Drug Calculations Inver Hills Community College Paramedic Program I. Kevin Johnson, AS,BS, NREMT-P

The new system of weights and measures will be a stumbling block and the source of difficulties for several generations â€Ś Itâ€™s just tormenting the people with trivia!! Napoleon I

Converting from one System to Another Units of Weight Metric 60 Milligrams (mg) 1 gram (g)

= =

Apothecary grains (gr) 1 grains (gr) 15

Units of Volume Metric 1 ml = 5 ml = 30 ml =

Apothecary 1 minum 15 - 16 m 1 dram 1 ounce

= = = =

Household 1 gtt 15 gtts 1 teaspoon 1 ounce

Converting mg to Grains Convert 300 mg to grains We want to cancel the mg and end up with grains

?gr 300 mg× ?mg Since 60 mg = gr 1, the fraction is:

gr1 60mg

gr1 gr 300 300mg × = = gr 5 60mg 60

The Metric System 9 1000 Îźg = 1 mg

9 1000 mL = 1 L

9 1000 mg = 1 g

9 1000 L = 1 kL

9 1000 g = 1 kg

9 1 mL = 1 cc = 1 cm3

To convert from one multiple to the other, move the decimal point 3 places in the direction indicated.

Kg

3

g

3

mg

3

Îźg

Converting lbs to kg Convert 200 lb to kg

Known = 1kg = 2.2 lb

1kg 200 200lbs × = = 90.9kg 2.2lbs 2.2 Two AM Rule: Divide the weight in pounds by 2

200lb ÷ 2 ≈ 100

Multiply by 10%

100 × 10% ≈ 10

Subtract the % from the quotient

100 − 10 = 90kg

Finding the Ordered Dose 9 The Doctor’s Order 9 amount of medication and the route

9 Concentration ¾ how much drug is in a given amount of fluid ¾ worded as “on Hand” ¾ Break it down to per mL values ¾ 100mg/5mL = 20mg/mL

9 What are You looking For? ¾ Identify unit of measurement to be administered to the patient

The Key 9 Organization ¾identify key components of problem 9 The Order 9 “What’s on Hand” 9 Looking for:

Find the Ordered Dose Dr. Kool orders 2 mg of Valium IV to a patient with seizure activity. You have a 5 mL vial that contains 10 mgs of Valium. (10mg/5mL). How many mLs are you going to draw up into a syringe?

Order: 2 mg Valium IV On Hand: Hand 10 mg/5 mL Valium Looking for: mL to be given

Ordered Dose Formula Method volume on hand Ă— ordered dose volume to be given ( X ) = concentration (mg)

5mL Ă— 2mg X= 10mg 10 X = ml 10

X = 1mL

Ordered Dose Ratio & Proportion Method On the left side of the proportion, put the known ratio:

10 mg : 5 mL :: On the right side, put the ration that is unknown:

10 mg : 5 mL :: 2 mg : X mL Multiply the extremes then multiply the means

10 X = 5 x 2 X = 1 mL

10 X = 10

Titrated Drugs 9 Specific dose of Drug given in small

increments “to effect” ¾Dose usually repeated Q 3 – 5 minutes

9 Example ¾2- 10 mg Versed for seizure control ¾2 – 10 mg MS for pain and B/P >100

Example of Titrated Med 9 Standing orders: ¾ 2 – 10 mg Versed IV for seizure control 9 On Hand: ¾ 10mg in 2 mL or 5 mg/mL 9 Problem ¾ How to give 2 mg increments accurately IVP 9 Answer ¾ Dilute to 10 mL of solution ¾ 2 mL of Versed with 8 cc of NS = 1 mg/mL

Find the Units per Kilogram 9 Recognize the order is based upon weight 9 Utilize the Key = Organization 9 Solve the problem 他Convert Pounds to Kilograms 他Order by Weight to a Basic Order 他Find the Ordered Dose

Units per Kilogram You are to give 10 mg/kg of Bretylium to 198 pound patient You have premixed syringes with 500 mg/10 mL. How many mLs will you administer? Order: 10 mg/kg On Hand: 500mg/10 mL Looking For: mL Ptâ€™s Weight: 198 lbs

Organize your pertinent Information

Units Per Kilogram 9 Step 1 - Convert lbs to Kg

198lb ÷ 2.2 = 90kg 9 Step 2 - Convert to Basic Order ordered dose × weight(kg) X= 1kg

X=

10mg × 90kg 1kg

9 Step 3 - Find the ordered Dose 500mg :10mL :: 900mg : XmL 500X = 9000

9000 X= mL 500

X = 18 mL

X = 900mg

Concentration 9 Goal 他to find out how many mg, mcg, or grams of a drug there are in 1 mL of solution 他usually mg/mL

9 Formula Solute (grams or milligrams of drug) X= Solvent (liters or milliliters of volume)

Calculating Concentration Formula Method One gram of lidocaine has been added to a 250 mL bag of Normal Saline. What is the concentration? Step 1 - set up the formula

Solute (grams or milligrams of drug) X= Solvent (liters or milliliters of volume)

1g lidocaine X= 250 mL D5W

Step 2 - Convert grams to milligrams 1000mg X= 250mL Step 3 - Do the math

1000mg 250 4mg X= รท = = 4mg / mL 250mL 250 1mL

Calculating Concentration Ratio & Proportion Method One gram of lidocaine has been added to a 250 mL bag of Normal Saline. What is the concentration? Step 1 - Place known concentration on the left 1000mg : 250 mL :: Step 2 - Place unknown concentration on the right 1000mg : 250mL :: (X)mg : 1mL Step 3 - Multiply the Means and Extremes

250 X = 1000 Step 4 - Write as: 4:1

1000 X= = 4mg 250

Calculate an IV Drip Rate 9 To determine how many drops per minute

are needed to infuse a desired volume of IV solution over a given time period 9 Example: Âžhow many gtts/min are needed to infuse 1000 mL of NS over 2 hrs using a Macro IV set?

9 Formula volume to be infused Ă— drip set rate gtts / min = infusion time in minutes

IV Drip Rate Calculation Dr. Feelgood orders 2 L of D5W1/2NS to be infused over 4 hours. Using a Macro tube drip set of 15gtts/mL, how many gtts/min will you adjust your IV set to deliver? Step 1: Set up the formula gtts/min =

2L × 15gtt/mL 4 hrs

Step 2: Convert to Proper Units & solve 3

2000 × 15 200 × 5 1000 gtts / min = = = = 125gtt / min 240 8 8 3

IV Drip with Medication 9 Usually ordered to administer a certain

number of mgs or mcgs or drug per minute. 9 May involve drawing up medication from a

vial and injecting it into a bag of solution. 9 You need to figure how much drug is

contained in 1 mL of the solution

IV Drip Rate Dimensional Analysis You are to administer lidocaine at a rate of 2 mg/min to a patient with an arrhythmia. You have a vial of Lidocaine that contains 1 g in 5 mL. You also carry a 250 mL bag of Normal Saline. Your administration set is a microdrip with a rate of 60 gtts/mL. How many drops/min will you set your IV set to drip? Step 1: Organize the information. Order: 2 mg lidocaine/min IV On Hand: 1 g lidocaine/5 mL Bag: 250 mL NS Adm set: 60 gtt/mL Looking for: gtt/min

IV Drip Rate Formula IV bag volume(mL) mg ordered adm set(gtt) X= × × Drug in Bag 1 min 1 mL

250mL 2mg 60 gtt x= × × 1000mg 1 min 1mL 25 2 60 gtt X= × × 10 1 min 1mL 300 gtt X= = 30 gtts / min 10 min

IV Drip Rate Rule of Fours Using the same problem, we calculate the following: & 60gtt = 1 mL 4mg=1mL 4 mg Desired Dose

60 3 mg

45

15 Gtts/min

30 2 mg

1 mg

IV Drips based on Patient Weight Example: An order is given to administer 10 mcg/kg/min of Dopamine. You have a vial that contains 200mg/10mL. Of Dopamine. You also have a 250 cc bag of NS & a microdrip IV set. Your Patient weighs 176 pounds. How will you set your drip rate? 9 9 9 9 9 9

Order: On Hand Bag: Adm. Set Ptâ€™s Weight: Looking for:

10mcg/kg/min 200 mg/10mL 250 cc NS 60 gtts 176 lbs gtts/min

IV Drips based on Patient Weight Calculation Step 1: Convert the patient’s weight to kg & calculate dose

176lb 1kg 10mcg × × = 800mcg / min 1 2.2lb 1kg Step 2: Calculate Drip Rate

250mL 800mcg 60 gtt X= × × 200000mcg 1 min 1mL

120 X= = 60 gtts / min 2

IV Drips based on Patient Weight Calculation Alternative Step1:Calculate the concentration 200 mg = 200000mcg 200000mcg : 250mL :: Xmcg ; 1 mL 250 X = 200000 200000 X= = 800mcg / mL 250 Step 2: Convert lbs to Kg 176/2.2 = 80kg Kg × ordered Dose × gtt set Step 3: Calculate Drip rate X=

80 × 10 × 60 X= = 60 gtt / min 800

concentration of drip

Solutions 9 A solution given as a percentage always

refers to this concentration ¾Grams of drug in 100 mL of solution

9 Therefore: ¾D5W = ¾5% Dextrose solution ¾5 grams of Dextrose for every 100 mL solution ¾500 mL bag = 25 grams of Dextrose

Solutions (continued) 9 Example #2 ¾ 2% Lidocaine ¾ 2 grams of Lidocaine in 100 mL solution ¾ 2000 mg in 100 mL solution ¾ 20 mg/mL

9 Example #3 ¾ 20% Lidocaine ¾ 20 grams in 100 mL ¾ 20000 mg in 100 mL ¾ 200 mg.mL