Math and Dosage Calculations for Medical Careers PowerPoint® to accompany Math and Dosage Calculations for Medical Careers Second Edition Booth • Whaley Chapter 12 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Specialized Calculations Chapter 12 Specialized Calculations

Learning Objectives When you have completed Chapter 12, you will be able to: Measure insulin doses accurately. Measure heparin dosage and flow rates, verifying that they fall within the normal daily range. Calculate the hourly flow rate for IV infusions ordered in milligrams per minute. Chapter 12

Learning Objectives (con’t) Calculate IV flow rates for medications ordered in mg/kg doses. Calculate IV flow rates for titrated medications. Determine the percentages of solutions, dilutions, and solids. Prepare solutions from a concentrate. Chapter 12

Introduction You may be required to have additional knowledge related to dosage calculations This special knowledge will require specialized calculations Insulin Heparin Critical care IV fluids Preparation of solutions Alligations Chapter 12

Insulin Insulin is a pancreatic hormone that stimulates glucose metabolism People who have low or no insulin production may have insulin-dependent diabetes They often need routine injections of insulin to keep their glucose (blood sugar) from rising to levels that could be life threatening Rotate injection sites Pancreas Chapter 12

Types of Insulin Beef and pork - extracted from cattle or pig pancreas Human - including genetically-engineered bacteria Synthetic - insulin lispro Clear - regular insulin Cloudy - Lente, NPH, and Ultralente insulins Chapter 12

Timing of Insulin Action Rapid-acting insulins Regular (R) and Semilente (S) insulins Administered 30 to 60 minutes before a meal Very rapid-acting insulin Insulin lispro Administered 15 minutes before a meal Chapter 12 8

Timing of Insulin Action (con’t) Intermediate-acting insulins Lente (L), NPH (N), Protamine Zinc (P) Long-acting insulin Ultralente (U) Lantus (new type of insulin) – maintains a constant blood level without peaks Chapter 12

Timing of Insulin Action (con’t) Onset The time when the insulin begins to lower the glucose level Peak The time at which the insulin’s effect is strongest Duration The length of time the effect of the insulin lasts Chapter 12

Timing of Insulin Action (con’t) Example: Regular dose of insulin given at 0700 onset: peak: duration: after 30 minutes, at 0730 2.5 to 5 hours after it is administered, between 0930 & 1200 will last about 8 hours, until 1530 Chapter 12

Timing of Insulin Action (con’t) Type Examples Onset Peak Duration rapid-acting Humulin R 30 min 2.5-5 hrs 8 hrs Humalog 15 min 30-90 min 6-8 hrs intermediate- acting Novolin L 2.5 hrs 7-15 hrs 22 hrs long-acting Humulin U 4-8 hrs 10-30 hrs 28 hrs mixed Humulin 70/30 2.5-12 hrs 24 hrs Chapter 12

Insulin Labels Manufacturer Concentration Expiration date Brand Name Type Storage Information Species Chapter 12

Insulin Labels (con’t) Concentration is usually listed twice Traditional dosage strength – 100 U/mL Concentration – U-100 (meaning that 100 units of insulin are contained in 1 mL of solution) Concentration may be U-500 Labels include type Beef Pork Human Chapter 12

Insulin Syringes Insulin administration is different from other types of injections. The syringe measures the amount of insulin rather than a volume of solution. Must use special insulin syringes marked in units. Chapter 12

Insulin Syringes (con’t) Standard U-100 syringes hold up to 100 units per 1mL solution Calibrated for every 2 units or some in each unit Smaller syringes hold up to 50 units (0.5 mL of solution) 30 units Chapter 12

Insulin Syringes (con’t) Rule 12 - 1 For more accurate measurements, use a 50-unit insulin syringe for insulin doses less than 50 units when available. Chapter 12

Insulin Syringes (con’t) Example - Decide which syringe to use. Ordered: HumulinR 55 units Answer – 100-unit syringe and fill it to between the 54 and 56 units line Chapter 12

Insulin Syringes (con’t) U-500 insulin is used for patients with highly elevated blood sugars. Insulin may be given by IV. Use tuberculin or standard syringe when U-500 or doses over 100 units are ordered. These doses will not fit in a 100-unit syringe. Chapter 12

Insulin Syringes (con’t) Rule 12 - 2 When using U-500 or a dose of insulin over 100 units use a tuberculin or standard syringe. Chapter 12

Insulin Syringes (con’t) Example: Determine amount of insulin to give. Ordered: Humulin R U-500 insulin 80 units Administer 0.16 mL in a tuberculin syringe Chapter 12

Measuring a Single Insulin Dose Patient Education Always wash your hands before handling insulin and syringes. If you are using an intermediate- or long-acting insulin (Lente, NPH, Ultralente, 70/30, or 50/50), roll the vial between your palms to mix the insulin until all of the insulin looks cloudy. Chapter 12

Measuring a Single Insulin Dose Patient Education (con’t) Cleanse the rubber stopper of the vial with an alcohol wipe, using a circular motion. Start at the center of the circle and work outward. Chapter 12

Measuring a Single Insulin Dose Patient Education (con’t) Draw up an amount of air equal to your insulin dose in the syringe. Pull back the plunger until the leading ring is aligned with the correct marking on the syringe. Chapter 12

Measuring a Single Insulin Dose Patient Education (con’t) Inject the air into the insulin vial. Chapter 12

Measuring a Single Insulin Dose Patient Education (con’t) Keeping the needle inserted through the stopper, turn the vial upside down. Draw up your ordered dose of insulin. Chapter 12

Measuring a Single Insulin Dose Patient Education (con’t) Avoid touching the needle during the procedure. Chapter 12 27

Insulin Combinations Two types of insulin may be ordered to allow the doctor more control over glucose levels. The combination of a rapid-acting insulin and an intermediate-acting insulin provides the patient with the rapid onset of the first and the lengthy duration of the second. Chapter 12

Insulin Combinations (con’t) The two types of insulin can be combined in one syringe. Some are automatically combined by the manufacturer. Novolin 70/30 is 70% intermediate-acting NPH insulin and 30% rapid-acting regular insulin. Humulin 50/50 is 50% NPH insulin and 50% regular insulin. Chapter 12

Insulin Combinations (con’t) Rule 12 – 3 When preparing a combined insulin dose, always draw up the rapid-acting insulin first. Remember: the insulin with a quicker onset is drawn up first. Chapter 12

Insulin Combinations (con’t) Example: Which one should be drawn up first? Ordered: Novolin (rapid-acting) R 20 units and Humulin (intermediate-acting) N 15 units Sub-Q now The rapid-acting Novolin R will be drawn into the syringe first. Chapter 12

Insulin Combinations (con’t) Rule 12 – 4 To prepare a combined insulin dose: Calculate the total dose of insulin: dose of rapid-acting insulin + dose of intermediate-acting insulin total dose insulin Chapter 12

Insulin Combinations (con’t) Rule 12 – 4: (con’t) Draw up an amount of air equal to the dose of intermediate-acting insulin. Inject it into the intermediate insulin vial, but do not draw up the dose. Withdraw the needle from this vial. Draw up an amount of air equal to the dose of rapid-acting insulin. Inject it into the rapid-acting insulin vial. Chapter 12

Insulin Combinations (con’t) Rule 12 – 4 (con’t) Without withdrawing the needle from the stopper, invert the vial. Draw up the dose of rapid-acting insulin. Carefully insert the needle through the stopper of the intermediate-acting insulin vial. Invert the vial, without injecting any of the rapid-acting insulin into the vial. Chapter 12

Insulin Combinations (con’t) Rule 12 – 4 (con’t) Draw up intermediate-acting insulin until the leading ring reaches the calibration indicating the total dose. If you accidentally draw up more than the total amount desired, do not push the excess back into the vial. You must begin the procedure again. Chapter 12

Insulin Combinations (con’t) Example: How many units will be in the syringe after both insulins have been drawn up into the syringe? Ordered: Humulin N 42 units and Humulin R 10 units Sub-Q daily Answer = 52 units total Chapter 12

Error Alert! When two types of insulin are combined, measure the correct amount of each. Chapter 12

Heparin Anticoagulant use in USP units Given to patients to reduce or prevent the blood from clotting Use as an irrigate to keep the blood from clotting in a heparin lock Chapter 12

Heparin (con’t) Rotate multiple injections of heparin to prevent bruising. Bruising and bleeding are a great concern for patients. Calculated dosages must be accurate. Chapter 12

Heparin Calculations For anticoagulant therapy Administer adults at a dosage of 20,000-40,000 units per 24 hours You must verify that the dose is within a safe range Through an IV, via electronic device, to ensure accuracy of the dose Chapter 12

Calculate Heparin Dosages Rule 12 - 5 To determine the rate to administer a solution containing heparin with an electronic device that measures the infusion in mL per hour find A, where D = rate of the desired dose Q = the dosage unit H = dose on hand A = amount to administer Chapter 12

Calculate Heparin Dosages (con’t) Example: Use your chosen calculation method to find hourly rate to administer IV heparin. Ordered: 1000 units/h IV heparin using an infusion pump On hand: 50,000 units heparin in 1000 mL D5W Answer: 20 mL/h Chapter 12

Calculate Heparin Dosages (con’t) Rule 12 - 6 To calculate the hourly dose (desired dose, D), multiply the total dosage by the hourly flow rate. Determine the following: H = dose on hand or total amount to administer Q = dosage units for the total amount A = amount to administer or the flow rate of the infusion Calculate using your chosen calculation method. Chapter 12

Calculate Heparin Dosages (con’t) Example: What is the hourly dose? Ordered: 30,000 units of IV Heparin in 500 mL to D5W to infuse at 25 mL/h Answer = 1500 units/h Chapter 12

Critical Care IV Medications IV medications used in critical care settings are fast-acting and potent Only a small amount is required to have an effect Given to alter or maintain Heart rate Cardiac output Blood pressure Respirations Chapter 12

Critical Care IV Medications (con’t) You must have the right medication for the right patient in the correct concentration Be certain that you are administering the proper dosage at the proper rate Can be given continuous, IV push or bolus Via volume-controlled burette Electronic infusion device Microdrip tubing Chapter 12

Calculating Critical Care Medications Rule 12 - 7 To convert a per minute order to an hourly rate: Convert the order to mL/min. Determine the following: D = rate of desired dose (mg or mcg/min) Q = dosage unit (mL) Chapter 12

Calculating Critical Care Medications (con’t) Rule 12 - 7 (con’t) To convert a per minute order to an hourly rate: H = dose on hand (total number of mg or mcg) A = amount to administer (mL/min) Use your chosen calculation method Chapter 12

Calculating Critical Care Medications (con’t) Rule 12 - 7 (con’t) To convert a per minute order to an hourly rate: 2. Convert the mL/min to mL/h Either by multiplying by 60 or if using dimensional analysis use the factor 60/1 as part of your equation Both ways the hourly flow rate will be determined in mL/h Chapter 12

Calculating Critical Care Medications (con’t) Example: Find the hourly flow rate. Ordered: 5000 mg Esmolol in 500 mL D5W at 8 mg/min via infusion pump Answer = 0.8 mL/min Chapter 12

Orders Based on Body Weight Many medication orders are based on body weight. Body weight calculations are relevant to IV medications for critically-ill patients. Example: Daily dosage may be 5 mg/kg/day. If patient weights 50 kg, you can use a proportion to calculate daily dose of 250 mg. Chapter 12

Orders Based on Body Weight (con’t) Rule 12 - 8 To find the IV flow rate based upon weight: Convert the weight to kg Determine the desired dose Calculate the amount to administer Calculate the flow rate Chapter 12

Orders Based on Body Weight (con’t) Example: Find the flow rate for an adult who weighs 187 lb. Ordered: Zofran 0.15 mg/kg IV over 15 min, started 30 min prior to chemo: repeat x2 at 4 h & 8 h On hand : Zofran 40 mg/20mL. Dilute injection with 50 mL of 5%DW Answer = 22.4 mL of Zofran over 15 min Chapter 12

Titrated Medications Critical-care meds are administered at varying rates depending on their effects on bodily functions. You must carefully monitor and adjust the rate of these medications. You must calculate the lowest and highest dosages. Chapter 12

Titrated Medications (con’t) Often you start the medications at the lower end and increase incrementally over time until the desired effect is achieved. You must calculate the total amount the patient has received. Start by measuring the total mL of infused solution. Infusion pumps have indicators that measure mL. Chapter 12

Titrated Medications (con’t) Rule 12 – 9 If you know the total amount of medication in the total volume of solution, as well as the volume of solution that the patient has received, then you can use a proportion to calculate the amount of medication the patient has received (the dose). total amount of medication amount of medication received total volume of solution volume of solution received = Chapter 12

Preparation of Solutions, Dilutions, and Solids Solutions are liquid mixtures containing 2 or more chemicals Solvent – used to dissolve other chemicals Solutes – chemicals dissolved in the solvent Common solvent is water Universal solvent Normal saline = 0.9% sodium chloride in every 100 mL of solution Chapter 12

Preparation of Solutions, Dilutions, and Solids (con’t) Common examples of manufacturer solutions Injections Eye drops Cough syrups You may have to prepare a solution “from scratch” Chapter 12

Percentage Concentrations Common way to express concentrations is in percentages. Percent means “per hundred.” How much solute is found in every 100 mL of solution? Chapter 12

Percentage Concentrations (con’t) Solid solute % = grams of the solute in 100 mL 2% lidocaine = contains 2 g of lidocaine in every 100 mL of solution Chapter 12

Percentage Concentrations (con’t) Liquid solute % = milliliters of the solute in 100 mL 70% isopropyl alcohol has 70 mL of isopropyl alcohol in every 100 mL solution Chapter 12

Percentage Concentrations (con’t) Solid solute and solid solvent % = grams of the solute in 100 g of the product 2% hydrocortisone ointment means that 100 g of ointment will contain 2 g of hydrocortisone Chapter 12

Preparing % Solutions and Solids You must first measure the solute Then add sufficient quantity of solvent to bring the total to desired volume Chapter 12

Preparing % Solutions and Solids (con’t) Example: A “recipe” for preparing 100 mL of 2% lidocaine solution would look like this: 2% Lidocaine Solution *qsad 100 mL Water 2 g Lidocaine *Qsad = “sufficient quantity to adjust the dimensions to” Chapter 12

Preparing % Solutions and Solids (con’t) Example: Write the recipe for preparing 100 g of 10% zinc oxide powder and petroleum jelly. 90 g Petroleum jelly 10 g Zinc oxide 10% zinc oxide Chapter 12

Preparing a Dilution from a Concentrate You may need to prepare a solution from a concentrated solution that is already prepared Alligation method Use of formula Chapter 12

Preparing a Dilution from a Concentrate (con’t) Rule 12 - 10 To prepare a dilution from a concentrate, determine: Vn = the volume needed Cn = the concentration needed Ca = the concentration(s) available* * If water is being used, one of the these concentration is zero. Then use the alligation method or formula to obtain your answer Chapter 12

Alligation Method Procedure Checklist 12-1 Write out a tic-tac-toe grid and fill in the following values. Find the total number of parts in the solution by adding the 2 values in the right column. Chapter 12

Alligation Method (con’t) Concentration of MORE concentrated solution Parts of the MORE concentrated solution needed The concentration needed Concentration of LESS concentrated solution Parts of the LESS concentrated solution needed Chapter 12

Alligation Method (con’t) Find the volume of 1 part by dividing the total number of parts into the volume needed. Multiply the volume of 1 part (answer from step 3) by the number in the top right of the grid. The result is the amount of the more concentrated solution needed. Chapter 12

Alligation Method (con’t) Add a sufficient quantity of the less concentrated solution to bring the final volume up to the desired volume. Chapter 12

Alligation Method (con’t) Example: How would you prepare 500 mL of 50% ethanol from 90% ethanol? Desired volume is 500 mL - you would dilute the 90% by adding water up to a final volume of 500 mL. Chapter 12

Preparing a Dilution from a Concentrate – Formula Method* 1. Identify the following information: Cn = the concentration needed Ca= the concentration available Vn = volume needed 2. Solve for: Va = the volume available *The formula method can only be used when one of the solutions has a concentration of 0%, such as water. Chapter 12

Preparing a Dilution from a Concentrate – Formula Method (con’t) Plug the values into the following formula: Cancel units Solve for the equation for Vn Chapter 12

Preparing a Dilution from a Concentrate – Formula Method Example: How would you prepare 500 mL of 50% ethanol from 90% ethanol? Answer: 278 mL of 90% ethanol solution is needed to prepare 500 mL of a 50% solution 50% Ethanol qsad 500 mL Water 278 mL 90% ethanol Chapter 12

Long-acting-Ultralente Apply Your Knowledge Match each label with its type. Very Rapid-Acting Rapid-Acting Very Rapid-Acting Long-Acting Long-acting-Ultralente Intermediate-Acting Long-Acting Rapid-Acting Which type of Insulin is not pictured? Chapter 12

Apply Your Knowledge The time at which the insulin’s effect is strongest is called: a. Onset b. Peak c. Duration Answer: b. Peak Chapter 12

Apply Your Knowledge Answer: 5 gtt/min Ordered: 500 mg dobutamine HCL in 100 mL D5W infusing at 2.4 mg/min with a macrotubing at 10gtt/mL How fast would you set the gtt/min? Answer: 5 gtt/min Chapter 12

Apply Your Knowledge Convert 165 lb to kg. Answer: 75 kg What formula can you use to calculate titration of medications? total amount of medication amount of medication received total volume of solution volume of solution received = Chapter 12

Specialized Calculations When on the brink of complete discouragement, success is discerning that the line between failure and success is so fine that often a single extra effort is all that is needed to bring victory out of defeat. -- Elbert Green Hubbard THE END Chapter 12