Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry

Photodynamic Actinometry Using Microspheres: Concept, Development and Responsivity¶

Photodynamic therapy (PDT) relies on three main ingredients, oxygen, light and photoactivating compounds, although the PDT response is definitively contingent on the site and level of reactive oxygen species (ROS) generation. This study describes the development of a novel, fluorescent-based actinometer microsphere system as a means of discerning spatially resolved dosimetry of total fluence and ROS production. Providing a high resolution, localized, in situ measurement of fluence and ROS generation is critical for developing in vivo PDT protocols. Alginate-poly-L-lysine-alginate microspheres were produced using ionotropic gelation of sodium alginate droplets, ranging from 80 to 200 microm in diameter, incorporating two dyes, ADS680WS (ADS) and Rhodophyta-phycoerythrin (RPE), attached to the spheres' inside and outside layers, respectively. To test the responsivity and dynamic range of RPE for ROS detection, the production of ROS was initiated either chemically using increasing concentrations of potassium perchromate or photochemically using aluminum tetrasulphonated phthalocyanine. The generation of singlet oxygen was confirmed by phosphorescence at 1270 nm. The resulting photodegradation and decrease in fluorescence of RPE was found to correlate with increased perchromate or PDT treatment fluence, respectively. This effect was independent of pH (6.5-8) and could be inhibited using sodium azide. RPE was not susceptible to photobleaching with light alone (670 nm; 150 Jcm(-2)). ADS, which absorbs light between 600 and 750 nm, showed a direct correlation between radiant exposure (670 nm; 0-100 Jcm(-2)) and diminished fluorescence. Photobleaching was independent of irradiance (10-40 mW cm(-2)). We propose that actinometer microspheres may provide a means for obtaining high spatial resolution information regarding delivered PDT dose within model systems during investigational PDT development and dosimetric information for clinical extracorporeal PDT as in the case of ex vivo bone marrow purging.

Determination of the optical properties of a two-layer tissue model by detecting photons migrating at progressively increasing depths

We have investigated a method for solving the inverse problem of determining the optical properties of a two-layer turbid model. The method is based on deducing the optical properties (OPs) of the top layer from the absolute spatially resolved reflectance that results from photon migration within only the top layer by use of a multivariate calibration model. Then the OPs of the bottom layer are deduced from relative frequency-domain (FD) reflectance measurements by use of the two-layer FD diffusion model. The method was validated with Monte Carlo FD reflectance profiles and experimental measurements of two-layer phantoms. The results showed that the method is useful for two-layer models with interface depths of >5 mm; the OPs were estimated, within a relatively short time (<1 min), with a mean error of <10% for the Monte Carlo reflectance profiles and with errors of <25% for the phantom measurements.

Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method

An exact solution of the time-dependent diffusion equation for the case of a two- and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.

Characterization of dysplastic tissue morphology and biochemistry in Barrett's esophagus using diffuse reflectance and light scattering spectroscopy

LSS and DRS are techniques that provide diagnostically useful information based on changes in the intensity of backscattered light that has experienced either a single or multiple scattering events. These changes can be detected effectively using statistical and model-based algorithms. In addition to providing a means to detect the presence of dysplasia noninvasively, the latter approach yields potentially significant insights into the processes that are involved in the development of dysplasia in BE. Because DRS and LSS provide complementary information to each other and to other spectroscopic modalities, such as fluorescence, it is possible that a combination of all these techniques will ultimately provide a highly accurate real-time method for detecting BE dysplasia. Extending point spectroscopic measurements to imaging of the esophagus will be challenging, but continuous progess in the development of powerful light sources, sensitive detectors, and micro-optical elements should allow this method to become a reality in the near future.

In vivo absorption and scattering spectroscopy of biological tissues

Different approaches for absorption and scattering spectroscopy of living tissues are discussed. In particular, a unique system for time-resolved reflectance and transmittance spectroscopy is presented, capable of acquiring in vivo absorption and scattering spectra of diffusive media between 600 and 1000 nm. A review of typical spectra obtained from a variety of tissue structures is shown, including female breast, forearm, abdomen, and forehead. A second-level analysis of the measured spectra permits an estimation of the concentrations of the key tissue absorbers, as well as of the Mie-equivalent scattering radii. Further, absorption and scattering spectra can be used to estimate the penetration depth of light in tissues as a function of wavelength, which is a crucial parameter in view of the possible application of optical in vivo molecular imaging in clinical diagnosis. Finally, an example of the applicability of the methodology to other biological media such as fruits and vegetables is shown.

Congruent MRI and near-infrared spectroscopy for functional and structural imaging of tumors

We present a combined near-infrared diffuse optical spectroscopy (DOS) and Magnetic Resonance Imaging (MRI) system for the study of animal model tumors. A combined broadband steady-state and frequency domain optical spectroscopy apparatus was integrated with the MRI. The physiological properties of tissue rendered by MRI, including vascular volume fraction and water, were compared with chromophore concentrations as determined from the parameters obtained by optical measurements. DOS measurements provided oxy-hemoglobin, deoxy-hemoglobin, and water concentration locally in tumors. A method for co-registration of the information obtained by both modalities was developed. Using Monte Carlo simulations, the optically sampled volume was superimposed on the MR images, illustrating which tissue structure was probed optically. Finally, two optical contrast agents, indocyanine green (ICG) and methylene blue (MB), were employed and their kinetics were measured by DOS system from different locations on the tumor and compared with Gd-DTPA enhancement maps obtained from MRI.

Analysis of the spatial distribution of polarized light backscattered from layered scattering media

The scattering of polarized light from a two layer scattering medium is investigated using Monte Carlo simulations. First order and normalized second order moments are used to analyze the spatial properties of the emerging light in different polarization states. Linearly and circularly polarized illumination is used to probe different depths. Absorption and layer thickness are varied and it is demonstrated that the determination of these values is aided by the inclusion of polarization information. The lateral and depth localization of light by polarization subtraction is also quantified. Potential applications of these techniques are burn depth and melanoma thickness measurements.

Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness

A dual wavelength time-resolved reflectance system was developed for monitoring haemoglobin saturation noninvasively. At each wavelength, the time-resolved reflectance data were fitted to a diffusion model of light propagation in a homogeneous, semi-infinite medium to yield the absolute scattering and absorption coefficients. The absorption coefficients were then used to calculate haemoglobin saturation. A two-layer phantom containing human erythrocytes in a scattering solution in the bottom layer was used to study system performance under more realistic conditions. The top layer was chosen to simulate either skin or fat and the oxygenation of the bottom layer, which corresponded to muscle, was controlled. The thickness of the fat layer was varied from 1.5 to 10 mm to investigate the effects of increasing the top layer thickness. These results, obtained with the simple diffusion model, were compared with simultaneous measurements of oxygenation made directly in the bottom layer. Errors in estimating haemoglobin saturation with this method ranged from 5-11% depending on the thickness of the top layer and its optical properties.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid monte carlo diffusion model

The general two-layer inverse problem in biomedical photon migration is to estimate the absorption and scattering coefficients of each layer as well as the top-layer thickness. We attempted to solve this problem, using experimental and simulated spatially resolved frequency-domain (FD) reflectance for optical properties typical of skin overlying muscle or skin overlying fat in the near infrared. Two forward models of light propagation were used: a two-layer diffusion solution [Appl. Opt. 37, 779 (1998)] and a hybrid Monte Carlo (MC) diffusion model [Appl. Opt. 37, 7401 (1998)]. MC-simulated FD reflectance data were fitted as relative measurements to the hybrid and the pure diffusion models. It was found that the hybrid model could determine all the optical properties of the two-layer media studied to ~5%. Also, the same accuracy could be achieved by means of fitting MC-simulated cw reflectance data as absolute measurements, but fitting them as relative ones is an ill-posed problem. In contrast, two-layer diffusion could not retrieve the top-layer optical properties as accurately for FD data and was ill-posed for both relative and absolute cw data. The hybrid and the pure diffusion models were also fitted to experimental FD reflectance measurements from two-layer tissue-simulating phantoms representative of skin-on-fat and skin-on-muscle baseline optical properties. Both the hybrid and the diffusion models could determine the optical properties of the lower layer. The hybrid model demonstrated its potential to retrieve quantitatively the transport scattering coefficient of skin (the upper layer), which was not possible with the pure diffusion model. Systematic discrepancies between model and experiment may compromise the accuracy of the deduced top-layer optical properties. Identifying and eliminating such discrepancies is critical to practical application of the method.

Recovery of optical parameters in multiple-layered diffusive media: theory and experiments

Diffuse photon density waves have lately been used both to characterize diffusive media and to locate and characterize hidden objects, such as tumors, in soft tissue. In practice, most biological media of medical interest consist of various layers with different optical properties, such as the fat layer in the breast or the different layers present in the skin. Also, most experimental setups consist of a multilayered system, where the medium to be characterized (i.e., the patient's organ) is usually bounded by optically diffusive plates. Incorrect modeling of interfaces may induce errors comparable to the weak signals obtained from tumors embedded deep in highly heterogeneous tissue and lead to significant reconstruction artifacts. To provide a means to analyze the data acquired in these configurations, the basic expressions for the reflection and transmission coefficients for diffusive-diffusive and diffusive-nondiffusive interfaces are presented. A comparison is made between a diffusive slab and an ordinary dielectric slab, thus establishing the limiting distance between the two interfaces of the slab for multiple reflections between them to be considered important. A rigorous formulation for multiple-layered (M-layered) diffusive media is put forward, and a method for solving any M-layered medium is shown. The theory presented is used to characterize a two-layered medium from transmission measurements, showing that the coefficients of scattering, mu'(s) , and absorption, mu(a) , are retrieved with great accuracy. Finally, we demonstrate the simultaneous retrieval of both mu;(s) and mu(a).

Corrections for inhomogeneities in biological tissue caused by blood vessels

In tissue optics, the assumption that blood is homogeneously distributed in tissue can give rise to miscalculations because blood is found only in blood vessels. In our paper randomly oriented blood vessels are treated as particles for which we obtained apparent absorption and scattering coefficients by means of the Monte Carlo method. Apart from this correction for the contribution of blood properties in tissue, a correction for the contribution of the surrounding tissue proved to be needed as well. The results found with our model were compared with available results from the literature.

Determining changes in NIR absorption using a layered model of the human head

A theoretical approach is presented to determine absorption changes in different compartments of a layered structure from distributions of times of flight of photons. In addition resulting changes in spatial profiles of time-integrated intensity and mean time of flight are calculated. The capability of a single-distance, time-domain method to determine absorption changes with depth resolution is tested on a layered phantom. We apply this method to in vivo measurements on the human head (motor stimulation, Valsalva manoeuvre) and introduce a small-sized time-domain experimental set-up suitable for bedside monitoring.

A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations

A photon diffusion model has been developed to calculate the steady-state spatially resolved fluorescence from pencil beam excitation in layered tissue. The model allows the calculation of both the excitation reflectance and the fluorescence escape for an arbitrary continuous depth distribution of tissue optical properties and fluorophore concentration. The validity of this model was verified by comparison with Monte Carlo simulations and experimental measurements using phantoms with tissue-like optical properties. The potential usefulness of the spatially resolved fluorescence was explored using the model and simulations of realistic drug distributions. It was shown that using this technique it may be possible to quantify the diffusion of a topically administered drug into the skin, or the photobleaching of a sensitizer during photodynamic therapy.

Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media

We have derived the space-time Green's function for the diffusion equation in layered turbid media, starting from the case of a planar interface between two random scattering media. This new approach for working directly in real space permits highly efficient numerical processing, which is a decisive criterion for the feasibility of the inverse problem in biomedical optics. The results obtained by this method in the case of a two-layered medium are compared with Monte Carlo simulations.

Anisotropy of light propagation in human skin

Using spatially resolved, steady state diffuse reflectometry, a directional dependence was found in the propagation of visible and near infrared light through human skin in vivo. The skin's reduced scattering coefficient mu(s)' varies by up to a factor of two between different directions of propagation at the same position. This anisotropy is believed to be caused by the preferential orientation of collagen fibres in the dermis, as described by Langer's skin tension lines. Monte Carlo simulations that examine the effect of partial collagen fibre orientation support this hypothesis. The observation has consequences for non-invasive diagnostic methods relying on skin optical properties, and it could be used non-invasively to determine the direction of lines of cleavage in order to minimize scars due to surgical incisions.

Monte carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain

We propose a hybrid Monte Carlo (MC) diffusion model for calculating the spatially resolved reflectance amplitude and phase delay resulting from an intensity-modulated pencil beam vertically incident on a two-layer turbid medium. The model combines the accuracy of MC at radial distances near the incident beam with the computational efficiency afforded by a diffusion calculation at further distances. This results in a single forward calculation several hundred times faster than pure MC, depending primarily on model parameters. Model predictions are compared with MC data for two cases that span the extremes of physiologically relevant optical properties: skin overlying fat and skin overlying muscle, both in the presence of an exogenous absorber. It is shown that good agreement can be achieved for radial distances from 0.5 to 20 mm in both cases. However, in the skin-on-muscle case the choice of model parameters and the definition of the diffusion coefficient can lead to some interesting discrepancies.

In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model

We have investigated the possibility of determining the optical coefficients of muscle in the extremities with in vivo time-resolved reflectance measurements using a layered model. A solution of the diffusion equation for two layers was fitted to three-layered Monte Carlo calculations simulating the skin, the subcutaneous fat and the muscle. Relative time-resolved reflectance data at two distances were used to derive the optical coefficients of the layers. We found for skin and subcutaneous fat layer thicknesses (l2) of up to 10 mm that the estimated absorption coefficients of the second layer of the diffusion model have differences of less than 20% compared with those of the muscle layer of the Monte Carlo simulations if the thickness of the first layer of the diffusion model is also fitted. If l2 is known, the differences are less than 5%, whereas the use of a semi-infinite model delivers differences of up to 55%. Even if l2 is only approximately known the absorption coefficient of the muscle can be determined accurately. Experimentally, the time-resolved reflectance was measured on the forearms of volunteers at two distances from the incident beam by means of a streak camera. The thicknesses of the tissues involved were determined by ultrasound. The optical coefficients were derived from these measurements by applying the two-layered diffusion model, and results in accordance with the theoretical studies were observed.

Experimental tests of different solutions to the diffusion equation for optical characterization of scattering media by time-resolved transmittance

A detailed investigation of the use of time-resolved trasmittance for the optical characterization of scattering media by use of different analytical solutions to the diffusion equation has been performed. A femtosecond Ti:sapphire laser working at 800 nm and a streak camera with a time resolution of a few picoseconds were employed. Different latex and Intralipid solutions as well as biological samples were investigated. Reduced scattering coefficients were evaluated, and good agreement with the Mie predictions was found. An estimation of the order of magnitude of the absorption coefficient was obtained for the low-absorbance samples examined. These studies confirm experimentally that time-resolved trasmittance can be employed usefully for evaluating s values of thick scattering samples when a proper theoretical description that takes into account realistic boundary conditions is used.

Influence of a superficial layer in the quantitative spectroscopic study of strongly scattering media

We have experimentally investigated the meaning of the effective optical absorption [mu(a)((eff))] and the reduced scattering [mu(s)?((eff))] coefficients measured on the surfaces of two-layered turbid media, using the diffusion equation for homogeneous, semi-infinite media. We performed frequency-domain spectroscopy in a reflectance geometry, using source-detector distances in the range 1.5-4.5 cm. We measured 100 samples, each made of one layer (thickness in the range 0.08-1.6 cm) on top of one semi-infinite block. The optical properties of the samples were similar to those of soft tissues in the near infrared. We found that the measured effective optical coefficients are representative of the underlying block if the superficial layer is less than ~0.4 cm thick, whereas they are representative of the superficial layer if it is more than ~1.3 cm thick.

Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium

We have examined the possibility of determining the optical properties of a two-layer medium by using a diffusion approximation radiation transport model [Appl. Opt. 37, 779 (1998)]. Continuous-wave and frequency-domain (FD) low-noise Monte Carlo (MC) data were fitted to the model. Marquardt-Levenberg and a simulated annealing algorithm were used and compared as optimization techniques. Our particular choice of optical properties for the two-layer model was consistent with skin and underlying fat in the presence of an exogenous chromophore [Appl. Opt. 37, 1958 (1998)]. The results are therefore specific to this set of optical properties. It was found that the cw diffusion solution could never be used to estimate all optical properties reliably. The combined cw and FD solutions could not be used to estimate some of the top-layer optical properties to an accuracy of better than 10%, although the absorption and the transport scattering coefficients of the bottom layer could be estimated to within 7% and 0.5%, respectively. No improvement was found from simultaneously fitting MC data at three different modulation frequencies. These results point to the need for a more accurate radiation transfer model at small source-detector separations.

Investigation of two-layered turbid media with time-resolved reflectance

Light propagation in two-layered turbid media that have an infinitely thick second layer is investigated with time-resolved reflectance. We used a solution of the diffusion equation for this geometry to show that it is possible to derive the absorption and the reduced scattering coefficients of both layers if the relative reflectance is measured in the time domain at two distances and if the thickness of the first layer is known. Solutions of the diffusion equation for semi-infinite and homogeneous turbid media are also applied to fit the reflectance from the two-layered turbid media in the time and the frequency domains. It is found that the absorption coefficient of the second layer can be more precisely derived for matched than for mismatched boundary conditions. In the frequency domain, its determination is further improved if phase and modulation data are used instead of phase and steady-state reflectance data. Measurements of the time-resolved reflectance were performed on solid two-layered tissue phantoms that confirmed the theoretical results.