Principle Hyperspectral imaging consists of recording a series of two-dimensional images of biological tissue over a narrow spectral band around discrete wavelengths, λ_{j}.^{15} The resulting set of images is called a hypercube and is denoted by *H(x, y*, λ_{j}), where *x* and *y* are the two spatial coordinates and λ_{j} is the spectral coordinate. In other words, each pixel in a hypercube corresponds to the local reflectance spectrum of the tissue.

Analysis of the hypercube can reveal the local concentration of tissue chromophores. Indeed, the reflectance spectra of human skin measured by a hyperspectral imaging system are affected by (1) melanin concentration, (2) thickness of the epidermis, (3) blood volume and oxygen saturation of the blood in the dermis, and (4) the scattering properties of the tissue.^{16} For example, hemoglobin absorption dominates the absorption spectrum of the dermis in the visible range.^{17–19} In addition, light absorption by melanin in the epidermis is strong in the ultraviolet (UV) range and smaller in the visible range.^{20–22}
reproduces the spectral molar absorption coefficients of melanin,^{23} oxyhemoglobin, and deoxyhemoglobin reported in the literature.^{24} Deoxyhemoglobin features a single absorption peak around 554 nm while oxyhemoglobin exhibits absorption peaks around 542 and 578 nm.^{16} These differences are the basis for reflectance spectroscopy, which enables visualization of microcirculation and local oxygen saturation of the perfusing blood in diabetic feet. However, reflectance spectra may need to be corrected for scattering by the epidermis and dermis and absorption by melanin, particularly for strongly pigmented skins.

Furthermore, quantitative assessment of tissue pigmentation by melanin and blood can be used to detect diabetic complications. In fact, acute and long term inflammation caused by infection or ulceration can lead to skin hyperpigmentation.^{25,26} This is typically observed in areas surrounding venous ulcers and other chronic wounds due to extravasation of red blood cells into the dermis, collections of hemosiderin within macrophages, and melanin deposition.^{25,27–29} Alternatively, extreme inflammation may eventually destroy melanocytes in the epidermis resulting in hypopigmentation in and around the ulcer site after ulcer healing.^{26} Hyperspectral imaging in the visible and near-infrared (NIR) parts of the spectrum has been used to determine the spatial distribution of oxygen saturation in the human skin.^{15} This technique has also been applied clinically to study diabetic neuropathy^{30} and predict the healing potential of diabetic foot ulcers.^{31,32}

Finally, Vande Berg and Rudolph^{33} performed a histological study of tissue surrounding pressure ulcers that are similar to diabetic foot ulcers. They noted that these regions had thinner epidermis when compared with adjacent healthy tissue. Furthermore, dermal collagen fibers were woven into thick bundles that were denser than healthy collagen and contained regions of scar tissue. Inflammatory cells and platelets were mixed among the collagen fibers. In some instances, blood vessels were occluded due to swelling, while in others they were hyperemic due to increased blood flow. Such changes in tissue microstructure have been shown to affect the scattering coefficient of skin.^{16} Thus, by detecting epidermal thickness and the skin's scattering coefficient, one could also detect structural changes that occur in the skin prior to ulceration or during healing.

Hyperspectral Image Analysis Two methods can be used to analyze the hypercube data collected experimentally. The first method treats skin as a semi-infinite medium. The second method treats skin as a two-layer medium consisting of a plane-parallel slab supported by a semi-infinite medium representing the epidermis and the dermis, respectively. These methods are discussed in detail in the next sections.

• Method 1. Modified Beer-Lambert Law and Calibration

The so-called apparent absorption of the tissue *A*_{obs}(x,y, λ_{j}) at the spatial coordinate *(x,y)* and at wavelength λ_{j} can be calculated using the modified Beer-Lambert law^{34} as

where *R*_{d}(*x,y*,λ_{j}) is the diffuse reflectance emerging around the normal direction and measured experimentally. The primary chromophores in the human skin responsible for absorption of visible light are oxyhemoglobin, deoxyhemoglobin, and melanin.^{16,18,35} Thus, the apparent absorption (or extinction) can be modeled as the sum of absorption from chromophores and scattering by the tissue:^{34}

where *M*_{i}(x,y) is the molar concentration of chromo- phore “i” at coordinate (*x,y*) (expressed in mol/liter) and ε_{i}(λ) is a spectral molar absorption coefficient [in cm^{−1}/(mol/liter)] while the subscripts *oxy, deoxy*, and *mel* refer to oxyhemoglobin, deoxyhemoglobin, and melanin, respectively. The mean free path *L* (in centimeters) is the average distance traveled by a photon within the tissue before it reemerges out of the tissue.^{34} The term *G* accounts for light scattering by the skin outside of the acceptance angle of the collector optics; it depends on the geometry of the collector optics and can be assumed to be independent of wavelength.^{16} The spectral molar absorption coefficients ε_{oxy}(λ_{j}), ε_{deoxy}(λ_{j}), and ε_{mel}(λ_{j}) were taken from the literature^{36–38} and are shown in . The mean free path *L* is unknown and so the products *M*_{oxy}(x,y)L, *M*_{deoxy}(x,y)L, and *M*_{mel}(x,y)L can be substituted by effective concentrations OXY(*x,y*), DEOXY(*x, y*), and MEL(*x, y*), respectively. Then, the four unknown parameters OXY, DEOXY, MEL, and *G* can be retrieved at each location (*x,y*) by minimizing the residual *r* given by

where the factor *s* was introduced to scale empirically the effective oxyhemoglobin concentration OXY to be 50 on average for a population of healthy subjects. Minimization of the residual *r* can be performed numerically with an optimization software such as the popular Levenberg-Marquardt algorithm.^{39} The effective total hemoglobin concentration, HEME, and the oxygen saturation, SO_{2}, at coordinate (x,y) are then calculated as HEME = OXY + DEOXY and SO2 = OXY/HEME, respectively.

• Method 2: Two-Layer Optical Skin Model

Analysis of the apparent absorption with the modified Beer-Lambert law can provide an estimate of oxygen saturation, melanin concentration, and total hemoglobin. However, it cannot be used to estimate epidermal thickness and the tissue spectral scattering coefficient. Instead, Yudovsky and Pilon^{40} developed an inverse method that can simultaneously determine (1) oxygen saturation, SO_{2}, (2) blood volume fraction, *f*_{blood}, (3) melanin concentration, *M*_{mel}, and (4) the tissue scattering coefficient, μ_{s,tr} (assumed to be identical for dermis and epidermis^{16}) from the same reflectance measurements.

The human skin was modeled as a plane-parallel slab representing the epidermis supported by a semi-infinite layer representing the dermis. Absorption in the epidermis is mainly due to melanin and was modeled as a function of the melanin concentration, *M*_{mel}.^{18,35} The spectral absorption coefficient of the dermis is determined primarily by the absorption of blood and flesh^{24} and depends on the blood volume fraction and the oxyhemoglobin and deoxyhemoglobin concentrations in the blood. Finally, the spectral transport scattering coefficient of both the epidermis and dermis were assumed to be equal and given by a power law.^{16} Then, the diffuse reflectance of skin was predicted by a rapid and accurate expression accounting for the distinct optical properties of the epidermis and dermis and given by^{41}

where ω_{tr,epi} and ω_{tr,derm} are the transport single scattering albedos of the epidermis and dermis, respectively, while *n*_{1} is the index of refraction of both layers. The reduced reflectance, *R**, is a function of a single semi-empirical parameter α and expressed as^{41}

The parameter *Y*_{epi} is the modified optical thickness defined as *Y*_{epi}=ζ(μ_{a,epi}+μ_{s,tr})*L*_{epi}, where *L*_{epi} is the physical thickness of the epidermis,^{42} and μ_{a,epi}(λ) and μ_{s,tr}(λ) are the absorption and transport scattering coefficients, respectively. The parameters ζ and α were given as polynomial expressions in terms of ω_{tr,epi} and ω_{tr,derm}, respectively.^{41} The function *R*_(*n*_{1}, ω_{tr}) appearing in **Equation (4)** is the diffuse reflectance of a semi-infinite homogeneous layer, with transport single scattering albedo ω_{tr} and index of refraction *n*_{1} given by^{41}

where ρ_{01}(*n*_{1}) is the normal-normal reflectivity of the tissue/air interface defined as

Expressions for

and

were given in Equations (26) and (27), respectively, of Yudovsky and Pilon.

^{41} The relative error between the semi-empirical model and Monte Carlo simulations was typically around 3% and never more than 8% for the optical properties of skin in the visible range.

^{41}The goal of the inverse method was to estimate the property vector

from the measured diffuse reflectance

*R*_{m}(λ

_{j}). This was achieved by finding an estimate vector

that minimizes the sum of the squared residuals δ expressed as

where

is the estimated spectral reflectance and

*K* is the number of wavelengths considered. OxyVu™ (HyperMed, Inc., Burlington, MA) measured the diffuse reflectance at

*K* =15 wavelengths between 500 and 660 nm. The residual was minimized iteratively at each coordinate (

*x,y*) using the constrained Levenberg-Marquardt algorithm.

^{39} The minimization was stopped once successive iterations of the algorithm no longer reduced δ(

*x,y*) by more than 10

^{−9} per iteration. Furthermore, multiple random initial guesses for

were attempted to prevent convergence to a local minimum.

Finally, this inverse method was successfully applied to *in vivo* normal-hemispherical reflectance measurements on the untanned inner forearm, medium tanned forehead, and strongly tanned outer forearm of subjects with lightly and strongly pigmented skin.^{43} The results were consistent with race, anatomical location, and tanning status of the subjects and with biopsy measurements reported in the literature.^{44–50} This article illustrates how this second method can be applied to monitor changes in epidermal thickness on diabetic feet known to have developed ulcers.

Hyperspectral Imaging For Diabetic Foot Wound Care Hyperspectral imaging has been used to assess tissue viability and health in diabetes patients at risk of foot ulceration.^{15,31,32,51,52} For example, Greenman *et al*.^{30} used hyperspectral imaging to generate oxygen saturation and total hemoglobin concentration maps of the forearms and feet of diabetic subjects with and without neuropathy, and of nondiabetic subjects. The study included 19 male and 17 female type 1 and 2 diabetes patients without neuropathy, 33 male and 18 female type 1 and 2 diabetes patients with neuropathy, and 11 male and 10 female nondiabetic subjects without neuropathy. None of the subjects were affected by foot ulceration. The average ages of the neuropathic, nonneuropathic, and control groups were 55, 54, and 47 years of age, respectively. The authors showed that the resting oxygen saturation averaged over the area surrounding the ulcer was lower among diabetic subjects with neuropathy than among both diabetic subjects without neuropathy and non- diabetic subjects. This suggests that diabetic neuropathy, which is a major contributor to ulceration,^{10,11} could be detected by hyperspectral tissue oximetry.

In a different study, Khaodhiar *et al*.^{32} measured *in vivo* oxyhemoglobin and deoxyhemoglobin concentrations using hyperspectral imaging near ulcer sites on the feet of type 1 diabetes patients. The study included (1) 6 male and 4 female diabetes patients between the ages of 38 and 64 having diabetic foot ulcers, (2) 8 male and 5 female diabetes patients between the ages of 24 and 68 without diabetic foot ulcers, and (3) 6 male and 8 female control subjects without diabetes or foot ulcers between the ages of 23 and 70. Hyperspectral imaging of the feet between 500 and 650 nm was performed at each visit for up to four times over a six-month period. The previously described Method 1 was used to analyze the images. Then, the authors developed an ulcer-healing prediction index based on the oxyhemoglobin and deoxyhemoglobin concentrations near the ulcer site that could distinguish ulcers that would heal from ulcers that would not heal, with a sensitivity and specificity of 93 and 86%, respectively.

This article discusses how hyperspectral imaging can be used in clinical setting to (1) predict the likelihood of ulcer healing and (2) identify tissue at risk of ulcerating before tissue damage becomes apparent to a caregiver.