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Principles of pressure transducers, resonance, damping and frequency response
EQUIPMENT AND CLINICAL PHYSICS
the patient is not advisable for safety reasons (see page 366). Modern machines have outputs completely isolated from earth (Figure 1) to minimize spurious diathermy circuits to earth. To make a complete electrical circuit for the maximum designed diathermy current to flow, the circuit must be completed from the active electrode connection to the active electrode (Figure 1), via the patient resistance, to the passive electrode, back to the passive electrode connection. In theory, if the passive electrode became disconnected, no current would flow. If an earthed object (e.g. a drip stand) touches the patient, it should have no effect, because it is not part of the return current path. However, there is the problem of stray capacitance.
Principles of pressure transducers, resonance, damping and frequency response Mark R Stoker Methods of direct pressure measurement Accurate recording of dynamic physiological pressures involves the conversion of the pressure waveform into an electrical signal by a transducer so that it can be amplified, processed and displayed by electronic equipment. Two alternative transducer arrangements are used clinically (Figure 1). • A miniaturized sensor can be placed within the patient on the tip of a catheter directly at the point of measurement. • A fluid-filled pathway or manometer can be used to link a catheter or cannula to a transducer placed some distance away from the site of measurement. Although catheter-tip sensor systems are the most accurate, they tend to be more expensive because of their greater complexity, are prone to fibrin deposition if used within the circulation, and cannot be recalibrated within the patient. Manometric transducer systems are therefore in more widespread clinical use. Various physical methods are used to convert pressure changes into an electrical signal; the most common is the strain gauge. A strain gauge transducer consists of: • a force-gathering element, usually a flexible diaphragm that is deformed by incident pressure waves, creating a measurable strain • elements that transform the strain into a proportional electrical signal • a housing that protects the first two elements and incorporates the electrical connections. The marked change in electrical resistance of a semiconductor in response to physical deformation forms the basis of the piezoresistive transducer. This comprises a thin silicon wafer forming the diaphragm, onto the peripheries of which are etched semiconductor resistors. Deformation of the diaphragm alters the electrical resistance of the resistors, which are placed in two pairs, such that one pair is subjected to radial stress as the other pair is stressed tangentially (Figure 2). Circuitry required for amplification, temperature compensation and calibration may also be included on the same silicon wafer using integrated circuit technology. Piezoresistive strain gauges are in widespread clinical use because they are small, cheap to manufacture, resistant to mechanical vibration, and possess high sensitivity (a large change in resistance in response to a small diaphragmatic distortion). Despite electronic compensation, piezoresistive strain gauges are susceptible to the effects of temperature, and are accurate only over a comparatively narrow temperature range.
Stray capacitance: capacitors are electrical components consisting of two parallel plates separated by an insulator (which can be air). They store charge, block the flow of DC, but allow AC to pass. They can be considered as frequency-dependent resistances, in which the resistance deceases as the frequency increases. Capacitors can be ‘natural’ in that the two ‘plates’ can be, for example, the passive electrode and the ground of the theatre (which can be indirectly connected to earth). This ‘capacitor’ will have a low capacitance value and pass minimal currents at domestic mains frequencies. However, it will present a much lower resistance at the higher diathermy frequencies and so other stray circuits can be formed, which can result in burns. For example, if there is a poor connection between the passive electrode and the patient, and a sharp earthed object touches the patient (Figure 3), then an alternate current path could be formed for the return current. The current in this case flows from A in Figure 3 to the active electrode, into the patient, then some of current leaves by the earthed object and flows to earth. To complete the circuit back to B, the current passes from earth to the passive electrode via the stray capacitance. Burns can arise at the connection between the sharp object and the patient, but can also arise at parts of higher current density where only certain parts of the passive electrode are touching the patient. The adverse burns can be minimized by ensuring that the passive electrode is securely and completely attached to the patient (so that the correct circuit is the most ‘attractive’ to the current). Also ensure that no other objects are touching the patient when the diathermy is on. Alarms are installed in the equipment (Figure 1) to warn users that the device is active, and to indicate faulty electrode connections, and stray leakage currents. The stray currents get worse with increasing frequency and, to minimize this effect, modern isolated systems are designed to operate at the lower frequency range of diathermy machines (500 kHz). Older machines used to operate at frequencies up to 2 MHz. Interference with other equipment Surgical diathermy uses radiowaves, with frequencies around the top end of the medium wave AM band. The equipment can therefore act as a short-range transmitter, and sensitive monitoring equipment, such as ECG monitors, can be a receiver for these signals. Ideally, the ECG electrodes and leads should be placed as far from the diathermy electrodes as possible, and care must be taken with interpretation when diathermy is in use. Pacemakers can be interfered with by a similar method, and sometimes the interference can result in the pacemaker wrongly detecting a fast heart rate. In these cases, the pacemaker should be put into a fixed-rate mode.
ANAESTHESIA AND INTENSIVE CARE MEDICINE 5:11
Mark R Stokerr is Consultant Anaesthetist at Peterborough Hospitals NHS Trust. He qualified from Oxford University and trained in anaesthesia in the Oxford and Anglia Regions. His interests include teaching and training, obstetric anaesthesia and public education.
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EQUIPMENT AND CLINICAL PHYSICS
Strain gauge transducer and Wheatstone bridge Piezoresistors R1 to R4 are integrated within a silicon wafer diaphragm in a Wheatstone bridge arrangement. A potential difference c is applied between points C and D. The bridge is zeroed so that it is balanced when no strain is applied, and no potential difference is measured between points A and B. In this condition the following applies: R1 R3 = R2 R4 The resistors are arranged so that when strain is applied to the diaphragm, a rise in the resistance of R1 and R4 is matched by a fall in the resistance of R2 and R3. This unbalances the bridge, and a potential difference proportional to the strain is measured between points A and B. Pairing the four resistors amplifies the imbalance in the bridge in response to strain and increases the sensitivity of the transducer
a
A
c R1
R2
C
D R3
R4
B b 2
a Disposable manometric pressure monitoring set showing a flush valve, b strain gauge housing and c electrical connector plug. Photograph courtesy of BD UK Ltd. b Intracranial pressure transducer connected to a monitor showing a miniaturized strain gauge at the tip off b intracranial catheter, c the intracranial pressure reading and d connecting lead. The natural frequency of the transducer is over 10 kHz. Photograph courtesy of Codman/Johnson & Johnson.
mid-thoracic level is commonly used. Each 10 cm height difference from this point equates to a hydrostatic error of 7.4 mm Hg from the true pressure reading. All pressure transducers require zero balancing to atmospheric pressure before use, and at regular intervals thereafter, to compensate for zero drift. This may be impossible for catheter-tip sensors in situ. Electronic monitoring equipment to which the transducer system is connected must also be suitably calibrated.
1
For any transducer, the electrical output should be directly proportional to the applied pressure over the required pressure range (linearity). The maximum earth leakage current for clinical pressure transducers should be small to avoid the risk of microshock. Figure 3 lists terms used to describe transducer performance. A Wheatstone bridge is used to detect the change in electrical resistance of a strain gauge (Figure 2). Strain gauges have been miniaturized to allow their use on the tip of catheters used to measure intracranial pressure (Figure 1). Other catheter-tip transducer systems use pressure-induced changes in the intensity of light travelling along a fibre-optic pathway to measure intracranial pressure.
Resonance Resonance occurs when the frequency of the in vivo driving oscillations matches the natural frequency of the driven transducer system, and oscillations of large amplitude are induced (Figure 4). This results in significant error by overshooting of the peaks and troughs in the actual pressure waveform, with an overestimation of the systolic pressure and underestimation of the diastolic pressure. The natural (or resonant) frequency is the frequency at which the undamped transducer system oscillates freely with maximal amplitude. The typical manometric pressure transduction system used in clinical practice is considered to be a second-order dynamic system, analogous to a bouncing ball. A second-order system is characterized by three mechanical parameters: • elasticity – the stiffness of the connector tubing and transducer diaphragm • mass – proportional to the diaphragm mass and the volume and density of fluid oscillating in the system • friction or viscous drag – the resistance to movement as the fluid oscillates.
Setting up a pressure transducer correctly is crucial to its accuracy. Manometric sets must be carefully primed with sterile flush solution at room temperature without pressurization of the solution bag to avoid micro and macro air bubble formation within the fluid pathway. A manometric transducer should be positioned carefully with an atmospheric air–fluid interface at the same level as the tricuspid valve. For supine patients in the operating theatre, the
ANAESTHESIA AND INTENSIVE CARE MEDICINE 5:11
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EQUIPMENT AND CLINICAL PHYSICS
Terms relevant to transducer performance
Resonance No damping
Amplitude of induced oscillations
Damping factor: a measure of the tendency of the measuring system to resist oscillation Dynamic response: the practical performance of the measurement system in clinical use. Determined primarily by the resonant frequency and damping factor Frequency response or bandwidth: the highest frequency the measuring system measures without distortion or attenuation of the signal. Should be about eight times the highest frequency component in the pressure signal Hysteresis: ability to produce the same output when the same increasing and then decreasing pressures are applied Linearity: the degree to which the electrical output of the transducer is directly proportional to the applied pressure Offset: the differential bridge voltage (in mV) at constant supply voltage, with no pressure applied and at reference temperature Precision: the accuracy of the measurement produced by the measurement system compared with the actual value Pressure range: the pressure range over which the accuracy of the measuring system lies within defined limits Repeatability: ability to produce the same output with consecutive applications of the same pressure Resolution: the smallest pressure change measurable by the system Sensitivity: the electrical output of the system in mV/mm Hg pressure change Thermal effect: the effect of temperature change on sensitivity, and offset (zero point) of transducer Zero drift: the change in zero balance due to a change in offset over time
X
Y Z f0d f0u Frequency of driving oscillations
As the frequency of driving oscillations increases, the amplitude of induced oscillations rises to a maximum at the natural or resonant frequency of the transducer system (ff0u). If the system is damped by absorbing some of the energy of the induced oscillations, the maximal amplitude attained is reduced. Damping also reduces the resonant frequency of the transducer c system (from f0u to f0d), and extends the flat range of the system from XY to XZ. The resonant frequency of a manometric transducer system is calculated as: Resonant frequency =
1
stiffness of diaphragm
2π
mass of oscillating fluid and diaphragm
4
to a damping factor of 0.7. At this level, the response of the pressure transducer accurately reflects the actual pressure change up to two-thirds of the natural frequency of the system in a close to linear fashion, and phase shift is minimal. Excessive damping is seen commonly in clinical practice, and results from compressible large air bubbles, blood clot, soft, more compliant connector tubing, numerous connections and stopcocks, and catheter kinks in the system. Overdamping leads to overestimation of diastolic pressure, underestimation of systolic pressure, and a widening and slurring of the arterial pressure waveform. Underdamping of the measurement system produced by extending the length of the connector tubing leads to reverberation of pressure waves and erroneous amplification of the signal. This leads to overestimation of systolic pressure and underestimation of diastolic pressure. The fast-flush technique is a bedside test that can be used to check for optimal damping of a manometric pressure measuring system (Figure 6).
3
The natural frequency of a second-order transducer system is proportional to its stiffness and inversely proportional to its mass (Figure 4). The resonant frequency of the system can therefore be raised by including a short, stiff, parallel-sided catheter joined to short, stiff, narrow-bore interconnecting tubing, together with a transducer with a stiff diaphragm. Damping Damping is the process whereby some of the energy of the driven oscillations within the measuring system is absorbed, thus reducing their amplitude. Damping also reduces the resonant frequency of a transducer system (Figure 4). The relationship between resonant frequency and damping is complex. Damping in the correctly functioning manometric system arises mainly from viscous drag in the fluid pathway, tubing connections and stopcocks. Damping increases by the third power of any decrease in the diameter of the tubing (33% narrower tubing increases damping by 135%), a far greater change than the rise in resonant frequency. As a consequence, the diameter of interconnecting tubing has the greatest effect on system performance. The damping factor is an index of the tendency of a transducer system to resist oscillation (Figure 5). Optimal damping is the amount of damping necessary to maximize the frequency response or flat range (see below) of the system and corresponds
ANAESTHESIA AND INTENSIVE CARE MEDICINE 5:11
Damped
Waveform reproduction Using Fourier analysis it is possible to reduce complex waveforms to a summation of simple sine or cosine waves or ascending harmonics, each of which has an increasing frequency and decreasing amplitude (Figure 7). Summation of the first eight to ten harmonics of an arterial blood pressure waveform gives an acceptably accurate representation of its shape. This number is required to track accurately the initial steep rate of rise in the pressure waveform corresponding to left ventricular ejection.
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EQUIPMENT AND CLINICAL PHYSICS
Damping of a manometric transducer system
With increasing degrees of damping, the system is progressively slower to respond to the applied change in pressure, and the increasing delay in the transducer output is termed phase shift f
X
X
Pressure
Pressure
Y
Y
t
t Time
Time d Damping ffactor > 1.0 (excessive with marked phase shift)
c Damping ffactor = 1.0 (critical) X Pressure
X Pressure
a In an underdamped transducer system, where the damping ffactor is < 0.7, significant overshoot and subsequent oscillation occurs when a stepwise pressure change from X to Y is imposed at time t. This results in a significant overestimation of the magnitude of the pressure change. b In an optimally damped system, where the damping ffactor is 0.7, overshoot is limited to 6–7% of the initial pressure change and no oscillation occurs. c In a critically damped system, where the damping ffactor is 1.0, the change in pressure is measured accurately with no overshoot. d In an excessively damped system with a damping ffactor > 1.0, the full magnitude of the pressure change may not be registered.
b Damping ffactor = 0.7 (optimal)
a Damping ffactor < 0.7 (significant overshoot error)
Y
Y
t
t Time
Time 5
The minimum bandwidth is the minimum frequency range over which measurement by a transducer system is sufficiently accurate to reproduce the first eight to ten harmonics of the in vivo pressure signal, resulting in an accurate electronic representation of the shape of the pressure waveform. For the measurement of arterial blood pressure, this should be equal to at least eight times the fundamental frequency of the expected heart rate. At 90 beats/min, a fundamental frequency of 1.5 Hz, the minimum bandwidth would be 12 Hz, with the first eight harmonics comprising sine waves with frequency 1.5, 3, 4.5, 6, 7.5, 9, 10.5 and 12 Hz. Progressively higher harmonics display rapidly decreasing amplitude, contribute less and less to the shape of the transduced waveform and are eventually lost within the ‘noise’ of the measuring system (Figure 7). Accurate reproduction of the amplitude of the pressure waveform, rather than its shape, requires accurate measurement of only the first five harmonics of the fundamental frequency. Most arterial pressure monitoring systems are designed to cope with heart rates up to a maximum of 180 beats/min (3 Hz fundamental frequency and therefore a minimum bandwidth of 24 Hz).
Fast-flush test Frequency f0
t0
The fast-flush or square wave test is performed by opening the valve of the continuous flush device such that flow through the measuring pathway rapidly rises to 30 ml/hour from the usual 1–3 ml/hour. The acute rise in pressure generates a square wave on the bedside monitor between time t0 and t1. When the fast–flush ceases, a sinusoidal pressure wave of fixed frequency and decreasing amplitude is generated. The frequency of the induced oscillations gives an approximation of the resonant frequency of the system, and appropriate damping should return the baseline pressure waveform within one or two oscillations
The frequency response, or flat range of a transducer system, is the highest frequency to which the system can be exposed before it registers significant overshoot. Accurate measurement to a limit of 10% greater than the actual pressure is generally acceptable. The frequency response must be equal to, or greater than, the minimum bandwidth explained above. The frequency response of the measuring system depends on its resonant frequency and the amount of damping. The ideal measuring system has a resonant frequency much higher than the frequencies to be measured. In this system, frequencies up to 20% of the resonant frequency will be accurately
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t1
6
reproduced and no damping is required. This is because initial resonance occurs at a frequency much higher than the necessary bandwidth for accurate waveform reproduction. Catheter-tip
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INTENSIVE CARE
Fourier analysis of the arterial pressure waveform
The role of tracheostomy in ICU
Amplitude
Ben N Barry Andrew R Bodenham 3 Hz +
0
12 Hz
Indications for tracheostomy in the ICU Tracheostomy is usually performed in critically ill patients to provide prolonged airway care during slow weaning from assisted ventilation. Several factors (which may coexist in an individual patient) indicate the need for tracheostomy (Figure 1). For example, survivors of severe sepsis may have persistent weakness from critical illness neuropathy or myopathy and be unable to clear pulmonary secretions unaided. Tracheostomy in the critically ill patient offers significant advantages over prolonged translaryngeal intubation. Less discomfort may allow a reduction in analgesic, sedative and muscle relaxant drugs; clearance of airway secretions, mouth care and enteral nutrition are all facilitated. Airway resistance and anatomical dead space are reduced, reducing the work of breathing and improving the speed and overall success in weaning from assisted ventilation. Tracheostomy allows a seamless transition between different modes of assisted ventilation and weaning modes without trials of extubation and reintubation. However, improved outcome has not been proven in large controlled trials. There is a reduced frequency of accidental extubation and endobronchial intubation. As the patient recovers, a fenestrated tracheostomy tube may be inserted
–
1.5 Hz Time The first or fundamental harmonic (1.5 Hz) together with the second c (3 Hz) and eighth (12 Hz) harmonics of a single blood pressure beat waveform are shown, for a heart rate of 90 beats/minute. Progressively higher harmonics display decreasing amplitude. As a consequence, only the first 8–10 harmonics need to be summed to reproduce the shape of the arterial pressure waveform accurately
7
sensors are the closest available systems to this ideal. For the more commonly used manometric systems, the total measuring chain, consisting of catheter or cannula, tubing, stopcocks and transducer, has a much lower resonant frequency, and damping is therefore vital for increasing accuracy. Optimally damped systems can accurately reproduce frequencies up to 67% of the resonant frequency. An optimally damped manometric transducer system with a resonant frequency of 36 Hz or more should therefore be able to reproduce the shape of the arterial pressure waveform accurately up to a heart rate of 180 beats/min. All manometric pressure monitoring systems introduce a degree of dynamic distortion into the pressure waveform. Some manufacturers produce complete pressure measurement systems where the performance of the entire measurement pathway has been measured dynamically using the GabarithTM test. The accuracy of these systems is guaranteed to lie within tightly defined limits.
Indications for tracheostomy in ICU • • • • • • 1
Ben N Barry worked as Consultant at Middlemore Hospital, Auckland, New Zealand before returning to St James's University Hospital, Leeds. He qualified from the Middlesex Hospital, London, and trained in Sheffield and Leeds. His interests include the management of septic shock, especially blood purification and monitoring of microvascular perfusion.
FURTHER READING Billiet E, Colardyn F. Pressure measurement evaluation and accuracy validation: the Gabarith test. Intens Care Med d 1998; 24: 1323–6. Runciman W B, Ludbrook G L. The measurement of systemic arterial blood pressure. In: Prys-Roberts C, Brown B R, eds. International practice of anaesthesia. Oxford: Butterworth-Heinemann, 1996.
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Prolonged weaning from assisted ventilation Acute or chronic neuromuscular conditions Poor cardiorespiratory reserve Bulbar dysfunction Brain injury Upper airway obstruction
Andrew R Bodenham is Consultant in Anaesthesia and Intensive Care at Leeds General Infirmary, UK. He qualified from St Bartholomew’s Hospital, London, and trained in anaesthesia and intensive care in London, Brisbane, Cambridge and Leeds. His research interests include airway care, vascular anaesthesia and vascular access techniques.
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the patient is not advisable for safety reasons (see page 366). Modern machines have outputs completely isolated from earth (Figure 1) to minimize spurious diathermy circuits to earth. To make a complete electrical circuit for the maximum designed diathermy current to flow, the circuit must be completed from the active electrode connection to the active electrode (Figure 1), via the patient resistance, to the passive electrode, back to the passive electrode connection. In theory, if the passive electrode became disconnected, no current would flow. If an earthed object (e.g. a drip stand) touches the patient, it should have no effect, because it is not part of the return current path. However, there is the problem of stray capacitance.
Principles of pressure transducers, resonance, damping and frequency response Mark R Stoker Methods of direct pressure measurement Accurate recording of dynamic physiological pressures involves the conversion of the pressure waveform into an electrical signal by a transducer so that it can be amplified, processed and displayed by electronic equipment. Two alternative transducer arrangements are used clinically (Figure 1). • A miniaturized sensor can be placed within the patient on the tip of a catheter directly at the point of measurement. • A fluid-filled pathway or manometer can be used to link a catheter or cannula to a transducer placed some distance away from the site of measurement. Although catheter-tip sensor systems are the most accurate, they tend to be more expensive because of their greater complexity, are prone to fibrin deposition if used within the circulation, and cannot be recalibrated within the patient. Manometric transducer systems are therefore in more widespread clinical use. Various physical methods are used to convert pressure changes into an electrical signal; the most common is the strain gauge. A strain gauge transducer consists of: • a force-gathering element, usually a flexible diaphragm that is deformed by incident pressure waves, creating a measurable strain • elements that transform the strain into a proportional electrical signal • a housing that protects the first two elements and incorporates the electrical connections. The marked change in electrical resistance of a semiconductor in response to physical deformation forms the basis of the piezoresistive transducer. This comprises a thin silicon wafer forming the diaphragm, onto the peripheries of which are etched semiconductor resistors. Deformation of the diaphragm alters the electrical resistance of the resistors, which are placed in two pairs, such that one pair is subjected to radial stress as the other pair is stressed tangentially (Figure 2). Circuitry required for amplification, temperature compensation and calibration may also be included on the same silicon wafer using integrated circuit technology. Piezoresistive strain gauges are in widespread clinical use because they are small, cheap to manufacture, resistant to mechanical vibration, and possess high sensitivity (a large change in resistance in response to a small diaphragmatic distortion). Despite electronic compensation, piezoresistive strain gauges are susceptible to the effects of temperature, and are accurate only over a comparatively narrow temperature range.
Stray capacitance: capacitors are electrical components consisting of two parallel plates separated by an insulator (which can be air). They store charge, block the flow of DC, but allow AC to pass. They can be considered as frequency-dependent resistances, in which the resistance deceases as the frequency increases. Capacitors can be ‘natural’ in that the two ‘plates’ can be, for example, the passive electrode and the ground of the theatre (which can be indirectly connected to earth). This ‘capacitor’ will have a low capacitance value and pass minimal currents at domestic mains frequencies. However, it will present a much lower resistance at the higher diathermy frequencies and so other stray circuits can be formed, which can result in burns. For example, if there is a poor connection between the passive electrode and the patient, and a sharp earthed object touches the patient (Figure 3), then an alternate current path could be formed for the return current. The current in this case flows from A in Figure 3 to the active electrode, into the patient, then some of current leaves by the earthed object and flows to earth. To complete the circuit back to B, the current passes from earth to the passive electrode via the stray capacitance. Burns can arise at the connection between the sharp object and the patient, but can also arise at parts of higher current density where only certain parts of the passive electrode are touching the patient. The adverse burns can be minimized by ensuring that the passive electrode is securely and completely attached to the patient (so that the correct circuit is the most ‘attractive’ to the current). Also ensure that no other objects are touching the patient when the diathermy is on. Alarms are installed in the equipment (Figure 1) to warn users that the device is active, and to indicate faulty electrode connections, and stray leakage currents. The stray currents get worse with increasing frequency and, to minimize this effect, modern isolated systems are designed to operate at the lower frequency range of diathermy machines (500 kHz). Older machines used to operate at frequencies up to 2 MHz. Interference with other equipment Surgical diathermy uses radiowaves, with frequencies around the top end of the medium wave AM band. The equipment can therefore act as a short-range transmitter, and sensitive monitoring equipment, such as ECG monitors, can be a receiver for these signals. Ideally, the ECG electrodes and leads should be placed as far from the diathermy electrodes as possible, and care must be taken with interpretation when diathermy is in use. Pacemakers can be interfered with by a similar method, and sometimes the interference can result in the pacemaker wrongly detecting a fast heart rate. In these cases, the pacemaker should be put into a fixed-rate mode.
ANAESTHESIA AND INTENSIVE CARE MEDICINE 5:11
Mark R Stokerr is Consultant Anaesthetist at Peterborough Hospitals NHS Trust. He qualified from Oxford University and trained in anaesthesia in the Oxford and Anglia Regions. His interests include teaching and training, obstetric anaesthesia and public education.
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Strain gauge transducer and Wheatstone bridge Piezoresistors R1 to R4 are integrated within a silicon wafer diaphragm in a Wheatstone bridge arrangement. A potential difference c is applied between points C and D. The bridge is zeroed so that it is balanced when no strain is applied, and no potential difference is measured between points A and B. In this condition the following applies: R1 R3 = R2 R4 The resistors are arranged so that when strain is applied to the diaphragm, a rise in the resistance of R1 and R4 is matched by a fall in the resistance of R2 and R3. This unbalances the bridge, and a potential difference proportional to the strain is measured between points A and B. Pairing the four resistors amplifies the imbalance in the bridge in response to strain and increases the sensitivity of the transducer
a
A
c R1
R2
C
D R3
R4
B b 2
a Disposable manometric pressure monitoring set showing a flush valve, b strain gauge housing and c electrical connector plug. Photograph courtesy of BD UK Ltd. b Intracranial pressure transducer connected to a monitor showing a miniaturized strain gauge at the tip off b intracranial catheter, c the intracranial pressure reading and d connecting lead. The natural frequency of the transducer is over 10 kHz. Photograph courtesy of Codman/Johnson & Johnson.
mid-thoracic level is commonly used. Each 10 cm height difference from this point equates to a hydrostatic error of 7.4 mm Hg from the true pressure reading. All pressure transducers require zero balancing to atmospheric pressure before use, and at regular intervals thereafter, to compensate for zero drift. This may be impossible for catheter-tip sensors in situ. Electronic monitoring equipment to which the transducer system is connected must also be suitably calibrated.
1
For any transducer, the electrical output should be directly proportional to the applied pressure over the required pressure range (linearity). The maximum earth leakage current for clinical pressure transducers should be small to avoid the risk of microshock. Figure 3 lists terms used to describe transducer performance. A Wheatstone bridge is used to detect the change in electrical resistance of a strain gauge (Figure 2). Strain gauges have been miniaturized to allow their use on the tip of catheters used to measure intracranial pressure (Figure 1). Other catheter-tip transducer systems use pressure-induced changes in the intensity of light travelling along a fibre-optic pathway to measure intracranial pressure.
Resonance Resonance occurs when the frequency of the in vivo driving oscillations matches the natural frequency of the driven transducer system, and oscillations of large amplitude are induced (Figure 4). This results in significant error by overshooting of the peaks and troughs in the actual pressure waveform, with an overestimation of the systolic pressure and underestimation of the diastolic pressure. The natural (or resonant) frequency is the frequency at which the undamped transducer system oscillates freely with maximal amplitude. The typical manometric pressure transduction system used in clinical practice is considered to be a second-order dynamic system, analogous to a bouncing ball. A second-order system is characterized by three mechanical parameters: • elasticity – the stiffness of the connector tubing and transducer diaphragm • mass – proportional to the diaphragm mass and the volume and density of fluid oscillating in the system • friction or viscous drag – the resistance to movement as the fluid oscillates.
Setting up a pressure transducer correctly is crucial to its accuracy. Manometric sets must be carefully primed with sterile flush solution at room temperature without pressurization of the solution bag to avoid micro and macro air bubble formation within the fluid pathway. A manometric transducer should be positioned carefully with an atmospheric air–fluid interface at the same level as the tricuspid valve. For supine patients in the operating theatre, the
ANAESTHESIA AND INTENSIVE CARE MEDICINE 5:11
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EQUIPMENT AND CLINICAL PHYSICS
Terms relevant to transducer performance
Resonance No damping
Amplitude of induced oscillations
Damping factor: a measure of the tendency of the measuring system to resist oscillation Dynamic response: the practical performance of the measurement system in clinical use. Determined primarily by the resonant frequency and damping factor Frequency response or bandwidth: the highest frequency the measuring system measures without distortion or attenuation of the signal. Should be about eight times the highest frequency component in the pressure signal Hysteresis: ability to produce the same output when the same increasing and then decreasing pressures are applied Linearity: the degree to which the electrical output of the transducer is directly proportional to the applied pressure Offset: the differential bridge voltage (in mV) at constant supply voltage, with no pressure applied and at reference temperature Precision: the accuracy of the measurement produced by the measurement system compared with the actual value Pressure range: the pressure range over which the accuracy of the measuring system lies within defined limits Repeatability: ability to produce the same output with consecutive applications of the same pressure Resolution: the smallest pressure change measurable by the system Sensitivity: the electrical output of the system in mV/mm Hg pressure change Thermal effect: the effect of temperature change on sensitivity, and offset (zero point) of transducer Zero drift: the change in zero balance due to a change in offset over time
X
Y Z f0d f0u Frequency of driving oscillations
As the frequency of driving oscillations increases, the amplitude of induced oscillations rises to a maximum at the natural or resonant frequency of the transducer system (ff0u). If the system is damped by absorbing some of the energy of the induced oscillations, the maximal amplitude attained is reduced. Damping also reduces the resonant frequency of the transducer c system (from f0u to f0d), and extends the flat range of the system from XY to XZ. The resonant frequency of a manometric transducer system is calculated as: Resonant frequency =
1
stiffness of diaphragm
2π
mass of oscillating fluid and diaphragm
4
to a damping factor of 0.7. At this level, the response of the pressure transducer accurately reflects the actual pressure change up to two-thirds of the natural frequency of the system in a close to linear fashion, and phase shift is minimal. Excessive damping is seen commonly in clinical practice, and results from compressible large air bubbles, blood clot, soft, more compliant connector tubing, numerous connections and stopcocks, and catheter kinks in the system. Overdamping leads to overestimation of diastolic pressure, underestimation of systolic pressure, and a widening and slurring of the arterial pressure waveform. Underdamping of the measurement system produced by extending the length of the connector tubing leads to reverberation of pressure waves and erroneous amplification of the signal. This leads to overestimation of systolic pressure and underestimation of diastolic pressure. The fast-flush technique is a bedside test that can be used to check for optimal damping of a manometric pressure measuring system (Figure 6).
3
The natural frequency of a second-order transducer system is proportional to its stiffness and inversely proportional to its mass (Figure 4). The resonant frequency of the system can therefore be raised by including a short, stiff, parallel-sided catheter joined to short, stiff, narrow-bore interconnecting tubing, together with a transducer with a stiff diaphragm. Damping Damping is the process whereby some of the energy of the driven oscillations within the measuring system is absorbed, thus reducing their amplitude. Damping also reduces the resonant frequency of a transducer system (Figure 4). The relationship between resonant frequency and damping is complex. Damping in the correctly functioning manometric system arises mainly from viscous drag in the fluid pathway, tubing connections and stopcocks. Damping increases by the third power of any decrease in the diameter of the tubing (33% narrower tubing increases damping by 135%), a far greater change than the rise in resonant frequency. As a consequence, the diameter of interconnecting tubing has the greatest effect on system performance. The damping factor is an index of the tendency of a transducer system to resist oscillation (Figure 5). Optimal damping is the amount of damping necessary to maximize the frequency response or flat range (see below) of the system and corresponds
ANAESTHESIA AND INTENSIVE CARE MEDICINE 5:11
Damped
Waveform reproduction Using Fourier analysis it is possible to reduce complex waveforms to a summation of simple sine or cosine waves or ascending harmonics, each of which has an increasing frequency and decreasing amplitude (Figure 7). Summation of the first eight to ten harmonics of an arterial blood pressure waveform gives an acceptably accurate representation of its shape. This number is required to track accurately the initial steep rate of rise in the pressure waveform corresponding to left ventricular ejection.
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EQUIPMENT AND CLINICAL PHYSICS
Damping of a manometric transducer system
With increasing degrees of damping, the system is progressively slower to respond to the applied change in pressure, and the increasing delay in the transducer output is termed phase shift f
X
X
Pressure
Pressure
Y
Y
t
t Time
Time d Damping ffactor > 1.0 (excessive with marked phase shift)
c Damping ffactor = 1.0 (critical) X Pressure
X Pressure
a In an underdamped transducer system, where the damping ffactor is < 0.7, significant overshoot and subsequent oscillation occurs when a stepwise pressure change from X to Y is imposed at time t. This results in a significant overestimation of the magnitude of the pressure change. b In an optimally damped system, where the damping ffactor is 0.7, overshoot is limited to 6–7% of the initial pressure change and no oscillation occurs. c In a critically damped system, where the damping ffactor is 1.0, the change in pressure is measured accurately with no overshoot. d In an excessively damped system with a damping ffactor > 1.0, the full magnitude of the pressure change may not be registered.
b Damping ffactor = 0.7 (optimal)
a Damping ffactor < 0.7 (significant overshoot error)
Y
Y
t
t Time
Time 5
The minimum bandwidth is the minimum frequency range over which measurement by a transducer system is sufficiently accurate to reproduce the first eight to ten harmonics of the in vivo pressure signal, resulting in an accurate electronic representation of the shape of the pressure waveform. For the measurement of arterial blood pressure, this should be equal to at least eight times the fundamental frequency of the expected heart rate. At 90 beats/min, a fundamental frequency of 1.5 Hz, the minimum bandwidth would be 12 Hz, with the first eight harmonics comprising sine waves with frequency 1.5, 3, 4.5, 6, 7.5, 9, 10.5 and 12 Hz. Progressively higher harmonics display rapidly decreasing amplitude, contribute less and less to the shape of the transduced waveform and are eventually lost within the ‘noise’ of the measuring system (Figure 7). Accurate reproduction of the amplitude of the pressure waveform, rather than its shape, requires accurate measurement of only the first five harmonics of the fundamental frequency. Most arterial pressure monitoring systems are designed to cope with heart rates up to a maximum of 180 beats/min (3 Hz fundamental frequency and therefore a minimum bandwidth of 24 Hz).
Fast-flush test Frequency f0
t0
The fast-flush or square wave test is performed by opening the valve of the continuous flush device such that flow through the measuring pathway rapidly rises to 30 ml/hour from the usual 1–3 ml/hour. The acute rise in pressure generates a square wave on the bedside monitor between time t0 and t1. When the fast–flush ceases, a sinusoidal pressure wave of fixed frequency and decreasing amplitude is generated. The frequency of the induced oscillations gives an approximation of the resonant frequency of the system, and appropriate damping should return the baseline pressure waveform within one or two oscillations
The frequency response, or flat range of a transducer system, is the highest frequency to which the system can be exposed before it registers significant overshoot. Accurate measurement to a limit of 10% greater than the actual pressure is generally acceptable. The frequency response must be equal to, or greater than, the minimum bandwidth explained above. The frequency response of the measuring system depends on its resonant frequency and the amount of damping. The ideal measuring system has a resonant frequency much higher than the frequencies to be measured. In this system, frequencies up to 20% of the resonant frequency will be accurately
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t1
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reproduced and no damping is required. This is because initial resonance occurs at a frequency much higher than the necessary bandwidth for accurate waveform reproduction. Catheter-tip
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INTENSIVE CARE
Fourier analysis of the arterial pressure waveform
The role of tracheostomy in ICU
Amplitude
Ben N Barry Andrew R Bodenham 3 Hz +
0
12 Hz
Indications for tracheostomy in the ICU Tracheostomy is usually performed in critically ill patients to provide prolonged airway care during slow weaning from assisted ventilation. Several factors (which may coexist in an individual patient) indicate the need for tracheostomy (Figure 1). For example, survivors of severe sepsis may have persistent weakness from critical illness neuropathy or myopathy and be unable to clear pulmonary secretions unaided. Tracheostomy in the critically ill patient offers significant advantages over prolonged translaryngeal intubation. Less discomfort may allow a reduction in analgesic, sedative and muscle relaxant drugs; clearance of airway secretions, mouth care and enteral nutrition are all facilitated. Airway resistance and anatomical dead space are reduced, reducing the work of breathing and improving the speed and overall success in weaning from assisted ventilation. Tracheostomy allows a seamless transition between different modes of assisted ventilation and weaning modes without trials of extubation and reintubation. However, improved outcome has not been proven in large controlled trials. There is a reduced frequency of accidental extubation and endobronchial intubation. As the patient recovers, a fenestrated tracheostomy tube may be inserted
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1.5 Hz Time The first or fundamental harmonic (1.5 Hz) together with the second c (3 Hz) and eighth (12 Hz) harmonics of a single blood pressure beat waveform are shown, for a heart rate of 90 beats/minute. Progressively higher harmonics display decreasing amplitude. As a consequence, only the first 8–10 harmonics need to be summed to reproduce the shape of the arterial pressure waveform accurately
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sensors are the closest available systems to this ideal. For the more commonly used manometric systems, the total measuring chain, consisting of catheter or cannula, tubing, stopcocks and transducer, has a much lower resonant frequency, and damping is therefore vital for increasing accuracy. Optimally damped systems can accurately reproduce frequencies up to 67% of the resonant frequency. An optimally damped manometric transducer system with a resonant frequency of 36 Hz or more should therefore be able to reproduce the shape of the arterial pressure waveform accurately up to a heart rate of 180 beats/min. All manometric pressure monitoring systems introduce a degree of dynamic distortion into the pressure waveform. Some manufacturers produce complete pressure measurement systems where the performance of the entire measurement pathway has been measured dynamically using the GabarithTM test. The accuracy of these systems is guaranteed to lie within tightly defined limits.
Indications for tracheostomy in ICU • • • • • • 1
Ben N Barry worked as Consultant at Middlemore Hospital, Auckland, New Zealand before returning to St James's University Hospital, Leeds. He qualified from the Middlesex Hospital, London, and trained in Sheffield and Leeds. His interests include the management of septic shock, especially blood purification and monitoring of microvascular perfusion.
FURTHER READING Billiet E, Colardyn F. Pressure measurement evaluation and accuracy validation: the Gabarith test. Intens Care Med d 1998; 24: 1323–6. Runciman W B, Ludbrook G L. The measurement of systemic arterial blood pressure. In: Prys-Roberts C, Brown B R, eds. International practice of anaesthesia. Oxford: Butterworth-Heinemann, 1996.
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Prolonged weaning from assisted ventilation Acute or chronic neuromuscular conditions Poor cardiorespiratory reserve Bulbar dysfunction Brain injury Upper airway obstruction
Andrew R Bodenham is Consultant in Anaesthesia and Intensive Care at Leeds General Infirmary, UK. He qualified from St Bartholomew’s Hospital, London, and trained in anaesthesia and intensive care in London, Brisbane, Cambridge and Leeds. His research interests include airway care, vascular anaesthesia and vascular access techniques.
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