Pharmacy Class Measurements and Calculations

Pharmaceutical Calculation Techniques and Terminologies

• The presentation covers pharmaceutical calculations and terminology, presented by Yibekal M, specializing in epidemiology.
• The date of the presentation is 12/8/2024.

Emulsion

• An emulsion is a dispersion where a liquid phase is distributed throughout another immiscible liquid phase (vehicle).
• Emulsions consist of at least two immiscible liquid phases.
• The dispersed phase is the internal phase, and the dispersion medium is the external or continuous phase.
• Advantages of emulsions include increased drug bioavailability (by administrating hydrophobic drugs in a dissolved state) and increased drug stability & prolonged drug action.
• Oil-in-water (o/w) emulsions have the aqueous phase comprising over 45% of the total weight, and use a hydrophilic emulsifier.
• Water-in-oil (w/o) emulsions have the oil phase as the continuous phase, predominantly for external use.
• Multiple emulsions contain droplets of another emulsion (e.g., w/o/w, o/w/o), relevant for delayed/sustained drug delivery systems.
• Microemulsions are visually homogeneous, isotropic systems with low viscosity.

Semisolid Dosage Forms

• Semisolid dosage forms, such as ointments, creams, gels, pastes, and lotions, can change shape upon force application.
• They are used for topical or systemic drug action.
• Topical applications can target local effects or systemic absorption.

Ointments

• Ointments are semisolid preparations for external application to skin or mucous membranes (medicated or non-medicated).
• They can act as emollients, protective barriers, or vehicles for medication incorporation.
• Ointment bases are categorized into oleaginous (hydrocarbon), absorption, water-removable, and water-soluble types.

Oleaginous Bases

• Oleaginous (hydrocarbon) bases have an emollient effect, protect against moisture loss, are greasy, and hard to wash off.
• Examples include petrolatum and waxes.

Absorption Bases

• Absorption bases are of two types, either permitting aqueous solutions or resulting in W/O emulsions, like hydrophilic petrolatum.

Water-Removable Bases

• Water-removable bases (creams) are easily washed from the skin.
• They are used as emollients and are oil-in-water emulsions.
• Examples include hydrophilic ointment and vanishing cream.

Water-Soluble Bases

• Water-soluble bases don't have oleaginous components and absorb water to the point of solubility.
• Examples include polyethylene glycol (PEG) ointment.

Creams

• Creams are semisolid dosage forms with one or more drug substances dissolved or dispersed in o/w or w/o emulsion bases.
• Creams are typically non-washable or washable.
• Creams are easier to spread and remove compared to ointments.

Gels

• Gels are semisolid systems with dispersions of small or large molecules in an aqueous liquid vehicle rendered jelly-like by a gelling agent.

Lotions

• Lotions are low- to medium-viscosity preparations for topical application to unbroken skin.
• They are liquid suspensions or emulsions of dispersed solid or liquid materials in an aqueous vehicle.
• Most lotions are oil-in-water (o/w) emulsions; water-in-oil emulsions (w/o) can be used too.

Pastes

• Pastes are semisolid dosage forms with a large proportion of solid components.
• Pastes are thicker and stiffer than other semisolid dosage forms.
• Pastes typically include solid particles (over 25%) dispersed in oleaginous ointments (like petrolatum).

Suppositories

• Suppositories are solid or semisolid masses for insertion into body orifices (rectum, urethra).
• They soften, melt, or dissolve, exerting local or systemic effects.
• Types include rectal suppositories (cylindrical and tapered).
• Vaginal suppositories are oval, typically weighing around 5 g.
• Urethral suppositories (bougies) are also used.
• Suppository bases should be physically and chemically stable; non-irritating, nontoxic, non-sensitizing, and physiologically inert. They should remain solid at room temperature but soften, melt, or dissolve readily at body temperature(melting temperature ranges for different types of bases are mentioned). -Cocoa butter as an example is shown to melt just below body temperature.
• Water-soluble and water-miscible bases have slower softening compared to cocoa butter.
• Bases such as glycerinated gelatin and polyethylene glycols are listed as examples of water-soluble and water-miscible bases.
• Foam is a liquid-based dispersion of gas dispersed as thin films.

Aerosols

• Aerosols are colloidal dispersions of liquids or solids in gases.
• Some aerosol emissions are for inhalation and others are for topical skin or mucous membrane application.

Measuring Pharmaceutical Quantities

Mathematical Review

• A fraction indicates a portion of a whole number, consisting of a numerator (top) and denominator (bottom).
• A proper fraction has a numerator smaller than its denominator, while an improper fraction has a numerator greater than or equal to its denominator.
• Accuracy represents the closeness of a measurement to the desired or actual quantity, while precision represents its reproducibility.

Accuracy & Precision

• Accuracy is the measure of how close a measurement is to the true value.
• Precision is the measure of how close repeated measurements are to each other.
• Pharmaceutical measurements require both accuracy and precision
• Examples include measurement discrepancies related to quantities to be weighed (e.g., 125 mg).

Significant Figures

• Rule #1: Digits other than zero are significant
• Rule #2: A zero between digits is significant
• Rule #3: Final zeros after a decimal point are significant
• Rule #4: Zeros used only to show the location of the decimal point are not significant

Ratio & Ratio Strength

• Ratio is the relative amount of two quantities (e.g., one to the other).
• A colon separates the numbers in a ratio.
• Ratios are used in pharmacy to express drug concentration, or weight/dose of a drug given in a delivery unit or volume.

Exercise Problems

• A variety of practice problems (using different drugs and dosages) are provided (cimetidine, metoclopramide & dicloxacillin).

Proportion

• Proportion represents the equality between two ratios.
• Proportions can be expressed in three standard forms (a:b = c:d or a/b = c/d).
• The extreme values are represented by "a" and "d".
• The mean values are represented by "b" and "c".
• Example exercise problems to demonstrate ratios and proportions involving specific drugs are provided.

Percent

• Percent is a type of ratio representing per hundred.
• To change a percent to a fraction, remove the percentage sign and place the number over 100, then reduce to the lowest terms.
• To change a percent to a decimal, remove the percentage sign and divide by 100.
• To convert a decimal into percentage, multiply the decimal value by 100 and add the percentage symbol.
• Examples demonstrating changing ratios, decimals, and percentages into one another are shown.
• Three different ways to demonstrate calculation of fractions.

System of Measurement Used in Pharmacy

• Pharmacy measurements require accurate weight and volume measurement.
• Measurement systems include Metric, Apothecary, Household, and Avoirdupois systems.
• Basic units for each of these measurement systems are given.

Metric System (International System of Units)

• Introduced in France in the late 1790s, it uses multiples of 10 to define various ranges of quantities.
• Its fundamental units include meters (length), kilograms (mass), and liters (volume).
• Prefixes are added to the base units (e.g., milli-, centi-, kilo-) to indicate subdivisions or multiples of 10. Units such as atto, femto, pico, nano, micro, milli, centi and deci and deca, hecto, kilo, myria, mega, giga, tera , peta and exa are included with their numerical value counterparts.

Guidelines for the Correct Use of the SI

• General guidelines for expressing units in scientific notation
• Periods are usually not added after unit symbols except at the end of a sentence or in headings

Units - Measurement, Weight, and Volume

• Measures of length are given.
• Measures of volume are given.

Exercise Problems

• A collection of practice problems showcasing the conversion between various measurement systems is provided (e.g., liters and milliliters, grams and kilograms).

Measure of Weight

• The basic unit of weight in the metric system is the gram (g).
• A gram is approximately equivalent to the weight of 1 cubic centimeter (cc) or 1 milliliter (mL) of water at 4°C
• Weight conversion tables are presented for basic units: kilogram (kg), dekagram (dag), hectogram (hg), decigram (dg), centigram (cg), milligram (mg), microgram (mcg).

Example Problems

• Various examples demonstrating practical calculations using different weight measurement conversions are included

Sensitivity and Capacity of Balances in Pharmacy

• Two main types of balances in prescription settings are Class A and B.
• Sensitivity is the smallest discernible weight change, and sensitivity requirements (SR) vary between classes.
• Capacity is the maximum measurable weight.

Percentage of Error

• Defined as the maximum potential error multiplied by 100 and divided by the desired amount.
• It has implications in weighing or measuring liquid quantities (e.g., volume measurement errors)

Example Calculation Problems

• Different example problems demonstrate calculations of percentage of error for different contexts (such as volume and weight measurements).

Apothecary System of Measurement

• Traditional system used for medication measurement in the past.
• Basic units include grain (gr), dram (dr), and ounce (oz).
• Conversion tables for apothecary and metric systems are presented.

Household System of Measurement

• Commonly used at home, without precise measuring equipment.
• Household units include teaspoonfuls (tsp), dessertspoonfuls (dtsp), tablespoonfuls (tbsp), ounces (oz), wine glasses, coffee cups, glasses, and quarts (qt).
• Corresponding values in the milliliters (ml) are listed

Avoirdupois System of Measurement

• The grain measurements are identical in the Avoirdupois and Apothecary systems.
• The units ounce (oz) and pound (lb) differ in the number of grains between these two systems.
• Conversion tables for Avoirdupois measurements are provided (e.g., kg to lb, oz to gr, gr to mcg).

Density, Specific Gravity, and Specific Volume

• Density is mass per unit volume (e.g., g/cc, g/mL)
• Specific gravity is the ratio of the weight of a substance to the weight of an equal volume of a standard (usually water).
• Specific volume is the reciprocal of specific gravity.
• Water is the standard for liquids and solids; Hydrogen is the standard for gases.
• Units and typical values for density, specific gravity, specific volume are discussed as well as corresponding example problems.

Percentage Preparations

• Percentage preparations express the amount of active and inactive ingredients in a preparation in terms of percentage concentrations.
• Types include weight-in-volume, volume-in-volume, and weight-in-weight percentages

Special Considerations in Percentage Calculations for Percentage Preparations

• The nature of the ingredients determines the calculation basis.

• Powdered substances dissolved or suspended in liquids are calculated on a weight-in-volume basis.

• Mixing powdered substances and/or liquid ingredients with a solid or semisolids is calculated on a weight-in-weight basis

• Liquid components in liquid preparations are calculated on a volume-in-volume basis

Percentage Preparations in Practice

• Percentage concentrations in labeling are restricted to cases where the active therapeutic agent (ATI) dosage is not specific.

Examples and Calculations of Percentage Preparations

• The presentation includes multiple exercise problems covering different types of percentage preparations and common units in pharmacy.

Ratio Strength Solutions

• Concentration expressions for weak solutions (or solids) are a different way of expressing percentage strengths.
• Percentage strength is a part per hundred ratio strength, whereby percentage & ratio strength conversion can be achieved via proportion.

Parts per Million (PPM) and Parts per Billion (PPB)

• PPM and PPB values are dimensionless & used to express the concentration of very dilute solutions by representing the ratio of 1 part substance per 1 million or 1 billion parts of the total mixture, respectively (e.g., fluoride level additions to drinking water).

Concentrations Based on Moles and Equivalents

• Molecular weights and moles of a compound are used in the comparison of two or more compounds.
• Molecular weight is the weight(in grams) of 1 mole (mol) of a compound.
• Equivalent weight is a compound's molecular weight divided by the number of valence or ionic charges in solution, accounting for the chemical activity of an electrolyte.
• One equivalent (Eq) is the number of grams in 1 mole of a compound divided by its valence.
• A milliequivalent (mEq) represents 1/1000 of its gram equivalent weight, in milligrams.
• Example illustrating how to calculate the concentration of a solution, in percent w/v, that contains 2 mEq of Potassium Chloride per milliliter is included.
• Values for common ions are provided in tables

Molarity, Normality, and Molality

• Molarity (M) is the moles of solute per liter of solution.
• Normality (N) is the gram equivalent weight of solute per liter of solution.
• Molality (m) is the moles of solute per kilogram of solvent.

International Units (IU)

• Units are amounts of medication with different sizes for each drug, standardized internationally.
• Examples use Vitamins, Insulin, Heparin and Penicillin.
• Concentrations are commonly (e.g., 100 units/mL or 500 insulin units per milliliter of solution or suspension)

Dilution and Concentration

• Dilution involves decreasing the concentration by adding a diluent.
• Concentration increases by adding more active ingredient or by evaporating the diluent.
• Problems involving dilution and concentration can be solved via the relationship of quantity1 × concentration1 = quantity2 × concentration2 (e.g., stock solution dilution).
• Percentage strengths of substances can be calculated via the equation above (e.g., dilute a 50% w/v stock solution to make 200 mL of a 5%w/v solution).
• Problems related to using different weights of multiple solutions to create a new solution (e.g., combining multiple preparations of Zn oxide ointment to create a 10% ointment) can be solved.

Enlarging and Reducing Formulas

• The need to prepare different amounts of a pharmaceutical product depends on the setting (community pharmacy, hospital, outsourcing, or manufacturing).
• Methods for expanding or reducing formulas (e.g. ratio or proportions, factor method) can be easily illustrated via example problems.

Calculating Doses

• Dosage calculations are often related to particular patient weight and age.
• Formulas based on adult dose and patient weight & age, can be used (Clark's rule, Young's rule, and Fried's rule).
• Body surface area (BSA) and adult dosage can also help determine the needed dosage for a child.

Pharmaceutical Equipment

• Various pieces of pharmaceutical equipment (e.g., mortars/pestles, water baths, beam/digital balances, spatulas, watch glasses, measuring cylinders, conical flasks, beakers, pipettes, droppers, electronic mortar & pestle, greasy proof paper & amber dispensing bottles, ointment slabs & ointment jars) and their uses are described.