General perturbative approach to the diffusion equation in the presence of absorbing defects: frequency-domain and time-domain results

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Method for Measuring Absolute Optical Properties of Turbid Samples in a Standard Cuvette

Many applications seek to measure a sample's absorption coefficient spectrum to retrieve the chemical makeup. Many real world samples are optically turbid, causing scattering confounds which many commercial spectrometers cannot address. Using diffusion theory and considering absorption and reduced scattering coefficients on the order of 0.01 per mm and 1 per mm, respectively, we develop a method which utilizes frequency-domain to measure absolute optical properties of turbid samples in a standard cuvette (45 mm by 10 mm by 10 mm). Inspired by the self calibrating method, which removes instrumental confounds, the method uses measurements of the diffuse complex transmittance at two sets of two different source-detector distances. We find: this works best for highly scattering samples (reduced scattering coefficient above 1 per mm); higher relative error in the absorption coefficient compared to the reduced scattering coefficient; accuracy is tied to knowledge of the samples index of refraction. Noise simulations with 0.1 percent amplitude and 0.1 deg (1.7 mrad) phase uncertainty find errors in absorption and reduced scattering coefficients of 4 percent and 1 percent, respectively. We expect that higher error in the absorption coefficient can be alleviated with highly scattering samples and that boundary condition confounds may be suppressed by designing a cuvette with high index of refraction. Further work will investigate implementation and reproducibility

Higher order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries

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Spectral and Spatial Dependence of Diffuse Optical Signals in Response to Peripheral Nerve Stimulation

Using non-invasive, near-infrared spectroscopy we have previously reported optical signals measured at or around peripheral nerves in response to their stimulation. Such optical signals featured amplitudes on the order of 0.1% and peaked about 100 ms after peripheral nerve stimulation in human subjects. Here, we report a study of the spatial and spectral dependence of the optical signals induced by stimulation of the human median and sural nerves, and observe that these optical signals are: (1) unlikely due to either dilation or constriction of blood vessels, (2) not associated with capillary bed hemoglobin, (3) likely due to blood vessel(s) displacement, and (4) unlikely due to fiber-skin optical coupling effects. We conclude that the most probable origin of the optical response to peripheral nerve stimulation is from displacement of blood vessels within the optically probed volume, as a result of muscle twitch in adjacent areas.National Institutes of Health (R01-NS059933); U.S. Army Medical Acquisition Activity (W81XWH-07-2-0011

Invariance properties of exact solutions of the radiative transfer equation

Abstract In this work, special invariance properties of a class of exact solutions of the radiative transfer equation (RTE) pertaining to a uniform Lambertian illumination of any non-absorbing homogeneous and inhomogeneous volume are presented and discussed. This class of solutions of the RTE traces a reference ground under which light propagation can be studied in a special simplified regime. Despite the difficulties to obtain general solutions of the radiative transfer equation, the condition of Lambertian illumination determines a unique regime of photon transport where quite easy and simple invariant solutions can be obtained in all generality for homogeneous and inhomogeneous geometries. These solutions are invariant both with respect to the geometry (size and shape of the volume) and with respect to the scattering properties, i.e. scattering coefficient, scattering function and homogeneity of the considered domain. Another evident advantage of these solutions is that they are exact solutions known with arbitrary precision and can thus be used as reference standard for photon migration studies

Relation between fluence rate and mean photons pathlengths: an alternative option for Monte Carlo-based-calculations of fluence

Usually, in biomedical optics, the average photon fluence rate, evaluated in a subvolume of a propagating medium, is obtained by Monte Carlo simulations by calculating the power deposited by photons absorbed in the subvolume. We propose an alternative method based on evaluating the average path length traveled by all photons injected within the subvolume. Application examples are given. This method also works for a zero absorption coefficient and for a nonconstant spatial distribution of the absorption coefficient within the subvolume. The proposed approach is a re-visitation of a well-known method applied to nuclear and radiation physics. The results obtained show that a potential advantage of the proposed method is that it can improve the convergence of Monte Carlo simulations. Indeed, when calculating the fluence in a region of interest with the proposed method, all photons passing through the region are considered. Whereas with the traditional approach, only absorbed" photons are considered. In the latter case, this can produce a poorer Monte Carlo statistic for the same number of photons launched

Domain Adaptation for Robust Workload Level Alignment Between Sessions and Subjects using fNIRS

Significance: We demonstrated the potential of using domain adaptation on functional Near-Infrared Spectroscopy (fNIRS) data to classify different levels of n-back tasks that involve working memory. Aim: Domain shift in fNIRS data is a challenge in the workload level alignment across different experiment sessions and subjects. In order to address this problem, two domain adaptation approaches -- Gromov-Wasserstein (G-W) and Fused Gromov-Wasserstein (FG-W) were used. Approach: Specifically, we used labeled data from one session or one subject to classify trials in another session (within the same subject) or another subject. We applied G-W for session-by-session alignment and FG-W for subject-by-subject alignment to fNIRS data acquired during different n-back task levels. We compared these approaches with three supervised methods: multi-class Support Vector Machine (SVM), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN). Results: In a sample of six subjects, G-W resulted in an alignment accuracy of 68 $\pm$ 4 % (weighted mean $\pm$ standard error) for session-by-session alignment, FG-W resulted in an alignment accuracy of 55 $\pm$ 2 % for subject-by-subject alignment. In each of these cases, 25 % accuracy represents chance. Alignment accuracy results from both G-W and FG-W are significantly greater than those from SVM, CNN and RNN. We also showed that removal of motion artifacts from the fNIRS data plays an important role in improving alignment performance. Conclusions: Domain adaptation has potential for session-by-session and subject-by-subject alignment of mental workload by using fNIRS data

Depth sensitivity of frequency domain optical measurements in diffusive media

The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been obtained in the frequency domain (where the source amplitude is modulated at radio-frequencies) by making use of analytical solutions of the photon diffusion equation in an infinite slab geometry. Furthermore, solutions for the relative contrast of AC, PH and DC signals when a totally absorbing plane is placed at a fixed depth of the slab have also been obtained. The solutions have been validated by comparisons with gold standard Monte Carlo simulations. The obtained results show that the AC signal, for modulation frequencies < 200 MHz, has a depth sensitivity with similar characteristics to that of the continuous-wave (CW) domain (source modulation frequency of zero). Thus, the depth probed by such a signal can be estimated by using the formula of penetration depth for the CW domain (Sci. Rep. 6, 27057 (2016)). However, the PH signal has a different behavior compared to the CW domain, showing a larger depth sensitivity at shallow depths and a less steep relative contrast as a function of depth. These results mark a clear difference in term of depth sensitivity between AC and PH signals, and highlight the complexity of the estimation of the actual depth probed in tissue spectroscopy.Postprint (published version

Two-step verification method for Monte Carlo codes in biomedical optics applications

Significance: Code verification is an unavoidable step prior to using a Monte Carlo (MC) code. Indeed, in biomedical optics, a widespread verification procedure for MC codes is still missing. Analytical benchmarks that can be easily used for the verification of different MC routines offer an important resource.Aim: We aim to provide a two-step verification procedure for MC codes enabling the two main tasks of an MC simulator: (1) the generation of photons' trajectories and (2) the intersections of trajectories with boundaries separating the regions with different optical properties. The proposed method is purely based on elementary analytical benchmarks, therefore, the correctness of an MC code can be assessed with a one-sample t-test.Approach: The two-step verification is based on the following two analytical benchmarks: (1) the exact analytical formulas for the statistical moments of the spatial coordinates where the scattering events occur in an infinite medium and (2) the exact invariant solutions of the radiative transfer equation for radiance, fluence rate, and mean path length in media subjected to a Lambertian illumination.Results: We carried out a wide set of comparisons between MC results and the two analytical benchmarks for a wide range of optical properties (from non-scattering to highly scattering media, with different types of scattering functions) in an infinite non-absorbing medium (step 1) and in a non-absorbing slab (step 2). The deviations between MC results and exact analytical values are usually within two standard errors (i.e., t-tests not rejected at a 5% level of significance). The comparisons show that the accuracy of the verification increases with the number of simulated trajectories so that, in principle, an arbitrary accuracy can be obtained.Conclusions: Given the simplicity of the verification method proposed, we envision that it can be widely used in the field of biomedical optics.</p