###### Abstract  
In this paper, we present a set of algorithms to enable the development of inexpensive hyperspectral sensors capable of estimating tissue oxygenation for wound monitoring. Estimation is conducted using the extended modified Lambert-Beer law, which has previously been proven robust to differences in melanin concentration. We introduce a novel wavelength selection algorithm that enables the estimation to be performed with high accuracy using only a small number (5-10) of wavelengths. Validation performed with Monte Carlo simulation data resulted in prediction errors <1%, with no significant differences among various skin types, for as few as five wavelengths under conditions representing both high precision instrumentation and more cost-effective sensors designed with inexpensive LEDs and/or filters. Validation with in vivo data collected from an occlusion study with 13 Asian volunteers showed statistically significant separation between the estimates for the at-rest and arterial occlusion states. Additional stability testing proved the proposed algorithms to be robust to small changes in the selected wavelengths as may occur in a real LED due to manufacturing tolerances and temperature fluctuations. This work concluded that the development of an inexpensive hyperspectral device for wound monitoring in all skin types is feasible using just a small number of wavelengths. tissue oxygenation; wound monitoring; hyperspectral imaging; wavelength selection; extended modified Lambert-Beer law; spectroscopy +
Footnote †: journal: Applied  
from diabetes [7]. According to the Centers for Disease Control and Prevention (CDC), the prevalence of diagnosed diabetes is highest among Native Americans and Alaskan Natives than among any other US racial group [8]. Compounding this, these communities also experience the healthcare difficulties of rural and low-access settings. More than 46 million Americans (15% of the US population) live in rural areas, and this cohort experiences a 17% higher rate of type 2 diabetes than urban residents while simultaneously suffering workforce shortages of primary and specialty care providers [9; 10]. The state of wound progression or healing is in large part influenced by the transport of oxygen to the affected area [11]. Tissue oxygenation (SO\({}_{2}\)), the percentage of oxygenated hemoglobin in the blood, is thus a key indicator of tissue health and a vital metric for monitoring diabetic foot wounds. Hyperspectral imaging (HSI) offers a non-contact, non-invasive method for estimating SO\({}_{2}\) in tissue near the affected area, making it an ideal tool for diabetic foot-wound monitoring [12]. Algorithms based on the Lambert-Beer law [13], Kubelka-Munk theory [14], and approximations to the radiative transfer equation (RTE) [15] have been developed to estimate SO\({}_{2}\) from hyperspectral information, and many of these algorithms have found their way into clinical devices such as the OxyVu system (Hypermed, MA, USA), the Kent Camera (Kent Imaging, Calgary, AB, Canada), and the TVITA system (Diaspective, Am Salzhaff, Germany) [16]. However, some researchers have noted disparities in SO\({}_{2}\) estimation accuracies for different skin types, with higher errors seen for patients with higher melanin concentration (i.e., darker skin) [17; 18; 19]. This presents a significant problem for monitoring wound progression in the most-affected populations. To improve the quality of diabetic foot-wound monitoring for those most in need, including those in rural areas, new cost-effective HSI devices are needed. Such devices must be inexpensive, portable, and robust to differences in melanin concentration. Despite their great promise, current HSI technologies fail to meet most (if not all) of these criteria. We seek to address these shortfalls by developing new algorithms and methods that will enable the creation of less complex and more accurate wound-monitoring devices.