# Question 17

Define and explain damping, resonance, critical damping and optimum damping.

Concise definitions were required with a clear explanation of the underlying physical principles.
The response time of the system, degree of overshoot, effect on amplitude, noise and ability to
faithfully reproduce frequencies relative to the natural resonant frequency were important
considerations.
Many candidates interpreted the question as relating to arterial lines and a detailed discussion
of the components and characteristics of an intra-arterial catheter and transducer system did not
attract marks.

## 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
• Damping:
• Damping is the process of the system absorbing the energy (amplitude) of oscillations
• Damping coefficient:
• An index of the tendency of the system to resist oscillations
• Given by the equation,
γ = c / 2m
where
γ is the damping coefficient,
c is the friction coefficient, and
m is the mass of the oscillating thing.
• A damping coefficient around 0.7 is optimal, >1.0 is overdamped, and <0.7 is underdamped.
• 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
• Critical damping: a damping coefficient of 1.0
• The oscillator returns to the equilibrium position as quickly as possible, without oscillating, and passes it only once.
• Occurs when the damping coefficient is equal to the resonant frequency of the oscillator
• The effects of 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.

## 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.