Time-domain Raman analytical forward solvers

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.

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.

Shining Light on Osteoarthritis: Spatially Offset Raman Spectroscopy as a Window into Cartilage Health

Articular cartilage is a complex tissue, and early detection of osteoarthritis (OA) is crucial for effective treatment. However, current imaging modalities lack molecular specificity and primarily detect late-stage changes. In this study, we propose the use of Spatially Offset Raman Spectroscopy (SORS) for non-invasive, depth-dependent, and molecular-specific diagnostics of articular cartilage. We demonstrate the potential of SORS to penetrate deep layers of cartilage, providing a comprehensive understanding of disease progression. Our SORS measurements were characterized and validated through mechanical and histological techniques, revealing strong correlations between spectroscopic measurements and both Young's modulus and depth of cartilage damage. By longitudinally monitoring enzymatically degraded condyles, we further developed a depth-dependent damage-tracking method. Our analysis revealed distinct components related to sample depth and glycosaminoglycan (GAG) changes, offering a comprehensive picture of cartilage health. Collectively, these findings highlight the potential of SORS as a valuable tool for enhancing OA management and improving patient outcomes.

Spatially Offset Raman Spectroscopy-How Deep?

Spatially offset Raman spectroscopy (SORS) is a technique for interrogating the subsurface composition of turbid samples noninvasively. This study generically addresses a fundamental question relevant to a wide range of SORS studies, which is how deep SORS probes for any specific spatial offset when analyzing a turbid sample or, in turn, what magnitude of spatial offset one should select to probe a specific depth. This issue is addressed by using Monte Carlo simulations, under the assumption of negligible absorption, which establishes that the key parameter governing the extent of the probed zone for a point-like illumination and point-like collection SORS geometry is the reduced scattering coefficient of the medium. This can either be deduced from literature data or directly estimated from a SORS measurement by evaluating the Raman intensity profile from multiple spatial offsets. Once this is known, the extent of the probed zone can be determined for any specific SORS spatial offset using the Monte Carlo simulation results presented here. The proposed method was tested using experimental data on stratified samples by analyzing the signal detected from a thin layer that was moved through a stack of layers using both non-absorbing and absorbing samples. The proposed simple methodology provides important additional information on SORS measurements with direct relevance to a wide range of SORS applications including biomedical, pharmaceutical, security, forensics, and cultural heritage.

Determination of inclusion depth in ex vivo animal tissues using surface enhanced deep Raman spectroscopy

This work presents recent developments in spatially offset and transmission Raman spectroscopy for noninvasive detection and depth prediction of a single SERS inclusion located deep inside ex vivo biological tissues. The concept exploits the differential attenuation of Raman bands brought about by their different absorption due to tissue constituents enabling to predict the inclusion depth. Four different calibration models are tested and evaluated to predict the depth of surface enhanced Raman scattering labelled nanoparticles, within an up to 40 mm slab of porcine tissue. An external measurement carried out in transmission mode, with a noninvasively built model on the analysed sample, is shown to be insensitive to variations of the overall thickness of the tissue yielding an average root-mean-square error of prediction of 6.7%. The results pave the way for future noninvasive deep Raman spectroscopy in vivo enabling to localise cancer biomarkers for an early diagnosis of multiple diseases.

Spatially Offset and Transmission Raman Spectroscopy for Determination of Depth of Inclusion in Turbid Matrix

We propose an approach for the prediction of the depth of a single buried object within a turbid medium combining spatially offset Raman spectroscopy (SORS) and transmission Raman spectroscopy (TRS) and relying on differential attenuation of individual Raman bands brought about by the spectral variation of matrix absorption (and scattering). The relative degree of the Raman band changes is directly related to the path length of Raman photons traveling through the medium, thereby encoding the information on the depth of the object within the matrix. Through a calibration procedure with root mean square error of calibration (RMSEC) = 3.4%, it was possible to predict the depth of a paracetamol (acetaminophen) inclusion within a turbid matrix consisting of polyethylene (PE) by monitoring the relative intensity of two Raman bands of paracetamol exhibiting differential absorption by the matrix. The approach was shown to be largely insensitive to variations of the amount of the inclusion (paracetamol) and to the overall thickness of the turbid matrix (PE) with a root mean square error of prediction (RMSEP) maintained below 10% for the tested cases. This represents a major advantage over previously demonstrated comparable depth determination Raman approaches (with the exception of full Raman tomography requiring complex mathematical reconstruction algorithms). The obtained experimental data validate the proposed approach as an effective tool for the noninvasive determination of the depth of buried objects in turbid media with potential applications including determining noninvasively the depth of a lesion in cancer diagnosis in vivo.

Time domain diffuse Raman spectrometer based on a TCSPC camera for the depth analysis of diffusive media

We present a time domain diffuse Raman spectrometer for depth probing of highly scattering media. The system is based on, to the best of our knowledge, a novel time-correlated single-photon counting (TCSPC) camera that simultaneously acquires both spectral and temporal information of Raman photons. A dedicated non-contact probe was built, and time domain Raman measurements were performed on a tissue mimicking bilayer phantom. The fluorescence contamination of the Raman signal was eliminated by early time gating (0-212 ps) the Raman photons. Depth sensitivity is achieved by time gating Raman photons at different delays with a gate width of 106 ps. Importantly, the time domain can provide time-dependent depth sensitivity leading to a high contrast between two layers of Raman signal. As a result, an enhancement factor of 2170 was found for our bilayer phantom which is much higher than the values obtained by spatial offset Raman spectroscopy (SORS), frequency offset Raman spectroscopy (FORS), or hybrid FORS-SORS on a similar phantom.

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.