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Review Article: Review Article

The Light–Tissue Interaction of Pulse Oximetry

Mannheimer, Paul D. PhD

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doi: 10.1213/01.ane.0000269522.84942.54
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Abstract

Clinical interest in monitoring oxygenation derives from the importance of the oxygen molecule to living organisms: without adequate delivery to the vital organs and tissues, metabolism cannot be supported and cells (and the organism) die. Pulse oximetry has been used for monitoring patient oxygenation during anesthesia since the mid 1980s and was quickly adopted as a standard of care for anesthesiology and critical care medicine (1,2). Its ability to provide early indications of hypoxemia, coupled with its ease-of-use, has popularized its adoption in many hospital and home settings. Many manufacturers provide multiple choices of monitoring configurations as well as reusable and single patient-use sensors to cover a broad range of patient populations and placement sites, all testament to the clinical and commercial success of the technology.

Pulse oximeters estimate the true hemoglobin oxygen saturation of arterial blood (Sao2) by measuring the heart beat-induced changes in light transmission through a blood-perfused tissue. Oxyhemoglobin (O2Hb) absorbs visible and infrared (IR) light differently than does deoxyhemoglobin (HHb) and appears bright red under white light illumination as opposed to the darker brown HHb. Isolating the color of the modulating signal component assesses the degree to which the arterial blood contains red O2Hb or brown HHb; contributions from other tissue components that absorb and scatter light are generally unchanging during this time scale and (in concept) minimally affect the estimate.

The basic mathematics of pulse oximetry can be derived through an algebraic manipulation of the Lambert–Beer Law (3). This fundamental tenant of spectroscopy describes how light intensity decays as it passes through a nonscattering, light-absorbing substance comprised of one or more components. Aoyagi used this concept when he engineered the first modern-era pulse oximeter in the early 1970s (4). Even today, several decades later, all commercially available pulse oximeters follow this same basic relationship. While effective in forming the mathematical basis, this simple derivation of pulse oximetry misses an important factor: light scatters as it travels through living tissues, significantly impacting the assumptions made in the Classical Lambert–Beer Law description of pulse oximetry.

The following work reviews the light–tissue interaction in pulse oximetry and those factors accommodated by the system’s empirical calibration. However, depending on the patient’s clinical status and how and where the sensor is applied, reading accuracy can be meaningfully impacted when remaining assumptions inherent in the technology are compromised. Understanding these factors and using sensors properly will help to ensure pulse oximetry provides accurate and reliable information.

LIGHT TRANSMISSION AND THE MATHEMATICS OF PULSE OXIMETRY

The fractional transmission (T) of light through a series of N optical filters can be written as the product of the transmission through each of the individual filters, since each one attenuates the light that is incident upon it:

where Iin and Iout are the incident and emerging light intensities, respectively. Unity transmission indicates that all of the incident light passes through the filter without loss, while zero transmission represents no light passing through. As suggested by Eq. 1, reordering or repartitioning the filters results in the same overall transmission. In pulse oximetry, conceptually, we can think of the transmission of the light traveling between the sensor’s emitters and photodetector as a similar series of optical filters:

where the two eta (η) terms refer, respectively, to the coupling efficiency of light emitted by the sensor’s light emitting diodes (LEDs) reaching the tissue and the efficiency with which the re-emerging light is collected by the photodetector. Each of the remaining terms refer to the light transmission through the skin’s pigment (melanin), the skin itself, bone, veins, arteries, and other absorbers such as tendons, capillaries, etc.

Absorbance (A) describes how much light does not pass through (absorbed), and is defined as the negative logarithm of transmission. Rewriting Eq. 2 in terms of absorbance,

Pulse oximetry focuses on the change in absorbance over the cardiac cycle. Consider each transmission term in Eq. 3 as being a function of time. Typically, only the arterial term changes over the time frame of a heart beat. Taking the time-derivative of Eq. 3 (or its difference at two points in time along the cardiac cycle) eliminates each of the terms except for Tarterial

The Lambert–Beer Law, dating back to the mid 1800’s (5) [as cited by Severinghaus and Astrup (6)], quantifies light absorbance along a well-defined path length in terms of the characteristics and concentrations of the uniform mixture of individual components:

where l is the path length through the medium, and βi and cXi are the spectral absorption characteristics and concentration of each of the ith substances in the optical path. The basic formulation of pulse oximetry comes from combining Eqs. 4 and 5. Considering the two primary light absorbers in the blood to be O2Hb and HHb, and measuring the ratio of cardiac-induced modulating light levels at two different wavelengths:

where in Eq. 6aR is the Modulation Ratio, λ1, λ2 refer to two wavelengths of light, and AC and DC refer to the alternating and average (constant) portions of the detected photosignals, respectively (Fig. 1). In Eq. 6b, S is the true arterial hemoglobin oxygen saturation value ranging from 0 to 1, and ΔcHba is used here to indicate the change of the arterial hemoglobin concentration within the optically probed tissue bed over the time increment.1 Most commonly, λ1 and λ2 are, respectively, near 660 nm (red light) and in the near IR near 900 nm or 940 nm. At high oxygen saturations, with the arterial blood comprising predominantly O2Hb, the detected red pulse amplitude (AC/DC) is approximately half the IR pulse amplitude. As the saturation decreases, with increasing amounts of HHb in the arterial blood, modulation of the red signal increases, while it shrinks slightly in the IR (Fig. 1). Solving Eq. 6b for the variable S results in an estimate of arterial oxygen saturation (Spo2), derived from the measured value of R (Fig. 2).

F1-3
Figure 1.:
Red and infrared light signals are modulated by the cycling blood volume in perfused tissues. At high Sao2, the red pulse amplitude (AC/DC, where “AC” is the alternating component and “DC” is the average component as indicated in the figure) is smaller than in the infrared, while the relative amplitudes are reversed at low saturation. Note the signal level waveform shape is inverted from a blood pressure waveform. The incremental increase in tissue blood concentration at systole results in less light reaching the photodetector than at diastole.
F2-3
Figure 2.:
Red/Infrared Modulation Ratio (R) versus Sao2. At high Sao2 (right side of the graph), pulse amplitude (or modulation) of the red signal is less than that of the infrared signal, while the reverse is true at low Sao2. Pulse oximeters measure R, the ratio of red to infrared pulse amplitudes (Eq. 6a), and estimate Sao2 by applying the calibration curve (the solid line) as depicted by the dashed line and arrow. Modulation Ratio is also sometimes referred to as “Y” or “φ”.

THE INFLUENCE OF LIGHT SCATTERING

The simple Lambert–Beer Law derivation of pulse oximetry assumes a single, well-defined light path common to each of the wavelengths that pass through the tissue. This results in the wavelength-independent l and ΔcHba terms in Eq. 6b presumably cancelling one another. Visible and near IR light, however, are strongly scattered by human tissue; the detected light is more accurately described as an ensemble of independent photon paths (7,8). Some of the detected photons travel shorter routes without migrating far from the direct line between the emitter and detector, and some scatter farther from this line without being absorbed or lost at a boundary (photons that are absorbed or lost cannot contribute to the photocurrent). The longer-traveled photon routes provide more interaction with blood, and the incremental difference between systolic and diastolic concentrations of tissue blood creates a greater impact on the relative number of survivors (greater detected pulse amplitude). Conversely, detected photons traversing the shorter distances are less exposed to the cycling blood level and survive with a more uniform likelihood between systolic and diastolic conditions (smaller detected pulse amplitude). In general, as the absorption of the light increases, detected light tends to come from the shorter paths (9). Figure 3 illustrates this graphically using the results of a random walk model for photons scattering through a slab [model construct similar to that described in (10)]. As the probability for a photon becoming absorbed at any given step increases (higher absorption), fewer surviving routes reach the periphery. Figure 4 provides the path length distributions according to Patterson et al. (7), considering the same scattering and absorption conditions. The final detected photosignal comprises a mixture of all surviving photon paths, and convolves pulse amplitudes coming from all of the various path lengths.

F3-3
Figure 3.:
Relative visitation probabilities based on a Monte-Carlo random walk of photons are shown for red light transmitted through a simulated homogeneous tissue slab in (a) the absence of absorption and (b) with absorption consistent with human tissues. Slab dimensions are approximately 10 mm by 20 mm, with the point emitter positioned at the top and point detector at the bottom. Regions traveled most commonly by the migrating photons that reach the detector are shown as dark blue, progressing through green, tan, and gray, each indicating decreasing visitation. Photons that are absorbed or reach the top or bottom surface other than at the detector are considered to be lost (not detected); their routes accordingly do not contribute.
F4-3
Figure 4.:
Path length distributions for detected photons are shown for the scattering-only (a) and scattering + absorption (b) conditions depicted in Figure 3. Each photon’s path length is effectively a product of the number of steps taken in its random walk to the detector and their step size. Notice that as the absorption increases, not only are fewer total photons detected, but the distribution shifts toward the shorter routes. The vertical dotted line in each curve indicates their respective mean path lengths 〈l〉 values that are several times greater than the physical separation between the emitter and photodetector (E–D separation). The likelihood that a surviving photon travels the minimum distance directly across the slab without being scattered away from the straight line is exceedingly small; path lengths less than the E–D separation are impossible.

To account for these effects in the Lambert–Beer Law model and Eq. 6, l may be replaced with 〈l〉, a representation of the effective mean path length of the detected light, combining all of the effects of scattering into a single term (10). Making this replacement results in the Modified Lambert–Beer Law (11). Commercial pulse oximeter systems are empirically calibrated in studies conducted on healthy adult volunteers to correlate the measured values of R (per Eq. 6a) to sampled arterial blood Sao2 values measured with a CO-oximeter (12). This empirical process incorporates the actual average ratio of red and IR ΔcHba·〈l〉-values observed in human tissues into the calibration.

REFLECTANCE VERSUS TRANSMISSION PULSE OXIMETRY

Is there a meaningful difference between reflectance and transmission pulse oximetry technology? From the perspective of light transmission through the tissue bed, the answer is no, provided the emitter-detector separations are comparable to each other and are on the order of many scattering-lengths or greater in magnitude (13). Once the photon has traveled a sufficient distance to have lost the history of its past (approximately 1 mm in tissue for pulse oximetry wavelengths), there is little, if any, difference where the detector is located. Indeed, reflectance and transmission are best thought of as convenient manufacturing terms for sensors that have emitters and detectors located on either the same or opposite sides of a tissue bed. (The term “reflectance” is an unfortunate descriptor for this type of sensor geometry, as it improperly implies a requirement for some form of subdermal mirror to reflect the light back to the detector. An alternative and more generic term is “surface sensor.”) From an optical perspective, both geometries measure the diffusion of light through a blood-perfused tissue bed. Figure 5 illustrates this as the glow of the red scattered light re-emerging from the tissue. In both cases, at a distance of several millimeters from the emitter, substantial volumes of tissue have been visited by the exiting photons, independent of which specific adjacent or opposing location is selected. This is further illustrated by observing the pulse amplitude of the photoplethysmograph using transmission and surface (reflectance) sensor geometries (Fig. 6). Pulse amplitude measured on the finger was approximately 3% in this example, regardless of emitter–detector orientation, while the measurement on the forehead, using the same surface sensor on the same individual, yielded a pulse amplitude closer to 1%.

F5-3
Figure 5.:
(a) When a finger is illuminated by a pulse oximetry sensor’s emitter placed under the pad, the entire fingertip glows. It matters very little if the detector were to be positioned across the finger about 1 cm from the emitter, or about 1 cm away on the same side—similar amounts and types of tissue are being probed by the detected light. (b) Sensors using the reflectance geometry similarly detect light that diffuses through the perfused tissue bed. Shown here is the emitter of a disassembled forehead sensor placed against the skin (hidden by its opaque plastic carrier). The sensor’s detector has been removed from the aperture to the right. Although the emitter and detector are positioned on the same side, the detected light penetrates well into the surrounding tissues.
F6-3
Figure 6.:
The photoplethysmographic pulse amplitude (infrared signal AC/DC) relates more to the anatomical site where the optics are placed than the sensor’s emitter and detector orientation. These waveforms were acquired from the author’s index finger using transmission (top) and reflectance (middle) geometries, while the bottom waveform comes from the forehead (acquired using the same reflectance sensor as with the middle waveform).

The relationship between the pulse oximeter’s measured value of R and blood Sao2 is very similar between transmission and reflectance geometry sensors, with the small difference readily accommodated by proper device calibration (unpublished data). Performance factors that are commonly attributed to the geometry of the sensor optics, such as weak signals or venous pulsation, are more appropriately related to the anatomy and physiology of the various sensor placement sites, and will be discussed further in a later section.

THE “PULSE” IN PULSE OXIMETRY

The difference in pulse amplitude between the forehead and finger noted above highlights an interesting and poorly understood aspect of pulse oximetry and photoplethysmography in general; where does the optical “pulse” actually come from? Pragmatically, this measure of signal strength (i.e., the magnitude of re-emerging light intensity variation that continuously cycles with the beating heart) comes directly from the modulating change in tissue opacity (optical density). Factors that have been noted to affect this include:

  1. The periodic increase and decrease in the tissue blood fraction (14),
  2. Spacing between the emitter and detector (wider separations associated with larger measured pulse amplitudes), and the depth of the pulsing vasculature (15), and
  3. The extinction coefficient of the modulating blood volume at the measurement wavelength (16).

Additional proposed contributors to the optical pulse include

  1. Volumetric and flow-dependent blood-scattering contributions from the erythrocytes in the blood (17),
  2. Pulsing flow in venules supplied by arteriovenous anastomoses (18),
  3. Venous pulsations, direct from the right heart or indirectly from adjacent arteries (19,20), and
  4. The degree of cutaneous vessel distensibility (i.e., local vessel compliance as affected by sympathetic stimuli) (21), as this would affect the changing local tissue blood fraction.

Larger pulsing vessels can also contribute to the optical pulse, but have been associated with disruptions to accurate pulse oximetry (22,23), and are absent from the distal regions of the finger or toe where strong pulsatile signals are commonly observed.

Empirically, pulse oximetry sensors placed on tissue regions with a rich presence of capillaries and arterioles (e.g., distal regions of the digits, the forehead, the earlobe, and nose) tend to demonstrate the strongest pulse amplitudes, at least in the absence of vasoconstriction that can affect most of these locations (24–26). Regions with very low vascular density, such as the skin of the torso, generally provide very weak optical pulse amplitudes. Indeed, taken in the extreme, a region devoid of vasculature would provide no change in light attenuation with the heart beat as it lacks blood flow altogether. While understanding the specific mechanism that creates the pulse remains an area of research, the optical pulse amplitude relates logically to the amount of distensible arterial vasculature that exists in the optically probed tissues.

TISSUE PERTURBATIONS AND PULSE OXIMETRY

Consider the ratio of the red and IR ΔcHba·〈l〉 values found in Eq. 6b (making the substitution of l with 〈l〉). As noted before, the system’s empirical calibration accommodates its nominal value for the sensors being used. Physio-optic changes in ΔcHba·〈l〉, however, if not equivalent in the red and IR channels, will create a bias between Spo2 and Sao2, independent of any additional engineering hardware, software, or signal processing considerations. For example, a change or “perturbation” in tissue hemoglobin content compared to the normal healthy adults used for calibration can alter the value of 〈lred/〈lIR and create a bias in R and, consequently, Spo2 readings. The ratio 〈lred/〈lIR inherently shrinks with Sao2 (〈l〉 decreases as light absorption increases) and is part of the calibration. With less than a normal amount of hemoglobin in the tissue, this ratio declines less with decreasing Sao2 since the impact to 〈l〉 from increasing HHb content is greater in the red than IR part of the optical spectrum. This changes the R versus Sao2 relationship in Figure 2, bending and rotating the curve clockwise about a point near 80% Sao2 (13,27). Indeed, the tendency for Spo2 to overestimate Sao2 at high Sao2, and more significantly, to underestimate it at low Sao2, has been observed in anemic patients (28).

Vascular heterogeneity (different regional values of ΔcHba) can also impact Spo2 if detected light paths at the multiple wavelengths differ significantly from one another. Similar to the decrease in 〈l〉 as absorption increases, the expanse of the detected light’s migration also decreases (29). If overlap in these migration paths is poor, the red and IR light may be modulated differently by uneven distributions of pulsing vasculature, affecting the value of R and its correlation to Sao2 (27). Additionally, migrating photons that encounter an opaque or strongly absorbing macroscopic object (such as a large blood vessel) will likely be removed from the ensemble before reaching the photodetector and consequently not contribute to the signal. Photon migration modeling suggests detected signals come predominantly from light that bypasses such objects and/or travels through regions with weaker absorption and scattering (30,31). (While attenuation is equivalent for light traveling through the middle of a 5-mm blood vessel as it is through a series of ten 0.5-mm diameter vessels, with scattering, much of the detected signal strength comes from photons that have traveled through only a limited portion of the series. With the larger vessel, opportunity to avoid the absorber is absent.) The presence of such distinct static objects, or more importantly, one or more that change synchronously with the cardiac pulse, can greatly influence Spo2 reading accuracy by disrupting the relationship between the measured value of R and the color of the underlying arterial blood (15,22,23). Numerous groups have developed physio-optic numerical models that explore such impact of homogeneous and nonhomogeneous tissue properties on pulse oximetry readings (10,13,15,17,32).

VENOUS PULSATION

One of the basic premises in pulse oximetry is that the change in optical density of the tissue due to the cardiac pulse comes only from arterial blood volume changes. Whether this is valid is unknown and relates back to discussions about the origins of the optical pulse. Nonetheless, the correlation of pulse oximeter Spo2 values to invasively sampled arterial blood Sao2 values is generally within a few percent. Several groups have observed situations in which tissue venous blood volume also appears to modulate synchronously with the cardiac cycle based on the appearance of the optical waveform morphology for sensors placed on the digits (19) or forehead (20). When both the arterial and venous blood “pulse” synchronously, pulse oximeter Spo2 readings can reflect a mixture of the arterial and local venous oxygen saturation levels (33). Application of mild pressure to the sensor, however, has been found effective in reducing this artifact, as it appears to reduce or eliminate the pulsing venous volume in the optically probed regions of the tissue (20,34).

OPTICAL SHUNTING

When a sensor is applied poorly or lifted from the skin, in either transmission or surface geometries, some of the emitter’s light may reach the detector while not passing through blood-perfused tissues (“shunted light”). Optical light shunts can exist external to the tissue (35,36), or in some conditions within the tissue itself if sufficient blood is forced out of the optically probed region (subdermal light shunt) (37). Optical shunting results in an artificial reduction of the plethysmograph pulse amplitude, independent of the underlying tissue blood volume changes or Sao2 level since some of the detected light is never exposed to the pulsing arterial blood content. Unless the impact at the multiple wavelengths precisely cancels in the ratio taken in Eq. 6a, the Spo2 reading will be affected. Whether the Spo2 readings over- or underestimate the true Sao2 depends on which of the red or IR signals (respectively) are more strongly shunted.

PHYSIO-OPTIC DO’S AND DON’TS

The presence of a resolvable pulse is a necessary but not sufficient condition for pulse oximetry.

While the basic principals of pulse oximetry may appear simple and elegant on the surface, the factors described above suggest there is more, literally, going on inside. Disruptions to the general optical environment present during a device’s development can affect Spo2 accuracy.

Patient conditions can at times challenge a pulse oximeter in acquiring a signal and some users may be compelled to improvise in order to obtain readings. Similarly, sensors are sometimes modified to extend the lifetime of otherwise “single patient-use” devices. Indeed, one can find numerous citations in the literature where authors describe off-label changes to the pulse oximeter sensor to target one or both of these goals (38–42). While it is not the intent of this discussion to categorically discredit such efforts, users should question whether these changes have maintained the optical integrity of the sensor and tissue site. Importantly, has the modified use been verified to provide proper Spo2 readings over the full or clinically relevant Sao2 range? Errors in readings tend to increase as the patient’s Sao2 decreases to <90% (13,15,23,27); spot-checking the agreement between Spo2 and Sao2 at normal high saturation levels does not, unfortunately, assure accuracy as the Sao2 decreases. Regulatory and international standards require manufacturers to demonstrate, when used as labeled in controlled settings, Spo2 reading accuracy meets its specified performance with data obtained and pooled over the full 70%–100% Sao2 span (12,43). This is intended to ensure safety and consistency among commercially available systems; no such direct validation requirement is imposed on users who may chose to use these products differently. It would be impractical to require manufacturers to test the myriad of creative ways products can be misused.

Modifications generally fall into two categories, each with its own set of potential disruptions to the assumptions of pulse oximetry:

  • (A)Placement of sensors on alternate locations: Some tissue sites are simply incompatible with reliable and accurate pulse oximetry. The risk is that any of at least three optical factors described earlier can affect readings: 1) optical shunting (externally or within the tissue); 2) unexpectedly low or high tissue blood volume; or 3) pulses created by larger pulsing vessels. As monitors become more sensitive to weak signal levels, improperly placed sensors may appear to provide an adequate pulse waveform yet suffer from a physio-optic disruption.
  • (B)Modifications to sensors: The optical design of a sensor intended for specific applications may not be compatible with others. Adapting a sensor by changing its housing or attachment method can further affect accuracy. This is particularly true if such modifications impact 1) optical shunting (externally or within the tissue), 2) the detected light’s path length, or 3) the path length ratio.

For example, when peripheral pulse amplitudes become too small to acquire or maintain a signal, it is not an uncommon practice for users to try to find better pulsatile signals by adhering and/or clipping sensors designed for use on a patient’s digit to an ear or across the forehead. While the resulting plethysmographic waveform, pulse rate and Spo2 values may appear normal, the presence of a true hypoxia may be missed (44). We have also reproduced this scenario in the laboratory (adhesive digit sensor placed across the forehead or wrapped around the ear) and found Spo2 readings to commonly overestimate the true Sao2, at times posting 100% Spo2 even when subjects are truly in the lower 70% range (unpublished data). Optically, these misapplied sensors are likely being affected by larger pulsing blood vessels and/or optical shunting (light traveling along the surface disproportionately shrinking the size of the red pulse amplitude).

To maintain accurate readings with pulse oximetry, as well as to ensure safety to the patient, sensors should only be used according to their labeled directions. Digit sensors, unless designed for use on other anatomical sites, should only be used on the digits. Reflectance and “Y-shaped” sensors should only be placed on the appropriate site(s) as directed in the labeling and not used elsewhere, even though these sensors’ geometries may appear to be compatible with other locations. The proper device calibration and compatibility may not extend to alternative locations. Additional wraps, adhesives, or elastic bands are not recommended unless the product requires their use or specifically offers them as an option.

SUMMARY

Pulse oximetry is based on a relatively straightforward application of the Lambert–Beer law, using the change in signals corresponding to the cardiac cycle to isolate and estimate the patient’s Sao2. Light scattering, however, influences some of the simplifications made which, under most clinical circumstances, can be accommodated through the empirical process manufacturers use to calibrate the system during its design. Since red and IR light diffuses through the tissue, pulse oximetry sensors can be configured for use on opposing or adjacent surfaces, provided placement sites offer sufficient signal strength and are absent factors known to influence accuracy. However, certain optical perturbations can violate the remaining assumptions and impact system performance. Tissue heterogeneity, significant changes in tissue blood volume, venous pulsations, or shunting of light can all meaningfully influence Spo2 readings, particularly at lower Sao2 levels, if not adequately mitigated in the product’s design or actual use. Users should be cautious in modifying sensors and/or using them on tissue sites not intended by the manufacturer (off-label use). Such practices may disrupt the optical integrity of the measurement and result in falsely reassuring Spo2 readings.

To recap a summary of these principals: The presence of a resolvable pulse is a necessary but not sufficient condition for pulse oximetry. Accurate and reliable readings require that the integrity of the optical signals be maintained so that the Modified Lambert–Beer law assumptions remain valid.

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1Some descriptions of pulse oximetry consider the tissue blood concentration to be constant over the duration of the cardiac pulse and model alternatively a path length change due to the increased arterial blood content. The more precise description would be to consider the l·cHba product to change over the cycle.
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