1. Chapter 12: Specialized Calculations
Math and Dosage Calculations for Health Care Third Edition Booth & Whaley
Chapter 12: Specialized Calculations

2. Learning Outcomes
12.1 Measure insulin doses accurately Measure heparin dosage and flow rates, verifying that they fall within the normal daily range Calculate the hourly flow rate for IV infusions ordered in milligrams per minute.

3. Learning Outcomes (cont.)
12.4 Calculate IV flow rates for medications ordered in mg/kg doses Calculate IV flow rates for titrated medications Determine the percentages of solutions, dilutions, and solids Prepare solutions from a concentrate.

4. Introduction These special calculations require extra effort
Specialized calculations include
Insulin
Heparin
Critical care IV fluids
Preparation of solutions
Alligations
These special calculations require extra effort

5. Insulin High Alert Medication
Pancreas
High Alert Medication
Pancreatic hormone that stimulates glucose metabolism
With low or no insulin production
Insulin-dependent diabetes
Routine injections of insulin needed to keep glucose (blood sugar) from rising
Generally administered Sub-Q (rotate sites)

6. Insulin – TYPES Beef and pork – derived from the pancreas
Human insulin
Replaced beef and pork in the U.S.
Produced using genetically engineered bacteria
Insulin Lispro
Synthetic form

7. Insulin – TIMING OF ACTION
Rapid-acting
Administer 30 to 60 minutes before meals
Regular (R) and Semi-lente (S)
Very rapid acting
Administer 15 minutes before meal
Insulin Lispro

8. Insulin – TIMING OF ACTION (cont.)
Intermediate-acting
Lente (L), NPH (N), and Protamine Zinc (P)
Long-acting
Ultralente (U)
Lantus
Newer type
Maintains constant blood levels

9. Insulin – TIMING OF ACTION (cont.)
Onset
Time when insulin begins to lower blood glucose
Peak
Time when insulin’s effect is the greatest
Duration
Length of time the effect of insulin lasts
Measured from the time of onset

10. Insulin – TIMING OF ACTION (cont.)
Example
Regular insulin injection administered at 0700
Onset – 30 minutes, 0730
Peak – 2.5 to 5 hours post administration, between 0930 and 1200
Duration – 8 h, until 1530

11. Insulin – TIMING OF ACTION (cont.)
Type
Examples
Onset
Peak
Duration
Rapid-acting
Humulin R
30 min
2.5-5 hrs
8 hrs
Humalog
15 min
30-90 min
6-8 hrs
Intermediate-acting
Novolin L
2.5 hrs
7-15 hrs
22 hrs
Long-acting
Humulin U
4-8 hrs
10-30 hrs
28 hrs
Mixed
Humulin 70/30
hrs
24 hrs

12. Insulin – LABELS Expiration date and lot # Manufacturer Concentration
Storage information
Type
Brand name
Species

13. Insulin – LABELS (cont.)
Concentration
Usually listed twice as
100 units/mL – traditional form
U-100 (100 units/mL) insulin
Source
Beef
Pork
Human

14. Insulin Syringes Marked in units Calibrated in 1 or 2 unit increments
Measures amount of insulin (units) not volume of solution
100 unit capacity
50 unit capacity
30 unit capacity
Calibrated in 1 or 2 unit increments

15. Insulin Syringes (cont.)
Rule 12-1
For more accurate measurements use a 50 unit capacity insulin syringe for insulin doses less than 50 units, and a 30 unit capacity insulin syringe for doses less than 30 units.

16. Insulin Syringes (cont.)
Example
Ordered: Humulin N 66 units Use a 100 unit capacity syringe Ordered: Humulin R 8 units Use a 30 unit capacity syringe

17. Insulin Syringes (cont.)
Rule 12-2
When using U-500 or a dose of insulin over 100 units use a tuberculin or standard syringe.
Calculate the amount to administer in milliliters.

18. Insulin Syringes (cont.)
Example
Determine amount of insulin to give. Ordered: Humulin R U-500 insulin, 120 units Amount to administer = 0.24 mL Use a tuberculin syringe

19. Patient Education: MEASURING A SINGLE INSULIN DOSE
1. Always wash your hands before handling insulin and syringes.
2. If you are using an intermediate- or long-acting insulin (Lente, NPH, Ultralente, 70/30, or 50/50), roll the vial between your palms to mix the insulin until all of the insulin looks cloudy.

20. Patient Education: MEASURING A SINGLE INSULIN DOSE (cont.)
3. Cleanse the rubber stopper of the vial with an alcohol wipe, using a circular motion.
Start at the center of the circle and work outward.

21. Patient Education: MEASURING A SINGLE INSULIN DOSE (cont.)
12-21
Patient Education: MEASURING A SINGLE INSULIN DOSE (cont.)
4. Draw up an amount of air equal to your insulin dose in the syringe.
Pull back the plunger until the leading ring is aligned with the correct marking on the syringe.

22. Patient Education: MEASURING A SINGLE INSULIN DOSE (cont.)
5. Inject the air into the insulin vial.
6. Keep the needle inserted through the stopper and turn the vial upside down.
Draw up your ordered dose of insulin.

23. Patient Education: MEASURING A SINGLE INSULIN DOSE (cont.)
7. Avoid touching the needle during the procedure. 23

24. Insulin Combinations Provide greater control over glucose levels
Two types of insulin
Intermediate-acting
Short-acting

25. Insulin Combinations (cont.)
Manufacturer combines some types
Novolin 70/30
70% NPH insulin
30% regular insulin
Humulin 50/50
50% NPH insulin
50% regular insulin

26. Insulin Combinations (cont.)
12-26
Insulin Combinations (cont.)
Insulin pens
Self-administration without having to draw up medication from separate bottles

27. Insulin Combinations (cont.)
Rule 12-3
When preparing a combined insulin dose, always draw up the rapid-acting insulin first.
Remember: the insulin with a quicker onset is drawn up first.
Clear then Cloudy
Clear
Cloudy

28. Insulin Combinations (cont.)
Example
Ordered: Novolin R 20 units and Humulin N 15 units Sub-Q now Draw up the rapid-acing (clear) insulin first 20 units of Novolin R Then draw up the intermediate-acting (cloudy) insulin 15 units of Humulin N

29. Insulin Combinations (cont.)
Rule 12-4 To prepare a combined insulin dose:
1. Calculate the total dose of insulin:
dose of rapid-acting insulin
+ dose of intermediate-acting insulin
total dose insulin

30. Insulin Combinations (cont.)
Rule 12-4 (cont.)
2. Draw up an amount of air equal to the dose of intermediate-acting insulin.
Inject it into the intermediate insulin vial, but do not draw up the dose.
Withdraw the needle from this vial.
3. Draw up an amount of air equal to the dose of rapid-acting insulin.
Inject it into the rapid-acting insulin vial.

31. Insulin Combinations (cont.)
Rule 12-4 (cont.)
4. Without withdrawing the needle from the stopper, invert the vial. Draw up the dose of rapid-acting insulin.
5. Carefully insert the needle through the stopper of the intermediate-acting insulin vial.
Invert the vial, without injecting any of the rapid-acting insulin into the vial.

32. Insulin Combinations (cont.)
Rule 12-4 (cont.)
6. Draw up intermediate-acting insulin until the leading ring reaches the calibration indicating the total dose.
If you accidentally draw up more than the total amount desired, do not push the excess back into the vial.
You must begin the procedure again.

33. Insulin Combinations (cont.)
Example
Ordered: Humulin N 42 units and Humulin R 10 units Sub-Q daily
How many units will be in the syringe after both insulins have been drawn up into the syringe?
52 units of insulin

34. Error Alert!
When two types of insulin are combined, measure the correct amount of each.

35. Practice
True/False Onset is the time when insulin begins to lower the glucose level. Duration is measured from the time the insulin dose was administered. When mixing insulins, draw up the cloudy before the clear. Insulin is administered using special syringes marked in units. T F
From the time of onset F
Clear then cloudy T

36. Heparin High Alert Medication Anticoagulant
Reduce or prevent blood clotting
Administered IV or Sub-Q (rotate sites)
Flush solution for heparin locks

37. Heparin (cont.) Measured in USP units
Dosage calculations must be accurate
Safe adult dosage range
20,000 to 40,000 units/24h
Verify that calculated doses fall within this range
Infuse using an infusion pump to ensure accuracy

38. Heparin – CALCULATIONS
Desired dose represents a flow rate
Quantity of units per period of time
Infuse using an infusion pump to ensure accuracy.
Drop rate used to verify pump rate or if the tubing is removed from the pump temporarily.

39. Heparin – CALCULATIONS (cont.)
Rule To determine the rate to administer a solution containing heparin with an electronic device that measures the infusion in mL per hour find A, where
D = rate of the desired dose
Q = dosage unit
H = dose on hand
A = amount to administer
Calculate using your chosen calculation method.

40. Heparin – CALCULATIONS (cont.)
Example
Use your chosen calculation method to find hourly rate to administer IV heparin.
Ordered: 1000 units/h IV heparin using an infusion pump
On hand: 50,000 units heparin in 1000 mL D5W
H = 50,000 units; Q = 1000 mL; D = 1000 units/h
A = 20 mL/h

41. Heparin – CALCULATIONS (cont.)
Rule To calculate the hourly dose (D), multiply the total dosage by the hourly flow rate. Determine the following:
H = dose on hand or total amount to administer
Q = dosage units for the total amount
A = amount to administer or the flow rate of the infusion
Calculate using your chosen calculation method.

42. Heparin – CALCULATIONS (cont.)
Example
What is the hourly dose?
Ordered: 30,000 units of IV heparin in 500 mL to D5W to infuse at 25 mL/h
H = 30,000 units; Q = 500 mL; A = 25 mL/h
D = 1500 units/h

43. Heparin – CALCULATIONS (cont.)
Example
Next determine if 1500 units/h is a safe dose.
36,000 units/day is within the safe range of 20,000 to 40,000 units/day

44. Practice
What is the hourly dosage for an infusion of 45,000 units heparin in 1200 mL of D5W infusing at 30 mL/h? Is this a safe dose?
Answer units/h
Is this a safe dose?
This is a safe dose.

45. Critical Care IV IV medications used in critical care settings
Fast-acting and potent
Narrow margin of safety
Administered continuous, IV push, or bolus
Used to alter or maintain
Heart rate
Cardiac output
Blood pressure
Respirations

46. Critical Care IV – PER MINUTE ORDERS
Rule 12-7 To convert a per minute order to an hourly rate:
1. Convert the order to mL/min. Determine the following:
D = rate of desired dose (mg or mcg/min)
Q = dosage unit (mL)
H = dose on hand (mg or mcg/min)
A = amount to administer (mL/min)
Calculate using your chosen calculation method.

47. Critical Care IV – PER MINUTE ORDERS (cont.)
Rule 12-7 (cont.)
2. Convert mL/min to mL/h
Either by multiplying by 60 or if using dimensional analysis use the factor 60/1 as part of your equation
Both ways the hourly flow rate will be determined in mL/h

48. Critical Care IV – PER MINUTE ORDERS (cont.)
Example
Find the hourly flow rate.
Ordered: 5000 mg Esmolol in 500 mL D5W at 8 mg/min via infusion pump
H = 5000 mg; Q = 500 mL; D = 8 mg/min
A = 0.8 mL/min × 60 = 48 mL/h

49. Critical Care IV – ORDERS BASED ON BODY WEIGHT
Rule 12-8 To find the IV flow rate based upon weight:
Convert the weight to kg
Determine the desired dose
Calculate the amount to administer
Calculate the flow rate

50. Critical Care IV – ORDERS BASED ON BODY WEIGHT (cont.)
Example
Find the flow rate for an adult weighing 187 lb.
Ordered: Acyclovir 5 mg/kg IV in 100 mL D5W over 1 hour, q 8 hours X 7 days
On hand : Acyclovir mg/20 mL. Label instructions are to dilute to a dosage strength of 7 mg/mL or less.
Convert wt to kg: 178 lb = 85 kg
Determine desired dose:
D = 425 mg

51. Critical Care IV – ORDERS BASED ON BODY WEIGHT (cont.)
Example (cont.)
Calculate amount to administer:
A = 8.5 mL
Calculate the flow rate:
8.5 mL Acyclovir mL D5W = 425 mg/108.5 mL
Dosage strength = 3.9 mg/mL (less than recommended; safe to administer)
Flow rate based on order is108.5 mL over 1 hr

52. Critical Care IV – TITRATED MEDICATIONS
Medications administered at rates based upon their effect
Upper and lower ranges
Require careful monitoring
Incrementally adjusted until desired affect is achieved
Calculate the highest and lowest dosages

53. Critical Care IV – TITRATED MEDICATIONS (cont.)
Rule 12-9
If you know the total amount of medication in the total volume of solution and the volume of solution that the patient has received, then you can use a proportion to calculate the amount of medication the patient has received (dose).

54. Critical Care IV – TITRATED MEDICATIONS (cont.)
Example
Your patient is receiving dopamine titrated to maintain his blood pressure. His infusion started with dopamine 800 mg/D5W 250 mL at a rate of 5 L/h. Over the last 3 h you have titrated the dopamine up to 12 mL/h to maintain the blood pressure. He has received 112 mL of the solution. How much dopamine has the patient received?

55. Critical Care IV – TITRATED MEDICATIONS (cont.)
Example (cont.)
Total amt of medication = 800 mg
Total amt of solution = 250 ml
Amount of solution received = 112 mL
800 mg x 112 = 250 x ?
Amount of medication received = mg

56. Practice
Find the appropriate flow rate: Ordered: Mezlin 250mg/kg/day IV q6h in 80 mL of D5W; infuse over 1 h On hand: Mezlin 20 g vial; reconstitute with 10 mL sterile water for each gram Patient weights 152 lb; use macrodrip tubing of 15 gtt/mL

57. Practice Answer Convert 152 lb to kg = 69.1kg
Find desired dose: D = 250mg x 69.1 = mg
Find mg per dose: mg/dose
Convert to grams: 4.32 g
Find amount to administer: 43.2 mL + 80 mL of D5W
Find flow rate: mL/h
Find drop rate: 31 gtt/min

58. Preparation of Solutions, Dilutions, and Solids
Liquid mixtures containing two or more different chemicals
Solvent
Liquid used to dissolve the other chemicals
Water – universal solvent
Solutes
The chemicals dissolved in the solvent

59. Preparation of Solutions, Dilutions, and Solids (cont.)
Manufacturer prepared solutions
Injections
Eye drops
Cough syrups
To prepare or dilute a solution you must know how the concentration of the solution is expresses

60. Percentage Concentration
Most common way to express concentration
If the solute is a solid – grams of solute per 100 mL solution
If the solute is a liquid – milliliters of solute per 100 mL solution
If both solute and solvent are solids – grams of solute in 100 g of solvent

61. Preparing % Solutions and Solids
Measure solute
Add sufficient quantity of solvent to make desired volume
Remember that the solute occupies part of the total volume

62. Preparing % Solutions and Solids (cont.)
Examples
A “recipe” for preparing 100 mL of 2% lidocaine solution would look like this:
The recipe for preparing 100 g of 10% zinc oxide powder and petroleum jelly
2 % Lidocaine Solution
Lidocaine
2 g
Water
qsad* 100 mL
10% Zinc Oxide
Zinc oxide
10 g
Petroleum jelly
90 g
*Qsad = “sufficient quantity to adjust the dimensions to”

63. Preparing a Dilution from a Concentrate
Mix a solution that is more concentrated than needed with one that is less concentrated than needed
Calculations for preparing dilutions
Alligation method
Formula method

64. Preparing a Dilution from a Concentrate (cont.)
Rule To prepare a dilution from a concentrate, determine:
Vn = the volume needed
Cn = the concentration needed
Ca = the concentration(s) available*
* If water is being used, one of the these concentration is zero.
Then use the alligation method or formula to obtain your answer.

65. Alligation Method Procedure Checklist 12-1
1. Write out a tic-tac-toe grid and fill in values.
2. Find the total number of parts in the solution by adding the 2 values in the right column.
Grid

66. Alligation Method (cont.)
Concentration of MORE concentrated solution
Parts of the MORE concentrated solution needed
The concentration needed
Concentration of LESS concentrated solution
Parts of the LESS
concentrated solution needed

67. Alligation Method (cont.)
Procedure Checklist 12-1 (cont.)
3. Find the volume of 1 part by dividing the total number of parts into the volume needed.
4. Multiply the volume of 1 part (answer from Step 3) by the number in the top right of the grid. The result is the amount of the more concentrated solution needed.
Grid

68. Alligation Method (cont.)
Procedure Checklist 12-1 (cont.)
5. Add a sufficient quantity of the less concentrated solution to bring the final volume up to the desired volume.

69. Alligation Method (cont.)
Example
How would you prepare 500 mL of 50% ethanol from 90% ethanol? Water is one diluent.
Add right column = 90 parts total
Determine volume of 1 part = 90 50 40

70. Alligation Method (cont.)
Example (cont.)
Determine the amount of the more concentrated solution needed =
5.56 mL/part x 50 parts of conc = 278 mL
Needed 278 mL of 90% ethanol to make 500 mL of a 50% ethanol solution.
Add qsad of water to make the total volume of 500 mL 90 50 40
50% Ethanol Solution
90% ethanol
278 mL
Water
Qsad 500 mL

71. Formula Method* Procedure Checklist 12-2
1. Identify the following information:
Cn = concentrated needed
Ca = concentration available
Vn = volume needed
2. Solve for: Va = volume available
*The formula method can only be used when one of the solutions has a concentration of 0%, such as water.

72. Formula Method* (cont.)
Procedure Checklist 12-2 (cont.)
3. Cancel units.
4. Solve for: Va = volume available.

73. Formula Method (cont.) Example
How would you prepare 500 mL of 50% ethanol from 90% ethanol?
Cn = 50%
Ca = 90%
Vn = 500 mL
Va = = 278 mL
50% Ethanol Solution
90% ethanol
278 mL
Water
qsad 500 mL

74. Practice
Find the amount of 95% ethyl alcohol that needs to be mixed with water to make 1.5 L of a 30% ethyl alcohol solution:
30% Ethanol Solution
90% ethanol
437.7 mL
Water
qsad* 1500 mL

75. Apply Your Knowledge Which type of Insulin is NOT pictured?
Match insulin type with correct label.
Intermediate-Acting
Long-Acting
Rapid-Acting
Very Rapid-Acting
Which type of Insulin
is NOT pictured?

76. Apply Your Knowledge
The time at which the insulin’s effect is strongest is called:
a. Onset
b. Peak
c. Duration

77. Apply Your Knowledge Answer 5 gtt/min
Ordered: 500 mg dobutamine HCL in 100 mL D5W infusing at 2.4 mg/min with a macrotubing at 10gtt/mL
How fast would you set the gtt/min?
Answer 5 gtt/min

78. Apply Your Knowledge Convert 165 lb to kg. Answer 75 kg
What formula can you use to determine the amount of medication received when medications are titrated?

79. End of Chapter 12 -- Elbert Green Hubbard
When on the brink of complete discouragement, success is discerning that the line between failure and success is so fine that often a single extra effort is all that is needed to bring victory out of defeat.
-- Elbert Green Hubbard