MATHS IN MEDICINEINCREDIBLE MATHS HUNTERS

The aim of this project was to discover how maths plays a major role in the world of technology and health. maths has been a part of almost all the tasks that we do from shopping to sleeping. In the daily life of health, we often come across situations when calculations become a major aspect. in the medicinal world we often find doctors and nurses using maths for calculating dosages, in CAT scans, in medicinal surveys,etc. group I explores this area of mathematics and ventures into the complicated world of maths in medicines. Apart from this Group I makes an attempt to explore the other side of the medicinal world.

AIM

Aristotle defined mathematics as: The science of quantity. It is said that Mathematics is the gate and key of the Science and therefore it cant be denied that Mathematics is a Science of all Sciences and art of all arts.Medicine is the applied science or practice of the diagnosis, treatment, and prevention of disease. Medicine has been used to diagnose and cure diseases since prehistoric times. 

INTRODUCTION

Both doctors and nurses use maths every day while providing health care for people around the world.  Doctors and nurses use math when they write prescriptions or administer medication.  Medical professionals use math when drawing up statistical graphs of epidemics or success rates of treatments.  Math applies to x-rays, mri  and CAT scans.  Numbers provide an abundance of information for medical professionals.  The careful logical reasoning that is necessary for the study of mathematics is an essential element of medical reasoning. 

INTRODUCTION

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary. Simple shapes can be described by basic geometry objects such as a set of two or more points, a line , a curve, a plane, a plane figure (e.g. square or circle), or a solid figure (e.g.cube or sphere).

MATHEMATICAL SHAPES

Medicines are identified on the basis of their imprint, shape or color. Some common shapes of medicines and their examples include:1. Capsule: Acebutolol, Antioxidant Formula, B Complex Softgel2. Round: B Complex with B12, Biotin 300mcg, Calcium Gluconate3. Hexagon: Acidophilus Captab, B Complex and C 4. Rectangle: Abilify Oral, Alprazolam Oral, Calcet Oral5. Pentagon: Ativan Oral, Avandia Oral, Cimetidine Oral

MATHEMATICAL SHAPES

Number System• Numbers play an important role in mathematics. There

are some particular types of numbers. Numbers can be classified into sets, called number systems. 

• The counting numbers are called natural numbers. Thus, N = {1, 2, 3, 4, 5, .....} is the set of all natural numbers.

• All natural numbers together with 0 (zero) form the set W of all whole numbers. Thus, W = {0, 1, 2, 3, 4, 5, ....} is the set of all whole numbers.

Number System in Medicines The production of medicines at a global scale is

huge. And therefore clearly the number system helps us to count the number of medicines manufactured each year, month or week.

For example: In India, in 2002, over 20,000 registered drug manufacturers in India sold $9 billion worth of formulations and bulk drugs. 

The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogramMass is used to determine the mass contained in various types of drugs.

MASS

WEIGHTThe weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton. Density is mass/volume. The concept of weight is used to find the weight of various liquids, drugs, injections ,etcThe weight of a Unit will vary from drug to drug; for example, in penicillin, which is an antibiotic, a substance which kills bacteria, the ability of the antibiotic is measured by it's power to kill bacteria.

Volume• The bodies occupying space are called

solids.• The space occupied by a solid body is

called its volume. The units of volume are cubic cm or cubic meters.

Volume in Medicines’

The volume of medicines is calculated in order to calculate the number of tablets that a prescription bottle will able to contain.

Volume in Medicines Pharmaceutical companies calculate the

volume of the medicines in order to prescribe the appropriate dosages for the patients. Thus, dosages are prescribed on the basis of volume and the age group of patients.

Volume in Medicines Pharmaceutical companies calculate

the volume of medicines in order to calculate the size of each cavity of the medicinal strip.

Decimals and Medicine

Most drug dosages are measured by weight in grams, milligrams or micrograms; however certain special drugs have other metric units that measure properties other than weightRules for Writing Drug Dosage Orders in the Metric System:1, We should always use decimals instead of fractions. 

2,When writing decimals that are smaller than 1, we should always put a leading zero before the decimal point. 

Fractions A fraction is a part of a whole.

Mathematically, we define fractions as the numbers of the form a/b, where a and b are whole numbers and b is not equal to 0.

Fractions in Medicines• Blood is full of a number of things. There are

the red cells, there are white cells, platelets, amber fluid (plasma), which contains different components, some already being used in medicine, others still in the research stage. These components are separated into fractions and are therefore called blood fractions.

LINEAR EQUATIONS AND MEDICINE

An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation in one variable.  Such an equation has only one solution. A solution is also called the 'root' of the given equations It can be used in the field of mathematics as often when doctors forget any dosage, the nurse forget the no. of medicines', it can be used effectively.

Ratio and Proportion• The ratio of two quantities a and b of the

same kind and in the same units is the fraction a/b.

• An equality of two ratios is called proportion. If a:b = c:d, then we say that a, b, c, d are in proportion and we write a:b::c:d.

Ratio and Proportion in Medicine

Nurses also use ratios and proportions when administering medication.  Nurses need to know how much medicine a patient needs depending on their weight.

Drug calculation formula for ratio/proportion: Dose Available = Dose OrderedVolume Available Volume Ordered

COMPOUND INTEREST

Compound interest is interest calculated on the principal amount invested, which is then added to the principal amount, and compounded again. Compound interest can be earned daily, weekly, monthly or yearly. Generally the more times an amount is compounded, the more money you can make. It is used in medicine as there are loans taken to compensate medical charges and so on.

Percentage Out of 100 equal parts, each part is known

as its hundredth part. By a certain percentage, we mean that

many hundredth. We denote x per cent by x%.

Thus x%= x/hundredths= x/100

Percentage in Medicines Percentage is used for a number of

reasons in the medical field: • It is used to depict an increase or decrease in the

manufacture of drugs or medicines in the medical field.

• Percentage is also used to depict the increase and decrease in the price of medicines.

• Percentage is also used to depict the percentage of medicines obtained from some source.

PROFIT AND LOSS

A financial statement that summarizes the revenues, costs and expenses incurred by a hospital during a specific period of time - usually a fiscal quarter or year. These records provide information that shows the ability of a hospital to generate profit by increasing revenue and reducing costs. The P&L statement is also known as a "statement of profit and loss", an "income statement" or an "income and expense statement".

STATISTICS

Statistics is the science of learning from data, and of measuring, controlling, and communicating uncertainty; and it thereby provides the navigation essential for controlling the course of scientific and societal advances

STATIST

ICS

PIE CHART

Pie charts are useful to compare different parts of a whole amount.  They are often used to present financial information.  E.g. A company's expenditure can be shown to be the sum of its parts including different expense categories such as salaries, borrowing interest, taxation and general running costs (i.e. rent, electricity, heating etc).A pie chart is a circular chart in which the circle is divided into sectors.  Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set.

STATIST

ICS

PIE CHART

No. of vaccines

2 months4 months6 months 8 moths10 months

STATIST

ICS

PIE CHARTSales

GREECEFRANCEAUSTRALIASPAINITALYFINALAND

STATIST

ICS

PIE CHARTSale of medicines

oralantidiabetics

ace inhilitators

antibiotics

systematic anti-histamines

Bar Graph• A bar graph is a pictorial representation of

numerical data in the form of rectangles(or bars) of uniform width and varying heights.

• The height of a column represents the frequency of the corresponding observation.

Bar Graph 1 The graph below depicts the UK schedule

for childhood immunization.

2 months 4 months 6 months 8 months 10 months0

1

2

3

4

5

6No. of Vaccines

Bar Graph 2 The graph below depicts the total

pharmaceutical expenditure per capita (2008).

Greece

France

Austria

Spain Ita

ly

Finlan

d0

100200300400500600700

Per Capita Emissions Per Capita Emissions

Bar Graph 3• The graph below depicts the sales of

medicines in the top 5 therapeutic classes, 2001.

Antipsychotics

Oral an

tidiabetics

ACE inhibito

rs

Antibiotics

Syste

matic a

ntihistam

...05

101520253035

Percentage growthPercentage growth

Mathematics of MRI NMRI uses magnetic fields to manipulate

magnetization in a way that makes it a conveniently measurable signal which encodes spatial location and density information.

Mathematically, with a correctly designed

sequence of magnetic field applications, the recorded signal is just a 2D Fourier transform.

Mathematics of MRI

Hardy Weinberg LawEvolution is not only the development of new species from older ones, as most people assume.  It is also the minor changes within a species from generation to generation over long periods of time that can result in the gradual transition to new species. The biological sciences now generally define evolution as being the sum total of the genetically inherited changes in the individuals who are the members of a population's gene pool.  It is clear that the effects of evolution are felt by individuals, but it is the population as a whole that actually evolves.  Evolution is simply a change in frequencies ofalleles in the gene pool of a population.  For instance, let us assume that there is a trait that is determined by the inheritance of a gene with two alleles--B and b.  If the parent generation has 92% B and 8% b and their offspring collectively have 90% B and 10% b, evolution has occurred between the generations.  The entire population's gene pool has evolved in the direction of a higher frequency of the b allele--it was not just those individuals who inherited the b allele who evolved.