118
`
`Design of pulse oximeters
`
`interrupted, as the R wave detected is no longer valid, and therefore the software
`used to eliminate motion artifacts will have to be terminated. An interrupt to the
`display/audio driver will start a routine to display the lead fall off information
`and generate some alarms. After this problem has been fixed, another interrupt
`would trigger the operation to resume. During interrupt routine execution the
`MBS stalls for a while until the process generating the interrupt has been
`serviced.
`Also, if the physician wants to refer to the pulse rate of the patient recorded
`a few minutes back, the interrupt raised will cause the current routine to branch,
`retrieve the data from the memory and continue with the recording. Usually
`while user-triggered interrupts are generated, the main routine continues with the
`measurements and has this raised interrupt serviced in parallel.
`
`8.8 POWER SUPPLY
`
`The power supplies present on most boards are switched mode power supplies
`(SMPS). A SMPS-based power supply is either in the flyback or the flyforward
`converter mode. Figure 8.13 shows the power supply present on the Nellcor N-
`200® '· which contains switching power
`supplies
`in
`flyback converter
`configuration. These power supplies are capable of generating low voltages at
`high currents. The supply is capable of providing 2 A at +5 V and 100 rnA at
`±18 V.
`
`Pulse
`width
`modulation
`
`+5 v
`
`Pulse
`width
`modulation
`
`+ 5 V, 2 A
`
`+18 V, 100 rnA
`
`-18 V, 100 rnA
`
`Figure 8.13 Basic power supply block diagram (adapted from Nellcor N-200® (Nellcor 1989)).
`
`The essence of a SMPS supply is the pulse width modulator (PWM). In
`figure 8.13 the two PWMs control the 5 V and the ±18 V supply. The PWM
`senses the de voltages at their inputs and controls the pulse width at the gates of
`switching F~Ts. A voltage regulator provides reference voltages for the two
`PWMs.
`Field effect transistors are characterized by the rise and fall times of their
`drain currents. As the gates of the FETs are slightly capacitive, there is a need to
`minimize the rise and fall times of the drain current. Schmitt inverters are
`present to provide low impedance active current drive to these capacitive gates.
`
`0135
`
`Apple Inc.
`APL1020 Part 2 of 2
`U.S. Patent No. 8,923,941
`
`

`
`Electronic instrument control
`
`119
`
`8.8.1 Recharging
`
`Battery charger circuits are necessary to charge up a battery in case of a power
`line failure. In such an application when the main system is on line a battery
`charging circuit charges up a battery making use of the ac line voltage. In case of
`emergencies, because of a line failure, this system is set into the battery operated
`mode. However there is only a limited usage time available. Moreover the system
`becomes more bulky.
`Figure 8.14 shows that ac power is taken from one of the secondaries of the
`transformers. It is rectified using a diode bridge arrangement (full wave
`rectifier) and filtered using a capacitor, to provide a positive voltage to the
`voltage regulator. Current limiting action is present via the use of a current(cid:173)
`sensing resistor and a set of current-limiting transistors. Potentiometers are
`provided to trim the battery charging voltage. In order to avoid back discharge
`from the battery when the ac power is removed, a diode is present. Keeping in
`mind the efficiency of a power system, the expected voltage is 85% of the voltage
`provided by the battery charging circuit.
`
`From power supply
`transformer secondary
`windings
`
`Current
`limiting
`transistor
`
`Figure 8.14 Battery charger block diagram (adapted from Nellcor N-200® (Nellcor 1989)).
`
`Battery output
`
`8.9 ALARMS
`
`When using pulse oximeters in critical applications, alarms are essential to give
`an indication to the physician that something is wrong. These alarms have to be in
`both audio and visual form. Comparators, power amplifiers, drivers and speakers
`constitute the audio alarm section. LCD bar graphs and blinkers are used for the
`visual section. Certain guidelines have been formulated by standardizing agencies
`such as the American Society for Testing and Materials (ASTM) regarding the
`color of the indicator, frequency of the indicator and the tone, audio level etc.
`Also the signals that need to be treated as emergency signal are classified (pulse
`rate, detached lead, etc).
`
`8.10 STORAGE
`
`Data concerning oxygen saturation and pulse rate can be collected and stored in
`memory. This may be used in the future to train the pulse oximeter system, using
`neural networks and artificial intelligence to generate control signals.
`Memories are selected using address lines and data lines are used to load and
`unload data from them. In order to make the most efficient use of this storage
`
`0136
`
`

`
`120
`
`Design qf pulse oximeters
`
`mechanism, some care has to be taken while designing the memory system. When
`no power is applied to the memory system there is danger of losing data.
`
`8.11 FRONT END DISPLAY
`
`This section includes the display terminal on the front end of the pulse oximeter.
`Liquid crystal displays (LCD) or LED displays are used depending on the clarity,
`resolution, power consumption, and even aesthetics. Push buttons in the form of
`feather touch buttons or conventional switches are provided. Interface points,
`alarm indicators, and other important features are also displayed.
`
`8.11.1 Front end driver circuit
`
`Figure 8.15 shows that the driver circuit consists of two major driving
`techniques, one for the digit and bargraph and the other for lightbar and other
`front panel indicators.
`
`Address/data line
`
`Chip
`select
`
`Latch..-.. ... -. Driverl---+----fllllll'"'i
`
`Power
`transistor
`bank
`
`Digit/bargraph display
`
`Segments within digit/bargraph
`display
`
`Lightbar display
`
`Latch +--111.-t
`
`Clear
`
`Chip select
`
`..---+------+-------Address/data information to the
`microprocessor
`
`Up/dow
`Octal
`buffer l"""'''lf------f-'ounter
`Counter value
`
`Channel A
`
`ChannelS
`
`Schmitt trigger
`
`To ADC and finally
`to the microprocessor
`
`Power up tester amplifier
`
`Figure 8.15 Generic display driver circuit.
`
`In order to clear the front panel display, a reset circuit consisting of
`capacitors and resistors is used. During reset, these components generate a small
`duration reset pulse that is sent to all the latches on the driver board. This reset
`pulse clears all the front panel display elements.
`Latches and decoders are used to generate the signals required to display
`information on the display elements. A set of power transistors are used to
`
`i
`!
`!
`
`1
`
`0137
`
`

`
`Electronic instrument control
`
`121
`
`generate the drive current required to turn on the display elements. A chip select
`decoder is used to select the latch-decoder combination depending on the type of
`display needed. In the circuit layout, signals are required for the digit/bargraph
`display, to select particular segments within the digit/bargraph display and signals
`for light bar display. The latches generate the information to be displayed via
`address
`information
`that comes
`from
`the microprocessor. After
`the
`microprocessor-based system has decided what is
`to be displayed, address
`information is sent to Character Generator ROMs (CG-ROMs) or Dynamic
`Display RAMs (DD-RAMs) which generate the digit/display information. In these
`devices, bit information pertaining to a particular character is stored at a specific
`address location. Depending on the address at the input, the required character is
`generated.
`
`8.11.2 Front panel control
`
`The chip select decoder is used to select the octal buffer, which reads in inputs
`from the buttons on the front panel and the up/down counter which reads in the
`control knob rotation information which is relayed through it.
`The control knob consists of a two-channel optical chopper, with the two
`channels mechanically 90 degrees out of phase with each other, and a dual
`channel optical slot detector. There are two Schmitt triggers, one per channel, to
`eliminate any transients present and to clean up the signal. The two channels are
`used to send control signals to the up/down counter. Depending on the direction
`in which the knob is turned, either the up or the down mode is selected. Channel
`A provides the clocking pulses for the counter and channel B provides the
`direction control, whether it is up or down. The processor reads the counter
`output to determine a change in the up/down mode of the counter. It then adds the
`count to the accumulated count. The processor then resets the counter.
`
`8.11.3 Power up display tests
`
`the first time the system runs a few
`When we power up the system for
`initialization tests. The software tests run are discussed in detail in chapter 9. The
`primary concern is to ensure that all the display elements are operational. We
`therefore have a power up tester amplifier which senses the power return line
`from the driver ICs by monitoring a voltage developed across a resistor. The
`driver ICs are used to boost the drive current into the segments of the digital
`displays. This is amplified and given to the ADC. The processor uses this signal
`during start up to check whether the display is faulty.
`
`8.12 SPEAKERS
`
`The speaker is an inductive load needing a positive and a negative signal. Figure
`8.16 shows that currents to these two inputs are controlled by two different paths.
`Depending on the address/data information the demultiplexer generates many
`signals like the VRED, VIR and the volume control signal. A sample-and-hold
`circuit is used to hold this signaL This signal is then passed via a series of power
`transistors to boost the current flowing into the speaker.
`A timer and counter chip generates a count using certain address/data
`information and temporarily saves it into a buffer. This tone signal is used to
`
`0138
`
`

`
`122
`
`Design of pulse oximeters
`
`control a FET switch which alternately connects or disconnects the speakers
`negative input to ground. The frequency of the tone signal (determined by the
`timer/counter chip) determines the pitch of the sound produced. A capacitor is
`present to smoothen the sound. A diode· is also present to suppress any transients
`from the inductive load.
`
`Address/data lines
`
`Demux
`
`Sample/hold
`
`Volume
`
`Amplifier
`and power
`transistor
`
`Speaker+
`
`Speaker-
`
`Address/data lines
`
`imer/
`ounter
`
`Switching
`FET
`
`Capacitor
`and
`diode
`
`Figure 8.16 Speaker driver block diagram (adapted from Nellcor N-200® (Nellcor 1989)).
`
`REFERENCES
`
`Cheung P W, Gauglitz K F, Hunsaker S W, Prosser S J, Wagner D 0 and Smith R E 1989
`Apparatus for the automatic calibration of signals employed in oximetry US patent 5,259,381
`Corenman J E, Stone R T, Boross A, Briggs D A and Goodmann DE 1990 Method and apparatus
`for detecting optical pulses US patent 4,934,372
`MRI 1992 Service Manual, model3500 MR-compatible oximeter (Bay Shore, NY: MRI)
`Nellcor 1989 Service Manual, N-200 Pulse Oximeter (Pleasanton, CA: Nellcor)
`Nellcor 1991 Service Manual, N-3000 Pulse Oximeter (Pleasanton, CA: Nellcor)
`New W Jr 1987 Pulse oximeter monitor US patent 4,653,498
`Nielsen L L 1983 Multi-wavelength incremental absorbance oximeter US patent 4,167,331
`Ohmeda 1988 Service Manual, Model 3740 Pulse Oximeter (Louisville, CO: Ohmeda)
`Pologe J A 1987 Pulse oximetry: Technical aspects of machine design Int. Anesth. Clinics 25 (3)
`137-53
`Protocol 1991 Service Manual (Beaverton, OR: Protocol)
`Sobusiak A C and Wiczynski G 1995 Specificity of SIF co-operating with optoelectronic sensor in
`pulse oximeter system Proc. SPIE 2634
`Wilber S A 1985 Blood constituent measuring device US patent 4,407,290
`Yoshiya I, Shimada Y and Tanaka K 1980 Spectrophotometric monitoring of arterial oxygen
`saturation in the fingertip Med. Biol. Eng. Comput. 18 27
`
`INSTRUCTIONAL OBJECTIVES
`
`8.1 Sketch the block diagram of the microprocessor subsystem, and highlight at least three main
`features that you think are vital for optimum operation of this system.
`8.2 Explain the signal flow in the pulse oximeter from the photodiode to the front-end display.
`8.3 Explain the kind of circuit protection associated with a patient module.
`8.4 Explain how communication is established between the various chips on the microprocessor
`based system.
`8.5 Describe the timing control involved in the microprocessor-based system.
`
`0139
`
`

`
`T
`
`Electronic instrument control
`
`123
`
`8.6 Explain the operation of the synchronous detector and the demultiplexer in the pulse oximeter
`system.
`8.7 Mention the need for active amplifiers and low-pass filters.
`8.8 Explain the analog-to--digital conversion action involved in the pulse oximeter.
`8. 9 Explain the function of the pattern generator.
`8.10 It is decided to improve the resolution of the ADC. List the steps you will take to improve the
`existing system. Explain how this will affect the system operation.
`8. 11 Explain the motivation for subtraction of the DC-level in the photodiode signal before the
`ADC.
`8. 12 Describe the components of an input module of a pulse oximeter.
`
`0140
`
`

`
`CHAPTER9
`
`SIGNAL PROCESSING ALGORITHMS
`
`Surekha Palreddy
`
`Pulse oxirneters measure and display the oxygen saturation of hemoglobin in
`arterial blood, volume of individual blood pulsations supplying the tissue, and the
`heart rate. These devices shine light through the tissue that is perfused with blood
`such as a finger, an ear, the nose or the scalp, and photoelectrically sense the
`transmittance of the light in the tissue. The amount of light that is transmitted is
`recorded as an electric signal. The signal is then processed using several signal
`processing algorithms to estimate the arterial oxygen saturation reliably in the
`presence of motion and other artifacts. Signal-processing algorithms implemented
`both in hardware and software play a major role in transforming the signals that
`are collected by the sensors and extracting useful information. In this chapter, the
`signal-processing to calculate Sa02 is discussed and ECG synchronization
`algorithms that enhance the reliability of Sa02 estimation and improve the signal(cid:173)
`to-noise ratio are discussed. Commercial pulse oximeters use various algorithms
`for ECG synchronization. Some of these algorithms are discussed with reference
`to commercially available pulse oximeters such as from Nellcor® and Criticare®.
`
`9.1 SOURCES OF ERRORS
`
`The three general sources of errors dealt with by signal-processing algorithms
`are the motion artifact, reduced saturation levels ( <80o/o) and low perfusion levels
`(Goodman and Corenman 1990). The motion artifact is a major problem that is
`usually due to the patient's muscle movement proximate to the oximeter probe
`inducing spurious pulses that are similar to arterial pulses. The spurious pulses
`when processed can produce erroneous results. This problem is particularly
`significant in active infants, and patients that do not remain still during
`monitoring. The quantity of motion required to disturb the signal is very small.
`Shivering and slight flexing of the fingers can make the signal erroneous.
`Another significant problem occurs in circumstances where the patient's
`blood circulation is poor and the pulse strength is very weak. For example, poor
`circulation occurs in cases of insufficient blood pressure or reduced body
`temperature. In such conditions, it is difficult to separate the true pulsatile
`component from artifact pulses because of the low signal-to-noise ratio. Several
`time-domain and frequency-domain signal-processing algorithms are proposed to
`
`124
`
`I
`
`I l
`
`0141
`
`

`
`Signal processing algorithms
`
`125
`
`enhance the performance of pulse oximeters with improved rejection of noise,
`spurious pulses, motion artifact, and other undesirable aperiodic waveforms.
`This chapter describes the algorithms required to estimate the arterial
`oxygen saturation based on the Beer-Lambert law.
`
`9.2 BEER-LAMBERT LAW
`
`Pulse oximetry measures the effect of arterial blood in tissue on the intensity of
`the transmitted light (Cheung et al 1989). The volume of blood in the tissue is a
`function of the arterial pulse, with a greater volume present at systole and a
`smaller volume present at diastole. Because blood absorbs most of the light
`passing through the tissue, the intensity of the light emerging from the tissue is
`inversely proportional to the volume of the blood present in the tissue. The
`emergent light intensity varies with the arterial pulse and can be used to indicate a
`patient's pulse rate. In addition, the absorbance coefficient of oxyhemoglobin is
`different from that of deoxygenated hemoglobin for most wavelengths of light.
`Differences in the amount of light absorbed by the blood at two different
`wavelengths can be used to indicate the hemoglobin oxygen saturation, which
`equals
`
`%Sa02 =[Hb02]/([Hb]+[Hb02])xlOO%.
`
`(9.1)
`
`The Beer-Lambert law governs the absorbance of light by homogeneous
`absorbing media. The incident light with an intensity I o impinges upon the
`that indicates the
`absorptive medium of characteristic absorbance factor A
`that is the reciprocal of the
`attenuating effect and a transmittance factor T
`absorbance factor ( 1/A). The intensity of the emerging light I 1 is less than the
`incident light 10 and is expressed as the product TI 0· The emergent light intensity
`In transmitted· through a medium divided into n identical components, each of
`unit thickness and the same transmittance factor T is equal to Tnio. In can be
`written in a more convenient base by equating Tn to e-an, where a
`is the
`absorbance of medium per unit length and is frequently referred to as the relative
`extinction coefficient. The relative extinction coefficient a is related to the
`extinction coefficient £ (discussed in chapter 4) as a = EC, where C is the
`concentration of the absorptive material. The expression for the intensity of the
`light In emerging from a medium can be given by the following general equation
`called the Beer-Lambert law.
`
`I
`I
`n = 0 e
`
`-ad
`
`(9.2)
`
`where In is the emergent light intensity, I o is the incident light intensity, a is the
`absorbance coefficient of the medium per unit length, d is the thickness of the
`medium in unit lengths, and the exponential nature of the relationship has
`arbitrarily been expressed in terms of base e. Equation (9 .2)
`is commonly
`referred
`to as the Beer-Lambert law of exponential light decay through a
`homogeneous absorbing medium (figure 9.1).
`
`0142
`
`

`
`I
`
`......-
`
`T
`d
`(a)
`
`126
`
`Design of pulse oximeters
`
`lo
`
`lo
`
`---1
`
`1/2
`
`~~~
`
`11 .. ,
`
`11 = 112 lo
`
`, lo
`
`---1
`.....
`
`a
`
`d
`
`....
`
`1/2
`
`(b)
`
`h
`
`(c)
`
`~
`
`11
`
`... ,
`
`I 12
`
`12 = 1/410
`
`.. I
`
`1111111
`
`UA
`
`~d
`
`p
`
`1/2
`
`~-------------
`13
`13 = 1/Sio
`
`Figure 9.1. A block diagram illustrating the transmittance of light through a block model of the
`components of a finger. (a) Incident light having an intensity of 10 impinges upon an absorptive
`medium with a characteristic transmittance factor T. (b) The effect of a medium divided into n
`identical components of unit thickness and same transmittance factor T on incident light intensity
`10 . (c) For a finger model, the baseline component of the unchanging absorptive elements and the
`pulsating component of the changing absorptive portion are represented (Cheung et al 1989).
`
`9.2.1 Estimation of oxygen saturation using the Beer-Lambert law
`
`The absorbance coefficients of oxygenated and deoxygenated hemoglobin are
`different at most wavelengths, except at the isosbestic wavelength. If a finger is
`exposed to incident light and the emergent light intensity is measured, the
`difference between the two is the amount of light absorbed, which contains
`information relating to the oxygenated hemoglobin content of the blood in the
`finger. The volume of blood contained in the finger varies with the arterial pulse.
`The thickness of the finger also varies slightly with each pulse, changing the path
`length for the light that is transmitted through the finger. Also, the precise
`intensity of the incident light applied to the finger is not easily determined.
`Hence, it is desirable to eliminate the effects of intensity of the incident light and
`the thickness of the path length in estimating oxygen saturation. The Beer(cid:173)
`Lambert law needs to be modified to eliminate the input light intensity and length
`of the path as variables.
`
`9. 2.1.1 Eliminating the input light intensity as a variable. The intensity of light
`transmitted through a finger is a function of the absorbance coefficient of both
`fixed components, such as bone, tissue, skin, and hair, as well as variable
`components, such as the volume of blood in the tissue. The intensity of light
`transmitted through the tissue, when expressed as a function of time is often said
`to include a baseline component, which varies slowly with time and represents the
`effect of the fixed components on the light, as well as a periodic pulsatile
`component, which varies more rapidly with time and represents the effect that
`changing tissue blood volume has on the light (Cheung et al 1989). The baseline
`component modeling the unchanging absorptive elements has a thickness d and an
`absorbance a. The pulsatile component representing the changing absorptive
`portion of the finger has a thickness of ~d and the relative absorbance of aA
`representing the arterial blood absorbance (figure 9.1(c)).
`
`I
`~
`
`0143
`
`

`
`+
`I
`
`The light emerging from the baseline component can be written as a function
`of the incident light intensity Io as follows
`
`Signal processing algorithms
`
`127
`
`(9.3)
`
`Likewise, the intensity of light I2 emerging from the pulsatile component is a
`function of its incident light intensity I 1 and can be written as follows
`
`I - I -aA!).d
`2- 1e
`
`(9.4)
`
`the light emerging
`Substituting the expression of I 1 in the expression for I 2,
`from the finger as a function of the incident light intensity Io is as follows
`
`I _I
`-[ad+ aA!).d]
`2- oe
`·
`
`(9.5)
`
`The effect of light produced by the arterial blood volume is given by the
`relationship between I2 and I1. Defining the change in transmittance produced by
`the arterial component as T !).A, we have
`
`(9.6)
`
`Substituting the expressions for I 1 and I 2 in the above equation yields the
`following:
`
`(9.7)
`
`The term Io in the numerator and the denominator can be canceled by
`eliminating the input light intensity as a variable in the equation. Therefore, the
`change in arterial transmittance can be expressed as
`
`_
`-aA!).d
`T
`!).A - e
`.
`
`(9.8)
`
`A device employing this principle in operation is effectively self-calibrating,
`and is independent of the incident light intensity Io.
`
`9.2.1.2 Eliminating the thickness of the path as a variable. The changing thickness
`of the finger, !)..d, produced by the changing arterial blood volume remains a
`variable in equation (9.8). To further simplify the equation, the logarithmic
`transformation is performed on the terms in equation (9.8) yielding the following
`
`(9.9)
`
`The variable !)..d can be eliminated by measuring arterial transmittance at two
`different wavelengths. The two measurements at two wavelengths provide two
`equations with
`two unknowns. The particular wavelengths selected are
`determined in part by consideration of a more complete expression of the arterial
`absorbance aA
`
`0144
`
`

`
`128
`
`Design of pulse oximeters
`
`(9 .1 0)
`
`where CXoA is the oxygenated arterial absorbance, £XDA is the deoxygenated
`arterial absorbance, and Sa02 is the oxygen saturation of arterial Hb. lXOA and
`aDA are substantially unequal at all light wavelengths in the red and near infrared
`wavelength regions except for the isosbestic vvavelength of 805 nm. With an Sa02
`of approximately 90o/o, the arterial absorbance aA is 90o/o attributable to the
`oxygenated arterial absorbance a 0 A, and 10% attributable to the deoxygenated
`arterial absorbance aDA· At the isosbestic wavelength, the relative contribution of
`these two coefficients to the arterial absorbance a A is of minimal significance in
`that both aoA and aDA are equal (figure 4.2).
`Wavelengths selected are in a range a'Nay from the approximate isosbestic
`wavelength that is sufficient to allow the two signals to be easily distinguished. It
`is generally preferred that the two wavelengths selected fall within the red and
`infrared regions of the electromagnetic spectrum. The ratio of the transmittance
`produced by the arterial blood component at red and infrared wavelengths
`follows from equation (9. 9).
`
`ln Tt...AR
`ln Tt...AIR
`
`-a A (ILR )L\.d
`-a A (AIR )~d
`
`(9 .11)
`
`where T t...AR equals the change in arterial transn1ittance of light at the red
`wavelength AR and Tt...AIR is the change in arterial transmittance at the infrared
`wavelength AJR. If the two sources are positioned at approximately the same
`location on the finger,
`the length of the light path through the finger
`is
`approximately the same for light emitted by each LED. Thus, the change in the
`light path resulting from arterial blood flow tid is approximately the same for
`both the red and infrared wavelength sources. For this reason, the ~d term in the
`numerator and the denominator of the right side of equation (9 .11) cancel,
`producing
`
`lnTt...AR
`lnTt...AIR
`
`aA(AR)
`aA(AIR)
`
`(9.12)
`
`Equation (9.12) is independent of the incident light intensity Io and the change in
`finger thickness ~d, attributable to arterial blood flow. Because of the complexity
`of the physiological process, the ratio indicated in equation (9.12) does not
`directly provide an accurate measurement of oxygen saturation. The correlation
`between the ratio of equation (9 .12) and actual arterial blood gas measurement is
`therefore relied upon to produce an indication of the oxygen saturation. Thus, if
`the ratio of the arterial absorbance at the red and infrared wavelengths can be
`determined, the oxygen saturation of the arterial blood flow can be extracted
`from independently derived, empirical calibration curves in a manner dependent
`on Io and !}..d. For simplicity, a measured ratio Ros is defined from equation
`(9.12) as
`
`(9 .13)
`
`0145
`
`

`
`Signal processing algorithms
`
`129
`
`9.3 RATIO OF RATIOS
`
`The Ratio of Ratios (Ros) is a variable used in calculating the oxygen saturation
`level. It is typically calculated by taking the natural logarithm of the ratio of the
`peak value of the red signal divided by the valley measurement of the red signal.
`The ratio is then divided by the natural logarithm of the ratio of the peak value of
`the infrared signal divided by the valley measurement of the infrared signal
`(Cheung et al 1989).
`
`9.3.1 Peak and valley method
`
`A photodiode placed on the side of a finger opposite the red and infrared LEDs
`receives light at both wavelengths transmitted through the finger. The received
`red wavelength light intensity varies with each pulse and has high and low values
`RH and RL, respectively. RL occurs during systole when arterial blood volume is
`at its greatest, while RH occurs during diastole when the arterial blood volurne is
`lowest
`(figure 9.2). Considering
`the exponential
`light decay
`through
`homogeneous media, it is observed that
`
`_ 1
`-[a(AR)d+aA(A.R)~d]
`R
`L - oe
`·
`
`Similarly,
`
`Taking the ratio of equations (9 .14) and (9 .15) and simplifying, we have
`
`RL =e-aA(/tR)~d
`RH
`
`Taking the logarithm of both sides of equation (9 .16) yields
`
`Similar expressions can be produced for the infrared signal.
`
`The ratiometric combination of equations (9 .17) and (9 .18) yields
`
`ln(~J
`ln (-IRL J
`
`IRH
`
`-a A (ILR )~d
`-a A (/LIR )~d
`
`(9.14)
`
`(9.15)
`
`(9.16)
`
`(9.17)
`
`(9 .18)
`
`0146
`
`

`
`130
`
`Design of pulse oximeters
`
`Because the ~d terms in the numerator and denominator of the right side of the
`equation (9 .19) cancel, as do the negative signs before each term, equation (9 .19)
`when combined with equation (9.13) yields
`
`(9.20)
`
`Thus, by measuring the minimum and the maximum emergent light intensities of
`both the red and infrared wavelengths (RL, RH, IRL, IRH), a value for the term
`Ros can be computed. Empirically derived calibration curves are then used to
`determine the oxygen saturation based on Ros-
`
`Red transmittance
`
`Infrared transmittance
`
`Light
`intensity
`
`Light
`intensity
`
`Time
`
`Time
`
`Figure 9.2. A graphical plot of transmitted light intensity converted into voltage. High (H) and
`low (L) signals are shown as a function of time of the transmittance of red (R) and infrared (IR)
`light through the finger.
`
`9.3.2 Derivative method: noise reduction software
`
`Yorkey (1996) derives the Ratio of Ratios by calculating using the separated AC
`and DC components of the measured signal. This mathematical derivation of the
`ratio of ratios is performed using the Beer-Lambert equation.
`
`(9.21)
`
`where /1 is the emerging light intensity, Io is the incident light intensity, a is the
`relative extinction coefficient of the material and L is the path length. In this
`method, the Ratio of Ratios is determined using the derivatives. Assuming the
`change in path length is the same for both wavelengths during the same time
`interval between samples, the instantaneous change in path length ( dUdt) must
`also be the same for both wavelengths.
`We can extend the general case of taking the derivative of eu to our case
`
`u du
`deu
`- -= e -
`dt
`dt
`
`(9.22)
`
`l
`
`0147
`
`

`
`Signal processing algorithms
`
`131
`
`Therefore~
`
`dL
`-a-.
`dt
`
`(9.23)
`
`(9.24)
`
`Here, I 1 is equal to the combined AC and DC component of the waveform and
`dl 11dt is equal to the derivative of the AC component of the waveform. Using two
`wavelengths we have
`
`( d/R jdt )j !R
`R of R = - - - - - -
`( d/IR jdt )j /IR
`
`(9.25)
`
`Instead of using the previous method of calculating the Ratio of Ratios based
`on the natural logarithm of the peak and valley values of the red and infrared
`signals, the value of the R of R can be calculated based on the derivative value of
`the AC component of the waveform.
`
`Light
`intensity
`
`AC component
`
`t1
`
`t3 t2
`
`Time
`
`Figure 9. 3. A waveform of the transmitted light intensity through a finger showing the AC
`component, the DC component and the DC offset.
`
`Note in discrete time
`
`(9.26)
`
`If we choose t2 and t1 to be the maximum and minimum of the waveform, we can
`refer to this difference as the AC value, and the denominator above evaluated at
`some point in time t3 in between t2 and t1 as the DC value. So,
`
`I R ( t 1 )
`I R ( t 2 ) -
`d/ R ( t) I dt
`/R(t3)
`/R
`__ __;..:__;. __ = - - - - - - - -
`d/IR (t) I dt
`/IR (t2)- /IR (t1)
`
`/IR
`
`/IR (t3)
`
`ACR
`DCR = R.
`ACIR
`DCIR
`
`(9.27)
`
`0148
`
`

`
`132
`
`Design of pulse oximeters
`
`Potratz ( 1994) implemented another improved method for noise reduction
`called the derivative method of calculating the Ratio of Ratios. To calculate the
`Ratio of Ratios based on the derivative formula, a large number of sampled
`points along the waveform are used instead of merely the peak and valley
`measurements. A series of sample points from the digitized AC and AC + DC
`values for the infrared and red signals are used to form each data point. A digital
`FIR filtering step essentially averages these samples to give a data point. A large
`number of data points are determined in each period. The period is determined
`after the fact by noting where the peak and valley occur (figure 9.3).
`From the AC signal, a derivative is then calculated for each pair of data
`points and used to determine the ratio of the derivatives for R and IR. A plot of
`these ratios over a period will ideally result in a straight line. Noise from the
`motion artifact and other sources will vary some values. But by doing the linear
`regression, a best line through a period can be determined, and used to calculate
`the Ratio of Ratios.
`linear
`a
`A problem with other systems was DC drift. Therefore,
`extrapolation was performed between two consecutive negative peaks of the
`waveform. This adjusts the negative peak of the waveform as if the shift due to
`the system noise did not occur. A similar correction can be calculated using the
`derivative form of the waveform. In performing the correction of the DC
`component of the waveform, it is assumed that the drift caused by noise in the
`system is much slower than the waveform pulses and the drift is linear. The
`linear change on top of the waveform can be described by the function
`
`g(t)=f(t)+mt+b
`
`(9.28)
`
`where m is equal to the slope of the waveform and b is equal to a constant.
`The linear change added to the waveform does not affect the instantaneous
`DC component of the waveform