you my Excel spreadsheet.

  4. When using 60gtts tubing:

    (Dopamine dose x kg weight)/26.7 = the dose

    Check it as many times as you want, you will be right on.

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