# Question 12

Explain resonance and its significance and the effects of damping on invasive arterial blood pressure measurement.

Many candidates gave detailed answers that involved the set up and components of the arterial line system that was not asked for in the question and did not attract marks. There was confusion around the correct use of the terms natural frequency, resonance frequency and harmonics – candidates that were able to describe these frequencies correctly went on to achieve a good mark – the graphs and discussion around optimal dampening, over and underdamped traces were often drawn poorly or without sufficient detail, and at times were not used within in the context of the answer. Descriptions of the clinical effect seen with over / under dampened traces on blood pressure was well described.

## Discussion

Resonance:

• The pressure transducer system can be described as a second-order dynamic system, a harmonic oscillator
• The natural frequency of the system is the frequency at which it will oscillate freely (in the absence of sustained stimulus)
• Resonance is the amplification of signal when is its frequency is close to the natural frequency of a system

Relevance to invasive blood pressure measurement

• An arterial waveform is a composite of many waveforms of increasing frequencies (harmonics), the amplitude of which decreases as their frequency increases.
• At least five harmonics must be analysed to accurately represent the pulse pressure
• At least eight harmonics must be analysed to represent the arterial pressure waveform with sufficient resolution to see the dicrotic notch
• The transducer system must therefore have a natural frequency well above the 8th harmonic frequency of a rapid pulse, i.e. higher than 24Hz

The effects of damping:

• Damping is the process of the system absorbing the energy (amplitude) of oscillations
• The transducer system must be adequately damped so that amplitude change due to resonance should not occur even when it is close to the system's natural frequency
• A system with minimal damping will reverberate, the natural frequency of the system will amplify the measured waves and therefore the pressure registered by the tranducer will be higher than the actual pressure.
• An over-damped system will produce underestimated values and slurred broad waveforms.
• The frequency response of a system (the flat range) is the range of frequencies over which there is minimal amplitude change from resonance, and this range should encompass the clinically relevant range of frequencies
• The natural frequency (and thus the frequency response) of an arterial line transducer can be interrogated using the fast flush test.

## References

Moxham, I. M. "Physics of invasive blood pressure monitoring." Southern African Journal of Anaesthesia and Analgesia 9.1 (2003): 33-38.

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.

Schwid, Howard A. "Frequency response evaluation of radial artery catheter-manometer systems: sinusoidal frequency analysis versus flush method.Journal of clinical monitoring4.3 (1988): 181-185.

Gardner, Reed M. "Direct blood pressure measurement—dynamic response requirements." Anesthesiology: The Journal of the American Society of Anesthesiologists 54.3 (1981): 227-236.