Critical care math using dimensional analysis

About RetrieverGirl, BSN, RN
Joined: Oct '08; Posts: 213; Likes: 127
RN; from US
Specialty: 9 year(s) of experience in Med/surg tele, home health, travel 
Jul 15, '13Here is the site that helped me the most:
DosageHelp.com  Helping Nursing Students Learn Dosage Calculations
Do you have to use dimensional analysis? I always thought it was too many steps to get to the same answer. 
Jul 15, '13Quote from arrisubI agree! I definitely prefer proportion method.Here is the site that helped me the most:
DosageHelp.com  Helping Nursing Students Learn Dosage Calculations
Do you have to use dimensional analysis? I always thought it was too many steps to get to the same answer. 
Jul 15, '13If you stick with dimensional way you are set....it will become second nature to you...the reference website is really good

Jul 16, '13Dimensional is also called Factor Label Method. I used it in engineering. Having all of the units cross out at the end so that you are left with just the correct units (mg, mm, lb, kg, volume per minute, whatever you wanted) is a nice check that you set up the equation correctly and have solved it correctly.

Jul 16, '13My only caveat about DA (other than it is often more complicated than necessary) is that so often I see students try to cram every possible bit of data in the question into the equation...and a lot of it is not needed for the answer. Examination writers know this and put distractors (wrong answers) that would result from doing that in the choices. Does make for a lot of confusion, and we see it here often.
Step back from every problem and ask what's really being asked, see if you can eyeball a possible answer range, and then determine how to solve for X in any way that works comfortably for you. 
Jul 16, '13Another problem with Dimensional Analysis (DA) is that it doesn't always work well in reallife situations. Sometimes, in actual clinical practice, the situation doesn't "fit" dimensional analysis very well. But I have never met a problem that didn't lend itself to the old proportion way of calculating things.
A third problem  which is perhaps my biggest gripe about Dimensional Analysis  is that I see many students and new nurses using it to "solve" math problems without really understanding what is going on with the situation. Taking care of a patient requires more than just solving an equation, it requires an understanding of the relationships between volumes, rates, dosages, etc. When young nurses just plug numbers into an equation and get an answer (as if for a test question), they often miss what is actually happening with the fluid/medication/etc. and the patient. The proportion method promotes an understanding of the quantities of meds/fluids/etc. involved  and that understanding is important for optimal patient care.
DA can work for test questions ... particularly if the questions are chosen to be wellsuited for DA. But its weakness show when the new grads struggle with actual practice situations. 
Jul 16, '13Honestly I don't always use dimensional analysis. But for some math problems it makes better sense to me. I also use ratio and proportion. I just want to get those this critical care math.

Jul 16, '13Why don't you post one of your critical care problems so we can see what you are having problems with. I find if you don't have a good grasp of DA and if you try to go between using DA and proportion you will get confused and screw up...DA is what I learned in chemistry....for me DA is so much easier once you learn it and really apply it without switching back and forth..jmho

Jul 16, '13I always use DA and I am always the first done with 100% on every math test. Smartest person is the one whose solution is the simplest and works.

Jul 16, '13Each method has its merits and bad points. DA is more geared for when you need to convert more than a few items in one problem and it has a built in answer checker if you keep track of the units, but it can be tedious and confusing at times. Ratio is great because it always works and you really don't need to memorize anything, but you have to keep each conversion separate. Formulaic is a shorter version of the ratio method, but you have to remember what needs to be divided or multiplied.
Personally I use whatever works best for the situation and to be honest I do half of the work in my head. It really depends on what you are trying to figure out. For an example,
You have an order to give 10 mcg/kg/min dopamine using IV tubing with a calibration of 60. Patient is 154 lb. Available is 800 mg in 500 ml NS.
Order;10 mcg/kg/min
Available;800 mg in 500 ml NS
weight; 154lb
For the formula method the weight must be converted to kg
Order;10 mcg/kg/min
Available;800,000 mcg in 500 ml NS or 1600 mcg/ml or 1.6mg/ml
weight; 154lb /2.2= 70 kg
To get the order multiply 10 mcg by 70kg to get 700 mcg/min,
Order;700 mcg/min
Available;800,000 mcg in 500 ml NS or 1600 mcg/ml
weight; 70 kg
to get the ml/min (700/800,000)*500=0.4375 rounded to 0.4 ml/min
If you wanted ml/hr (700*500*60)/800,000=26.25 ml/hr round to 26 ml/hr
If you really want to go old school you could calculate gtt/min, in that case you take the 0.4 ml and multiply by the drip set, which in this case is 60.
0.4*60=24gtt/min
It only looks ugly because I am showing all possible products and the steps.
I would assume you are programming a pump to ml/hr and usually iv drugs have a concentration already on them of xmg/ml or xmcg/ml in the case of dopamine. Note that I pulled a real drug concentration and dosage (except you might start at 25mcg/kg/min) off the internet for this example. Dopamine is mix 400 mg in 250 ml of NS or 800 mg in 500 ml NS to produce a concentration of 1600 mcg/ml, which is what you get if you divide 800,000 mcg by 500 ml. Knowing the concentration of the drug takes a lot of work out of calculating the flow rate. If you know the dose is 700mcg/min and the concentration is 1600 mcg/ml, if you divide the order by the available you get mil/min, and if you multiply that by 60 you get ml/hr. so, (700/1600)*60= 26.25 ml/hr rounded to 26 ml/hr. If you are going to do a titration of the medication ((xmcg * kg)/concentration)* 60 min=mL/hr may simplify it if you already know the weight in Kg and the concentration. The short version is ((D/Q)*V= ml, where as D is the dose, Q is the amount of medication in the fluid and V is the amount of fluid and ml is the amount to administer. The long version if you already know the weight in Kg but not concentration it would be, (((10mcg/1000)*70)/800)*500)*60=26.25 ml/hr rounded to 26 ml/hr, could be done on a calculator on the fly. and if you only know the weight in lb, you can add that to the calculation too. So the long long version is...
(((10mcg/1000)*154)/2.2/800)*500)*60=26.25 ml/hr rounded to 26 ml/hr Basically what this string is list of conversions. I would not want to try to remember that even if it is calculator friendly.
If this is something you have to calculate often and on the fly, I would figure out the weight and concentration first, write them down and use this version,
((xmcg * kg)/concentration)* 60 min=mL/hr
Then if the dose is titrated from 10 mcg/kg/min to 15mcg/kg/min, you could calculate this faster. ((15*70)/1600)*60=39.37ml/hr or 39 ml/hr 
Jul 17, '13This is an excellent site!!!!! DosageHelp.com  Helping Nursing Students Learn Dosage Calculations
and this is an excellent one for dimensional analysis....http://www.davesems.com/files/drug_d...lculations.pdf 
Jul 17, '13It is hard to give an example because it seems as though the test questions are always much harder than the practice problems that we get. However, my downfall is with mcg/kg/min. If I remember correctly it was dopamine 800 mg/500 mL with a flow rate of 15 ml/hr. Patient weight 154 lbs. How many mcg/kg/min is the patient receiving? These are the problems that I use dimensional analysis because I see everything laid out when there are so many steps with the conversions. RLtinker I appreciate your help, but that method for these kinds of problems thoroughly confuse me