# Pressure Transduction

Describe the principles of measurement, limitations, and potential sources of error for pressure transducers, and their calibration

Describe the invasive and non-invasive measurement of blood pressure and cardiac output including calibration, sources of errors and limitations

A transducer converts one form of energy to another. Pressure transducers converts a pressure signal to an electrical signal, and require several components:

• Catheter
• Tubing
• Stopcock
• Flush
• Transducer

This system must be calibrated in two ways:

• Static calibration
Calibrates to a known zero.
• Dynamic calibration
Accurate representation of changes in the system.

## Static Calibration

Static calibration involves:

• Leveling the transducer (typically to the level of the phlebostatic axis at the right atrium, or the external auditory meatus)
A change in transducer level will change the blood pressure due to the change in hydrostatic pressure (in cmH2O).
• Zeroing the transducer
• Opening the transducer to air
• Zeroing the transducer on the monitor
A change in measured pressure when the transducer is open to air is due to drift, an artifactual measurement error due to damage to the cable, transducer, or monitor.

## Dynamic Calibration

Dynamic calibration ensures the operating characteristics of the system (or dynamic response) are accurate. Dynamic response is a function of:

• Damping
How rapidly an oscillating system will come to rest.
• Damping is quantified by the damping coefficient or damping ratio
• Describes to what extent the magnitude of an oscillation falls with each successive oscillation
• Calculated from the ratio of the amplitudes of successive oscillations in a convoluted fashion:
, where:
• Resonant Frequency
How rapidly a system will oscillate when disturbed and left alone.
• When damping is low, it will be close to the natural frequency (or undamped resonant frequency)
• Damping and natural frequency are used (rather than the physical characteristics) as they are both easily measured and accurate in describing the dynamic response
• These properties are actually determined by the systems elasticity, mass, and friction, but it is conceptually and mathematically easier to use damping and resonance

### Pressure Waveforms and Dynamic Response

• The dynamic response required is dependent on the nature of the pressure wave to be measured
• Accurately reproducing an arterial waveform requires a system with a greater dynamic response compared to a venous waveform
• An arterial pressure waveform is a periodic (repeating) complex wave, that can be represented mathematically by Fourier analysis
• Fourier analysis involves expressing a complex (arterial) wave as the sum of many simple sine waves of varying frequencies and amplitudes
• The frequency of the arterial wave (i.e., the pulse rate) is known as the fundamental frequency
• The sine waves used to reproduce it must have a frequency that is a multiple (or harmonic) of the fundamental frequency
• Increasing the number of harmonics allows better reproduction of high-frequency components, such as a steep systolic upstroke
• Accurate reproduction of an arterial waveform requires up to 10 harmonics - or 10 times the pulse rate
• An arterial pressure transducer should therefore have a dynamic response of 30Hz
• This allows accurate reproduction of blood pressure in heart rates up to 180bpm (180 bpm = 3Hz, 3Hz x 10 = 30Hz)

### Resonance

• If high frequency components of the pressure waveform approach the natural frequency of the system, then the system will resonate
• This results in a distorted output signal and a small overshoot in systolic pressure.

### Damping

A pressure transduction system should be adequately damped:

• An optimally damped waveform has a damping of 0.64. It demonstrates:
• A rapid return to baseline following a step-change, with one overshoot and one undershoot
• A critically damped waveform has a damping coefficient of 1. It demonstrates:
• The most rapid return to baseline possible following a step-change without overshooting
• An over-damped waveform has a damping coefficient of >1. It demonstrates:
• A slow return to baseline following a step-change with no oscillations
• Slurred upstroke
• Absent dicrotic notch
• Loss of fine detail
• An under-damped waveform has a damping coefficient close to 0 (e.g. 0.03). It demonstrates:
• A very rapid return to baseline following a step-change with several oscillations
• Systolic pressure overshoot
• Artifactual bumps

Optimally damped waveforms are accurate for the widest range of frequency responses:

### Testing Dynamic Response

Dynamic response can be tested by inducing a step-change in the system, which allows calculation of both the natural frequency and the damping coefficient. Clinically, this is performed by doing a fast-flush test.

• Fast flush valve is opened during diastolic runoff period (minimises systemic interference)
• The pressure wave produced indicates the natural frequency and damping coefficient of the system:
• The distance between successive oscillations should be identical and equal to the natural frequency of the system
• The ratio of amplitudes of successive oscillations gives the damping coefficient

### Optimising Dynamic Response

The lower the natural frequency of a monitoring system, the smaller the range of damping coefficients which can accurately reproduce a measured pressure wave. Therefore, the optimal dynamic response is seen when the natural frequency is as high as possible. This is achieved when the tubing is:

• Short
• Wide
• Stiff
• Free of air
Introducing an air bubble will increase damping (generally good, since most systems are under-damped), however it will lower the natural frequency and is detrimental overall.

## Footnotes

### Fundamentals of Pressure Measurement

Pressure exerted by a static fluid is due to the weight of the fluid, and is a function of:

• Fluid density (in kg.L-1)
• Acceleration (effect of gravity, in m.s-2)
• Height of the fluid column

This can be derived as follows:

• , therefore
• Combining the above equations:
• This is usually expressed as:
• Note that this expression does not require the mass or volume of the liquid to be known
• This is why pressure is often measured in height-substance units (e.g. mmHg, cmH2O)

## References

1. Brandis K. The Physiology Viva: Questions & Answers. 2003.
2. Alfred Anaesthetic Department Primary Exam Program
3. Miller, RD. Clinical Measurement of Natural Frequency and Damping Coefficient. In: Anesthesia. 5th Ed. Churchill Livingstone.
Last updated 2021-08-23