48 th Annual Meeting. A Review of Pharmacy Calculations for Pharmacy Technicians. Metric System of Measurement. Disclosure. Common Conversions

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1 48 th Annual Meeting A Review of Pharmacy Calculations for Pharmacy Technicians Nina Pavuluri, Ph.D. Navigating the Oceans of Opportunity Metric System of Measurement Base Unit Factor Name Symbol 1 (g, L) = kilo k 0.01 hecto h 0.1 deka da 1 base unit (g, L) 10 deci d 100 centi c 1000 milli m or 10 6 micro mc, µ or 10 9 nano n Disclosure I do not have a vested interest in or affiliation with any corporate organization offering financial support or grant monies for this continuing education activity, or any affiliation with an organization whose philosophy could potentially bias my presentation Common Conversions Apothecary Metric Commonly used equivalents 1 grain 64.8mg 65mg 1 ounce 31.1g 30g 1 pound (lb) 373.2g 454g 1 minim fluid ounce fluid ounce gallon 2.2lb 1kg Objectives Review conversion of measurements within the metric systems of weight and volume Explain the processes of ratio and proportion, percentage and dilution and concentration Help understand intravenous flow rates, and solving dosage problems Reading, interpreting, and solving calculation problems encountered in the preparation and distribution of prescriptions/medication orders Conversions and Dimensional Analysis Identify the quantity to be converted as well as any conversion factors that you will need. Terms that are equal to each other may be written in the form of a fraction. 0.1mg? mcg 0.1mg * 1000mcg 100mcg 1mg 0.1mg 100mcg 1

2 Examples Convert 1g/dL to g/ 1dL* L 1g dl * 1L 10dL 100 1g 100 1%w / v Percent weight -in-volume, %w/v is number of grams in g 0.9% w/ v 100 Eg.: A certain injectable contains 2mg of a drug per solution. What is the strength expressed in %w/v? Express weight in gram 1g 2mg * 1000mg 0.002g Set up the proportion and solve for the unknown 0.002g 1? g 0.002g or simply 100 *100 =0.2g/100= 0.2%w/v= 0.2g/dL Ratio and Proportion Used when two expressions are directly related to one another Eg: How many mg of Demerol is present in 5 when there is 15mg of Demerol in 1?? mg 15mg 1? mg 5 15mg *5 1 75mg Percent weight -in-weight, %w/w number of grams in 100g Eg.: How many grams of dextrose must be added to 475 of water to make a 65% (w/w) solution? xg (x 475)g 65g 100g 100x 65x x g Ratio and Proportion A child weighing 28 lb is to receive 4 mg of phenytoin per kilogram of body weight daily as an anticonvulsant (Dose= 4mg/kg/day). How many milliliters of pediatric phenytoin suspension containing 30 mg per 5 ml should the child receive per day? 4mg 2.2lb?mg 28lb ; =50.909mg Source; 30mg mg? Percent volume -in-volume, %v/v number of milliliters in 100 Eg.: A dermatologic lotion contains 1.25 of liq. Phenol in 500. Calculate the percentage strength (%v/v) for the label ? %v / v 2

3 Milligram percent, mg% number of milligrams in 100 Gram per deciliter = %w/v number of grams in 100 Dilution and Concentration Eg.: Rx Clindamycin Phosphate 1.5% Alcohol (52% v/v) qs ad 120 The pharmacy has no clindamycin phosphate powder but does have clindamycin phosphate sterile solution, 150mg/ in vials. From the label, the technician learns that the solution is aqueous. a)how many of the clindamycin phosphate sterile solution should the technician use in filling the prescription? b)how many of 52% alcohol is required? Dilution and Concentration Source Product C 1Q 1 C 2Q 2 How many of a 100mg/ concentrate of Rhus toxicodendron extract should be used to prepare the following prescription? Rx Rhus Toxicodendron extract 10μg/ Sterile water for injection qs 100 Sig: As directed Source Pr oduct a) C s Q s C p Q p 150mg / *Q s 1.5% *120 The units should be the same on both sides of the equation 1.5g 1.5% = mg 15mg / mg / *Q s 15mg / *120 Q s 12 b)volume contraction is observed, when alcohol and water (aqueous solutions) are mixed. Hence, it is strongly advised that the volume of alcohol required be not calculated by subtracting the volume of source from the total volume of the prescription. A sufficient volume of alcohol (qs) is used to make up the final volume. Source Pr oduct C s Q s C p Q p [100mg / ]*Q p 10 g/ *100 Units should be the same on both sides of the equations 10 g* 1mg 1000 g 0.01mg [100mg / ]*Q p 0.01mg /*100 Q p 0.01 of concentrate Reconstitution of Powders Certain medications including antibiotics are unstable when stored in solution form Dry powders must be reconstituted with a sterile diluent Instructions are supplied indicating the volume of diluent to be added Powdered drug may/may not contribute to the final volume 3

4 Example A pharmacy receives a medication order to prepare 600,000 units of penicillin G sodium to be added to 1L of D5W. A vial of penicillin G sodium containing a million units is on hand and the directions on the vial state Add 4.6 sterilized water for 200,000 units/. How many of the reconstituted solution must be added to the 1L D5W bag? Rate of flow V D Rate of Flow (R) t R = rate of flow (gtt/min) V = total volume to be infused (ml) D = drop factor (gtt/ml) t = total time of infusion (in minutes) Take 4.6 of sterilized water (as per instructions on the vial) Add to the powder in the vial and shake well Source: 200,000 units/ Proportion; 200,000 units 600,000units ; 3 1? Withdraw 3 of the reconstituted solution using a syringe Add to the 1L D5W Example Eg.: An intravenous fluid of 1000 ml of Ringer s Injection was started in a patient at 8:00 A.M. and was scheduled to run for 12 hrs. At 3:00 P.M. it was found that 800 ml of the fluid remained in the bottle. At what rate of flow should the remaining fluid be regulated using an IV set that delivers 15 drops per ml in order to complete the administration of the fluid in the scheduled time? Rate of Flow of Intravenous Fluids (drops per min) IV fluids: For adequate hydration of patients or sometimes for administering potent medications (Medicated IV drips). Usually operated by IV infusion pumps. Drop Factor: drops/ml Standard IV solution sets: gtt (drops) per ml Microdrip sets; Drop factor :60 gtt/ml. Fluid remaining: 800; Time remaining 5hr=300minutes Formula Method Rate V * D 800 *15gtt / 40gtt /min t 300min Proportion Method min? ; min 15gtt 1? gtt ; 40gtt

5 Dimensional Analysis? gtt gtt 800 *15 min * 1 40gtt /min 300min Example How many meqs of Ca 2+ are represented in a solution containing 140mg CaCl 2.2H 2 O in 100? (Mol. Wt. 147) wt. in mg *valence # meq Mol.wt. = 140* mEq Milliequivalents Electrolytes in TPNs to correct electrolyte imbalance Expressed in units known as milliequivalents (meq) Measure of the chemical activity of an electrolyte Related to ionic charges and takes valence into consideration Total Parenteral Nutrition Large volume parenteral fluids containing essential nutrients Include vitamins, trace minerals, antibiotics and other medications Equations TPNs Mol. wt. meq wt. = valence wt. in mg # meq = meq wt. wt. in mg *valence(charge) # meq Mol.wt. TPN Solution Formula Calcium gluconate 2.5mEq Heparin 1000 units Component Source 10 vial containing 12 meq 5 vial containing 500units/ Sodium chloride 30mEq 20 vial containing 25% solution To be added to: 500 of 50% dextrose injection 500 of 8.5% amino acids injection 5

6 Calcium gluconate: 12mEq mEq ; 2.08? Heparin : 500unit unit ; 2? Sodium chloride: 25g Source 20 of 25% = 20 of 100 5g wt.in mg*valence 5000 *1 # meq Mol.wt mEq 85.47mEq 30mEq ; ? Milliequivalents Example You have been instructed to add 15 of sodium chloride to a patient s IV bag. Using the label shown, calculate how many milliequivalents of sodium chloride will be in 15 of solution. Solution 1: Using the ratio-proportion method, 4mEq 1? meq ; 60mEq 15 Proportion Example How many milligrams of medication are in 6 of the solution shown in this label? 20mg 2? mg ; 60mg 6 Unit Calculation Example A patient is to receive a bolus (concentrated) dose of heparin. If the dose is 7500 units and you have a vial with the label shown, how many milliliters will you prepare? 5000units 1 Solution 1: Using the ratio-proportion method, 7500units? ; 1.5 Percentage Strength Example If there are 30 g of dextrose in 500 of the solution, what is the percentage of solution? Solve by using the 30g equation: 500? g 100 ;6g 6g /100 6% Infusion Rate If there is a flow rate of 40 gtt/min using a 15 drop set, how many liters will be delivered over 24 hours? Solution 2: This problem can also be calculated using the dimensional analysis method. R V * D t V *15gtt / 40gtt /min 24*60min 1L V 3840 * L 6

7 Questions? 7