Calculation of Doses

Dose : is the quantitative amount administered or taken by a patient for the produced medicinal effect. may be expressed as: a single dose, the amount taken at one time; A daily dose; may be subdivided and taken in divided doses, two or more times per day depending on the characteristics of the drug and the illness. A total dose, the amount taken during the time-course of therapy. The schedule of dosing {e.g., four times per day for 10 days) is referred to as the dosage regimen.

Doses

Interpreting Labels Meaning Label Info This ratio tells the amount of medication in each ml of solution 25 mg/ml Ratios written this way always mean grams per milliliter 1:4 Amount of medication (in grams) in every 100 ml of solution 30% Equation tells the amount of medication in the given volume 40 mg = 2cc Units per ml (100 units per ml in this case) U-100 This ratio tells the number of milli- equivalents per milliliter of solution 20 mEq/ml

Commonly used abbreviations

English AND ROMAN NUMERALS English and Roman numerals are used interchangeably to express quantity or degree of measure. Roman numbers are formed by combining the following letters according to the rules Roman numbers English numbers Ss ½ I 1 V 5 X 10 L 50 C 100 D 500 M 1000

English AND ROMAN NUMERALS 1- To repeat a Roman number doubles its value. I =1; II=2 2. To place a letter to the right of a Roman number adds its value to that number. V=5; VI=6. 3. To place a letter to the left of a Roman number decreases the value of that number by the amount of the number added. V=5; IV=4.

Systems of Measurement and Conversion There are three primary systems 1 - the metric system, The metric system is widely used in dosage calculations. It uses powers of the basic units of measure are the gram, liter, and meter. A gram measures weight, a liter measures fluid, and a meter measures length. The metric system also uses prefixes to describe how much of the basic unit: Kilo =1000 times the basic unit. Centi =1/100 of the basic unit or 0.01. Milli = 1/1000 of the basic unit or 0.001. Micro =1/1,000,000 of the basic unit or 0.000001.

METRIC BASIC EQUIVALENTS 1 Kg. = 1000 Gm. 1 Gm. = 1000 mg. 1 mg. = 1000 migrogram . 1 ml. = 1 c.c. 1 L. = 1000 c.c. or 1000 ml.

2- Apothecary system, is another method of expressing units of measure. It is an old system and is not used exclusively because it is not standardized. That means that each measure is an approximate amount, It is different from the metric system in the following ways: 1- It uses Roman numerals (ss = 1/2, i = 1, iv = 4, v = 5, ix =9, x =10) 2. The unit is written before the amount (gr i, gr ss, gr iv) 3. Fractions are written as common fractions (gr. 1/150). The only exception is ½, which is written as is .

The basic units of measure that are commonly used are the 1- grain,: measures weight and is written gr. 2- Ounce : measures liquid amounts and is written like a cursive Ҙ but with an extra hump on top = 3- Dram: Used to measure smaller amounts of liquid medicine. It is written just like a cursive Ҙ . 4- minim. Tiny amount of liquid medicine. A minim equals a drop. It is written like a cursive ᶆ and sometimes it has a long tail.

APOTHECARY BASIC EQUIVALENCES (60 minims) = 1 fluid dram (8 fluid drams) = I fluid ounce (16 fluid ounces) = 1 pint (2 pints) = 1 quart (4 quarts) = 1 gallon

3- the household system The Household Unit of Measure is the most commonly recognized by laypeople. It includes 1- drops, is written gtt teaspoons, is written tsp or t tablespoons, is written Tbsp, or T and cup is written C

HOUSEHOLD EQUIVALENTS 60 drops (gtts.) = 1 teaspoon (t.) 3 teaspoons = 1 Tablespoon (T.) 2 Tablespoons = 1 ounce 8 ounces = 1 cup (C.).

Conversion Between Systems: YOU MUST KNOW 1- Known the unit of measure 2- Known the equivalent unit of measure 3- Desired unit of measure 4- Unknown equivalent (X)

• BASIC EQUIVALENCES

Example: How many grams are there in 500mg? ( The known ratio is 1000 mg = 1 gm) X = 500 ÷1000 X = 0.5 gm. Example: 20 mg is equal to how many grains? ( The known ratio is 60 mg = 1 gr) Use the above formula: 60 mg : 1gr :: 20 mg : X gr 60 X = 20 X = 20 ÷60 X = grain 1/3.

CALCULATION OF ORAL DOSAGES Oral dosage forms of medications include Tablets Capsules - Liquids Only scored tablets are intended to be divided Enteric-coated tablets cannot be crushed Sustained-release capsules cannot be opened and mixed with food or fluid.

Dosage Calculations Three-step approach: Convert: All units of measurement must be in same system and all units must be in same size If not, convert before proceeding Think Estimate reasonable amount of drug to administer Calculate Set up ratio between dosage on hand and desired dosage Dosage on hand Dosage desired Amount on hand Amount desired

Example Need 100 mg and have 50 mg per tablet Want to give twice the equivalent of each tablet Dosage on hand Dosage desired Amount on hand Amount desired Cross-multiply 50mg 100 mg 1 tablet X TABLTE 50 X = 100 X = 2 tablets

Example2 Order: Flagyl 0.75 g p.o. t.i.d. (three times per day) Available: Flagyl 500 mg tablets How many tablets per dose are needed? Step 1: Convert Units are same system, but size is different Equivalent: 1 g = 1,000 mg Set up ratio: Dosage on hand Dosage desired Amount on hand Amount desired Cross-multiply 1g 0.75 g 1000 X mg X = 1,000 * 0.75 X = 750 mg

How many 500 mg tablets should be required to administer 750 mg? Cross-multiply 500 mg 750 mg 1 tablet X tablets 500 X =750 X = 1.5 tablet

Example Order: Codeine sulfate gr3/4 p.o. q. 4 h p.r.n. (take as needed) • Available: Codeine sulfate 30 mg tablet • Calculate one dose Step 1: Convert Approximate equivalent gr i = 60 mg Set up ratio gr 1 gr3/4 60 mg X mg X= 45 mg , Codeine ¾ gr =45 mg

Step 2: Think Estimate giving more than one tablet but less than two tablets Step 3: Calculate Order: Codeine 45 mg p.o. q. 4 h • Available: Codeine 30 mg per tablet Set up ratio 30 mg 45 mg 1 tablet X tablets 30 X =45 X= 1.5 tablets needed for each dose

Calculating Dosages for Oral Liquids Use same three steps • Doses calculated in mL Example 1: – Order: Cefaclor 100 mg p.o. q.i.d. (four times per day) – Available: Cefaclor 125 mg per 5 mL – Calculate one dose 125 mg 100 mg 5 mL X mL 125 X= 500 , X= 4 mL Cefaclor needed per dose.

Order :phenobarbital elixir 0.2 gm hs the drug available in 20 mg/5ml (Dose desired ) × drug form Dose available 0.2gm 20mg/5ml 200mg 20mg/5ml 20mg :5 ml :: 200mg :X ml =50ml/dose

Parenteral medication Three method 1- A prefilled syringe labeled with a certain dosage in a certain volume (ex: demerol 100mg in 1ml) 2- A single or multiple-dose ampule labeled with a certain dosage in certain volume (ex: epinephrine 1:1000 in 0.1 ml). 3- A vial with a powder or crystals that must be mixed with saline solution ,the drug my be measured in grains ,grams, milligrams or unit .the amount of solution to be added varies and must be calculated according to the instruction with vial .generally intradermal and subcutaneous involve very small amount of solution whereas IV need 50 ml or more

the equation is Drug available : dilution = Dose desired : X Order : digoxin 0.2 mg I.M drug a available as 0.5 mg /ml Dose desired Drug available 0.2mg × 1ml 0.5mg 2/5 × 1 ml = 0.4ml X volume which dissolved it

CALCULATION OF PARENTERAL DOSAGES Parenteral means injection of drugs into the tissue or fluids of the body. Calculating Dose as Volume the volume you want to administer = Dosage desired X volume which dissolved it Amount available Example : A patient is prescribed 200mg of Furosemide I.V. The ampoules available contain 250mg in 10mL. What volume containing the drug do you need to administer? What you WANT X what it is IN What you have GOT 200 mg × 10 mL = 8 mL 250 mg

Drug Strengths & Stated Concentrations How much fluid is required (Volume) = What you HAVE (mg) CONCENTRATION (mg/mL) Example A patient is prescribed 250mg of Aciclovir I.V. Aciclovir has to be initially reconstituted with water for injection, then added to a bag of compatible infusion fluid, giving a final concentration of 5mg/mL. How much infusion fluid should be used dilute the reconstituted Aciclovir to achieve this final concentration? What you HAVE (mg) 250 mg = 50 mL CONCENTRATION (mg/mL) 5mg/mL

ADVANCED DOSAGE CALCULATIONS: Include 1- reconstitution of powered drugs, 2- insulin administration 3- calculating safe pediatric dosages of medications.

Reconstitution OF Powder Drugs A- On the drug label or the package insert will state the diluents to be used and the exact amount to be added. When adding a solution or diluents to the powder, you will notice that the directions will state the volume and dose after the solution has been added. B- Use the formula method: Administration = Dose × volume Available

Example A patient is to receive Penicillin 200mg IV every 6 hours. The label on the vial reads: add 1.8 mL of sterile water diluents. On the label it states, after reconstitution the vial will contains 250 mg/mL( the dosage supply amount).  200 mg X 1 mL = 0.8 mL 250 mg You would prepare 0.8 mL to administer in the IV to your patient

INSULIN ADMINISTRATION To determine the amount of the short-acting insulin to administer, depending on label

Types of insulin dosg form The standardized measure called a unit. Is available in 10 ml vials and two strengths (U-100 units per 1 ml U-500(500 units per 1 ml this five times stronger than U-100 If not insulin syringe available must be calculated by formula by which tuberculin syringe Number of minims to administrated = Insulin desired Insulin available × 16 minims

insulin syringe tuberculin syringe

CALCULATING SAFE PEDIATRIC DOSAGES Pediatric patients, which include both infants and children, require special dosing that is adjusted for their 1- body weight. the most commonly used method is stated as mg/kg 2- A number of formulas have been used throughout the years to determine the best dose for pediatric patients 3- by Body Surface Area.

Pediatric Formulas Children need lower dosages of medication compared to adults. Three formulas are used to help calculate a pediatric dosage based on whatever information is available.

EXAMPLE An infant, 15 months old and, needs Streptomycin Sulfate, which is usually administered to adults as 1 gm (1000 mg), as a daily IM injection. What is the appropriate dosage for the infant? Pediatric Dose = 15 (Age in months) * 1000 mg (Adult Dose) 150 Pediatric Dose = 15 × 1000 Pediatric Dose = 0.1 * 1000 Pediatric Dose = 100 mg

Now, let’s reexamine using Young’s Rule, which uses the child’s age in years. The age of a 15-month-old could be expressed as 1.25 years old, since he or she has lived for 12 months (1 year) _ 3 months (1/4 or 0.25 of a year). Pediatric Dose = 1.25 (Age in years) × 1000 mg (Adult Dose) 13.25 (Age of child + 12)   Pediatric Dose = 1.25 * 1000 13.25 Pediatric Dose = 0.094 * 1000 Pediatric Dose = 94 mg

Calculating drip rates 1- Calculation the flow rates for IV fluid administration . Two concepts must be understood A- flow rates : measured in drops per minute B- drops factor :number of drops per milliliter of liquid .this different for different manufactures of IV infusion equipment As general range between 10 and 15 drops per milliliter Drop factor × Milliliters per minute = flow rate (drops/ minute

10 (drop factor) × 2ml /min =20 drops/minute 2- EX 1- EX :Order (N.S) IV infusion to run at a slow rate to keep vein open, the rate is to be at 2 ml/minute .the IV infusion set delivers 10 drops/ml. the goal is to determine the flow rate in drops/minute 10 (drop factor) × 2ml /min =20 drops/minute 2- EX Order 1000 ml normal saline to be administered in 5h (DF=15) Total of fluid to give = flow rate (drops/miniute Total time (minutes) 1000 × 15 = 1500ml = 50 drops /minute 300min 300min × drop factor

Note

Drip flow regulation is controlled by tightening or releasing the roller clamp (white plastic clamp) and counting the drops falling into the drip chamber. For microdrip administration sets note that: drops/minute = mls/hour

Calculating infusion rates for infusion devices calculation of the volume to be delivered per hour calculation of the number of drops to be administered per hour calculation of the number of drops to be delivered in one minute. The following equation can be used : gtt/m1 cc/hour x-------------- = gtt/min Min/hour cc/ hour = volume / hour gtt = drop min = minute

The prescriber ordered:intravenous Ancef 1 g IVPB q4h The package insert information is as follows: Add 50 mL sterile water to the bag of Ancef 1 g and infuse in 30 min. The tubing is labeled 20 drops per milliliter. Calculate the flow rate in drops per minute for this antibiotic. The patient receives 50 mL in 30 minutes. You want to change this flow rate from mL per minute to an equivalent flow rate in drops per minute.

Calculation of IV Drip Rate Using an Electronic Pump Solve: The physician orders 1 L of D5 W over 12 hours Formula mL/hour: Total Volume to infuse (mL) = mL/h Time (h) 1 L = 1000 mL 1000 mL = 83 mL/hour 12

1000 mL of D5W is to infuse at 125 mL/hour. How many hours will it take for this liter of fluid to be completed? Formula for Infusion Time Total volume to infuse = Infusion time (h) mL/h 1000 mL = 8 hours 125 mL/h In summary, 1000 mL at 125 mL/hour will take 8 hours.

Calculating Dosage by Body Surface Area In some cases, body surface area (BSA) may be used rather than weight in determining drug dosages. This used to calculating dosages for children, those receiving cancer therapy, burn patients, and patients requiring critical care. A patient’s BSA can be estimated by using formulas nomograms.

BSA Formulas BSA, which is measured in square meters (m2) can be determined by using either of the following two mathematical formulas Formula for metric units

Example Find the BSA of an adult who is 183 cm tall and weighs 92 kg. Because this example

Example What is the BSA of a man who is 4 feet 10 inches tall and weighs 142 pounds? First you convert 4 feet 10 inches to 58 inches. Because the example has household units (pounds and inches), we use the following formula: 5.1286 5.12

2- Nomograms BSA can also be approximated by using a chart called a nomogram . The nomogram includes height, weight, and body surface area. If a straight line is drawn on the nomogram from the patient’s height (left column) to the patient’s weight (right column), the line will cross the center column at the approximate BSA of the patient. Examle child weighing 15 kg and measuring 100 cm in height has a BSA of 0.64 m2

Body surface area (BSA) In the example shown, a child weighing 15 kg and measuring 100 cm in height has a BSA of 0.64 m2 Body surface area (BSA) of Children

dose calculated as follows Dose for child = BSA for child × adult dose 1.73 m2 (average adult BSA) Examples: If the adult dose of a drug is 75 mg, what would be the dose for a child weighing 40 lb and measuring 32 in. in height? (Use the body surface area method.) Answer. From the nomogram, the BSA = 0.60 m2 0.60 (m2) X 75 mg =26 mg 1.73 (m2),

The nomogram in designed specifically for determining the BSA of adults may be used in the same manner as the one previously described. The adult dose is then calculated as follows

Examples: If the usual adult dose of a drug is 120 mg, what would be the dose based on BSA for a person measuring 6 ft tall and weighing 200 Answer BSA (from the nomogram) = 2.13 m2 (2.13 m2 X 120 mg=147.75 mg or 148mg 1.73 m2)

Another BSA Equation

Example: Calculate the BSA for a patient measuring 165 cm in height and weighing 65 kg

The nomogram in designed specifically for determining the BSA of adults may be used in the same manner as the one previously described. The adult dose is then calculated as follows

Examples: If the usual adult dose of a drug is 120 mg, what would be the dose based on BSA for a person measuring 6 ft tall and weighing 200 Answer. BSA (from the nomogram) = 2.13 m2 (2.13 m2/1.73 m2) X 120 mg=147.75 mg or 148 mg,