copyright © 2007 by saunders, inc., an imprint of elsevier inc. pharmacology math chapter 33

Copyright © 2007 by Saunders, Inc., an imprint of Elsevier Inc.

Pharmacology Math

Chapter 33

Copyright © 2007 by Saunders, Inc., an imprint of Elsevier Inc. Slide 2

Drug Management

The medical assistant must be absolutely certain that the medication prepared and administered to the patient is exactly what the physician ordered.

Although drugs often are delivered by the pharmacy in unit dose packs, the dosage ordered may differ from the dose on hand.

In this case the medical assistant must be prepared to calculate the correct dose accurately.


Dosages

There is no margin of error in drug calculations. Even minor mistakes may result in serious complications.

The MA must take meticulous care in calculating all drug dosages.

If the dosage ordered by the physician is different from the dosage on hand, the MA must complete three basic steps.


Three Steps for Correct Dosage

1. Based on the type of system printed on the label, determine if the physician order is in the same mathematic system of measurement.

If the systems vary (the order is in teaspoons but the label states the medication is to be prepared in milliliters), then accurately convert the order to match the system on the label.

2. Perform the calculation in equation form, using the appropriate formula.

3. Check your answer for accuracy, and ask someone you trust to confirm your calculations.


Accurate Dose

All three of these steps must be completed before the medication is dispensed and administered.

Confirm your calculations with the physician if you have any doubt about their accuracy.


Accurate Dose (cont’d)


Drug Labels

Accurately read the drug label to determine if the physician order and the packaged drug use the same system of measurement.

Examples:

– Physician orders 10 ml of a drug and the drug label states there are 20 ml/cc.

– Physician orders 4 g of a drug and the medication label states there are 2 g/tab.

– Physician orders 6 mg of a drug and the medication label reads there are 12 mg/scored tab.


Drug labels


Label Terms

Strength: The potency of the drug. Stated as a percent of drug in the solution (2% epinephrine); as a solid weight (g, mg, lb, gr); or as a milliequivalent or unit.

Dosage: The size or amount of medication in the drug unit. Could be in ml, tsp, or a number of tabs. For example, label reads “Imitrex, 6 mg/0.5 ml,” which means there are 6 mg of Imitrex in each 0.5 ml.

Solute: Pure drug dissolved in a liquid to form a solution.

Solvent (Diluent): The liquid, usually sterile water, that dissolves the solute.


Systems of Measurement

Physician may order medication in a strength that is different than the one identified on the drug label.

– Example: orders 2 gr of the drug but the label states there are 120 mg/tab

Before determining how many tablets to administer, the MA must first convert the strength of the physician order to match the strength of the dose on the label since that is the medication that is available for administration.

3 different systems of measurement: metric, apothecary, and household.


Metric System

Metric system of weights and measures is used throughout the world as the primary system for weight (mass), capacity (volume), and length (area).

Based on units of 10– Each larger unit of measure is 10 times the previous unit of

measure.

– Fractions are written as decimals (1½ L = 1.5 L).

– Cubic centimeter = milliliter (1 cc holds 1 ml).

– Amount or volume of a liquid medication is expressed in milliliters.

– Weight or strength of a solid medication is expressed in grams.


Conversions to Smaller Units

Units in the metric system are converted by moving the decimal point in multiples of 10.

When going from larger to smaller units of measure, as in converting grams to milligrams, the answer will be a larger number, so move the decimal point to the right.– 0.35 g = 350 mg

– OR multiply 0.35 g × 1000 = 350 mg


If converting smaller units of measurement to larger ones as in milliliters to liters, the answer will be a smaller number, so move the decimal point to the left. – 150 ml = 0.15 L

– OR divide 150 ml by 1000 = 0.15 ml

Conversions to Larger Units


Metric System Equivalents

The following equivalents can be used to make conversions in the metric system.

1 kg = 1000 g

1 g = 1000 mg

1 mg = 0.001 g or 1/10,000 g

1 kl = 1000 liters

1 L = 1000 ml

1 ml = 0.0001 L or 1/1000 L


Apothecary System

In the apothecary system the basic unit of weight for a solid medication is the grain (gr) and the basic unit of volume for a liquid medication is the minim (M).

As in the metric system, these two units are related: the grain is based on the weight of a single grain of wheat, and the minim is the volume of water that weighs 1 gr.


System to System Equivalents

15 gr = 1 g = 1000 mg

5 gr = 0.3 g = 300 mg

1 quart = 1000 cc

1 fl oz = 30 ml

1 fl dr = 4 ml

15 M = 1 ml

1 M = 0.06 ml


Household Measurements The household system is used in most U.S. households.

Although this system of measurement is important for the patient at home who has no knowledge of the metric or apothecary systems, it is not completely accurate. The household system should never be used in the medical setting.

The basic measure of weight is the pound (lb) and of volume is the drop (gtt).– 1 gtt = 1 M

– 60 gtt = 1 tsp

– 3 tsp = 1 Tbsp (tablespoon)

– 2 Tbsp = 1 oz

– 8 oz = 1 cup


Conversions between Systems

Formula:

Drug Have × Wanted = Unit wanted in new system Have

• Drug Have—unit of measure that is on label (1 g/tab)

• Wanted—amount or strength ordered by physician

• Have—conversion (15 gr = 1 g)

Order: Administer 30 gr of Lasix

Label: 1 g Lasix/tab

1 g × 30 gr = 2 g = 2 tabs 15 gr


Calculating Drug Dosages for Administration

Based on the strength of the drug and the amount as stated on the label

– Example: 15 mg/tab means that each tablet in the bottle contains 15 mg of the drug, OR 250 mg/cc means that for each cc in the vial there is 250 mg of the drug.

– Standard Formula

Available Strength = Available AmountOrdered Strength Amount to Give


Pediatric Doses and Fried's Law

Most important factor in determining the amount of a drug that should be administered to children is the weight of the child.

Even a minor miscalculation may be dangerous.

This calculation is for children younger than 1 year and is based on the age of the child in months compared with a child 12½ years old.

Pediatric dose = Child's age in months Adult dose 150 months


Young's Rule

Young's rule is for children older than 1 year

Pediatric dose = _Child's age in years__ Adult dose Child's age in years + 12


Clark's Rule

This rule is based on the weight of the child.

This system is much more accurate, because children of any age can vary greatly in size and body weight.

Pediatric dose = Child's weight in pounds Adult dose 150 pounds


West's Nomogram

West's nomogram uses a calculation of the body surface area of infants and young children to determine the pediatric dose.

Pediatric dose = BSA of child in m2 × Adult dose

1.7 m2

(Average adult BSA = 1.7 m2.)


West’s Nomogram


Reconstitution

Reconstituting powdered injectables requires adding an amount of solvent (as recommended on the drug label) to a vial of powdered or crystal medication.

Once the solute and solvent are mixed in the vial, a solution of medication is formed with a strength based on equivalents printed on the drug label.

Once the medication is mixed, carefully read the label to determine how much of the drug must be withdrawn to equal the physician’s order.

Use the standard conversion formula to determine the accurate dose for administration.

copyright © 2007 by saunders, inc., an imprint of elsevier inc. pharmacology math chapter 33

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