A Brief Overview of Pharmacy Calculations for Pharmacy

A Brief Overview of Pharmacy Calculations for Pharmacy Technicians Maine Pharmacy Association and Maine Society of Health-System Pharmacists Sesquicentennial Anniversary Meeting October 14, 2017 Tianzhi Yang, BS, Ph. D Associate Professor of Pharmaceutical Sciences Husson University School of Pharmacy

LEARNING OBJECTIVES Ø Discuss and explain ratio and proportion and dimensional analysis methods to solve pharmacy calculation problems Ø Recognize and express units among the pharmacy math systems, especially the metric systems Ø Define and express percentage strength of a medication expressed as weight/weight, weight/volume or volume/volume Ø Discuss and explain parenteral IV flow rate calculations

PHARMACEUTICAL CALCULATIONS TWO BASIC METHODS USED: 1. Ratio and Proportion 2. Dimensional Analysis

RATIO AND PROPORTION Ø Ratio: A relation of two numbers expressed as a fraction. e. g. 1/3 or 1: 3 Ø Proportion: The equality of two ratios If a = c b d Then a = bc or b = ad d c or c = ad or d = bc b a Ø Ratio and Proportion method is based on the concept that one component is in proportion to another.

RATIO AND PROPORTION Example 1: If one capsule contains 50 mg of Benadryl, how many milligrams of Benadryl would be contained in 10 capsules? 1 capsule = 10 capsules 50 mg x = 10 x 50 1 = 500 mg

RATIO AND PROPORTION Example 2: If a solution of Na. Cl contains 2 g in 50 ml of solution, how many grams of Na. Cl in 100 ml of solution? 2 g = 50 ml xg 100 ml x = 2 X 100 = 50 200 50 = 4 g

RATIO AND PROPORTION – REAL LIFE One person's error killed Elisha Crews Bryant, hospital officials said: “a miscalculation overdosed the pregnant 18 -yearold with a magnesium sulfate meant to slow her labor. She got 16 grams when she should have gotten 4 grams. The young mother began having trouble breathing, went into cardiac arrest and could not be revived. ” Pregnant 18 Year Old Dies After Hospital Error (2006)

RATIO AND PROPORTION – REAL LIFE Ø Patient received 16 grams Magnesium Sulfate, fatal dose. Ø Patient should have received 4 grams. Ø The hospital had 25 g/50 ml Magnesium Sulfate. Ø How many milliliters of this Magnesium Sulfate (25 g/50 ml) should the patient have received to obtain 4 grams?

RATIO AND PROPORTION – REAL LIFE How many milliliters of this Magnesium Sulfate (25 g/50 ml) should the patient have received to obtain 4 grams? 25 g = 4 g 50 ml x = 8 ml

TRY ONE – RATIO AND PROPORTION How many milliliters must be drawn from an ampule of Prochlorperazine labeled "10 mg/2 ml" in order to obtain a dose of 7. 5 mg?

DIMENSIONAL ANALYSIS Ø Ø Based on cancelling out the units of measures Steps: ü Step 1: find the ratio that is in the problem ü Step 2: set up the problem around the ratio so that the units cancel out. The unit that is left (i. e. the unit that does not cancel out with the other units) should correspond to the unit needed for the answer to the problem Ø Especially useful in calculating IV flow rates

DIMENSIONAL ANALYSIS SCHEME ? (Wanted Unit) = Conversion Given Quantity/ Factor as Needed ratio = Conversion Computation = Wanted Quantity and Unit Conversion Factor as Needed

DIMENSIONAL ANALYSIS Example 1: If an antibiotic preparation contains 5 g of penicillin V potassium in 200 m. L of solution, how many milligrams of the antibiotic would be contained in each teaspoonful dose? 1) 5 g = 5000 mg 1 tsp = 5 ml 2) ? mg = 5000 mg 200 ml = 125 mg x 5 ml

DIMENSIONAL ANALYSIS Example 2: An order is written for 375 mg of ampicillin to be given intravenously every 6 hours to a child weighing 15 kg. Ampicillin is available in a 1 g/50 ml concentration. Calculate the volume in milliliters needed for a single 375 mg dose. ? ml = 50 ml x 1 g = 18. 75 ml 1 g x 375 mg 1000 mg

TRY ONE – DIMENSIONAL ANALYSIS A patient receives a solution by IV infusion at a rate of 30 drops/min. How much solution (milliliters) is infused in 2 hours if the infusion set has a drop factor of 15 drops/m. L?

CONVERSIONS – WEIGHTS AND MEASURES ØCommon prefixes in the metric system • Kilo (k) = 103 = 1000 as in kg • Deci (d) a 10 th or 10 -1 as in d. L • Centi (c) a hundredth or 10 -2 as in cm • Milli (m) a thousandth or 10 -3 as in m. L or mg • Micro (μ) a millionth or 10 -6 as in mcg • Nano (n) a billionth or 10 -9 as in ng

EXAMPLES OF METRIC SYSTEM UNITS Weight 1 kg = 1000 g 1 g = 1 gram 1 mg = 0. 001 g (10 -3 g) 1 mcg = 10 -6 g 1 ng = 10 -9 g Volume 1 L = 1 liter 1 d. L = 0. 1 L 1 m. L = 0. 001 L (10 -3 L)

CONVERSION EQUIVALENTS AMONG PHARMACY MATH SYSTEMS ØVolume • 1 teaspoon = 5 m. L • 1 tablespoon = 15 m. L • 1 fl oz = 29. 6 (30) m. L • 1 pint = 16 fl oz; 473 m. L • 1 quart = 2 pints; 946 ml • 1 gallon = 4 quarts; 3785 m. L • 1 cup = 8 oz Ø Weight • 1 kilogram = 2. 2 lb • 1 ounce = 28. 4 (30) g • 1 pound = 454 g Ø Length • 1 inch = 2. 54 cm • 1 foot = 12 inch

CONVERSIONS Example 1: How many fluid ounce are contained in 3 Liters? 1) Unit conversion factors : 1 L = 1000 ml 1 fluid oz = 30 ml 2) ? fl oz = 1 fl oz x 30 ml = 100 fl oz 1000 ml 1 L x 3 L

CONVERSION Example 2: A patient weighing 220 pounds is given a drug which is dosed at 5 mg per kg of body weight. Calculate the amount of drug needed for one dose for this patient. 1) 220 lb 2. 2 2) 5 mg 1 kg = 100 kg = x mg 100 kg Using dimensional analysis: ? mg = 5 mg x 1 kg x 220 lb 1 kg 2. 2 lb = 500 mg x = 500 mg

TRY SOME CONVERSIONS (1) 1 Liter = ? ml (2) 110 lb = ? kg (3) 1 tsp = ? ml (4) 1 mg = ? mcg

CONCENTRATIONS Ø Measure of how much of a given substance that is mixed with some other substances Ø Frequently expressed by: • Percentage strength • Ratio strength • Milliequivalents (per m. L or L) • Molarity (mol/L or mmol/L) • Osmolarity (Osmol/L or m. Osmol/L)

CONCENTRATIONS – PERCENTAGE STRENGTH Ø % – Parts per 100 parts • weight-in-volume (w/v) g / 100 m. L • volume-in-volume (v/v) m. L / 100 m. L • weight-in-weight (w/w) g / 100 g Ø 100 parts – Total product quantity (weight or volume)

PERCENTAGE STRENGTH Example 1: How many grams of sodium chloride are provided by 500 ml of normal saline (hint: normal saline is 0. 9% Na. Cl). 0. 9 g = xg 100 ml 500 ml x = 4. 5 g

PERCENTAGE STRENGTH Example 2: How many grams of hydrocortisone is available in a 60 g tube of 1% hydrocortisone cream? 1 g = 100 g xg 60 g x = 0. 6 g

PERCENTAGE STRENGTH Example 3: A 30 ml of a liquid astringent was contained in 200 ml of lotion. Calculate the percent strength of the liquid astringent. 30 ml = x ml 200 ml 100 ml x = 15 ml --> 15%

TRY ONE - PERCENTAGE Calculate the amount of alcohol in 1 liter of a 70% alcohol solution?

PARENTERAL IV FLUID FLOW RATE ØIV fluid flow rate (infusion rate): rate that an IV medication leaves bag and enters patient’s blood stream; amount or volume of drug a patient will receive over a given period of time ØExpressed as a volume or amount per unit time; e. g. , ml/hour; ml/min; drops/min; mg/hr Ø Flow rate = volume / time ØBy manipulating the flow rate formula, there are three types of questions: Flow rate Volume Time

FLOW RATE EXAMPLE A patient receives 1 L of IV solution over a 3 hour period. Calculate the flow rate in ml/hr. Flow rate = volume / time = 1000 m. L / 3 hours = 333 m. L/hour Another way – dimensional analysis ? ml/hr = 1000 ml x 1 L 1 L 3 hrs = 333 ml/hr

SOLVE FOR TIME Ø By manipulating the rate formula, we can solve for time Ø The equation becomes: Time = Volume / flow rate

FLOW RATE - TIME EXAMPLE If an IV is run at 50 ml/hr, how long will a 500 -ml bag last? Time = Volume / flow rate = 500 ml 50 ml/hr = 10 hours Another way – dimensional analysis ? hr = 1 hr x 50 ml 500 ml = 10 hrs

SOLVE FOR VOLUME Ø By manipulating the rate formula, we can solve for volume Ø The equation becomes: Volume = rate x time

FLOW RATE - VOLUME EXAMPLE How many ml of IV solution would be required to run an IV for 12 hours at a rate of 60 ml/hr? Volume = 60 ml x 12 hrs hr = 720 ml Another way – dimensional analysis ? ml = 60 ml × 12 hr = 720 ml 1 hr

ONE MORE EXAMPLE A patient receives a solution by IV infusion at a rate of 36 drops/min. How much solution (milliliters) is infused in 3 hours if the infusion set has a drop factor of 15 drops/m. L? Method 1 - use formula: Volume = rate x time rate = 36 drops x 1 ml = 2. 4 ml/min 15 drops Volume = 2. 4 ml x 180 min = 432 ml min Method 2 - Another way “dimensional analysis” ? ml = 1 ml x 36 drops x 60 min x 3 hr = 432 ml 15 drops 1 min 1 hr

TRY ONE - FLOW RATE You have a 1. 5 liter bag that needs to be run over 12 hours. What is the flow rate in ml/min?

Self-Assessment Question #1 How much (in grams) potassium chloride is needed to prepare one liter of 3% potassium chloride solution? A. 0. 3 g B. 1 g C. 3 g D. 30 g

Self-Assessment Question #2 The dose of an antibiotic is 40 mg/kg once daily. How much (in mg) of the antibiotic per dose should be given to a patient who weighs 40 lb? A. 168 mg B. 727 mg C. 960 mg D. 1600 mg

Self-Assessment Question #3 Three liters of D 5 W is to be infused over 24 hours, using an IV set that delivers 15 drops/ml. Calculate the flow rate in drops/minute. A. 31 drops/min B. 55 drops/min C. 69 drops/min D. 82 drops/min

Self-Assessment Question #4 Griseofulvin oral suspension contains 125 mg/5 m. L. A physician prescribed 250 mg twice a day for 2 weeks for a patient. How many milliliters of griseofulvin should be dispensed in order to fill this prescription? A. 100 ml B. 150 ml C. 280 ml D. 473 ml

Thank you! Let me know if you have any questions. Tianzhi Yang, BS, Ph. D Associate Professor of Pharmaceutical Sciences Husson University School of Pharmacy 1 College Circle, Bangor, ME 04401 Phone: 207 -992 -1946 Fax: 207 -992 -1954 Email: Yangt@husson. edu