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### Calculations

### Practice your Powder Volume on Handout necessary

Warmup- Continue working on the problem from Tuesday- TPN.

Objectives- The student will be able to perform calculations pertinent to PhT.

Ratio and Proportions

- Understanding ratios and proportions is important for PhT. If you understand them, you can perform many of the calculations you will need for your job.
- Ratio- relationship between 2 units.
- Like a to b can be stated as a/b

- Proportion two equal ratios form a proportion.
- a/b = c/d

Ratio and Proportion- IV Flow Rate

- You may have to provide a flow rate or rate of administration.
- They are calculated using ratio and proportion equations.
- They are usually done in ml/hour but may need to be done in ml/minute.

Steps for IV Flow Rate

- Define the variable and correct ratios
- Define the unknown variable
- Establish the known ratios
- Establish the unknown rations

- Set-up the proportion equation
- Establish the x equation
- Factor and solve
- Express solution in correct units

Steps in action

- If you have an order for KCl 10 mEq and K Acetate 15 mEq in D5W 1000 mL to run at 80 mL/hr, you would. . .

- Define the variable and correct ratios
- Define the unknown variable > x=ml
- Establish the known ratios > 80 mL/60 min
- Establish the unknown rations > x mL/1 min

Steps in action

- If you have an order for KCl 10 mEq and K Acetate 15 mEq in D5W 1000 mL to run at 80 mL/hr, you would. . .

2. Set-up the proportion equation.

xmL / 1 min = 80 mL / 60 min

3. Establish the x equation.

x ml = 1 min times 80 ml/60 min

4. Factor and solve.

Xml = 1 times 80 mL/ 60 min = 1.33

And Finally. . .

5. Express solution in correct units.

The flow rate would be 1.33 ml/minute.

Remember that IV Flow Rate calculations may need to be calculated by gtts/min, gtts/ml, or may need to solve the amount of time before an IV bag will go empty (like in TPN).

Now you perform Ratio and Proportion

- Do the problems on your handout under ratio and proportion

ALLIGATIONS

- Alligation is a way for a PhT to mix a solution of the same ingredient from two different strengths of solutions.
- The problem could be solved with algebra, but using the alligation method is a simpler, faster, yet still accurate- Sounds like crazy fun, Right?

ALLIGATION

- To use allligation, you create a grid with 3 columns and 3 rows.

Strength of Lower strength Component (L)

H-P = Relative amount needed to prepare P

Desired strength of Product (P)

Strength of higher strength Component (H)

P-L = Relative amount of H needed to prepare P

For Example

What are the relative amounts of 70% alcohol and 40% alcohol needed to prepare 60% alcohol? (However in this example, since the value of P is higher than that of L, you will be subtracting L from P. You cannot have a negative number.

Strength of Lower strength Component (L)= 40

70-60

(H-P)

= 10 parts needed of L

Desired strength of Product (P)= 60

Strength of higher strength Component (H)= 70

60-40

(P-L)

= 20 parts needed of H

After you have found that

- So. . . You have to find how much of the exact proportion of each part by adding the values in both of the right-hand column (10+20) to get the total part value of the product (30) and then dividing each part by the total value. So. . . The amount of 70% alcohol will be 20/30 and the amount of the 40% alcohol will be 10/30.

70-60

(H-P)

=10 parts needed of L

Desired strength of product (P): 60

60-40

(P-L)

=20 parts needed of H

Example

- So using our alligation that we just did, how many mL of 70% alcohol should be mixed with with how many mL of 40% alcohol to prepare 300 mL of 60% alcohol?
- To solve for the volume of H:
300 mL P x 20 mL H/30 mL P = 200 mL H

- To solve for the volume of L:
300 mL P x 10 mL L/30 mL P = 100 mL L

So when 200 mL of 70% alcohol are mixed with 100 mL of 40% alcohol, the resulting solution is 300 mL of 60% alcohol.

Now you work on your sheet with alligations.

Powder Volume

- Some medication that are dispensed in liquid dosage form are manufactured and provided to the pharmacy as powders. The powders are then constituted or mixed with a specific volume of liquid to produce a desired strength of the liquid dosage form.

There are two different types of calculations that may be necessary

- Determining the strength or concentration of a product when different volumes or diluent are added.

- Determining how to change the concentration or strength of the constituted dosage form by varying the amount of diluent.

Powder Volume necessary

- For Calculations with powders for constitution, the following relationship exists:
- The final volume of the constituted product (FV)
=

The volume of the diluent D) + the powder volume (PV)

Or

FV = D +PV

Powder Volume necessary

- Example
- The directions for mixing a liquid antibiotic state when 80 mL of water are added to the contents of the bottle, the resulting volume is 150 mL. Determine the Powder Volume or (PV).
- FV = D + PV
- 150 mL = 80 mL + PV
- PV = 150 Ml – 80 mL = 70 mL

Children’s Doses necessary

Most doses in U.S.P (United States Pharmacopoeia) and other drug references are for adults. Usually, drugs that can be taken by children have doses provided by the manufacturer.

However, when a dose is not provided

for, the adult dose must be lowered.

Children’s Doses: One Formula necessary

Clark’s Rule:

Weight of child/150lb x adult dose = dose for child

150 lbs is considered an avg adult. However, this is not very precise because there are many other factors. Like. . . Ht, Wt, Age, Condition, and on and on.

Children’s Doses Another Formula necessary

Body Surface Area Formula

Child BSA times adult dose/average adult bsa = child dose

Body Surface Area (BSA) is based on height and weight. It is always given in square meters (m2). 1.73 m2 is used as an average for bsa for adults.

Nomogram can calculate the bsa of an adult or child.

NOMOGRAM necessary

http://manuelsweb.com/ped_dose_nomo.htm#top

Children’s Doses necessary

- http://www.globalrph.com/bsa2.cgi
- However, BSA formulas are generally solved on computers today, Ahhhh, thank goodness.
- Both of these, however, can lead to incorrect doses and are not always appropriate, and
- Although the pediatrician will prescribe the dose, you should always double check the manufacturer’s instructions as well as the formula.

Children’s Doses necessary

- Children’s doses are stated by kg of body wt (dose/kg).
- Remember- 1 kg = 2.2 lbs
- If an antibiotic IV prescribed for an infant is to be 15mg/kg twice a day, and the baby weighs 18lbs, how much drug is to be given for one dose?

Business calculations necessary

Usual and Customary Price U&C- The lowest price charged if a patient pays cash, on that day, for that drug.

U&C is determined at the corporate level.

The computers are usually programmed to figure this out.

Calculations for Business necessary

- If Rx prices are determined using the following formula:
- Average wholesale price (AWP) + professional fee = selling price
- And the professional fee is determined using the following chart
- And the AWP for 30 cap of Amoxicillin is $3.50, what is the retail price of the Rx?

What about Discounts necessary

- If the medication is $8.49 and the patient is qualified to receive a 5% discount, how much will he or she end up paying?

Business- Gross & Net Profit necessary

- The Gross profit is the difference between the selling price and the acquisition cost.
- Gross Profit = Selling price – acquisition cost

- Net Profit is the difference between the selling price of the Rx and the sum of all costs associated with filling the Rx.
- Net Profit = Selling Price – acquisition cost – dispensing fee