# Question 24

Describe the potential causes, and effects, of resonance and damping on an invasive arterial blood pressure trace.

For a good answer candidates were expected to mention 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. The pressure measuring system has a resonant frequency
at which oscillations occur, and 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. The resonant frequency can
be increased by using a short, wide, stiff catheter. In respect to damping, some damping is
inherent in any system and acts to slow down the rate of change of signal between the
patient and pressure transducer. Mention of causes of damping and the optimal damping
coefficient (0.677) were expected. An under-damped system is one whereby resonance
occurs causing the signal to oscillate and overshoot (damping factor <0.7) and an overdamped is one whereby the signal takes a long time to reach equilibrium but will not
overshoot. It may not reach equilibrium in time for a true reading to be given (damping factor >1.0). Both resonance and damping can alter the measured systolic and diastolic values but the mean pressure is not affected

## 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.