M. Tidmarsh E.S. Lin
BLOOD PRESSURE MEASUREMENT
MEASUREMENT OF GAS FLOW
MEASUREMENT OF GAS AND VAPOUR CONCENTRATIONS
CARBON DIOXIDE MEASUREMENT
MEASUREMENT OF pH
MEASUREMENT OF DEPTH OF ANAESTHESIA
TEMPERATURE MEASUREMENT MEASUREMENT OF HUMIDITY MEASUREMENT OF PAIN
Clinical measurement in anaesthesia is usually concerned with the direct measurement of a physical quantity such as the pressure, flow or concentration of a gas. Alternatively assessment of a physiological parameter such as neuromuscular blockade, depth of anaesthesia or pain levels may be required. In these instances measurement is made indirectly, using a related physical variable such as a stimulated muscle twitch, the electroencephalogram or a visual analogue scale.
The process of measurement is performed using apparatus that can be referred to as the measurement system. This may be as simple as a ruler with pencil and paper or as sophisticated as the integrated electronic monitoring systems available in operating theatres and intensive care units. In the final analysis data obtained must be interpreted, but note below:
The data obtained by making measurements can only be interpreted correctly if:
• The relationship between the data and the physical quantity or parameter being measured is understood.
• The characteristics of the measurement system are known. Measurement Systems
Measurement of a physical quantity is a process in which the quantity being measured provides an input to a measurement system, which then processes this input to yield an output in the form of a reading or display. This concept is illustrated in Figure CM.1, where a measurement system is represented as a "black box' with an input and output.
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i Transmission piilti
i Signal conditioning unit
Figure CM. 1 ''Black box" analogy for a measurement system
The measurement system consists of component "black boxes' representing:
• A transducer - a detecting element to convert the quantity being measured (the input) into usable data or a signal, usually an electrical signal. Examples of common transducers are:
Microphone, which converts sound to an electrical signal
Thermistor, which converts temperature variations into an electrical signal
Piezoelectric crystal, which converts pressure variations into an electrical signal
• A transmission path - the means by which the transducer signal is transferred to the signal conditioning unit or the display unit. Examples include an electrical or optic cables, a length of tubing or an infrared link
• A signal-conditioning unit - processes the transducer signal to make it suitable for display or storage. Signal processing includes functions such as amplification, filtering, and analogue to digital conversion. It may occur before or after the signal passes along the transmission path
ANALOGUE AND DIGITAL METHODS OF SIGNAL DISPLAY
Oscilloscope Moving Coil Meter Chart Recorder
Digital Voltmeter Light Emitting Diodes Liquid Crystal Display
Magnetic Tape Chart
Computer Hard Disk Floppy Disc Magnetic Tape CD ROM
• A display or storage unit - provides the output of the system as a display and also stores the signals or data. It may employ analogue or digital methods, which are detailed in Figure CM.2
The performance of a measurement system can be characterized by its static and dynamic characteristics. These determine the relationship between the quantity being measured (input) and the reading (output).
Static characteristics define the performance of a measurement system when it is dealing with an input which is not changing (or changing only slowly). Under these circumstances there is enough time for the system to reach a steady-state before the measured quantity changes, so that the output follows changes in the input accurately. Static characteristics include:
• Accuracy - closeness between the measurement obtained and the "true' value of the quantity being measured, e.g. if a pressure has a "true' value of 10 cmH2O, an accurate system may read 10.01 cmH2O and may be described as having an accuracy of 0.1%. In an inaccurate system reading 11 cmH2O the accuracy may be quoted as 10% (Figure CM.3a)
• Sensitivity - relationship between changes in the output reading of the system and changes in the measured quantity. The sensitivity of a pressure measurement system may be described as the change in output signal voltage for a given change in pressure, e.g. 1 volt per cmH2O for a sensitive system or 100 mV per cmH2O for a system 10 times less sensitive. Less sensitive systems will cover a wider range of pressure measurement than sensitive systems (Figure CM.3b)
• Linearity - in a linear measurement system the output reading varies in proportion to the measured quantity. Thus, in a linear pressure measurement system, if the pressure doubles the output voltage will double. When the output voltage is plotted against the input pressure, a straight line is obtained. The gradient of this line gives the sensitivity of the system. It is usually desirable for a system to be linear and any non linearity may be quoted as a percentage of the operating range of the instrument (Figure CM.3b). Some instruments may be intrinsically non linear reflecting their underlying mechanism, e.g. hot wire ammeter, or rotameter
• Hysteresis - a property of a measurement system that produces an error dependent on whether the measured value is decreasing or increasing. Hysteresis in a mechanical device is caused by elastic energy stored in the system, or frictional losses between moving parts. Figure CM.3c shows how hysteresis in a measurement system produces errors in the measurement of increasing and decreasing pressures
Figure CM.3. Static characteristics of a measurement system: (a) accuracy, (b) sensitivity and (c) hysteresis
• Drift - variation in the reading from an instrument that is not caused by change in the measured quantity. It is usually caused by the effect of internal or external temperature changes on the measurement system, and unstable components in the system
Every system requires a certain time to settle to a steady-state when presented with a change in its input. This response time may affect the accuracy of the measurement, since if the input is changing rapidly, the measuring system may not have adequate time to reach steady-state and, thus, will not give an accurate reading. The dynamic characteristics of a system reflect its ability to respond to rapidly changing inputs.
An important dynamic characteristic of any measurement system is its response to a rapid increase in input or a 'step' function (Figure CM.4). This can be simulated by dipping a thermometer at room temperature into boiling water, or rapidly opening a tap connecting a pressure gauge to a pressurized container. In a perfect measuring instrument, the output or 'step response' produced by a step input, should also be a step function occurring instantaneously to give a reading of the measured quantity.
Figure CM.4 Step input to a measurement system
In practice, the step response differs from the ideal due to the properties of the system, and the output only reaches a 'true' steady-state value after a finite time. The time lag for an instrument between a 'step' input and the output reaching its final value, is reflected by:
• Response time - time taken from occurrence of the 'step' input to the instrument output reaching 90% of its final value
• Rise time - time taken for the output of the instrument to rise from 10 to 90% of its final value Damping in a Measurement System
The step response of an instrument may also fall short of the ideal in the shape of the output signal produced. Some examples are shown in Figure CM.5, where in curve (a) the output overshoots and oscillates about the true value. In curve (b) the response does not reach the true value in the time plotted; in curve (c) the output reaches a steady reading of the true value within the shortest time compatible with no overshoot. The property that determines these effects in the step response is called the 'damping' of the system.
All instruments will possess damping that affects their dynamic response. This includes mechanical, hydraulic, pneumatic and electrical devices. In an electromechanical device such as a galvanometer there are mechanical moving parts such as the meter needle and bearings. Damping in these components arises from frictional effects on their movement. This may arise unintentionally or may be applied as part of the instrument design to control oscillation of the needle when it records a measurement. In a fluid- (gas or liquid) operated device, damping occurs due to viscous forces that oppose the motion of the fluid. While damping in electrical systems is provided electronically by electrical resistance which opposes the passage of electrical currents.
Uhdaf damped (4]
Uhdaf damped (4]
Figure CM.5 Effects of damping on the step response of a system
Figure CM.5 Effects of damping on the step response of a system
Note particularly that:
Damping is an important factor in the design of any system. In a measurement system it can lead to inaccuracy of the readings or display:
Underdamping can result in oscillation and overestimation of the measurement
Overdamping can result in underestimation of the measurement
Critical damping is usually an optimum compromise resulting in the fastest steady-state reading for a particular system, with no overshoot or oscillation
Any measurement system in practice will only respond to a restricted range of frequencies, either by design or due to the limitations of its components. Thus, if the system were to be tested with input signals of the same amplitude but different frequencies it would only produce an output over a limited range of frequencies. Within this frequency range the system may respond more sensitively to some frequencies than others. The response of the system (system gain) plotted against signal frequency is called the frequency response of the system (Figure CM.6).
Figure CM.6. Frequency response of a system off of)
Figure CM.6. Frequency response of a system
The highest frequency that a system responds to is the high 'cut-off frequency, above which input signals will produce no output. An example of such a cut-off is in the frequency response of the human auditory system, which at best may have a high 'cut-off1 frequency of 20 kHz. Similarly a system may possess a low cut-off frequency, the lowest frequency audible by the human ear being 15 Hz. The frequency range between low and high cut-off frequencies is referred to as the bandwidth.
Any input signal can be characterized by its frequency spectrum that defines the different frequency components, into which the signal can be resolved. The frequency response of a measurement system does not cover the spectrum of a signal thus blocking part of the input signal. Alternatively, an instrument may be more sensitive or attenuate certain frequencies, causing it to give falsely high or low readings, within its operating frequency range. This can occur at natural frequencies or resonances. Distortion of a signal is illustrated in Figure CM.7.
It might initially be assumed that the ideal frequency response for a system would be one with equal sensitivity at all frequencies from very low to very high frequencies (i.e. a flat response from 0 to ro Hz), but this would also enable 'noise' to pass through the system with the measurement signal, thus causing error and distortion.
The frequency response of a mechanical system is determined by its inertial and compliance elements equivalent to masses and springs), while in an electrical circuit it is determined by the inductances and capacitances. There is often a design compromise between providing accuracy and reducing noise levels.
Figure CM.7. Causes of signal distortion
Figure CM.7. Causes of signal distortion
A measurement system may possess natural frequencies or resonances determined by inertial and compliance elements in a mechanical system (or inductances and capacitances in an electrical circuit). These resonances appear as peaks in the systems frequency response and can produce distortion in a signal display and errors in the readings (Figure CM.8). Good design practice can ensure that these resonances do not lie in the operating frequency range of the instrument, or ensure appropriate levels of damping to smooth out these unwanted peaks.
Phase Shift Response
Fourier analysis demonstrates how a signal is composed of a series of component frequencies. In a signal being measured each component wave will
Figure CM.8 Example of a resonant frequency undergo a different delay in time or phase shift (a phase shift is a time delay expressed as an angle, i.e. the units are degrees or radians) introduced by its passage through the measurement system. If a measurement system significantly alters the relative phases between the components of a signal passes it can distort the signal. Any measurement system will have a 'phase shift response', consisting of the phase shift occurring at different frequencies, which can be plotted against the frequency axis. This phase shift response will be dependent on the components of the system, and can be responsible for distortion or errors in an instrument.
In modern measuring instruments the transducer usually produces an electrical current or voltage, which varies according to the measured parameter. This voltage or current is a signal. Signals in clinical measurement are usually voltage signals or 'biological potentials'. Most biological potentials vary in time, many in a repetitive or cyclical fashion, e.g. electrocardiogram, airway pressure during respiration. Some signals such as the electroencephalogram and evoked potentials are not cyclical but vary irregularly.
The characteristics of some common biological potentials are outlined in Figure CM.9. Electrical signals can be described in the following ways:
• As a voltage (or current) varying in time - any signal can be represented as a voltage (or current) plotted along the 'time' axis, i.e. it is a 'time-variant' signal. The height of the signal above the time axis is measured in volts, millivolts or microvolts (V, mV, |V) (Figure CM.10). If a current, it will be in amps, milliamps or micro-amps (A, mA, |A). The
COMMON BIOLOGICAL SIGNALS
Frequency range (Hz)
Figure CM. 10 Voltage signal that varies with time - square wave amplitude of a signal is the range of variation (volts or amps) between maximum and minimum values
• As periodic or non periodic - a signal that varies with a repeating pattern in time, at regular intervals is said to be periodic (Figure CM.11). Each cycle of the signal has the same shape or waveform, and possesses a period, T = duration of one cycle (s), a frequency (Hz) and an amplitude, the maximum swing in voltage or current, spanned by the signal. The simplest type of periodic signal is a sine wave
• As analogue or digital - an analogue signal is continuous in time and the magnitude of the signal varies smoothly without discernible increments. The signal is, thus, analogous to most natural varying processes. Signals produced by transducers are usually analogue signals. A digital signal is produced from an analogue signal by sampling the signal at regular intervals, and recording the magnitude with changes in fixed increments rather than on a continuous varying scale. Such a signal can be represented completely by a set of numbers. This adapts the signal for processing by digital systems and manipulation by computer, which can have significant advantages (Figure CM.12)
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Figure CM. 11 Periodic voltage signal - sine wave
• As a series of frequency components - a mathematical method of analysis was invented by Jean Fourier (a French mathematician) in 1822. This has evolved both theoretically and practically to become one of the most powerful tools used in signal processing. Application of Fourier analysis to a signal enables it to be described by its 'frequency spectrum'
Frequency Spectrum of a Signal
In describing a signal by its frequency spectrum consider that:
• Any signal varying continuously in time can be broken down into a collection of sine and cosine waves, which if added together yield the original signal
• The component waves exist as sine-cosine pairs at the same frequency
• Each pair of components has a combined amplitude and can be plotted as a point on the 'frequency' axis giving the frequency spectrum for the signal
Fourier analysis, thus, describes the conversion of a signal into its frequency components. Fourier analysis is most suitable for periodic signals, but can still be used for non periodic waveforms using an approximation which treats the waveform as if it were a periodic signal with a very long period.
A signal may be modified by any of the components of the measurement system. If the changes introduced are intentional, they represent 'signal processing' or 'signal conditioning'. Unwanted alteration of the signal by the system is distortion and introduces error. The addition of unwanted components to the signal by the system or from outside electrical interference is called 'noise'. These unwanted components can be added to a signal changing its value at any instant and its appearance on display. This may occur due to noise being generated in the measurement system itself, or due to the 'pick up' of interference from external sources such as diathermy or fluorescent lighting.
Signal-to-noise (S/N) ratio - in some cases the noise signals may be so large as to obscure the measurement signal altogether. An awareness of the magnitude of noise components in the signal is necessary to assess the accuracy of the measurements. This can be expressed by the S/N ratio, which is the ratio of signal amplitude to noise amplitude expressed in decibels (Figure CM.13).
Signal processing modifies a measurement signal by using various functions, for example:
• Amplification, to make it suitable for display, storage or transmission - many biological signals are very small in amplitude (e.g. electroencephalogram (EEG) signals may be microvolts, while ECG signals may be millivolts). Such signals are usually too small to drive display or storage units, and require amplification. Low amplitude signals are also unsuitable for transmission since noise signals picked up may be of similar or greater amplitude giving a low S/N ratio and obscuring the signal
Figure CM.13 Illustration of signal-to-noise ratio: (a) signal,
Figure CM.13 Illustration of signal-to-noise ratio: (a) signal,
• Filtering to remove noise - often noise signals are in a different frequency range from the wanted measurement signal. In these cases the noise can be reduced by using filters to block out the unwanted frequencies. A low-pass filter rejects all frequencies above a given threshold. Such a filter would be used to avoid high frequency interference from a source like diathermy. A high-pass filter rejects low frequencies below a set threshold, whereas a notch filter rejects a specific frequency, such as 50 Hz to avoid pick up from mains cables
• Spectral analysis - a signal is usually displayed as a time varying voltage or current. In some cases (e.g. cerebral function monitoring) a display of the signal frequency spectrum is required, which can be achieved using electronic processing. A common method first converts the analogue signal to a digital signal, and then applies a mathematical algorithm called the Fast Fourier Transform (FFT). Transformation of a signal to its spectral components can also make some processing functions such as filtering easier and more accurate. It also enables more complex analysis to be readily performed by computers
• Analogue to digital (A to D) conversion - often required before applying other processing functions, and is always necessary in order for the signal to be stored and analysed in a computer. This is because most electronic manipulation of signals uses digital electronics as opposed to analogue methods
• Averaging to remove noise - in some cases the amplitude of the measurement signal may only be a fraction of the noise amplitude (i.e. S/N ratio is very low), and when displayed the wanted signal may be completely obscured by noise. If the wanted signal is repetitive and the noise is random in time, multiple repetitions and summations of the combined signal, lead to an increase of the S/N ratio as the random noise cancels itself out. This is called averaging and is used in the extraction of evoked potentials, where the evoked signal is only a few millivolts in amplitude, hidden in background noise. Averaging > 2000 repetitions may be required to obtain a clear signal
As previously noted, the components of a measuring system can be considered as 'black boxes' in the way that the measurement system as a whole has been examined as a 'black box'. Thus, an amplifier is simply an electronic 'black box' which when presented with an electrical signal at its input produces an output which is of greater amplitude. The purpose of an amplifier in measuring systems is to increase the power of a low amplitude signal in order that it can be used to drive a display or storage unit. An amplifier contains an electronic circuit that requires a power supply, and channels power from this power supply into the signal increasing the voltage, current or both voltage and current.
Characteristics of an amplifier include:
• Gain, which is the ratio of the amplitude of the output signal (AO) to the input signal (A1). It is usually expressed as decibels (db). Such units may be used to express any ratio by taking 10 times the log10 of the ratio). Thus, if the output amplitude produced by an amplifier, AO, is 100 times the input amplitude, A1:
Amplifier gain = tOlng (Aj/Ai)
• Frequency response and phase response - an amplifier will be characterized by these responses as a result of its circuit design, just as the complete instrument will have these responses dependent on the combined effects of its component parts
• Upper cut-off frequency, which is the upper frequency limit, above which signals are blocked or 'cut-off. Measured in Hertz (Hz)
• Lower cut-off frequency, the lower frequency limit below which signals are blocked or "cut-off1
• Bandwidth, which is the extent of the frequency range passed by a system or amplifier, i.e. the amplifier only amplifies signals within this frequency range. It, therefore, lies between upper and lower cut-off frequencies and is also measured in frequency units (Hz)
• Input impedance, which is the electrical impedance "seen' by the transducer signal at the input of the amplifier. Maximum power transfer takes place when the input impedance of the amplifier matches the output impedance of the transducer. Measured in ohms
• Output impedance, the electrical impedance seen looking' back into the output terminals of the amplifier. Maximum transfer of signal power from the amplifier requires matching of the output impedance to the input impedance of the transmission path or the display unit
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