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Tuesday, October 23, 2007

Pharmacology: Calculating Drug Dosages Part 2

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Pharmacology: Special Considerations



Medications that are measured in units (u) and milliequivalents (mEq) as well as reconstitution of powders will be discussed in this chapter. Heparin, insulin, and antibiotics are the most common medication measured in mEq, but many other electrolytes are also measured in this system.

Units
Insulin, used to control blood sugar, is available in several types. All are measured in the same way: “U-100”, the international standard. This means that 1 ml of insulin contains 100 units (u) of insulin regardless of type (regular, NPH, Humulin, etc). With this information insulin doses could be calculated and any regular 1 cc syringe used to administer it. However, due to the accuracy needed in measuring insulin doses to titrate blood sugar, special syringes calibrated in units are always used in hospital settings. There are no such standardized devices for administering heparin and antibiotics. These medication doses must be calculated in the same way we used the formula to do the problems in Chapter 2.

Example A. MD Order: Heparin 3000 units SC bid
Drug Label: Heparin 5000 units/ml
Conversion Factor: none
1. The desired quantity
3000 u



2. The dose available
3000 u x 1ml
5000 u

3. No conversion factor
4. Set up the formula using “X”.
3000 u x 1ml = X
5000 u

5. Cancel out all like measurement units.
3000 u x 1ml = X
5000 u

6. Multiply across the tops and bottoms.
3000 x 1 ml = 3000 ml = X
5000 5000

7. Divide by denominator.
3000 ml = 3 ml = 0.6 ml = X
5000 5

8. Assess your answer and double-check your arithmetic.
X = 0.6 ml
The desired quantity (3000 u) is less than the dose available (5000 u), so it is logical to give 0.6 ml which is an acceptable sc dose of medication.

Example B. MD Order: PCN 1,000,000 u IM bid
Drug Label: PCN 5,000,000 u per 10 ml
Conversion Factor: none
1. The desired quantity
1,000,000 u

2. The dose available
1,000,000 u x 10 ml
2,000,000 u

3. No conversion factor because units are the same
4. Set up the formula using “X”.
1,000,000 u x 10 ml = X
2,000,000 u

5. Cancel out all like measurement units.
1,000,000 u x 10 ml = X
2,000,000 u


6. Multiply across the tops and bottoms.
1,000,000 x 10 ml = 10,000,000 ml = X
5,000,000 5,000,000

7. Divide by denominator.
10,000,000 ml = 2 ml = X
5,000,000

8. Assess your answer and double-check your arithmetic.
X = 2ml
The desired quantity is less than the close available. Therefore it is logical to give 2 ml which is less than 10 ml. 2ml is an acceptable IM dose.

Milliequivalents
As was stated before, electrolytes are usually measured in milliequivalents (mEq). Potassium chloride (KCl) is used most commonly. Again, the same formula is used to calculate doses whether it is for an IV or oral dose.

Example A. MD Order: KCl 30 mEq PO q day
Drug Label: KCl 20 mEq per 5 ml
Conversion Factor: none
1. The desired quantity
30 mEq

2. The dose available
30 mEq x 5 ml
20 mEq

3. No conversion factor
4. Set up the formula using “X”.
30 mEq x 5 ml = X
20 mEq

5. Cancel out all like measurement units.
30 mEq x 5 ml = X
20 mEq

6. Multiply across the tops and bottoms.
30 x 5 ml = 150 ml = X
20 20

7. Divide by denominator.
150 ml = 7.5 ml = X
20

8. Assess your answer and double-check your arithmetic.
X = 7.5 ml
The desired quantity is greater than the dose available; therefore it is logical to give 7.5 ml which is larger than 5 ml.


Example B. MD Order: Add 20 mEq KCl to the next IV
Drug Label: KCl mEq per 1 ml
Conversion Factor: none
1. The desired quantity
20 mEq

2. The dose available
20 mEq x 1ml
2 mEq

3. No conversion factor
4. Set up the formula using “X”.
20 mEq x 1ml = X
2 mEq

5. Cancel out all like measurement units.
20 mEq x 1ml = X
2 mEq

6. Multiply across the tops and bottoms.
20 x 1 ml = 20 ml = X
2 2

7. Divide by denominator.
20 ml = 10 ml = X
2

8. Assess your answer and double-check your arithmetic.
X = 10 ml
The desired quantity is greater than the dose available. It is logical to give 10 ml which is greater than 1 ml. 10 ml is an acceptable dose to add to an IV.

Reconstituting Powders
Powdered forms of drugs are often used because they retain their potency longer. Most reconstitution is done in pharmacies but there will be times when the nurse needs to know how to do this. The drug label or package insert contains all the information needed to reconstitute the powder. If a special diluting fluid (diluent) is needed, it should be with the vial; otherwise sterile water or NS for injection is used as indicated (Figs. 3-1, 3-2). A sterile syringe and aseptic technique is always used. The time and the date that the powder was reconstituted along with the initials of the nurse who did it should always be placed on the drug bottle if it is a multiple dose vial. The volume of any reconstituted solution will always be greater that the volume of diluent alone because the powder itself will add to the total volume.






Most vials have discussions so that only one solution strength is reconstituted. A few give choice of strengths (Fig. 3-3) which can be achieved by adding different amounts of diluent. Any time there is a choice of strengths the final strength (concentration) should be clearly indicated on the vial.



For example, another penicillin G label might give the following choices:

Amt. diluent added Approximate units per ml of solutions
75 ml 250,000 u/ml
33 ml 500,000 u/ml
11.5 ml 1,000,000 u/ml

If you were giving 500,000 u per dose, you would choose to add 33 ml of diluent to that each dose would be 1 ml. For a dose of 2,000,000 u IM, you would add 11.5 ml of diluent so that you could administer 2 ml. Remember: on the label you would also need to indicate the strength of the solution you mixed.
After reconstitution, dosage calculations would be done if necessary, using the same problems.

Chapter IV: Pediatric Dosage Calculations

There are several formulas used to calculate pediatric dosages: Clark’s rule, body surface area (BSA), using nomograms, and body weight or mg/kg. Don’t despair! The two most common methods of prescribing pediatric medications today use body weight and BSA; both methods will be reviewed in this chapter.
All pediatric dosage calculations involve two steps. First, you need to determine whether or not the dose amount is within a safe range. It is the nurse’s responsibility to check the dosages ordered to see if they are in the normal dosage range before administering them. The information needed to determine this can be found on the drug label, package insert, drug references, or formularies. Second, the amount of drug to be administered needs to be calculated just as was done in the previous chapters.

Body Weight
Most healthcare agencies in the United States weigh in pounds because that is what we are familiar with. Most drug literature uses kilograms. Therefore, you can almost always expect to convert pounds to kilograms before you can determine a pediatric dosage. The conversion factor necessary for this is: 1 kg = 2.2 lb. To convert from pounds to kilogram, divide by 2.2. To convert from kilograms to pounds, multiply by 2.2. Most of us prefer to state our weight in kilograms because it is smaller!
The information needed to calculate the safe dosage range can either be found on the label or in the PDR, hospital formulary, or other drug reference. This calculation is usually a 2-step process: first, you need to calculate the minimum and maximum for normal daily doses, and then you need to divide by the number of doses in a 24-hour period.

Example A. MD Order: Amoxicillin 150 mg po q8h for an 18 kg child
Drug Label: Amoxicillin 125 mg/5 ml
Conversion Factor: none
For minimum dose:
20 mg x 18 kg = 360 mg/day
q8h = 3 doses/day
360 mg = 120 mg/dose
3 doses
For maximum dose:
40 mg x 18 kg = 720 mg/day
q8h = 3 doses/day
720 mg = 240 mg/dose
3 doses

Normal range is:
120 mg to 240 mg/dose
The desired quantity is 150 mg d8h, which falls within the normal range. It was also ordered q8h which is in divided doses. It is safe to administer.

NOTE: If the dose was 50 mg q8h, it would be low and the physician should be called. If the dose was 300 mg q8h, it would be high and the physician should be called. If the dose was 500 mg q day, it is not in divided doses and the physician should be notified.

1. The desired quantity.
150 mg

2. The dose available.
150 mg x 5 ml
125 mg

3. No conversion factor.
4. Set up the formula using “X”.
150 mg x 5 ml = X
125 mg

5. Cancel out all like measurement units.
150 mg x 5 ml = X
125 mg

6. Multiply across the tops and bottoms.
150 x 50 ml = 750 ml = X
125 125

7. Divide by denominator.
750 ml = 6 ml = X
125

8. Asses your answer and double-check your arithmetic.
X = 6 ml
The desired quantity is great than the dose available. Therefore, it is logical to give 6 ml which is greater than 5 ml.


Then proceed to calculate the amount to be administered as was done with the previous examples.

Example B. MD Order: Cloxacillan 150 mg q6h for a 30 lb child
Drug Label: Cloxacillan 125 mg/5 ml
Usual Pediatric Dose: 50 mg/kg/day q6h in 4 equally divided doses
Conversion Factor: for weight, 1 kg = 2.2 lb

Convert weight:
30 lb x 1 kg = 13.3 kg
2.2 lb

For usual pediatric dose (there is no range in this example)
50 mg x 13.3 = 665 mg/day

Divided into 4 equal doses:
665 mg = 166.25 mg/dose
4 doses

NOTE: The desired quantity, 150 mg, is a little low, but still within an acceptable range since we are working with large numbers. Another acceptable dose would be 175 mg q6h, which is a little high. Either dose would be easy to administer given the drug concentration on the label. Dosage amounts of less than 150 mg or greater than 175 mg should be questioned.

REMEMBER: (especially with small children) Discrepancies in doses become more significant when small numbers of mg are ordered. The difference between 0.1 mg and 0.2 mg is more significant than between 166 mg and 175 mg. If the dose ordered was 0.1 mg and the dose administered was off by 0.1 mg (a very small number) the dose would be doubled! However, if the dose ordered was 170 mg and the dose administered was too high by 5 mg (a large number) the dose would not be compromised and the patient unlikely to experience any ill effects.

Body Surface Area (BSA)
BSA is most frequently used to calculate antineoplastic drug doses. It is determined by comparing a child’s height and weight on a graph called a nomogram. Figure 4-1 is the West nomogram, which will be used in the examples in this chapter.

------------ nomogram -------------

Figure 4-1. West’s nomogram. Plot child’s height and weight; draw a line between the two points. The point where lines intersect the surface area (SA) line is the child’s body surface area.


There are two ways to use this nomogram. If the child is of normal height for weight, you can calculate BSA using just the child’s weight. In the boxed column in the nomogram you can see that a child weighing 70 pounds has a BSA of about 1.10. If the child’s height and weight are not in proportion, plot the height on the left and the weight on the right. Draw a line between the two points, and where it intersects the surface area (SA) line is the child’s SA or BSA in square meters (m²). For example, a child who is 40 inches tall and weighs 40 pounds has a BSA of 0.72 m². It is important to note that the weight can be expressed in pounds or kilograms and the height in inches or centimeters. Also note that the calibrations between major divisions are not always the same, so read them carefully.

Nomogram Examples
Example A. A child who weighs 30 pounds and us 35 inches tall and has a BSA of 0.59 m².
Example B. A child who weighs 12 kg and is 58 inches tall has a BSA of 0.66 m².

Dosage Calculations Using BSA
Some pediatric medications specify doses in mg or u per m². If you know the BSA, all you have to do is multiply the recommended by the BSA. If the recommended dosage is given as a range per m², calculate the minimum and maximum by multiplying by the BSA.

Example A. The dosage recommended is 10 mg per m². The child has a BSA of 0.59 m².

10 mg x 0.59 m² = 5.9

The recommended dose would be 5.9 mg. If the dose was significantly higher or lower, notify the physician. Calculate the dose to be administered by checking the available concentration and using the formula from Chapter 2.

Example B. The dosage recommended is 5 mg to 20 mg per m². The child’s BSA is 1.2 m².

Minimum dose: 5 mg x 1.2 m² = 6.0 mg
Maximum dose: 20 mg x 1.2 m² = 24 mg
Normal range: 6 mg to 24 mg
If the dose ordered is within this range, it is usually alright to administer. Calculate doses to administer as in Chapter 2.

For pediatric medications that do not specify the dose per m², use the following formula. After calculating the child’s dose, compare it to those ordered. If the dose is accurate, calculate the dose to be administered as in Chapter 2.

Child Dose = BSA (m²) x Usual Adult Dose
1.7

Example A. Child’s BSA: 0.98 m².

Usual adult dose of drug ordered: 500 mg.
Child Dose = 0.98 x 500 mg = 0.58 x 500 mg = 290 mg
1.7
Example B. Child’s BSA: 1.19 m².
Usual adult dose of drug ordered: 10 cc
Child Dose = 1.19 x 10 cc = 0.99 x 10 cc = 11.9 or 12 cc
1.7

Chapter V: IV Rates

Last, but not least, we come to IV rates. You’ve come along way from Chapter 1, so let’s look at this as the home stretch! Calculating IV drip rates and electronic IV regulators will be covered in this chapter.

To calculate an IV drip rate you need three pieces of information:
1. the amount of fluid to be infused,
2. the drop (gtt) factor of the tubing, and
3. length of time should be part of the physician’s order for main IVs and on the label for IV piggyback (IVPB) medications.
Remember, time should be in minutes. The drop factor or number of drops per ml is located on the IV tubing package. Every hospital uses two or more sizes of IV tubing: regular or macrodip tubing which is 10, 15 or 20 gtt per 1 ml; and mini-or microdip tubing which is 60 gtt per 1 ml.
Now that we know what data we need, let’s put it together in a formula.

Volume to be infused x gtt factor = Drip rate
Infusion time (in minutes)

Example A. MD Order: 2000 cc D5 W over 24 hours.
IV tubing package: 20 gtt/min

1. Volume to be infused.
2000 cc

2. Drop factor.
2000 cc x 20 gtt/cc

3. Infusion time in minutes.
2000 cc x 20 gtt/cc
1440 min

4. Set up formula using “X” to represent the drip rate
2000 cc x 20 gtt/cc = X
1440 min

5. Cancel out all like measurement units.
2000 cc x 20 gtt/cc = X
1440 min

6. Multiply across the tops and bottoms.
2000 x 20 gtt = 40,000 gtt = X
1440 min 1440 min

7. Divide by denominator.
40,000 gtt = 27.8 gtt/min = X
1440 min

8. Round off answer to next highest whole number and double-check arithmetic.
X = drip rate = 28 gtt/min

Example B. MD Order: Kefzol 500 mg IVPB q8h
IVPB label: Kefzol 500 mg in 100 cc NS; infuse in 20 min
IV tubing package: 15 gtt/cc

1. Volume to be infused.
100 cc

2. Drop factor.
100 cc x 15 gtt/cc

3. Time in minutes.
100 cc x 15 gtt/cc
20 min

4. Set up formula using “X” to represent the drip rate
100 cc x 15 gtt/cc = X
20 min

5. Cancel out all like measurement units.
100 cc x 15 gtt/cc = X
20 min

6. Multiply across the tops and bottoms.
100 x 15 gtt = 1500 gtt = X
20 min 20 min

7. Divide by denominator.
1500 gtt = 75 gtt/min = X
20

8. Round off answer to next highest whole number and double-check arithmetic.
X = drip rate = 75 gtt/min

Example C. MD Order: 1000 cc NS to run at 125 cc/hr
IV tubing package: 15 gtt/cc

1. Volume to be infused.
125 cc

Note: Since I knew that 125 cc was to infuse in one hour, I used these numbers instead of calculating that the 1000 cc would infuse in 8 hrs and converting that to 480 min. Fewer mistakes are made with smaller numbers.

2. Drop factor.
125 cc x 10 gtt/cc

3. Time in minutes.
125 cc x 10 gtt/cc
60 min

4. Set up formula using “X” to represent the drip rate
125 cc x 10 gtt/cc = X
60 min

5. Cancel out all like measurement units.
125 cc x 10 gtt/cc = X
60 min

6. Multiply across the tops and bottoms.
125 x 10 gtt = 1250 gtt = X
60 min 60 min

7. Divide by denominator.
1250 gtt = 20.8 gtt/min = X
60 min

8. Round off answer to next highest whole number and double-check arithmetic.
X = drip rate = 21 gtt/min

Division Factor
If you know the rate in mL/hr as in Example C, you can calculate the flow rate by using a division factor. The division factor for any IV set can be determined by dividing 60 (min/hr) by the set drop factor (10, 15, 20 or 60).



The formula would then be:
Drip rate = ml/hr
Division Factor

Example A. MD Order: 1000 cc NS at 125 ml/hr
IV tubing package: 10 gtt/ml

1 Drop rate = 125 = 20.8 = 21 gtt/min
6

Example B. MD Order: 1000 cc Ringer’s Lactate
IV tubing package: 15 gtt/ml

1 Drop rate = 200 = 50 gtt/min
4

Rate in ML/HR
If the MD order does not give the rate in ml/hr, it can be calculated very simply. Divide the volume to be infused by the number of hours over which to infuse.

Volume to be infused = ml/hr
Hours to infuse

MD Order: 1000 ml RL over 8 hours
1000 ml = 125 ml/hr
8 hr

MD Order: 1500 ml DSNS over 24 hours
1500 ml = 62.5 ml/hr = 63 ml/hr
24 hr

Electronic IV Regulators
Electronic IV regulators – pumps and controllers – usually use flow rates in ml/hr when they are being set up. Older ones may use gtt/min. Controllers and pumps are useful in that they alarm when flow is interrupted but the nurse is still responsible for monitoring the IV Electronic devices can malfunction and can infuse fluid into an infiltrated IV site without the alarm going off.






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