2.1.

Near-Infrared Instrumentation

Details of the frequency domain near-infrared instrument have been described previously.^{21, 22} Briefly, an optical fiber was used to deliver intensity modulated light $\left(70\mathrm{MHz}\right)$ to the tissue from three diode lasers ( $\lambda =685$ , 780, and $830\mathrm{nm}$ ). Four optical fiber bundles were used to deliver backscattered light from the tissue to avalanche photodiode (APD) detectors and quadrature (I/Q) demodulators. The in-phase $\left(I\right)$ and quadrature $\left(Q\right)$ signals from each detector were measured; these were determined by the attenuated amplitude and phase shift of the registered scattered light. All optical fibers were immobilized on a Teflon probe, with the four detector fibers fixed at distances of 4, 8, 12, and $16\mathrm{mm}$ from the source fiber.

It is possible to calculate the absorption coefficient $\left({\mu }_a\right)$ and reduced scattering coefficient $\left({\mu }_s^{\prime }\right)$ of tissue from the amplitude and phase shift of scattered NIR light using the diffusion approximation if the minimum distance between source and detector fibers in the probe is greater than two transport lengths.^{23, 24} The transport length $\left(l^{*}\right)$ represents the distance of propagation of a collimated beam of light before it becomes effectively isotropic, and can be approximated by $1∕{\mu }_s^{\prime }$ when ${\mu }_s^{\prime }⪢{\mu }_a$ , as is the case in tissue. The photons undergo multiple light scattering in tissue, which is a strong nonhomogeneous medium, because the various tissue structures are characterized by large differences in their refractive index. For a typical tissue with an anisotropy factor $g=<\cos \theta >$ of about 0.80 to 0.95, where $\theta$ is mean angle of scattering, a scattering event happens every $50\text{to}200\mu \mathrm{m}$ and light becomes completely diffuse after one transport length. Values of ${\mu }_s^{\prime }$ in human tissue at wavelengths of $685\text{to}830\mathrm{nm}$ typically range from $5\text{to}20{\mathrm{cm}}^{-1}$ ,²⁰ therefore the transport length $l^{*}$ ranges from approximately $0.5\text{to}2\mathrm{mm}$ , since $l^{*}$ is the inverse of the reduced scattering coefficient ${\mu }_s^{\prime }$ . This suggests that the smallest source-detector distance that can be used in probe design for the diffusion approximation to be valid would be $2\text{to}4\mathrm{mm}$ . Our probe has a minimum distance between source and detector fibers of $4\mathrm{mm}$ , and therefore is within the diffusion approximation regime. Closed analytical solutions to the diffusion equation have been derived for semi-infinite measurement geometries that are typical of noninvasive tissue measurements,²⁵ when sources and detectors are placed on an air-tissue interface and the optical fiber source is modeled as an isotropic point light source. The final equations describing the absorption and scattering coefficients from measurements of light intensity and phase shift as a function of the source-detector separation distance are included in Ref. 21.

The human study lasted for more than a year and it was therefore necessary to test the stability of our device during the course of such measurements. To accomplish this, an optical phantom made of silicone (XP565, Silicones, Incorporated, High Point, North Carolina) with dispersed particles of $\mathrm{Ti}{\mathrm{O}}_2$ (diameter $0.9\text{to}1.6\mu \mathrm{m}$ , Alfa Aesar, Ward Hill, Massachusetts) to act as scatterers and carbon black acetylene microspheres (50% compressed, diameter $0.042\mu \mathrm{m}$ , Alfa Aesar) to absorb light²² was measured before each patient measurement session. The measured absorption coefficients from the silicone phantom over the course of $61\text{weeks}$ are shown in Fig. 1 . Standard error remained at less than 3% throughout the period of the study.

Fig. 1

Measured values of ${\mu }_a$ in a silicone optical phantom over a $61\text{-week}$ period. Solid lines represent average values for the entire measurement period. Average values of ${\mu }_a$ $(\text{mean}\pm \mathrm{SD})$ at 685, 780, and $830\mathrm{nm}$ were $0.054\pm 0.0014$ , $0.059\pm 0.0016$ , and $0.064\pm 0.0018{\mathrm{cm}}^{-1}$ , respectively.

Oxyhemoglobin concentration $\left(\left[\mathrm{Hb}{\mathrm{O}}_2\right]\right)$ and deoxyhemoglobin concentration ([Hb]) were determined using the method described by Shah ²⁶ When it is assumed that oxyhemoglobin, deoxyhemoglobin, and water are the primary chromophores at our selected wavelengths, Eq. 1 can be used to describe the relationship between measured values of absorption coefficient $\left({\mu }_{a,\text{measured}}^{\lambda }\right)$ and the concentrations of hemoglobin and water:

Values of $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Hb] were derived from the experimental values of ${\mu }_{a,\text{measured}}^{\lambda }$ through a least-squares fitting method. Specifically, the values of $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Hb] are used as fitting parameters to minimize the following expression:

2.2.

Human Subjects

11 subjects with diabetes and chronic wounds were recruited from the Drexel University Wound Healing Center in Philadelphia, Pennsylvania. All patients were between 18 and $65\text{years}$ of age, had documented diabetes mellitus for at least $6\text{months}$ , and had an ankle or foot wound with a minimum surface area of $1{\mathrm{cm}}^2$ that was secondary to the complications of diabetes, including vascular disease and/or neuropathy. All patients received standard wound care, which included weekly or biweekly debridement, treatment with moist wound healing protocols, and offloading when appropriate. In some patients, active wound healing agents such as topical growth factors, hyperbaric oxygen, and bioengineered skin substitutes were employed. Details about the size of each wound, duration of measurements, and the active treatments used on each wound are shown in Table 1 .

Table 1

Size, duration, and active treatments used on each wound.

Of the 11 wounds enrolled in the study, five wounds healed completely in less than $15\text{weeks}$ , three wounds resulted in amputation, and three wounds remained unhealed at the end of the study, as shown in Table 1. Four of the five healed wounds required no surgical intervention prior to closure, while one wound underwent surgical debridement and the application of a bioengineered skin substitute (Apligraf^®, Organogenesis, Incorporated, Canton, Massachusetts) after $18\text{weeks}$ of participation in the study, and reached closure after an additional $17\text{weeks}$ . Data obtained prior to surgical intervention were classified as a nonhealing wound, while data obtained after surgery were classified as a healing wound, bringing the total number of wounds to 12 (five healing and seven nonhealing).

All diffuse NIR measurements were conducted prior to wound debridement on a weekly or biweekly basis. During each measurement session, the wounds of each patient were interrogated using the NIR instrument in up to ten different locations. Measurement locations were chosen based on the geometry and size of each wound, and can be classified into four general locations: 1. directly on the wound, 2. on intact skin at the edge of the wound, 3. on nonwound tissue of the contralateral limb symmetric to the wound location if available, and 4. on nonwound tissue on the ipsilateral limb at a distance of at least $2\mathrm{cm}$ from the wound. The measurement locations for a typical diabetic foot ulcer are shown in Fig. 2 . The NIR device was configured to complete one measurement in approximately $3\sec$ , and at all measurement locations the probe was held in continuous contact with the wound or skin tissue until eight to ten successive measurements were obtained over a period of approximately $30\sec$ . The means and standard deviations of the detected amplitudes and phase shifts were computed at each measurement location, and measurements were discarded and repeated if the percent deviation was greater than 15% over the course of each $30\text{-}\sec$ measurement period. This was done to eliminate errors caused by motion artifacts from the patient or clinician. Further validation was performed to ensure that uniform contact was made between each detector fiber and the wound or skin. We fit the experimentally measured amplitude and phase to the analytical solution of the diffusion approximation for semi-infinite geometry, where the $\log \left(I^{*}{r}^2\right)$ and the phase show a linear dependence on $r$ ( $r$ is the distance between source and detector, and $I$ is the intensity of scattered light registered by the detector). Measurements that did not exhibit good fitting were likely to have had nonuniform fiber/tissue contact and were discarded. Tegaderm transparent sterile dressing (3M Health Care, Saint Paul, Minnesota) was used to cover the fiber optic probe during all measurements. Our previous experience/results suggest that the presence of Tegaderm does not affect the measured NIR coefficients.²¹

Fig. 2

(a) Diagram of the positions at which NIR measurements were obtained from a representative subject. The dark oval on the heel represents a typical diabetic foot ulcer. Gray rectangles represent the eight different probe locations used during a measurement session. (b) Photograph of the probe (coin included for size reference). The fiber on the left delivers light from the lasers to the tissue, while the remaining four fibers deliver back-scattered light from the tissue to the photodetectors. Fibers are spaced equidistantly at $4\mathrm{mm}$ apart. The dimensions of the Teflon probe are $3.6\times 0.4\times 0.6\mathrm{cm}$ $(\text{length}\times \text{width}\times \text{height})$ .

Wounds were digitally photographed using a Fujifilm Finepix s700 digital camera during each measurement session with cross-polarizing filters to reduce surface reflection. A ruler was held in the imaging plane of each photograph to allow the calculation of absolute wound area. The boundaries of each wound were manually traced using a computer mouse and Microsoft Paint software, and then wound areas were calculated from the traced photographs using an image analysis code developed with Matlab (Mathworks, Incorporated, Natick, Massachusetts) software. This image analysis code counts the number of pixels within the traced wound boundary, and then calculates the wound area by approximating the size of each pixel from the image of the ruler that was present in the imaging plane of each wound.

3.1.

Results from Diabetic Foot Ulcers

In both healing and nonhealing wounds, values of the NIR absorption coefficient ${\mu }_a$ and calculated values of $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Tot Hb] concentration according to Eq. 1 were obtained at the wound center, the wound edges, and control sites. All parameters had higher values for the wounds as compared to the control (nonwound) sites.

In all healing wounds, the values of $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Tot Hb] at the wound center and edge sites decreased and converged to the values measured at the control sites. This is illustrated in Fig. 3, which shows plots of hemoglobin concentrations during the course of the study for a typical healing wound. The area of this wound was over $6{\mathrm{cm}}^2$ at the beginning of the study, and closed after ten weeks of monitoring.

Fig. 3

Wound size and hemoglobin data for a representative healed wound that was located on the frontal region of a foot that had previously lost all toes to amputation. Upper left: digital photographs from selected time points. Scale bars represent $1\mathrm{cm}$ . Upper right: wound area as determined through analysis of digital photographs (◆). Lower: oxyhemoglobin concentration $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ , deoxyhemoglobin concentration [Hb], and total hemoglobin concentration [Tot Hb] from each measurement day. Each data point represents the mean of measurements obtained from the center of the wound (●), the edges of the wound (△), a control site on the wounded foot (+), and a control site on the nonwounded foot (x).

In contrast, values of $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Tot Hb] in all nonhealing wounds remained greater than the control sites and did not converge over the course of the study. This is illustrated in Fig. 4, which shows plots of hemoglobin concentrations for a typical nonhealing wound. The area of this wound decreased by only approximately 50% over the course of $37\text{weeks}$ , after which a below-the-knee amputation was performed.

Fig. 4

Wound size and hemoglobin data for a representative nonhealing wound located on the plantar metatarsal region of the foot. Upper left: digital photographs from selected time points. Scale bars represent $1\mathrm{cm}$ . Upper right: wound area as determined through analysis of digital photographs (◆). Lower: oxyhemoglobin concentration $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ , deoxyhemoglobin concentration [Hb], and total hemoglobin concentration [Tot Hb] from each measurement day. Each data point represents the mean of measurements obtained from the center of the wound (●), the edges of the wound (△), and a control site on the nonwounded foot (x). A suitable control site on the wounded foot was unavailable due to the size of the wound and prior amputations.

Figure 5 shows plots of hemoglobin concentrations for a unique case in which the wound initially appeared to be healing, decreasing in size from $31.5{\mathrm{cm}}^2\text{to}1.6{\mathrm{cm}}^2$ during the initial $17\text{weeks}$ of the study. In contrast to the initial wound size trend, NIR data from the wound site did not show convergence with the nonwound data, as is characteristic of healing wounds in this study. This wound never closed completely and required surgical intervention after week 25. This is an example of how diffuse NIR could provide clinicians with a better assessment of wound status than the superficial measurements of wound size.

Fig. 5

Wound size and hemoglobin data for a nonhealing wound located on the plantar metatarsal region of the foot that decreased in size during the initial $17\text{weeks}$ of monitoring, but did not close completely and eventually needed surgical intervention after week 25. Dashed red lines are used to highlight the time period during which the hemoglobin data differed from the wound size data Upper left: digital photographs from selected time points. Scale bars represent $1\mathrm{cm}$ . Upper right: wound area as determined through analysis of digital photographs (◆). Lower: oxyhemoglobin concentration $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ , deoxyhemoglobin concentration [Hb], and total hemoglobin concentration [Tot Hb] from each measurement day. Each data point represents the mean of measurements obtained from the center of the wound (●), the edges of the wound (△), and a control site located approximately $10\mathrm{cm}$ from the wound (+). A suitable control site on the nonwounded foot was unavailable due to prior amputations.

3.2.

Rates of Change in Optical Data

To analyze our clinical data, we have tried to identify common parameters that describe the trends we observed and are representative of the clinical outcomes. In our analysis, the rate of temporal change of hemoglobin concentration can be estimated by fitting the data from each wound to a linear trend line. The limited amount of experimental data collected during this study combined with the data accuracy do not allow us the use of a more complicated fitting model at this time. The slopes of these trend lines correspond to the rates of change in optical properties with time, and have proven useful in quantifying the progress of a healing wound in our study. The slopes calculated from the hemoglobin concentration trend lines are referred to as the rates of change in each wound, and are shown for wound center and edge measurements in Fig. 6 . In all healing wounds, negative rates of change were observed for $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Tot Hb]. In all nonhealing wounds, the rates of change for $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Tot Hb] were close to zero or slightly positive. The rate of change for [Hb] concentration was close to zero in both healing and nonhealing wounds. The mean rates of change in healing and nonhealing wounds are compared for all hemoglobin concentrations ([Tot Hb], $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ , and [Hb]) in Fig. 7 . A statistically significant difference between the slopes of healing and nonhealing wounds was obtained for the total hemoglobin concentration and the oxyhemoglobin concentration.

Fig. 6

Rates of change in hemoglobin concentration for all wound measurements. (a) Oxyhemoglobin concentration at wound centers, (b) oxyhemoglobin concentration at wound edges, (c) deoxyhemoglobin concentration at wound centers, (d) deoxyhemoglobin concentration at wound edges, (e) total hemoglobin concentration at wound centers, and (f) total hemoglobin concentration at wound edges. White bars represent data from healing wounds; black bars represent data from nonhealing wounds. The center location of one wound could not be measured due to its size and geometry. Therefore, data from only 11 wounds are presented in (a), (c), and (e) compared to data from 12 wounds in (b), (d), and (f).

Fig. 7

Mean rates of change in hemoglobin concentration: healing versus nonhealing wounds. Error bars represent standard deviation. One-tailed, heteroscedastic t-tests were used to test the difference between the rates of change in healing and nonhealing wounds. ${}^{*}\mathrm{p}<0.05$ .

3.3.

Predictive Capability of Optical Data

The predictive capability of the rates of change in DPDW data would need to be determined through a study of more patients with measurements taken at more time points. However, as a first approximation, the rates of temporal change of [Tot Hb] and $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ in each wound were calculated by fitting the data from the first ten weeks of measurements to a linear trend line. The slopes of the ten-week trend lines are shown in Fig. 8 . A threshold level for changes in [Tot Hb] or $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ may be selected such that a rate of change below the selected threshold is classified as a “healing wound,” and a rate of change above the selected threshold is classified as a “nonhealing wound.” Such a classification system would allow prediction of healing outcome after ten weeks of NIR measurements. Table 2 shows the number and percent of healing and nonhealing wounds from this study that would have been correctly classified for two different threshold levels. It is clear that more data are needed to allow one to determine the threshold value of the slope that will distinguish healing from nonhealing wounds. It is likely that the period of time needed to establish a predictive trend could be reduced if measurements were conducted more frequently. The average number of data points during each subject’s first ten weeks in our study was 5.0. We chose to evaluate trends using ten weeks of data because five measurements appear to be adequate to establish a statistically reliable trend line. If, in a future study, DPDW measurements were conducted every week, we believe that it would be possible to establish a predictive trend line in only five weeks.

Fig. 8

Ten-week rates of change in $\left[\mathrm{Hb}{\mathrm{O}}_2\right]$ and [Tot Hb] from the centers of all wounds. White bars represent data from healing wounds; black bars represent data from nonhealing wounds.

Table 2

Prediction capability of changes in [HbO2] and [Tot Hb] for various thresholds.

3.4.

Statistical Characterization of Healing and Nonhealing Wound Data

In addition to the rate of change of hemoglobin concentration, the statistical characteristics of these data from a wound may provide an indicator of healing potential. Visual comparison of Figs. 3, 4, 5 reveals more week-to-week variability in the nonhealing data than in the healing data. To quantify variability differences, the root mean square deviation (RMSD) of experimental data from the fitted first-order polynomials was calculated using the following equation:

Fig. 9

Normalized RMSD of the lines fitted to hemoglobin concentration measured at the centers of wounds (left) and the edges of wounds (right).