Introduction to Pulse oximetry

Sagar G V

August 21, 2012

1 What is oximetry ?

Figure 1: A pulse oximeter

The heart pumps blood to the lungswhere haemoglobin in the red bloodcells is oxygenated. This oxygenatedblood is then pumped to various partsof the body via the arteries. Arte-rial blood gas saturation (SpO2) isthe percentage of haemoglobin in thearteries that is oxygenated.

SpO2 =[HbO2]

[Hb] + [HbO2](1)

where [Hb] and [HbO2] are theconcentrations of de-oxygenated andoxygenated haemoglobin in the ar-teries respectively. SpO2 can be es-timated by measuring the absorp-tion of light as it passes through thebody. Oximetry is the measurementof blood gas saturation. Pulse oxime-try is a non-invasive method of oximetry which involves flashing two LEDsalternately. This article describes the principle behind pulse oximetry.

2 What does it tell us?

It tells us if the person is getting enough oxygen. Arterial oxygen saturationof healthy people will be in the range 94%-99%. Anything below 90% indi-cates insufficient supply of oxygen. Low SpO2 can be due to problems in thelungs causing insufficient perfusion of oxygen to the blood or in the blood cellsthemselves as in the case of anaemia. In newborns, low SpO2 is indicative ofSepticemia (infection), Congenital heart defects, anaemia, respiratory distresssyndrome etc.

3 Beer-Lambert Law

Beer-Lambert law states that the absorbance of light as it passes through asample is proportional to the thickness of the sample and the concentration of

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the absorbent.dI I[C]dt

where dI is the infinitesimal change in light intensity as it passes through asample of concentration [C] and thickness dt. Thus, for a large sample,

I = I0e[C]t

where I0 is the intensity of the incident light and is the absorption co-efficient,t is the thickness of the sample.

4 Making measurements

Light from an LED is transmitted through the human body (usually finger orear lobe) and the intensity of the light that passes through is measured. Wellassume that the light intensity of the LED is proportional to the current throughit and that the current in a photodiode is directly proportional to the light thatfalls on it.

Figure 2: System Description

4.1 Start with an LED

We shall now send light from a red LED through a finger and measure howmuch light passes through. Beer-Lambert law tells us

IrxR = ItxRetissueR[tissue]l1HbO2R[HbO2]l1HbR[Hb]l1 (2)

where symbols have their usual meaning and the R suffix indicates thatthe quantity is corresponding to the red light. The absorption is divided intoabsorption due to tissues, oxy haemoglobin and deoxy haemoglobin.

To obtain SpO2, the ratio of [Hb] to [HbO2] is needed. Eq. 2 does not allowus to compute this ratio by mere knowledge of the currents in the transmittingLED and receiving photo diode.

4.2 Beating heart to the rescue

The thickness of the artery oscillates as the heart beats. Correspondingly, thedetected current also varies at the heart rate. This means that we can take theratio of the maximum and minimum received currents over the duration of aheart beat to eliminate the effect of the surrounding tissues. This is because the

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Figure 3: Thickness modulation in the arteries

ratio will depend on the arterial expansion and contraction while the backgroundgets subtracted away.

IrxRpeakIrxRtrough

= eHbO2R[HbO2](l2l1)+HbR[Hb](l2l1) (3)

The required ratio of [HbO2] to [Hb] in Eq. (3) still depends on the amount bywhich the arteries expand.

4.3 Use two LEDs !

The dependence on the expansion of the arteries as the heart beats can beeliminated if we take measurements with two different LEDs, a red LED and anIR LED. To keep the detected current separate and to lower power consumption,

Figure 4: Depiction of when the LEDs are flashed

neither LEDs are continuously turned on. They are flashed alternately and thedetected current is measured. The maximum heat rate is around 250 beats perminute. Flashing the LEDs at a 100Hz keeps the sampling system well abovethe nyquist rate. We first compute the ratio in Eq. 3, take the logarithm andthen compute the ratio of this quantity for two different LEDs as shown below.

IrxIRpeakIrxIRtrough

= eHbO2IR[HbO2](l2l1)+HbIR[Hb](l2l1) (4)

ln

(IrxRpeakIrxRtrough

)= HbO2R[HbO2](l2 l1) + HbR[Hb](l2 l1) (5)

ln

(IrxIRpeakIrxIRtrough

)= HbO2IR[HbO2](l2 l1) + HbIR[Hb](l2 l1) (6)

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From Eqs 5 and 6,

R =ln(

IrxRpeakIrxRtrough

)ln(

IrxIRpeakIrxIRtrough

) = HbO2R[HbO2] + HbR[Hb]HbO2IR[HbO2] + HbIR[Hb]

(7)

Combining Eq. (7) and Eq. (1), we have,

SpO2 =HbR HbO2RR

HbR HbO2R + (HbO2R + HbIR)R(8)

Substituting typical values[1] gives us,

SpO2 =0.81 0.18R0.63 + 0.11R

100%

Therefore, to compute SpO2, we need to compute R which needs measurementof the peak and trough of the detected current in the photo-diode as red andIR LEDs are alternately flashed.

5 Accuracy needed of current measurement

We would like to have an idea of the required resolution of the current in thephotodiode given the required accuracy in estimating the SpO2. From Eq. (8),

S =0.2025

(0.63 + 0.11R)2R

We are particularly interested in the accuracy of the SpO2 around 92% be-cause 90% is usually the threshold below which doctors recommend supportfor oxygenation. Also insurance companies usually require that the SpO2 levelfall below 88% for them to pay for artificial oxygenation. At this point, R =0.8. If the maximum tolerated S is 1% around this point, the correspondingworst-case error in computing R should be below 0.025. At other points suchas 60%, the accuracy is not as important and an error of even 3% is tolerable.

The peak and trough of the detected current are usually very close to eachother. We may write R as,

R =ln(IR+IRacIRIRac

)ln(IIR+IIRacIIRIIRac

)where IR and IIR are the dc currents in the photodiode due to the red andinfra red LEDs. We can approximate this as,

R = 1 + 2IRacIR 2I

IRac

IIR

From this,

R = 2I

[1

IR+

1

IIR

]

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I =

(IRIIR

IR + IIR

)R

2(9)

if we make the simplifying assumption that IR IIR, we getI

I=R

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Although this assumption is not true, it gives us an idea of the resolution re-quired of the current. For R = 0.025, this indicates that 8 bits of resolutionis necessary. If IR = IIR = 100nA, then these equations indicate that theresolution in current measurement should be 0.625nA.

6 Calibration

We would like to calibrate the instrument and measure its accuracy over therange of useful SpO2 for a large number of people. Accurate calibration isdifficult because a highly accurate measurement of blood gas saturation requiresdrawing blood from people and directly measuring oxygen saturation. This isquite inconvenient. So, in most commercial pulse oximeters, SpO2 is assumedto follow a quadratic polynomial in R.

SpO2 = a+ bR+ cR2

where are a,b,c are best-fit co-efficients obtained by fitting a second orderpolynomial to a graph of measured R of the instrument to be calibrated vs.readings(SpO2) from a pre-calibrated pulse oximeter for different test subjects.

References

[1] M. Tavakoli, L. Turicchia, and R. Sarpeshkar, An Ultra-Low-Power PulseOximeter Implemented with an Energy-Efficient Transimpedance Ampli-fier, IEEE Transactions on Biomedical Circuits and Systems, Vol. 4, No. 1,pp. 27-38, Feb. 2010.

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