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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 5, Iss. 7 — Jul. 1, 2014
  • pp: 2362–2375
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Quantifying tissue mechanical properties using photoplethysmography

Tony J. Akl, Mark A. Wilson, M. Nance Ericson, and Gerard L. Coté  »View Author Affiliations


Biomedical Optics Express, Vol. 5, Issue 7, pp. 2362-2375 (2014)
http://dx.doi.org/10.1364/BOE.5.002362


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Abstract

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

1. Introduction

Photoplethysmography (PPG) is one of the commonly used methods to record the pulse non-invasively [1

1. J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas. 28(3), R1–R39 (2007). [CrossRef] [PubMed]

]. 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

2. G. Cennini, J. Arguel, K. Akşit, and A. van Leest, “Heart rate monitoring via remote photoplethysmography with motion artifacts reduction,” Opt. Express 18(5), 4867–4875 (2010). [CrossRef] [PubMed]

, 3

3. W. Verkruysse, L. O. Svaasand, and J. S. Nelson, “Remote plethysmographic imaging using ambient light,” Opt. Express 16(26), 21434–21445 (2008). [CrossRef] [PubMed]

] to non-invasive perfusion tracking and imaging [4

4. A. A. Kamshilin, V. Teplov, E. Nippolainen, S. Miridonov, and R. Giniatullin, “Variability of microcirculation detected by blood pulsation imaging,” PLoS ONE 8(2), e57117 (2013). [CrossRef] [PubMed]

, 5

5. M. Sandberg, Q. Zhang, J. Styf, B. Gerdle, and L. G. Lindberg, “Non-invasive monitoring of muscle blood perfusion by photoplethysmography: evaluation of a new application,” Acta Physiol. Scand. 183(4), 335–343 (2005). [CrossRef] [PubMed]

], but pulse oximetry remains the most common and widely adapted application of PPG [6

6. T. Aoyagi, “Pulse oximetry: its invention, theory, and future,” J. Anesth. 17(4), 259–266 (2003). [CrossRef] [PubMed]

, 7

7. V. Kamat, “Pulse oximetry,” Indian J. Anaesth 46, 261–268 (2002).

].

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

8. T. R. Dawber, H. E. Thomas Jr, and P. M. McNamara, “Characteristics of the dicrotic notch of the arterial pulse wave in coronary heart disease,” Angiology 24(4), 244–255 (1973). [CrossRef] [PubMed]

, 9

9. S. C. Millasseau, J. M. Ritter, K. Takazawa, and P. J. Chowienczyk, “Contour analysis of the photoplethysmographic pulse measured at the finger,” J. Hypertens. 24(8), 1449–1456 (2006). [CrossRef] [PubMed]

]. For example, the pulse wave velocity can be used for monitoring blood pressure changes [10

10. K. Meigas, R. Kattai, and J. Lass, “Continuous blood pressure monitoring using pulse wave delay,” Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1–423, 3171–3174 (2001). [CrossRef]

]. Similarly, the waveform shape can be employed to assess arterial stiffening due to aging and cardiovascular problems [8

8. T. R. Dawber, H. E. Thomas Jr, and P. M. McNamara, “Characteristics of the dicrotic notch of the arterial pulse wave in coronary heart disease,” Angiology 24(4), 244–255 (1973). [CrossRef] [PubMed]

, 9

9. S. C. Millasseau, J. M. Ritter, K. Takazawa, and P. J. Chowienczyk, “Contour analysis of the photoplethysmographic pulse measured at the finger,” J. Hypertens. 24(8), 1449–1456 (2006). [CrossRef] [PubMed]

, 11

11. E. Zahedi, K. Chellappan, M. A. Ali, and H. Singh, “Analysis of the effect of ageing on rising edge characteristics of the photoplethysmogram using a modified Windkessel model,” Cardiovasc. Eng. 7(4), 172–181 (2007). [CrossRef] [PubMed]

, 12

12. S. C. Millasseau, R. P. Kelly, J. M. Ritter, and P. J. Chowienczyk, “Determination of age-related increases in large artery stiffness by digital pulse contour analysis,” Clin. Sci. 103(4), 371–377 (2002). [PubMed]

]. 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) [13

13. A. Manduca, T. E. Oliphant, M. A. Dresner, J. L. Mahowald, S. A. Kruse, E. Amromin, J. P. Felmlee, J. F. Greenleaf, and R. L. Ehman, “Magnetic resonance elastography: non-invasive mapping of tissue elasticity,” Med. Image Anal. 5(4), 237–254 (2001). [CrossRef] [PubMed]

] and ultrasound elastography [14

14. M. Hirata, S. M. F. Akbar, N. Horiike, and M. Onji, “Noninvasive diagnosis of the degree of hepatic fibrosis using ultrasonography in patients with chronic liver disease due to hepatitis C virus,” Eur. J. Clin. Invest. 31(6), 528–535 (2001). [CrossRef] [PubMed]

] 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

15. B. Hinz, “Tissue stiffness, latent TGF-beta1 activation, and mechanical signal transduction: implications for the pathogenesis and treatment of fibrosis,” Curr. Rheumatol. Rep. 11(2), 120–126 (2009). [CrossRef] [PubMed]

17

17. J. A. Clark, J. C. Cheng, and K. S. Leung, “Mechanical properties of normal skin and hypertrophic scars,” Burns 22(6), 443–446 (1996). [CrossRef] [PubMed]

]. 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 [18

18. Organ Procurement and Transplantation Network (OPTN) and Scientific Registry of Transplant Recipients, (SRTR). OPTN / SRTR 2011 Annual Data Report. Rockville, MD: Department of Health and Human Services, Health Resources and Services Administration, Healthcare Systems Bureau, Division of Transplantation; 2012.

]. These patients have the highest graft rejection risk in the first two weeks following the surgery [19

19. J. Quiroga, I. Colina, A. J. Demetris, T. E. Starzl, and D. H. Van Thiel, “Cause and timing of first allograft failure in orthotopic liver transplantation: a study of 177 consecutive patients,” Hepatology 14(6), 1054–1062 (1991). [CrossRef] [PubMed]

]. During this period, the graft monitoring standard relies on frequent blood tests for liver enzymes and biopsies [20

20. B. Eghtesad, C. M. Miller, and J. J. Fung, “Post-liver transplantation management,” in Cleveland Clinic:Current Clinical Medicine, 2ed., W. D. Carey, eds. (Elsevier Saunders, Philadelphia, 2009), pp. 564–570.

, 21

21. P. E. Hickman, J. M. Potter, and A. J. Pesce, “Clinical chemistry and post-liver-transplant monitoring,” Clin. Chem. 43(8 Pt 2), 1546–1554 (1997). [PubMed]

]. 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

22. T. J. Akl, R. Long, M. J. McShane, M. N. Ericson, M. A. Wilson, and G. L. Coté, “Optimizing probe design for an implantable perfusion and oxygenation sensor,” Biomed. Opt. Express 2(8), 2096–2109 (2011). [CrossRef] [PubMed]

25

25. M. Ericson, S. Frank, C. Britton, J. Baba, S. Lee, T. McKnight, M. Bobrek, E. Farquhar, T. Akl, and G. Cote, “A custom electronics platform for implantable perfusion sensor development,” Future of Instrumentation International Workshop (FIIW), 63–66 (2011). [CrossRef]

]. 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

26. P. Thampanitchawong and T. Piratvisuth, “Liver biopsy:complications and risk factors,” World J. Gastroenterol. 5(4), 301–304 (1999). [PubMed]

, 27

27. B. Terjung, I. Lemnitzer, F. L. Dumoulin, W. Effenberger, H. H. Brackmann, T. Sauerbruch, and U. Spengler, “Bleeding complications after percutaneous liver biopsy. An analysis of risk factors,” Digestion 67(3), 138–145 (2003). [CrossRef] [PubMed]

] and 40% of patients undergoing liver biopsies experience pain [28

28. R. Bataller and D. A. Brenner, “Liver fibrosis,” J. Clin. Invest. 115(2), 209–218 (2005). [CrossRef] [PubMed]

]. Biopsies also suffer from sampling errors due to tissue heterogeneity [28

28. R. Bataller and D. A. Brenner, “Liver fibrosis,” J. Clin. Invest. 115(2), 209–218 (2005). [CrossRef] [PubMed]

]. 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 [29

29. P. Zakharov, M. S. Talary, and A. Caduff, “A wearable diffuse reflectance sensor for continuous monitoring of cutaneous blood content,” Phys. Med. Biol. 54(17), 5301–5320 (2009). [CrossRef] [PubMed]

] or an imaging PPG system [3

3. W. Verkruysse, L. O. Svaasand, and J. S. Nelson, “Remote plethysmographic imaging using ambient light,” Opt. Express 16(26), 21434–21445 (2008). [CrossRef] [PubMed]

, 30

30. F. P. Wieringa, F. Mastik, and A. F. van der Steen, “Contactless multiple wavelength photoplethysmographic imaging: a first step toward “SpO2 camera” technology,” Ann. Biomed. Eng. 33(8), 1034–1041 (2005). [CrossRef] [PubMed]

] 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

31. N. Stergiopulos, B. E. Westerhof, J. J. Meister, and N. Westerhof, “The four-element windkessel model,” Proceedings of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol 18, Pts 1–5 18, 1715–1716 (1997).

, 32

32. N. Westerhof, J. W. Lankhaar, and B. E. Westerhof, “The arterial Windkessel,” Med. Biol. Eng. Comput. 47(2), 131–141 (2009). [CrossRef] [PubMed]

].

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. [25

25. M. Ericson, S. Frank, C. Britton, J. Baba, S. Lee, T. McKnight, M. Bobrek, E. Farquhar, T. Akl, and G. Cote, “A custom electronics platform for implantable perfusion sensor development,” Future of Instrumentation International Workshop (FIIW), 63–66 (2011). [CrossRef]

]. 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
Fig. 1 Schematic of the PPG signal showing the AC and DC signals.
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

31. N. Stergiopulos, B. E. Westerhof, J. J. Meister, and N. Westerhof, “The four-element windkessel model,” Proceedings of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol 18, Pts 1–5 18, 1715–1716 (1997).

, 32

32. N. Westerhof, J. W. Lankhaar, and B. E. Westerhof, “The arterial Windkessel,” Med. Biol. Eng. Comput. 47(2), 131–141 (2009). [CrossRef] [PubMed]

]. 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.

2.2 Phantom preparation

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 [37

37. M. Stevanov, J. Baruthio, and B. Eclancher, “Fabrication of elastomer arterial models with specified compliance,” J. Appl. Physiol. 88(4), 1291–1294 (2000). [PubMed]

]. 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
Fig. 3 Stress-strain curves for the three PDMS phantoms.
shows the raw data from the tensile tests of two of the phantoms.

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
Fig. 4 Schematic of the in vitro setup showing the PPG benchtop system, the peristaltic pump, and the flow circuit used to mimic the portal vein. The insets on the bottom left and bottom right show PPG waveforms collected during an upstream and a downstream occlusion respectively.
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 [31

31. N. Stergiopulos, B. E. Westerhof, J. J. Meister, and N. Westerhof, “The four-element windkessel model,” Proceedings of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol 18, Pts 1–5 18, 1715–1716 (1997).

]. 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) [32

32. N. Westerhof, J. W. Lankhaar, and B. E. Westerhof, “The arterial Windkessel,” Med. Biol. Eng. Comput. 47(2), 131–141 (2009). [CrossRef] [PubMed]

]. An extensive review of Windkessel models and their relation to physiologic parameters was reported by Westerhof et al. [32

32. N. Westerhof, J. W. Lankhaar, and B. E. Westerhof, “The arterial Windkessel,” Med. Biol. Eng. Comput. 47(2), 131–141 (2009). [CrossRef] [PubMed]

]. 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
Fig. 5 Schematic of the four-element Windkessel model used to simulate the arterial pulse.
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. [39

39. N. H. Ballal, “Mathematical modeling of arterial blood flow using Windkessel model,” Sudan Medical Monitor (SMM) 6(2011).

]:
i(t)={I0.sin(π.mod(t,60/HR).HR60.ts,mod(t,60/HR)HR60.ts0,otherwise
(1)
where I0 represents the peak blood flow and was set to 500 mL/s. HR is the heart rate in beats per minute (bpm) and ts is the ratio of the systole time divided by the cardiac cycle time. HR and ts were set to 70 bpm and 0.4 respectively. “mod” refers to the modulo operation.

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
Fig. 6 (a) Modeled blood flow. (b) Three pressure waveforms with different mechanical properties showing the changes in the pulse shape.
. 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

1. J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas. 28(3), R1–R39 (2007). [CrossRef] [PubMed]

, 9

9. S. C. Millasseau, J. M. Ritter, K. Takazawa, and P. J. Chowienczyk, “Contour analysis of the photoplethysmographic pulse measured at the finger,” J. Hypertens. 24(8), 1449–1456 (2006). [CrossRef] [PubMed]

].

IPmaxP
(2)

3. Results

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 [40

40. M. Ziol, A. Handra-Luca, A. Kettaneh, C. Christidis, F. Mal, F. Kazemi, V. de Lédinghen, P. Marcellin, D. Dhumeaux, J.-C. Trinchet, and M. Beaugrand, “Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C,” Hepatology 41(1), 48–54 (2005). [CrossRef] [PubMed]

]. 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
Fig. 7 Pulse measured from a soft (11.7 KPa) and a stiff (61 KPa) phantom (left and right respectively)
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
Fig. 8 Changes in the pulse rise time with compliance.
, 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.

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
Fig. 10 Example of a downstream (left column) and an upstream occlusion (right column). In both cases, the amplitude of the pulse (top line) decreases indicating a drop in flow level. The rise time (bottom line) increased only in the case of downstream occlusions.
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
Fig. 11 Bar plot of the rise time during upstream (USO) and downstream (DSO) occlusions for the 11.7 and 61 KPa phantoms. The error bars correspond to +/− one standard deviation.
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. [41

41. R. G. Gosling and M. M. Budge, “Terminology for describing the elastic behavior of arteries,” Hypertension 41(6), 1180–1182 (2003). [CrossRef] [PubMed]

]. 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
Fig. 12 Changes in the rise time and fall time of the PPG pulse for different simulated compliance values using the Windkessel model. The green region indicates the range for normal tissue while the red correspond to fibrotic tissue at different stages. The right panel shows the data after conversion of the compliance values to YM.
).

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) [42

42. D. S. Baim and W. Grossman, Grossman's Cardiac Catheterization, Angiography, and Intervention, 7th ed. (Lippincott Williams & Wilkins, Philadelphia, 2006).

]. 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
Fig. 13 Changes in the pulse rise and fall time for different levels of vascular resistance. The green region indicates the normal range while the red corresponds to increased vascular resistance that can be caused by downstream vascular complications.
.

4. Discussion

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 [43

43. C. J. Bruns, D. Neuhof, H. Erasmi, and T. Schmitz-Rixen, “In vivo biomechanical properties of three different graft materials in peripheral vascular surgery,” Int. J. Angiol. 7(1), 52–56 (1998). [CrossRef]

] and are indicators of hepatic health [44

44. M. Umut Ozcan, S. Ocal, C. Basdogan, G. Dogusoy, and Y. Tokat, “Characterization of frequency-dependent material properties of human liver and its pathologies using an impact hammer,” Med. Image Anal. 15(1), 45–52 (2011). [CrossRef] [PubMed]

46

46. P. J. Wang, F. He, D. H. Liao, J. Zhang, W. C. Li, Y. F. Zhang, T. Z. Huang, X. Y. Li, and Y. J. Zeng, “The impact of age on incremental elastic modulus and incremental compliance of pig hepatic portal vein for liver xenotransplantation,” Xenotransplantation 16(1), 5–10 (2009). [CrossRef] [PubMed]

]. 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

47. G. Varotti, G. L. Grazi, G. Vetrone, G. Ercolani, M. Cescon, M. Del Gaudio, M. Ravaioli, A. Cavallari, and A. Pinna, “Causes of early acute graft failure after liver transplantation: analysis of a 17-year single-centre experience,” Clin. Transplant. 19(4), 492–500 (2005). [CrossRef] [PubMed]

, 48

48. U. Settmacher, B. Stange, R. Haase, M. Heise, T. Steinmüller, W. O. Bechstein, and P. Neuhaus, “Arterial complications after liver transplantation,” Transpl. Int. 13(5), 372–378 (2000). [CrossRef] [PubMed]

]. 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.

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.

5. Conclusion

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.

Acknowledgments

This research was funded by a bioengineering research partnership (BRP) grant from NIH, (#5R01-GM077150).

References and links

1.

J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas. 28(3), R1–R39 (2007). [CrossRef] [PubMed]

2.

G. Cennini, J. Arguel, K. Akşit, and A. van Leest, “Heart rate monitoring via remote photoplethysmography with motion artifacts reduction,” Opt. Express 18(5), 4867–4875 (2010). [CrossRef] [PubMed]

3.

W. Verkruysse, L. O. Svaasand, and J. S. Nelson, “Remote plethysmographic imaging using ambient light,” Opt. Express 16(26), 21434–21445 (2008). [CrossRef] [PubMed]

4.

A. A. Kamshilin, V. Teplov, E. Nippolainen, S. Miridonov, and R. Giniatullin, “Variability of microcirculation detected by blood pulsation imaging,” PLoS ONE 8(2), e57117 (2013). [CrossRef] [PubMed]

5.

M. Sandberg, Q. Zhang, J. Styf, B. Gerdle, and L. G. Lindberg, “Non-invasive monitoring of muscle blood perfusion by photoplethysmography: evaluation of a new application,” Acta Physiol. Scand. 183(4), 335–343 (2005). [CrossRef] [PubMed]

6.

T. Aoyagi, “Pulse oximetry: its invention, theory, and future,” J. Anesth. 17(4), 259–266 (2003). [CrossRef] [PubMed]

7.

V. Kamat, “Pulse oximetry,” Indian J. Anaesth 46, 261–268 (2002).

8.

T. R. Dawber, H. E. Thomas Jr, and P. M. McNamara, “Characteristics of the dicrotic notch of the arterial pulse wave in coronary heart disease,” Angiology 24(4), 244–255 (1973). [CrossRef] [PubMed]

9.

S. C. Millasseau, J. M. Ritter, K. Takazawa, and P. J. Chowienczyk, “Contour analysis of the photoplethysmographic pulse measured at the finger,” J. Hypertens. 24(8), 1449–1456 (2006). [CrossRef] [PubMed]

10.

K. Meigas, R. Kattai, and J. Lass, “Continuous blood pressure monitoring using pulse wave delay,” Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1–423, 3171–3174 (2001). [CrossRef]

11.

E. Zahedi, K. Chellappan, M. A. Ali, and H. Singh, “Analysis of the effect of ageing on rising edge characteristics of the photoplethysmogram using a modified Windkessel model,” Cardiovasc. Eng. 7(4), 172–181 (2007). [CrossRef] [PubMed]

12.

S. C. Millasseau, R. P. Kelly, J. M. Ritter, and P. J. Chowienczyk, “Determination of age-related increases in large artery stiffness by digital pulse contour analysis,” Clin. Sci. 103(4), 371–377 (2002). [PubMed]

13.

A. Manduca, T. E. Oliphant, M. A. Dresner, J. L. Mahowald, S. A. Kruse, E. Amromin, J. P. Felmlee, J. F. Greenleaf, and R. L. Ehman, “Magnetic resonance elastography: non-invasive mapping of tissue elasticity,” Med. Image Anal. 5(4), 237–254 (2001). [CrossRef] [PubMed]

14.

M. Hirata, S. M. F. Akbar, N. Horiike, and M. Onji, “Noninvasive diagnosis of the degree of hepatic fibrosis using ultrasonography in patients with chronic liver disease due to hepatitis C virus,” Eur. J. Clin. Invest. 31(6), 528–535 (2001). [CrossRef] [PubMed]

15.

B. Hinz, “Tissue stiffness, latent TGF-beta1 activation, and mechanical signal transduction: implications for the pathogenesis and treatment of fibrosis,” Curr. Rheumatol. Rep. 11(2), 120–126 (2009). [CrossRef] [PubMed]

16.

S. P. Glasser, D. K. Arnett, G. E. McVeigh, S. M. Finkelstein, A. J. Bank, D. J. Morgan, and J. N. Cohn, “Vascular compliance and cardiovascular disease: a risk factor or a marker?” Am. J. Hypertens. 10(10), 1175–1189 (1997). [CrossRef] [PubMed]

17.

J. A. Clark, J. C. Cheng, and K. S. Leung, “Mechanical properties of normal skin and hypertrophic scars,” Burns 22(6), 443–446 (1996). [CrossRef] [PubMed]

18.

Organ Procurement and Transplantation Network (OPTN) and Scientific Registry of Transplant Recipients, (SRTR). OPTN / SRTR 2011 Annual Data Report. Rockville, MD: Department of Health and Human Services, Health Resources and Services Administration, Healthcare Systems Bureau, Division of Transplantation; 2012.

19.

J. Quiroga, I. Colina, A. J. Demetris, T. E. Starzl, and D. H. Van Thiel, “Cause and timing of first allograft failure in orthotopic liver transplantation: a study of 177 consecutive patients,” Hepatology 14(6), 1054–1062 (1991). [CrossRef] [PubMed]

20.

B. Eghtesad, C. M. Miller, and J. J. Fung, “Post-liver transplantation management,” in Cleveland Clinic:Current Clinical Medicine, 2ed., W. D. Carey, eds. (Elsevier Saunders, Philadelphia, 2009), pp. 564–570.

21.

P. E. Hickman, J. M. Potter, and A. J. Pesce, “Clinical chemistry and post-liver-transplant monitoring,” Clin. Chem. 43(8 Pt 2), 1546–1554 (1997). [PubMed]

22.

T. J. Akl, R. Long, M. J. McShane, M. N. Ericson, M. A. Wilson, and G. L. Coté, “Optimizing probe design for an implantable perfusion and oxygenation sensor,” Biomed. Opt. Express 2(8), 2096–2109 (2011). [CrossRef] [PubMed]

23.

M. N. Ericson, M. Wilson, G. Cote, C. L. Britton, W. Xu, J. Baba, M. Bobrek, M. Hileman, M. Moore, and S. Frank, “Development of an implantable oximetry-based organ perfusion sensor,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 3, 2235–2238 (2004). [PubMed]

24.

M. N. Ericson, M. A. Wilson, G. L. Coté, J. S. Baba, W. Xu, M. Bobrek, C. L. Britton, M. S. Hileman, M. R. Moore, M. S. Emery, and R. Lenarduzzi, “Implantable sensor for blood flow monitoring after transplant surgery,” Minim. Invasive Ther. Allied Technol. 13(2), 87–94 (2004). [CrossRef] [PubMed]

25.

M. Ericson, S. Frank, C. Britton, J. Baba, S. Lee, T. McKnight, M. Bobrek, E. Farquhar, T. Akl, and G. Cote, “A custom electronics platform for implantable perfusion sensor development,” Future of Instrumentation International Workshop (FIIW), 63–66 (2011). [CrossRef]

26.

P. Thampanitchawong and T. Piratvisuth, “Liver biopsy:complications and risk factors,” World J. Gastroenterol. 5(4), 301–304 (1999). [PubMed]

27.

B. Terjung, I. Lemnitzer, F. L. Dumoulin, W. Effenberger, H. H. Brackmann, T. Sauerbruch, and U. Spengler, “Bleeding complications after percutaneous liver biopsy. An analysis of risk factors,” Digestion 67(3), 138–145 (2003). [CrossRef] [PubMed]

28.

R. Bataller and D. A. Brenner, “Liver fibrosis,” J. Clin. Invest. 115(2), 209–218 (2005). [CrossRef] [PubMed]

29.

P. Zakharov, M. S. Talary, and A. Caduff, “A wearable diffuse reflectance sensor for continuous monitoring of cutaneous blood content,” Phys. Med. Biol. 54(17), 5301–5320 (2009). [CrossRef] [PubMed]

30.

F. P. Wieringa, F. Mastik, and A. F. van der Steen, “Contactless multiple wavelength photoplethysmographic imaging: a first step toward “SpO2 camera” technology,” Ann. Biomed. Eng. 33(8), 1034–1041 (2005). [CrossRef] [PubMed]

31.

N. Stergiopulos, B. E. Westerhof, J. J. Meister, and N. Westerhof, “The four-element windkessel model,” Proceedings of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol 18, Pts 1–5 18, 1715–1716 (1997).

32.

N. Westerhof, J. W. Lankhaar, and B. E. Westerhof, “The arterial Windkessel,” Med. Biol. Eng. Comput. 47(2), 131–141 (2009). [CrossRef] [PubMed]

33.

R. Sahni, “Noninvasive monitoring by photoplethysmography,” Clin. Perinatol. 39(3), 573–583 (2012). [CrossRef] [PubMed]

34.

L. Bernardi and S. Leuzzi, “Laser Doppler flowmetry and Photoplethysmography: basic principles and hardware,” in Bioengineering of the Skin: Cutaneous Blood Flow and Erythema, E. Berardesca, P. Elsner, and H. I. Maibach, eds. (CRC Press, 1995).

35.

R. Long, T. King, T. Akl, M. N. Ericson, M. Wilson, G. L. Coté, and M. J. McShane, “Optofluidic phantom mimicking optical properties of porcine livers,” Biomed. Opt. Express 2(7), 1877–1892 (2011). [CrossRef] [PubMed]

36.

H. C. Hong, C. M. Chen, Y. C. Chou, and C. H. Lin, “Study of novel electrical routing and integrated packaging on bio-compatible flexible substrates,” Microsyst. Technol. 16(3), 423–430 (2010). [CrossRef]

37.

M. Stevanov, J. Baruthio, and B. Eclancher, “Fabrication of elastomer arterial models with specified compliance,” J. Appl. Physiol. 88(4), 1291–1294 (2000). [PubMed]

38.

T. J. Akl, T. J. King, R. Long, M. J. McShane, M. Nance Ericson, M. A. Wilson, and G. L. Coté, “Performance assessment of an opto-fluidic phantom mimicking porcine liver parenchyma,” J. Biomed. Opt. 17(7), 077008 (2012). [CrossRef] [PubMed]

39.

N. H. Ballal, “Mathematical modeling of arterial blood flow using Windkessel model,” Sudan Medical Monitor (SMM) 6(2011).

40.

M. Ziol, A. Handra-Luca, A. Kettaneh, C. Christidis, F. Mal, F. Kazemi, V. de Lédinghen, P. Marcellin, D. Dhumeaux, J.-C. Trinchet, and M. Beaugrand, “Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C,” Hepatology 41(1), 48–54 (2005). [CrossRef] [PubMed]

41.

R. G. Gosling and M. M. Budge, “Terminology for describing the elastic behavior of arteries,” Hypertension 41(6), 1180–1182 (2003). [CrossRef] [PubMed]

42.

D. S. Baim and W. Grossman, Grossman's Cardiac Catheterization, Angiography, and Intervention, 7th ed. (Lippincott Williams & Wilkins, Philadelphia, 2006).

43.

C. J. Bruns, D. Neuhof, H. Erasmi, and T. Schmitz-Rixen, “In vivo biomechanical properties of three different graft materials in peripheral vascular surgery,” Int. J. Angiol. 7(1), 52–56 (1998). [CrossRef]

44.

M. Umut Ozcan, S. Ocal, C. Basdogan, G. Dogusoy, and Y. Tokat, “Characterization of frequency-dependent material properties of human liver and its pathologies using an impact hammer,” Med. Image Anal. 15(1), 45–52 (2011). [CrossRef] [PubMed]

45.

P. J. Wang, W. C. Li, G. M. Xi, H. Q. Wang, Z. H. Zhang, B. C. Yao, W. Tang, Z. H. Deng, and X. H. Zhang, “Biomechanical study of hepatic portal vein in humans and pigs and its value in liver transplantation,” Transplant. Proc. 41(5), 1906–1910 (2009). [CrossRef] [PubMed]

46.

P. J. Wang, F. He, D. H. Liao, J. Zhang, W. C. Li, Y. F. Zhang, T. Z. Huang, X. Y. Li, and Y. J. Zeng, “The impact of age on incremental elastic modulus and incremental compliance of pig hepatic portal vein for liver xenotransplantation,” Xenotransplantation 16(1), 5–10 (2009). [CrossRef] [PubMed]

47.

G. Varotti, G. L. Grazi, G. Vetrone, G. Ercolani, M. Cescon, M. Del Gaudio, M. Ravaioli, A. Cavallari, and A. Pinna, “Causes of early acute graft failure after liver transplantation: analysis of a 17-year single-centre experience,” Clin. Transplant. 19(4), 492–500 (2005). [CrossRef] [PubMed]

48.

U. Settmacher, B. Stange, R. Haase, M. Heise, T. Steinmüller, W. O. Bechstein, and P. Neuhaus, “Arterial complications after liver transplantation,” Transpl. Int. 13(5), 372–378 (2000). [CrossRef] [PubMed]

49.

E. L. Carstensen, K. J. Parker, and R. M. Lerner, “Elastography in the management of liver disease,” Ultrasound Med. Biol. 34(10), 1535–1546 (2008). [CrossRef] [PubMed]

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(280.1415) Remote sensing and sensors : Biological sensing and sensors

ToC Category:
Optics of Tissue and Turbid Media

History
Original Manuscript: April 1, 2014
Revised Manuscript: May 23, 2014
Manuscript Accepted: June 16, 2014
Published: June 19, 2014

Citation
Tony J. Akl, Mark A. Wilson, M. Nance Ericson, and Gerard L. Coté, "Quantifying tissue mechanical properties using photoplethysmography," Biomed. Opt. Express 5, 2362-2375 (2014)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-5-7-2362


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References

  1. J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas.28(3), R1–R39 (2007). [CrossRef] [PubMed]
  2. G. Cennini, J. Arguel, K. Akşit, and A. van Leest, “Heart rate monitoring via remote photoplethysmography with motion artifacts reduction,” Opt. Express18(5), 4867–4875 (2010). [CrossRef] [PubMed]
  3. W. Verkruysse, L. O. Svaasand, and J. S. Nelson, “Remote plethysmographic imaging using ambient light,” Opt. Express16(26), 21434–21445 (2008). [CrossRef] [PubMed]
  4. A. A. Kamshilin, V. Teplov, E. Nippolainen, S. Miridonov, and R. Giniatullin, “Variability of microcirculation detected by blood pulsation imaging,” PLoS ONE8(2), e57117 (2013). [CrossRef] [PubMed]
  5. M. Sandberg, Q. Zhang, J. Styf, B. Gerdle, and L. G. Lindberg, “Non-invasive monitoring of muscle blood perfusion by photoplethysmography: evaluation of a new application,” Acta Physiol. Scand.183(4), 335–343 (2005). [CrossRef] [PubMed]
  6. T. Aoyagi, “Pulse oximetry: its invention, theory, and future,” J. Anesth.17(4), 259–266 (2003). [CrossRef] [PubMed]
  7. V. Kamat, “Pulse oximetry,” Indian J. Anaesth46, 261–268 (2002).
  8. T. R. Dawber, H. E. Thomas, and P. M. McNamara, “Characteristics of the dicrotic notch of the arterial pulse wave in coronary heart disease,” Angiology24(4), 244–255 (1973). [CrossRef] [PubMed]
  9. S. C. Millasseau, J. M. Ritter, K. Takazawa, and P. J. Chowienczyk, “Contour analysis of the photoplethysmographic pulse measured at the finger,” J. Hypertens.24(8), 1449–1456 (2006). [CrossRef] [PubMed]
  10. K. Meigas, R. Kattai, and J. Lass, “Continuous blood pressure monitoring using pulse wave delay,” Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1–423, 3171–3174 (2001). [CrossRef]
  11. E. Zahedi, K. Chellappan, M. A. Ali, and H. Singh, “Analysis of the effect of ageing on rising edge characteristics of the photoplethysmogram using a modified Windkessel model,” Cardiovasc. Eng.7(4), 172–181 (2007). [CrossRef] [PubMed]
  12. S. C. Millasseau, R. P. Kelly, J. M. Ritter, and P. J. Chowienczyk, “Determination of age-related increases in large artery stiffness by digital pulse contour analysis,” Clin. Sci.103(4), 371–377 (2002). [PubMed]
  13. A. Manduca, T. E. Oliphant, M. A. Dresner, J. L. Mahowald, S. A. Kruse, E. Amromin, J. P. Felmlee, J. F. Greenleaf, and R. L. Ehman, “Magnetic resonance elastography: non-invasive mapping of tissue elasticity,” Med. Image Anal.5(4), 237–254 (2001). [CrossRef] [PubMed]
  14. M. Hirata, S. M. F. Akbar, N. Horiike, and M. Onji, “Noninvasive diagnosis of the degree of hepatic fibrosis using ultrasonography in patients with chronic liver disease due to hepatitis C virus,” Eur. J. Clin. Invest.31(6), 528–535 (2001). [CrossRef] [PubMed]
  15. B. Hinz, “Tissue stiffness, latent TGF-beta1 activation, and mechanical signal transduction: implications for the pathogenesis and treatment of fibrosis,” Curr. Rheumatol. Rep.11(2), 120–126 (2009). [CrossRef] [PubMed]
  16. S. P. Glasser, D. K. Arnett, G. E. McVeigh, S. M. Finkelstein, A. J. Bank, D. J. Morgan, and J. N. Cohn, “Vascular compliance and cardiovascular disease: a risk factor or a marker?” Am. J. Hypertens.10(10), 1175–1189 (1997). [CrossRef] [PubMed]
  17. J. A. Clark, J. C. Cheng, and K. S. Leung, “Mechanical properties of normal skin and hypertrophic scars,” Burns22(6), 443–446 (1996). [CrossRef] [PubMed]
  18. Organ Procurement and Transplantation Network (OPTN) and Scientific Registry of Transplant Recipients, (SRTR). OPTN / SRTR 2011 Annual Data Report. Rockville, MD: Department of Health and Human Services, Health Resources and Services Administration, Healthcare Systems Bureau, Division of Transplantation; 2012.
  19. J. Quiroga, I. Colina, A. J. Demetris, T. E. Starzl, and D. H. Van Thiel, “Cause and timing of first allograft failure in orthotopic liver transplantation: a study of 177 consecutive patients,” Hepatology14(6), 1054–1062 (1991). [CrossRef] [PubMed]
  20. B. Eghtesad, C. M. Miller, and J. J. Fung, “Post-liver transplantation management,” in Cleveland Clinic:Current Clinical Medicine, 2ed., W. D. Carey, eds. (Elsevier Saunders, Philadelphia, 2009), pp. 564–570.
  21. P. E. Hickman, J. M. Potter, and A. J. Pesce, “Clinical chemistry and post-liver-transplant monitoring,” Clin. Chem.43(8 Pt 2), 1546–1554 (1997). [PubMed]
  22. T. J. Akl, R. Long, M. J. McShane, M. N. Ericson, M. A. Wilson, and G. L. Coté, “Optimizing probe design for an implantable perfusion and oxygenation sensor,” Biomed. Opt. Express2(8), 2096–2109 (2011). [CrossRef] [PubMed]
  23. M. N. Ericson, M. Wilson, G. Cote, C. L. Britton, W. Xu, J. Baba, M. Bobrek, M. Hileman, M. Moore, and S. Frank, “Development of an implantable oximetry-based organ perfusion sensor,” Conf. Proc. IEEE Eng. Med. Biol. Soc.3, 2235–2238 (2004). [PubMed]
  24. M. N. Ericson, M. A. Wilson, G. L. Coté, J. S. Baba, W. Xu, M. Bobrek, C. L. Britton, M. S. Hileman, M. R. Moore, M. S. Emery, and R. Lenarduzzi, “Implantable sensor for blood flow monitoring after transplant surgery,” Minim. Invasive Ther. Allied Technol.13(2), 87–94 (2004). [CrossRef] [PubMed]
  25. M. Ericson, S. Frank, C. Britton, J. Baba, S. Lee, T. McKnight, M. Bobrek, E. Farquhar, T. Akl, and G. Cote, “A custom electronics platform for implantable perfusion sensor development,” Future of Instrumentation International Workshop (FIIW), 63–66 (2011). [CrossRef]
  26. P. Thampanitchawong and T. Piratvisuth, “Liver biopsy:complications and risk factors,” World J. Gastroenterol.5(4), 301–304 (1999). [PubMed]
  27. B. Terjung, I. Lemnitzer, F. L. Dumoulin, W. Effenberger, H. H. Brackmann, T. Sauerbruch, and U. Spengler, “Bleeding complications after percutaneous liver biopsy. An analysis of risk factors,” Digestion67(3), 138–145 (2003). [CrossRef] [PubMed]
  28. R. Bataller and D. A. Brenner, “Liver fibrosis,” J. Clin. Invest.115(2), 209–218 (2005). [CrossRef] [PubMed]
  29. P. Zakharov, M. S. Talary, and A. Caduff, “A wearable diffuse reflectance sensor for continuous monitoring of cutaneous blood content,” Phys. Med. Biol.54(17), 5301–5320 (2009). [CrossRef] [PubMed]
  30. F. P. Wieringa, F. Mastik, and A. F. van der Steen, “Contactless multiple wavelength photoplethysmographic imaging: a first step toward “SpO2 camera” technology,” Ann. Biomed. Eng.33(8), 1034–1041 (2005). [CrossRef] [PubMed]
  31. N. Stergiopulos, B. E. Westerhof, J. J. Meister, and N. Westerhof, “The four-element windkessel model,” Proceedings of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol 18, Pts 1–5 18, 1715–1716 (1997).
  32. N. Westerhof, J. W. Lankhaar, and B. E. Westerhof, “The arterial Windkessel,” Med. Biol. Eng. Comput.47(2), 131–141 (2009). [CrossRef] [PubMed]
  33. R. Sahni, “Noninvasive monitoring by photoplethysmography,” Clin. Perinatol.39(3), 573–583 (2012). [CrossRef] [PubMed]
  34. L. Bernardi and S. Leuzzi, “Laser Doppler flowmetry and Photoplethysmography: basic principles and hardware,” in Bioengineering of the Skin: Cutaneous Blood Flow and Erythema, E. Berardesca, P. Elsner, and H. I. Maibach, eds. (CRC Press, 1995).
  35. R. Long, T. King, T. Akl, M. N. Ericson, M. Wilson, G. L. Coté, and M. J. McShane, “Optofluidic phantom mimicking optical properties of porcine livers,” Biomed. Opt. Express2(7), 1877–1892 (2011). [CrossRef] [PubMed]
  36. H. C. Hong, C. M. Chen, Y. C. Chou, and C. H. Lin, “Study of novel electrical routing and integrated packaging on bio-compatible flexible substrates,” Microsyst. Technol.16(3), 423–430 (2010). [CrossRef]
  37. M. Stevanov, J. Baruthio, and B. Eclancher, “Fabrication of elastomer arterial models with specified compliance,” J. Appl. Physiol.88(4), 1291–1294 (2000). [PubMed]
  38. T. J. Akl, T. J. King, R. Long, M. J. McShane, M. Nance Ericson, M. A. Wilson, and G. L. Coté, “Performance assessment of an opto-fluidic phantom mimicking porcine liver parenchyma,” J. Biomed. Opt.17(7), 077008 (2012). [CrossRef] [PubMed]
  39. N. H. Ballal, “Mathematical modeling of arterial blood flow using Windkessel model,” Sudan Medical Monitor (SMM) 6(2011).
  40. M. Ziol, A. Handra-Luca, A. Kettaneh, C. Christidis, F. Mal, F. Kazemi, V. de Lédinghen, P. Marcellin, D. Dhumeaux, J.-C. Trinchet, and M. Beaugrand, “Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C,” Hepatology41(1), 48–54 (2005). [CrossRef] [PubMed]
  41. R. G. Gosling and M. M. Budge, “Terminology for describing the elastic behavior of arteries,” Hypertension41(6), 1180–1182 (2003). [CrossRef] [PubMed]
  42. D. S. Baim and W. Grossman, Grossman's Cardiac Catheterization, Angiography, and Intervention, 7th ed. (Lippincott Williams & Wilkins, Philadelphia, 2006).
  43. C. J. Bruns, D. Neuhof, H. Erasmi, and T. Schmitz-Rixen, “In vivo biomechanical properties of three different graft materials in peripheral vascular surgery,” Int. J. Angiol.7(1), 52–56 (1998). [CrossRef]
  44. M. Umut Ozcan, S. Ocal, C. Basdogan, G. Dogusoy, and Y. Tokat, “Characterization of frequency-dependent material properties of human liver and its pathologies using an impact hammer,” Med. Image Anal.15(1), 45–52 (2011). [CrossRef] [PubMed]
  45. P. J. Wang, W. C. Li, G. M. Xi, H. Q. Wang, Z. H. Zhang, B. C. Yao, W. Tang, Z. H. Deng, and X. H. Zhang, “Biomechanical study of hepatic portal vein in humans and pigs and its value in liver transplantation,” Transplant. Proc.41(5), 1906–1910 (2009). [CrossRef] [PubMed]
  46. P. J. Wang, F. He, D. H. Liao, J. Zhang, W. C. Li, Y. F. Zhang, T. Z. Huang, X. Y. Li, and Y. J. Zeng, “The impact of age on incremental elastic modulus and incremental compliance of pig hepatic portal vein for liver xenotransplantation,” Xenotransplantation16(1), 5–10 (2009). [CrossRef] [PubMed]
  47. G. Varotti, G. L. Grazi, G. Vetrone, G. Ercolani, M. Cescon, M. Del Gaudio, M. Ravaioli, A. Cavallari, and A. Pinna, “Causes of early acute graft failure after liver transplantation: analysis of a 17-year single-centre experience,” Clin. Transplant.19(4), 492–500 (2005). [CrossRef] [PubMed]
  48. U. Settmacher, B. Stange, R. Haase, M. Heise, T. Steinmüller, W. O. Bechstein, and P. Neuhaus, “Arterial complications after liver transplantation,” Transpl. Int.13(5), 372–378 (2000). [CrossRef] [PubMed]
  49. E. L. Carstensen, K. J. Parker, and R. M. Lerner, “Elastography in the management of liver disease,” Ultrasound Med. Biol.34(10), 1535–1546 (2008). [CrossRef] [PubMed]

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