1. Clinical Medical Assisting
Chapter 7: Dosage Calculations

2. Objectives Understand ratio and proportion.
Use the metric, household, and apothecary systems of measurement and convert between metric and apothecary systems.
Understand units of medication dosage.
Correctly calculate dosages for adults and children.
Cut and paste from you will be able to from front of chapter

3. Chapter Overview
This chapter covers important topics relating to pharmaceutical measurements and basic dosage calculations necessary to ensure that a patient receives the correct dose or amount of medication. A mistake in a calculation or measurement will lead to underdosing or overdosing. This could then lead to inadequate treatment or drug toxicity. Many dosage-related tasks performed by a medical assistant will relate to mathematics and calculations, and these tasks require proficiency in basic arithmetic skills.

4. Ratio and Proportion
The ratio and proportion method can be used to calculate dosages.

5. Ratios
A representation of how two similar quantities are related to each other

6. Equivalent Ratios
Equivalent ratios are found by multiplying or dividing both sides of the ratio by the same number.

7. Example 1
To find an equivalent ratio for 1:2 multiply both sides by 2. (1 × 2):(2 × 2) = 2:4

8. Example 2
To find an equivalent ratio for 50:200 divide both sides by 25 (50 ÷ 25):(200 ÷ 25) = 2:8.

9. Proportions
An equation that states two ratios are equal.

10. Example
When the terms of a proportion are multiplied, the cross products are equal. Example: [2/8] = [5/20] 2 × 20 = 8 × 5 40 = 40

11. Cross Multiplication
Multiplication of the numerator of the first fraction by the denominator of the second fraction, and the multiplication of the denominator of the first fraction by the numerator of the second fraction.

12. Means & Extremes
Means are the numbers directly to the left and right of the equal sign and the extremes are the two outer numbers.

13. Calculating the Value of a Missing Term in a Proportion
Example : 5:15 = x:45 Step 1: Multiply the means: 15 × x = 15x Step 2: Multiply the extremes: 5 × 45 = 225 Step 3: Set up the equation (remember, the means equal the extremes): 15x = 225 Step 4: Divide both sides of the equation by 15 to find the value of x: 15x ÷ 15 = 225 ÷ 15 x = 15 Step 5: Replace the x in the proportion with 15: 5:15 = 15:45 (five is to 15 as 15 is to 45)

14. Ratio-Proportion Method for Dosage Calculations
The concentration of a stock solution (a solution of known concentration) and the dose needed for administration are often known while he volume of the dose is the unknown. A ratio or proportion can be established to solve for the missing value.

15. Example
A ratio or proportion can be established to solve for the missing value. Dosage on Hand: Amount on Hand = Dosage Desired: Amount Desired

16. Example (con’t)
A physician prescribes 1,000mg of acetaminophen suspension and all that is available is a stock suspension of 500mg/15mL. How many milliliters of acetaminophen suspension would you give to the patient to fulfill the order?

17. Example (con’t)
Step 1: The supply dosage and the amount prescribed are the same units, no conversion is necessary. Step 2: Set up the equation and calculate solving for x. 500mg:15mL = 1,000mg:xmL (15 × 1,000mL) = (500 × x) 15,000 ÷ 500 = 500x ÷ = x Step 3: Insert the answer back into the proportion to identify the units. Answer: 30mL

18. Converting a Ratio to a Percent
Convert the ratio to a fraction, selecting the first number as the numerator and the second number as the denominator. Then multiply the fraction by a number such that the denominator of the product equals 100. Express the final value followed by a percent sign.

19. Example
Example: 1:25 Step 1: 1:25 = [1/25] Step 2: [1/25] × [4/4] = [4/100] Step 3: [4/100] = 4%

20. Converting a Percent to a Ratio
Express the percent as a fraction, with a denominator of 100. Reduce the fraction to its most simplified form, if possible. Then express the final value as a ratio, designating the numerator as the first number and the denominator as the second number.

21. Example
Example: 4% Step 1: 4% = [4/100] Step 2: [4/100] = [2/50] = [1/25] Step 3: 1:25

22. Systems of Measurement
Systems of measurement used to calculate dosages are:
The common household system
The metric system, and
The apothecary system
International units
Milliequivalents

23. Household System of Measurement
Includes drops, teaspoons, tablespoons, fluid ounces, cups, pints, quarts, and gallons for measuring liquid. Includes ounces and pounds for measuring weight.

24. Apothecary System of Measurement
An outdated system of measurement previously used in medicine and science (a pound in the apothecary system is based on 12 ounces).

25. Metric System of Measurement
Legal standard of measurement for pharmacy and medicine in the United States
Based on the decimal system
Multiples of 10

26. Prefixes Used in the Metric System
Meaning
Conversion
Micro-
One millionth
Base unit × 10‒6
Milli-
One thousandth
Base unit × 10‒3
Centi-
One hundredth
Base unit × 10‒2
Deci-
One tenth
Base unit × 10‒1
Deka-
Ten times
Base unit × 101
Hecto-
One hundred times
Base unit × 102
Kilo-
One thousand times
Base unit × 103

27. Fundamental Units Used in the Metric System
Meter (m), measures length or distance
Liter (L), for measuring liquid volume
Gram (g), for measuring dry weight

28. Examples of Meters
1 millimeter(mm) = meter 1 centimeter (cm) = 0.01 meter 1 decimeter (dm) = 0.1 meter 1 meter (m) = 1 meter 1 dekameter (dam) = 10 meters 1 hectometer (hm) = 100 meters 1 kilometer (km) = 1,000 meters

29. Examples of Grams
1 microgram (mcg) = gram 1 milligram (mg) = gram 1 centigram (cg) = 0.01 gram 1 decigram (dg) = 0.1 gram 1 gram (g) = 1 gram 1 dekagram (dag) = 10 grams 1 hectogram (hg) = 100 grams 1 kilogram (kg) = 1,000 grams

30. Examples of Liters
1 microliter (mcL) = L 1 milliliter (mL) = .001 L 1 centiliter (cL) = 0.01 L 1 deciliter (dL) = 0.1 L 1 liter (L) = 1 liter 1 dekaliter (daL) = 10 L 1 hectoliter (hL) = 100 L 1 kiloliter (kL) = 1,000 L

31. Converting Between Systems of Measurement

32. International Units (IU)
Drugs measured in international units include:
Insulin, heparin, and vitamin D
The IU per milligram varies with each drug
Standard conversion factors are not possible

33. Calculating Drug Doses, Dosages, and Quantities
There are many methods for accurately calculating drug quantity, as well as expressing and communicating the treatment regimen.

34. Dose and Dosage
A dose of a drug is the quantity that is intended to be administered.
Dosage refers to the determination and regulation of the size, frequency, and number of doses.

35. Determining Doses Based on Weight
The usual adult dose for most drugs is based on an average body weight of 70kg,m or 154 lbs.

36. Determining Doses Based on Body-Surface Area
A representation of a patient’s weight and height relative to each other.

37. Example
BSA is calculated using the following equation: BSA (m2) = [Height (cm) × Weight (kg)/36,000][1/2] If inches and pounds are used to measure height and weight, respectively, the following equation can be used: BSA (m2) = [Height (in) × Weight (lb)/3,131][1/2]

38. Pediatric Patients
Newborns are especially sensitive to the actions of certain drugs because of immature or abnormal liver or kidney function, which are required for healthy drug metabolism. Doses based directly on a child’s BSA or body weight are the safest and most common choices to establish pediatric doses.

39. Nomogram
A graph that estimates the BSA of the patient based on height and weight.

40. BSA
Is determined by drawing a straight line from the patient’s height to the patient’s weight. Intersection of the line with the surface area column is the estimated BSA.

41. BSA Formula
[BSA of Child (m2)/1.7 (m2)] × Adult Dose = Child Dose This formula is based on the average adult who weighs 140 pounds and has a BSA of 1.7 m2

42. Example
A five-year-old child who is 40 inches tall and weighs 38 pounds has just been prescribed an antibiotic for an infection. The average adult dose of antibiotic is 50mg/mL. What dosage should this patient receive according to the BSA method?

43. Example (con’t)
Step 1: Use the following formula: [BSA of Child (m2)/1.7 (m2)] × Adult Dose = Child Dose Step 2: Plug the given values into the formula: [0.7 m2/1.7 m2 × [50mg/1] = child’s dose Step 3: 0.7 × 50 ÷ 1.7 × 1 = [35/1.7] Step 4: Simplify: 20.5mg Step 5: Use the ratio-proportion method: [50mg/1mL] = [20. 5mg/xmL] Step 6: Cross multiply 50mg × xmL = 1mL × 20.5mg = 50x = 20.5 Step 7: Solve for x [50x/50] = [20.5/50] x = 0.41mL

44. Young’s Rule
Used to determine pediatric doses based on age: Pediatric Dose = [Age of Child (Years)/Age of Child (Years) + 12] × Adult Dose

45. Example
11-year-old girl weighs 70 pounds If the usual dose of a medication is 500mg, using Young's rule, what would the dose of medication be for the girl?

46. Example (con’t)
Step 1: Use the following formula: Pediatric Dose = [Age of Child (Years)/Age of Child (Years) + 12] × Adult Dose Step 2: Plug the given values into the formula: [11/11+12] × 500mg Step 3: Convert both sides of the equation into fractions: [11/23] × [500/1]mg Step 4: Multiply the numerators: 11 × 500 = 5,500 Step 5: Multiply the denominators: 23 × 1 = 23 Step 6: Divide the product of the numerators by the product of the denominators: 5,500 ÷ 23 = 239 Answer: The pediatric dose is 239mg

47. Clark’s Rule
Used to determine pediatric doses based on weight. Pediatric Dose = [Weight of Child (Pounds) × Adult Dose/150 lb]

48. Example
Consider the same 11-year-old girl, who weighs 70 pounds. If the usual dose of a medication is 500mg, using Clark's rule, what would the dose of medication be for the girl?

49. Example (con’t)
Step 1: Use the following formula: Pediatric Dose = [Weight of Child (Pounds) × Adult Dose/150 lb] Step 2: Plug the given values into the formula: 70 lb × 500mg ÷ 150 lb Step 3: Calculate the product of the first part of the equation: 70 × 500mg = 35,000mg Step 4: Divide the product by 150: 35,000mg ÷ 150 = 233mg Answer: The pediatric dose is 233mg

50. Summary
A ratio represents how two quantities are related to each other
Proportions are equivalent ratios, often used to calculate unknown quantities or concentrations in pharmacy.
Percents are the number of parts per 100 total parts
The metric system is the most accurate, and preferred, system of measurement