Dose Calculations

1
Dose Calculations
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4
2
Systems of Measure

• Three common systems still used today
• Each deals with units of mass and volume
• Metric
• Apothecary
• Household

3
Metric System

• Most commonly used
• Considered the most convenient since based on
  units of 10
• Basic units are
• Meter Length
• Liter Volume
• Gram (Weight) Mass

4
Metric System

• Length
• 1 kilometer (km) 1000 meters
• 1 hectometer 100 meters
• 1 decameter 10 meters
• Meter
• 1 decimeter 1/10 meter
• 1 centimeter (cm) 1/100 meter
• 1 millimeter (mm) 1/1000 meter

• Volume
• 1 kiloliter 1000 liters
• 1 hectoliter 100 liters
• 1 decaliter 10 liters
• Liter (L)
• 1 deciliter 1/10 liter
• 1 centiliter 1/100 liter
• 1 milliliter (ml) 1/1000 liter

• Weight
• 1 kilogram (kg) 1000 grams
• 1 hectogram 100 grams
• 1 decagram 10 grams
• Gram
• 1 decigram 1/10 gram
• 1 centigram 1/100 gram
• 1 milligram (mg) 1/1000 gram

1 Gram 1 ml 1 cc 1 Kg 1000 g 2.2 lbs 1
mcg (µg) one-millionth of a gram (0.000001 g)
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Apothecary System

• Old system of measurement
• Considered to be less precise and convenient
• Basic units are
• Minim Volume
• Grain (Weight) Mass
• Written prescriptions place abbreviations before
  a roman numeral (gr V 5 grains)
• ¼ of a grain would be written as gr ¼ not 0.25 gr

1 Grain (gr) 60 65 mg 1 dram 60 gr 8 dr 1
oz 16 oz 1 lb
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Household System

• Approximate system of measurement
• Basic units are
• Weight ounces, pounds
• Volume glass, cup, tablespoon, drop, quart,
  pint and gallon

1 t 4 5 ml 1 T 15 16 ml 1 pt 500 ml 1
qt 1000 ml 2 pt 1 in 2.54 cm
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Dose calculations

• As a paramedic you will have to calculate drug
  doses, infusion rates and strengths of drugs in
  the field.
• Remember
• All units of measure must be converted to the
  same unit and system
• The computed dose must be assessed to determine
  if it is reasonable
• Use the same method of calculation every time

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Concentrations

• Refers to the strength of the drug (how many of
  one thing is present in something else)
• 10 mg of drug in 1 ml of solution
• Accomplished by dividing the weight of the drug
  by the volume of fluid it is in

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Concentrations

• Some drugs are labeled as a percentage
• Refers to of grams in 100 ml of solution
• 1 Lidocaine 1 g of Lidocaine in 100 ml
• 10 MgSO4 10 g of MgSO4 in 100 ml
• D5W 5 Dextrose in water
• 5 g of dextrose in 100 ml of Water
• A 10 ml of 10 MgSO4 has 1 g of drug per 10 ml
  (or 100 mg/ml)

10 g MgSO4 100 ml

100 mg/ml
10 MgSO4

10000 mg 100 ml

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Calculations

• Three common types
• Basic Formula (Most common)
• Dimensional analysis
• Ratios and proportions
• May also see the T method

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Dimensional Analysis

• Sets up all conversion factors in one equation
  and separated by X
• To solve calculation
• Set up the equation
• Cancel pairs of units of numerator/denominator
• Multiply the numerators
• Multiply the denominators
• Divide the numerator by the denominator

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Dimensional Analysis

• Example 1
• You are to administer fentanyl 50 mg IM. You
  have 75 mg of the drug in a 1 ml solution. How
  many ml will you give?

50 ml 75
2 ml 3
0.66 ml
ml
1 ml 75 mg
X
50 mg 1




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Dimensional Analysis

• Example 2
• You are to administer 5 mg IV of valium. You
  have 10 mg of the drug in a 1 ml solution. How
  many ml will you give?

5 ml 10
1 ml 2
0.5 ml
ml
1 ml 10 mg
X
5 mg 1




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Ratio and Proportions

• Compares two numbers and works like a fraction
• Example
• Administer morphine 3 mg IV. You have 10 mg in 1
  ml of solution. How many ml will you give?
• 10 mg 1 ml 3 mg x ml

Means

• Therefore
• 10x 3
• x 3/10
• x 0.3 ml

Extremes
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Basic Formula

• D desired dose Want
• H concentration of the drug Have
• V volume the drug is supplied in Volume

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Calculation 1

• The adult patient with nausea has no allergy to
  Dimenhydrinate. The appropriate dose is 20 mg.
  How many milliliters will be administered?
• D 20 mg
• How is Gravol supplied?
• 50 mg in a 5 ml vial
• H 50 mg
• V 5 ml

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Calculation 1
Dose
D H
X
V

• What is a side effect of Gravol?
• Burning within the vein
• How can it be diminished?
• Dilute with saline prior to administration

5 ml
20 mg 50 mg
X

100 ml 50


2 ml
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Calculation 2

• An average size adult patient is actively
  seizing. The appropriate dose for diazepam is
  2.5 mg to 5.0 mg IVP.
• How is valium supplied?
• 10 mg in 2 ml
• Calculate the administration for the smallest dose

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Calculation 2
Dose
D H
X
V

2 ml
2.5 mg 10 mg
X

5 ml 10

0.5 ml

20
Calculation 3

• With the same patient, calculate the
  administration for the largest dose (5.0 mg)

21
Calculation 3
Dose
D H
X
V

• Why can valium not be diluted with saline?
• Is oil based
• What would happen if it was diluted in saline?
• Seizure Salad Dressing

2 ml
5 mg 10 mg
X

10 ml 10

1.0 ml

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Calculation 4

• A 28 y/o male has a fracture to the left tib/fib.
  His pain is 10/10. The appropriate dose for
  morphine sulfate is 2.5 5 mg.
• How is morphine supplied?
• 10 mg in 1.0 ml
• Calculate the administration for the smallest dose

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Calculation 4
Dose
D H
X
V

1 ml
2.5 mg 10 mg
X

2.5 ml 10

0.25 ml

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Calculation 5

• With the same patient, calculate the
  administration for the largest dose (5.0 mg)

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Calculation 5
Dose
D H
X
V

• How can an ACP administer morphine more
  accurately and safely?
• Dilute 10 mg in 9 ml of saline in a 10 cc syringe
• What is the concentration of the drug now?
• 1 mg/ml

1 ml
5 mg 10 mg
X

5 ml 10

0.5 ml

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Calculation 5
Dose
D H
X
V

• What are 3 potential side effects of morphine?
• Nausea, hypotension, respiratory depression
• How can we treat these effects?

1 ml
5 mg 10 mg
X

5 ml 10

0.5 ml

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Calculation 6

• A 70 y/o female is in extremis due to dyspnea
  preceded by two weeks of general malaise. She is
  lethargic, warm to the touch, diaphoretic, and
  has an Sa O2 of 80 on 100 O2. You decide to
  intubate. The appropriate dose for Versed is 2.0
  5.0 mg.
• How is Versed supplied?
• 10 mg in 2 ml
• Calculate the administration for the 2.0 mg dose

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Calculation 6
Dose
D H
X
V

2 ml
2.0 mg 10 mg
X

4.0 ml 10

0.4 ml

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Calculation 7

• With the same patient, calculate the
  administration for the largest dose (5.0 mg)

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Calculation 7
Dose
D H
X
V

2 ml
5 mg 10 mg
X

10 ml 10

1 ml

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Calculation 8

• A 70 y/o male is c/o dyspnea. He has a PHx of
  CHF and on exam has rales in all lungs fields.
• He is on Furosemide 40 mg PO but has not had any
  in two days since his prescription ran out and
  has not been refilled.
• What is the most appropriate method of
  determining how much lasix the patient should
  receive?
• Contact OLMC
• How is Lasix supplied?
• 40 mg in 4 ml
• Calculate the administration for the 40 mg dose

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Calculation 8
Dose
D H
X
V

4 ml
40 mg 40 mg
X

160 ml 40

4 ml

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Calculation 9

• You are called for a 24 y/o female, third
  trimester, who presents with grand mal seizures.
  Her husband states she has been bedridden with
  HTN X 3 weeks and denies any other PHx,
  medications or drug use.
• The protocol for seizures with eclampsia states 1
  g of magnesium sulfate
• How is MgSO4 supplied?
• 5 g in 10 ml
• Calculate the administration dose

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Calculation 9
Dose
D H
X
V

10 ml
1 g 5 g
X

10 ml 5

2 ml

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Calculation 10

• The pt is a 49 y/o female who presents with
  dyspnea, tachycardia and pallor.
• She is normotensive, has Sa O2 of 98 on RA and a
  regular, narrow complex tachycardia on the
  monitor with a rate of 178.
• Protocol states that Adenosine is the appropriate
  medication with a starting dose of 6.0 mg.
• How is Adenosine supplied?
• 6 mg in 5 ml
• Calculate the administration dose

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Calculation 10
Dose
D H
X
V

5 ml
6 mg 6 mg
X

30 ml 6

5 ml

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Calculation 11

• Your pt is a 55 y/o male c/o weakness. O/E the
  pt is pale, diaphoretic and has a slow regular
  pulse at 40 with a BP of 90/60. The ECG shows a
  sinus bradycardia with no ectopics.
• Atropine is indicated. The dose is 0.5 mg
• How is Atropine supplied?
• 1 mg in 10 ml
• Calculate the administration dose

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Calculation 11
Dose
D H
X
V

10 ml
0.5 mg 1.0 mg
X

5 ml 1

5 ml

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Calculation 12

• You are called to the home of an 18 y/o female
  who has been stung by a bee. She has a known
  allergy. She was unable to self administer her
  epi pen due to device malfunction.
• Your standing orders are for 0.3 mg SQ of 11,000
  solution.
• How is Epinephrine 11,000 supplied?
• 1 mg in 1 ml
• Calculate the administration dose

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Calculation 12
Dose
D H
X
V

1 ml
0.3 mg 1.0 mg
X

0.3 ml 1

0.3 ml

41
Weight Specific Dosing

• Some medications require a Dose based on the
  patients weight. (Typically in kilograms)
• May be a bolus or an infusion
• 1.5 mg/kg of Lidocaine bolus in an arrest
  protocol
• 5 µg/kg/min of Dopamine
• To calculate the dose multiply the dose in units
  (g, mg, µg) by the pts weight in kg.

42
Calculation 13

• The pt is a 60 y/o female who presents
  unresponsive falling a fall down a flight of
  stairs. She has snoring respirations, purposeful
  movements of her arms, and an obvious deformity
  to her left parietal region. You decide to
  sedate and intubate the pt. Following the
  administration of Versed, prior to intubating you
  are to administer Lidocaine. She weighs
  approximately 110 lbs.
• How is Lidocaine supplied?
• 100 mg in 5 ml
• Calculate the administration dose

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Calculation 13

• First convert the weight of this patient
• Then calculate the desired dose

Weight
110 lb 2.2 kg/lb
50 kg


Desired Dose
50 kg X 1.5 mg/kg
75 mg


44
Calculation 13
Dose
D H
X
V

5 ml
75 mg 100 mg
X

375 ml 100

3.75 ml

45
Calculation 14

• The pt is a 40 y/o, 220 lb male. He is 1 week
  post operative bowel surgery, released from
  hospital 3/7 ago, responsive but lethargic
• His Sa O2 is 95 on RA, HR 124 Reg and Weak, BP
  70/40.
• Your interventions are 100 O2 and a 1 L bolus of
  NaCl and has not shown a hemodynamic change. The
  protocol states 5 µg/kg/min infusion of dopamine.

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Calculation 14

• What do we need to know?
• How is dopamine supplied?
• 800 mg in 500 ml of D5W
• Weight of pt in kg
• How much dopamine is to be delivered per minute
• Concentration of dopamine per gtt
• How many gtts per minute (will do this next
  module)

220 lb 2.2 kg/lb
Weight
100 kg


Desired Dose
100 kg X 5 µg/kg/min
500 µg/min


800 mg 500 ml
1600 µg/ml
Concentration
1. 6 mg/ml



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Practical Session

• Using the D Kit. Identify all the medications
  found within it and document the following
• Name
• Concentration
• Indications
• Contraindications
• Dosing parameters
• Appropriate calculation of dose

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To continue

• We will continue calculations next month during
  the IV session of the program.