Using numbers and handling data
Using numbers and handling data

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Using numbers and handling data

3.5 Line graphs

To illustrate how to create and use line graphs, we will use the example of a calibration curve.

A calibration curve is a type of line graph in which the response of a measuring device to a series of known concentrations of a substance is plotted. You can then make a measurement of an unknown sample - in the case we're about to examine, blood serum samples from new-born infants - and use the calibration curve to work out what concentration of substance is present.

SAQ 6

Think of a type of machine that can perform measurements to give readings that can then be used to make a standard curve.

Answer

A spectrophotometer provides these types of measurement data, which can be used to produce standard curves.

Box 5 Spectrophotometers explained

A spectrophotometer is an instrument that determines how much light of a particular colour is absorbed by a liquid sample. The more there is of a coloured substance in the solution, the more light will be absorbed (i.e. the less light passes through the solution). After measuring how much light is absorbed by a series of solutions containing known concentrations of the coloured substance, you can draw a graph of this data and use it to calculate the concentration of that substance in an unknown sample from a measurement of how much light it absorbs.

Here's how a spectrophotometer works:

  1. White light from a bulb (source) is focused into a narrow beam by passing it through a thin slit.

  2. A prism is used to split the beam of white light into its component colours, in the same way that water droplets can split sunlight into its component colours to make a rainbow. Different colours of light have a different wavelength: the distance between the peaks of the light waves, measured in nanometres (where 1 nanometre is 10-9 metres). For an idea of scale, individual virus particles range in size from about 20-300 nm).

  3. A second thin slit, just after the prism, can be moved from side to side to select just one colour of light to pass through to the sample.

  4. The light passes through a container with the liquid sample inside (usually the light passes through 1 cm thickness of the liquid).

  5. A light detector measures how much light is transmitted through the sample, and compares this with how much light was emitted by the source. The difference between these values gives a measure of how much light was absorbed by the sample: i.e. the absorbance (A), often also called the optical density (OD). The absorbance varies with wavelength, so measurements of this type always specify the wavelength of light that was shone through the sample. In the following example with C-reactive protein, the wavelength was 450 nm, so this would be quoted as A450 or OD450.

This process is summarised below in Figure 10, which also gives an indication of the wavelengths of different parts of the visible light spectrum.

Figure 10
Figure 10 A spectrophotometer measures how much light of a certain wavelength is absorbed by a liquid

In this particular example, we are looking at how the concentration of C-reactive protein (CRP: a blood component produced in response to infection) changes the intensity of a blue-coloured test solution: the more CRP present, the more intense the blue colour becomes. The intensity of the blue colour is determined using a spectrophotometer to measure the Optical Density at 450 nm (O.D. 450 nm). More specifically, this is a measure of the amount of a blue light with a wavelength of 450 nanometres (450 nm) that is absorbed by a known thickness of the solution before the light reaches a detector.

When making a calibration curve, the following points need to be considered:

  1. What is the expected range of concentrations?

    • The range of blood serum CRP concentrations that might be encountered in infants, and the level of infection that this correlates with, are as follows:

    • normal: <2 μg/ml

    • sepsis: >22 μg/ml

    • dying: >120 μg/ml

    • Where < means 'less than' and > means 'more than'.

    • (Romagnoli et al., 2001)

    • From these values, a range of known standards containing between 0-100 μg/ml CRP should cover the most likely range of infant serum CRP concentrations.

  2. Am I within the working range of the instrument?

    • Many instruments are only accurate over a specific range of values. As we continue to increase the CRP concentration, the blue dye will become more and more intense. However, this can't continue forever and after a point the solution will be saturated with blue dye. Beyond that the solution can't get any more intense, no matter how much CRP we add. As we begin to reach this saturation point, the measurements will plateau out to the maximum value as CRP is increased. The most reliable part of the calibration curve covers the middle range of concentrations, where it is closest to being a straight line. For this reason, it is called the linear part of the graph.

  3. How random or 'noisy' is the assay and the measuring device?

    • Depending on the precision of the measuring device you may not get the same reading every time from the same sample. To compensate for this it is a good idea to repeat the sample measurement two or three times and then calculate the average or mean value. For example, if you repeated the measurement of the same sample once, then you'd add both results together and then divide the resulting figure by 2 to find the average value.

With these points in mind, Figure 11 shows a table and graph of OD450 values measured using a series of known concentrations of CRP.

Figure 11
Figure 11 Calibration curve for CRP

In general, the x-axis is used to represent a variable that changes in a consistent way, or in a way that you can control (here, it's the known concentrations of CRP that you have measured out). The y-axis is normally used to represent a variable that you measure but may not be able to affect directly (in this case the optical density of the CRP test solutions that you read from the measuring device).

The small circular symbols on the graph mark the measured data points and they are joined by a curved line.

Notice that the graph shows a positive correlation between the two variables: the more CRP that is present, the larger the optical density reading. Other types of data may show a negative correlation between the variables, whereby one of the measured entities decreases as the other increases, e.g. the further you drive your car, the less petrol you have in the petrol tank.

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