medmathpharmacology 111201105331-phpapp01
TRANSCRIPT
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Med MathMaking Nurses’ Lives
Simple in Numbers
Dr. Cyruz P. TuppalRN, RM, RT, MSN, MASPED,
DMS, [email protected]@yahoo.com
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Tips for success
Pick one method, that is easiest for YOUStudy itLearn itPractice itPractice itPractice it
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Topics
Apothecary SystemWeight and Temperature ConversionsMetric SystemMed Math Administration Doses Weight Based Doses Drip Rate Calculations
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Apothecary System
Phased out and replaced by metric systemBasic Units: grain (gr), dram (dr), drop (gtt), ounce, (oz), pint (pt), quart (qt)Equivalents
1dr = 1 tsp = 60 gtts3tsp = 1 Tbsp
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Weight Conversion
Fact: 1 kilogram (kg) = 2.2 pounds (lbs)Fact: Weight in kgs X 2.2 = weight in pounds
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Conversion Practice
80 kilogram patient, what is weight in pounds
kilograms X 2.2 = pounds
80 X 2.2 = 176 lbs.
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Conversion Practice
100 kilogram patient, what is weight in pounds
kilograms X 2.2 = pounds
100 X 2.2 = 220 lbs.
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Weight Conversion
Fact: 1 kilogram (kg) = 2.2 pounds (lbs)Fact: Weight in kgs X 2.2 = weight in poundsFact: Weight in pounds / 2.2 = weight in kilograms
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Conversion Practice
245 lb patient, what is weight in kilograms
lbs / 2.2 = kilograms
245 / 2.2 = 111.36 kgs
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Conversion Practice
140 lb patient, what is the weight in kilograms
lbs / 2.2 = kilograms
140 / 2.2 = 63.63 kilograms
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Conversion Practice
The easy way…
Half of weight in pounds, subtract 10%
Example: 180 lbs . . . . . 9010% of 90 = 981 kilograms
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Conversion Practice
180 lb patient, what is the weight in kilograms
lbs / 2.2 = kilograms180 / 2.2 = 81.82 kilograms
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KNOW YOUR WEIGHT CONVERSIONS!!!!!
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Temperature Conversions
Fahrenheit: Water Freezes at 32º F Water Boils at 212º F
Celsuis: Water Freezes at 0º C Water Boils at 100º C
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Temperature Conversions
Fahrenheit CelsiusSubtract 32 from the temperatureMultiply by 0.556 or 5/9
98.6 – 32 = 66.6
66.6 X 0.556 = 37.03 = 37º C
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Practice
Convert 103º F to Celsius
103 – 32 = 71
71 X 0.556 = 39.48º C
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Temperature Conversions
Celsius FahrenheitMultiply by 1.8Add 32
37º X 1.8 = 66.666.6 + 32 = 96.6º F
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Practice
Convert 44º C to Fahrenheit
44 X 1.8 = 79.2
79.2 + 32 = 111.2 º F
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On your own
120 º F Celsius76.4 º F Celsuis
60 º C Fahrenheit24 º C Fahrenheit
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Metric System
System of 10 (base 10)No fractions only decimalsEASY!
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Metric System
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Metric System
Deca 10Hecto 100Kilo 1000
Deci0.1Centi 0.01Mili 0.001
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Metric System
Gram = gLiter = lKilogram = kgMilliliter = mLMilligram = mgCubic centimeter = ccMicrogram = g
1 L = 1000 mL1 mL = 1 cc1 g = 1000 mg1 mg = 1000 g1cc = 1 mL1 g = 0.001 mg1 mg = 0.001 g
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The math
Adding – keep the decimal points in lineSubtracting – see aboveMultiplying – multiply without regard to decimals then add decimal placesDividing – make the divisor a whole number and add zeroes to the dividend
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Addition
4.3795+ 5.2389---------------
9.6184
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Subtraction
9.6184- 5.2389---------------
4.3795
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Multiplication
34.76X 4.935-------------- 17154060
Add decimal places = 5 171.54060 = 171.5406
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Division
.75 / .995 75 / 99.5 move
decimal--------------0.7537
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Converting
1g = 1000mg so… g mg X1000
1mg = 1000 µg so… mg g X 1000
1g = ???? g = 1,000,000 g
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Converting
500mL = 0.5L so… mL L /1000
The Bottom Line…To convert from the base to mili X
1000To convert from mili to the base /
1000To convert from mili to X
1000To convert from base to X
1000000
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Standard Administration
The long formula
dose desired X volume on hand
Volume to administer = ------------------------------------
dose on hand
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Example
Orders call for 0.5mg Atropine for symptomatic bradycardia. You have 1mg in 10 mL pre-filled syringe
0.5 mg X 10 mL------------------ = volume to
administer 1.0 mg
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Example
mg’s cancel out0.5 X 10mL = 5mL
0.5 mg X 10 mL------------------ = 5 mL
1.0 mg
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Another Example
You have 100mg Furosemide in a 10mL vial. The order is for 40mg
80 mg X 10 mL------------------ = volume to
administer 100 mg
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Example
mg’s cancel out80 X 10mL = 800mL/100 = 8
80 mg X 10 mL------------------ = 8 mL
100 mg
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Catching on?
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Try it on your own
Benadryl – 50 mg in 2 mLOrders are for 12.5 mgShow your work
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Benadryl
12.5 mg X 2 mL------------------ = volume to
administer 50 mg
12.5 X 2 = 25 / 50 = 0.5 mL
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The easy way
Set up an equationCross MultiplyDivideSound like algebra?
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The easy way
Order is for 45 mg BenadrylYou have 50 mg in 2 mL
50 45--- --- 2 X
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The easy way
50 45--- --- 2 X
Multiply 45 X 2 = 90Divide 90 by 50 = 1.8
So… you would administer 1.8 mL = 45 mg
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Another example
Order is for 3 mg ValiumYou have 10 mg in 2 mL
10 3--- -- 2 X
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Another example
10 3--- -- 2 X
Multiply 3 X 2 = 6Divide 6 by 10 = 0.6
So… you would administer 0.6 mL = 3 mg
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Finally, the good stuff
Order is for 145 µg of Fentanyl CitrateYou have 300 mcg in 5 mL
300 145----- ----- 5 X
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The good stuff
300 145----- ----- 5 X
Multiply 145 X 5 = 725Divide 735 by 300 = 2.42 = 2.4
So… you would administer 2.4 mL = 145 mg
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Weight Based Dosage
1. Convert weight to kgs.2. Calculate the dose to give3. Calculate the volume to
administer
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Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.
1. Convert the weight to kilograms. 185 / 2.2 = 84 kgsOr 93 – 9.3 = 83.7 = 84 kgs
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Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.
2. Calculate the dose to give 84 kgs X 1.5 mg = 126 mg
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Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.
3. Calculate the volume to administer
126 mg is the dose we want to give 10 mL pre-filled syringe containing
100 mg
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Weight Based Dosage
126 mg X 20 mL------------------ = volume to
administer 200 mg
126 X 20 = 2520 / 200 = 12.6 mL
So, one complete syringe containing 10 mL plus approx. 2.6 mLfrom a second syringe
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Weight Based Dosage
Pediatric2mg/kg Benadryl for a 25 lb patient
1. Convert weight to kilograms 25 / 2.2 = 11.36 kgsOr 12.5 – 1.2 = 11.3 kgs
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Weight Based Dosage
Pediatric2mg/kg Benadryl for a 25 lb patient
2. Calculate the dose to give 11.3 kgs X 2 mg/kg = 22.6 mg
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Weight Based Dosage
Pediatric2mg/kg Benadryl for a 25 lb patient
3. Calculate the volume to administer
22.6 mg X 1 mL-------------------- = 0.45 mL 50 mg
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Or the easy way
We know we want 2mg/kgThe child ways 11.3 or roughly 11 kgsThe dose will be 22mg
50 22--- --- 1 X
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Or the easy way
50 22--- --- 1 X
22 X 1 = 22 / 50 = 0.44 mL
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Drip Rate Calculations
Facts: In a 60 drop set, 60 drops = 1 mL In a 10 drop set, 10 drops = 1 mL In a 15 drop set, 15 drops = 1 mL Medications are usually given in 60 gtt sets Doesn’t mean you cannot give it in a 10 gtt
set A 60 drip set is usually called a microdrip A 10 drip set is usually called a macrodrip
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Microdrips
60 gtts = 1 mLIf your dose was 1 mL / hr what would your drip rate be?
1 gtt / minute
Why?60 gtts = 1 mL (our dose)1 drop / min = 60 gtts/hr = 1 mL = 60 gtts
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Easy huh?
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Let’s try another
Using a 60 drop set, the dose is 30 mL/hr60 gtts = 1 mL30 mL = 1800 gtts1800 gtts/60 min = 30 gtts/min
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And another
Using a 60 drop set, the dose is 45 mL/hr60 gtts = 1 mL 45 mL = 2700 gtts2700 gtts / 60 min = 45 gtts / hr
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Dose not in mL/hror
mL/min?
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No sweat…
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Understanding Concentration of drug in fluid
A liter bag of fluid = 1000 cc or 1000 mLIf you add 800 mg of a drug to 1000 mL of fluid, what would ur ratio of drug to fluid be?
800 mg X mg---------- --------1000 mL 1 mL
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Drug in fluid
800 mg X mg---------- --------1000 mL 1 mL
800 X 1 = 800 / 1000 = 0.8 mg/mL
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Drug in fluid
400 mg X mg---------- --------250 mL 1 mL
400 X 1 = 400 / 250 = 1.6 mg / mLConvert mg mcg Dopamine1.6 X 1000 = 1600 mcg / mL
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You do it
You add 1 gram of Lidocaine to 250 mL NSThe answer should be in mg/mL
Survey Says….
1 gm = 1000 mg
1000 mg in 250 mL = 4mg/mL
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Not mL/hr but mg/min
Lidocaine 2mg/minMixed 1gm/250ml
1000mg = 1gm1000mg/250ml = 4mg/ml
Drip rate = 30gtts/min
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Why?
4mg/mlThe dose is 2mg/minUsing a microdrip (60) 60gtts=1ml4mg/min = 602mg/min = 301mg/min = 15
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The Math
Drug order (mg/min) X IV Drip rate (gtts/ml)
-------------------------------------------Drug concentration (mg/ml) X 1min
2mg/min X 60 gtts/ml--------------------------
4mg/ml X 1min
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2mg/min X 60 gtts/ml--------------------------
4mg/ml X 1min
2 X 60 120-------- = ---4 X 1 4
30 gtts
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Putting it ALL together
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Dopamine
Weight BasedOver time (mcg/kg/min)
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Weight based over time
Order is for 7mcg/kg/minDrug on hand is 800 mgDrip Set is 60gtts/mlPt weight is 220 lbsIV solution 500mL NS
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1. Convert Weight from lbs to kgs2. Convert measurements (mgs
µg)3. Determine µg/mL4. Formula
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Step 1: Convert Weight
220 lbs kgs220 / 2.2 = 100 kgs
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Step 2: Convert Measurements
800 mg µgMg µg = X 1000800,000 µg
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Step 3: Determine µg/mL
800,000 µg / 500 mL1600 µ / mL
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Step 4: Formula
Drug order (µg/kg) X weight (kgs) X drip rate
---------------------------------------------------Concentration on hand (µg/ml) X
time (min)
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Step 4: Formula
7 µg/kg X 100 kgs X 60 gtts/mL---------------------------------------
1600 µg/mL X 1 min
7 X 100 = 700 X 60 = 4200
4200 / 1600 = 26.25 = 26 gtts/min
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Another
Order is for 5 µg/kg/minDrug on hand is 800 mg = 800,000 µg60 Drop setPt weighs 175 lbsIV solution 500 mL NS
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Step 1: Convert Weight
175 lbs / 2.2 = 79.5 ~ 79 kgs87.5 – 8.7 = 78.8 ~ 79 kgs
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Step 2: Convert Measurements
800 mg µg800,000 µg
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Step 3: Determine µg/mL
800,000 mcg / 500 mL1600 mcg / mL
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Step 4: Formula
Drug order X weight X drip rate---------------------------------------
Conc on hand X time
5 mcg/kg X 79 kgs X 60-----------------------------1600 mcg/mL X 1 min
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Step 4: Formula
5 X 79 X 60 = 2370023700 / 1600 = 14.81 ~ 15 gtts/min
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An easy check to your work
For 5 µg / kg / minTake weight in pounds (175)Drop the last digit (17)Subtract 1 (16) in the ballpark, not completely accurate