Possible Error in Reflection Pulse Oximeter Readings as a Result of Applied Pressure
Possible Error in Reflection Pulse Oximeter Readings as a Result of Applied Pressure
Fine, Ilya;Kaminsky, Alexander
2019-10-24 00:00:00
Hindawi Journal of Healthcare Engineering Volume 2019, Article ID 7293813, 7 pages https://doi.org/10.1155/2019/7293813 Research Article Possible Error in Reflection Pulse Oximeter Readings as a Result of Applied Pressure Ilya Fine and Alexander Kaminsky Elfi-Tech Ltd., 2 Prof. Bergman St., Science Park, 76705 Rehovot, Israel Correspondence should be addressed to Ilya Fine; ilyafine@elfi-tech.com Received 26 August 2019; Accepted 30 September 2019; Published 24 October 2019 Academic Editor: Norio Iriguchi Copyright © 2019 Ilya Fine and Alexander Kaminsky. ,is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Pulse oximetry is one of the most widely used techniques in modern medicine. In pulse oximetry, photoplethysmography (PPG) signals are measured at two different wavelengths and converted into the parameter Gamma, which is used to calculate the oxygen saturation of arterial blood. Although most pulse oximetry sensors are based on transmission geometry, the reflection mode is required for different form factors such as the forehead or wrists. In reflection oximetry, local pressure is applied to the measurement surface. We investigated the relationship between applied pressure and Gamma and found that for the reflection mode, Gamma tends to increase with increasing applied pressure. To explain this, we described the PPG signal in terms of two alternative models: a volumetric model and a Scattering- Driven Model (SDM). We assumed that the application of external pressure results in a decrease in local blood flow. We showed that only SDM correctly qualitatively describes Gamma as a function of the decrease in blood flow. We concluded that both described models coexist and that the relative influence of each depends on the measurement geometry and blood perfusion in the skin. calculates AC/DC at 670 nm and AC/DC at 940 nm. ,e 1. Introduction ratio of these two ratios is called Gamma. ,en, empirically 1.1. Alternative PPG Signal Models: Volumetric Model and derived calibration curves are used to estimate SPO based Scattering Driven Model. Pulse oximetry, which is based on on the Gamma. Pulse oximetry technology is robust and photoplethysmography (PPG), has become the standard successful because the calculated SPO manifests a very weak technique for noninvasive monitoring of arterial oxygen dependence on local blood volume, skin pigmentation, saturation. Pulse oximetry measures arterial blood hemo- hematocrit, and finger size. In practice, two types of geo- globin saturation (SPO ). SPO is the fraction of oxygen- metric configurations of pulse oximeters are widely used. 2 2 saturated hemoglobin relative to total hemoglobin [1, 2]. ,e most common geometry is when the light source shines PPG signal is strongly dependent on the absorption of light through the biological tissue, and the photodetector is lo- by hemoglobin which, in turn, depends on the wavelength of cated on the other side of the measured object. ,is type of the light used. ,e principle of operation of pulse oximetry is geometry is called transmission pulse oximetry and is based on the difference in the absorption spectrum of oxy typically used on the tip of the finger. With another type of (HbO ) and deoxyhemoglobin (Hb) in the visible and in- configuration called reflective oximetry, the light sources frared spectral regions. HbO absorbs more light in the near- and detector or detectors are located on one side of the tissue infrared part of the spectrum (810–990 nm) and lesser light [3]. ,is configuration is applied on the forehead, on the in the red part of the spectrum (630–690 nm). In the most arm, or other places where it is not possible to use the commonly used mode of operation, the light source of a pair transmission technique [4]. of red (670 nm) and infrared (940 nm) light-emitting diodes ,e PPG signal is commonly associated with changes in (LEDs) is used. ,e measured signals consist of a DC local blood volume. It is assumed that the amount of blood component and pulsatile (AC) component. Pulse oximetry in the illuminated perfused tissue fluctuates at the rate of the 2 Journal of Healthcare Engineering scattering of light occurring during the aggregation and heartbeat, as does light transmission or refraction. According to this volumetric model, the periodic changes in disaggregation of red blood cells. Nevertheless, for a pulsating signal in vivo, there is no blood volume result in changes in the intensity of the measured light. Some studies have questioned the unique- direct evidence that the aggregation model can be used as at ness of the volumetric model for explaining the origin of the least an additional phenomenon of the PPG if not as an PPG signal. For example, Hocherman and Palti [5] simul- alternative. ,e aim of this work was to check (a) whether the taneously measured volumetric changes at the fingertip aggregation model can correctly describe quantitatively the directly, using fluid plethysmography, and optical trans- experimentally known Gamma values used in pulse oximetry mission. ,ey gradually increased the applied pressure on and (b) whether Gamma is affected by local blood flow. the fingertip until the volumetric signal disappeared; how- ever, the prominent pulsatile optical signal was still ob- 2. Pulse Oximetry Parameter “Gamma” in served. In another study, the authors performed Doppler Terms of Scattering and Absorption of RBC fluorometry and PPG measurements simultaneously in bone [6]. Although a prominent PPG signal was recorded, there 2.1. Light Intensity as a Function of Scattering and Absorption was no significant periodic increase in blood volume in bone by RBCs. Diffusion theory for light transmission in tissue is resulting from vasodilation or the opening of collaterals. a commonly accepted way to model light propagation in a In in vitro studies [7], blood was periodically pumped high-scattering isotropic turbid media such as biological through a rigid glass cuvette, and a pulsatile optical signal tissue [16, 17]. ,e key model parameters of effective at- resembling a typical PPG was obtained. In this article, it was tenuation coefficient μ (λ, t) of the blood, or inverse dif- eff shown that such a pulsatile signal is associated with the effect fusion length, and blood layer thickness x(t) are used to of red blood cell (RBC) aggregation or rouleau formation. describe light propagation characteristics through a me- Aggregation of red blood cells (RBCs) results in the formation dium. ,e intensity of transmitted light (I) is a function of of linear or branched structures called rouleaux [8]. However, these two parameters: in capillary and arterioles, it is reasonable to assume that the development of the branched structures is limited, and linear I(t) � Iμ (t), x(t). (1) eff aggregates prevail. ,e average length of the RBC aggregates is where the effective attenuation coefficient for an ensemble of dependent on shear forces and thus, varies periodically with RBCs can be defined by the following approximation [18]: changes in the blood flow [9, 10]. According to this re- ������������������������ lationship, the frequency of disassembling and reassembling ∗ 2 ′ (2) μ (λ, t) � 3 · μ (λ) + μ (λ) · μ (λ, t), a a s eff the aggregates is controlled by the heartbeat, which evokes shear force modulation [11]. ,ese processes are definitely fast where μ (λ) is the absorption coefficient and μ (λ, t) � a s enough to result in optical transparency pulsations at the μ (λ, t) · [1 − g(λ, t)], where μ (λ, t) is the scattering co- s s frequency of the heartbeat. Various theoretical approaches efficient, and g is the scattering anisotropy. have been applied to describe light-scattering process in terms ,e light absorbance of RBCs is a function of oxyhe- of RBCs size and orientation [12, 13]. Eventually, changes in moglobin and deoxyhemoglobin. Oxygen saturation SPO is the length and concentration of scattering particles lead to defined as the ratio of the concentration of oxyhemoglobin changes in the scattering of light and accordingly, in the in- [HbO ] and that of deoxyhemoglobin [Hb] plus [HbO ]: 2 2 tensity of transmitted light. HbO ,us, the following question arises: Is it possible to 2 SPO � (3) observe the manifestations of RBC aggregation in vivo? HbO + [Hb] Shvartsman and Fine [14] showed that if the blood flow is ,e average absorption coefficient is given by the fol- stopped by applying pressure greater than systolic pressure, lowing expression: then the intensity of the light passing through the fingertip gradually increases. Indeed, in stasis, RBCs spontaneously μ (λ) � SPO · σ + 1 − SPO · σ · ρ, (4) a 2 HbO (λ) 2 Hb(λ) aggregate to form long linear stacks, which may result in a decrease in light scattering. With respect to pulsatile blood where σ and σ are the absorption cross sections of HbO (λ) Hb(λ) flow, the length of the aggregate depends on the hemody- oxy- and deoxyhemoglobin, respectively, and ρ is the namic characteristics of the blood in a particular vessel. ,e concentration of erythrocytes particles and is defined as rouleaux are easily disrupted by shear forces. ,e aggre- ρ � H/V, where V is the volume of the particles and H is the gation and disaggregation of RBCs are dynamic processes. hematocrit value. We can assume that arterial blood is al- ,is shear-dependent variation is the primary cause of the most entirely oxygenated, so μ (λ) ≈ μ . For radiation a HbO (λ) non-Newtonian behavior of blood in human blood vessels propagating through a statistically homogeneous random [10]. As blood pressure increases to its peak, the flow velocity medium, the attenuation as a function of the optical length is and shear rate gradually increase, and as the pressure de- close to exponential [19]. ,e validity of the exponential creases, the velocity and shear rate decrease. ,erefore, the approximation for light transmission in perfused tissue is mean size of RBC aggregates is governed by shear forces. As also fortified by the fact that the Gamma used in pulse the shear rate increases, the size of the aggregates decreases. oximetry is independent of the amount of blood. Only the Based on these facts, Fine [15] proposed a model that ex- exponential dependence of light transmission on the plains the PPG signal in terms of modulation of the thickness of blood removes the dependence of Gamma on Journal of Healthcare Engineering 3 the thickness of the finger. ,is is the basis of pulse oximetry. Aggregates ,erefore, we assumed that the degree of attenuation of the transmitted light intensity in the medium in which the tissue is penetrated by blood vessels is determined by the following exponential expression: 1 RBC 2 RBC 3 RBC 4 RBC I(t) ∼ exp − μ (t) · x(t) . (5) eff Figure 1: Aggregation of RBCs is approximated by an ellipsoid as the number of RBCs increases. ,e exponential dependence of I(t) is predetermined by the diffusion properties of the surrounding tissue. ,us, it is not paradoxical that the pulse oximeter functions correctly used an ellipsoid with a revolution of a given size, axial ratio, only because of the presence of light-scattering tissue. ,e and orientation that could be approximated by a suitable scattering coefficients of the blood volume can be expressed equivalent sphere [23]. ,e effects of the difference between in terms of the scattering cross section and RBC concen- the volumes of the ellipsoid and the equivalent sphere can be tration ρ(t): accounted for using a corrected refractive index m for the equivalent sphere: μ (λ, t) � σ (λ, t) · P · ρ(t), (6) s s m � 1 + (m − 1) · χ(Ω), (7) where σ (λ, t) is the scattering cross section, and P is the packing factor, initially introduced by Twersky [20]; it ranges where m is the refractive index of the particle relative to the surroundings, χ(Ω) can be expressed in terms of axial ratio from 0.2 to 0.65. For a suspension of single RBCs, P � (1 − H)(1.4 − H). ,us, μ (λ, t) � σ (λ, t) · P · ρ(t) · [1 − g(λ, t)]. parameters of the ellipsoid and the angle (Ω) of incidence of s s light relative to the main axis of the ellipsoid. We assumed ,e PPG signal is characterized by changes in the in- that the incident light interacts with an ensemble of ran- tensity of the light after it passes through blood and tissue. domly oriented RBC aggregates, so the scattering cross ,e associated pressure waves give rise to periodic changes section and χ(Ω) should be averaged over all possible di- in the optical properties of the measured blood vessels. rections by using equation (7). ,erefore, we calculated the However, we are interested in the specific mechanism that mean values of μ and g using the adjusted Mie equations for causes the changes in the optical properties of the perfused an ellipsoid composed of n RBCs (n � 1–10) (Figure 2). tissue being measured. We considered two different mechanisms that may be responsible for the changes in light intensity as a function of time. One mechanism is called the 2.2. Expressions for Gamma. In pulse oximetry, the value of volumetric model. ,is is the most accepted model of PPG, SPO is determined entirely by Gamma, which is defined as whereby during the systolic phase, a pressure wave leads to the ratio of the pulsatile (AC) and nonpulsatile (I) com- an increase in blood volume in the tissue. ,us, in equation ponents of the red and infrared signals and is known as the (1), only x is a function of time. ratio of ratios: ,e second, alternative model is known as the scattering- driven model (SDM) whereby the blood pressure wave delta I λ , t /I λ , t 1 1 Gamma � , (8) induces changes in the light-scattering characteristics of delta I λ , t /I λ , t 2 2 blood, most likely through the RBC aggregation-disaggre- gation mechanism. ,e changes in RBC aggregation are where delta (I) is associated with the AC component of the signal. AC represents the amplitude of the PPG signal. For driven by variations in the shear rate. Formally, we assume that just μ (λ, t) depends on time. Periodic changes in speed small changes in AC, Gamma can be approximated by the so-called parametric slope, given by can lead not only to changes in RBC aggregation but also to a change in the orientation of the RBCs or the density of RBC z ln I λ , t /zt Gamma � . (9) distribution in the vessels [10]. All these phenomena are z ln I λ , t /zt associated with a change in light scattering. To describe the light scattering by RBCs, we used the Mie Next, we called Gamma for the SDM as GammaS and [21] solution, which provides a complete solution for de- Gamma for the volumetric model as GammaV. ,e im- termining the scattering cross section value and the phase- portant property of Gamma is that its value is practically scattering function. Steinke and Shepherd [22] showed that unaffected by the local blood volume, blood hematocrit, the Mie model can be used to describe light scattering by measurement geometry, and tissue hematocrit. ,is implies RBCs. To adjust the Mie theory for use with RBC aggregates, that Gamma has the striking feature of an invariant that we used the following simplified model: when RBCs stick depends upon absorption and scattering properties only. together in a chain, the new scattering entity can be ap- Gamma can be converted into SPO using an experimentally proximated as a spheroid (Figure 1). For short aggregates, obtained calibration curve. the spheroid is flattened, while it becomes elongated with an To derive an explicit expression for Gamma, we used increase in the number of particles. equations (2)− (5), (7), and (9). In the most general case, According to the Mie model, to calculate the scattering z ln Iμ λ , t , μ λ , x(t)/zt s 1 a 1 cross section, the radius of the sphere, r, and relative re- Gamma � . (10) z ln Iμ λ , t , μ λ , x(t)/zt s 2 a 2 fractive index are required. To circumvent this problem, we 4 Journal of Healthcare Engineering 320 0.994 0.993 0.992 0.991 0.99 0.989 0.988 140 0.987 1 2341 56 78 90 121 3 4 579 6 80 Number of RBCs in the aggregate Number of RBCs in the aggregate 670 nm 670 nm 940 nm 940 nm (a) (b) Figure 2: (a) Scattering coefficient as a function of number of RBCs in the aggregate and (b) reduced scattering as a function of number of RBCs in the aggregate. Using equation (10), we calculated Gamma as a function this way, we investigated the dependence of Gamma on the of the size of the rouleaux for the volumetric model and the level of local pressure for several form factors: fingertip SDM. ,e only time-dependent parameter for the volu- (transmission and reflection), wrist, and forehead. metric model is x: For pulse oximetry, we used a standard optical system that consisted of two LEDs at 660 and 940 nm and a pho- z ln Iμ λ , μ λ , x(t)/zx s 1 a 1 GammaV � . (11) todetector (PD) with an amplifier. ,e digitized signal was z ln I μ λ , μ λ , x(t) /zx s 2 a 2 stored in a computer for further processing and analysis. Inflatable silicone cushions were used to create local pressure For the SDM model, x is fixed, and μ and particle (Figure 4). concentration ρ are functions of time: ,e pressure level in the cushions was set using a pressure ′ ′ ′ z ln Iμ λ , t , μ λ , x/zμ λ zμ λ , t /zt s 1 a 1 s 1 s 1 controller, which was managed by software on the computer. GammaS � × . ′ ′ ′ z ln Iμ λ , t , μ λ , x/zμ λ zμ λ , t /zt s 2 a 2 s 2 s 2 ,e difference between the pressure in the cushion and the pressure applied to the skin was taken into account [24]. In our (12) case, the experimentally determined pressure transfer function To calculate Gamma, we chose commonly used wave- was defined as P � 0.92 · P − 20 [torr]. In the re- Skin Balloon lengths of 660 and 940 nm and SPO �100%, which ap- flection mode, the LEDs and photodiode (PD) are mounted proximately corresponds to the normal level of oxygenation side-by-side on the same planar substrate. A flexible substrate of arterial blood. Figures 3(a) and 3(b) show the estimated was used to adjust the shape of the tissue (Figure 5). GammaS and GammaV as a function of the average size of the RBC aggregates. Gamma gradually increases with in- 3.2. Results. Figure 6 shows the experimental data for creasing aggregate size, whereas for the volumetric model, Gamma, as a function of applied pressure for reflection GammaV has a weak dependence on the length of the ag- geometry measured at three different locations: the finger, gregate. For one RBC or a small rouleau, the difference the wrist, and the forehead. ,e Gamma was calculated by between GammaS and GammaV is small, and their values using equation (8). Each point on the graph was obtained by are close to the range of the experimental values known in averaging several measurements. In all cases, Gamma tended pulse oximetry. to increase with increasing pressure. Figure 7 shows the behavior of Gamma for transmission 3. Experimental Results and Discussion geometry and reflection geometry. ,e cuff pressure was gradually increased to 120 torr and then gradually decreased 3.1. Experimental System. ,e goal of our study was to to the initial pressure. In most cases, the change in Gamma examine experimentally the behavior of Gamma for two for transmission geometry was very subtle. types of measurement geometry: reflection and trans- mission. ,e idea was to create conditions under which the average length of RBC aggregates could be increased by 3.3. Discussion. We analyzed different possible causes of the changing the local blood flow. A decrease in blood flow dependence of Gamma on the pressure applied. For re- velocity should lead to a shift in dynamic equilibrium upon flection geometry, one can speculate that applied pressure which the average length of the aggregates should increase. may induce the so-called crosstalk effect. In other words, the We reduced the blood flow velocity by applying pressure. In external pressure applied to the tissue “squeezes” the blood Scattering coefficient in 1 (mm) g -reduced scattering coefficient Journal of Healthcare Engineering 5 SPO = 100%, scattering driven model (660 nm, 940 nm) SPO = 100%, volumetric model (660 nm, 940 nm) 2 2 0.76 0.52 0.74 0.51 0.72 0.5 0.7 0.49 0.68 0.48 0.66 0.47 0.64 0.46 26 35749 8 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Average number of erythrocytes in one aggregate Average number of erythrocytes in one aggregate (a) (b) Figure 3: Gamma dependence on RBC aggregation length for (a) SDM and (b) volumetric model. Reflection Transmission 0.9 0.85 PD 0.8 0.75 0.7 0.65 LEDs R, IR 0.6 Figure 4: Measurement setup for reflection and transmission. 0.55 0.5 PD LED LED PD 0.45 Balloon 0.4 10 20 30 40 50 60 70 80 90 100 Pressure, Torr Tissue Tissue Flexible substrate Figure 6: Gamma as a function of applied pressure at different (a) (b) locations for reflection geometry. Squares: fingertip; triangles: forehead; circles: wrist. Filled and open symbols indicate the two Figure 5: (a) Curved surface of the tissue (finger). (b) Flat surface sets of measurements taken at the different locations. of the tissue (forehead). ,ese changes are due to the applied pressure. We found out of the capillaries of the dermis, which leads to direct that the measured changes in Gamma were significantly leakage of the specular component of light from the LED to greater than those estimated by equation (13). ,us, the the detector. To test this assumption, we made the following crosstalk effect is not sufficient to explain the results. To assessment: assume that the increase in the baseline of the reaffirm this conclusion, we conducted experiments using PPG signal (DC component) as the pressure increases is different PPG sensor geometries by using bases (distances) entirely due to crosstalk. In this case, the effect of crosstalk of L � 4 mm and L � 12 mm between the LED and the PD. on the Gamma value should be maximal. To obtain the ,e crosstalk effect for L � 12 mm was qualitatively the same measured Gamma value caused by the alleged crosstalk, we as that for L � 4 mm, and the crosstalk effect for L � 12 mm substituted the experimentally measured change in the DC was supposed to be negligible. ,us, for reflection geometry, for the red (δI ) and infrared (δI ) channels into the R IR we concluded that applied pressure has an effect on Gamma following expression: regardless of the sensor geometry. I I + δI R IR IR We explained our experimental results for reflection ge- Gamma Crosstalk � Gamma · · . I I + δI IR R R ometry by assuming that the applied pressure results in a (13) decrease in blood flow velocity and shear rate in the arteriole GammaS GammaV Gamma 6 Journal of Healthcare Engineering 4. Conclusion 0.8 120 In summary, we showed the dependence of Gamma on the pressure applied to blood vessels in pulse oximetry. ,e experimental result was explained by applying a model in 0.7 80 which the pulsatile changes in the intensity of the reflected light result from the variations in the average size of RBC aggregates. ,e average aggregate size at each instant of time depends on the size of the vessel and the speed of blood flow. 0.6 40 Both volumetric and aggregation models of the PPG signal yield similar Gamma values for small aggregates. With in- creasing aggregate length, the behavior of Gamma differs between the two models. ,erefore, we assumed that the two 20 30 40 50 60 70 80 90 100 110 underlying mechanisms of the PPG signal are superimposed. Time, sec ,e relative contribution of each of these mechanisms may Figure 7: Gamma as a function of applied pressure on the finger for depend on the form factor, measurement geometry, and transmission (dashed lines) and reflection (solid line) geometry. blood flow conditions. Right ordinate axis is the applied pressure, and the green line is the pressure as a function of time (in torr). Data Availability ,e raw PPG data used in this study are available from the vessels. Following this process, the dynamic balance between corresponding author upon request. the formation and the destruction of aggregates shifts toward longer aggregates. According to the prediction of the SDM, Gamma should increase, as was observed in our experiments. Conflicts of Interest However, a similar effect is not observed in transmission ,e authors have no relevant financial interests in the geometry. ,is is explained by the significant connection manuscript and no other potential conflicts of interest. between vessel diameter and shear rate forces. Relatively large arteries with diameters between 150 and 242 μm are located at the hypodermal-dermal junction [25]. ,e arte- References rioles in the papillary dermis vary from 17 to 26 μm in [1] E. D. Chan, M. M. Chan, and M. M. Chan, “Pulse oximetry: diameter and represent terminal arterioles. ,ey are located understanding its basic principles facilitates appreciation of its at the very “bottom” of the dermis. ,e arterioles and ve- limitations,” Respiratory Medicine, vol. 107, no. 6, pp. 789– nules involved in cutaneous microcirculation form two 799, 2013. important plexuses in the dermis: an upper horizontal [2] Y. Hay, O. Cohen, I. 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