# 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 cmH_{2}O). **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:

, where:

- Damping is quantified by the

**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)

- When damping is low, it will be close to the

- 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)

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

### 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 rapid return to baseline following a
- 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**

- The most rapid return to baseline possible following a step-change
- 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

- The

### 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:

- , therefore
- Combining the above equations:
- This is usually expressed as:

- 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, cmH
_{2}O)

## References

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