# Pressure transducers for haemodynamic measurements

This chapter is relevant to Section G6(ii)  of the 2023 CICM Primary Syllabus, which asks the exam candidate to "describe the principles of measurement, limitations, and potential sources of
error for pressure transducers, and their calibration".
It is unclear why this ended up in the cardiovascular section of the syllabus, and why "measurement of flow, pressure and volume of gases" ended up in Section W(iv), under Principles of Measurement and Equipment. Pressure transducers are common to the measurement of all sorts of fluid compartments, and there is nothing uniquely cardiovascular about them.  However, to take advantage of this confusion, it is possible to use the pressure transducer article as a convenient segue into the discussion of arterial line pressure transducer setup, which is as good an example as any to demonstrate the underlying principles.

In summary:

• Definitions:
• A transducer is a device which converts energy from one form to another.
• Common piezoelectrical pressure transducers convert kinetic energy into a change in electrical resistance
• By completing a limb of a Wheatstone bridge circuit, this change in resistance can be measured
• Piezoresistive strain gauge sensors
• Usually a thin semiconductive silicone membrane
• This membrane changes its resistance whenever it undergoes deformation
• It is usually built into an integrated circuit which contains the Wheatstone bridge circuit and other electronic components
• Wheatstone bridge
• This is a circuit with four resistors:

• Three have a known resistance and the fourth (Rx) is the semiconducting membrane.
• If the ratio of resistance in the R1/R2 limb is the same as the resistance of the R3/Rx limb, there should be no current flowing through the galvanometer VG.
• The variable resistor R2 is adjusted until the current drops to zero (which is when the resistance of R2 is the same as the resistance of Rx)
• Thus, the resistance of Rx, and therefore pressure, is determined.

Insofar as published peer-reviewed sources go, one cannot go past Wilkinson and Outram (2008), Stoker (2004) or the significantly more detailed Gilbert (2012). All three articles are called  "Principles of pressure transducers, resonance, damping and frequency response" and all are stuck behind Elsevier's brick paywall, making them useless to people who actually need them. The financially disadvantaged trainee will be glad to hear that all useful information of these three sources has been sucked out, digested and rearranged into the summary which follows.

## Design of disposable pressure transducers

A transducer by definition is a device which converts energy from one form to another. By that definition, a pressure transducer should convert the kinetic energy produced by changes in pressure into electrical energy. Most of the commonly used disposable electronic pressure sensors don't completely satisfy that definition, as they tend to be piezoresistive strain gauges which complete a Wheatstone bridge circuit. This means the device changes its resistance in response to changes in pressure.

Each manufacturer will have their own specifications for these devices. Generally, one should expect characteristics which match human physiological parameters. It would be unexpected for anything inside the human organism to generate a sustained fluid compartment pressure more negative than -50 mmHg, or more positive than +300 mmHg. These boundaries are representative of the usual disposable transducer operating ranges.

The manufacturers save money by not over-engineering these devices to measure absurd pressures.  There is no point having a transducer calibrated to accurately measure the difference between 90,000 kPa and 90,001 kPa unless one expects it to be used in the environment of equatorial Venus.  Similarly, the manufacturers save money by lowering accuracy standards to something well below what might be expected of laboratory equipment. If you are a scientist measuring pressure for your experiment, you will buy one supremely accurate device. If you are the director of an ICU, you will buy ten thousand disposable devices with "good enough" accuracy. From an ISO standard point of view, "good enough" is an error of 1-2%. In the context of MAP measurement, it is the difference between a MAP of 65 and a MAP of 66 or 64.

## Piezoresistive strain gauge sensors

The most commonly used disposable sensor mechanism takes advantage of the fact that a semiconductor changes its resistance to current whenever it is deformed in some way. These have the benefit of having a high sensitivity, i.e. undergoing a fairly large change in their resistance in response to a relatively minor change in pressure. This property changes with temperature. Such piezoresistive pressure transducers are usually accurate in the range of 15°C to 40°C. Fortunately, this pressure range is still broader than the typical temperature variation of even the most poorly air-conditioned ICU ward.

Usually, the semiconductor sensor takes the form of a thin silicone membrane. The diagram exaggerates the deflection of this membrane; typically in a medical sensor system, the membrane is deformed by some tiny microscopic fraction of the already microscopic thickness of that membrane. These things used to be about 1cm in diameter and were at one stage made of metal (in the 1950s).  However modern sensors are silicon wafers about 0.02mm in diameter, with the rest of the circuit components (temperature compensation circuits, Wheatstone bridge components, signal conditioning circuits) also etched into the same wafer.

Measurements of pressure need to be made in reference to some sort of baseline. This reference pressure can be a total vacuum (in which case you are measuring absolute pressure changes, i.e. as compared to a pressure of zero). In medical systems, there is no point of having an expensive vacuum chamber for a reference, and the system uses atmospheric pressure as a reference.

## The Wheatstone bridge circuit

The Wheatstone bridge circuit is the component of the pressure transducer which allows the transducer to calculate the change in resistance which results from the change in pressure.

It is a circuit with four resistors, of which three have a known resistance and the fourth (Rx) is the semiconducting membrane. VG is a galvanometer which measures the current flowing between D and B.  Essentially, if the ratio of resistance in the R1/R2 limb is the same as the resistance of the R3/Rx limb, there should be no current flowing through that galvanometer. R2 is a variable resistor, and can be adjusted. So, you adjust the resistance of R2 until the current drops to zero (which is when the resistance of R2 is the same as the resistance of Rx). Alternatively, you can calculate what the Rx resistance is using Kirchhoff's circuit laws, which is what ends up happening in the common hospital-grade blood pressure monitor.

## References

Wilkinson, M. B., and M. Outram. "Principles of pressure transducers, resonance, damping and frequency response." Anaesthesia & Intensive Care Medicine 10.2 (2009): 102-105.

Stoker, Mark R. "Principles of pressure transducers, resonance, damping and frequency response." Anaesthesia & intensive care medicine 5.11 (2004): 371-375.

Gilbert, Michael. "Principles of pressure transducers, resonance, damping and frequency response." Anaesthesia & Intensive Care Medicine 13.1 (2012): 1-6.

Myers, Kenneth. "The investigation of peripheral arterial disease by strain gauge plethysmography." Angiology 15.7 (1964): 293-304.

Lambert, Edward H., and Earl H. Wood. "The use of a resistance wire, strain gauge manometer to measure intraarterial pressure." Experimental Biology and Medicine 64.2 (1947): 186-190.