Download ppt - © 2010 The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill 12-1 Math and Dosage Calculations for Health Care Third Edition Booth & Whaley

© 2010 The McGraw-Hill Companies, Inc. All rights reservedMcGraw-Hill

12-1

Math and Dosage Calculations for Health

Care Third EditionBooth & Whaley

Chapter 12: Specialized Calculations


Learning Outcomes

12.1 Measure insulin doses accurately.

12.2 Measure heparin dosage and flow rates, verifying that they fall within the normal daily range.

12.3 Calculate the hourly flow rate for IV infusions ordered in milligrams per minute.

12-2


Learning Outcomes (cont.)

12.4 Calculate IV flow rates for medications ordered in mg/kg doses.

12.5 Calculate IV flow rates for titratedmedications.

12.6 Determine the percentages of solutions, dilutions, and solids.

12.7 Prepare solutions from a concentrate.

12-3


Introduction

Specialized calculations include Insulin

Heparin

Critical care IV fluids

Preparation of solutions

Alligations

These special calculations require extra effort

12-4


Insulin

High Alert Medication

Pancreatic hormone that stimulates glucose metabolism

With low or no insulin production

Insulin-dependent diabetes

Routine injections of insulin needed to keep glucose (blood sugar) from rising

Generally administered Sub-Q (rotate sites)

12-5

Pancreas


Insulin – TYPES

Beef and pork – derived from the pancreas

Human insulin Replaced beef and pork in the U.S. Produced using genetically engineered bacteria

Insulin Lispro Synthetic form

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Insulin – TIMING OF ACTION

Rapid-acting Administer 30 to 60 minutes before mealsRegular (R) and Semi-lente (S)

Very rapid acting Administer 15 minutes before mealInsulin Lispro

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Insulin – TIMING OF ACTION (cont.)

Intermediate-actingLente (L), NPH (N), and Protamine Zinc (P)

Long-acting Ultralente (U) Lantus

Newer typeMaintains constant blood levels

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Onset Time when insulin begins to lower blood glucose

Peak Time when insulin’s effect is the greatest

Duration Length of time the effect of insulin lasts Measured from the time of onset

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Regular insulin injection administered at 0700

Onset – 30 minutes, 0730

Peak – 2.5 to 5 hours post administration, between 0930 and 1200

Duration – 8 h, until 1530

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ExampleExample


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Type Examples Onset Peak Duration

Rapid-acting Humulin R 30 min 2.5-5 hrs 8 hrs

Rapid-acting 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

30 min 2.5-12 hrs 24 hrs



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Insulin – LABELS

Expiration date and lot #

ManufacturerConcentration

Brand nameSpecies

Type Storage information


Insulin – LABELS (cont.)

Concentration Usually listed twice

as 100 units/mL –

traditional form U-100 (100 units/mL)

insulin

Source Beef Pork Human

12-13


Insulin Syringes

Marked in unitsMeasures amount of insulin (units)

not volume of solution• 100 unit capacity• 50 unit capacity• 30 unit capacity

Calibrated in 1 or 2 unit increments

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Insulin Syringes (cont.)

Rule 12-1Rule 12-1For more accurate measurements use a 50 unit capacity insulin syringe for insulin doses less than 50 units, and a 30 unit capacity insulin syringe for doses less than 30 units.

12-15


Ordered: Humulin N 66 units

Use a 100 unit capacity syringe

Ordered: Humulin R 8 units

Use a 30 unit capacity syringe


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Example

Example



Rule 12-2 Rule 12-2 When using U-500 or a dose of insulin over 100 units use a tuberculin or standard syringe.

Calculate the amount to administer in milliliters.

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Determine amount of insulin to give.

Ordered: Humulin R U-500 insulin, 120 units

Amount to administer = 0.24 mL

Use a tuberculin syringe

12-18

ExampleExample


Patient Education: MEASURING A SINGLE INSULIN DOSE

1. Always wash your hands before handling insulin and syringes.

2. 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.

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Patient Education: MEASURING A SINGLE INSULIN DOSE (cont.)

3. Cleanse the rubber stopper of the vial with an alcohol wipe, using a circular motion.

Start at the center of the circleand work outward.

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4. 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.

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5. Inject the air into the insulin vial.

6. Keep the needle inserted through the stopper and turn the vial upside down.

Draw up your ordered dose of insulin.

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7. Avoid touching the needle during the procedure.

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23



Insulin Combinations

Provide greater control over glucose levels

Two types of insulinIntermediate-actingShort-acting

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Insulin Combinations (cont.)

Manufacturer combines some typesNovolin 70/30

70% NPH insulin30% regular insulin

Humulin 50/5050% NPH insulin50% regular insulin

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Insulin pensSelf-administration

without having todraw up medicationfrom separatebottles

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Rule 12-3Rule 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.

Clear then Cloudy

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Clear Cloudy



Ordered: Novolin R 20 units and Humulin N 15 units Sub-Q now

Draw up the rapid-acing (clear) insulin first

20 units of Novolin R

Then draw up the intermediate-acting (cloudy) insulin

15 units of Humulin N

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ExampleExample



Rule 12-4 Rule 12-4 To prepare a combined insulin dose:

1. Calculate the total dose of insulin:

dose of rapid-acting insulin + dose of intermediate-acting insulin

total dose insulin

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Rule 12-4 Rule 12-4 (cont.)

2. 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.

3. Draw up an amount of air equal to the dose of rapid-acting insulin.

Inject it into the rapid-acting insulin vial.

12-30




4. Without withdrawing the needle from the stopper, invert the vial. Draw up the dose of rapid-acting insulin.

5. 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.

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6. 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.

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Ordered: Humulin N 42 units and Humulin R 10 units Sub-Q dailyHow many units will be in the syringe after both insulins have been drawn up into the syringe?

52 units of insulin

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ExampleExample


Error Alert!

When two types of insulin are combined, measure the correct amount of each.

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Practice

True/False

Onset is the time when insulin begins to lower the glucose level.

Duration is measured from the time the insulin dose was administered.

When mixing insulins, draw up the cloudy before the clear.

Insulin is administered using special syringes marked in units.

12-35

F

F

T

T

From the time of onset

Clear then cloudy


Heparin

High Alert Medication

Anticoagulant Reduce or prevent blood

clotting• Administered IV or

Sub-Q (rotate sites) Flush solution for

heparin locks

12-36


Heparin (cont.)

Measured in USP unitsDosage calculations must be

accurateSafe adult dosage range

• 20,000 to 40,000 units/24h• Verify that calculated doses fall

within this range

Infuse using an infusion pump to ensure accuracy

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Heparin – CALCULATIONS

Desired dose represents a flow rate

Quantity of units per period of time

Infuse using an infusion pump to ensure accuracy.

Drop rate used to verify pump rate or if the tubing is removed from the pump temporarily.

12-38


Heparin – CALCULATIONS (cont.)

Rule 12-5Rule 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 = dosage unit

H = dose on hand

A = amount to administer

Calculate using your chosen calculation method.

12-39



Use your chosen calculation method to find hourly rate to administer IV heparin.Ordered: 1000 units/h IV heparin using an infusion pumpOn hand: 50,000 units heparin in 1000 mL D5W

H = 50,000 units; Q = 1000 mL; D = 1000 units/h

A = 20 mL/h

12-40

Example

Example



Rule 12-6Rule 12-6 To calculate the hourly dose (D), multiply the total dosage by the hourly flow rate. Determine the following:

H = dose on hand or total amount to administerQ = dosage units for the total amountA = amount to administer or the flow rate of the

infusion


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What is the hourly dose?

Ordered: 30,000 units of IV heparin in 500 mL to D5W to infuse at 25 mL/h

H = 30,000 units; Q = 500 mL; A = 25 mL/h

D = 1500 units/h

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Example

Example



Next determine if 1500 units/h is a safe dose.

36,000 units/day is within the safe range of 20,000 to 40,000 units/day

12-43

Example

Example


Practice

What is the hourly dosage for an infusion of 45,000 units heparin in 1200 mL of D5W infusing at 30 mL/h? Is this a safe dose?

Answer 1125 units/h

Is this a safe dose?

This is a safe dose.

12-44


Critical Care IV

IV medications used in critical care settings Fast-acting and

potent Narrow margin of

safety

Administered continuous, IV push, or bolus

Used to alter or maintain Heart rate Cardiac output Blood pressure Respirations

12-45


Critical Care IV – PER MINUTE ORDERS

Rule 12-7 Rule 12-7 To convert a per minute order to an hourly rate:

1. Convert the order to mL/min. Determine the following:

D = rate of desired dose (mg or mcg/min)

Q = dosage unit (mL)

H = dose on hand (mg or mcg/min)

A = amount to administer (mL/min)


12-46


Critical Care IV – PER MINUTE ORDERS (cont.)


2. Convert 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

12-47


Critical Care IV – PER MINUTE ORDERS (cont.)

Find the hourly flow rate.

Ordered: 5000 mg Esmolol in 500 mL D5W at 8 mg/min via infusion pump

H = 5000 mg; Q = 500 mL; D = 8 mg/min

A = 0.8 mL/min × 60 = 48 mL/h

12-48

Example

Example


Critical Care IV – ORDERS BASED ON BODY WEIGHT

Rule 12-8Rule 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

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Critical Care IV – ORDERS BASED ON BODY WEIGHT (cont.)

Find the flow rate for an adult weighing 187 lb.

Ordered: Acyclovir 5 mg/kg IV in 100 mL D5W over 1 hour, q 8 hours X 7 days

On hand : Acyclovir 1000 mg/20 mL. Label instructions are to dilute to a dosage strength of 7 mg/mL or less.

Convert wt to kg: 178 lb = 85 kg

Determine desired dose:

D = 425 mg

12-50

Example

Example


Critical Care IV – ORDERS BASED ON BODY WEIGHT (cont.)

Calculate amount to administer:

A = 8.5 mL

Calculate the flow rate:

8.5 mL Acyclovir + 100 mL D5W = 425 mg/108.5 mL

Dosage strength = 3.9 mg/mL (less than recommended; safe to administer)

Flow rate based on order is108.5 mL over 1 hr

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Example (cont.)

Example (cont.)


Critical Care IV – TITRATED MEDICATIONS

Medications administered at rates based upon their effect Upper and lower ranges

Require careful monitoring

Incrementally adjusted until desired affect is achieved

Calculate the highest and lowest dosages

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Critical Care IV – TITRATED MEDICATIONS (cont.)

Rule 12-9Rule 12-9If you know the total amount of medication in the total volume of solution and 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 (dose).

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Your patient is receiving dopamine titrated to maintain his blood pressure.

His infusion started with dopamine 800 mg/D5W 250 mL at a rate of 5 L/h.

Over the last 3 h you have titrated the dopamine up to 12 mL/h to maintain the blood pressure.

He has received 112 mL of the solution.

How much dopamine has the patient received?

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Example

Example



Total amt of medication = 800 mg

Total amt of solution = 250 ml

Amount of solution received = 112 mL

800 mg x 112 = 250 x ?

Amount of medication received = 358.4 mg

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Example (cont.)

Example (cont.)


Practice

Find the appropriate flow rate:

Ordered: Mezlin 250mg/kg/day IV q6h in 80 mL of D5W; infuse over 1 h

On hand: Mezlin 20 g vial; reconstitute with 10 mL sterile water for each gram

Patient weights 152 lb; use macrodrip tubing of 15 gtt/mL

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Practice

Answer

Convert 152 lb to kg = 69.1kg

Find desired dose: D = 250mg x 69.1 = 17275 mg

Find mg per dose: 4318.75 mg/dose

Convert to grams: 4.32 g

Find amount to administer: 43.2 mL + 80 mL of D5W

Find flow rate: 123.2 mL/h

Find drop rate: 31 gtt/min

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Preparation of Solutions, Dilutions, and Solids

Solutions Liquid mixtures containing two or more different

chemicals

Solvent Liquid used to dissolve the other chemicals Water – universal solvent

Solutes The chemicals dissolved in the solvent

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Preparation of Solutions, Dilutions, and Solids (cont.)

Manufacturer prepared solutionsInjectionsEye dropsCough syrups

To prepare or dilute a solution you must know how the concentration of the solution is expresses

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Percentage Concentration

Percent Most common way to express concentration

If the solute is a solid – grams of solute per 100 mL solution

If the solute is a liquid – milliliters of solute per 100 mL solution

If both solute and solvent are solids – grams of solute in 100 g of solvent

12-60


Preparing % Solutions and Solids

Measure solute

Add sufficient quantity of solvent to make desired volume

Remember that the solute occupies part of the total volume

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Preparing % Solutions and Solids (cont.)

A “recipe” for preparing 100 mL of 2% lidocaine solution would look like this:

The recipe for preparing 100 g of 10% zinc oxide powder and petroleum jelly

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*Qsad = “sufficient quantity to adjust the dimensions to”

Examples

Examples

2 % Lidocaine Solution

Lidocaine 2 g

Water qsad* 100 mL

10% Zinc Oxide

Zinc oxide 10 g

Petroleum jelly 90 g


Preparing a Dilution from a Concentrate

Mix a solution that is more concentrated than needed with one that is less concentrated than needed

Calculations for preparing dilutionsAlligation methodFormula method

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Preparing a Dilution from a Concentrate (cont.)

Rule 12-10Rule 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.

12-64


Alligation Method

Procedure Checklist 12-1 Procedure Checklist 12-1

1. Write out a tic-tac-toe grid and fill in values.

2. Find the total number of parts in the solution by adding the 2 values in the right column.

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Grid


Alligation Method (cont.)

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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



Procedure Checklist 12-1 Procedure Checklist 12-1 (cont.)

3. Find the volume of 1 part by dividing the total number of parts into the volume needed.

4. 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.

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Grid




5. Add a sufficient quantity of the less concentrated solution to bring the final volume up to the desired volume.

12-68



How would you prepare 500 mL of 50% ethanol from 90% ethanol? Water is one diluent.

Add right column = 90 parts total

Determine volume of 1 part =

12-69

Example

Example

90 50

50

0 40



Determine the amount of the more concentrated solution needed =

5.56 mL/part x 50 parts of conc = 278 mL

Needed 278 mL of 90% ethanol to make 500 mL of a 50%

ethanol solution.

Add qsad of water to make the total volume of 500 mL

12-70

Example (cont.)Example (cont.)

90 50

50

0 40

50% Ethanol Solution

90% ethanol 278 mL

Water Qsad 500 mL


Formula Method*

Procedure Checklist 12-2Procedure Checklist 12-2

1. Identify the following information: Cn = concentrated needed

Ca = concentration available

Vn = volume needed

2. Solve for: Va = volume available

12-71

*The formula method can only be used when one of the solutions has a concentration of 0%, such as water.


Formula Method* (cont.)


3. Cancel units.

4. Solve for: Va = volume available.

12-72


Formula Method (cont.)

How would you prepare 500 mL of 50% ethanol from 90% ethanol?

Cn = 50%

Ca = 90%

Vn = 500 mL

Va = 277.7 = 278 mL

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Example

Example


90% ethanol 278 mL

Water qsad 500 mL


Practice

Find the amount of 95% ethyl alcohol that needs to be mixed with water to make 1.5 L of a 30% ethyl alcohol solution:

12-74


90% ethanol 437.7 mL

Water qsad* 1500 mL


Apply Your Knowledge

2-75

Match insulin type with correct label.

Which type of Insulin is NOT pictured?

Long-Acting

Very Rapid-Acting

Intermediate-Acting

Rapid-Acting



The time at which the insulin’s effect is strongest is called:a. Onsetb. Peakc. Duration

12-76



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

12-77



Convert 165 lb to kg.

Answer 75 kg

12-78

What formula can you use to determine the amount of medication received when medications are titrated?


End of Chapter 12

12-79

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