Diffuse optics (DO) encompasses a range of photonics tools based on the study of random photon migration in highly scattering media—biological tissues in particular. Due to its unique features, DO is emerging as a powerful means for clinical or homecare diagnostics.¹ The basic physics of DO is related to the detection of temporal or spatial alteration in photon distribution re-emitted on the tissue surface.² Due to the low power (typically few mW) of injected near-infrared light (600- to 1100-nm range), DO is inherently noninvasive. The photon temporal (or spatial) distribution carries information on the absorption—ultimately related to tissue chemical composition, such as water, lipid, collagen content, oxy- and deoxy-hemoglobin concentration, cytochrome c-oxidase³—and scattering properties—linked to tissue microstructure. Further, DO is one of the few noninvasive modalities capable of providing functional information, e.g., brain or muscle activation.⁴ It can be operated noncontact through remote light illumination and collection.⁵ It explores the tissue well below the skin at depths of up to 2 to 4 cm. It can provide quantitative operator-independent assessment of the tissue status, such as hemoglobin oxygenation level in the brain. Finally, it is highly scalable, sharing the same technology from large clinical tomographic systems down to wearable devices or homecare appliances.⁶ For all these aspects, DO is attracting more and more interest in many fields, such as monitoring vital signs like brain oxygenation in critical care or during interventions,⁷ tumor diagnostics as for breast cancer,⁸ investigating the impact of lifestyle and nutrition on our body,⁹ or other fields such as neuroscience and psychology,¹⁰ sports, and leisure.¹¹ Even further, the operator independence, the depth sensitivity, and the scalability in addition to noninvasiveness make this option attractive for telemedicine and homecare of patients remotely.

Functional Near‐Infrared Spectroscopy (fNIRS) aims to recover changes in tissue optical parameters relating to tissue hemodynamics, to infer functional information in biological tissue. A widely‐used application of fNIRS relies on continuous wave (CW) methodology that utilizes multiple distance measurements on human head for study of brain health. The typical method used is spatially resolved spectroscopy (SRS), which is shown to recover tissue oxygenation index (TOI) based on gradient of light intensity measured between two detectors. However, this methodology does not account for tissue scattering which is often assumed. A new parameter recovery algorithm is developed, which directly recovers both the scattering parameter and scaled chromophore concentrations and hence TOI from the measured gradient of light‐attenuation at multiple wavelengths. It is shown through simulations that in comparison to conventional SRS which estimates cerebral TOI values with an error of ±12.3%, the proposed method provides more accurate estimate of TOI exhibiting an error of ±5.7% without any prior assumptions of tissue scatter, and can be easily implemented within CW fNIRS systems. Using an arm‐cuff experiment, the obtained TOI using the proposed method is shown to provide a higher and more realistic value as compared to utilizing any prior assumptions of tissue scatter.

Continuous wave (CW) functional near-infrared spectroscopy (fNIRS)-based optical imaging is a neuroimaging technique used to non-invasively monitor functional activity in the brain by tomographic reconstruction of the hemodynamic activity. These reconstructions can be used in clinical applications such as patient monitoring,¹ psychology studies,^2,3 and functional brain mapping.⁴ It is a relatively inexpensive technology and nonionizing in nature as compared with the alternative neuroimaging tools such as magnetic resonance imaging, computed tomography, or positron emission tomography. CW-NIRS-based imaging relies on the measurements of the light intensity, using multi-distance overlapping source-detector (SD) channels. NIR light sources placed on the scalp emit light into the head that traverses through the scalp, skull, cerebro-spinal fluid (CSF), and cerebral regions, and the back-scattered light is measured by detectors placed on the scalp at certain distances from the sources. The spectrally varying optical properties of the medium that contribute to variation of the measured light intensities are then reconstructed using a diffusion theory-based inverse model, from which 3D recovery of optical properties of the medium is often termed as diffuse optical tomography (DOT).

Near-infrared spectroscopy (NIRS) is widely used as a non-invasive method to monitor the hemodynamics of biological tissue. A common approach of NIRS relies on continuous wave (CW) methodology, i.e. utilizing intensity-only measurements, and, in general, assumes homogeneity in the optical properties of the biological tissue. However, in monitoring cerebral hemodynamics within humans, this assumption is not valid due to complex layered structure of the head. The NIRS signal that contains information about cerebral blood hemoglobin levels is also contaminated with extra-cerebral tissue hemodynamics, and any recovery method based on such a priori homogenous approximation would lead to erroneous results. In this work, utilization of hyper-spectral intensity only measurements (i.e., CW) at multiple distances are presented and are shown to recover two-layered tissue properties along with the thickness of top layer, using an analytical solution for a two-layered semi-infinite geometry. It is demonstrated that the recovery of tissue oxygenation index (TOI) of both layers can be achieved with an error of 4.4%, with the recovered tissue thickness of 4% error. When the data is measured on a complex tissue such as the human head, it is shown that the semi-infinite recovery model can lead to uncertain results, whereas, when using an appropriate model accounting for the tissue-boundary structure, the tissue oxygenation levels are recovered with an error of 4.2%, and the extra-cerebral tissue thickness with an error of 11.8%. The algorithm is finally used together with human subject data, demonstrating robustness in application and repeatability in the recovered parameters that adhere well to expected published parameters.

The forward model in diffuse optical tomography (DOT) describes how light propagates through a turbid medium. It is often approximated by a diffusion equation (DE) that is numerically discretized by the classical finite element method (FEM). We propose a nonlocal diffusion equation (NDE) as a new forward model for DOT, the discretization of which is carried out with an efficient graph-based numerical method (GNM). To quantitatively evaluate the new forward model, we first conduct experiments on a homogeneous slab, where the numerical accuracy of both NDE and DE is compared against the existing analytical solution. We further evaluate NDE by comparing its image reconstruction performance (inverse problem) to that of DE. Our experiments show that NDE is quantitatively comparable to DE and is up to 64% faster due to the efficient graph-based representation that can be implemented identically for geometries in different dimensions. The proposed discretization method can be easily applied to other imaging techniques like diffuse correlation spectroscopy which are normally modeled by the diffusion equation.