Pharmaceutical calculation Dr Hayder B Sahib Pharmaceutical calculations

Pharmaceutical calculation Dr. Hayder B Sahib

• Pharmaceutical calculations is the area of study that applies the basic principles of mathematics to the preparation and safe and effective use of pharmaceuticals. • Mathematically, pharmacy : The use of calculations in pharmacy is varied and broad-based. It includes (1) calculations performed by pharmacists in traditional as well as in specialized practice settings and within operational and research areas in industry, (2) Academia and government.

• The scope of pharmaceutical calculations includes computations related to: • (1) Chemical and physical properties of drug substances and pharmaceutical ingredients • (2) Biological activity and rates of drug absorption, physical distribution, metabolism and excretion (pharmacokinetics) • (3) Statistical data from basic research and clinical drug studies

• (4) Pharmaceutical product development and formulation • (5) Prescriptions and medication orders including drug dosage, dosage regimens, and patient compliance • (6) Pharmacoeconomics; and other areas. • For each of these areas, there is a unique body of knowledge. • Some areas are foundational whereas others are more specialized, constituting a distinct field of study.

• In community pharmacies, pharmacists receive, fill, and dispense prescriptions, and provide relevant drug information to ensure their safe and effective use. • Prescriptions may call for prefabricated pharmaceutical products manufactured in industry, or, they may call for individual components to be weighed or measured by the pharmacist and compounded into a finished product. • In hospitals and other institutional settings, medication orders are entered on patients’ charts. • Prescriptions and medication orders may be handwritten by authorized health professionals or transmitted electronically.

• In the preparation of pharmaceuticals, both medicinal and nonmedicinal materials are used. • The medicinal components (active therapeutic ingredients or ATIs) provide the benefit desired. • The non-medicinal ( pharmaceutical ingredients) are included in a formulation to produce the desired pharmaceutical qualities, as physical form, chemical and physical stability, rate of drug release, appearance, and taste. • Whether a pharmaceutical product is produced in the industrial setting or prepared in a community or institutional pharmacy, pharmacists engage in calculations to achieve standards of quality. The difference is one of scale. In pharmacies, relatively small quantities of medications are prepared and dispensed for specific patients.

• In industry, large-scale production is designed to meet the requirements of pharmacies and their patients on a national and even international basis. • The latter may involve the production of hundreds of thousands or even millions of dosage units of a specific drug product during a single production cycle. • The preparation of the various dosage forms and drug delivery systems containing carefully calculated, measured, verified, and labeled quantities of ingredients enables accurate dosage administration.

A Step-Wise Approach Toward Pharmaceutical Calculations • Success in performing pharmaceutical calculations is based on: • • an understanding of the purpose or goal of the problem; an assessment of the mathematics process required to reach the goal; and, implementation of the correct arithmetic manipulations. • For many pharmacy students, particularly those without pharmacy experience, difficulty arises when the purpose or goal of a problem is not completely understood.

• Step 1. Take the time necessary to carefully read and thoughtfully consider the problem prior to engaging in computations. An understanding of the purpose or goal of the problem and the types of calculations that are required will provide the needed direction and confidence. • Step 2. Estimate the dimension of the answer in both quantity and units of measure (e. g. , milligrams) to satisfy the requirements of the problem. • Step 3. Perform the necessary calculations using the appropriate method both for efficiency and understanding. For some, this might require a step-wise approach whereas others may be capable of combining several arithmetic steps into one. Mathematical equations should be used only after the underlying principles of the equation are understood.

• Step 4. Before assuming that an answer is correct, the problem should be read again and all calculations checked. • In pharmacy practice, pharmacists are encouraged to have a professional colleague check all calculations prior to completing and dispensing a prescription or medication order. • Further, if the process involves components to be weighed or measured, these procedures should be double-checked as well. • Step 5. Consider the reasonableness of the answer in terms of the numerical value, including the proper position of a decimal point, and the units of measure. Common and Decimal Fractions

• Common fractions • are portions of a whole, expressed at 1⁄3, 7⁄8, and so forth. They are used only rarely in pharmacy calculations nowadays. • It is recalled, that when adding or subtracting fractions, the use of a common denominator is required. • The process of multiplying and dividing with fractions is recalled by the following examples.

• Examples: • If the adult dose of a medication is 2 tea spoonsful (tsp. ), calculate the dose for a child if it is 1⁄4 of the adult dose. • 1/4 x 2 tsp. /1= 2/4= 1/2 tsp. , answer • If a child’s dose of a cough syrup is 3⁄4 teaspoonful and represents 1⁄4 of the adult dose, calculate the corresponding adult dose. • 3/4 tsp/ ¼= 3/4 tsp. x 4/1=3 x 4/4 x 1 tsp. = 12/ 4 tsp. = 3 tsp. , answer • NOTE: When common fractions appear in a calculations problem, it is often best to convert them to decimal fractions before solving.

• 1/ 8 = 1 /8 = 0. 125. • To convert a decimal fraction to a common fraction, express the decimal fraction as a ratio and reduce. • Thus, 0. 25 = 25/ 100=1/4 or 1⁄4. • The term Percent and its corresponding sign, %, mean ‘‘in a hundred. ’’ So, 50 Percent (50%) means 50 parts in each one hundred of the same item. • Exponential Notation • Many physical and chemical measurements deal with either very large or very small numbers. Because it often is difficult to handle numbers of such magnitude in performing even the simplest arithmetic operations, it is best to use exponential notation or powers of 10 to express them. • Thus, we may express 121 as 1. 21 x 102, 1210 as 1. 21 x 103, and 1, 210, 000 as 1. 21 x 106.

• When numbers are written in this manner, the first part is called the coefficient, customarily written with one figure to the left of the decimal point. • The second part is the exponential factor or power of 10. • In the multiplication of exponentials, the exponents are added. • For example, 102 x 104 =106. In the multiplication of numbers that are expressed in exponential form, the coefficients are multiplied in the usual manner, and then this product is multiplied by the power of 10 found by algebraically adding the exponents.

• Examples: • If 3 tablets contain 975 milligrams of aspirin, how many milligrams should be contained in 12 tablets? 3 (tablets) / 12 (tablets) =975 (milligrams)/ x (milligrams) = 3900 milligrams, answer. • If 3 tablets contain 975 milligrams of aspirin, how many tablets should contain 3900 milligrams? • 3 (tablets)/ x (tablets)= 975 (milligrams)/ 3900 (milligrams)= 12 tablets, answer. • If 12 tablets contain 3900 milligrams of aspirin, how many milligrams should 3 tablets contain? • 12 (tablets)/ 3 (tablets)= 3900 (milligrams)/ x (milligrams)= 975 milligrams, answer. • If 12 tablets contain 3900 milligrams of aspirin, how many tablets should contain 975 milligrams? • tablets _ 3 tablets, answer.