3.1.

Human Study

All procedures involving human subjects were reviewed and approved by the Institutional Review Boards at Magee Rehabilitation Hospital and Drexel University. Participants included 20 healthy subjects (HSs) and 11 rehabilitation (spinal cord injury) patients admitted at Magee Rehabilitation Hospital in Philadelphia.

HSs, 18 years of age or older, with no history of PI, diabetes, venous, or arterial disease were recruited to optimize the measurement protocol, assess feasibility, evaluate ease of use, and compare measured optical parameters in the sacral area to data collected from rehabilitation patients. After the robustness of the device and newly designed probe had been tested, rehabilitation patients were recruited.

Eligible patients had intact sacrococcygeal skin with nonblanchable redness (i.e., either a stage 1 PI or DTI²⁶). Patients were ineligible for the study if they suffered from diabetes, venous, or arterial disease or had a previous history of sacrococcygeal stage 2, 3, or 4 PIs.

Table 1 shows demographic information on three rehabilitation patients who developed open PIs (POs) and eight patients who did not develop open ulcers (PNOs).

Table 1

Demographic information for all enrolled subjects.

3.2.

Measurement Protocol

The measurement protocol shown in Fig. 1 consisted of three stages: baseline, applied pressure, and released pressure. First, during the baseline stage, the subject was moved into a lateral position on a hospital bed and baseline measurements were obtained by gently touching the optical probe to the subject’s sacrococcygeal skin for 1 to 2 min. A sterile transparent dressing (Tegaderm, 3M, Corp) was used to cover the probe during each measurement session, in accordance with universal precautions. Next, during the applied pressure stage, the subject was moved into the supine position with body weight applying pressure to the sacral area for 8 to 10 min. This position simulates conditions that may lead to PI development if sustained for a longer period of time. During the last stage of the protocol when the pressure was released, the subject was moved from the supine position back to the lateral position, and optical measurements were continued for another 2 to 3 min similar to baseline measurements. During each stage, the measurement cycle was 6 s, during which DCS correlation functions were measured for 3 s and DNIRS data were obtained for 3 s.

Fig. 1

The three stages of the measurement protocol. The patient begins in the lateral position during the baseline stage, then is moved to the supine position for the applied pressure stage, and finally is moved back to the lateral position to release the pressure.

Measurement sessions were performed four times over the course of two weeks or until the patient developed an open PI, which appeared on the skin surface (stage 2, 3, 4, or unstageable PI). Two weeks after the last measurement session, each patient was examined to determine whether an open PI had developed.

3.3.

Diffuse Correlation Spectroscopy Instrumentation

DCS was used to measure microcirculatory blood flow in potentially damaged sacral tissue. A long-coherent length ($\sim 10\mathrm{m}$) laser (CrystaLaser, Reno, Nevada) emission traveled through a multimode optical fiber to the tissue. A four-channel single photon counting module (SPCM) (Pacer, Palm Beach Gardens, Florida) registered the scattered light that was brought back from tissue by four single mode fibers (core diameter $\sim 5\mu \mathrm{m}$). The output of the SPCM was connected to a multitau correlator (Correlator.com, Shenzhen, China), which computed a temporal correlation function (TCF) of scattered light intensity selected based on the photon arrival times. This multitau correlator was selected because it analyzes TCF across a wide range of $\tau$ (${10}^{-6}$ to ${10}^{-1}$), which is necessary because tissue is a multiscattering regime where the characteristic time strongly depends on the number light scattering events.^30–33

3.4.

Diffuse Near-Infrared Spectroscopy Device

The frequency domain DNIRS device measures tissue optical properties ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$. Measured values of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ can be used to determine absolute values of blood flow index (BFI) from experimental TCF when the DCS system is operated simultaneously with the DNIRS system in the same tissue volume.

A DNIRS system with two avalanche photodiode detectors and eight multimode ($62.5/125\mu \mathrm{m}$) source fibers delivering 160 MHz intensity-modulated light (685 and 830 nm) was used to calculate tissue optical properties. For more details on the DNIRS system, see Ref. 34. An optical switch (Dicon) was used to deliver one wavelength of light to one source fiber at a time. Backscattered light was collected via two detector fibers (1-mm core). Amplitude and phase shift values, as functions of 16 source–detector separations (i.e., eight sources and two detectors), were fit to the diffusion approximation model in semi-infinite geometry, and optical properties were calculated.³⁵ These ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ values were used for the calculation of BFI.³⁰

To verify the consistency of the DNIRS system throughout the study, we measured the optical properties of a silicone phantom before each measurement session, and variation in calculated ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ did not exceed 10%. Because our DCS system operates at a wavelength of 785 nm while the DNIRS system operates at 685 and 830 nm, we adjusted the measured values of ${\mu }_{\mathrm{s}}^{\prime }$ by interpolating between ${\mu }_{\mathrm{s}}^{\prime }$ measured at 685 and 830 nm. When fitting measured values of scattered light intensity and phase changes, we rejected measurements with root-mean-square deviations between experimental data and fitting were greater than 25%.

3.5.

Optical Probe Design

To measure the response of sacral tissue to applied pressure, an optical probe was developed. This probe, pictured in Fig. 2, was used for DCS and DNIRS measurements during all three stages of our protocol: baseline, applied pressure, and released pressure.

Fig. 2

Schematic drawing of the optical probe used during the human study protocol. Small prisms were fixed onto the ferrals of each fiber to redirect the light 90 deg, so measurements could be taken during all three stages of the protocol. The typical separation between the DNIRS sources is approximately 4.3 mm while the separation between DCS source and detector is about 5.2 mm.

The probe immobilized and protected the DCS and DNIRS optical fibers by integrating them into a 3-D-printed acrylonitrile butadiene styrene fixture that was embedded within a silicone pad. Ninety deg optical prisms (2 mm per side) were fixed to the ferrule tip of each fiber using optical adhesive that redirects light into the vertical direction when patients are in the supine position with their sacral skin above the silicone pad. The single source–detector separation for DCS fibers was 6 mm, corresponding to a measurement depth of approximately 2 to 5 mm.^36,37 The DNIRS part of the probe has source–detector separations ranging between 6 and 16 mm, corresponding to measurement depths of 2 to 9 mm. We evaluate the penetration depth as the value of order of square root of product of the source–detector distance and $1/{\mu }_{\mathrm{s}}^{\prime }$, i.e., $\sqrt{\rho \times 1/{\mu }_{\mathrm{s}}^{\prime }}$, where $\rho$ is the source–detector separation. The optical power of light transmitted through the fibers with prisms was approximately 90% of the transmission from the same fibers without prisms. A polarized film was placed in front of DCS detector fibers.

3.6.

Modeling Diffuse Correlation Spectroscopy Data

Within the diffusion regime of light propagation in a tissue, the field TCF for an infinite medium takes the form³⁰

Beginning with the pioneering works^32,38 on diffusive wave spectroscopy (DWS), the MSD is commonly explained in terms of the Brownian diffusion

For numerical evaluation, it is convenient to present the decay parameter $K$ as follows:

Estimating reduced scattering and absorption coefficients ${\mu }_{\mathrm{s}}^{\prime }=10{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{a}}=0.1{\mathrm{cm}}^{-1}$, respectively, and taking typical values $k\approx 10\mu {\mathrm{m}}^{-1}$ and $\alpha D_b={0.510}^{-8}{\mathrm{cm}}^2/\mathrm{s}$, we conclude that the second term dominates for delay times exceeding $\tau >{10}^{-4}\mathrm{s}$, and we come to a nonanalytic, square-root dependence on time

DWS has been studied primarily using this nonanalytic approximation.^32,38 Note that this nonanalyticity makes the $N$-order method,³⁹ based on the Taylor expansion method, nonjustified.

For smaller delay times and larger absorption coefficients, the parameter $K$ exhibits a linear dependence on time

Besides the widely accepted diffusive model of the scatterers dynamics, there has been considered also the random velocity model,⁴⁰ wherein the MSD is proportional to the second moment of the velocity

Using the Brownian model, one takes the RBC diffusion coefficient, multiplied with $\alpha$, as the index of blood flow, ${\mathrm{BFI}}_{\text{Browning}}=\alpha D_b$. Within the convective MSD model, the BFI in Ref. 41 is calculated as the root of second moment of velocity, ${\mathrm{BFI}}_{\text{convect}}=\sqrt{\alpha ⟨V^2⟩}$. Therefore, it is seen that even the dimensions of these quantities are different.

Both models can be considered simultaneously as a mixed model.

In recent work,⁴² the Monte Carlo simulations were performed presenting the MSD as the sum of contributions of the convective and diffusive movements of RBCs; in particular, the diffusion coefficient and RBC velocity were calculated using an artificial-specific picture of parallel oriented capillaries with a given radius, optical coefficients of blood and surrounding tissues, and Poiseuille-like velocity profile. However, Boas et al.⁴² admit that the experimental data primarily reflect the diffusive character of the RBC dynamics.

Practically, assuming that the velocity profile in a cylindrical blood vessel takes the Poiseuille-like form, Boas et al.⁴² have shown for such a detailed model of blood circulatory system that DCS mainly measures RBC shear-induced diffusion. Based on results of the Monte Carlo simulations, the authors found that the BFI, which is shown to quantify tissue perfusion, is linearly proportional to blood flow, dependent on the hemoglobin concentration and blood vessel diameter.

The measured TCF of intensity, $g_2(\tau )=⟨I(r,t)\times I(r,t+\tau )⟩/{⟨I(r,t)⟩}^2$, is the quadratic form of the field TCF due to the Siegert relationship

4.1.

Temporal Correlation Functions as Markers for Prediction of Pressure Injury Development

Representative TCFs, measured by our DCS instrumentation, are shown in Fig. 3. Delay time, ${\tau }_{\exp }$, was calculated from the TCF where the function decreased by a factor of $e$ (mathematical constant $e=2.72\dots$) because, according to the theoretical concept, the TCF shape is nearly exponential. The raw TCF curves obtained from POs during baseline measurements had smaller delay $\tau$ compared with TCFs of HSs and PNOs.

Fig. 3

(a) Typical experimental TCF of intensity for all three groups of patients for baseline. The PO (dark line), PNO (gray line), and healthy volunteers (dotted line). Representative curves were taken from PO1D2, PNO1D1, and HS7D1. Positions of vertical lines indicate the value of ${\tau }_{\exp }$. (b) Histogram of TCFs ($n=19$) during the baseline stage of one measurement session for PO1D2, PNO1D1, and HS7D1. The registration time of each TCF is $\sim 1.5\mathrm{s}$, and the histograms are divided into bin sizes of ${10}^{-5}\mathrm{s}$.

Detailed results are shown for POs in Fig. 4, in which ${\tau }_{\exp }$ values are lower than ${\tau }_{\exp }$ for PNOs and HSs.

Fig. 4

Experimental ${\tau }_{\exp .\text{baseline}}$ obtained during the all baseline measurement sessions for HSs ($n=34$ measurement sessions), PNOs ($n=28$), and POs ($n=10$). The bottom bar represents the minimum while the top error bar is the maximum, the bottom line of the box represents the first quartile, top line of the box is the third quartile, and middle line is the median.

The ratios of ${\tau }_{\exp .\text{pressure}}$ during applied pressure to ${\tau }_{\exp .\text{baseline}}$ during baseline were calculated and illustrated in Fig. 5. We observed an increase of about nine times in ${\tau }_{\exp }$ when POs were moved to the supine position and pressure was applied to the sacral area, whereas for PNOs and HSs, the increase was only approximately two times.

Fig. 5

The ratios of ${\tau }_{\exp .\text{pressure}}$ obtained during applied pressure measurements to baseline ${\tau }_{\exp .\text{baseline}}$ are shown on graphic. The data from all sessions for HSs ($n=34$ measurement sessions), PNOs ($n=28$), and POs ($n=10$) are included in each of the boxes and whiskers. The bottom bar represents the minimum while the top error bar is the maximum, the bottom line of the box represents the first quartile, top line of the box is the third quartile, and middle line is the median. A 1-tailed $t$-test indicates a significant difference ($5\times {10}^{-7}$) between PNO and PO subjects.

4.2.

Analysis of Diffuse Near-Infrared Spectroscopy Optical Properties

The optical properties ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ in DNIRS measurements are determined from fitting the scattered amplitude and phase change values as function of 16 source–detector separations $\rho$ to the semi-infinite approximation of the diffusion model.^31,43 Using the criteria for data accuracy verification described in Sec. 3.4, 3 of 10 PO and 11 of 28 PNO data points were excluded from this analysis. We suppose that some of these measurements were not stable for two reasons: first, we did not have uniform contact between the skin and the probe due to body curvature in the sacrum area, particularly in the supine position where we cannot adjust the probe under the patient’s body. Second, patient motion artifacts (for example muscle spasms) may have contributed to this problem.

Table 2 shows the average ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ values for each stage and each patient group.

Table 2

Mean (standard deviation) of absorption (μa) and reduced scattering coefficients (μs′) for PNOs, POs, and silicone phantom measured at λ=830  nm before each measurement session.

As shown in Sec. 3.6, BFI can be determined using measured values of ${\mu }_{\mathrm{a}}$, ${\mu }_{\mathrm{s}}^{\prime }$, and ${\tau }_{\exp }$. Therefore, the changes in ${\tau }_{\exp }$ across different stages of our measurement protocol and the differences in ${\tau }_{\exp }$ between subjects that we presented above in Sec. 4.1 may be related to changes in the optical properties of the tissue (${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$) or the motion of blood cells within the probed volume of tissue. To estimate the relative sensitivity of ${\tau }_{\exp }$ to changes in each of these factors, we calculated the dependence of ${\tau }_{\exp }$ on ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ for fixed values of BFI. We found a weak dependence of ${\tau }_{\exp }$ on ${\mu }_{\mathrm{a}}$. Specifically, ${\tau }_{\exp }$ changed by only 19% as values of ${\mu }_{\mathrm{a}}$ ranged from 0.05 to $0.17{\mathrm{cm}}^{-1}$, values that are typically seen in tissue. In principle, ${\tau }_{\exp }$ shows a dependence on ${\mu }_{\mathrm{s}}^{\prime }$. For example, ${\tau }_{\exp }$ decreased by a factor of approximately 3 as values of ${\mu }_{\mathrm{s}}^{\prime }$ increased from 5 to $15{\mathrm{cm}}^{-1}$, as shown in Fig. 6.

Fig. 6

Dependence of ${\tau }_{\exp }$ on ${\mu }_{\mathrm{s}}^{\prime }$ for values 5 to $15{\mathrm{cm}}^{-1}$ calculated using the diffusion approximation model (triangles) and Monte Carlo simulation model (squares).

We observe from Fig. 4 that values of ${\tau }_{\exp }$ during baseline measurements in PNOs were 2 to 3 times greater than those measured in POs. However, the average measured values of ${\mu }_{\mathrm{s}}^{\prime }$ in PNOs ($10.3{\mathrm{cm}}^{-1}$) were only slightly smaller than those measured in POs ($11.0{\mathrm{cm}}^{-1}$). This difference in ${\mu }_{\mathrm{s}}^{\prime }$ does not account for the much larger difference in ${\tau }_{\exp }$; therefore, we conclude that the observed differences in ${\tau }_{\exp }$ are primarily attributable to differences in blood flow. Similarly, most of the observed 10 times increase of ${\tau }_{\exp }$ in PO subjects between the baseline and applied pressure phases of our protocol can likely be attributed to changes in blood flow rather than changes in ${\mu }_{\mathrm{s}}^{\prime }$, since Table 2 shows that values of ${\mu }_{\mathrm{s}}^{\prime }$ only increased from 11.0 to $12.7{\mathrm{cm}}^{-1}$.

The simulations reported in Fig. 6 were performed within the framework of an algorithm described previously.³⁴ We chose $\alpha D_b={0.510}^{-8}{\mathrm{cm}}^2/\mathrm{s}$. To account for the temporal decay of the TCF, the weight of the $n$’th simulated photon was multiplied by the factor $\exp [-{\mathrm{k}}^2⟨\mathrm{\Delta }{\mathrm{r}}^2(\tau )⟩{\mu }_{\mathrm{s}}^{\prime }{\mathrm{R}}_n/3]$, or for Brownian diffusion $\exp (-2\alpha D_B\tau {\mu }_{\mathrm{s}}R\sum _j{q}_j^2)$,^32,38 where $R$ and $q_j$ are the random values of the optical path and wave transfer at the $j$-order of scattering, respectively; summing is performed over scattering orders.

We calculated BFI by fitting the experimental TCF using the Brownian model with $D_B$ as the unknown parameter for the average experimental ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ in each protocol stage.

The shift from baseline to released pressure shows a BFI that is systematically declining after every measurement session for all POs, as seen in Fig. 7 and Table 3. PO1 and PO2 both show BFI shifts that cross the $x$-axis, indicating that the average blood flow during released pressure was lower than the average baseline blood flow, while PO3 showed a single large drop in BFI during released pressure before the wound opened the following day.

Fig. 7

Change in BFI between baseline and released pressure stages of the measurement protocol. POs (striped) exhibit a consistent drop in the magnitude of blood flow during the released pressure stage from day to day, while no specific pattern is observed in PNOs (solid). Only three PNOs are displayed because the same temporal trends are seen in all other PNOs.

Table 3

Slopes calculated using the change in BFI between baseline and released pressure stages during consecutive measurement sessions show a strong negative trend for all POs.

The released pressure stage, as the patient is moved from a load bearing position back to a lateral position, was of particular interest since it showed a temporal trend, which allowed further distinction between POs and PNOs. The systematic decrease for POs may further indicate a progression in the structural deterioration of the microvasculature from day to day until eventual ulceration. It is important to note that only two measurement sessions were performed on PO3 due to ulceration prior to the third session; the downward trend, however, is still apparent.