2013B08 Describe the effects of resonance and damping on an invasive arterial blood pressure tracing.

 

List:

·     Arterial line: components, how it works, accuracy

·     Physics of SHM: definitions

·     Dynamic accuracy

 

Arterial line:

Components

·  Cannula with anti-clot

·  Compressible tubing with saline

·  Pressure transducer: diaphragm with four strain gauges (conductor)

·  Saline bag under pressure

·  1-3mL/h infusion and ability to flush

·  Electronic display

Function

·  Continuous column between arterial blood and transducer

·  ↑↓ oscillations in pressure -> displacement of diaphragm -> stretch/relax strain gauges -> ↑/↓ electrical resistance -> amplification -> arterial trace

·  Accuracy improved by multiple strain gauges +/- Wheatstone bridge

Accuracy

Static:

·  Zero relative to atmospheric pressure

·  Time calibration: observe steadiness at zero

·  Height calibration: e.g. move transducer against a standard

Dynamic:

·  Optimise damping

·  Minimise resonance

 

Physics of simple harmonic motion:

Natural frequency (FN)

·  Definition: tendency of a system once disturbed to oscillate at a particular frequency about its equilibrium position.

·  Determinants: FN ∝ potential energy (stiffness) / kinetic energy (mass)

o Potential energy ∝ tube elastance x diaphragm elastance

o Kinetic energy ∝ (length x tube compliance x density) / (radius)

Fundamental frequency (F0)

·  Lowest frequency oscillation within a system (e.g. heart rate in ABP trace)

Resonance

·  Definition: where repeated disturbance of a system at its natural frequency (or at a close multiple of it) causes increasing amplitude of oscillation

·  Effect on ABP trace: ↑SBP, ↓DBP, ↔mAP, contributes to peripheral dicrotic notch

Damping

·  Definition: minimization of oscillatory amplitude through viscous and frictional forces

·  Equation: damping ∝ (Length x volume of displacement x viscosity) / (diameter x density)

·  Damping coefficient: index of rate of decay of oscillations

·  Optimal damping: balance between maximizing response speed and minimizing overshoot

·  Effect on ABP trace: ↓SBP, ↑DBP, ↔mAP, delayed waveform, loss of high frequency components e.g. incisura

 

 

To ensure dynamic accuracy:

Minimise resonance

Aim:

·     FN ≥ 10x F0 hence resonance unlikely to occur

·     Flat frequency response at or near the measured frequencies

·     No exaggeration of amplitude of measured frequencies

Means:

·     ↑potential energy (stiffness): non-compliant tubing and diaphragm

·     ↓ kinetic energy: short, wide, non-compliant tubing and low density fluid

Optimise damping

Aim:

·     Flat frequency response up to 2/3 of FN

·     Minimal phase distortion i.e. minimal and more homogenous lag

·     Damping coefficient 0.64

·     Exactly two oscillations after fast flush test

·     <7% overshoot overall

·     <2% overshoot for harmonics (if Fourier analysis performed)

Means:

·     Intact cannula, no kink, no clot, no bubbles

·     System design

Graph

 

*Note: modern systems are underdamped, but natural frequency is high enough to obviate resonance*

 

 

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