CALCULATIONS IN PHARMACOLOGY

Posology is a vital part of medical and pharmaceutical practice and study, not just for humans, but also for animals. It is the science of determining and understanding drug dosage, as based on research into a huge number of factors. To a limited or extensive degree, posology may be studied by anyone who wants to become a doctor, nurse, pharmacist, veterinarian, or pharmacologist.

Medications are great, and they have been valuable to the sum of veterinary and human medicine. They may cure some diseases completely, and they may greatly reduce symptoms of others. The issue of exactly what amount to give is one that must be carefully considered. Digitalis, for instance, can improve heart function, and it can kill people easily. Deciding how to give the right dose is thus extremely important, and those administering this drug need to know how to prescribe it appropriately. In order to write a prescription, Physician must have understanding about the units used in weighing and measuring the medicinal agents.

Weight: It is a measure of the gravitational force acting on the body. Weight is directly proportional to the body mass. The mass is constant everywhere and based on inertia where as weight varies slightly with altitude, temperature and pressure. The effects of these factors are not considered unless very precise weighing and large quantity are involved.

Measure: It is the determination of the volume or extent of a body. Temperature and pressure have pronounced effect, especially on gases and liquids. These factors are therefore considered when making precise measurements. For the quantification of weights and measures there are two systems used.

THE METRIC SYSTEM:

Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795. During this evolution the use of these systems has spread throughout the world. Multiples and submultiples of metric units are related by powers of ten and their names are formed with prefixes. This relationship is compatible with the decimal system of numbers and it contributes greatly to the convenience of metric units. In the early metric system there were two fundamental or base units, the metre for length and the gram for mass. The other units of length and mass, and all units of area, volume, and compound units such as density were derived from these two fundamental units.

BASIC UNITS OF THE METRIC SYSTEM

Meter: It is the unit of length upon which the other units of the metric system are based. One meter is equal to 1/40,000,000 of the earth’s polar circumference. One meter is equal to 39.37 inches. It is abbreviated as “m”.

Liter:  It is the basic unit of volume used to measure liquids. One liter is equal to the volume of one cubic decimeter of water at 4°C. It is abbreviated as “l”.

Gram: The gram is the basic unit of weight used to weigh solids. One gram is equal to the weight of one milliliter of distilled water at 4°C. It is abbreviated as “g or Gm”.

In 1944 the council on pharmacy and chemistry of the American Medical Association adopted the metric system exclusively. The advantage of the metric or decimal system, and its simplicity, brevity and its adoptively to every day need are now conceded universally. In many experimental procedures, including some in the pharmaceutical sciences, very small quantities (and occasionally very large) of the weight, length, volume, time or radioactivity are measured. To avoid the use of various numbers with many zero in such cases, the NIST recognized prefixes to be used to express fractions or multiple of the International System of Units, which was established in 1960 by the General Conference on Weights and Measures the recognized prefixes, which in used are adjoined to an appropriate unit (as, for example, in such quantities as nanogram, picomole, microcurie, microsecond, or, megavolt) are defined as under in table 1.

S.NO	FACTIONS	PREFIX	SYMBOL	MULTIPLE	PREFIX	SIMBLE
1	10-1	deci	d	10	deca	da
2	10-2	centi	c	102	hecto	h
3	10-3	milli	m	103	kilo	k
4	10-6	micro	µ	106	miga	M
5	10-9	nano	n	109	giga	G
6	10-12	pica	P	1012	tera	T
7	10-15	femto	F	1015	peta	P
8	10-18	atto	a	1018	exa	E

Table 1: Recognized prefixes with fractions and symbols

Some of the metric weights are listed in the table 2 below. The prefixes, which indicate multiples, are of Greek derivation: deka, 10; hector, 100; kilo,1000. Fractions of the units are expressed by Latin prefixes: deci, 1/10; centi, 1/100; milli, 1/1000.

S.NO	METRIC WEIGHT	EQUAL TO	EQUIVALENT WEIGHT
1	1 microgram   µg	=	0.000001g
2	1 milligram     mg	=	0.001g
3	1 centigram     cg	=	0.01g
4	1 decigram       dg	=	0.1g
5	1 gram               g	=	1g
6	1 decagram      dag	=	10g
7	1 hectogram     hg	=	100g
8	1 kilogram         kg	=	1000g

Table 2: Recognized prefixes with fractions and symbols                               

S.NO	UNIT	INCHES	MM	µM	NM	A
1	1 inch	1	25.4	25400	2.54×107	2.54×108
2	1mm	0.0394	1	1000	106	107
3	1µm	3.94×10-5	10-3	1	1000	10000
4	1nm	3.94×10-8	10-6	10-3	1	10
4	1A(Angstrom)	3.94×10-9	10-7	10-4	0.1	1

Table 3: Equivalent linear measurements

                                                               

S.NO	METRIC LEQUID MEASURES	EQUIVALENT
1	1 microliter(µL)	0.000001L
2	1 mililiter(mL)	0.001L
3	1 centiliter(cL)	0.01L
4	1 deciliter(dL)	0.1L
5	1 liter(L)	1L
6	1 dekaliter(dL)	10L
7	1 hectoliter(hL)	100L
8	1 kiloliter(kL)	1000L

Table 4: Equivalent Metric liquid measurements

THE ENGLISH SYSTEM

This system grew out of the creative way that people measured for themselves.  Familiar objects and parts of the body were used as measuring devices.  For example, people measured shorter distances on the ground with their feet. These measures had their origins in a variety of cultures –Babylonian, Egyptian, Roman, Anglo-Saxon, and Norman French. The ancient "digit," "palm," "span" and "cubic" units of length slowly lost preference to the length units "inch," "foot," and "yard."

Roman contributions include the use of 12 as a base number (the foot is divided into 12 inches) and the words from which we derive many of our present measurement unit names. For example, the 12 divisions of the Roman "pes," or foot were called unciae. Our words "inch" and "ounce" are both derived from that Latin word.

The "yard" as a measure of length can be traced back to early Saxon kings. They wore a sash or girdle around the waist that could be removed and used as a convenient measuring device. The word "yard" comes from the Saxon word "gird" meaning the circumference of a person’s waist.

In English system of measurement, avoirdupois and apothecary system of weight measurement are used in handling medicine. It must be emphasized that pharmacist may buy their drugs by avoirdupois weight.

Avoirdupois system: The word avoirdupois is from Anglo-Norman French aveir de peis literally "goods of weight". This term originally referred to a class of merchandise: aveir de peis, "goods of weight", things that were sold in bulk and were weighed on large steelyards or balances. There are two major theories regarding the origins of the avoirdupois system. The older theory is that it originated in France. A newer theory is that it is based on the weight system of Florence. The avoirdupois weight system is thought to have come into use in England circa 1300. It was originally used for weighing wool. In the early 14th century several other specialized weight systems were used, including Troy weights (used by goldsmiths) and the weight system of the Hanseatic League with a 16-ounce pound of 7200 grains and an 8-ounce mark. However, the main weight system, used for coinage and for everyday use, was based on the 12-ounce Saxon pound of 5400 grains, also known as the Tower pound. From the 14th century until late 16th century, the avoirdupois pound was also known as the wool pound or the avoirdupois wool pound. The basic unit of weight in the avoirdupois system is the grain (gr). The larger units are the ounce (oz) and the pound (lb).

Grain: A grain is a unit of measurement of mass that is nominally based upon the mass of a single seed of a cereal. From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definition of units of mass.

Ounce: It is a unit of mass with several definitions, the most commonly used of which are equal to approximately 28 grams. The ounce is used in a number of different systems, including various systems of mass that form part of the imperial and United States customary systems. Its size can vary from system to system. The most commonly used ounces today are the international avoirdupois ounce and the international troy ounce. The avoirdupois ounce is the most commonly used ounce today. It is defined to be one sixteenth of an avoirdupois pound which is equal to 7,000 grains. One ounce is therefore equal to 437.5 grains. On January 1, 2000, it ceased to be a legal unit of measure within the United Kingdom for economic, health, safety or administrative purposes, but remains a familiar unit, especially amongst older people. The troy ounce is equal to 480 grains. It is equal to exactly 31.1034768 grams. There are 12 troy ounces in the troy pound which is equal to 5760 grains.

Pound: The avoirdupois pound, also known as the wool pound, first came into general use. It was initially equal to 6992 troy grains. It is also equal to 16 ounces. During the reign of Queen Elizabeth, the avoirdupois pound was redefined as 7,000 grains.

The 1878 Act said that contracts worded in terms of metric units would be deemed by the courts to be made according to the Imperial units defined in the Act, and a table of metric equivalents was supplied so that the Imperial equivalents could be legally calculated. Thus defining, in UK law, metric units in terms of Imperial ones. The equivalence for the pound is given as 1 lb = 453.59265 g or 0.45359 kg, which would make the kilogram weigh approximately 2.2046213 lb. In 1883, it was determined jointly by the Standards Department of the Board of Trade and the Bureau International that 0.4535924277 kg was a better approximation, and this figure, rounded to 0.45359243 kg was given legal status by an Order in Council in May 1898. However in 1963 a new Weights and Measures Act reversed this relationship and the pound was defined for the first time as a mass equal to 0.45359237 kg to match the definition of the international pound agreed in 1959. To convert from the avoirdupois system to the metric system, one must know the conversion factors, which are 1 gr = 65 mg, 1 g = 15.4 gr, 1 oz = 28.4 g and 1 kg = 2.2 lb.

Apothecary system: The apothecary system is one of the oldest systems of measurement used when calculating drug dosages. This system originated in Greece, and eventually made its way to England where it was used during the late 1600s, being brought by the colonist to America where it evolved and became a modified system of trading measurements. While there has been a definite trend towards using the metric system, some physicians still use the apothecary system when prescribing certain medications such as aspirin and digitalis. The basic unit of measurement used for weight in the apothecary system is the grain (gr). One pound contains 12 ounces (℥), an ounce contains 8 drachms, and a drachm (ʒ) contains 3 scruples or 60 grains. Care should be taken not to confuse the ounce and pound of the apothecary system with their counterparts in the avoirdupois system. This exact form of the system was used in the United Kingdom; in some of its former colonies it survived well into the 20th century. The apothecaries' system of measures is a similar system of volume units based on the fluid ounce. For a long time, medical recipes were written in Latin, often using special symbols to denote weights and measures. The pound, ounce and grain being identical to the avoirdupois pound, ounce and grain. In the United Kingdom, a reform in 1824 made the avoirdupois pound the primary weight unit but this had no effect on apothecaries' weights. However, the Medicinal Act of 1858 apothecary system was completely abolished in favor of the standard Avoirdupois system. In the United States, the apothecary system remained official until it was abolished in 1971. This system also contains units for fluid measurement. The basic unit of measurement used for volume is the minim (m). A minim is equal to the quantity of water in a drop that also weights 1 grain. A fluid dram is equivalent to 60 minims and a fluid ounce is equal to eight fluid drams and 16 fluid ounces in one pint; two pints equals one quart; and, there are four quarts in one gallon.