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Hospital Calculations Calculations Related to Common Hospital Formulations

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الحسابات الصيدالنية في المستشفيات

الدكتور أنس البهنسي

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Lecture Objectives

Understand the prescription components.

Ability to read Latin signa.

The use of the metric system and understand the apothecary and avoirdupois systems with the ability to make conversions.

Solve proportional calculations.

The ability to render a solution isotonic using NaCl or Boric Acid.

Apply skills to produce new concentrations out of a different concentration with a specific volume.

Solve calculations related to injectable medications, including reconstitution, milliequivalent concentrations, and dose calculations.

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Prescriber Name, Address and Phone

Date

Patient Name Address Age

Superscription

Paracetamol 500mg #30

Inscription: Name of

Medication and number of

units

Subscription Directions to the dispenser like: Dissolve tablets in 3 oz of simple syrup

Usually in Latin

Take 1-2 tablets qid PRN Transcription

Signa Refills: DAW

Signature

Co

mp

on

en

ts of P

rescrip

tion

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Co

mm

on

Latin A

bb

reviation

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• A prescription reads:

– Trandate 300mg po BID F7D.

– You only have Trandate 150mg in stock

– How many tablets do you dispense????

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Example

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The Metric System

• A measurement system based on subdivisions and multiples of 10; made up of three basic units: meter, gram, and liter

– Temperature

– Distance

– Volume

– Weight

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Common Metric Units

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Apothecary Measures

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Avoirdupois Measures

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Household Measures

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© Paradigm Publishing, Inc. 12

Temperature

• Conversions

°F = (1.8 x °C) + 32°

°C = (°F - 32°) ÷ 1.8

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IV Room Calculations

IV Room Lingo:

• Stock solution: the most concentrated form of a drug that you can put your hands on.

• Bag: flexible, soft plastic container filled with a sterile fluid.

• Standard Concentration: a set volume and concentration of a commonly-made medication

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A List of Standard Concentrations for A Hospital

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Proportional Calculations:

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𝒂

𝒄=𝒙

𝒃

𝒙 =𝒂𝒃

𝒄

Only true if you make sure all units cancel out, leaving the ones you want

(Dimensional Analysis)

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• You need to mix a syringes filled with 1g of Cefazolin in 20ml diluent. Your stock solution contains 200mg/ml Cefazolin.

• How many mls of the stock solution you need to draw and put in the 20ml syringes then add the diluent.

• Solution:

–𝟏𝟎𝟎𝟎𝒎𝒈

𝒙 𝒎𝒍=

𝟐𝟎𝟎𝒎𝒈

𝟏 𝒎𝒍

– 𝒙 =𝟏𝟎𝟎𝟎𝑿𝟏

𝟐𝟎𝟎= 𝟓𝒎𝒍

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Example

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• Very important when mixing solutions for instillation into the body fluids.

• The term is used to describe the number of milliosmoles in a given amount of solution(1L).

• Blood osmolarity is around 300mOsmol/L.

• Infusion of solutions with different osmolarity with the bloodstream will result in shifting of the fluids between blood cells and the serum.

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Osmolarity and Tonicity

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• Tonicity is the term used for osmolarity when it is used in the context of body fluids.

• Accordingly solutions can be:

– Hypotonic

– Isotonic

– Hypertonic

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Osmolarity and Tonicity

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• Step 1: Write your units 𝒎𝑶𝒔𝒎𝒐𝒍

𝑳

• Step 2: Line up available data:

– D5W=5𝑔 𝐷𝑒𝑥𝑡𝑟𝑜𝑠𝑒

𝑑𝐿

– 𝑀𝑊:180𝑚𝑔 𝐷𝑒𝑥𝑡𝑟𝑜𝑠𝑒

𝑚𝑚𝑜𝑙𝑒

– Osmolarity: 𝑚𝑂𝑠𝑚𝑜𝑙

𝑚𝑚𝑜𝑙𝑒

• Step 3: Perform calculations:

–𝟓𝟎𝟎𝟎𝒎𝒈

𝟏𝟖𝟎𝒎𝒈=27.8mOsmol/dL 𝒕𝒐𝒏𝒊𝒄𝒊𝒕𝒚 =

𝟐𝟕𝟖𝒎𝑶𝒔𝒎𝒐𝒍

𝑳

– Isotonic

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Example

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• To ensure isotonicity we need to equate everything administered to NaCl solution.

• Considerations:

– Amount of drug in solution

– NaCl equivalent of the drug (E).

– NaCl concentration nearest to blood concentration: Normal Saline 0.9%NaCl.

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Osmolarity and Tonicity

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How to determine (E)?

• The best way to examine the difference between the freezing point of the drug and NaCl. (both are driven by the number of particles)

• We do not have the equipment or the time to calculate.

• Use Remington’s: The Science and Practice of Pharmacy

•𝑬 =𝟓𝟖.𝟖

𝟏.𝟖 𝒎𝒘

𝒊

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Example

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= 0.34 which means that:

1 g of Silver Nitrate is equal to 0.34g of NaCl

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Once you know the amount of drug, its E-value, the volume you need to make,

1. Calculate total amount of NaCl needed for the product. (multiply NS concentration by the desired volume)

2. Multiply total drug amount in g by (E).

3. Subtract 2 from 1. to determine the amount of NaCl to be added.

4. Complete calculations to determine the amount of other drugs ingredients that needed to be added.

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Example

• Find the quantity of NaCl required to be added to the following compounded prescription

• NaCl equivalent of

Chlorbutanol is 0.18

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Amount of NaCl to render the total

volume isotonic: 𝟎.𝟗

𝟏𝟎𝟎× 𝟓𝟎 =0.45g

Amount of NaCl represented by Chlorbutanol: 0.5 X 0.18= 0.09g

Amount need to be added of NaCl to render it isotonic: 0.45-0.09=0.36g

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Example

• E values: – Chlorbutanol: 0.18 – Zinc Sulfate: 0.15 – Boric Acid: 0.52

• Solution: – Amount of NaCl to render the total volume isotonic:

0.9

100× 30 = 0.27𝑔

– Chlorbutanol: 0.1×0.18= 0.018𝑔 – Zinc Sulfate: 0.05×0.15 = 0.0075𝑔 – Amount of NaCl to be added: 0.27-(0.018+0.0075)=0.245𝑔 – Amount of Boric Acid:

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𝑥 = 0.47𝑔

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Homework

• The prescriber orders tobramycin 1% ophthalmic solution, 10ml.

• You have sterile preservative free tobramycin stock solution with a concentration of 40mg/ml, as well as NaCl in crystalline form.

• Tobramycin MW=468 • E=0.07 • What is the amount of NaCl need to be added to turn

the solution isotonic • What is the amount of tobramycin stock solution

needed to be added.

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Answers need to be submitted by email or paper no longer than next week

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• The algebraic method:

– CL: Concentration of the initial commercial product (the product with the smallest concentration).

– VF: The desired final volume of the product.

– CH: Concentration of stock solution.

– X: Volume of stock solution that is needed to be added.

– CF: Concentration of the final desired pharmaceutical preparation.

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Diluting and Concentration

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• The algebraic method:

– We need to start with initial concentration CL, remove part of it VF-X, replace the removed part with the same amount of the stock solution CHX, then we will have the correct volume VF of the desired final concentration CF.

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𝑿 = 𝑉𝐹(𝐶𝐿 − 𝐶𝐹)

(𝐶𝐿 − 𝐶𝐻)

Diluting and Concentration

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Example

• A prescription for Hyrdrocortisone2% cream 30g.

• In the pharmacy we have a tube of Hydrocortisone1% cream 30g, and a tube of Hydrocortisone2.5% cream 30g.

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𝑿 = 𝑉𝐹(𝐶𝐿 − 𝐶𝐹)

(𝐶𝐿 − 𝐶𝐻)

𝑿 = 30(1% − 2%)

(1% − 2.5%)= 20g

20g of H-sone 2.5% +10g of H-sone 1% We have 30g of Hydrocortisone2%

This equation will work for all situations where you desire to dilute or concentrate a product and end up with the same

amount or volume at which you started.

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Homework

• Solve the previous problem if the prescriber is asking for a total quantity of 50g:

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Reconstitution Calculations

Assuming that the dry powder volume does not contribute to the final volume,

how many mls of the reconstituted solution must be used to obtain the

600,000IU of Penicillin G Na from original concentration of 1,000,000IU/5ml

1 × 106

5𝑚𝑙=6 × 105

𝑥 𝑚𝑙

𝑥 = 3𝑚𝑙

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Milliequivalent Calculations

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Example How many

milliequivalents of Ca ions are in a solution

containing 40mg/100mL

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• Intravenous infusion flow rate: – Drop factor: drops per milliliter.

– Number of drops per minute can be calculated:

– gtt/min =𝑚𝑙𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑡𝑜 𝑏𝑒 𝑖𝑛𝑓𝑢𝑠𝑒𝑑 𝑋 𝑑𝑟𝑜𝑝 𝑓𝑎𝑐𝑡𝑜𝑟

ℎ𝑜𝑢𝑟𝑠 𝑜𝑓 𝑎𝑑𝑚𝑖𝑛𝑖𝑠𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑋 60 min(1ℎ𝑟)

– The above formula can be simplified to:

𝑹 =𝑽𝑫

𝑻

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R= rate of iv infusion (gtt/min)

V= Total volume to be infused (ml)

D= drop factor (gtt/ml)

T= total time of infusion (min)

Injectable Medicines

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Example

• iv solution (1000ml) was started 8:00AM was scheduled to run for 12hrs.

• At 3:00PM it was found that 800ml remained.

• At what rate should the remaining fluid be regulated to complete the administration in the scheduled time.

• The iv settings is set to deliver 15 drops/ml.

Solution:

• Fluid remaining= 800ml • Time remaining= 5hrs or

5X60 = 300 mins • Number of drops per

min= 𝟖𝟎𝟎𝑿𝟏𝟓

𝟓𝑿𝟔𝟎= 𝟒𝟎𝒈𝒕𝒕/𝒎𝒊𝒏

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Example

• If 800ml are infused in 300min?

𝟖𝟎𝟎𝒎𝒍

𝟑𝟎𝟎𝒎𝒊𝒏=

𝒙 𝒎𝒍

𝟏 𝒎𝒊𝒏

→ 𝒙 = 𝟐. 𝟔𝟕𝒎𝒍

• If 15 drops are contained in 1ml how many drops are contained in 2.67ml?

𝟏𝟓 𝒈𝒕𝒕

𝟏 𝒎𝒍=

𝒙 𝒈𝒕𝒕

𝟐. 𝟔𝟕 𝒎𝒍

→ 𝒙 = 𝟒𝟎 𝒈𝒕𝒕

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Insulin Dosage

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Typ

es o

f In

sulin

Syr

inge

s

The strength of insulin is measured by units of activity/ml Syringes are calibrated according to the strength of insulin used

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Example:

• A patient is required to take 10 units of U-40 isophane insulin and 100 units of U-100 protamine zinc insulin.

• What volume (ml) of each type of insulin is needed to provide the required dose?

Solution: • U-40 insulin contains 40 units /ml. • U-100 insulin contains 100 units/ml.

𝟒𝟎 𝒖𝒏𝒊𝒕𝒔

𝟏 𝒎𝒍=

𝟏𝟎 𝒖𝒏𝒊𝒕𝒔

𝒙 𝒎𝒍

𝒙𝑼−𝟒𝟎 = 𝟎. 𝟐𝟓𝒎𝒍 𝒐𝒇 𝑼 − 𝟒𝟎

𝟏𝟎𝟎 𝒖𝒏𝒊𝒕𝒔

𝟏 𝒎𝒍

𝒙𝑼−𝟏𝟎𝟎 = 𝟏𝒎𝒍 𝒐𝒇 𝑼 − 𝟏𝟎𝟎

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Heparin Dosage

• The normal adult heparinizing dose is 20,000 to 40,000 units in 24 hrs.

• Heparin is usually ordered in units per hour.

• It can also be ordered to be infused at specific infusion rate of ml per hr.

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Example

• A heparin dose of 120units/hr/kg is ordered for a patient undergoing surgery.

• How many mls of an injection containing 5,000units/ml should be administered to the 220lb patient?

• Solution:

•𝟏𝟐𝟎 𝒖𝒏𝒊𝒕𝒔

𝟐.𝟐 𝒍𝒃=

𝒙 𝒖𝒏𝒊𝒕𝒔

𝟐𝟐𝟎 𝒍𝒃

𝒙 = 𝟏𝟐, 𝟎𝟎𝟎 𝒖𝒏𝒊𝒕𝒔

•𝟓𝟎𝟎𝟎 𝒖𝒏𝒊𝒕𝒔

𝟏 𝒎𝒍=

𝟏𝟐,𝟎𝟎𝟎 𝒖𝒏𝒊𝒕𝒔

𝒙 𝒎𝒍

𝒙 = 𝟐. 𝟒𝒎𝒍

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abahnassi@gmail.com

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Anas Bahnassi PhD RPh

Hospital Pharmacy

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