The Use of Maths in Medicine

Maths is used every day in hospitals, surgeries and many more healthcare facilities around the world. As a prospective medical student, I wanted to know more about the huge role that this discipline plays in the world of medicine, and so I did some research and came up with the following conclusions.

One of the most basic and common use of maths in medicine is prescriptions and drug dosing. Most medications have guidelines for dosage amounts in mg/kg, and so doctors need to figure out how many milligrams of medication each patient will need, depending on their weight. There is a big role here for conversions, as sometimes patients will only know their weight in pounds or stone, and so this will have to be changed quickly by the doctor or nurse to the right units. This is extremely important as a wrong drug dosage could mean a life or death decision, especially if the drug being administered to the patient is especially potent and so could be toxic if given in high amounts, or if a patient is desperately in need of a drug, and not enough is given to that patient. Doctors must also determine how long a prescription will last, as this figure can be in days, weeks or months, and so healthcare professionals must be able to give the right amount of drug to a patient over a specific period of time, without the patient needing to come back as they don’t have enough of their medication.

Another important factor to consider is how long the medication needs to stay inside the patient.  This will determine how often the patient needs to take their medication in order to keep a sufficient amount of the medicine in the body. The amount of medicine in the body decreases by a certain amount in a specific time (e.g. 10%hour^-1), and this can be expressed as a rational number- 1/10. This rational constant creates a geometric sequence, as the amount decreases by a fixed ratio each time unit, and so doctors can use this concept to decide how often a patient needs to take their prescribed medication.

Another common use of maths in the medical field is for the calculation of one’s BMI, which is a number derived from an adults weight and height to judge whether they are of a healthy weight. This is a very common equation, used to test people’s weight all around the world, and shows that healthcare professionals have to be able to use equations with the right units; however, one’s BMI is not a very good indicator of healthy weight. I say this as, when you ‘plug’ weight into the equation to calculate a patient’s BMI, it doesn’t consider whether the weight is muscle or fat, and so a bodybuilder could be classified as ‘obese’ on the BMI scale even though they are healthy.

One of the more less-commonly known uses of maths in this field is through Extracorporeal Shockwave Lithotripsy, which is used to treat kidney and gallstones non-invasively. This technique is all thanks to the reflective properties of an ellipse, which can be seen in the diagram to the left. Shockwaves are generated at one focus and will reflect off the ellipse and pass through the second focus- creating a unique property which allows ESWL to take place. In order for the lithotripter to work, the patient’s stone must be at one focus point of the ellipsoid and the shockwave generator at the other focus.  The patient is then laid on the table and moved into position next to the lithotripter. Doctors then use a fluoroscopic x-ray machine to get a visual on the stone, allowing the focus to be at the precise location of the stone.  A water-filled cushion is then wrapped around the machine and rests on the patient’s side; this acts as a sort of buffer for the machine, as the water allows the shockwaves to travel through the body’s tissues safely because water and the soft tissue have the same density. The stone has a larger density and so is then shattered by the shockwaves. This is a popular choice for patients as it is quick, relatively safe and non-invasive, and so is available on the NHS.

In conclusion, mathematics plays a crucial role in medicine as it directly impacts people’s lives, and so it is very important for healthcare professionals to be very accurate in their mathematical calculations.