# Question 12

Describe the effects of resonance and damping on an invasive arterial blood pressure tracing.

Many candidates seemed to get some of the basic concepts but few were able to expand on
simple concepts.
It was expected that candidates could describe that the arterial pressure waveform is made
up of many different sine waves (as determined by Fourier Analysis) with each sine wave
having a specific frequency. Every system has its own natural oscillatory frequency, or
resonant frequency. If this is less than 40 Hz, it falls within the range of frequencies present
in the blood pressure waveform and oscillations may produce a sine wave which is
superimposed on the blood pressure wave form.
Some damping is inherent in any system and acts to slow down the rate of change of signal
between the patient and pressure transducer. It may be caused by air bubbles or blood clots
or occlusion. This reduces the deflection of the transducer diaphragm and hence the size of
the waveform. The effect of damping on temporal response was rarely mentioned.
Accurate graphical representations of invasive pressure traces are important. Many
candidates provided poor drawings without axis, labels, reference to normal or discussion in
text.

## 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
• 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
• Damping:
• Damping is the process of the system absorbing the energy (amplitude) of oscillations
• Optimal damping: A damping coefficient of  around 0.64-0.7
• Maximises frequency response
• Minimises overshoot of oscillations
• Minimises phase and amplitude distortion
• Corresponds to 2-3 oscillations following an arterial line flush test
• The effects of resonance and damping:
• 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
• 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.
• A hyper-resonant (underdamped) system (damping coefficient <0.7) will oscillate excessively and overestimate the peak and trough measurements
• An overdamped system (damping coefficient > 1.0) will report lower peaks and troughs
• An optimally damped system (a damping coefficient of  around 0.64-0.7) maximises frequency response, minimises overshoot of oscillations and minimises phase and amplitude distortion

## 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.