Photoplethysmography (PPG) is a non-invasive optical method that can be used to detect blood volume changes in the microvascular bed of tissue. The PPG signal comprises two components; a pulsatile waveform (AC) attributed to changes in the interrogated blood volume with each heartbeat, and a slowly varying baseline (DC) combining low frequency fluctuations mainly due to respiration and sympathetic nervous system activity. In this report, we investigate the AC pulsatile waveform of the PPG pulse for ultimate use in extracting information regarding the biomechanical properties of tissue and vasculature. By analyzing the rise time of the pulse in the diastole period, we show that PPG is capable of measuring changes in the Young’s Modulus of tissue mimicking phantoms with a resolution of 4 KPa in the range of 12 to 61 KPa. In addition, the shape of the pulse can potentially be used to diagnose vascular complications by differentiating upstream from downstream complications. A Windkessel model was used to model changes in the biomechanical properties of the circulation and to test the proposed concept. The modeling data confirmed the response seen in vitro and showed the same trends in the PPG rise and fall times with changes in compliance and vascular resistance.
© 2014 Optical Society of America
Photoplethysmography (PPG) is one of the commonly used methods to record the pulse non-invasively . It can be used to measure changes in optical absorption due to variation in blood volume in the interrogated tissue. PPG sensors illuminate tissue with various wavelengths of light and collect the remainder of the light after it travels through tissue. These sensors can be divided into two categories depending on the probe formation and the location of light collection. The first approach is transmission which uses a photodetector and a light source on opposite sides of the tissue to measure optical intensity after light has propagated through tissue. The second approach is reflectance, in which the light source and photodetector are placed on the same surface of the tissue to measure the diffuse reflectance of light. The pulsatile blood flow causes changes in the tissue blood volume. This leads to variation in optical absorption which modulates the intensity of the collected light. PPG has been used in various applications ranging from heart rate monitoring [2, 3] to non-invasive perfusion tracking and imaging [4, 5], but pulse oximetry remains the most common and widely adapted application of PPG [6, 7].
The aforementioned applications rely on the frequency of the pulse and its amplitude on various wavelengths to extract the desired physiologic information (hemoglobin oxygen saturation, perfusion, heart rate, respiratory rate, etc.). However, the waveform of the pulse has been shown to carry substantial information about the biomechanical state of the cardiovascular network [8, 9]. For example, the pulse wave velocity can be used for monitoring blood pressure changes . Similarly, the waveform shape can be employed to assess arterial stiffening due to aging and cardiovascular problems [8, 9, 11, 12]. These methods measure the peripheral pulse to assess systemic changes. However, to our knowledge, there are no PPG based methods to assess local tissue mechanical changes that are critical in the diagnosis and monitoring of various diseases that affect tissue composition and blood flow. Current non-invasive methods of measuring mechanical properties are based mainly on Magnetic Resonance Elastography (MRE)  and ultrasound elastography  which are not suitable for continuous monitoring. Non-invasive measurements of local tissue mechanical properties can be of great importance to monitoring and diagnosing a wide variety of conditions such as liver fibrosis, lung fibrosis, wound healing, tissue burns monitoring, edema, and many others [15–17]. Our research has been primarily focused on the application of monitoring hepatic tissue and diagnosing vascular complications of liver transplants.
Every year, around 6,000 patients receive a liver transplant in the United States alone . These patients have the highest graft rejection risk in the first two weeks following the surgery . During this period, the graft monitoring standard relies on frequent blood tests for liver enzymes and biopsies [20, 21]. These tests often detect complications in a late stage increasing the risk on the patient’s life. Our group is working on developing an implantable optical sensor with telemetry capabilities to monitor transplanted organs and provide feedback to the medical staff in real-time [22–25]. The system is a three wavelengths PPG sensor that can measure perfusion and oxygenation changes simultaneously. We believe that, by using the pulse waveform, we can provide more information to the medical staff to assess the state of the graft and complement these measurements. For example, an occlusion in a vein or an artery leads to a decreased level of perfusion. However, an occlusion in the vein results in an increase downstream resistance to pulsatile flow while an arterial occlusion does not affect the resistance experienced by the blood in the organ. This can be observed in the shape of the pulse and can be used to differentiate arterial and venous complications which are treated differently by the medical care providers.
In addition, after initial diagnosis, liver failure is confirmed by performing a biopsy. Liver biopsy is an invasive procedure associated with various complications [26, 27] and 40% of patients undergoing liver biopsies experience pain . Biopsies also suffer from sampling errors due to tissue heterogeneity . A non-invasive optical system that can measure mechanical properties can be used to guide biopsies to account for heterogeneity and reduce the number of needed biopsies. The proposed concept can be applied to a point PPG sensor  or an imaging PPG system [3, 30] to scan the hepatic tissue and create a map of mechanical properties. In this work, we apply this concept to a point sensor for continuous graft monitoring.
Specifically in this paper, we present in vitro results showing the ability of using the pulse waveform to quantify tissue phantom compliance and diagnose vascular complications. The results are supported by numerical simulations using a Windkessel Model [31, 32].
2. Materials and methods
2.1 Signal processing and instrumentation
A custom bench-top PPG system was used to collect the data. The system was described in detail by Ericson et al. . In summary, the system uses three time-multiplexed light emitting diodes (LEDs) emitting light at different wavelengths in the red to near infrared spectral region (central wavelengths of 735, 805, and 940 nm). The diffuse reflectance is collected using a single photodetector. The collected signal on each wavelength is filtered and split into two channels. The first channel provides an amplified version of the AC component of the PPG while the second channel provides the slowly varying DC component of the PPG signal. The AC and DC channels are both needed when performing perfusion and oxygenation measurements. However, in this work, since our interest is focused on the pulsatile waveform, only the AC channel was used in the processing. Figure 1 shows a schematic of the collected signal before filtration and separation of the AC and DC components.
To understand the reasoning behind the signal processing, we start by a simplified description of the origin of the pulse. When blood flows into a capillary bed, it encounters an impedance due to the size and distribution of the vessels, the compliance of the vessels and surrounding tissue, and many other factors that depend on the mechanical structure of the tissue and vasculature. In addition, it also encounters a back flow due to a reflected wave generated at an impedance mismatch point such as the peripheral vessels or the aortic valve. These properties give the pulse its shape, which is different from the shape of the cardiac output (blood flow out of the heart).
One method of describing the process is from an electrical circuit perspective. The liver during the diastole can be thought of as a simple resistive-capacitive (RC) electric circuit where the resistance is the vascular resistance to the flow and the capacitance is the compliance of the hepatic circulation. The capacitor discharge describes the emptying of the hepatic blood content into the main circulation. The current represents the blood flow while the electric potential (voltage) mimics the blood pressure that controls the blood volume in the capillary bed. This concept is commonly used in studying biomechanical systems [31, 32]. When the resistance increases the time constant (τ = R*C), which represents the temporal response of the system, also increases. This increase in resistance is indicative of a downstream vascular blockage or narrowing. Note that when the narrowing or blockage takes place upstream from the measurement site, the resistance experienced by the hepatic blood during diastole is unaffected and the time constant is not expected to change. Similarly, a capacitance decrease is indicative of a decrease in compliance or rather stiffening of the tissue that can be due to a variety of conditions such as hepatic edema, which is very common after transplant, or fibrosis.
To obtain a quantifiable measure of this time constant, we measure the rise time in the PPG pulse which corresponds to the diastole phase . The rise time was defined as the time between the foot of the pulse and the peak. To avoid any errors due to noise causing fluctuations during these periods, we used the time between the point that is 10% larger than the valley and the point that is 10% lower that the peak as shown in Fig. 2. All measurements were made using automated software developed in MATLAB (Mathworks, Natick, MA). Note that the data in Fig. 2 shows the optical intensity corresponding to a simulated pulse. The optical intensity changes in the opposite direction of the blood pressure and that is why the pulse looks inverted (an increase in pressure corresponds to an increase in absorption which leads to a decrease in intensity). This is explained in more detail in previous review article and book chapter [1, 34].
2.2 Phantom preparation
The proposed concept was tested in a series of in vitro phantom studies. Polydimethyl-siloxane (PDMS) phantoms were fabricated with different curing parameters to adjust their mechanical properties. PDMS was mixed with various optical absorbers (blue food coloring and black India ink) and scatterers (100 nm and 0.5-1 µm Aluminum Oxide powder) to mimic the optical properties of hepatic tissue in the 630 – 1,000 nm wavelength range. The recipe was described in detail in a previous report by our group . The phantoms mimic the structures of the portal vein (PV), the main blood and nutrients supplier to the liver. The curing parameters that control the PDMS mechanical properties include the curing temperature, curing time, and the concentration of the curing agent. A detailed study on the effects of curing parameters on the Young’s Modulus (YM) of PDMS was reported by Hong et al. . Note that the addition of the optical scatterers and absorbers changes the mechanical properties of PDMS.
For the purpose of this study, three different sets of phantoms were fabricated. The curing time and temperature were 24 hours and 60 °C for all three phantoms while the PDMS to curing agent volumetric ratio was changed between 30:1, 40:1, and 45:1 v/v which yielded a Young’s modulus (YM) of 11.7, 15, and 61 KPa respectively. All YM measurements were obtained from stress-strain curve measurements acquired by an Instron 3345 (Instron, MA, USA). The calculations were made using an automated program developed in MATLAB. Note that compliance of a structure is inversely proportional to the incremental modulus (C∝1/E) and a larger YM indicates a less compliant material . All the reported measurements are for the PDMS with the optical absorbing and scattering agents included, which yields a higher YM in comparison to clear PDMS. Figure 3 shows the raw data from the tensile tests of two of the phantoms.
Similarly, to avoid handling blood, an optical mixture of various optical dyes was used to mimic the optical properties of oxygenated hemoglobin. The mixture was described in detail in previous reports .
2.3 In vitro setup
The phantoms described above were connected to a fluidic circuit to mimic the pulsatile blood flow. A peristaltic pump controlled via a virtual instrument (VI) designed in LabVIEW was used to control the pulsatile flow. The phantoms were perfused with the dye mixture and c-clamps were placed on the tubing on either side of the phantom to occlude flow when needed. The PPG probe was placed on top of the phantom and held in place with a mechanical arm. Figure 4 shows a schematic of the system. The insets show the PPG signal collected from the phantom experiments during a downstream and an upstream occlusion. Note the change in the waveform when a downstream occlusion is performed. In both cases the occlusion causes a reduction in flow which leads to a decrease in the pulse amplitude.
2.4 Windkessel model
To study the expected performance of the system theoretically over a wider range of physiologic conditions, we developed a four element (R, C, L, r) Windkessel model . The resistive and capacitive elements (R and C) in this model can be explained as mentioned earlier in the Signal processing and instrumentation section. In summary, the resistance, R, represents the peripheral/downstream resistance. The capacitive element, C, represents the compliance of the microvasculature and tissue. In addition, an inductance is added to the model to account for the inertia of blood flow. Finally, r is the characteristic impedance of the circulatory system under investigation and is typically much smaller than R (5-7% of R) . An extensive review of Windkessel models and their relation to physiologic parameters was reported by Westerhof et al. . The differential equations governing the behavior of this model were developed by applying circuit theory and solved numerically using software developed in MATLAB. Figure 5 shows a schematic of the four element Windkessel model.
Note that this model is not meant to be an accurate representation of hepatic circulation but more of a general model to mimic physiologic signals and highlight the expected changes in the pulse with various parameters. The blood flow was modeled by Eq. (1) as reported by Ballal et al. :
As discussed earlier, the modeled pulse (blood pressure and/or volume) mimics the change in optical absorption. To determine the changes in optical intensity measured by the PPG sensor, we used the approximation shown in Eq. (2). This approximation can be used since we are not as interested in the amplitude of the pulse as we are in its waveform. The blood flow signal and three different pressure waveforms obtained by the Windkessel model are shown in Fig. 6. These three waveforms were used to mimic data found in the literature to validate the performance of the model. The shape of the pulses is similar to in vivo data reported in literature [1, 9].
3.1 In vitro studies
3.1.1 Compliance changes
For the initial studies, two phantoms were developed and used in the testing. The phantoms have a Young’s modulus of 11.5 and 61 KPa which mimic the change from normal hepatic tissue to the last stage of fibrosis . The different phantoms were placed in the flow circuit described above and the benchtop PPG system was used to measure the pulsatile signal. Figure 7 shows two waveforms measured from the different phantoms.
The rise time was measured from one minute of continuous data for each phantom. This was repeated three times for each phantom and the average and standard deviation were calculated accordingly. As depicted in Fig. 8, the rise time decreased with increased Young’s modulus (decreased compliance). The left panel shows the PPG signal measured from the two different phantoms and the change in the rise time. Each phantom was placed in the flow circuit three different times and the average rise time is shown in the bar plot of the right panel. The error bars correspond to +/− one standard deviation. Note that the rise time is also affected by the changes in the flow circuit (tubing material, tubing dimensions, pump, connectors, etc.). The rise time decreased from 305.6 +/− 8.88 ms to 195.3 +/− 10.2 ms for the 11.7 KPa and 61 KPa phantoms respectively.
To obtain a more accurate trend of the rise time over the range of interest, a third PDMS phantom with a YM in between the two original values was prepared and data was recollected from all three phantoms. The phantom’s YM was 15 KPa as tested by the Instron tensile tester. Figure 9 shows the data from the three phantoms. Note that the values changed from the previous experiment since they depend on the flow circuit (i.e. tubing, pumps, etc.) which was modified between the two experiments.
3.1.2 Diagnosing vascular complications
For each of the phantoms, after collecting baseline data for 30 – 60 s, flow was occluded using a c-clamp either upstream or downstream from the phantom. For the first occlusion, the clamp was tightened until a visual decrease in pulse amplitude was observed. The same number of turns on the c-clamp was used for every occlusion afterwards. During both upstream and downstream occlusions, the amplitude of the PPG signal decreased indicating a decrease in the pulsatile flow. However, in the case of downstream occlusions, an increase in the PPG rise time was recorded which is due to the increase in the resistance. This was not observed during upstream occlusions. Figure 10 shows examples of a downstream and an upstream occlusion. In both cases, the rise time in the recovery period, after the occlusion was released, was the same as the baseline value.
This experiment was repeated three times for each type of occlusion. The bar graphs in Fig. 11 show the average and standard deviation of all runs for the 11.7 and 61 KPa phantoms.
3.2 Modeling results
To test the proposed concept over a wider range of parameters that cover the full physiologic range, we used the Windkessel model described earlier. The compliance was changed between 0.35 and 3.25 cm3/mmHg which correspond to Young’s moduli of 73.2 to 7.9 KPa respectively. This conversion was made by assuming that the vessel is expanding only in the radial direction and using the equations for elastic modulus and compliance as reported by Gosling et al. . Note that the relationship between compliance and Young’s modulus is not linear. The compliance is proportional to the inverse of the modulus (C∝1/E). Similar to the in vitro data, the rise time increased for higher compliance levels while the fall time decreased (Fig. 12).
Because the rise time depends on parameters other than the compliance such as the resistance in the flow circuit, we scaled our in vitro results to fit the model. Specifically, the data from the lowest YM (11.7 KPa) was scaled to the rise time curve obtained by the Windkessel model and the same scaling factor was used for the other two phantoms. This scaling does not affect the trend of the data and helps compare the trend from the theory to that of the in vitro data. The dots in the right panel of Fig. 12 show the scaled data from the in vitro studies (data from Fig. 9).
To mimic vascular occlusions, we modeled the case of increased resistance. The normal physiologic range of systemic vascular resistance is typically in the range of 11.25 to 18 mmHg.min/L (1,170 +/− 270 dynes-sec/cm5) . We modeled resistance changes between 8.3 and 27.3 mmHg.min/L which covers the normal range and the elevated resistance range as shown in Fig. 13.
The mechanical properties of tissue can be significant for a number of medical applications. In particular for our work, mechanical properties are of great importance to the success of transplant surgeries  and are indicators of hepatic health [44–46]. In this paper, we showed the ability of using the waveform of the PPG signal to monitor changes in compliance and diagnose vascular complications that are the second most common cause of graft failure after primary graft non function [47, 48]. The proposed concept can be used in sensing systems for continuous graft monitoring or point interrogation, and potentially in imaging systems (i.e. iPPG) for rapid assessment of tissue mechanical properties.
The sensitivity to compliance changes in the physiologic range was shown theoretically through modeling and confirmed in vitro using PDMS based phantoms. The YM of hepatic tissue for healthy individuals has been shown in previous reports to be around 5.5 KPa (Stage F0-1) . This value is higher for vessels, for example the portal vein YM was reported by Wang et al. to be 32.04 +/− 5.65 KPa for a pressure of 75 mmHg . Tissue compliance has been reported to decrease 3 to 10 times with the development of fibrosis [40, 44, 49] which results in a similar increase in its YM. For our in vitro studies, phantoms were developed with YM of 11.7, 15 and 61 KPa and the analysis of the PPG rise time showed a significant decrease with the increase of the YM. In addition, to test the expected changes over a wider range of mechanical properties, the concept was applied to signals generated from a Windkessel model. YM levels in the range of 7 to 73 KPa were tested and the results are similar to the in vitro experiments. Note that the absolute values of the rise time are different since these values depend on various other factors that were not accounted for in vitro such as the blood flow pattern, downstream resistance of the pipes or vessels, and viscosity of the fluid. If this system is used in vivo, all these systemic variables can be accounted for by a second PPG measurement on a different site in the body (i.e. peripheral PPG on the fingers or ear lobe). The model shows that the PPG rise time is most sensitive to changes in the compliance below 15 KPa which coincides with the range of mechanical properties of healthy individuals and early stages of fibrosis which is the most critical range for monitoring. By fitting the in vitro data to a calibration model similar to the one obtained from the Windkessel simulations, we found that our PPG system has a standard error of 4 KPa.
The results show that the proposed concept is also able to discriminate downstream vascular complications from upstream complications. Downstream vascular complication (i.e. stenosis) can result in an increased vascular resistance which leads to an increase in the PPG rise time. This is opposite to the stiffening of the tissue that results in a decrease in the rise time. Simulation data show the same trends in the rise time of the pulse confirming the proposed approach. The error bars from the data collected in these experiments are very small suggesting that the system can resolve minute changes in downstream resistance. However, the method used to increase the downstream resistance (c-clamps) in our in vitro studies is not quantitative and thus we did not attempt to quantify the resolution of the system. Note that the periodic variation seen during data collection is due to the pressure buildup in the flow circuit which results in increased resistance leading to backflow and an increase in the rise time. This was thoroughly discussed and quantified in a previous report by our group describing the PDMS phantoms’ performance . Part of the error seen during the occlusion periods (Fig. 11) is due to the variation in the pressure induced by the c-clamp between the different occlusion periods.
In addition to the changes in the PPG pulse rise time, the fall time of the pulse changes in the opposite direction. This was seen in the phantom experiments and the Windkessel modeling. In this work, we elected to use the rise time because it is more sensitive and showed a larger response to compliance and resistance changes. This trend is the same in the modeling and in vitro data.
The data integration time used in this work is roughly 60 seconds. However, as seen in Fig. 10, the rise time measurement is very stable and the only variation is due to the back flow that mimics the respiratory effect seen in vivo.
In this manuscript, we analyzed a PPG waveform collected in vitro using new PDMS based phantoms that mimic tissue elasticity, and used a simplified Windkessel model to examine a broader physiologic range. The modeling results are in agreement with the data collected in vitro. The system used in this research showed a resolution to YM changes of 4 KPa. The modeling and in vitro results show that the PPG signal has strong potential for ultimate use in non-invasive monitoring of tissue mechanical properties due to the sensitivity of the pulse shape to changes in compliance and vascular resistance. In particular, the approach has the potential of staging liver fibrosis that changes the YM from 5.5 KPa (F0-1) up to 48 KPa (F4). In addition, the concept can potentially be applied to monitor changes in downstream resistance which can be used to detect and diagnose vascular complications.
This research was funded by a bioengineering research partnership (BRP) grant from NIH, (#5R01-GM077150).
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