1. Dimensional Analysis and Drug Dosage Calculations

2. Converting Units DIMENSIONAL ANALYSIS
Changing from one unit to another unit requires:
1) Same type of measurement
- you cannot convert length into mass
2) A conversion factor

3. Conversion Factors
Mathematical Ratio of the two units you are converting
Ex: Conversion of inches to centimeters
1 inch = 2.54 cm
Possible Conversion Factors
1 in or cm
2.54 cm in
Choose the conversion factor that puts what you are converting to over what you are converting from

4. Fence Post Method
Covert 15.0 ft to cm

5. Fence Post Method
Covert 15.0 ft to cm

6. Fence Post Method
Covert 15.0 ft to cm
15. 0 ft

7. Fence Post Method
Covert 15.0 ft to cm
15. 0 ft
12 in
1ft

8. Fence Post Method
Covert 15.0 ft to cm
15. 0 ft
12 in
2.54 cm
1ft
1 in

9. Fence Post Method
Covert 15.0 ft to cm
15. 0 ft
12 in
2.54 cm
1ft
1 in

10. Fence Post Method Covert 15.0 ft to cm 15. 0 ft 12 in 2.54 cm = 457 cm

11. Conversion Examples $12.00 to quarters 56 yards to feet
67 dimes to quarters
18.57 kg to mg
19.84 ft to m
mL to L
48 quarters
168 feet
26.8 quarters
1.857 X 107 mg
6.047 m
12.45 L

12. Multiple Dimensions
The number of dimensions determines the number of conversions
Area is two dimensions (length x width) so two conversions are needed
12.5 m2 to cm2
25.0 ft3 to cm3

13. Conversions in the Denominator
Unlike numerator conversions where “what you want goes over what you have”, denominator conversions are opposite = “what you want goes under what you have”
Basically, the units have to cancel  the beauty of the fence post method

14. Conversion Examples 55.0 g/L to g/mL 25.0 mi/hr to ft/sec
30.0 kg/m2 to g/cm2
0.055 g/mL
36.7 ft/sec
3.00 g/cm2

15. Drug Dosage Calculation
Reading Drug Labels
Trade Name
Amount and Form
NDC Number
Generic Name
Dosage Strength
Contraindications
Storage Directions
Manufacturer

16. Drug Labels Trade Name: Brand name or proprietary name
Generic Name: Official name of drug
NDC number: identifies the labeler, product, and trade package size
Dosage Strength: amount per unit measure
Form: capsule, tablet, liquid…..
Route: administration pathway
Amount: Number of doses
Directions: Storage directions
Contraindicators: the DO NOTs of the meds

17. 1. Trade Name: Generic Name: Dosage Strength: Form: Amount: Route:
Directions:
NDC Number:
9. Contraindicators:

19. Cost Comparison (Amazon.com)
Aleve: 270 tablets for $16.40
Naproxen Sodium: 400 tablets for $13.77

20. Drug Dosage Calculations
Calculation of Oral Dosage
“po” = by mouth
Ex: Prescription Augmentin 500 mg po daily

22. Ex: Prescription Augmentin 500 mg po daily

23. Ex: Prescription Augmentin 500 mg po daily
1 tablet
250 mg

24. Ex: Prescription Augmentin 500 mg po daily
1 tablet
= 2 tablets
250 mg

25. Examples
1) The order states Kantrex (antibiotic) 400 mg IM q12 h. The drug is supplied as 0.5 g/2 mL. How many mL should be administered?

26. Examples
The order states Kantrex 400 mg IM q12 h. The drug is supplied as 0.5 g/2 mL. How many mL should be administered? IM = q12 h =

27. Examples
The order states Kantrex 400 mg IM q12 h. The drug is supplied as 0.5 g/2 mL. How many mL should be administered? IM = Intramuscular q12 h = every 12 hours

28. 400 mg

29. 400 mg
1 g
1000 mg

30. 400 mg
1 g
2.0 mL
1000 mg
0.5 g

31. 400 mg
1 g
2.0 mL
1000 mg
0.5 g

32. 400 mg
1 g
2.0 mL
= 1.6 mL
Every 12 hrs
1000 mg
0.5 g

33. A patient has an order for enalprilat (blood pressure medicine)0
A patient has an order for enalprilat (blood pressure medicine)0.625 mg daily IVPB (intravenous piggy back). The entralprilat is diluted to 50 mL of D5W (dextrose 5% in water) and is to be infused over 20 minutes. The tubing drop factor is 60 gtt/mL. At what rate, in drops per minute, should the IVPB be programmed?

35. All the med goes into the 50 mL.
Not calculating the dose (that is mg), you are calculating the rate that it is administered.
Therefore you are calculating 50 mL in 20 minutes at a rate of 60 gtts/min.
50.0 mL
20.0 min

36. All the med goes into the 50 mL.
Not calculating the dose (that is mg), you are calculating the rate that it is administered.
Therefore you are calculating 50 mL in 20 minutes at a rate of 60 gtts/min.
50.0 mL
60 gtt mL
20.0 min

37. All the med goes into the 50 mL.
Not calculating the dose (that is mg), you are calculating the rate that it is administered.
Therefore you are calculating 50 mL in 20 minutes at a rate of 60 gtts/min.
50.0 mL
60 gtt
= 150 gtt/min mL
20.0 min

38. Review Problem
A patient is receiving dopamine at 12 mL/h. The concentration of dopamine is 200 mg in 250 mL of 0.9% NS. Calculate the micrograms per kilogram per minute. The patient’s weigh is 70kg.

39. Pediatric Dosage Calculation
1. Convert weight of child to kilograms.
2.2 pounds = 1 kg
2. Find the S&T (Safe and Therapeutic Dose Range) of the medicine.
3. Calculate the S&T range for the child and compare to the prescribed order.

40. Examples
Calculate the S&T dose range of ibuprofen for a child who weighs 36 lbs. Ibuprofen is available 100 mg/5mL. How many mL would you administer for the ordered dose to be S&T if that range is 5 to 10 mg/kg/dose q6-8 h?

41. Examples
Calculate the S&T dose range of ibuprofen for a child who weighs 36 lbs. Ibuprofen is available 100 mg/5mL. How many mL would you administer for the ordered dose to be S&T if that range is 5 to 10 mg/kg/dose q6-8 h?
36 lbs
1 Kg
2.2 lbs

42. Examples
Calculate the S&T dose range of ibuprofen for a child who weighs 36.0 lbs. Ibuprofen is available 100 mg/5mL. How many mL would you administer for the ordered dose to be S&T if that range is 5 to 10 mg/kg/dose q6-8 h?
36.0 lbs
1 Kg
2.2 lbs
= 16.4 Kg

43. Examples
Calculate the S&T dose range of ibuprofen for a child who weighs 36.0 lbs. Ibuprofen is available 100 mg/5mL. How many mL would you administer for the ordered dose to be S&T if that range is 5 to 10 mg/kg/dose q6-8 h?
16.4 Kg
5 mg
1Kg
16.4 Kg
10 mg
1Kg

44. Examples
Calculate the S&T dose range of ibuprofen for a child who weighs 36.0 lbs. Ibuprofen is available 100 mg/5mL. How many mL would you administer for the ordered dose to be S&T if that range is 5 to 10 mg/kg/dose q6-8 h?
16.4 Kg
5 mg
1Kg
5 mL
100 mg
= 4.1 mL
16.4 Kg
10 mg
5 mL
= 8.2 mL
100 mg
1Kg

45. 5 mg
1Kg
5 mL
100 mg
= 4.1 mL
36.0 lbs
1 Kg
2.2 lbs

46. An infant is admitted to the hospital to rule out sepsis
An infant is admitted to the hospital to rule out sepsis. The infant weighs 8 lbs and ampicillin is prescribed. Calculate the S&T 24 hour dosage range for this infant with a possible severe infection. The recommended dose is 200 to 400 mg/kg/24 h.

47. Obstetric Dosage
The physician ordered 1000 mL D5W with 10 units oxytocin intravenously. Begin at 1 mU/min (mU = milliunit, 1000 milliunits = 1 unit) and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 20 mU/min. Calculate the beginning IV rate (mL/hr).

48. The physician ordered 1000 mL D5W with 10 units oxytocin intravenously
The physician ordered 1000 mL D5W with 10 units oxytocin intravenously. Begin at 1 mU/min (mU = milliunit, 1000 milliunits = 1 unit) and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 20 mU/min. Calculate the beginning IV rate (mL/hr).
1 mU
= mL/hr
min

49. The physician ordered 1000 mL D5W with 10 units oxytocin intravenously
The physician ordered 1000 mL D5W with 10 units oxytocin intravenously. Begin at 1 mU/min (mU = milliunit, 1000 milliunits = 1 unit) and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 20 mU/min. Calculate the beginning IV rate (mL/hr).
60 min
1 mU
= mL/hr
min
1 hr

50. The physician ordered 1000 mL D5W with 10 units oxytocin intravenously
The physician ordered 1000 mL D5W with 10 units oxytocin intravenously. Begin at 1 mU/min (mU = milliunits, 1000 milliunits= 1 unit) and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 20 mU/min. Calculate the beginning IV rate (mL/hr).
60 min
1 unit
1 mU
= mL/hr
min
1 hr
1000 mU

51. The physician ordered 1000 mL D5W with 10 units oxytocin intravenously
The physician ordered 1000 mL D5W with 10 units oxytocin intravenously. Begin at 1 mU/min (mU = milliunit, 1000 milliunits = 1 unit) and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 20 mU/min. Calculate the beginning IV rate (mL/hr).
1000 mL
60 min
1 unit
1 mU
= mL/hr
min
10 unit
1 hr
1000 mU

52. The physician ordered 1000 mL D5W with 10 units oxytocin intravenously
The physician ordered 1000 mL D5W with 10 units oxytocin intravenously. Begin at 1 mU/min (mU = milliunit, 1000 milliunits = 1 unit) and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 20 mU/min. Calculate the beginning IV rate (mL/hr). What is the maximum IV rate (mL/hr)?
1000 mL
60 min
1 unit
1 mU
= 6 mL/hr
min
10 unit
1 hr
1000 mU

53. The physician has ordered 500 mL D5W with 20 units oxytocin IV
The physician has ordered 500 mL D5W with 20 units oxytocin IV. Begin at 1 mU/min and then increase by 1 mU/min every 30 minutes until contraction begin. The maximum dose is 30 mU/min. What is the initial and maximum flow rate for the IV (mL/hr)?

54. IV + Bolus Dosage
Bolus: a larger, more concentrated dose given prior to the steady IV dose to help speed response time
It is also the mushy ball of chewed food that you swallow. But these are not the same thing.

55. The physician has ordered 1000 mL lactated Ringer’s with 20 g magnesium sulfate. You are to administer a bolus with 4g/30 min, then maintain a continuous infusion at 2g/h.
1) Calculate the IV rate (mL/h) for the bolus order.
2) Calculate the continuous rate (mL/h).

56. The physician order Amikacin 150 mg IM q8 h. The following is available. How many mL should be administered?