Mathematics in Medicine
Functional numeracy is as essential to an aspiring medical professional as functional literacy. As a physician, perhaps the most important mathematical skills you will need are:
1. Basic mathematical knowledge sufficient to calculate drug doses, concentrations, etc.
2. An understanding of the core statistical concepts most commonly represented in the medical literature.
3. Knowledge of algebra to understand calculations of acid–base status, etc.
4. Ability to appreciate whether or not results are mathematically plausible.
(Nusbaum, 2006)
The careful logical reasoning that is necessary for the study of mathematics is an essential element of clinical reasoning. Although you do not need higher mathematics to get through medical school, you will need the ability to manipulate numbers, including fractions, ratios, powers of 10 and logarithms. You will also need a basic understanding of probability, graphs and simple algebra. You will need to rearrange equations and convert between units of measure.
While some of you will be very confident with these fundamental skills, our experience with new medical students has shown that many of you are simply not comfortable with basic math, perhaps because you have not used these skills for a long time. Have a go at the following exercises, which will give you an idea of the level required.
- Read the sections about resistance in series and parallel circuits. Next, read a little about hemodynamics.
The diagram below depicts a vascular bed consisting of vessels organized both in series and parallel. The resistance (R1 – R5) of each vessel is indicated. The pressure at point A is 60 mm Hg and the pressure at point D is 10 mm Hg.
a) What is the flow through the system (point A to point D)?
A) 2 mL/min
B) 5 mL/min
C) 10 mL/min
D) 20 mL/min
E) 40 mL/min
b) What is the pressure at point B?
2. Consider the following two equations concerning cardiac output.
Equation 1: Fick Principle: CO = VO2 / (Ca-Cv)
Cardiac output is equal to Oxygen Consumption (VO2) divided by the arterial oxygen concentration (Ca) minus venous oxygen concentration (Cv).
Equation 2: CO = HR x SV
Cardiac output is equal to heart rate (HR) times stroke volume (SV).
A group of high school varsity soccer teams in upstate New York agreed to undergo physical tests as part of a wellness study being conducted by a local university. The following data were collected from a student during a stress test on a treadmill.
Heart rate = 100 beats/min
Arterial pressure = 140/80 mmHg
Oxygen consumption = 500 ml O2/min
Aorta oxygen content = 25 ml O2/100 ml blood
Pulmonary artery oxygen content = 20 ml O2/100 ml blood (*pulm artery carries venous blood)
End diastolic volume = 130ml
Use the data above to determine the student’s stroke volume (mL/min).
A) 10
B) 40
C) 50
D) 100
E) 120
3. The Starling equation describes the movement of fluid across capillary membranes. Net Driving Pressure = (capillary hydrostatic pressure + interstitial oncotic pressure) – (interstitial hydrostatic pressure + plasma oncotic pressure).
The figure below represents experimental data obtained from a frog capillary bed. The broken line illustrates how the direction (filtration or absorption) of fluid passing across the capillary wall (Y-axis) changes as a function of capillary hydrostatic pressure (X-axis). If interstitial hydrostatic pressure is 5 and plasma oncotic pressure is 15, what is the interstitial oncotic pressure when net driving pressure is 0?
A) O mm Hg
B) 5 mm Hg
C) 10 mm Hg
D) 15 mm Hg
E) 20 mm Hg
4. a) A bag contains 4 black balls and 8 white balls. A ball is drawn at random from the bag. It is replaced and a second ball is drawn.
What is the probability that the ball was the same colour on both occasions?
b) A waiting room contains 4 alcoholics and 8 diabetics. A patient is called at random from the waiting room. After seeing the doctor, the patient goes home. A second patient is called.
What is the probability that both patients had the same complaint?
Click here for the answers.
If any of these questions were difficult for you, or you simply want to brush up on basic math skills, click the links below to learn more.
Multiplication tables
Fractions
Ratio and proportion
Arithmetic
Probability
Graphs
Algebra
Maths for Medics
(Note: These are just examples of places to learn basic math skills, some suggestions. Any good college or high school resource will do fine.)
