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Calculations in Pharmacology

By: Pharma Tips | Views: 6433 | Date: 21-Aug-2013

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.

Calculationsin Pharmacology

Posology is a vital part ofmedical and pharmaceutical practice and study, not just for humans, but alsofor animals. It is the science of determining and understanding drug dosage, asbased 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.

Medicationsare great, and they have been valuable to the sum of veterinary and humanmedicine. They may cure some diseases completely, and they may greatly reducesymptoms of others. The issue of exactly what amount to give is one that mustbe carefully considered. Digitalis, for instance, can improve heart function,and it can kill people easily. Deciding how to give the right dose is thusextremely important, and those administering this drug need to know how toprescribe it appropriately. In order to write a prescription, Physician musthave understanding about the units used in weighing and measuring the medicinalagents.

Weight: It is a measure of the gravitationalforce acting on the body. Weight is directly proportional to the body mass. Themass is constant everywhere and based on inertia where as weight variesslightly with altitude, temperature and pressure. The effects of these factorsare not considered unless very precise weighing and large quantity areinvolved.

Measure: It is the determination of the volumeor extent of a body. Temperature and pressure have pronounced effect,especially on gases and liquids. These factors are therefore considered whenmaking precise measurements. For the quantification of weights and measuresthere are two systems used.

THE METRIC SYSTEM:
Metricsystems of units have evolved since the adoption of the first well-definedsystem in France in 1795. During this evolution the use of these systems hasspread throughout the world. Multiples and submultiples of metric units arerelated by powers of ten and their names are formed with prefixes. Thisrelationship is compatible with the decimal system of numbers and itcontributes greatly to the convenience of metric units. In the early metricsystem there were two fundamental or base units, the metre for length and thegram 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 twofundamental units.

BASIC UNITS OF THEMETRIC SYSTEM
Meter: It is the unit of length upon whichthe other units of the metric system are based. One meter is equal to1/40,000,000 of the earth’s polar circumference. One meter is equal to 39.37inches. It is abbreviated as “m”.

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

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

In 1944 the council on pharmacy andchemistry of the American Medical Association adopted the metric systemexclusively. The advantage of the metric or decimal system, and its simplicity,brevity and its adoptively to every day need are now conceded universally. Inmany 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 numberswith many zero in such cases, the NIST recognized prefixes to be used toexpress fractions or multiple of the International System of Units, which wasestablished in 1960 by the General Conference on Weights and Measures therecognized prefixes, which in used are adjoined to an appropriate unit (as, forexample, 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: Recognizedprefixes with fractions and symbols

Some of the metric weights are listedin the table 2 below. The prefixes, which indicate multiples, are of Greekderivation: deka, 10; hector, 100; kilo,1000. Fractions of the units areexpressed 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: Recognizedprefixes 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: Equivalentlinear 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
Thissystem 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 slowlylost preference to the length units "inch," "foot," and"yard."

Romancontributions include the use of 12 as a base number (the foot is divided into12 inches) and the words from which we derive many of our present measurementunit names. For example, the 12 divisions of the Roman "pes," or footwere called unciae. Our words "inch" and "ounce" are bothderived from that Latin word.

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

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

Avoirdupois system: Theword avoirdupois is from Anglo-Norman French aveir de peisliterally "goods of weight". This term originally referred to a classof merchandise: aveir de peis, "goods of weight", things thatwere sold in bulk and were weighed on large steelyards or balances. There aretwo major theories regarding the origins of the avoirdupois system. The oldertheory is that it originated in France. A newer theory is that it is based onthe weight system of Florence. The avoirdupois weight system is thought to havecome 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 theHanseatic 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, wasbased on the 12-ounce Saxon pound of 5400 grains, also known as the Towerpound. From the 14th century until late 16th century, the avoirdupois pound wasalso known as the wool pound or the avoirdupois wool pound. The basic unit ofweight 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 massthat is nominally based upon the mass of a single seed of a cereal. From theBronze Age into the Renaissance the average masses of wheat and barley grainswere part of the legal definition of units of mass.

Ounce: It isa unit of mass with several definitions, the most commonly used of which areequal to approximately 28 grams. The ounce is used in a number of differentsystems, including various systems of mass that form part of the imperial andUnited States customary systems. Its size can vary from system to system. Themost commonly used ounces today are the international avoirdupois ounce and theinternational troy ounce. The avoirdupois ounce is the most commonly used ouncetoday. It is defined to be one sixteenth of an avoirdupois pound which is equalto 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 foreconomic, health, safety or administrative purposes, but remains a familiarunit, especially amongst older people. The troy ounce is equal to 480 grains.It is equal to exactly 31.1034768 grams. There are 12 troy ouncesin the troy pound which is equal to 5760 grains.

Pound: The avoirdupois pound, also known asthe wool pound, first came into general use. It was initially equal to 6992troy grains. It is also equal to 16 ounces. During the reign of QueenElizabeth, the avoirdupois pound was redefined as 7,000 grains.
The1878 Act said that contracts worded in terms of metric units would be deemed bythe courts to be made according to the Imperial units defined in the Act, and atable of metric equivalents was supplied so that the Imperial equivalents couldbe legally calculated. Thus defining, in UK law, metric units in terms ofImperial ones. The equivalence for the pound is given as 1 lb =453.59265 g or 0.45359 kg, which would make the kilogram weighapproximately 2.2046213 lb. In 1883, it was determined jointly by theStandards Department of the Board of Trade and the Bureau International that0.4535924277 kg was a better approximation, and this figure, rounded to0.45359243 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 andthe pound was defined for the first time as a mass equal to 0.45359237 kgto match the definition of the international pound agreed in 1959. To convertfrom the avoirdupois system to the metric system, one must know the conversionfactors, 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 theoldest systems of measurement used when calculating drug dosages. This systemoriginated in Greece, and eventually made its way to England where it was usedduring the late 1600s, being brought by the colonist to America where itevolved and became a modified system of trading measurements. While there hasbeen a definite trend towards using the metric system, some physicians stilluse the apothecary system when prescribing certain medications such as aspirinand digitalis. The basic unit of measurement used for weight in the apothecarysystem 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 apothecarysystem with their counterparts in the avoirdupois system. This exact form ofthe system was used in the United Kingdom; in some of its former colonies itsurvived well into the 20th century. The apothecaries' system of measures is asimilar system of volume units based on the fluid ounce. For a long time,medical recipes were written in Latin, often using special symbols to denoteweights and measures. The pound, ounce and grain being identical to the avoirdupoispound, ounce and grain. In the United Kingdom, a reform in 1824 made the avoirdupoispound the primary weight unit but this had no effect on apothecaries' weights.However, the Medicinal Act of 1858 apothecary system was completely abolishedin favor of the standard Avoirdupois system. In the United States, theapothecary system remained official until it was abolished in 1971. This systemalso contains units for fluid measurement. The basic unit of measurement usedfor volume is the minim (m). A minimis equal to the quantity of water in a drop that also weights 1 grain. A fluid dram is equivalent to 60 minimsand a fluid ounce is equal to eightfluid drams and 16 fluid ounces in one pint;two pints equals one quart; and,there are four quarts in one gallon.
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