1. Math and Dosage Calculations for Medical Careers
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Math and Dosage Calculations for Medical Careers
Second Edition
Booth • Whaley
Chapter 12
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2. Specialized Calculations
Chapter 12
Specialized Calculations

3. Learning Objectives When you have completed
Chapter 12, you will be able to:
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.
Chapter 12

4. Learning Objectives (con’t)
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.
Chapter 12

5. Introduction
You may be required to have additional knowledge related to dosage calculations
This special knowledge will require specialized calculations
Insulin
Heparin
Critical care IV fluids
Preparation of solutions
Alligations
Chapter 12

6. Insulin
Insulin is a pancreatic hormone that stimulates glucose metabolism
People who have low or no insulin production may have insulin-dependent diabetes
They often need routine injections of insulin to keep their glucose (blood sugar) from rising to levels that could be life threatening
Rotate injection sites
Pancreas
Chapter 12

7. Types of Insulin Beef and pork - extracted from cattle or pig pancreas
Human - including genetically-engineered bacteria
Synthetic - insulin lispro
Clear - regular insulin
Cloudy - Lente, NPH, and Ultralente insulins
Chapter 12

8. Timing of Insulin Action
Rapid-acting insulins
Regular (R) and Semilente (S) insulins
Administered 30 to 60 minutes before a meal
Very rapid-acting insulin
Insulin lispro
Administered 15 minutes before a meal
Chapter 12 8

9. Timing of Insulin Action
(con’t)
Intermediate-acting insulins
Lente (L), NPH (N), Protamine Zinc (P)
Long-acting insulin
Ultralente (U)
Lantus (new type of insulin) – maintains a constant blood level without peaks
Chapter 12

10. Timing of Insulin Action
(con’t)
Onset
The time when the insulin begins to lower the glucose level
Peak
The time at which the insulin’s effect is strongest
Duration
The length of time the effect of the insulin lasts
Chapter 12

11. Timing of Insulin Action
(con’t)
Example:
Regular dose of insulin given at 0700
onset:
peak:
duration:
after 30 minutes, at 0730
2.5 to 5 hours after it is administered, between 0930 & 1200
will last about 8 hours, until 1530
Chapter 12

12. Timing of Insulin Action
(con’t)
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
Chapter 12

13. Insulin Labels Manufacturer Concentration Expiration date Brand Name
Type
Storage Information
Species
Chapter 12

14. Insulin Labels (con’t)
Concentration is usually listed twice
Traditional dosage strength – 100 U/mL
Concentration – U-100 (meaning that 100 units of insulin are contained in 1 mL of solution)
Concentration may be U-500
Labels include type
Beef
Pork
Human
Chapter 12

15. Insulin Syringes
Insulin administration is different from other types of injections.
The syringe measures the amount of insulin rather than a volume of solution.
Must use special insulin syringes marked in units.
Chapter 12

16. Insulin Syringes (con’t)
Standard U-100 syringes hold up to 100 units per 1mL solution
Calibrated for every 2 units or some in each unit
Smaller syringes hold up to
50 units (0.5 mL of solution)
30 units
Chapter 12

17. Insulin Syringes (con’t)
Rule
For more accurate measurements, use a 50-unit insulin syringe for insulin doses less than 50 units when available.
Chapter 12

18. Insulin Syringes (con’t)
Example -
Decide which syringe to use.
Ordered: HumulinR 55 units
Answer – 100-unit syringe and fill it to between the 54 and 56 units line
Chapter 12

19. Insulin Syringes (con’t)
U-500 insulin is used for patients with highly elevated blood sugars.
Insulin may be given by IV.
Use tuberculin or standard syringe when U-500 or doses over 100 units are ordered.
These doses will not fit in a 100-unit syringe.
Chapter 12

20. Insulin Syringes (con’t)
Rule
When using U-500 or a dose of insulin over 100 units use a tuberculin or standard syringe.
Chapter 12

21. Insulin Syringes (con’t)
Example:
Determine amount of insulin to give.
Ordered: Humulin R U-500 insulin 80 units
Administer 0.16 mL in a tuberculin syringe
Chapter 12

22. Measuring a Single Insulin Dose Patient Education
Always wash your hands before handling insulin and syringes.
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.
Chapter 12

23. Measuring a Single Insulin Dose Patient Education (con’t)
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.
Chapter 12

24. Measuring a Single Insulin Dose Patient Education (con’t)
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.
Chapter 12

25. Measuring a Single Insulin Dose Patient Education (con’t)
Inject the air into the insulin vial.
Chapter 12

26. Measuring a Single Insulin Dose Patient Education (con’t)
Keeping the needle inserted through the stopper, turn the vial upside down.
Draw up your ordered dose of insulin.
Chapter 12

27. Measuring a Single Insulin Dose Patient Education (con’t)
Avoid touching the needle during the procedure.
Chapter 12 27

28. Insulin Combinations
Two types of insulin may be ordered to allow the doctor more control over glucose levels.
The combination of a rapid-acting insulin and an intermediate-acting insulin provides the patient with the rapid onset of the first and the lengthy duration of the second.
Chapter 12

29. Insulin Combinations (con’t)
The two types of insulin can be combined in one syringe.
Some are automatically combined by the manufacturer.
Novolin 70/30 is 70% intermediate-acting NPH insulin and 30% rapid-acting regular insulin.
Humulin 50/50 is 50% NPH insulin and 50% regular insulin.
Chapter 12

30. Insulin Combinations (con’t)
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.
Chapter 12

31. Insulin Combinations (con’t)
Example: Which one should be drawn up first?
Ordered: Novolin (rapid-acting) R 20 units and Humulin (intermediate-acting) N 15 units Sub-Q now
The rapid-acting Novolin R will be drawn into the syringe first.
Chapter 12

32. Insulin Combinations (con’t)
Rule 12 – 4
To prepare a combined insulin dose:
Calculate the total dose of insulin:
dose of rapid-acting insulin
+ dose of intermediate-acting insulin
total dose insulin
Chapter 12

33. Insulin Combinations (con’t)
Rule 12 – 4: (con’t)
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.
Draw up an amount of air equal to the dose of rapid-acting insulin.
Inject it into the rapid-acting insulin vial.
Chapter 12

34. Insulin Combinations (con’t)
Rule 12 – 4 (con’t)
Without withdrawing the needle from the stopper, invert the vial. Draw up the dose of rapid-acting insulin.
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.
Chapter 12

35. Insulin Combinations (con’t)
Rule 12 – 4 (con’t)
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.
Chapter 12

36. Insulin Combinations (con’t)
Example:
How many units will be in the syringe after both insulins have been drawn up into the syringe?
Ordered: Humulin N 42 units and Humulin R 10 units Sub-Q daily
Answer = 52 units total
Chapter 12

37. Error Alert!
When two types of insulin are combined, measure the correct amount of each.
Chapter 12

38. Heparin Anticoagulant use in USP units
Given to patients to reduce or prevent the blood from clotting
Use as an irrigate to keep the blood from clotting in a heparin lock
Chapter 12

39. Heparin (con’t)
Rotate multiple injections of heparin to prevent bruising.
Bruising and bleeding are a great concern for patients.
Calculated dosages must be accurate.
Chapter 12

40. Heparin Calculations For anticoagulant therapy
Administer adults at a dosage of 20,000-40,000 units per 24 hours
You must verify that the dose is within a safe range
Through an IV, via electronic device, to ensure accuracy of the dose
Chapter 12

41. Calculate Heparin Dosages
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 = the dosage unit
H = dose on hand
A = amount to administer
Chapter 12

42. Calculate Heparin Dosages (con’t)
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
Answer: 20 mL/h
Chapter 12

43. Calculate Heparin Dosages (con’t)
Rule
To calculate the hourly dose (desired 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.
Chapter 12

44. Calculate Heparin Dosages (con’t)
Example:
What is the hourly dose?
Ordered: 30,000 units of IV Heparin in 500 mL to D5W to infuse at 25 mL/h
Answer = 1500 units/h
Chapter 12

45. Critical Care IV Medications
IV medications used in critical care settings are fast-acting and potent
Only a small amount is required to have an effect
Given to alter or maintain
Heart rate
Cardiac output
Blood pressure
Respirations
Chapter 12

46. Critical Care IV Medications (con’t)
You must have the right medication for the right patient in the correct concentration
Be certain that you are administering the proper dosage at the proper rate
Can be given continuous, IV push or bolus
Via volume-controlled burette
Electronic infusion device
Microdrip tubing
Chapter 12

47. Calculating Critical Care Medications
Rule
To convert a per minute order to an hourly rate:
Convert the order to mL/min. Determine the following:
D = rate of desired dose (mg or mcg/min)
Q = dosage unit (mL)
Chapter 12

48. Calculating Critical Care Medications (con’t)
Rule (con’t)
To convert a per minute order to an hourly rate:
H = dose on hand (total number of mg or mcg)
A = amount to administer (mL/min)
Use your chosen calculation method
Chapter 12

49. Calculating Critical Care Medications (con’t)
Rule (con’t)
To convert a per minute order to an hourly rate:
2. Convert the 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
Chapter 12

50. Calculating Critical Care Medications (con’t)
Example:
Find the hourly flow rate.
Ordered: 5000 mg Esmolol in 500 mL D5W at 8 mg/min via infusion pump
Answer = 0.8 mL/min
Chapter 12

51. Orders Based on Body Weight
Many medication orders are based on body weight.
Body weight calculations are relevant to IV medications for critically-ill patients.
Example:
Daily dosage may be 5 mg/kg/day.
If patient weights 50 kg, you can use a proportion to calculate daily dose of 250 mg.
Chapter 12

52. Orders Based on Body Weight (con’t)
Rule
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
Chapter 12

53. Orders Based on Body Weight (con’t)
Example:
Find the flow rate for an adult who weighs 187 lb.
Ordered: Zofran 0.15 mg/kg IV over 15 min, started 30 min prior to chemo: repeat x2 at 4 h & 8 h
On hand : Zofran 40 mg/20mL. Dilute injection with 50 mL of 5%DW
Answer = 22.4 mL of Zofran over 15 min
Chapter 12

54. Titrated Medications
Critical-care meds are administered at varying rates depending on their effects on bodily functions.
You must carefully monitor and adjust the rate of these medications.
You must calculate the lowest and highest dosages.
Chapter 12

55. Titrated Medications (con’t)
Often you start the medications at the lower end and increase incrementally over time until the desired effect is achieved.
You must calculate the total amount the patient has received.
Start by measuring the total mL of infused solution.
Infusion pumps have indicators that measure mL.
Chapter 12

56. Titrated Medications (con’t)
Rule 12 – 9
If you know the total amount of medication in the total volume of solution, as well as 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 (the dose).
total amount of medication amount of medication received
total volume of solution volume of solution received =
Chapter 12

57. Preparation of Solutions, Dilutions, and Solids
Solutions are liquid mixtures containing 2 or more chemicals
Solvent – used to dissolve other chemicals
Solutes – chemicals dissolved in the solvent
Common solvent is water
Universal solvent
Normal saline = 0.9% sodium chloride in every 100 mL of solution
Chapter 12

58. Preparation of Solutions, Dilutions, and Solids (con’t)
Common examples of manufacturer solutions
Injections
Eye drops
Cough syrups
You may have to prepare a solution “from scratch”
Chapter 12

59. Percentage Concentrations
Common way to express concentrations is in percentages.
Percent means “per hundred.”
How much solute is found in every 100 mL of solution?
Chapter 12

60. Percentage Concentrations (con’t)
Solid solute
% = grams of the solute in 100 mL
2% lidocaine = contains 2 g of lidocaine in every 100 mL of solution
Chapter 12

61. Percentage Concentrations (con’t)
Liquid solute
% = milliliters of the solute in 100 mL
70% isopropyl alcohol has 70 mL of isopropyl alcohol in every 100 mL solution
Chapter 12

62. Percentage Concentrations (con’t)
Solid solute and solid solvent
% = grams of the solute in 100 g of the product
2% hydrocortisone ointment means that 100 g of ointment will contain 2 g of hydrocortisone
Chapter 12

63. Preparing % Solutions and Solids
You must first measure the solute
Then add sufficient quantity of solvent to bring the total to desired volume
Chapter 12

64. Preparing % Solutions and Solids (con’t)
Example:
A “recipe” for preparing 100 mL of 2% lidocaine solution would look like this:
2% Lidocaine Solution
*qsad 100 mL
Water
2 g
Lidocaine
*Qsad = “sufficient quantity to adjust the dimensions to”
Chapter 12

65. Preparing % Solutions and Solids (con’t)
Example:
Write the recipe for preparing 100 g of 10% zinc oxide powder and petroleum jelly.
90 g
Petroleum jelly
10 g
Zinc oxide
10% zinc oxide
Chapter 12

66. Preparing a Dilution from a Concentrate
You may need to prepare a solution from a concentrated solution that is already prepared
Alligation method
Use of formula
Chapter 12

67. Preparing a Dilution from a Concentrate (con’t)
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
Chapter 12

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

69. Alligation Method (con’t)
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
Chapter 12

70. Alligation Method (con’t)
Find the volume of 1 part by dividing the total number of parts into the volume needed.
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.
Chapter 12

71. Alligation Method (con’t)
Add a sufficient quantity of the less concentrated solution to bring the final volume up to the desired volume.
Chapter 12

72. Alligation Method (con’t)
Example:
How would you prepare 500 mL of 50% ethanol from 90% ethanol?
Desired volume is 500 mL - you would dilute the 90% by adding water up to a final volume of 500 mL.
Chapter 12

73. Preparing a Dilution from a Concentrate – Formula Method*
1. Identify the following information:
Cn = the concentration needed
Ca= the concentration available
Vn = volume needed
2. Solve for:
Va = the volume available
*The formula method can only be used when one of the solutions has a concentration of 0%, such as water.
Chapter 12

74. Preparing a Dilution from a Concentrate – Formula Method (con’t)
Plug the values into the following formula:
Cancel units
Solve for the equation for Vn
Chapter 12

75. Preparing a Dilution from a Concentrate – Formula Method
Example:
How would you prepare 500 mL of 50% ethanol from 90% ethanol?
Answer: 278 mL of 90% ethanol solution is needed to prepare 500 mL of a 50% solution
50% Ethanol
qsad 500 mL
Water
278 mL
90% ethanol
Chapter 12

76. Long-acting-Ultralente
Apply Your Knowledge
Match each label with its type.
Very Rapid-Acting
Rapid-Acting
Very Rapid-Acting
Long-Acting
Long-acting-Ultralente
Intermediate-Acting
Long-Acting
Rapid-Acting
Which type of Insulin
is not pictured?
Chapter 12

77. Apply Your Knowledge
The time at which the insulin’s effect is strongest is called:
a. Onset
b. Peak
c. Duration
Answer: b. Peak
Chapter 12

78. 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
Chapter 12

79. Apply Your Knowledge Convert 165 lb to kg.
Answer: 75 kg
What formula can you use to calculate titration of medications?
total amount of medication amount of medication received
total volume of solution volume of solution received =
Chapter 12

80. Specialized Calculations
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
THE END
Chapter 12