Clinical Medical Assisting Chapter 7: Dosage Calculations

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

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.

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

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

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

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

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

Proportions An equation that states two ratios are equal.

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

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.

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

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)

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.

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

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?

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 ÷ 500 30 = x Step 3: Insert the answer back into the proportion to identify the units. Answer: 30mL

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.

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

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.

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

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

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.

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).

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

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

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

Examples of Meters 1 millimeter(mm) = 0.001 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

Examples of Grams 1 microgram (mcg) = 0.000001 gram 1 milligram (mg) = 0.001 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

Examples of Liters 1 microliter (mcL) = 0.000001 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

Converting Between Systems of Measurement

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

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

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.

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.

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

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]

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.

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

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.

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

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?

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

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

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?

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

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

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?

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

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