The Rule of Six in Infusion Part 2 - The Pros and Cons

For the last one week, there has been some interesting discussion in my group on the use of the rule of six for infusion. I have previously written a blog post on this.

According to an article (click here to access), the rule of six is not optimal for patient safety - which I sincerely agree.

Some of the points raised in that article:

1. the rule of 6 is not followed consistently. Some practitioners use it; others don’t. Those who don't maybe confused by the infusion prepared by another managing team (usually the previous team). For example, if the A&E team follow the rule of six, and the ICU team does not, this may cause confusion; and therefore the next team may discard the previously prepared solutions. For that matter, I think it is vital that whoever prepare the infusion, should label properly x mg in 100 ml, y ml/Hr = y mcg/kg/min

2. Pediatric drug solutions that have been prepared using the rule of 6 can result in fluid overload when dose adjustments are necessary. For example, if a dopamine infusion rate were increased from 5 mcg/kg/minute to 10 mcg/kg/minute, a small infant would receive 10 ml/hour, or the daily fluid requirement with this solution alone. This is a perfectly valid point and I would be very cautious in applying the rule of six in such a case.

Nevertheless, most of these errors highlighted are human errors, not the errors with the rule of six itself. These has been highlighted in an article in Medscape that I linked in my previous post.

In essence, the rule of six is a mathematical principle just like Kinetic Energy = 1/2 mv sq. Being a mathematical principle means it is independent of the weight, the types of drugs, and the dosages. And when something is a mathematical formula, it means you can prove it from first principle. You just need to prove it once, convinced about it and can start using it.

Some have advocated to do direct calculation for each infusion. For example,

for IV Dopamine infusion

with an estimated weight = 70kg

and to run at 10mcg/kg/min

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

50ml NS: 200,000mcg dopamine

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

(10mcg * 70 * 60)/4000

= 42,000/4000=10.5ml/hr

So we run the dopamine 10.5ml/hr

For a 70-kg man, 200 mg dopamine in 50 ml, if you want 10 mcg/kg/min, you need to give 10.5ml/hr.

If using rule of six, we need to give 210 mg in 50 ml if we want to run 10 ml/hr in order to achieve 10mcg/kg/min.

If we don't want to waste another ampoule of 200 mg just to obtain the extra 10mg, we will just use one ampoule.

So how much are we actually giving if we infuse 10 ml/hr in a 200 mg in 50 ml solution?

Let's calculate backwards:

200 mg in 50 ml

so 1 ml means 4 mg

10 ml means 40 mg

10 ml in 1 hour or 60 min, which means every one min, the dose is (40/60) mg.

1 mg = 1000 mcg

and the weight is 70 kg, so the actually dose given is actually (40/60*1/70*1000) mcg/kg/min, that is, 9.5 mcg/kg/min

9.5 mcg/kg/min vs 10 mcg/kg/min?? Is there a huge difference here?

So, rather than saying that we start 10 mcg/kg/min, we can start 9.5 mcg/kg/min and we titrate accordingly. There is no need to be rigid here.

Furthermore, how sure are you in the first place the weight is actually precisely 70 kg? Maybe the weight is only 60 kg.

In other words, the 10.5 ml/hr obtained from direct calculation is more accurate than 10 ml/hr from the rule of six (if and only if) the patient's weight is precisely 70 kg.

In the rule of six, we either give (6*BW) mg in 100 cc, that is, (6*70) = 420 mg in 100ml OR 210 mg in 50 ml, or we give an estimate of 200 mg in 50 ml. It is not practical to break another 200 mg ampoule just to extract that 10 mg.

But as mentioned, that is actually not a big problem especially in adults because of 2 reasons:

1. We can always adjust the sliding scale and titrate according to patient's requirement. If BP is still low, titrate up; if BP improved, taper down.
2. The weight 70 kg is often an estimated weight only unless you actually put the patient on weighing machine.

Similarly,

• for noradrenaline, we are assuming Wt ~ 65 or 130 kg, because noradrenalines come in 4-mg ampoule (if 65 kg, 4 mg in 50cc means 1 ml/hr = 0.02 mcg/kg/min, if 130 kg means, 4 mg in 50cc, 1 ml/hr = 0.01 mcg/kg/min)
• for dobutamine, we are assuming Wt ~ 80 kg because dobutamine comes in 250-mg ampoules.

But if you were to do direct calculation, then you will have to re-calculate every time you change:

• the dosage
• the weight of the patient
• the type of medications

How about now if we want to run 15 mcg/kg/min for the same 50 kg patient for dopamine? Or IV noradrenaline infusion for 80 kg on 1 mcg/kg/min?

Let's put it this way: if I have the time to calculate one by one, then by all means, I will do the direct calculation. I will do the direct calculation if I only one patient to manage. It is also more accurate if the weight is precisely known.

Furthermore, I know my mathematical skills cannot be trusted in times of emergency when the infusion is needed within minutes! I might calculate wrongly, I might get confused or I might miss the decimal points, in which case, I might give 10 times or 100 times more than needed (which I believe this is more dangerous than not giving the optimal dosing when applying rule of six).

Bottom line, whether you do direct calculation or the rule of six, you still need to be vigilant and cannot be careless. You should doubly check again to make sure you have done the right calculation.

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


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.