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Tuesday, October 23, 2007

Pharmacology: Calculating Drug Dosages

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Nursing Pharmacology: System of Drug Measurement



Introduction
Accurate dose calculation is essential to administering drugs safely. It is also one of the keys to passing the medication portion of NCLEX exams and the medication and dosage calculation tests that most are necessary to prove competencies to accreditation organizations like JCAHO (Joint Commission of Accreditation of Healthcare Organization).
If this makes you even more tense than the mere mention of the word math, take a deep breath and try to relax. Math is only as difficult as you make it…and this supplement is designed to simplify the basic concepts for you. “Easy for her to say”, you’re thinking! Just keep in mind that if you follow the same approach each time you determine dosage conversions and calculate dosages, these activities will quickly become second nature and you will be well on your way to confident and competent medication administration.

Drug Measurement Systems
Let’s start with a basic assessment of systems. This time, instead of assessing body systems we’ll be talking about assessing the use of drug measurement systems. All measurement systems include measures for volume, weight and length. However, not all drug measurement systems commonly use all types of measures.
There will also be instances when it is necessary to change or “convert” from one unit of measure to another. This is called a conversion. To do this, you will have to use a conversion factor. A conversion factor is an equivalent between the two units of measure with which you are working. Conversions can be both within the same measurement system and between different measurement systems. Conversion factors within measurement systems are included with each system as it is discuss here. Conversion factors between measurement systems are found in Table 2-1: Common Healthcare Equivalent Conversions.
When physicians order drugs, they use the metric system, apothecary system or the household measurement system. The metric system is the most common of the three, is use world-wide and is the system chosen by most manufacturers for new drugs.

Metric System
This drug measurement system is the most simplistic of the three. In the metric system all units of measure differ by multiples often. Therefore, converting one kind of units to another within this system is often done by moving the decimal point.
The basic units of measurement are the gram (g) for weight, the liter (l) or (L) for volume, and the meter (m) for length. Prefixes are used in combination with these measures to identify larger and smaller units of measure. The most common larger prefix measurement is “kilo-(k)” meaning one thousand. The smaller prefixes are “centi-(c)” for one-hundredth (1/100), “milli-(m)” for one-thousandth (1/1000) and micro “micro-(mc)” for one-millionth of gram. The Greek letter “ยต” is often used instead of “mc”.





Apothecary System
Because the apothecary system is older than the metric system, it is rapidly becoming antiquated and is less and less used within the healthcare setting. This system employs lower case Roman numerals, with the unit of measure placed after the Roman numeral. The use of other ancient symbols and abbreviations reflects the system’s historical base in ancient alchemy and pharmaceutical practices. It is important to keep in mind that even thought the conversion factors in the apothecary system are not always exact, the calculations you perform with them will fall within acceptable clinical standards. The most frequently used apothecary measurements are noted below.



Household System
The household system of measurement is the system most familiar to the people in the United States. It is used in most prescriptions for liquid medications and over-the counter (OTC) medications. Discrepancies over conversions between the measures and amounts within each limit its use in healthcare settings.

Special Measures
Some pharmaceutical manufacturers have developed special measurement systems for their drugs, such as the use of “units” for insulin, heparin, and some antibiotics. These, along with another type of unit, the milliequivalent (mEq), will be discussed in Chapter Three.




Nursing Pharmacology:Dosage Calculations



In many healthcare settings medication are dispensed from the pharmacy in unit doses. A unit dose is a prepackaged and labeled dose of medication. Often, the drug manufacturer does the pre-packaging of its medications in the most commonly use dose amounts. This saves nursing time in that nurses do not actually have to prepare medications from stock bottles. Instead, the medications for each patient are usually located in drawers labeled for that patient.
As wonderful as this may sound, the unit dose has not eliminated the need for doing any dosage calculations when preparing medications. Sometimes prescribed doses are larger or smaller than the amounts in which the drugs are packaged. Also, there will be times when the requirements of the physician order and the nature of the drug on hand require that we use a conversion.

Using Conversion
Conversions are one of the most important aspects of dosage calculations, whether they are conversions from one measurement systems to another (as from apothecary to metric) or conversions within the same measurement system (as from grams to milligrams). Therefore if is necessary to be familiar with a few equivalents. An equivalent is a measure that is approximately equal in volume, weight between measurement systems (i.e., 1 g is equivalent to 1000 mg or 1 kg is equivalent to 2.2 lb). Table 2-1 details the most commonly used basic equivalents in the healthcare setting. It is essential to memorize the conversion factors in this table both for safety in administering professional settings. Don’t worry, these equivalencies will become second nature before you know it!

Fractions
Now a brief review of fractions so that we are all at the same starting point. Let’s look at the fraction x/y. X is the numerator or top number. Y is the denominator or lower number. These terms will be used frequently in dosage calculations.
Another term that is frequently used when multiplying fractions is to “cancel out”. This means that if you had a “4” in the numerator and a “4” in the denominator you could cross them out or cancel them out without affecting the final answer. The same is true for units of measure. In a properly set up calculation, all measurement units will cancel out except those in which we plan to administer the medication. Thus, the measurement units of the answer to any dosage calculation should never be in question and can server as another “double-check” that you have calculated correctly.
Just one more hint to help make that arithmetic a little less confusing: change any Roman numerals to Arabic numbers as you set up the equation to solve your problem. Most people are more familiar with and more comfortable working with numbers like 1, 5 and 10 rather than their Roman counterparts.

Setting Up the Calculations
Now let’s take a look at a typical medication order. When looking at a medication order, ask yourself the 3 questions:

1. What did the physician order? (Desired Quantity)
2. What do I have on hand (Does Available)
3. What conversion factor do I need? (Conversion Factor)

The desired quantity is the physician’s order and the dose is written as it appears in the order (i.e., 10mg, v gr) . The dose available is found on the drug label. It is expressed for calculating purposes as a quantity (tablet, number of capsules, ml)/amount (dosage). For example, if the label states 1 tablet = v(5) gr, the dose available is 1 tablet/v gr or 1 tablet/5 gr; if the label states 3 capsules = 300 mg, the dose available is 3 capsules/300mg. Remember the quantity of tablets, capsules, or ml is always in the numerator of the dose available; the amount (or dosage) is in the denominator. The conversion factor is obtained from an equivalency table (and soon from memory!) To decide which equivalent measure should be in the numerator and which should be in the denominator, look at the units of measure in the desired quantity. The units of measure in the desired quantity should be in the denominator of the conversion factor (i.e. if the desired quantity is 100 mg and the equivalent conversion factor is 1000 mg = 1 g, then the conversion factor for this example in fraction form should be 1 g/100mg)

In the following example we will use the information that we have from answering these questions to fill in the following formula.



This is a simple formula that uses ratio and proportion which will help you both correctly set up and solve dosage calculations problems. The actual math is no more complicated than multiplication and simple division, but is necessary to memorize this formula. Always remember to go back and assess your answer when you’re finished; does it make logical sense? For example, if your answer states you should give 10 tablets of aspirin, it is not logical to give this many pills at one time. Any time your answer indicates that you should administer more than 3 pills you should go back and check the problem again. Also, make it a habit to double-check your math. Just because an answer seems to be logical, it does not necessarily mean that your math is correct. Always remember to set your problem up first and then perform the arithmetic. Now let’s follow this process through;




Example A. MD Order: ASA 300 mg PO q4h prn pain
Drug Label: ASA 1 tablet = v gr (which we know from our knowledge of fractions if the same as and can be restated as 1 tablet/v gr or 5)

Conversion Factor: i gr or 1 gr = 60 mg (which we know from the discussion above is the same as 1 gr/60mg)

1. The desired quantity (MD order) is the first element of the question.
300 mg

2. The dose available (Drug label) is the second element of the equation. Remember: the quantity, in this case 1 tab, is in the numerator.

300 mg x 1 tab
----------------
5 gr

3. The conversion factor (from an equivalency table or memory) is the third element of the equation. Remember: units of measure in the desired quantity, in this case mg, should be in the denominator.

300 mg x 1 tab x 1 gr
----- ------
5 gr 60 mg

4. Set up the formula using “X” to represent the dose to be administered.

300 mg x 1 tab x 1 gr = X
------ -----
5 gr 60 mg

5. Cancel out all like measurement units leaving only the units to be administered.

300 mg x 1 tab x 1 gr = X
------ -----
5 gr 60 mg

6. Multiply across the tops and bottoms of the fractions.

300 x 1 x 1 tab = 300 tab = X
--------------- ------
5 x 60 300

7. Divide by denominator

300 tab = X
-------
300

8. Assess your answer and double check your arithmetic.

X = 1 tablet
Yes, it is logical to give one tablet.


This method also can be used when a conversion factor is not required. A conversion factor is not required if the measurement units in the desired quantity (MD order) are the same as the measurement units in the dose available (Drug label).

Example B. MD Order: Lasix 40 mg IV now
Drug Label: Lasix 20 mg/2 ml
Conversion Factor: none
1. The desired quantity (MD order) is the first element of the equation.
40 mg

2. The dose available (Drug label) is the second element of the equation. Remember: the quantity in this case 2 ml, is in the numerator.

40 mg x 2 ml
-----
20 mg

3. No conversion factor is needed because the measurement units in the desired quantity and dose available are the same.

4. Set up the formula using “X” to represent the dose to be administered.

40 mg x 2 ml = X
-----
20 mg

5. Cancel out all like measurement units leaving only units to be administered.
40 mg x 2 ml/20 mg = X



6. Multiply across the tops and bottoms of the fractions.

40 x 2 ml/20 = 80 ml/20 = X


7. Divide by denominator.

80 ml = X
-----
20

8. Assess your answer and double-check your arithmetic.
X = 4 ml
The desired quantity, 40 mg, is more than 20 mg (the dose available) therefore it is logical to give 4 ml which is more than 2 ml. 4 ml is also an acceptable dose for IV bolus medication.


Example C. MD Order: Feosol (Iron) v gr PO bid
Drug Label: Iron 1 tab = 300 mg
Conversion Factor: 1 gr = 60 mh

1. The desired quantity. Remember: change Roman numerals to Arabic numbers.

5 gr

2. The dose available

5 gr x 1 tab
------
300 mg

3. The conversion factor.
5 gr x 1 tab x 60 mg
300 mg 1 gr

4. Set up the formula using “X”
5 gr x 1 tab x 60 mg = X
300 mg 1 gr

5. Cancel out all like measurement units.
5 gr x 1 tab x 60 mg = X
300 mg 1 gr

6. Multiply across the tops and bottoms.
5 x 1 tab x 60 = 300 tab = X
300 300

7. Divide by denominator.
300 tab = X
300

8. Assess your answer and double-click your arithmetic.
X = 1 tab
Yes, it is logical to give one tab.


Example D. MD Order: Ampicillin 0.5 g po q6h
Drug Label: Ampicillin 250 mg/capsule
Conversion Factor: 1g = 1000 mg
1. The desired quantity
0.5 g

2. The dose available
0.5 g x 1 capsule
250 mg

3. The conversion factor
0.5 g x 1 cap x 1000 mg
250 mg 1 g

4. Set up the formula using “X”
0.5 g x 1 cap x 1000 mg = X
250 mg 1 g

5. Cancel out all like measurement units.
0.5 g x 1 cap x 1000 mg
250 mg 1 g

6. Multiply across the tops and bottoms.
0.5 g x 1 cap x 1000 = 500 cap = X
250 250

7. Divide by denominator.
500 cap = X
250

8. Assess your answer and double check your arithmetic.
X = 2 capsules
The desired quantity, 500 mg (0.5 g), is greater than the dose available, 250 mg, therefore it is logical to give 2 caps which is greater than 1 cap.

Example E. MD Order: Dixogin 0.125 mg po qd
Drug Label: Dixogin 0.05 mg/ml
Conversion Factor: none
1. The desired quantity
0.125 mg

2. The dose available
0.125 mg x 1 ml
0.05 mg

3. No conversion factor
4. Set up the formula using “X”
0.125 mg x 1 ml = X
0.05 mg

5. Cancel out all like measurement units.
0.125 mg x 1 ml = X
0.05 mg

6. Multiply across the tops and bottoms.
0.125 x 1 ml = 0.125 ml = X
0.05 0.05

7. Divide by denominator.
0.125 ml = X
0.05

8. Assess your answer and double check your arithmetic.
X = 2.5 ml
The desired quantity, 0.125 mg is greater than the dose available, 0.05 mg. Therefore, it is logical to give 2.5 ml which is greater than 1 ml.


Continuation...





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