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

Master answer

Definitions

Natural frequency: the frequency at which a system oscillates when not subjected to a continuous or repeated external force.

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts.

Resonant frequency:  The frequency of a dynamic system at which the amplitude of response to an oscillating force is a relative maximum is known as a resonant frequency (OR) A natural frequency of vibration determined by the physical parameters of the vibrating object.

Damping:  the property of a system that diminishes resonance.

Critical Damping: Occurs when the damping coefficient (DC or γ gamma) is equal to the undamped resonant frequency of the oscillator.

Optimum Damping: Level of damping which provides a compromise between the speed of the system with its accuracy

Undamped simple harmonic oscillator

• obeys hooke’s law
• motion is sinusoidal in time
• demonstrates a single resonant frequency.

Resonance

Invasive arterial blood pressure is a driven harmonic oscillator

• An external force (pulsations of the heart) adds to the oscillations of the system (the tubing/transducer etc).
• If the frequency of the driving force is similar to, or a harmonic of, the natural frequency of the system then the result is amplification

Arterial waveform is a complex summation of multiple simple sinusoidal waveforms (a fourier series)

• The frequency of the arterial wave (i.e., the pulse rate) is known as the natural or 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

In most clinical systems

• Natural resonant frequency is 10 to 15 Hz
• Primary frequency of the arterial waveform (the heart rate is 60 to 120 bpm or 1 to 2 Hz)
• However the higher frequency components of the more complex arterial waveform are closer to the natural resonant frequency and are amplified to a larger degree.

To minimize the potential of amplification and improve the dynamic accuracy of the real arterial pressure, system should have resonant frequency  >> than 6-8 times frequency of the system being measured:

• Should have noncompliant (i.e. stiff) tubing
• Total mass of liquid in the system should also be minimized (shorter/thinner tubes)
• air bubbles or blood clots or occlusion should be eliminated

Damping

the property of a system that diminishes resonance.

• Damping:
  • decreases the magnitude of the oscillations
  • allows the system to come to rest at a new value.
• Degree of damping determines the rate at which the system achieves that new value.

System can be:

• Underdamped (DC < 0.7):
  • Reaches the zero position quickly
  • Oscillates around it
  • Causes falsely ↑ SBP and falsely ↓ DBP
• Critically damped (DC = 1):
  • Quickest approach to zero amplitude for a damped oscillator without overshoot.
  • Occurs when the damping coefficient (DC or γ gamma) is equal to the undamped resonant frequency of the oscillator.
• Optimal damping (DC = 0.64):
  • Provides a compromise between the speed of the system with its accuracy
  • Minimises overshoot of oscillations, phase and amplitude distortion, and provides maximal frequency response
• Overdamped (DC > 1):
  • The approach to zero is slower
  • Very slow to respond
  • Causes falsely ↓ SBP, falsely ↑ DBP and loss of fine details of waveform (Eg. dichrotic notch)

Bedside Flush Test:

• The degree of damping in an invasive arterial line system can be determined by the bedside flush test
  • Briefly open the continuous flush device to produce a square wave

Gladwin / Sakurai / JC 2020

Answer by Gladwin, JC, Sakurai