Children’s Dosages

Objectives

• Calculate 24-hour drug doses and divided doses for specific weights.

• Calculate safe dose ranges in mg/kg, mcg/kg, and square meters of body surface area (BSA).

• Calculate reconstituted pediatric drug doses and small-volume IV flow rates for children.

• Evaluate orders and safe dose range calculations.

• Make a decision:

Give medication (within therapeutic range).

Hold medication and clarify promptly (overdose or underdose).

• Analyze medication errors using critical thinking.

Introduction

The trend for increased medication administration safety is to customize all dose orders based on body weight or body surface area and condition, along with other safeguards. Powerful high-alert drugs and most drugs for at-risk populations such as infants and children, adults who are extremely frail, and people who are underweight or overweight often require several steps for safe administration. This chapter will focus on customized dosing of pediatric medication orders to provide practice with smaller fractional amounts of medication and ounce to pound to kg weight conversion, but the principles, skills, and steps for calculation apply to adults as well.

Dosages Based on Body Weight and Surface Area

Infants and children have special medication needs because of their smaller size and weight as well as larger body surface area (BSA) per kilogram of body weight. They have varying capabilities of drug absorption, digestion, distribution, metabolism, and excretion. It is very important for the nurse to check current references for pediatric medication orders and to double-check safe dose ranges (SDRs) to prevent errors and injury. Minute doses that require scrupulous mathematics may be ordered. Pediatric and intensive care nurses use written pediatric drug guidelines and calculators to determine weights and verify SDRs.

The two methods currently used for calculating safe pediatric doses are based on (1) body weight in mg/kg or mcg/kg and (2) body surface area in square meters (m²) using a scale called a nomogram.

mg/kg Method (Weight-Based Dosing)

The most frequently used calculation method for customized dosing is mg per kg. References usually state the safe amount of drug in mg per kg for a 24-hour period to be given in one or more divided doses. You may also see mcg per/kg cited for therapeutic doses when very small amounts of medication are to be given.

Steps to Solving mg/kg Problems

Step 1

Estimate the weight in kilograms by dividing the pounds in half *; then calculate the weight in kilograms using 2.2 lb = 1 kg equivalency (divide pounds by 2.2). Use a calculator.

a. If the weight is in pounds, convert the pounds directly into kilograms (one-step calculation).

b. If a weight is in pounds and ounces, convert the ounces to the nearest tenth of a pound and add this to the total pounds. Then convert the total pounds into kilograms to the nearest tenth (two-step calculation). (Refer to page 279 for kilogram-to-pound conversions and page 13 for rounding instructions.)

Step 2

Calculate the safe dose range (SDR) using a calculator and current safe dose recommendations found in the drug literature or drug handbook for this weight child in mg per kg or mcg per kg.

Step 3

Compare and evaluate the 24-hr ordered dose with the recommended SDR. Be sure the comparisons are for the same frequency!

Step 4

If safe, calculate the actual dose to be administered using written ratio and proportion. If the ordered dose is less than or more than the SDR, hold the medication and clarify promptly.

Shortcut Steps

1. Weight in kg

2. SDR

3. Compare with order

4. Calculate dose if safe to give

RULE

All pediatric medication administration begins with an accurate weight (Step 1) and a calculation of the SDR (Step 2).

Example

Ordered: EryPed (erythromycin ethylsuccinate suspension) 150 mg po q6h for an infant with an infection. The infant weighs 15 lb, 6 oz today. The literature states that the SDR is 30 to 100 mg per/kg per day in four divided doses for severe infections.

Step 1

Estimate the infant’s weight.

a. Pounds to kilograms: 15 lb ÷ 2 = 7.5 kg
Calculate the actual weight.

b. Two-step conversion because ounces are involved.
Ounces to pounds: 6 oz ÷ 16 = 0.37 lb. Add part of pound to total pounds. The infant thus weighs 15.4 lb.
Pounds to kilograms: 15.4 lb ÷ 2.2 = 7 kg (close to estimate)

Step 2

The SDR recommended for children more than 1 month of age is 30 to 100 mg/kg per day po in four divided doses.

hoiv-range calculation:	30 mg × 7 kg = 210 mg (low SDR) per day + 4	= 52.5 mg/dose
High-range calculation:	100 mg × 7 kg = 700 mg (high SDR) per day + 4	= 175 mg/dose

Step 3

Compare and evaluate: The SDR recommended for this child’s weight is 210 to 700 mg total q24h in four divided doses.

Ordered: 150 mg q6h or 150 mg × 4 or 600 mg total in 24 hr.

Step 4

Decision: Give medication. Administering 600 mg for the day is within the SDR of 210 to 700 mg in four divided doses.

Calculate the individual dose (write out and prove).

HINT

Review and analyze the logic of these four steps.

CLINICAL ALERT

Avoid two potential errors when converting pounds and ounces to kilograms. First, ounces must be converted to part of a pound before converting total pounds to kilograms; for example, 6 oz does not convert to 0.6 lb. Second, 15.4 lb does not equal 15.4 kg.

Don’t forget the second step—convert the total pounds to kilograms.

WORKSHEET 12A

Answers on page 420

Calculator Practice

RULE

Calculators are used in pediatric and adult care units for long division and multiplication problems. Dividing ounces by 16 will give the pound equivalent in the first step of two-step problems. Dividing or multiplying by 2.2 will give pound and kilogram equivalents.

1. Estimate the weights, then use a calculator to convert from pounds to kilograms or kilograms to pounds. Round to the nearest tenth.* Double-check all work.

a. 14 lb (1 or 2 steps?) b. 12 lb, 2 oz (1 or 2 steps?)
Estimate: Estimate:
Actual: Actual:

c. 10 lb d. 14 kg
Estimate: Estimate:
Actual: Actual:

e. 10 kg
Estimate:
Actual:

2. Calculate the 24-hr total dose in milligrams.

a. 150 mg q8h b. 200 mg q6h

c. 400 mcg q4h d. 50 mg tid

e. 750 mcg q12h

3. Calculate the unit dose.

a. 1 g in 4 equally divided doses b. 750 mg divided tid

c. 2 g in 4 to 6 equally divided doses d. 16 g a day in 2 to 4 divided doses

e. 500 mg in 4 divided doses

4. Calculate the SDR in milligrams for the following weights. Note that the answers will only be in milligrams or micrograms because x, the unknown, is a dosage measurement not a weight measurement. You want to know how many milligrams a day and milligrams per dose are safe for this patient. (2.2 lb = 1 kg)

SDR PER KG; WEIGHT	SDR FOR THIS WEIGHT
a. 10 mg/kg; weight is 5 kg	______safe total mg/day
b. 5 to 8 mg/kg; weight is 7.3 kg	______SDR for the day in mg
c. 6 to 8 mg/kg; weight is 8 lb	______SDR for the day in mg
d. 3 to 6 mg/kg; weight is 5 lb, 8 oz	______SDR for the day in mg
e. 200 to 400 mcg/kg; weight is 4 lb, 6 oz	______SDR for the day in mg

5. Ordered: Drug X, 50 mg tid. SDR: 2 to 3 mg/kg given in three divided doses. Child’s weight is 18 kg.

a. SDR for 24 hr

b. SDR per dose

c. Total ordered dose for day and per dose

d. Evaluation and decision: Safe or unsafe to give? Why?

WORKSHEET 12B

Answers on page 421

Safe Dose Range (SDR) Practice

For each problem, use a calculator to determine the child’s weight in kilograms to the nearest tenth, calculate the SDR, and compare it with the order. If the total dose for 24 hours is excessive, the unit dose is automatically excessive. Evaluate the order and make a decision.

1. Give medication (within SDR for unit dose and 24-hr dose).

2. Hold and clarify promptly (overdose or underdose).

1. Weight: 20 lb
SDR in literature: 2 to 4 mg per kg per day
Ordered: 50 mg daily

a. Estimated weight in kg:

b. Actual weight in kg:

c. SDR for this child:

d. Dose ordered:

e. Evaluation and decision:

2. Weight: 33 lb
SDR in literature: 100 to 200 mcg per kg per day in divided doses
Ordered: 0.5 mg tid

a. Estimated weight in kg:

b. Actual weight in kg:

c. SDR for this child:

d. Dose ordered:

e. Evaluation and decision:

3. Weight: 25.4 lb
SDR in literature: 10 to 30 mg per kg per day in divided doses
Ordered: 100 mg tid

a. Estimated weight in kg:

b. Actual weight in kg:

c. SDR for this child:

d. Dose ordered:

e. Evaluation and decision:

4. Weight: 85 lb
SDR: 10 to 15 mg/kg/day in 4 to 6 divided doses
Ordered: 100 mg q6h

a. Estimated weight in kg:

b. Actual weight in kg:

c. SDR for this child:

d. Dose ordered:

e. Evaluation and decision:

5. Weight 5 lb
SDR: 10 to 20 mcg/kg/day
Ordered: 0.03 mg four times daily

a. Estimated weight in kg:

b. Actual weight in kg:

c. SDR for this child:

d. Dose ordered:

e. Evaluation and decision:

BSA Method (mg/m²)

The term “body surface area” refers to the total area exposed to the outside environment. The estimated BSA in square meters (m²) is derived from height and weight measurements by using a mathematical formula. It is considered the most reliable way to calculate therapeutic dosages.

This method may be used to calculate safe dosages of antineoplastic drugs, of new drugs, and of drugs for special populations such as infants, children, frail elderly patients, and patients with cancer. It may also be used to double-check medication orders for safe dosage.

Example

Child weighs 33 lb (15 kg) and has a BSA of 0.55 m².

ORDERED: 20 mg/kg	vs ORDERED: 20 mg/m²	vs ORDERED 20 mg/lb
20 mg : 1 kg ::	20 mg : 1 m² ::	20 mg : 1 lb ::
x mg : 15 kg	xmg : 0.55	x mg : 33 lb
x = 20 × 15 = 300 mg	x = 20 × 0.55 = 11 mg	x = 20 × 33 = 660 mg

As seen, the doses calculated range from 11 mg to 660 mg and, depending on the unit of measurement, reflect extremely large differences. This illustrates the need to check not only the numbers but also the units of measurement.

The West nomogram in Figure 12-1 allows the user to plot the estimated square meters of BSA by using height and weight measurements.

FIGURE 12-1 West nomogram for estimation of body surface area (BSA). A, The estimated BSA in square meters for children of normal height for weight is determined by reading the m² at the alignment point with the child’s weight in pounds in the highlighted column. The red line denoted by the arrow reveals that an infant weighing 10 lb has an approximate BSA of 0.27 m². B, The BSA in square meters for children who are *under* weight or *over*weight (refer to pediatric standard growth charts and development grids for normal height and weight ranges for pediatric groups) is determined by connecting the child’s plotted weight in the left column and plotted height in the right column with a straight line and reading the intersection point on the SA (surface area) column, as indicated by the arrow on the red line. This illustrates an estimated BSA of 0.28 m² for an infant of 60 cm height weighing 4.5 kg. Reading the SA column requires that height and weight be plotted in the same system of measurement metric or pounds/inches. (Nomogram modified with data from Berhrman RE, Kleigman RM, Jenson HB: Nelson textbook of pediatrics, ed 18, Philadelphia, 2007, Saunders.)

Although the pharmacy usually supplies BSA calculations, the nurse has the option of estimating safe dosages easily and rapidly by using a mathematical formula and a calculator and entering the patient’s height and weight data.

Calculating BSA (m²) Using a Mathematical Formula

There are two formulas for calculating BSA (m²), and both use height and weight dimensions.

A. Formula using only metric system

B. Formula using only pounds and inches

Weight (kg)×Height (cm)3600=m2 BSA

Weight (lb)×Height (in)3131=m2 BSA

Note the differences in the divisors. The formulas must be used exactly as shown.

Directions: Use a calculator. Use the metric formula. Determine the BSA in square meters for a child with a weight of 20 kg and a height of 95 cm.

Step 1

Multiply the kilograms by centimeters first and divide the result by 3600 (20 × 95 = 900/3600 = 0.527)

Step 2

Obtain the square root of 0.527 by pushing the square root button. Round your answer to the nearest hundredth.

20×953600=0.5270.527=0.725=0.73 m2

Compare this answer with the West nomogram (see Figure 12-1). Create a straight line between 20 kg and 95 cm and read the result in the surface area (SA) column on the nomogram. Take care to plot the height and weight on the metric graph—;the outside columns. When reading the results (m²) columns, be sure to note the value of each calibrated line on the scale at the intersection point.

You may use either the nomogram or the formula. The formula method is more accurate, and if you have a calculator on hand, it is faster.

A square meter is slightly larger than a square yard. Visualize a square meter or a square yard of skin. As seen on the nomogram, a child of 90 lbs has only about 1 square meter of BSA (1 m²). Use one of the formulas to calculate your own BSA.

CLINICAL ALERT

Nurses are not usually expected to calculate BSA. The pharmacy provides the BSA calculations. Nurses do have a critical responsibility to distinguish the difference in a medication order and dosage based in mg/lb or mg/kg of weight and an order based on mg/m² of BSA (e.g., 20 mg/kg vs 20 mg/m² vs 20 mg/lb).

WORKSHEET 12C

Answers on page 422

Comparing BSA-Based (mg/m²) Dosages with mg/lb and mg/kg Orders

Use the West nomogram (page 282), highlighted section for children of normal height and weight, to obtain the BSA (m²) based on weight.

Calculate the dose to be given based on the mg/m² and dose ordered.

	WT in lb	BSA in m²	DOSE ORDERED	DOSE TO BE GIVEN
1.	4 1b	0.15	10 mg/m²	10 × 0.15 = 1.5 mg
2.	6 1b	_____	15 mg/m²	_____
3.	10 lb	_____	5 mg/m²	_____

Calculate the dose for the same-weight children in mg/lb measurements, as illustrated in Problem 4.

	WT in lb	DOSE ORDERED	DOSE TO BE GIVEN
4.	4 1b	10 mg/lb	4 × 10 = 40 mg
5.	6 1b	15 mg/lb	_____
6.	10 lb	5 mg/lb	_____

Calculate the dose to be given in mg/kg measurements, as illustrated in Problem 9. Divide lb by 2.2 to obtain kg.

	WT in kg (to nearest tenth)	DOSE ORDERED	DOSE TO BE GIVEN
7.	4 lb = 1.8 kg	10 mg/kg	10 × 1.8 = 18 mg
8.	6 lb =_____kg	2 mg/kg

9. Using a calculator, obtain the BSA in m² (to the nearest hundredth for a child with a height of 60 cm and a weight of 100 kg using the appropriate BSA formula on page 281: ____________

10. Using a calculator, obtain the BSA in m² for a child with a height of 30 in and weight of 35 lb using the appropriate BSA formula on page 281: ______________

CLINICAL ALERT

Consider the patient safety implications when mg/m², mg/lb, and mg/kg are erroneously interchanged. This mistake has resulted in serious errors. The nurse must understand the differences among these three terms and focus to ensure that the correct values are being used when calculating the dose.

WORKSHEET 12D