2.1.

Optical Methods

The frequency domain DPDW instrument illuminated the animal tissue with four diode lasers in the NIR window at wavelengths of 685, 780, 830, and $950\mathrm{nm}$ , with its intensity modulated by a radio frequency $\omega =70\mathrm{MHz}$ .³⁴ A schematic of the device and a detailed description can be found elsewhere.³⁴ Backscattered light was delivered to four detector blocks based on avalanche photodiodes (APD) and quadrature $(I∕Q)$ demodulators. The $I$ and $Q$ signals in each detector were measured; these were determined by the attenuated amplitude $A_{\mathit{att}}$ and phase shift ${\Theta }_{\mathit{log}}$ of the registered scattered light. The output power at the end of the source fiber ranges from $5\text{to}7\mathrm{mW}$ , for all four wavelengths.

The diffusion approximation can be used to calculate absorption ${\mu }_a$ and reduced scattering ${\mu }_s^{\prime }$ coefficients of tissue based on the solution of the time-dependent diffusion equation assuming a semi-infinite tissue geometry.^{35, 36} We used the closed form analytical solutions to the diffusion equation for calculating the optical properties of animal tissue.³⁶ The so-called extrapolated condition for semi-infinite media is a good approximation in noninvasive clinical applications where the fluence rate is nonzero at the boundary.

During this diffusion and “snake-like” propagation of light in the tissue, light is attenuated in intensity and also subjected to a phase shift that reflects the mean flight time of photons through the strongly scattering medium (tissue). The reduced scattering coefficient is defined as a function of the scattering coefficient ${\mu }_s$ , ${\mu }_s^{\prime }={\mu }_s(1-g)$ , where the average cosine angle of scattering $g\sim 0.9$ for biological tissue and its inverse is defined as the mean transport length $l^{*}$ . Usually after propagation of more than two or three $l^{*}$ , photons have no memory of the incident direction of light; we can then assume that the radiance is quasi-isotropic.

For most biological tissues ${\mu }_s^{\prime }$ is between 5 and $15{\mathrm{cm}}^{-1}$ and its value determines the design of the appropriate experimental probe. In our studies, we assumed that ${\mu }_s^{\prime }\sim 10{\mathrm{cm}}^{-1}$ for animal tissue and designed an optimal probe. The scattering coefficient calculated from our studies was very close to the assumed value of $10{\mathrm{cm}}^{-1}$ , corresponding to $l^{*}$ around $1\mathrm{mm}$ . Because the smallest source-detector separation of our probe $\left(4\mathrm{mm}\right)$ is larger than $3\ast l^{*}$ , the diffusion approximation will be valid.

The optical fibers were inserted in a Teflon probe of length $25\mathrm{mm}$ and width $7\mathrm{mm}$ , with a separation between source and detector fibers of $\rho =4$ , 8, 12, and $16\mathrm{mm}$ . It is possible to estimate the probable penetration depth of diffuse light $D_v$ in the tissue as function of the source-detector separation $\rho$ by using diffusion theory. A detailed investigation of this problem can be found in Refs. 37, 38, but a rule of thumb often applied is that $D_v\sim (1∕3-1∕2)$ $\rho$ .

2.2.

Calibration Procedures

The measured intensity of scattered light $A_{\mathit{att}}$ depends not only on the tissue properties, but also on the sensitivity of the APD, the coupling to the detectors fibers, the transmission of the optical fibers, and the gain of each detector block. The phase shift ${\Theta }_{\mathit{log}}$ may be different in each channel because the optical and electrical signal delay depends on fiber length and coupling, the length of the RF coaxial cables, and any delays in the detector circuits. Instrument calibration is performed to allow us to separate variability due to the instrument hardware components from sample and measurement variability. An equidistant probe is constructed to conduct the first instrument calibration. The four detector fibers are inserted in a Teflon probe with the same source-detector separation of $12\mathrm{mm}$ . The probe is placed on the surface of a liquid optical phantom (Liposyn, Abbott Laboratories, Chicago, Illinois) that simulates tissue optical properties in a semi-infinite geometry. The set of calibration coefficients that equalizes the amplitude and phase of the second, third, and fourth detector relative to the first detector is determined. All subsequent experimental data are corrected using this set of calibration coefficients.³⁴

It should be noted that the use of a Liposyn solution as an optical phantom for experiments that span several days is not the best approach, because the solution changes optical properties due to phase separation and degradation. An additional factor that contributes to operator variability when using Liposyn is the repeatability of placing the solid plastic probe exactly on the surface of the solution. Use of the semi-infinite approximation relies on perfect contact between the solid and liquid interface, without any air gap and also without immersing the probe in the liquid. Solid phantoms can overcome some of these challenges. Silicone optical phantoms were the method of choice for calibrating the NIR device because these models do not change optical properties during the time course of our experiments. Cylindrical phantoms made of silicone with dispersed particles of titanium dioxide to act as scatters and carbon black to act as an absorber were used.³⁹ Cylinders with diameter of $90\mathrm{mm}$ and thickness of $45\mathrm{mm}$ were synthesized from silicone XP565 with activator (platinum catalyzed from Silicones Inc., High Point, North Carolina); $\mathrm{Ti}{\mathrm{O}}_2$ particles with diameters between 0.9 and $1.6\mu \mathrm{m}$ simulated tissue scattering, and carbon black acetylene, 50% compressed, $99.9+\%$ (metals basis) $(\text{diameter}=0.042\mu \mathrm{m})$ , simulated light absorption. Both $\mathrm{Ti}{\mathrm{O}}_2$ and carbon black were obtained from Alfa Aesar (Ward Hill, Massachusetts).

We optimized the preparation of these models including intensity and time of mixing, the order of addition of the components, and the crosslinking reaction to ensure phantoms of desired composition with no air bubbles. We verified the absence of microbubbles by sectioning the phantoms in thin layers and observing their surfaces under an optical microscope.

Typical of any device that measures light intensity, our instrument has a limited range where the electrical output signal is proportional to the optical power of the input signal. A second calibration was conducted to define the region of saturation that occurs at an output signal of around $100\mathrm{mV}$ . The linearity range for the device used in this study was $>50\mathrm{dB}$ . Typical magnitudes of the $I$ and $Q$ demodulation signals were in the range of $2\text{to}70\mathrm{mV}$ . Offset for our instrument, defined as the signal measured without any light, was measured before every experiment on an animal and has not exceeded $500\mu \mathrm{V}$ for any experiment, with an average value around $250\mu \mathrm{V}$ throughout our studies. This calibration experiment allows us also to calculate the noise-equivalent power for our device, which was equal to $5\mathrm{pW}∕\mathrm{Hz}$ .

2.3.

Animal Models

We have used hairless rats as the animal model for studying tissue optical properties during wound healing. This is a model that is widely used and accepted for studying skin and wound properties.^{40, 41} The absence of hair removes the complications of inflammation introduced by shaving the wound site and does not interfere with the optical measurements.

Animal procedures were conducted in accordance with the Guide for the Humane Care and Use of Laboratory Animals.⁴² The experimental protocol was approved by Drexel University’s Institutional Animal Care and Use Committee. During the course of the study, all animals were supplied with food and water ad libitum and were housed in individual cages. We performed two independent studies as described below.

2.3.1.

First study

Three female hairless Sprague Dawley rats, $5\text{to}6\text{weeks}$ old and approximately $150\mathrm{g}$ each, were purchased from Charles River Laboratory (Wilmington, Massachusetts). A measurement protocol was developed over the course of $15\text{weeks}$ , and when measurements began the rats weighted approximately $300\mathrm{g}$ each. The rats were monitored with NIR for $48\text{days}$ (Fig. 1 ), with independent measurements taken usually every $3\text{to}4\text{days}$ . On the 48th day, one quarter-sized $\left(4.6{\mathrm{cm}}^2\right)$ full thickness wound (Fig. 2 ) was inflicted on the left dorsal area of each animal to produce a wound animal model on all rats.

Fig. 1

Timeline of animal studies.

Fig. 2

Probe placement locations (dark rectangles) in animal model. Each animal was wounded on the left dorsum, and measurements were performed on (1) the center of the wound, (2) the edge of the wound, and (3) healthy tissue on the right dorsum, symmetric to the wound location.

A full thickness wound is a superficial wound where the epidermis and dermis are removed to expose the underlying tissue. It is different from an incision wound, and it heals by contraction. Sixteen series of optical measurements were performed on the wound and on skin bordering the edge of the wound. Symmetrical measurements were performed on the right dorsal side of all animals (Fig. 2).

2.4.

Immunohistochemistry

3.1.

Baseline

The stability and accuracy of the frequency domain NIR instrument used in the study is demonstrated in Fig. 3 , which tracks the absorption and reduced scattering coefficients over the course of $50\text{days}$ measured in silicone phantoms. Standard error remained at less than 4% throughout the period of the study.

Fig. 3

Daily average values of (a) ${\mu }_a$ and (b) ${\mu }_s^{\prime }$ in a silicone optical phantom over a $50\text{-}\text{day}$ period. Each point represents the average of measurements taken on the same day. Solid lines represent average values for the entire measurement period.

To be able to detect the small changes in optical properties occurring during wound healing, the NIR device used must exhibit very good stability. Otherwise it would be impossible to discern systematic device drift from actual physiological changes. The $48\text{-}\text{day}$ and $36\text{-}\text{day}$ periods of in vivo measurements prior to wound surgery in the first and second studies, respectively, allowed us to determine with high consistency the local values of ${\mu }_a$ and ${\mu }_s^{\prime }$ for the animals.

These form the baseline measurements for assessing changes in optical properties during our wound healing studies. Combined results of baseline measurements for ${\mu }_a$ and ${\mu }_s^{\prime }$ from both animal studies are shown in Fig. 4 for $685\mathrm{nm}$ . The error bars in Fig. 4 indicate the between-animal variation, which was less than 15% percent of the average values of ${\mu }_a$ and ${\mu }_s^{\prime }$ for each time point in study 2. Similar results were obtained for 785- and $830\text{-}\mathrm{nm}$ measurements. Baseline measurements for three representative rats are presented in Fig. 5 . Within-animal variation was less than 15% of the average values of ${\mu }_a$ and ${\mu }_s^{\prime }$ for each animal in the second study.

Fig. 4

Average absorption and scattering coefficients for all animals measured as a function of time. Baseline values of (a) left dorsal ${\mu }_a$ , (b) right dorsal ${\mu }_a$ , (c) left dorsal ${\mu }_s^{\prime }$ , and (d) right dorsal ${\mu }_s^{\prime }$ at $685\mathrm{nm}$ from study 1 and study 2. Each point represents the average of measurements taken on that day; error bars represent the standard deviation. In both studies, baseline optical measurements were taken at symmetric locations on the left and right dorsa of each animal. The average data of baseline stability obtained during the second study (black points) is a better indicator of device stability because of the higher number of animals $(n=12)$ compared to $n=3$ in the first study (gray points).

Fig. 5

Left dorsal baseline values of (a) ${\mu }_a$ and (b) ${\mu }_s^{\prime }$ from three representative rats. Each point represents the average of three measurements and error bars represent the standard deviation.

If we compare these in vivo data with those obtained from phantoms it is clear that in addition to the noise from the laser diodes, electronics, and fibers, being common to both in vitro and in vivo measurements, additional noise emanates from physiological changes in the animal tissue during our experiments. Several reasons may be responsible for such changes. The size of the rat is small, even compared with a $2\text{-}\mathrm{cm}$ probe. The rats were anesthetized during measurements and unable to move; however, breathing may have contributed to unintended change in probe positioning. The food supply was provided ad libitum, and this may have affected the amount of blood at the measurement sites at various times. Rats have been growing during the period of baseline measurements, and therefore, a slightly different tissue volume was examined as time went on.

Attention is drawn to the fact that the absorption coefficient is systematically higher for the left dorsal side as compared with the right one, for all animals at all time points (Fig. 4). During the second study, the differences in ${\mu }_a$ between the two sides range from $0.01\text{to}0.015{\mathrm{cm}}^{-1}$ and this may be due to asymmetry in the animal physiology. We only report this observation for the second study because in this case we have more representative statistics.

3.2.

Optical Properties during Wound Healing

In our experiments, wound size was determined by calculating wound surface area from cross-polarized digital images, which were taken at the same time the NIR data was collected. The image analysis tool IMAGE PRO (Media Cybernetics, Silver Spring, Maryland) was used to calculate the area of each wound. Although the original size of each wound was large relative to the size of the rat, the wound healing rate was very fast for this model (as with all healthy animals) and is evidence of the intense physiological changes in the animal during healing. A normalized wound area was obtained by calculating the ratio of wound area each day to the initial wound area on the day of surgery (day 0). Average normalized wound areas are presented in Fig. 6 (study 2). Wound healing rate in this animal model exhibits a nonlinear behavior as reported by Chen ² From our data, we can observe the healing rate is fast between days 3 and 10 and then decelerates at time points 15 to 24 to achieve full wound closure.

Fig. 6

Normalized wound area as a function of healing time for rats in study 2. Each point represents the average of all rats $(n=12)$ and error bars represent the standard deviation. Wound surgery was performed on day 0. The data points on days 0 and 3 are connected by a dashed line because from Chen (Ref. 2) it is known that the rate exhibits highly nonlinear behavior prior to day 3.

We monitored the change of optical properties during wound healing for all animals. Changes of optical properties at $685\mathrm{nm}$ as a result of our experiments are shown in Fig. 7 . The absorption coefficient of the wound is increasing during wound healing and asymptotically approaches a value that is higher by $0.035\text{to}0.040{\mathrm{cm}}^{-1}$ , or 35% to 40% (Fig. 7, open squares and triangles) compared with the nonwounded site (Fig. 7, filled diamonds) throughout the experiment. The difference in ${\mu }_a$ between wound and nonwound tissue is statistically significant $(p<0.01)$ after day 5. The difference in ${\mu }_s^{\prime }$ between wound and nonwound tissue is statistically significant $(p<0.05)$ after day 3. Similarly shaped healing curves were observed at other wavelengths, with ${\mu }_a$ at $780\mathrm{nm}$ increasing by $0.030\text{to}0.035{\mathrm{cm}}^{-1}$ (approximately 35%) and ${\mu }_a$ at $830\mathrm{nm}$ increasing by $0.040\text{to}0.045{\mathrm{cm}}^{-1}$ (approximately 40%) when compared with the nonwounded site.

Fig. 7

(a) ${\mu }_a$ and (b) ${\mu }_s^{\prime }$ at $685\mathrm{nm}$ during wound healing (average ± standard deviation) for animals in study 2. Wound surgery was performed on day 0. Open triangles represent measurements taken on the edges of the wounds; open squares represent measurements taken at the center of the wounds; and closed 20 diamonds represent control measurements on the nonwounded site. (c) ${\mu }_a$ and (d) ${\mu }_s^{\prime }$ at $685\mathrm{nm}$ during wound healing (average ± standard deviation) for animals in study 2. Wound surgery was performed on day 0. Open squares represent measurements taken at the center of the wounds, and closed diamonds represent control measurements on the nonwounded site. Two-tailed paired $t$ -tests were performed to compare wound center and control data at each time point ( ${}^{*}p<0.01$ , ${}^{**}p<0.05$ ).

Increasing values of ${\mu }_a$ as the wound is healing could be due to angiogenesis and neovascularization, and this was supported by immunohistochemical analysis where vessel ingrowth increased with time in lectin-stained images of blood vessels (Fig. 8 —endothelial cells are stained with green color).

Fig. 8

Lectin-stained images of wound tissue on (a) day 5, (b) day 10, and (c) day 21 after wound surgery. Vascular structures appear bright against a black ground. The number and size of vascular structures increases as the wound heals. Scale bars represent $25\mu \mathrm{m}$ .

As may be seen from Fig. 7, the values of ${\mu }_a$ obtained from measurements on the center of the wounds are identical (within experimental error) to the absorption coefficients obtained from measurements of the periwound area particularly for the first several measurements when the wounds are large in size compared with the probe size.

This remained consistent in both animal studies and can be explained by the geometry of our experiments. Studies of photon penetration depth at these wavelengths with geometry similar to the one we have used have shown that a probe having a source-detector separation of $16\mathrm{mm}$ registers scattered light from a tissue volume up to $5\mathrm{mm}$ beneath its surface.³⁸ The similarity between optical properties measured at the wound center and wound periphery provides evidence that the measured tissue is located beneath the skin’s surface, and therefore overlapping tissue volumes are interrogated as the probe is positioned on the center or the periphery of the wound. This observation may have clinical utility because it indicates that a wound could be monitored without the fiber optic probe touching directly the surface of an open wound.

The data on Fig. 7 suggest that during normal wound healing, the optical properties of tissue at NIR wavelengths change measurably, and therefore, healing may be followed by measuring changes of the absorption coefficient of the wound. Oxyhemoglobin concentration $\left(\left[\mathit{Hb}{\mathrm{O}}_2\right]\right)$ and deoxyhemoglobin concentration $\left(\left[\mathit{Hb}\right]\right)$ were calculated from the values of ${\mu }_a$ and ${\mu }_s^{\prime }$ using a modified form of the Beer-Lambert equation:

Fig. 9

Mean ± standard deviation of oxyhemoglobin $\left[\mathit{Hb}{\mathrm{O}}_2\right]$ , deoxyhemoglobin $\left[\mathit{Hb}\right]$ , and total hemoglobin $[\mathit{Hb}{\mathrm{O}}_2+\mathit{Hb}]$ during wound healing for animals in study 2. Wounds were inflicted on day 0.

Fig. 10

Oxygen saturation during wound healing for animals in study 2. Wounds were inflicted on day 0.

This small change supports the findings by Hunt, ⁴⁷ who suggested that oxygen saturation is not a sensitive measure of wound healing because hemoglobin delivery to the wound environment is disrupted by microvasculature damage, vasoconstriction, and clotting in the area surrounding a wound.⁴⁸However, the optical properties of tissue change measurably in this animal model during wound healing in contrast to the insignificant change of oxygen saturation. Therefore, tissue absorption coefficients may have adequate sensitivity to be good global indicators of changes during wound healing.