Application limits of the scaling relations for Monte Carlo simulations in diffuse optics. Part 1: theory.

Monte Carlo (MC) is a powerful tool to study photon migration in scattering media, yet quite time-consuming to solve inverse problems. To speed up MC-simulations, scaling relations can be applied to an existing initial MC-simulation to generate a new data-set with different optical properties. We named this approach trajectory-based since it uses the knowledge of the detected photon trajectories of the initial MC-simulation, in opposition to the slower photon-based approach, where a novel MC-simulation is rerun with new optical properties. We investigated the convergence and applicability limits of the scaling relations, both related to the likelihood that the sample of trajectories considered is representative also for the new optical properties. For absorption, the scaling relation contains smoothly converging Lambert-Beer factors, whereas for scattering it is the product of two quickly diverging factors, whose ratio, for NIRS cases, can easily reach ten orders of magnitude. We investigated such instability by studying the probability-distribution for the number of scattering events in trajectories of given length. We propose a convergence test of the scattering scaling relation based on the minimum-maximum number of scattering events in recorded trajectories. We also studied the dependence of MC-simulations on optical properties, most critical in inverse problems, finding that scattering derivatives are ascribed to small deviations in the distribution of scattering events from a Poisson distribution. This paper, which can also serve as a tutorial, helps to understand the physics of the scaling relations with the causes of their limitations and devise new strategies to deal with them.

Two-layer reconstruction of Raman spectra in diffusive media based on an analytical model in the time domain.

We derive and validate an analytical model that describes the migration of Raman scattered photons in two-layer diffusive media, based on the diffusion equation in the time domain. The model is derived under a heuristic approximation that background optical properties are identical on the excitation and Raman emission wavelengths. Methods for the reconstruction of two-layer Raman spectra have been developed, tested in computer simulations and validated on tissue-mimicking phantom measurements data. Effects of different parameters were studied in simulations, showing that the thickness of the top layer and number of detected photon counts have the most significant impact on the reconstruction. The concept of quantitative, mathematically rigorous reconstruction using the proposed model was finally proven on experimental measurements, by successfully separating the spectra of silicone and calcium carbonate (calcite) layers, showing the potential for further development and eventual application in clinical diagnostics.

Real-Time Dual-Wavelength Time-Resolved Diffuse Optical Tomography System for Functional Brain Imaging Based on Probe-Hosted Silicon Photomultipliers.

Near-infrared diffuse optical tomography is a non-invasive photonics-based imaging technology suited to functional brain imaging applications. Recent developments have proved that it is possible to build a compact time-domain diffuse optical tomography system based on silicon photomultipliers (SiPM) detectors. The system presented in this paper was equipped with the same eight SiPM probe-hosted detectors, but was upgraded with six injection fibers to shine the sample at several points. Moreover, an automatic switch was included enabling a complete measurement to be performed in less than one second. Further, the system was provided with a dual-wavelength ( 670 n m and 820 n m ) light source to quantify the oxy- and deoxy-hemoglobin concentration evolution in the tissue. This novel system was challenged against a solid phantom experiment, and two in-vivo tests, namely arm occlusion and motor cortex brain activation. The results show that the tomographic system makes it possible to follow the evolution of brain activation over time with a 1 s -resolution.

Frequency offset Raman spectroscopy (FORS) for depth probing of diffusive media.

We present a new technique, frequency offset Raman spectroscopy (FORS), to probe Raman spectra of diffusive media in depth. The proposed methodology obtains depth sensitivity exploiting changes in optical properties (absorption and scattering) with excitation wavelengths. The approach was demonstrated experimentally on a two-layer tissue phantom and compared with the already consolidated spatially offset Raman spectroscopy (SORS) technique. FORS attains a similar enhancement of signal from deep layers as SORS, namely 2.81 against 2.62, while the combined hybrid FORS-SORS approach leads to a markedly higher 6.0 enhancement. Differences and analogies between FORS and SORS are discussed, suggesting FORS as an additional or complementary approach for probing heterogeneous media such as biological tissues in depth.

Multiple-view diffuse optical tomography system based on time-domain compressive measurements.

Compressive sensing is a powerful tool to efficiently acquire and reconstruct an image even in diffuse optical tomography (DOT) applications. In this work, a time-resolved DOT system based on structured light illumination, compressive detection, and multiple view acquisition has been proposed and experimentally validated on a biological tissue-mimicking phantom. The experimental scheme is based on two digital micromirror devices for illumination and detection modulation, in combination with a time-resolved single element detector. We fully validated the method and demonstrated both the imaging and tomographic capabilities of the system, providing state-of-the-art reconstruction quality.

Time-domain Raman analytical forward solvers.

A set of time-domain analytical forward solvers for Raman signals detected from homogeneous diffusive media is presented. The time-domain solvers have been developed for two geometries: the parallelepiped and the finite cylinder. The potential presence of a background fluorescence emission, contaminating the Raman signal, has also been taken into account. All the solvers have been obtained as solutions of the time dependent diffusion equation. The validation of the solvers has been performed by means of comparisons with the results of "gold standard" Monte Carlo simulations. These forward solvers provide an accurate tool to explore the information content encoded in the time-resolved Raman measurements.

Fast silicon photomultiplier improves signal harvesting and reduces complexity in time-domain diffuse optics.

We present a proof of concept prototype of a time-domain diffuse optics probe exploiting a fast Silicon PhotoMultiplier (SiPM), featuring a timing resolution better than 80 ps, a fast tail with just 90 ps decay time-constant and a wide active area of 1 mm2. The detector is hosted into the probe and used in direct contact with the sample under investigation, thus providing high harvesting efficiency by exploiting the whole SiPM numerical aperture and also reducing complexity by avoiding the use of cumbersome fiber bundles. Our tests also demonstrate high accuracy and linearity in retrieving the optical properties and suitable contrast and depth sensitivity for detecting localized inhomogeneities. In addition to a strong improvement in both instrumentation cost and size with respect to legacy solutions, the setup performances are comparable to those of state-of-the-art time-domain instrumentation, thus opening a new way to compact, low-cost and high-performance time-resolved devices for diffuse optical imaging and spectroscopy.

Time domain functional NIRS imaging for human brain mapping.

This review is aimed at presenting the state-of-the-art of time domain (TD) functional near-infrared spectroscopy (fNIRS). We first introduce the physical principles, the basics of modeling and data analysis. Basic instrumentation components (light sources, detection techniques, and delivery and collection systems) of a TD fNIRS system are described. A survey of past, existing and next generation TD fNIRS systems used for research and clinical studies is presented. Performance assessment of TD fNIRS systems and standardization issues are also discussed. Main strengths and weakness of TD fNIRS are highlighted, also in comparison with continuous wave (CW) fNIRS. Issues like quantification of the hemodynamic response, penetration depth, depth selectivity, spatial resolution and contrast-to-noise ratio are critically examined, with the help of experimental results performed on phantoms or in vivo. Finally we give an account on the technological developments that would pave the way for a broader use of TD fNIRS in the neuroimaging community.

Nondestructive optical detection of monomer uptake in wood polymer composites.

A noninvasive method to assess the local monomer concentration within a wooden matrix, post monomer impregnation, by time-resolved diffuse optical spectroscopy is demonstrated. A data analysis technique for improving accuracy, which takes account of changes in the refractive index during the monomer uptake, has been employed. This technique can be potentially applied in the wood industry for the study of polymer composites as well as in cultural heritage science for noninvasively monitoring the penetration of chemical compounds used for consolidation or conservation purposes.

Forward solvers for photon migration in the presence of highly and totally absorbing objects embedded inside diffusive media.

In this paper, after a critical review of the literature, we present two forward solvers and a new methodology for description of photon migration in the presence of totally absorbing inclusions embedded in diffusive media in both time and CW domains. The first forward solver is a heuristic approach based on a higher order perturbation theory applied to the diffusion equation (DE) [denoted eighth-order perturbation theory (EOPT)]. The second forward solver [denoted eighth-order perturbation theory with the equivalence relation (EOPTER) ] is obtained by combining the EOPT solver with the adoption of the equivalence relation (ER) [J. Biomed. Opt.18, 066014 (2013)]. These forward solvers can possibly overcome some evident limitations of previous approaches like the theory behind the so-called banana-shape regions or exact analytical solutions of the DE in the presence of highly or totally absorbing inclusions. We also propose the ER to reformulate the problem of a totally absorbing inclusion in terms of another inclusion having a finite absorption contrast and a re-scaled volume. For instance, we have shown how this approach can indeed be used to simulate black inclusions with the Born approximation. By means of comparisons with the results of Monte Carlo simulations, we have shown that the EOPTER solver can model totally absorbing inclusions with an error smaller than about 10%, whereas the EOPT solver shows an error smaller than about 20%, showing a performance largely better than that observed with solvers proposed previously.

Diffuse optics using a dual window fast-gated counter.

In this paper we demonstrate the advantages of a fast-gated counter in achieving high count-rate and reducing costs of timing equipment in a time-resolved diffuse optical spectroscopy setup. We experimentally prove the equivalence between the fast-gated counter we developed and a traditional time-correlated single-photon counting setup in terms of depth sensitivity and signal-to-noise ratio. Additionally, we show the suitability of this device for bilayer analysis and to estimate the absorption coefficient of homogeneous diffusing media. Finally, we present a proof-of-principle arterial occlusion measurement on a healthy volunteer to validate the proposed approach in a real application. Fast-gated counters can dramatically reduce both costs and complexity in time-resolved multichannel systems, while achieving high count-rate, thus offering a great advantage in applications like brain and muscle functional imaging.

Optical signatures of thermal damage on ex-vivo brain, lung and heart tissues using time-domain diffuse optical spectroscopy.

Thermal therapies treat tumors by means of heat, greatly reducing pain, post-operation complications, and cost as compared to traditional methods. Yet, effective tools to avoid under- or over-treatment are mostly needed, to guide surgeons in laparoscopic interventions. In this work, we investigated the temperature-dependent optical signatures of ex-vivo calf brain, lung, and heart tissues based on the reduced scattering and absorption coefficients in the near-infrared spectral range (657 to 1107 nm). These spectra were measured by time domain diffuse optics, applying a step-like spatially homogeneous thermal treatment at 43 °C, 60 °C, and 80 °C. We found three main increases in scattering spectra, possibly due to the denaturation of collagen, myosin, and the proteins' secondary structure. After 75 °C, we found the rise of two new peaks at 770 and 830 nm in the absorption spectra due to the formation of a new chromophore, possibly related to hemoglobin or myoglobin. This research marks a significant step forward in controlling thermal therapies with diffuse optical techniques by identifying several key markers of thermal damage. This could enhance the ability to monitor and adjust treatment in real-time, promising improved outcomes in tumor therapy.

Tutorial on methods for estimation of optical absorption and scattering properties of tissue.

Significance: The estimation of tissue optical properties using diffuse optics has found a range of applications in disease detection, therapy monitoring, and general health care. Biomarkers derived from the estimated optical absorption and scattering coefficients can reflect the underlying progression of many biological processes in tissues. Aim: Complex light-tissue interactions make it challenging to disentangle the absorption and scattering coefficients, so dedicated measurement systems are required. We aim to help readers understand the measurement principles and practical considerations needed when choosing between different estimation methods based on diffuse optics. Approach: The estimation methods can be categorized as: steady state, time domain, time frequency domain (FD), spatial domain, and spatial FD. The experimental measurements are coupled with models of light-tissue interactions, which enable inverse solutions for the absorption and scattering coefficients from the measured tissue reflectance and/or transmittance. Results: The estimation of tissue optical properties has been applied to characterize a variety of ex vivo and in vivo tissues, as well as tissue-mimicking phantoms. Choosing a specific estimation method for a certain application has to trade-off its advantages and limitations. Conclusion: Optical absorption and scattering property estimation is an increasingly important and accessible approach for medical diagnosis and health monitoring.

Initial non-invasive in vivo sensing of the lung using time domain diffuse optics.

The in vivo diagnosis and monitoring of pulmonary disorders (caused for example by emphysema, Covid-19, immature lung tissue in infants) could be effectively supported by the non-invasive sensing of the lung through light. With this purpose, we investigated the feasibility of probing the lung by means of time-resolved diffuse optics, leveraging the increased depth (a few centimeters) attained by photons collected after prolonged propagation time (a few nanoseconds). We present an initial study that includes measurements performed on 5 healthy volunteers during a breathing protocol, using a time-resolved broadband diffuse optical spectroscopy system. Those measurements were carried out across the spectral range of 600-1100 nm at a source-detector distance of 3 cm, and at 820 nm over a longer distance (7-9 cm). The preliminary analysis of the in vivo data with a simplified homogeneous model revealed a maximum probing depth of 2.6-3.9 cm, suitable for reaching the lung. Furthermore, we observed variations in signal associated with respiration, particularly evident at long photon propagation times. However, challenges stemming from both intra- and inter-subject variability, along with inconsistencies potentially arising from conflicting scattering and absorption effects on the collected signal, hindered a clear interpretation. Aspects that require further investigation for a more comprehensive understanding are outlined.

Statistics of maximum photon penetration depth in a two-layer diffusive medium.

We present numerical results for the probability density function f(z) and for the mean value of photon maximum penetration depth zmax> in a two-layer diffusive medium. Both time domain and continuous wave regime are considered with several combinations of the optical properties (absorption coefficient, reduced scattering coefficient) of the two layers, and with different geometrical configurations (source detector distance, thickness of the upper layer). Practical considerations on the design of time domain and continuous wave systems are derived. The methods and the results are of interest for many research fields such as biomedical optics and advanced microscopy.

Recipes to make organic phantoms for diffusive optical spectroscopy.

Three recipes are presented to make tissue constituent-equivalent phantoms of water and lipids. Different approaches to prepare the emulsion are proposed. Nature phantoms are made using no emulsifying agent, but just a professional disperser; instead Agar and Triton phantoms are made using agar or Triton X-100, respectively, as agents to emulsify water and lipids. Different water-to-lipid ratios ranging from 30% to 70% by mass were tested. A broadband time-resolved diffuse optical spectroscopy system was used to characterize the phantoms in terms of optical properties and composition. For some water/lipid ratios the emulsion fails or the phantom has limited lifetime, but in most cases the recipes provide phantoms with a high degree of homogeneity [coefficient of variation (CV) of 4.6% and 1.5% for the absorption and reduced scattering coefficient, respectively] and good reproducibility (CV of 8.3% and 12.4% for absorption and reduced scattering coefficient, respectively).

Characterization of the Optical and Thermal Properties of Cardiac Tissue as a Function of Temperature.

In this work, we devised the first characterization of the optical and thermal properties of ex vivo cardiac tissue as a function of different selected temperatures, ranging from room temperature to hyperthermic and ablative temperatures. The broadband (i.e., from 650 nm to 1100 nm) estimation of the optical properties, i.e., absorption coefficient (µa) and reduced scattering coefficient $({\mu ^{\prime}}_s)$, was performed by means of time-domain diffuse optics. Besides, the measurement of the thermal properties was based on the transient hot-wire technique, employing a dual-needle probe to estimate the tissue thermal conductivity (k), thermal diffusivity (α), and volumetric heat capacity (Cv). Increasing the tissue temperature led to variations in the spectral characteristics of µa (e.g., the redshift of the 780 nm peak, the rise of a new peak at 840 nm, and the formation of a valley at 900 nm). Moreover, an increase in the values of ${\mu ^{\prime}}_s$ was assessed as tissue temperature raised (e.g., for 800 nm, at 25 °C ${\mu ^{\prime}}_s = 9.8{\text{ c}}{{\text{m}}^{{\text{ - 1}}}}$, while at 77 °C ${\mu ^{\prime}}_s = 29.1{\text{ c}}{{\text{m}}^{{\text{ - 1}}}}$). Concerning the thermal properties characterization, k was almost constant in the selected temperature interval. Conversely, α and Cv were subjected to an increase and a decrease with temperature, respectively; thus, they registered values of 0.190 mm2/s and 3.03 MJ/(m3•K) at the maximum investigated temperature (79 °C), accordingly.Clinical Relevance- The experimentally obtained optical and thermal properties of cardiac tissue are useful to improve the accuracy of simulation-based tools for thermal therapy planning. Furthermore, the measured properties can serve as a reference for the realization of tissue-mimicking phantoms for medical training and testing of medical instruments.

Interstitial null-distance time-domain diffuse optical spectroscopy using a superconducting nanowire detector.

Significance: Interstitial fiber-based spectroscopy is gaining interest for real-time in vivo optical biopsies, endoscopic interventions, and local monitoring of therapy. Different from other photonics approaches, time-domain diffuse optical spectroscopy (TD-DOS) can probe the tissue at a few cm distance from the fiber tip and disentangle absorption from the scattering properties. Nevertheless, the signal detected at a short distance from the source is strongly dominated by the photons arriving early at the detector, thus hampering the possibility of resolving late photons, which are rich in information about depth and absorption. Aim: To fully benefit from the null-distance approach, a detector with an extremely high dynamic range is required to effectively collect the late photons; the goal of our paper is to test its feasibility to perform TD-DOS measurements at null source-detector separations (NSDS). Approach: In particular, we demonstrate the use of a superconducting nanowire single photon detector (SNSPD) to perform TD-DOS at almost NSDS ( ≈ 150 µ m ) by exploiting the high dynamic range and temporal resolution of the SNSPD to extract late arriving, deep-traveling photons from the burst of early photons. Results: This approach was demonstrated both on Monte Carlo simulations and on phantom measurements, achieving an accuracy in the retrieval of the water spectrum of better than 15%, spanning almost two decades of absorption change in the 700- to 1100-nm range. Additionally, we show that, for interstitial measurements at null source-detector distance, the scattering coefficient has a negligible effect on late photons, easing the retrieval of the absorption coefficient. Conclusions: Utilizing the SNSPD, broadband TD-DOS measurements were performed to successfully retrieve the absorption spectra of the liquid phantoms. Although the SNSPD has certain drawbacks for use in a clinical system, it is an emerging field with research progressing rapidly, and this makes the SNSPD a viable option and a good solution for future research in needle guided time-domain interstitial fiber spectroscopy.

Fast time-domain diffuse correlation spectroscopy with superconducting nanowire single-photon detector: system validation and in vivo results.

Time-domain diffuse correlation spectroscopy (TD-DCS) has been introduced as an advancement of the "classical" continuous wave DCS (CW-DCS) allowing one to not only to measure depth-resolved blood flow index (BFI) but also to extract optical properties of the measured medium without using any additional diffuse optics technique. However, this method is a photon-starved technique, specially when considering only the late photons that are of primary interest which has limited its in vivo application. In this work, we present a TD-DCS system based on a superconducting nanowire single-photon detector (SNSPD) with a high quantum efficiency, a narrow timing response, and a negligibly low dark count noise. We compared it to the typically used single-photon avalanche diode (SPAD) detector. In addition, this system allowed us to conduct fast in vivo measurements and obtain gated pulsatile BFI on the adult human forehead.

Time domain diffuse Raman spectroscopy using single pixel detection.

Diffuse Raman spectroscopy (DIRS) extends the high chemical specificity of Raman scattering to in-depth investigation of thick biological tissues. We present here a novel approach for time-domain diffuse Raman spectroscopy (TD-DIRS) based on a single-pixel detector and a digital micromirror device (DMD) within an imaging spectrometer for wavelength encoding. This overcomes the intrinsic complexity and high cost of detection arrays with ps-resolving time capability. Unlike spatially offset Raman spectroscopy (SORS) or frequency offset Raman spectroscopy (FORS), TD-DIRS exploits the time-of-flight distribution of photons to probe the depth of the Raman signal at a single wavelength with a single source-detector separation. We validated the system using a bilayer tissue-bone mimicking phantom composed of a 1 cm thick slab of silicone overlaying a calcium carbonate specimen and demonstrated a high differentiation of the two Raman signals. We reconstructed the Raman spectra of the two layers, offering the potential for improved and quantitative material analysis. Using a bilayer phantom made of porcine muscle and calcium carbonate, we proved that our system can retrieve Raman peaks even in the presence of autofluorescence typical of biomedical tissues. Overall, our novel TD-DIRS setup proposes a cost-effective and high-performance approach for in-depth Raman spectroscopy in diffusive media.