Pressure Transduction

Describe the principles of measurement, limitations, and potential sources of error for pressure transducers, and their calibration

Describe the invasive and non-invasive measurement of blood pressure and cardiac output including calibration, sources of errors and limitations

A transducer converts one form of energy to another. Pressure transducers converts a pressure signal to an electrical signal, and require several components:

• Catheter
• Tubing
• Stopcock
• Flush
• Transducer

This system must be calibrated in two ways:

• Static calibration
  Calibrates to a known zero.
• Dynamic calibration
  Accurate representation of changes in the system.

Static Calibration

Static calibration involves:

• Leveling the transducer (typically to the level of the phlebostatic axis at the right atrium, or the external auditory meatus)
  A change in transducer level will change the blood pressure due to the change in hydrostatic pressure (in cmH₂O).
• Zeroing the transducer
  • Opening the transducer to air
  • Zeroing the transducer on the monitor
    A change in measured pressure when the transducer is open to air is due to drift, an artifactual measurement error due to damage to the cable, transducer, or monitor.

Dynamic Calibration

Dynamic calibration ensures the operating characteristics of the system (or dynamic response) are accurate. Dynamic response is a function of:

• Damping
  How rapidly an oscillating system will come to rest.
  • Damping is quantified by the damping coefficient or damping ratio
    • Describes to what extent the magnitude of an oscillation falls with each successive oscillation
    • Calculated from the ratio of the amplitudes of successive oscillations in a convoluted fashion:
      $D = \sqrt{(\ln{D_2 \over D_1})^2 \over \pi^2 + (\ln{D_2 \over D_1})^2 }$, where:

• Resonant Frequency
  How rapidly a system will oscillate when disturbed and left alone.
  • When damping is low, it will be close to the natural frequency (or undamped resonant frequency)

• Damping and natural frequency are used (rather than the physical characteristics) as they are both easily measured and accurate in describing the dynamic response
• These properties are actually determined by the systems elasticity, mass, and friction, but it is conceptually and mathematically easier to use damping and resonance

Pressure Waveforms and Dynamic Response

• The dynamic response required is dependent on the nature of the pressure wave to be measured
• Accurately reproducing an arterial waveform requires a system with a greater dynamic response compared to a venous waveform

• An arterial pressure waveform is a periodic (repeating) complex wave, that can be represented mathematically by Fourier analysis
• Fourier analysis involves expressing a complex (arterial) wave as the sum of many simple sine waves of varying frequencies and amplitudes
  • The frequency of the arterial wave (i.e., the pulse rate) is known as the 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
  • Accurate reproduction of an arterial waveform requires up to 10 harmonics - or 10 times the pulse rate
  • An arterial pressure transducer should therefore have a dynamic response of 30Hz
    • This allows accurate reproduction of blood pressure in heart rates up to 180bpm (180 bpm = 3Hz, 3Hz x 10 = 30Hz)

Resonance

• If high frequency components of the pressure waveform approach the natural frequency of the system, then the system will resonate
• This results in a distorted output signal and a small overshoot in systolic pressure.

Damping

A pressure transduction system should be adequately damped:

• An optimally damped waveform has a damping of 0.64. It demonstrates:
  • A rapid return to baseline following a step-change, with one overshoot and one undershoot
• A critically damped waveform has a damping coefficient of 1. It demonstrates:
  • The most rapid return to baseline possible following a step-change without overshooting
• An over-damped waveform has a damping coefficient of >1. It demonstrates:
  • A slow return to baseline following a step-change with no oscillations
  • Slurred upstroke
  • Absent dicrotic notch
  • Loss of fine detail
• An under-damped waveform has a damping coefficient close to 0 (e.g. 0.03). It demonstrates:
  • A very rapid return to baseline following a step-change with several oscillations
  • Systolic pressure overshoot
  • Artifactual bumps

Optimally damped waveforms are accurate for the widest range of frequency responses:

Testing Dynamic Response

Dynamic response can be tested by inducing a step-change in the system, which allows calculation of both the natural frequency and the damping coefficient. Clinically, this is performed by doing a fast-flush test.

• Fast flush valve is opened during diastolic runoff period (minimises systemic interference)
• The pressure wave produced indicates the natural frequency and damping coefficient of the system:
  • The distance between successive oscillations should be identical and equal to the natural frequency of the system
  • The ratio of amplitudes of successive oscillations gives the damping coefficient

Optimising Dynamic Response

The lower the natural frequency of a monitoring system, the smaller the range of damping coefficients which can accurately reproduce a measured pressure wave. Therefore, the optimal dynamic response is seen when the natural frequency is as high as possible. This is achieved when the tubing is:

• Short
• Wide
• Stiff
• Free of air
  Introducing an air bubble will increase damping (generally good, since most systems are under-damped), however it will lower the natural frequency and is detrimental overall.

Footnotes

Fundamentals of Pressure Measurement

Pressure exerted by a static fluid is due to the weight of the fluid, and is a function of:

• Fluid density (in kg.L^-1)
• Acceleration (effect of gravity, in m.s^-2)
• Height of the fluid column

This can be derived as follows:

• $Pressure = {Force \over Area} = {Mass \times Acceleration \over Area}$
• $Density = {Mass \over Volume}$, therefore $Mass = Volume \times Density$
• Combining the above equations:
  $Pressure = {Density \times Volume \times Acceleration \over Area} = Density \times Length \times Acceleration$
  • This is usually expressed as: $Pressure = \rho .h.g$

• Note that this expression does not require the mass or volume of the liquid to be known
• This is why pressure is often measured in height-substance units (e.g. mmHg, cmH₂O)

References

1. Brandis K. The Physiology Viva: Questions & Answers. 2003.
2. Alfred Anaesthetic Department Primary Exam Program
3. Miller, RD. Clinical Measurement of Natural Frequency and Damping Coefficient. In: Anesthesia. 5th Ed. Churchill Livingstone.