Principles of temperature measurement

This chapter is relevant to Section R2(i) of the 2023 CICM Primary Syllabus, which expects the trainees to "describe the measurement of body temperature". This area of expertise was previously tested in the Second Part Exam and seems to have emigrated into the Primary with the first edition of the syllabus document. It appears as if this topic specifically has not appeared in the written papers since Question 19 from the first paper of 2016,  which makes it more, rather than less likely, to appear in the future. To gird their loins for this eventuality, the exam candidates are presented with the following brief account, which focuses on the most likely SAQ stems for this topic (physical principles, advantages and disadvantages of the most common devices).

Desirable properties of a medical temperature monitoring device: 

• Specific (only temperature), sensitive to 0.1ºC in the 35-42 ºC rrnage, reliable, calibratable, cheap, easy to train for use, mechanically robust and chemically inert, small, capable of automated unattended function for monitoring, and capable of rapid response to changes in temperature.

Types of devices:

• Electrical vs. non-electrical
• Contact vs. noncontact

Liquid in glass thermometers:

• Principles: Heat is transduced as a change in the volume of a heated liquid, which is represented as a change in the position of a fluid level. A substance with a large termal coefficient of volume expansion (β) such as mercury or alcohol is used.
• Mechanism:  a thin walled glass-filled tube contains the liquid; liquid meniscus is read through the walls of the tube. Glass in the wall magnifies the size of the fluid column.
• Advantages: cheap, easy to use, reliable in operation, require no calibration
• Disadvantages: slow, invasive, fragile, contain toxic elements, not auto-recording, inherent measurement error from manual reading 

Bourdon gauge thermometers

• Principles: Heat is transduced as a change in the pressure of liquid contained inside the probe, transmitted to the gauge via non-compressible liquid 
• Advantages: can be read at a distance from the site of measurement; wide temeprature range; mechanically resilient
• Disadvantages: same as liquid-in-glass

Bimetallic strip thermometers

• Principles: a coiled (spiral or helical) length of two different metals sandwiched together, which expand unequally on one side, causing the strip to deform and deflect the position of a gauge.
• Advantages: Cheap, durable, not requiring calibration
• Disadvantages: Low accuracy, poor sensitivity, slow response, invasive

Thermal resistance thermometers (platinum wire)

• Principles: Heat-related change in the resistance of a conductor (usually platinum) is measured by the drop in current being passed through it.
• Advantages: Sensitive, reliable, durable, rapidly responsive, wide range of temperatures, the gold standard for lab calibration
• Disadvantages: Expensive, invasive, requires training to use

Thermistors

• Principles: Heat is transduced as a change in the resistance of a metal oxide semiconductor 
• Advantages: Cheap, mass-produced and disposable, sensitive over the relevant range, mechanically robust, chemically inert
• Disadvantages: Drifts from calibration, unreliable sensistivity, cannot be reused (degraded by heat of sterilisation), could theoretically self-heat and become inaccurate

Thermocouples

• Principles: A potential difference is generated at the junction of two different conductors when it is exposed to heat (Seebeck effect)
• Advantages: Sensitive, reliable, durable, rapidly responsive, easily  miniaturised, 
• Disadvantages: not cheap, needs to be reuseable, require recalibration

Infra-red temperature readers

• Principles: Heat radiation in the human temperature range is emitted as IR radiation with a wavelength of 10 - 12 μm, and this can be filtered and used to generate a current in a thermocouple
• Advantages: Noncontact, noninvasive, easily cleaned between patients, sensitive within the required range
• Disadvantages: less accurate, depends on the IR emission of the measured surface, i.e. may not measure the core temperature

The most important preparation resource for this would have to be the relevant chapter of Davis & Kenny (4th ed, p.114-119), and it is advised that much of it be committed to memory, as the examiners lauded the regurgitated knowledge of those candidates who did so ("candidates who did well reproduced the content of the chapter on temperature measurement in the recommended text book"). The reader who imperils their exam chances by ignoring this level of  directness is instead detoured into Sessler (2021) or the bottom half of Childs (2018), which are probably the best short overview sof the scientific basis behind the different methods of temperature measurement. For the CICM trainee, Cereda et al (2004) will probably not be enough, and McGee's Principles and methods of temperature measurement (1988) will probably be too much.

Physical principles of temperature measurement

To measure anything, one needs to have some fundamental elements in place. Without gazing  philosophically into the dismal wastelands of metrology, we should agree that in order to measure anything, we need to be able to reproduceably detect a change between two points and then establish  these along an ideally linear, non-arbitrary measurement scale, with an ordered relationship between the intervals. We use Celsius in medicine mostly because of the convenient small numbers. In reality Kelvin would probably be "better" in the sense that it is based on the theoretical thermodynamic concept of temperature and is a meaningful ratio scale (i.e a doubling of the Kelvin temperature means a doubling of the thermal energy content), but here we are. 

Engineering principles of temperature measurement

Temperature, the measure of the average internal energy of a system, can only be measured when that system decides to share its energy with the measurement device. From this it follows that the temperature measurement device design will be based on some mechanism of heat transfer, and this gives us one possible method of classifying them:

• Contact thermometers, i.e. those that measure temperature because body heat is conducted directly to them
• Non-contact thermometers, i.e. those that measure radiative heat loss

This would be good enough for government work, but unsatisfying from the standpoint of perfect scientific accuracy,  as the "contact" group would end up lumping together a whole host of devices with very different engineering properties and performance characteristics, and moreover would tend to exclude a range of measurement techniques which are in common use outside of medicine and which do not fit into this definition.  A change in thermal energy is thankfully easy to detect, as it causes numerous physical and chemical changes in the properties of matter, and therefore leaves us with multiple options on how to detect it. The choice of mechanism therefore comes down to things like size, reliability (i.e. consistency of repeated measurements), accuracy, capacity for recalibration, cost, type of output signal (continuous vs. intermittent) , response time, cost, and the range of temperatures  we are interested in. As an extreme example, McGee lists a range of physical mechanisms which are exploited for the measurement of temperature:

• Thermal expansion (liquid, gas, solid)
• Vapour pressure
• Electrical resistance
• Thermoelectric effect
• Magnetic susceptibility (cerium-magnesium nitrate)
• Thermal "noise" (Josephson junction)
• Flow rate (pyrometric cone)
• Light intensity
• Heat emission (IR)
• Superconduction
• Sound velocity (acoustic thermometry)
• Nuclear quadripole vibration
• Heat content calorimetry

But no CICM trainee should ever be expected to explain the temperature monitoring applications of the Josephson effect, so surely one has to draw the line somewhere. Arbitrarily, that line is defined by what is, and what is not, mentioned in Davis & Kenny (4th ed, p.114-119) and Middleton (2021, ch.4) which are the official CICM textbooks for this topic. Remixed, their classification of devices relevant to medicine would have to be something like this:

• Non-electrical
  • Liquid-in-glass (eg mecrury thermometer)
  • Bourdon effect (pressure change of a gas)
  • Bimetallic strip
• Electrical
  • Change in the resistance of a conductor (thermistor)
  • Thermocouple (Seeback effect)
• Radiative
  • Infra-red

Specifically, "electrical, non-electrical and infrared" is the example classification given in the examiner comments to Question 19 from the first paper of 2016, taken directly from Davis & Kenny.  This classification will be followed here, and all effort will be directed to avoid any digressions on the more interesting mechanisms of temperature monitoring, to maintain some kind of grip on the attention of the time-poor exam candidate. Additionally, though it would be worth mentioning that the human touch itself is a method of temperature assessment,  it would be an unpopular method for the serial measurement of core body temperature, and probably not worth mentioning in a written answer.

The desirable properties of a thermometer

What do we want from these? The list of properties, if one thinks about this for a minute, is quite extensive. This one was adopted from McGee, but 

• They should measure only temperature. In other words, the device should not respond to, for example, changes in pressure.  
• They should be sensitive within the required range for medicine. Most of the values we are interested in lay within a very narrow range (1-2 ºC on either side of 37) and the device should be able to report decimal fractions within this range.
• They should have reliability within the range of interest, i.e. they should be able to maintain a linear response to changes in temperature. In reality none of them are like this and most require some kind of curve fitting to achieve truly scientific precision, but in practice the range over which this becomes important is much larger than what is required at the bedside.
• They should maintain their sensitivity and reliability over time, or they should have the capability of recalibration 
• They should be cheap, as it would be ideal for them to be disposable between patient uses to maintain infection control
• They should be easy to use, making it easier to train staff.
• They should be stable mechanically, i.e. the patient should not be able to destroy these by the action of chewing on them in their state of half-sedated absentmindedness.
• They should be stable chemically, i.e. neither should they contain toxic ingredients that could contaminate the patient, nor should they become affected by conventional cleaning methods and products (eg. autoclaving and bleaching).
• They should be small. Space in an ICU is already occupied by a million other devices; and for that matter space inside the ICU patient's body cavities is also already crowded.
• They should be capable of a rapid response, which may give them the opportunity to measure rapid changes of temperature for applications such as thermodilution cardiac output measurement.
• They should report data, i.e. they should be capable of automated remote operation, unattended (which is the essence of monitoring)

Liquid-in-glass thermometers

The order of appearance of thermometer technologies in this chapter is roughly in parallel to their historical development, which is for some reason the convention in the literature. This probably makes no sense to the modern trainee, whose experience of life (let alone of medicine) has not included any direct contact with a mercury thermometer. Still, thermometers that operate on the basis of liquid expansion remain cheap and ubiquitous, even though mercury has become uncommon in this economy. 

These devices take advantage of the fact that all things tend to expand with heat in a predictable and reproduceable manner. Specifically the change in volume can be expressed as 

ΔV = βVΔT, 

where ΔV is a change in volume, ΔT is the change in temperature and β is the thermal expansion coefficient of the material. This variable ranges widely:

Material	Coefficient of volume expansion β (per 1° C)
Quartz	1 × 10– 6
Quartz	1 × 10– 6
Glass	27 × 10– 6
Concrete	36 × 10– 6
Gold	42 × 10– 6
Aluminium	75 × 10– 6
Mercury	180 × 10– 6
Water	210 × 10– 6
Ethyl alcohol	1100 × 10– 6
Most gases	3400 × 10– 6
Liquid nitrogen	9 × 10– 3

Because a digression on the factors underlying this property of matter would take us into the metallurgy of plutonium, it will suffice to leave the reader with the understanding that the thermal expansion of gases liquids is generally vastly greater than that of solids per unit temperature, and so was noticeable without any sophisticated techniques, with the result being some of the earliest temperature measurement devices were based on this property.

Why not just use water? It is not as if lakes of mercury were sloshing around in the 1740s when Anders Celsius was at his most active, but mercury became the liquid of choice for these devices, mostly because it does not cling to glass, and does not have the annoying tendency to expand with freezing at 0 ºC. North Europeans were at the forefront of thermometer technology and Europe has a tendency to become beautiful in the winter, meaning that any instrument marketed there would have to have a measurement range extending well below the freezing point of water. It is unknown what liquid an equatorial civilization would have used in their thermometers had they been given half a chance, but it would surely have been a less toxic and expensive liquid. 

Then why not alcohol? To be sure, that's probably what you'll buy if you enter a pharmacy these days, and famously Otto Von Guericke’s thermometer from the 1600s was filled with brandy, but alcohol is also an ineffective fluid for temperature measurement. Sure, it freezes  far below the freezing point of water (-115 °C) but it boils at 78.5 °C, which restricts its useful range

For medicine, none of these are disadvantages, as we frequently handle materials much more toxic than mercury, and none of our patients are normally hotter than 78.5°C or colder than 0 °C. The disadvantages of the liquid-in-glass thermometer are mostly related to convenience:

• The column of fluid is tiny, and requires a cylinder of glass to magnify it, which increases measurement error (as the glass also magnifies and distorts the scale)
• It takes some time (2-3 min) to equilibrate with the measured surface. Though usually a temperature measurement is not so time-sensitive that it might call for an instant result, there are some applications (eg. thermodilution measurement of cardiac output) that call for faster data output. 
• Glass itself expands, albeit less 
• The stem of the thermometer, where the scale is, is usually not immersed in the patient's heat, and cools the column of fluid as it ascends
• It is hard to measure core temperature with these, as they need to be introduced into a body cavity and then retrieved a time later to be closely scrutinised.

To make the device easier to read and to remove the reader of the result to some distance from the surface of the device that has recently been inside a rectum,  various gauge-based devices have been developed, of which perhaps the most common is the Bourdon gauge thermometer.

This thing is essentially a pressure gauge,  and measures the effect of expansion of a pocket of mercury or some volatile liquid on the pressure inside a chamber. As the change in pressure is predictably associated with the change in temperature, these devices can reliably transduce one into the other, and display the result on a dial where the pressure change moves an arrow across a dial. The advantage here is that an incompressible liquid can be used to transmit the change in pressure to a dial which can remain some distance from the site of measurement. The disadvantage, of course, is that a bulb filled with mercury or something equally unpleasant is still inserted into the patient and then connected to an exterior device by some necessarily rigid tubing. The popularity of these devices for medical use has never been very great, owing to the availability of cheaper methods which were only equally intrusive, and in the modern era these devices are generally found in applications which would not be survived by delicate electronics, eg. where a sustained tolerance to extreme thermal, chemical or mechanical abuse is expected. As an example, Baumer Group sell these lovely devices in stainless 1.4404 (316L)  steel with a temperature range of -200 to +800 °C and the promise to resist "corrosive gasses and liquids" and "aggressive atmosphere". 

Bimetallic strip thermometers

Like liquids, solids expand with heat, but unlike liquids they do not pose a risk of their glass vial smashing accidentally inside the patient, spilling toxic contents. Unfortunately the degree of expansion for each degree of temperature will generally be very small, the linear expansion coefficient for even the most expansile metals (Ti-Nb alloy) still being in the order of 163 × 10^-6 per 1 °C, meaning that the change in length for one meter of material will be about 0.163 mm for every degree increase in temperature. In other words, one would not build a thermometer which relies on the uses to be able to detect a change of this magnitude. Instead, this effect can be exploited to deflect the position of an arrow on a dial, for example by the action of a coiled (spiral or helical) length of a bimetallic composite, where a length of two such materials sandwiched together will expand unequally on one side, causing the strip to bend.

This is the principle one still finds in use within meat thermometers, for example. The simplicity of the design and the cheapness of the construction is the greatest advantage of these, as there is nothing to break and the absolute minimum of moving parts. There is probably nothing more durable (the probe is literally just a length of conductive metal) and the temperature range within which they will operate is impressive, being theoretically limited only by the structural integrity of the metals involved. 

Resistance thermometers, thermistors and thermocouples

The electrical methods of measuring temperature are separated from the non-electrical by Davis and Kenny (5th ed), as that must have seemed like a defining distinction for these authors. There are three main variants of this, and it does not seem likely that the CICM trainee will ever be asked to comment on their characteristics beyond some basic statements on their function. The literature again tends to present these devices in order of their commercial appearance, as if this was the most logical way to do it, but no better method presents itself. 

Platinum wire resistance thermometers exploit the fact that the conductivity of conductors changes with temperature, which is also the principle that operates inside your incandescent filament lamps. This property is represented in terms of the temperature coefficient of resistance (α) , which is the rate of rise of resistance per unit temperature. This relationship is nice and linear when it is graphed, which is a superficial layer of deceptive calm: as temperature rises, the resistance rises, and as resistance rises the current heats the resistor more, leading to a spiral where temperature and resistance escalate exponentially and turn the conductor into a cloud of angry ions.

We can use this property to measure the temperature of a conductor by passing a known current through it. The ammeter connected to the end of such a conductor would then measure a lower current, and the drop in current would then be easy to relate to the change in temperature by means of calibration (i.e. comparing the measurements to known standard values).The reader interested in an explanation of how these devices work in detail and why a Wheatstone bridge is required for their operation are invited to delve into  O'Sullivan (1966), which is actually a paper from the world of architectural engineering. As each conductor may have slightly different properties (length, crossectional thickness, chemical composition) and each ammeter device could be equally idiosyncratic, the latter step is essential, but we can estimate how a given material may perform on the basis of its temperature coefficient of resistance, of which a table is presented below:

Material	α per 1ºC
Manganese	1.0 x 10 -5
Zinc	3.7 x 10-3
Aluminum	3.8 x 10-3
Silver	3.82 x 10-3
Copper	3.93 x 10-3
Platinum	3.93 x 10-3
Tungsten	4.5 x 10-3
Mild steel	6.6 x 10-3
Iron	6.41 x 10-3
Nickel	6.41 x 10-3
Mercury	8.9 x 10-3
Graphite	-2.0 x 10-4
Carbon (graphite)	-4.8 x 10-4
Germanium	-50 x 10-3
Silicon	-70 x 10-3

It is presented below for no specific reason, as the temperature coefficient of resistance for platinum: (the most commonly chosen resistor for a resistance thermometer) is an unremarkable 3.93 x 10^-3, similar to the markedly cheaper copper and the positively budget aluminium. The reason for choosing platinum is completely unrelated to this property. Platinum is delightfully ductile, which makes it easy to stretch into fine wires of a consistently small diameter, is chemically inert enough to suspend into angry corrosive sludge, and has a very high melting point which means it will remain a wire (and not a puddle) over a broad range of temperatures. For this reason, platinum resistance thermometers are still used in high temperature applications (eg. for measuring the temperatures inside nuclear reactors, where the operating range for some reason needs to reliably exceed 900 ºC, presumably so that the terrified engineers have something to stare at while the core catastrophically self-disassembles). The heat resistance and predictable stable properties make these devices a gold standard against which other temperature measurement systems are calibrated, bur because they tend to use all kinds of posh materials, their use is limited to well-funded  government laboratories by their expense. 

Fortunately, semiconducting metal oxides can do the same thing but more cheaply and over a range of temperatures that has meaning for the non-incinerated human being. For example, whereas copper changes its conductivity by 0.39% for every 1°C change at room temperature, a typical oxide thermistor changes its conductivity by about 4% per 1°C. For some reason, the older noble metal conductor thermometers are still called "resistance thermometers", and the metal oxide versions became known as as "thermistors"',  which is just a portmanteau of "thermal" and "resistors". 

The advantage of a semiconductor thermistor is mostly related to cost. One can purchase an incredible amount of vanadium oxide for the price of a relatively small platinum ingot, making it possible to mass-manufacture these devices, and to even make them disposable.  The disadvantage, however, is that these devices often must be disposable, as their construction often sacrifices reliability to cost. The devices generally cannot be exposed to a high temperature (eg. what might be required for autoclaving) without experiencing a drift from calibration. In fact just in the course of their routine function their accuracy may falter, which is why the platinum electrode remains a laboratory calibration standard, and they do not.  Their nonlinear range of response over the measurement range means that they often cannot measure preposterous temperatures (as the electronics of the monitor will not know how to interpret the signal outside of a narrow range), which means profound hypothermia may require a different probe. Theoretically, the device also receives a direct current and is a resistor, which means it could theoretically begin to self-heat and upset its own measurement (though in reality, the magnitude of the current used is minuscule). 

Thermocouples are the third option. These devices take advantage of the Peltier-Seebeck effect, which is a weird thing that happens at the junction of two dissimilar conductive materials. When heat is applied to one of the conductors, the valence electrons from that conductor will flow to the cooler conductor, creating a measurable (albeit small) potential difference.  This Seebeck effect is the inverse of the Peltier effect, which may be  familiar to the deep nerd community of PC cooling enthusiasts as the drop in temperature that develops when a current is passed through a junction between two dissimilar conductors. 

This voltage is usually very small (the highest Seebeck coefficient, for selenium, is 900 μV per ºK) but it's enough to be detected by sensitive equipment, and the response is relatively linear (in contrast to the hysterically hyperboloid response of the thermistor sensors).  Another advantage is that the measurement element, like in the case of the simple bimetallic strip thermometer, simply a length of metal. It can be made into an extremely small form factor and the choice of components can be focused on selecting chemically inert materials that will remain well-behaved even after days and weeks immersed in body fluids, as any combination of two dissimilar conductive materials is theoretically suitable (though the Instrument Socienty of America recognises only twelve combinations).   That no current needs to be applied to the device is laudable because it can be expected not to heat itself and is therefore capable of measuring extremely small changes in temperature very precisely. The small size also means that the probe will exchange heat with the patient extremely rapidly, and be able to quickly report transient changes in temperature.  That the probes are usually metallic also makes them reusable as they can be heat-sterilised between patients. The disadvantage is, they have to be sterilised between patients, as their cost usually forbids reuse (some of the materials required for this application are molybdenum, tungsten, iridum and rhenium). The low efficiency of the Seebeck effect means that only a tiny fraction of the heat energy is converted into a potential difference and the sensitive of the device is greatly dependent on signal amplification, which can introduce error. One half of the conductor needs to remain at reference temperature, otherwise the electronics of the device need to integrate some compensatory formula to adjust the reading (a "cold-junction compensator").

Infra-red  thermometers

The devices listed above all suffer from one common limitation, that being the need to be in sustained contact with the sweaty slimy bug-filled body surfaces and cavities of the patient. In short, non-contact measurement would be the widely preferred method if these devices could speak and vote. Infra-red measurement of temperature is the most common noncontact method used in clinical medicine, and usually relies on the measurement of the IR radiation being emitted by some part of the patient. The operation of these devices rests on the application of the Stefan-Boltzmann law,  i.e. that every piece of matter that is not at absolute zero will emit radiation of a wavelength and intensity which is related to its temperature. The range of temperatures required to produce visible light (wavelengths of 400-700 nm) is extremely high (eg. surface of the sun) and so the usual emission spectrum of the human body is only usually expected to remain within a wavelength range of 10 - 12 μm, i.e. in the infra-red. 

From the intensity and wavelength of the emitted IR radiation the temperature of the emitter can be calculated. Speakman & Ward (1998) explain this in much better detail, perhaps with more math and more references to barn owls than is required for the CICM exam. In short, the principle of function for the least expensive devices is still thermocoupling: IR radiation emitted by the patient warms the junction of conductors and a voltage is generated. The specific IR spectrum is isolated by filtering, and 

for each wavelength the maximum amount of radiation depends only on the temperature of the emitter. The main advantage of these devices (that one does not need to touch the patient) is offset by the disadvantage of only being able to measure the surface temperature, the human tissues being entirely opaque to infrared light. As the temperature of the skin can fluctuate considerably, this is obviously imperfect, and methods of overcoming this limitation (eg. measuring the temperature of the blood from exposed blood-filled surfaces such as the tympanic membrane) tend to eliminate the benefits of being a non-contact measurement technique, as the sensor still ends up getting shoved into  a waxy hairy orifice.