Wednesday, August 25, 2010

The Rule of SIX in Drug Dosing and Infusion

Image credited to zeathiel at stock.xchng


Supposed as a junior medical officer, you want to start dopamine infusion for a patient in hypovolemic shock (with persistent low BP despite adequate fluid resuscitation). You look up at the drug formulary (just to counter-check) and it states that the dosage for dopamine is "5 mcg/kg/min, increasing gradually using 5-10 mcg/kg/min increments......". Most drug formularies will list dopamine dosages in the form of xxx mcg/kg/min.

So, you decide to start the patient on 10 mcg/kg/min. You remember well what you were taught in med school: dopamine infusion in the range 3 - 5 mcg/kg/min is predominantly for its dopaminergic effect (dopaminergic receptors are present abundantly in the mesenteric vasculature, brain, heart and the kidneys); dosing range from 5 - 10 mcg/kg/min is predominantly for its beta effects and dosage ranges above 10mcg/kg/min up to 20 mcg/kg/min is for its alpha effects.

You inform the staff nurse on duty: "Staff nurse, could you start dopamine infusion for this patient, start with 10 mcg/kg/min, titrating until a desirable blood pressure achieved. Erm.. I think this patient's weight is around 70 kg" Unfortunately, the staff nurse on duty is a junior staff nurse. She looks at you and said "Doctor, can you tell me how do I prepare for the infusion? Each ampoule of dopamine is 200 mg." You look a little bit annoyed, thinking to yourself "you mean you didn't learn that in your nursing school???" Regardless, still the sole responsibility of giving clear, concise and detailed instruction rests on the shoulder of the doctor in charge. You cannot blame the staff nurse of whether she learns that in nursing school or not.

Since you can't get an "answer" from the junior staff nurse, you turn around and ask a senior staff nurse. The senior staff nurse said, "Doctor, I don't know about this 10 mcg/kg/min. But from my experience, if you break open 1 ampoule of dopamine (200 mg) and diluted it into 50 cc, usually most doctors will run the drug at 10 ml/hr.

Huh??? You got more confused!!!

The above scenario is not uncommonly seen. Many nurses, from my experience, either do not understand or have forgotten about the correlation between the xxx mcg/kg/min that is stated in most books and the actual running of how many ml/hr of the diluted dopamine in 100-ml or 50-ml syringe.

The secret of calculating that is by using the RULE of SIX for drug infusion. And I am amazed how many medical students do not know this and how many of them actually do not even know how to derive this formula.

So, in this blog post, I will first prove that this formula is true by deriving it from basic mathematics and then to discuss on the variants of this formula for the ease of practicality.

The Rule of Six for drug infusion states that:

When (6 * body weight of patient) mg of a drug is diluted in 100 ml,

every ml/hr of the drug infused is equal to one mcg/kg/min

In other words,
(6 * BW) mg diluted in 100ml, 1 ml/hr = 1 mcg/kg/min, where BW - body weight

How do we derive that formula? Basic simple algebra......
We break up that equation into two parts:
1 ml/hr ..................... (A)
1 mcg/kg/min ......................(B)

and then we will attempt to prove that (A) = (B)


Now, let's look at the first part of the equation, part (A), namely 1 ml/hr

Let's assume BW = a kg
So,
(6a) mg of Drug A ---- in 100 ml (diluted into 100 ml)

therefore,
1 ml of Drug A = (6a)mg/100

But 1 ml of Drug A is infused over 1 hour (= 60 min)

Therefore, for every min, the amount of drug A infused is:
(6a)mg/(100*60)

But every 1 mg = 1000 mcg.
Therefore, for every min, the amount of drug A infused is:
(6a)*1000 mcg/(100*60)

simplify the equation, for every min, the amount of drug A infused is:
(a) mcg

In other words, part A of the equation (1 ml/hr) can be written as:
(a) mcg...........................(1)


Now, look at part B of the equation, 1 mcg/kg/min

We have assumed that the BW = a kg,

therefore, for every min, the amount of drug A infused is:
(a) mcg............................(2)

Since, (1) = (2), therefore
1 ml/hr = 1 mcg/kg/min if (6*BW) mg of the drug is diluted into 100 ml.

Unfortunately, 100-ml syringes are not easily available in my hospitals. Most of the large syringes are 50-ml syringes.

Nevermind, the rule of 6 can still be applied, but for 50-ml dilution,

(3*body weight) mg of drug A in 50 ml, 1 ml/hr = 1 mcg/kg/min

(this simply because 50 = 100/2, therefore we take 6/2, which is 3 !!).

In other words, the rule of 6 can also be written as:

When (3 * body weight of patient) mg of a drug is diluted in 50 ml,

every ml/hr of the drug infused is equal to one mcg/kg/min


and, by using the same premise,

When (0.3 * body weight of patient) mg of a drug is diluted in 50 ml,

every ml/hr of the drug infused is equal to 0.1 mcg/kg/min


and...

When (0.03 * body weight of patient) mg of a drug is diluted in 50 ml,

every ml/hr of the drug infused is equal to 0.01 mcg/kg/min


Now, let's come back to our case scenario.

Let's apply the rule of 6 in our case. The patient's body weight is 70 kg. Most adults' body weight would be in the range of 60 - 70- kg. Assuming that we are going to dilute into 50 ml, therefore we use the variant:


When (3 * body weight of patient) mg of a drug is diluted in 50 ml,

every ml/hr of the drug infused is equal to one mcg/kg/min

Therefore,
(3*70) mg of dopamine is diluted in 50 ml, every ml/hr is equal to 1 mcg/kg/min.
In other words, 210 mg of dopamine is diluted in 50 ml, 10 mcg/kg/min requires 10 ml/hr.

210 mg ~ approximately 200 mg. Remember that most dopamine ampoules contain 200 mg each.

Therefore, for convenience sake, break open 1 ampoule of dopamine (200 mg), dilute in 50 ml, and just run 10 ml/hr (that will give you 10 mcg/kg/min). No wonder that's what the senior staff nurse said! You see, most drugs are prepared in such a way that it is convenient to use (especially for adult patients) and most people (especially those in places like emergency departments and ICUs), doctors and staff nurses included, are doing it routinely without really understand the principles behind.

In other words, you would not have much problem, if you are infusing drugs such as dopamine, where the drug ampoules are conveniently prepared.

But you will have troubles when it comes to pediatric patients (where the Rule of 6 is particularly useful) and when it comes to infusing other drugs such as adrenaline or noradrenaline (also known as epinephrine and norepinephrine respectively).

Adrenaline infusion, for example, the dosage range is 0.05 mcg/kg/min - 0.2 mcg/kg/min. So how are you going to prepare the dilution and rate of infusion? Bearing in mind too that most adrenaline ampoules come in 1mg/ml packaging. If you apply the rule of 6, then you will have to take your time to break 200 ampoules!! (while the patient is hanging there in a state of shock). Furthermore, since the dosage range is around 0.05 mcg/kg/min, the rate infused per min will be in the decimals - minute amount!

Therefore, we use this variant of the rule:

When (0.03 * body weight of patient) mg of a drug is diluted in 50 ml,

every ml/hr of the drug infused is equal to 0.01 mcg/kg/min

So, for adrenaline, (0.03 * 70) mg of adrenaline diluted in 50 cc, 1 ml/hr = 0.01 mcg/kg/min.

Therefore, for convenience, you just need to break 2 or 3 ampoules (2 - 3 mg) of adrenaline, dilute it to become 50 ml, and infuse at the rate of 5 ml/hr (if you are aiming for 0.05 mcg/kg/min). Bearing in mind too that the rule need not to be applied rigidly, because in the first place, the weight that you estimate is just as it is - an estimation. You can always titrate the infusion rate up and down. But the decimal point and the variant of the rule you are going to use must be decidedly correct because there has been anecdotal report that states that a baby died as a result of "misplaced decimal point (when applying the rule of 6) and the preparation of a dopamine infusion that was 10 times more concentrated than required" (Click on the link to read the article).

I disagree with the writer of that article that the use of the Rule of 6 should be abandoned. The rule of 6 is just a scientific, standalone formula that can be derived objectively from first principles. It is neutral. It is only when we do not understand the principles behind properly, then we will just follow blindly and thus, courting disaster!

Happy infusing!

© 2010 by Dr. Keng Sheng CHEW

Creative Commons License
The Rule of SIX in Drug Dosing and Infusion by Dr. Keng Sheng CHEW is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

14 comments:

jimbocyberdoc said...

Thanks for sharing this. Very useful. :)

David said...

Thx... really appreciated. Hadn't heard of these before!

Greetings from a ER and blogging college in Sweden
(http://pricelesselectricalactivity.blogspot.com)

hoay mei said...

thanks dr chew...now i more understand it...really appreciate ur effort to help us understand more^^

PG said...

TQ Dr Chew..

just for sharing..i always use this formula:

http://pgmedic.blogspot.com/2010/06/drug-infusion-formula.html

TQ
-Hafizi

PG said...

Dear Dr Chew

just to share,im using this formula:
http://pgmedic.blogspot.com/2010/06/drug-infusion-formula.html

wt=70kg
we plan to run 10mcg/kg/min
but the infusion pump machine in ml/hr

200mg(200,000mcg)dopamine diluted in 50ml NS

50ml NS:200,000mcg dopamine
1ml NS=200,000/50=4000mcg dopamine

mcg/kg/min to run--> ml/hr

:so

(10mcgx70x60)/4000
=42,000/4000=10.5ml/hr

So we can run the dopamine 10.5ml/hr

TQ
-Hafizi

Dr Basitz said...

Thank Dr Chew.. before this I just memorize the rules & most of the time when nurses/ students ask me how we derives the equation, I also scracth my head =D .. Thnk God I became a Doctor & not a mathematician hehehehe..

cksheng74 said...

@David,

I visited your blog http://pricelesselectricalactivity.blogspot.com/ and find lots of excellent links there. I have put a link to your blog in my lists of useful links. Thanks so much.

David said...

Thanks! I will be posting a lot in the coming weeks about "e-learning emergency medicine" as I am giving a lecture about it soon to my colleges! Greetings from Sweden.

cksheng74 said...

@Hafizi (@PG),
Thanks for sharing.
Glad you find it useful.
I have included a link back to your blog in my list of useful blogs.

cksheng74 said...

@David,

Thanks!
Will look out for it and will put up links to EM.RAP as well. I didn't know EM.RAP TV stream videos are free access. I only knew EM.RAP audio requires subscription.

Any chance if you could put a link to my blog at site?

Thanks,
Chew

mangoandjojoba said...

owh this is extremely helpful!!

Anonymous said...

great post thanks

David said...

A little late perhaps... I've been away having children!

Of course I'll link to your blog, I am planning to list a blogroll on the sidebar, "the blogs I read"

Keep up the good work!

dgm said...

thank you, great Post , excellent derivation of the formula.

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