Efficient computation of the steady-state and time-domain solutions of the photon diffusion equation in layered turbid media.

Accurate and efficient forward models of photon migration in heterogeneous geometries are important for many applications of light in medicine because many biological tissues exhibit a layered structure of independent optical properties and thickness. However, closed form analytical solutions are not readily available for layered tissue-models, and often are modeled using computationally expensive numerical techniques or theoretical approximations that limit accuracy and real-time analysis. Here, we develop an open-source accurate, efficient, and stable numerical routine to solve the diffusion equation in the steady-state and time-domain for a layered cylinder tissue model with an arbitrary number of layers and specified thickness and optical coefficients. We show that the steady-state ([Formula: see text] ms) and time-domain ([Formula: see text] ms) fluence (for an 8-layer medium) can be calculated with absolute numerical errors approaching machine precision. The numerical implementation increased computation speed by 3 to 4 orders of magnitude compared to previously reported theoretical solutions in layered media. We verify our solutions asymptotically to homogeneous tissue geometries using closed form analytical solutions to assess convergence and numerical accuracy. Approximate solutions to compute the reflected intensity are presented which can decrease the computation time by an additional 2-3 orders of magnitude. We also compare our solutions for 2, 3, and 5 layered media to gold-standard Monte Carlo simulations in layered tissue models of high interest in biomedical optics (e.g. skin/fat/muscle and brain). The presented routine could enable more robust real-time data analysis tools in heterogeneous tissues that are important in many clinical applications such as functional brain imaging and diffuse optical spectroscopy.

Noninvasive Optical Assessment of Implanted Tissue-Engineered Construct Success In Situ.

Quantitative diffuse reflectance spectroscopy (DRS) was developed for label-free, noninvasive, and real-time assessment of implanted tissue-engineered devices manufactured from primary human oral keratinocytes (six batches in two 5-patient cohorts). Constructs were implanted in a murine model for 1 and 3 weeks. DRS evaluated construct success in situ using optical absorption (hemoglobin concentration and oxygenation, attributed to revascularization) and optical scattering (attributed to cellular density and layer thickness). Destructive pre- and postimplantation histology distinguished experimental control from stressed constructs, whereas noninvasive preimplantation measures of keratinocyte glucose consumption and residual glucose in spent culture media did not. In constructs implanted for 1 week, DRS distinguished control due to stressed and compromised from healthy constructs. In constructs implanted for 3 weeks, DRS identified constructs with higher postimplantation success. These results suggest that quantitative DRS is a promising, clinically compatible technology for rapid, noninvasive, and localized tissue assessment to characterize tissue-engineered construct success in vivo. Impact statement Despite the recent advance in tissue engineering and regenerative medicine, there is still a lack of nondestructive tools to longitudinally monitor the implanted tissue-engineered devices. In this study, we demonstrate the potential of quantitative diffuse reflectance spectroscopy as a clinically viable technique for noninvasive, label-free, and rapid characterization of graft success in situ.

Direct estimation of the reduced scattering coefficient from experimentally measured time-resolved reflectance via Monte Carlo based lookup tables.

A heuristic method for estimating the reduced scattering coefficient (µs') of turbid media using time-resolved reflectance is presented. The technique requires measurements of the distributions of times-of-flight (DTOF) of photons arriving at two identical detection channels placed at unique distances relative to a source. Measured temporal shifts in DTOF peak intensities at the two channels were used to estimate µs' of the medium using Monte Carlo (MC) simulation-based lookup tables. MC simulations were used to compute temporal shifts in modeled reflectance at experimentally employed source-detector separations (SDS) for media spanning a wide range of optical properties to construct look up tables. Experiments in Intralipid (IL) phantoms demonstrated that we could retrieve µs' with errors ranging between 6-25% of expected (literature) values, using reflectance measured across 650-800 nm and SDS of 5-15 mm. Advantages of the technique include direct processing of measured data without requiring iterative non-linear curve fitting. We also discuss applicability of this approach for media with low scattering coefficients where the commonly employed diffusion theory analysis could be inaccurate, with practical recommendations for use.

Hybrid Monte Carlo simulation with ray tracing for fluorescence measurements in turbid media.

We present a hybrid Monte Carlo simulation method with geometrical ray tracing (hMC-GRT) to model fluorescence excitation and detection in turbid media by optical imaging or spectroscopy systems employing a variety of optical components. hMC-GRT computational verification was achieved via reflectance and fluorescence simulations on epithelial tissue models in comparison with a standard Monte Carlo code. The mean difference between the two simulations was less than 5%. hMC-GRT experimental verification employed depth-sensitive steady-state fluorescence measurements using an aspherical lens on two-layered tissue phantoms. hMC-GRT predictions agreed well with experimental results, achieving less than 3.5% error for measurements at the phantom surface. Verification results demonstrate that the hMC-GRT simulation has the potential to become a useful computational toolbox for designing tissue fluorescence imaging and spectroscopy systems. In addition, the hMC-GRT approach enables a wide variety of applications for computational modeling of fluorescence in turbid media. The source codes are available at https://github.com/ubioptronics/hMC-GRT.

Noninvasive Optical Assessment of Implanted Engineered Tissues Correlates with Cytokine Secretion.

Fluorescence lifetime sensing has been shown to noninvasively characterize the preimplantation health and viability of engineered tissue constructs. However, current practices to monitor postimplantation construct integration are either qualitative (visual assessment) or destructive (tissue histology). We employed label-free fluorescence lifetime spectroscopy for quantitative, noninvasive optical assessment of engineered tissue constructs that were implanted into a murine model. The portable system was designed to be suitable for intravital measurements and included a handheld probe to precisely and rapidly acquire data at multiple sites per construct. Our model tissue constructs were manufactured from primary human cells to simulate patient variability based on a standard protocol, and half of the manufactured constructs were stressed to create a range of health states. Secreted amounts of three cytokines that relate to cellular viability were measured in vitro to assess preimplantation construct health: interleukin-8 (IL-8), human ß-defensin 1 (hBD-1), and vascular endothelial growth factor (VEGF). Preimplantation cytokine secretion ranged from 1.5 to 33.5 pg/mL for IL-8, from 3.4 to 195.0 pg/mL for hBD-1, and from 0.1 to 154.3 pg/mL for VEGF. In vivo optical sensing assessed constructs at 1 and 3 weeks postimplantation. We found that at 1 week postimplantation, in vivo optical parameters correlated with in vitro preimplantation secretion levels of all three cytokines (p < 0.05). This correlation was not observed in optical measurements at 3 weeks postimplantation when histology showed that the constructs had re-epithelialized, independent of preimplantation health state, supporting the lack of a correlation. These results suggest that clinical optical diagnostic tools based on label-free fluorescence lifetime sensing of endogenous tissue fluorophores could noninvasively monitor postimplantation integration of engineered tissues.

Development of a spatially offset Raman spectroscopy probe for breast tumor surgical margin evaluation.

The risk of local recurrence for breast cancers is strongly correlated with the presence of a tumor within 1 to 2 mm of the surgical margin on the excised specimen. Previous experimental and theoretical results suggest that spatially offset Raman spectroscopy (SORS) holds much promise for intraoperative margin analysis. Based on simulation predictions for signal-to-noise ratio differences among varying spatial offsets, a SORS probe with multiple source-detector offsets was designed and tested. It was then employed to acquire spectra from 35 frozen-thawed breast tissue samples in vitro. Spectra from each detector ring were averaged to create a composite spectrum with biochemical information covering the entire range from the tissue surface to ∼2 mm below the surface, and a probabilistic classification scheme was used to classify these composite spectra as "negative" or "positive" margins. This discrimination was performed with 95% sensitivity and 100% specificity, or with 100% positive predictive value and 94% negative predictive value.

Monte Carlo model of spatially offset Raman spectroscopy for breast tumor margin analysis.

We have previously demonstrated the discrimination of two layers of soft tissue, specifically normal breast tissue overlying breast tumor, using spatially offset Raman spectroscopy (SORS). In this report, a Monte Carlo code for evaluating SORS in soft tissues has been developed and compared to experimental results. The model was employed to investigate the effects of tissue and probe geometry on SORS measurements and therefore to develop the design strategies of applying SORS for breast tumor surgical margin evaluation. The model was used to predict SORS signals for different tissue geometries difficult to precisely control experimentally, such as varying normal and tumor layer sizes and the addition of a third layer. The results from the model suggest that, using source-detector separations of up to 3.75 mm, SORS can detect sub-millimeter-thick tumors under a 1 mm normal layer, and tumors at least 1 mm thick can be detected under a 2 mm normal layer.

Do fluorescence decays remitted from tissues accurately reflect intrinsic fluorophore lifetimes?

Fluorescence spectroscopy and imaging methods, including fluorescence lifetime sensing, are being developed for noninvasive tissue diagnostics. The purpose of this study was to identify and quantify those factors affecting the accurate recovery of fluorophore lifetimes from inhomogeneous tissues in vivo. A Monte Carlo code was developed to numerically simulate time-resolved fluorescence measurements on layered epithelial tissues. Simulations were run with experimental parameters matching previously reported clinical studies in the gastrointestinal tract. The results demonstrate that variations in fluorescence decay time as large as those detected clinically between normal and premalignant tissues (approximately 2 ns) could be simulated by variations in tissue morphology or biochemistry, even when intrinsic fluorophore lifetimes were held constant.

Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods.

A Monte Carlo model developed to simulate time-resolved fluorescence propagation in a semi-infinite turbid medium was validated against previously reported theoretical and computational results. Model simulations were compared to experimental measurements of fluorescence spectra and lifetimes on tissue-simulating phantoms for single and dual fibre-optic probe geometries. Experiments and simulations using a single probe revealed that scattering-induced artefacts appeared in fluorescence emission spectra, while fluorescence lifetimes were unchanged. Although fluorescence lifetime measurements are generally more robust to scattering artefacts than are measurements of fluorescence spectra, in the dual-probe geometry scattering-induced changes in apparent lifetime were predicted both from diffusion theory and via Monte Carlo simulation, as well as measured experimentally. In all cases, the recovered apparent lifetime increased with increasing scattering and increasing source-detector separation. Diffusion theory consistently underestimated the magnitude of these increases in apparent lifetime (predicting a maximum increase of approximately 15%), while Monte Carlo simulations and experiment were closely matched (showing increases as large as 30%). These results indicate that quantitative simulations of time-resolved fluorescence propagation in turbid media will be important for accurate recovery of fluorophore lifetimes in biological spectroscopy and imaging applications.