Pulse Oximeter Laboratory

John G. Webster, http://www.engr.wisc.edu/bme/courses/bme310.html (Bioinstrumentation)
Dissertation Swiss Federal Institute of Technology, Jürg Wyser, Measurement of the arterial oxygen saturation in the airplane
Hamamatsu technotes: www.hamamatus.com
Optical properties of Hemoglobin and blood: http://omlc.ogi.edu/spectra/hemoglobin/index.html

Hemoglobin is a protein and the main component of red blood cells. Hemoglobin transports oxygen from the lungs, where oxygen tension (partial pressure of oxygen) PO₂ is high, to the tissues, where oxygen tension is low. Oxygen saturation, SO₂, is defined as the ratio of the amount of bound oxygen to the total oxygen capacity.

where [HbO₂] is the concentration of oxyhemoglobin, and [RHb] is the concentration of deoxyhemoglobin. If the hemoglobin molecule is bound to oxygen then one has oxy-hemoglobin or [HbO₂]. If the hemoglobin molecule is bound to carbon monoxide then one has carboxy-hemoglobin or [HbCO]. If the hemoglobin molecule is bound to nothing then one has deoxy-hemoglobin or [RHb] or reduced hemoglobin. If the hemoglobin molecule has broken down then one has met-hemoglobin. These all have different spectra but here we concentrate on [HbO₂] and [RHb].

Oxygen saturation is calculated as a percent or fraction.

In healthy adults arterial oxygen saturation (SO₂) is approximately 97%. This depends on physiological parameters as well as on the oxygen partial pressure of the inspired air. In venous blood the oxygen saturation is approximately 75%.

For later calculation it is also useful to see that:

[RHb] = [HbO₂] (1-HbO₂SAT)/HbO₂SAT

Oxygen saturation measurements are made in order to determine the response to therapeutic intervention (e.g. supplemental oxygen administration or mechanical ventilation) and/or diagnostic evaluation (e.g. the effect of exercise on O₂ levels). Oxygen saturation measurements are also needed to monitor the severity and progression of some diseases. SO₂ can be determined by using spectrophotometry.

Optical absorption measurement

The determination of the concentration of a light-absorbing substance in a solution using a spectrophotometer is based on the discoveries of four individuals. Bouguer and Lambert noted that transmittance of light through an absorbing material, such as that contained in a cuvette, decreases exponentially with an increase in the light path through the cuvette. Beer and Bernard observed that the concentration of a substance in solution [less than 10^–2 M (molar)] is directly related to its absorbance. An amalgamation of these two discoveries is known as Beer’s Law, as stated by Bouguer: “Equal thickness of an absorbing material will absorb a constant fraction of the energy incident upon it.” (Wheeler, 1998) This relationship is

where

I₀= radiant power arriving at the cuvette

I = radiant power leaving the cuvette

a = absorptivity of the sample (extinction coefficient)

L = length of the path through the sample

c = concentration of the absorbing substance

Transmittance is the ratio of light intensity leaving the cuvette I to light intensity entering the cuvette I₀

Absorbance (A) is exponentially related to the reciprocal of transmittance.

As the concentration of the substance in solution increases (or decreases), the transmittance varies logarithmically and inversely. The fraction of incident light absorbed by a substance in solution at a particular wavelength is a constant characteristic of the substance called absorptivity, a. Let the length of the light path (usually the inner diameter of the cuvette) be a constant, L, and the concentration of the substance in solution be c. The relation of these parameters to the total absorbance is expressed as:

A = aLc

where a is in liters per gram times centimeters, L is in cm, and c is in grams per liter. Absorptivity is often replaced by molar absorptivity, e, expressed in liters per mole times centimeters. Epsilon is a constant corresponding to a 1 molar solution of the absorbing substance, with a light path of L = 1 cm at a given wavelength. Epsilon is also called molar extinction coefficient [cm^-1 /(moles/liter)]. Hence, absorbance can be expressed as

Optical properties of hemoglobin

Optical properties of hemoglobin have been well characterized and are presented in the next figures in the form of absorption measurements of blood (see next paragraph about blood).

The extinction coefficients of both hemoglobin species are equal at the isosbestic wavelengths (e.g. 548, 568, 587, 805 nm), while reduced hemoglobin [RHb] is more transparent (smaller extinction coefficient) than oxyhemoglobin [HbO₂] in the infrared region and more absorbing in the red.

Some databases list absorption properties of hemoglobin in equivalent. However one of the best resources for Hemoglobin optical data is available at http://omlc.ogi.edu/spectra/hemoglobin/summary.html. Values for the molar extinction coefficient were compiled by Scott Prahl using data from W. B. Gratzer, Med. Res. Council Labs, Holly Hill, London and N. Kollias, Wellman Laboratories, Harvard Medical School, Boston. Data shown there is presented as oxy and deoxy-hemoglobin spectra in terms of molar extinction coefficient Epsilon. To convert from the molar extinction coefficient to absorbance A one needs to multiply by the molar concentration and the path length. For example, if x is the number of grams per liter and a 1 cm cuvette is being used, then the absorbance is given by

using 66,500 as the gram molecular weight of hemoglobin.

Blood

Hemoglobin has a normal concentration of 150 g / liter of blood and permits whole blood to carry 65 times more oxygen than does plasma at a PO₂ of 100 mm Mercury. Hematocrit determines the fraction of the blood that is red blood cells. The red blood cells are primarily composed of hemoglobin (95% of the dry mass).

When arterial blood is 90% saturated, some of the hemoglobin molecules have four oxygen atoms bound, some have three, and a few have tow or one. The statistical average of all oxygen bound to hemoglobin molecules relative to the total amount that can be bound is its oxygen saturation. One gram of functional hemoglobin combines with 1.34 ml O₂, the O₂ capacity of normal blood is

(150 g Hb/liter)(1.34ml O₂ g Hb) = 200ml O₂/liter.

Assume one liter of blood contains 150 g Hemoglobin. Then to convert the molar extinction coefficient to an absorption coefficient, multiply by the molar concentration and 2.303 (because absorption is based on the natural log),

µ_a(lambda) = (2.303) (lambda) (150 g/liter)/(66,500 g Hb/mole) = 0.0054 (lambda)

where µ_a is the absorption coefficient in (cm^-1) and (lambda) is the molar extinction coefficient for the wavelength of interest. The absorption coefficient is based on the natural logarithm while the molar extinction coefficient is based on log10.

[RHb] and [HbO₂] in mixture

If two molecules with two different absorption spectra are mixed in solution and they do not interact when they are mixed, the total optical absorption is the sum of the absorptions due to the individual chromophores. In case of a non scattering medium the concentration of two molecules can be easily determine with two measurements. Here the two molecules are called Hb and HbO₂.

where L is the path length, A was measured at two wavelengths (lambda 1 and lambda 2) and the extinction coefficients were obtained from published data.

Substituting this in the equation for HBO₂SAT (oxygen saturation) results in

If one of the wavelengths is chosen to be an isosbestic point this expression is even simpler and takes the form of a measurement ratio minus a constant.

If we consider realistic tissue the average photon path length (distance a photon travels on average in tissue) is not simply determined by absorption but also depends on tissue scattering. In general the average path length increase when absorption decreases or scattering increases. If the two measurement wavelengths are close we can assume that the scattering at wavelength 1 and wavelength 2 are similar. Furthermore in soft tissue scattering is normally much larger than absorption. Therefore it is safe to assume that at both wavelengths the photons travel the same (or close the same) average length and we have an ideal condition where the path length L is the same for both wavelengths and oxygen saturation is not depending on tissue scattering.

Arterial versus venous blood

To measure SO₂non invasively, we shine light through the finger or earlobe. But then we measure a mixed sample of venous and arterial blood. To measure the arterial blood alone, we use the pulse oximeter technique which considers only the oscillating components of the optical signals.

Pressure and blood flow in arteries is described by complex fluid dynamic models. However we only need to consider the propagation of the pressure pulse in arteries which normally is sharply increasing during heart contraction, decreasing until the aorta valve is closed and can have a second peak after wards when backflow to the heart stops (see figure below).

If we simply assume the vessels are elastic, the diameter of the arteries and capillaries will increase during every heart beat in a proportional manner. This increase results in variable path length of the light passing the arterial blood volume. All other components will stay constant.

As shown below we have a component that is representing absorption and scattering in the skin, bone, fatty tissue and venous system. An other pulsating component is the arterial blood flow. Since we normally do not know what output of the LED is nor how well we collect light we will be only interested in the amplitude of the oscillating signal.

Measurement wavelengths

An oximeter uses a spectrophotometer to measure light transmission at two wavelengths to calculate SO_2.By using four wavelengths, the oximeter can also measure carboxyhemoglobin ([COHb]) and methemoglibin ([MetHb]). If we use even more wavelengths we have an over determined mathematical system (more measurements than unknowns) which can be solved with a least squares method:

Using Matlab this would be solved using the qr decomposition: [Q,R]=qr(ε’ ε) while Q’ = Q-¹ and R=Q’ (ε’ ε) and ε’ ε =Q R. The concentrations [Hb], [HbO₂] and [Hb?] are R\(Q’ (ε’ A).

_{Ideally blood oxygenation is measured at
least at two wavelengths straddling an isosbestic point, because if oxygenation
changes, the measured optical signal is increasing at one wavelength while it
is decreasing at the other wavelength, which amplifies the difference between
both signals and reduces measurement error.}

_{It can be seen that the largest difference in
absorption between oxy and deoxy hemoglobin is around 660 nm. Intuitively one
can expect that changes in the optical signal will be largest at this
wavelength when oxygenation changes. Analytically one can calculate an
absorbance equivalent to 50% oxygenation and derive Absorbance by blood
oxygenation which results in:}

_{At the largest value the largest signal
changes are expected.}

_{At 660 nm the absorption coefficient for blood
is between 1.7 cm-1 (100% HBO2) and 17 cm-1 (100% RHb). The reduced scattering
coefficient is in the range of 10-100 cm-1 for soft tissue. If the finger is 1
cm in diameter we can assume that our signal will be attenuated by at least 3
to 4 orders of magnitude in the red and near infrared while in the visible
range this would increase by an other 2 orders of magnitude.}

_{Light emitting diodes (LEDs) are available in
the blue, green, yellow, red and infrared wavelength range. To measure a
reasonable signal (large signal changes when oxygenation changes and a signal
that can be detected with simple amplifiers) it is best to choose wavelengths
in the red and infrared. In this laboratory we have chosen “ultra bright” LEDs
with an emission peak at 660 nm and 940 nm.}

Pulse oximeter math

We will need to know what signal components we need to measure and there fore we should take a look at the oscillating versus the constant components.

The arterial Absorbance has a DC and an AC (oscillating) component. The DC component is defined by the sum of all artery diameters when there is no pulse propagating through them. The AC component is defined by the vessel enlargement when a pulse propagates. We can isolate the AC component (maximal amplitude minus minimal amplitude) while the arterial DC component blends with all the other DC signals originating form other tissue constituents such as skin, bone, and the venous blood.

Because we can isolate the oscillating component and because it is only defined by arterial blood flow we can calculate arterial oxygenation with:

Oxygen saturation was defined previously for a stationary system as:

This does not change if we replace the absorbance by an oscillating component.

In order to determine the arterial absorbance component at the two different wavelengths we need to look at the detector signal. This will help to figure how the DC and AC components play together:

There is a DC and an AC detector signal. The DC signal is the maximal detector signal since it represents the arteries in undilated conditions. The DC+AC signal is the lowest detector signal. If we divide the AC+DC signal by the DC signal we will get independent from several components: the initial light source intensity and also all DC components in the absorbance equation as well as detector sensitivities or amplifications:

Therefore we need to measure both the maximal signal from our photo detector as well as the minimal signal to create the absorbance from only the oscillating arterial component.

Hardware

The pulse oximeter hardware consist of two channels. Each channel is equipped with a light source, a photo detector, an amplifier that converts the output of the photo detector in to voltage, a low pass filter, an optional notch or high pass filter and data acquisition hardware (next figure).

Since we need to measure at two wavelengths simultaneously we need to operate the two channels simultaneously. The photo detectors need to be equipped with optical filters that block the light from either 660 or 940 nm. Alternatively one could measure with one photo detector and modulate the intensity of both LEDs with different frequencies. The detected signal would then be demodulated electronically at those frequencies which is called lock-in detection. We will not use this technique.

The calculation section showed that you will need to know the total intensity on your detector as well as the oscillating component. If you use a high pass filter to further enhance the oscillating component you will need to measure 4 channels (the average DC component, the oscillating component for each of the two channels). It is possible to tune your circuit so that you do not need a high pass filter.

Photo detectors principle of operation

The P-layer material is located at the active surface and the N material at the substrate form a PN junction which operates as a photoelectric converter. The usual P-layer for a silicon photodiode is formed by selective diffusion of boron, to a thickness of approximately 1 µm or less and the neutral region at the junction between the P- and N-layers is known as the depletion layer. By varying and controlling the thickness of the outer P-layer, substrate N-layer and bottom N+layer as well as the doping concentration, the spectral response and frequency response can be controlled.

When light strikes a photodiode, the electron within the crystal structure becomes stimulated. If the light energy is greater than the band gap energy Eg, the electrons are pulled up into the conduction band, leaving holes in their place in the valence band (see Figure below).

These electron-hole pairs occur throughout the P-layer, depletion layer and N-layer materials. In the depletion layer the electric field accelerates the electrons toward the N-layer and the holes toward the P-layer. Of the electron-hole pairs generated in the N- layer, the electrons, along with electrons that have arrived from the P-layer, are left in the N-layer conduction band. The holes at this time are being diffused through the N-layer up to the depletion layer while being accelerated, and collected in the P-layer valence band. In this manner, electron-hole pairs which are generated in proportion to the amount of incident light are collected in the N- and P- layers. This results in a positive charge in the P-layer and a negative charge in the N-layer. If an external circuit is connected between the P- and N-layers, electrons will flow away from the N-layer, and holes will flow away from the P-layer toward the opposite respective electrodes.

Voltage - Current characteristics

When a voltage is applied to a photodiode in the dark state, the V-l characteristic observed is similar to the curve of a conventional rectifier diode as shown in the figure shown below:

However, when light strikes the photodiode, the initial curve shifts to (Pi). When the amount of incident light is increased the curve shifts in parallel further towards position (4Pi, 4 times as much light as at Pi). If the photodiode terminals are shorted, a photocurrent Isc is proportional to the light intensity and will flow in the direction from the anode to the cathode. If the circuit is open, an open circuit voltage Voc or Voc' will be generated with the positive polarity at the anode (voltaic).

The short circuit current Isc is extremely linear with respect to the incident light level. When the incident light is within a range of 10^-12 to 10^-2 W, the achievable range of linearity is higher than 9 orders of magnitude, depending on the type of photodiode and its operating circuit. The lower limit of this linearity is determined by the NEP (noise equivalent power), while the upper limit depends on the load resistance and reverse bias voltage.

A typical spectral response of a photodiode is shown below. At longer wavelengths the photon energy is insufficient to produce an electron whole pair in silicon. At shorter wavelengths the enclosure (quartz or standard glass) will not transmit the light on to the detector substrate or the electron and whole pair will recombine because it was generated to close to the anode.

Detection circuits

A silicon photodiode can be approximate with a current source, a capacitor and a resistor. With an increase active area, more photons can be captured and more electrons can be generated. With a larger active area the internal capacity also increases and the response time is slower.

The simplest operation is to connect the photo diode to an oscilloscope with an internal large resistance. The frequency response will be low since it is limited by

For fast and linear operation the current created in the photodiode needs to be converted with a transimpedance amplifier to voltage. The photodiode is virtually shorted. As seen in the second figure above.

For faster operation a bias voltage can be applied between the anode and cathode (first diagram in next figure). This increases the depletion layer and increases the separation speed of the electron whole pair because the electrostatic field (which is created by the bias voltage) accelerates positive and negative charges. It also results in a smaller internal capacity. The sensitivity is not increased and an additional dark current will result (current generated without light hitting the detector). A larger dark current also results in more noise.

If no amplification is necessary the fastest response can be achieved with the first circuit shown below. Since response time is not critical for our application we will chose a simple amplifier as shown in the third circuit below. Since we already used a precision differential amplifier for the ECG laboratory the circuit for this type amplifier is also shown.

We will need to amplify the detected signal significantly and a 1M Ohm resistor is an appropriate choice. The bandwidth of the amplifier should be limited to about 300 to 500 Hz (0.53 nF … 0.32nF).
Other Components

Light source

Don Klipstein's LED main page: http://misty.com/people/don/ and the AND LED application notes included in this document are good further readings.

The components pre-chosen for this laboratory are a red and an infrared LED. The operation voltage of your circuit needs to be chosen based on the requirements of your amplifiers. Therefore you need to limit the current flowing through the LED to approximately 20 mA as shown in Figure 1 in the AND LED application note.

- Red, 660nm, 20 mA, 12degrees view angle, 37 cents, ultra bright AND180CRP

- Infrared, 940 nm, 20 mA, 1.3 VDC, $1.79, Radioshack high output IR LED or Fairchild 880nm, 100mA, 1.7V.

Detectors

The detectors chosen for this laboratory are photo diodes with integrated color glass filters.

- Infrared, SLD-70IR2 700-900 nm, active area 9 square mm, approx $3

- Red, SLD-70BG2 400-700 nm, active area 9 square mm, approx. $3

Low and high pass filters

For your ECG project you already implemented active low and high pass filters. The same frequency response can be chosen for the high pass as well as the low pass filter. For active filter design a chapter from Horowitz and Hill has been included in the appendix. One could choose a 2 pole Butterworth filter.

The frequency limits are calculated with

Butterworth 2 pole low pass filter: With R=100kOhm and C=0.005 micro F the upper frequency limit is 300 Hz.

Butterworth 2 pole high pass filter: With R=330k Ohm and C=10 microF the lower frequency limit is 0.05 Hz.

An optional notch filter to eliminate 60 Hz from the supply lines is shown in the next figure:

For the suppression of 50 Hz, C should be 4.7 microF, 2C 10 microF, R 680 Ohm and R/2 340 Ohm. For 60 Hz suppression these values would need to be adapted.

Before the signals are recorded they may need to be amplified with a standard non inverting operation amplifier circuit using an 741 type OPAMP shown in the figure below. The Gain is defined as 1+(R2/R1).

LED and detector holder

A “flying construction” of the LED and detector circuit is very sensitive to motion artifacts. A mechanical design that allows the 5mm LEDs and the Silonex detectors to be glued in place is shown in the appendix. The design can be simplified and Acrylic tubing can be replaced with PVC tubing from Home Depot. Manufacturing costs for the design are between $50 - $100. A simplified version is probably less than one dollar.

For this laboratory a few holders equipped with LED and detectors are supplied by the instructor.

Laboratory instructions

Week 1:

The wires attached to the sensors and emitters are encoded the following way: black wire is ground, red is IR and white is red.

1) Connect the LEDs to a power supply and verify the operation of the IR LED by measuring the current through it. The LEDs can take approximately 30 mA. If you connect them directly to more than 1.5V they will burn out. Please check the technical specifications for your LED to find the proper forward current. Then calculate the proper resister that you will need to place in series to achieve this current. The resistor is smaller than 1k Ohm if you feed 10V.

2) Connect the detectors directly to the oscilloscope with and choose a 1MOhm internal resistance. Your signal will change depending on the amount of light you put on them. If you turn on the LED you should see a couple of 100mV and you can block the detector to see a drop.

3) Amplify the detector current with a standard operation amplifier as explained earlier in this document. When no object is placed in the beam path the output will be saturated. Paper will not block the IR beam path completely. The feedback resistor will be in the range of 100K to 1MOhm. You should be able to achieve about 5V output with your finger in the beam path in the IR path.

4) If your finger is in the beam path you should be able to see a small pulsing component on top of your signal by setting the scope to 100m Volt/division. Since your DC component might be in the range of 5V you will need to adjust your position on the screen so that your ground/0V is far of the display.

5) Please read the introductions and the calculations to the pulse oximeter lab.

Week 2:

1) Limit the bandwidth and lower the noise with a low pass filter by adding a capacitor to your trans-impedance amplifier.

2) Measure data during 10 seconds with LabView. You will remove the room lights for that (why?).

3) Extract the amplitude of the oscillating signal component.

4) Create the ratio of both measurements. You should use the log of your extracted amplitude before you create the ratio (why?).

5) Repeat the measurement before and after you hold your breath for as long as possible and create the ratio again. Measure at least a minute after you stopped holding your breath.

6) How much did your signals change?

Optional:

1) Do it in real time.

2) Calibrate the signal to HbO₂SAT by assuming you measure 97% oxygenation during normal breathing conditions. There are multiple reasons why your measured signal would need calibration. You might get room light onto your detector. You might get light not traveling through your finger on the detector. Your extinction coefficient is not 100% correct because the emitter is at a slightly different wavelength. Your filter is not blocking all the light from the other channel.

If it does not work:

- The IR channel works better than the red channel. Check that one first.

- Check that your LED consumes the appropriate amount of current. If there is no current there will be no emission. The current is measured by placing the multi meter is series with a power supply cable.

- Check your photo detector by simply hooking it up to the oscilloscope. You should be able to change the measured signal level by simply putting your hand around the detector. Check you amplifier.

- Never build a circuit without a circuit diagram.

Appendix

- Filter circuits

- Emitter detector holder design