Proceedings Volume 5859

Photon Migration and Diffuse-Light Imaging II

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Proceedings Volume 5859

Photon Migration and Diffuse-Light Imaging II

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Volume Details

Date Published: 25 August 2005
Contents: 7 Sessions, 34 Papers, 0 Presentations
Conference: European Conferences on Biomedical Optics 2005 2005
Volume Number: 5859

Table of Contents

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Table of Contents

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  • New Technologies
  • Poster Session
  • Functional Optical Imaging of the Brain I
  • Functional Characertization and Monitoring of Malignant and Normal Tissues
  • Functional Optical Imaging of the Brain II
  • Diffuse Spectroscopy and Fluorescence Tomography
  • Photon Migration Theory
  • Poster Session
New Technologies
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Fluorescence spectroscopy in tissue phantoms for improved depth resolution in tissue imaging
A way to determine the depth of an embedded fluorescent object, for example deep-lying tumors marked with a fluorescent probe, is to detect fluorescent light that has propagated through the medium at two different wavelength bands. A ratio can then be calculated between the corresponding intensities. The wavelength regions should be chosen such that there is a difference in the absorption in the medium. This spectral information could be used as a complement in other methods, for example in tomography, due to its straightforward implementation. In this study we have performed phantom measurements to determine the depth of a fluorescent object, filled with fluorophores. The transmission of yellow and red fluorescence was measured and a ratio of yellow to red fluorescence was calculated for several depths in tissue with a thickness of 2 cm. The ratio showed a clear dependence on the depth of the object.
Measurement of intracellular oxygen levels using fluorescence lifetime imaging microscopy (FLIM)
Dhruv Sud, Wei Zhong, David Beer, et al.
Intracellular oxygen levels were measured in vivo under physiological-temperature controlled conditions by monitoring the fluorescence lifetime of the oxygen sensitive dye ruthenium tris(2,2'-dipyridyl) dichloride hexahydrate (RTDP). We employed fluorescence lifetime imaging microscopy (FLIM) and an independent oxygen sensor to calibrate changes in RTDP lifetime with corresponding changes in oxygen level. The FLIM method reproducibly quantified oxygen levels in living human cells cultured from a (Barrett's) adenocarcinoma columnar cell line (SEG-1). Approaches such as those developed here should prove useful for studying oxygen gradients in 3-D biological specimens and for monitoring cellular metabolic status.
TIR fluorescence reader for selective detection of cell membranes
Thomas Bruns, Wolfgang S. L. Strauss, Reinhard Sailer, et al.
A novel setup for fluorescence measurements of surfaces of biological samples, in particular cell membranes, is described. The method is based on multiple total internal reflections (TIR) of a laser beam at the surface of a multi-well plate, such that 96 individual samples are excited simultaneously. Main prerequisites are an appropriate thickness and high transmission of the glass bottom, a non-cytotoxic adhesive, and appropriate glass rods for TIR illumination. Fluorescence from the cell surface is detected simultaneously using an integrating CCD camera and appropriate optical filters. For validation of the system, cells incubated with the fluorescence marker NBD as well as transfected cells expressing a fluorescent membrane protein are used. In addition, intracellular translocation of a fluorescent protein kinase c fusion protein upon stimulation is examined. The method appears well suitable for high throughput screening (HTS), since neither washing of the samples nor any readjustment of the equipment after changing of individual plates are necessary.
In vitro characterization of gap junctional intercellular communication by gap-FRAP technique
M. Abbaci, J.-R. Stines, M. Barberi-Heyob, et al.
Gap junctional intercellular communication (GJIC) has been shown to be involved in the carcinogenesis process. Gap-FRAP (Fluorescence Recovery After Photobleaching) technique could be used to estimate gap junctions functionality and their potential involvement for distinguish normal and cancer cells. In this study, the gap-FRAP technique was used to analyse functional gap-junction-mediated communication for cell lines with different GJIC status. Gap-FRAP data and connexin 43 protein expression decreased for FaDu cancer cell line, in contrast to fibroblast and KB positives cell lines. To check the involvement and functionality of gap junctions in the restitution of the fluorescence after photobleaching, we used a gap junction channel inhibition assay with 18 α-glycyrrhetinic acid. Our results indicate that the degree of gap junctional intercellular communication could be estimated by this technique in vitro.
Interferometric tracking of two particles with dynamic optical traps
Dirk Neumayer, Peter Kaiser, Ernst H.K. Stelzer, et al.
Optical potential landscapes for diffusing particles can be generated by time-multiplexing (scanning) an optical trap and additionally modulating the trapping laser power. We show that it is possible to determine the lateral and axial positions of several particles in parallel with some 10 nm precision and at kHz rates by using dynamic back focal plane interferometry. This allows measuring the interaction of diffusing, (non-) functionalized particles in a confined volume. The scan frequency of the optical trap can be optimized for interaction measurements with high dynamic or temporal resolution, given a data sampling frequency of 1MHz.
Poster Session
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In vivo macroscopic HPD fluorescence reflectance imaging on small animals bearing surface ARO/NPA tumor
Maddalena Autiero, Luigi Celentano, Paolo Laccetti, et al.
Recently multimodal imaging systems have been devised because the combination of different imaging modalities results in the complementarity and integration of the techniques and in a consequent improvement of the diagnostic capabilities of the multimodal system with respect to each separate imaging modality. We developed a simple and reliable HematoPorphyrin (HP) mediated Fluorescence Reflectance Imaging (FRI) system that allows for in vivo real time imaging of surface tumors with a large field of view. The tumor cells are anaplastic human thyroid carcinoma-derived ARO cells, or human papillary thyroid carcinoma-derived NPA cells. Our measurements show that the optical contrast of the tumor region image is increased by a simple digital subtraction of the background fluorescence and that HP fluorescence emissivity of ARO tumors is about 2 times greater than that of NPA tumors, and about 4 times greater than that of healthy tissues. This is also confirmed by spectroscopic measurements on histological sections of tumor and healthy tissues. It was shown also the capability of this system to distinguish the tumor type on the basis of the different intensity of the fluorescence emission, probably related to the malignancy degree. The features of this system are complementary with those ones of a pixel radionuclide detection system, which allows for relatively time expensive, narrow field of view measurements, and applicability to tumors also deeply imbedded in tissues. The fluorescence detection could be used as a large scale and quick analysis tool and could be followed by narrow field, higher resolution radionuclide measurements on previously determined highly fluorescent regions.
Functional Optical Imaging of the Brain I
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3D optical tomography of the neonatal brain
A. P. Gibson, T. Austin, N. Everdell, et al.
Optical tomography is a medical imaging technique which can provide images of haemodynamic parameters and oxygenation at the bedside. Here, we examine two approaches to optical tomography which are intended to provide information about perinatal brain injury. First, we reconstruct static 3D images showing the increase in blood volume and decrease in oxygenation associated with intra-ventricular haemorrhage. Second, we present the first 3D optical tomography images of the whole head during motor evoked responses and show that the peak of activation can be localised to within 11 mm of the estimated position of the motor cortex.
System for the measurement of blood flow and oxygenation in tissue applied to neurovascular coupling in brain
Matthias Kohl-Bareis, Christoph Leithner, Heike Sellien, et al.
We designed a system incorporating the independent measurement of blood flow and oxygenation of haemoglobin. This is based on laser-Doppler spectroscopy with NIR wavelengths which gives a measure for changes in blood flow or tissue perfusion as well as reflectance spectroscopy in the VIS wavelength range for the calculation of the oxygenated and deoxygenated haemoglobin components. The co-registration of these parameters allows the neurovascular coupling of brain to be investigated. This is demonstrated by recording functional activity of the rat brain during electrical forepaw stimulation.
Improvements in brain activation detection using time-resolved diffuse optical means
Bruno Montcel, Renee Chabrier, Patrick Poulet
An experimental method based on time-resolved absorbance difference is described. The absorbance difference is calculated over each temporal step of the optical signal with the time-resolved Beer-Lambert law. Finite element simulations show that each step corresponds to a different scanned zone and that cerebral contribution increases with the arrival time of photons. Experiments are conducted at 690 and 830 nm with a time-resolved system consisting of picosecond laser diodes, micro-channel plate photo-multiplier tube and photon counting modules. The hemodynamic response to a short finger tapping stimulus is measured over the motor cortex. Time-resolved absorbance difference maps show that variations in the optical signals are not localized in superficial regions of the head, which testify for their cerebral origin. Furthermore improvements in the detection of cerebral activation is achieved through the increase of variations in absorbance by a factor of almost 5 for time-resolved measurements as compared to non-time-resolved measurements.
A time-domain NIR brain imager applied in functional stimulation experiments
Heidrun Wabnitz, Michael Moeller, Adam Liebert, et al.
We developed a time-domain brain imager that is based on picosecond diode lasers, a multimode fiber switch and multi-channel time-correlated single photon counting. It allows to record time-resolved diffuse reflectance for 16 source-detector pairs within typically 1 s. Data analysis was based on the evaluation of moments of measured distributions of times of flight of photons. To show the relevance of these moments for achieving depth selectivity, three-dimensional sensitivities of integral, mean time of flight and variance to absorption changes were calculated using a perturbation approach based on the diffusion equation for photon density for a homogeneous semi-infinite medium. It turned out that variance is almost exclusively sensitive to deep layers, whereas the integral reflects changes in deep as well as in superficial layers. The lateral resolution of the imager was demonstrated by a phantom experiment. Results of a motor stimulation experiment on a healthy volunteer strongly suggest that variance reveals mainly the cerebral activation whereas the integral may additionally contain significant systemic contributions.
Functional Characertization and Monitoring of Malignant and Normal Tissues
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Monitoring of radiation therapy response of head and neck tumors by non-invasive optical blood flow measurements
U. Sunar, H. Quon, J. Zhang M.D., et al.
The aim is to evaluate the usefulness of optical blood flow measurements for predicting early tumor response to radiation therapy in patients with head and neck tumors. The results suggest a correlation between tumor blood flow changes with clinical outcome.
Muscle oxygenation during exercise under hypoxic conditions assessed by spatially resolved broad-band NIR spectroscopy
Dmitri Geraskin, Petra Platen, Julia Franke, et al.
Near-infrared spectroscopy (NIRS) is used for the non-invasive measurement of muscle oxygenation during an incremental cycle test in healthy volunteers. A broad band spatially resolved system is used that allows the reliability of current algorithms to be inspected with the main emphasis on tissue oxygen saturation (SO2) and oxygenated and deoxygenated haemoglobin concentrations. Physiological conditions were modulated by changing oxygen supply from normal (21 % O2 in inspired air) to conditions corresponding to 2000 and 4000 m altitude above sea level (15.4 and 11.9 % O2). Under these hypoxic conditions the decrease in SO2 with increased exercise power is highly correlated with the oxygen content of the inspired air. There is a clear correlation with physiological parameters (heart rate, pulse oxymetry, blood gas, lactate, spirometric data). Skin oxygenation parameters are compared to those of muscle.
Experimental assessment of analytical models for estimating tumor optical properties in laser pulse mammography
D. Grosenick, B. Wassermann, R. Macdonald, et al.
We analyzed measured and simulated phantom data for absorption and reduced scattering coefficients of embedded spherical inhomogeneities using various analytical models, based on diffusion theory. The model of diffraction of photon density waves was found to be superior to the empirical, non-linear perturbation model (Pade approximants) whereas linear perturbation theory considerably underestimates absorption in the range of absorption coefficients and spherical volumes most relevant to tumors detected by optical mammography.
NIR image reconstruction using a single-rotating-source/detector scanning device
Min-Cheng Pan, Chien-Hong Cheng, Wei-Hua Huang, et al.
The research aims at developing an NIR tomography system using a single rotating source/detector scanning device associated with an image reconstruction scheme. Several simulation results concerning the phantom with one, two or three targets are presented. Additionally, the developed system is validated by a hemoglobin phantom inserted by another different volume density one.
Functional Optical Imaging of the Brain II
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Estimation of path length factor for measurement of haemoglobin concentration in the exposed cortical tissue
K. Sakaguchi, T. Tachibana, K. Yokoyama, et al.
The change in oxy- and deoxy haemoglobin in the cortical tissue caused by brain function can be measured from multi-spectral images of exposed cortex. We cannot ignore the wavelength dependence of mean optical path length of detected light to calculate the accurate changes in concentrations of oxy- and deoxy- haemoglobin in the cortical tissue. The optical path length factor, which reflects the wavelength dependence of mean optical path length, is experimentally estimated from the multi-spectral images of exposed cortex of guinea pigs. The optical path length factor improves the accuracy in changes in concentrations of oxy- and deoxy-haemoglobin obtained from the multi-spectral images.
Design and characterization of a fast 16-source 64-detector time-resolved system for functional NIR studies
D. Contini, A. Pifferi, L. Spinelli, et al.
We developed a fast 16-source 64-detector time-resolved system for functional NIR studies. Description of the main blocks of the system (source, optics, detection, acquisition, and control) and system characterization are presented.
Diffuse Spectroscopy and Fluorescence Tomography
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Dynamic time-resolved diffuse spectroscopy based on white light generation in a photonic crystal fiber
C. D'Andrea, A. Bassi, J. Swartling, et al.
We present a detailed characterization of a time-resolved diffuse spectrophotomer based on supercontinuum light generation in a photonic crystal. We also present the first in vivo real-time dynamic spectral measurements by monitoring tissue oxygenation changes.
A time-resolved multi-wavelength fluorescence diffuse optical tomography system for small animal imaging
Bruno Montcel, Renee Chabrier, Patrick Poulet
A tomographic approach, relying on diffuse near infrared photons to image the optical properties of tissues and the inner distribution of fluorescent probes is described. The method should improve the spatial resolution and quantification of fluorescence signals, thanks to multiple-projection acquisitions and to a reconstruction procedure using the principles of diffuse optical tomography. The scanner assembled uses picosecond laser diodes, an eight-anode photo-multiplier tube (PMT) and time-correlated single photon counting. Two sets of laser heads, each operating at four wavelengths, are fitted with furcated optical fibers, providing two sequential sources of light positioned on the animal or object studied. Multimode optical fibers are used to detect light at eight output points on the animal or object. These fibers are connected to the PMT, with an air-gap allowing the insertion of an optical filter to reject the excitation wavelength. The light sources and detectors can be rotated to increase the number of projections recorded. For the reconstruction process, the coordinates of the body surface of the animal to be imaged are necessary. These are acquired by interferometry, using a conoscope and an XY scanning system, before the animal is entered in the scanner. The profiles measured at the excitation wavelengths are used to compute absorption and reduced scattering images and perfusion/oxygenation images of the animal. Fluorescence images, free from diffusion and absorption artefacts, can then be computed with a-priori knowledge of the optical images of the animal. The scanner, its performances and images of light-scattering and fluorescent phantoms are presented.
Quantifiability and image quality in noncontact fluorescence tomography
Ralf B. Schulz, Joerg Peter, Wolfhard Semmler, et al.
Non-contact detection schemes for optical or fluorescence tomography offer several advantages compared to classic approaches, most importantly the ability to obtain images with a CCD in the absence of a matching fluid or fiber optics. This allows the acquisition of high density datasets, as well as simplified experimental procedures. Herein we create a unified framework for contact and non-contact detection procedures and present experimental results that show the ability of the non-contact method to quantify the concentration of fluorochromes hidden in turbid media as well as the improvement in image quality between conventional and non-contact detection.
Photon Migration Theory
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Modelling the influence of interfaces and multiple layers on light propagation in a slab geometry with the radiative transport equation
Rachid Elaloufi, Simon Arridge
In this paper, we solve the radiative transfer equation for slab geometry, taking into account rigourously the interfaces. We use the discrete ordinate method. We underline the important role of interfaces in the ballistic regime and also the diffuse regime. The angular distribution and amplitude of transmitted flux is sensitive to refractive index. We also solve the RTE for a multilayered geometry slab and show the sensitivity of the angular distribution of transmitted and reflected fluxes for thin layers.
Solutions to the transport equation using variable order angular basis
Stephen Wright, Martin Schweiger, Simon R. Arridge
In this paper the solution to the transport equation will be considered using the Pn Method. Although this technique has been applied to two and three dimensional problems it can be computationally expensive when a high order of approximation is required for convergence of the problem. In this paper results will be presented that indicate a potential solution to this problem by utilising an adaptive Pn approach where the order of angular basis is varied according to the local complexity of the domain. This substantially reduces the computational cost of assembly and solution of the linear system. Results for a two-dimensional circular test problem are presented and compared to a standard solution with uniform order of angular basis.
Image reconstruction using spatial sensitivity profile with the constraint of spatial frequency in image for near-infrared topography
The spatial resolution of current near-infrared topography is not enough for clinical application. In this study, the image reconstruction algorithm using prior knowledge about spatial sensitivity profile in the tissue and constraint of spatial frequency in image was proposed and was evaluated by simulation. The spatial resolution of topographic image obtained from the image reconstruction method is better than that obtained from the conventional mapping-interpolation method. The most appropriate cut-off frequency for the constraint for the image reconstruction method depends on the arrangement of fibres.
Adaptive diffusion regularization method of inverse problem for diffuse optical tomography
This paper develops and analyzes the performance of an adaptive diffusion regularization method with a specific algorithm reconstruction method called the Lagged Diffusivity Newton-Krylov method for Diffuse Optical Tomography inverse problem.
Light propagation in a cubic biological tissue having anisotropic optical properties
The light propagation in biological tissue having anisotropic optical properties is investigated. Monte Carlo simulations employing the phase function of infinitely long cylindrical scatterers and the Henyey-Greenstein function are performed and compared to spatially-resolved reflectance measurements of semi-infinite turbid media. In addition, simulations are shown for the spatially-resolved reflectance and transmittance from the surfaces of cubic turbid media. It is found that the light propagation in anisotropic turbid media is very different compared to turbid media that have isotropic optical properties. For example, it is observed that the light which is incident perpendicular to the top surface of the cube may be transmitted mainly from a single lateral side.
Space-varying restoration of diffuse optical tomograms reconstructed by the filtered backprojection algorithm
Alexander B. Konovalov, Dmitry V. Mogilenskikh, Vladimir V. Lyubimov
Possibility is investigated to enhance spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method. The PAT method is based on a concept of average statistical trajectory of light energy transfer from point source to point detector. The inverse problem of diffuse optical tomography reduces to solution of an integral equation with integration by conventional PAT. In the result for reconstruction of diffuse optical images the conventional algorithms of projection tomography can be applied, including filtered backprojection algorithm. The shortcoming of the PAT method is that it reconstructs images blurred in the result of averaging by photons spatial distribution contributing into the signal measured by a detector. To enhance resolution we apply a spatially variant blur model based on interpolation of spatially invariant point spread functions simulated for different image regions. To restore tomograms two iterative algorithms for solution of system of linear algebraic equations are used: conjugate gradient algorithm for least squares problems and modified residual norm steepest descent algorithm. It is shown that one can achieve 27% enhancement of spatial resolution.
Poster Session
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Independent component analysis for three-dimensional optical imaging and localization of a fluorescent contrast agent target embedded in a slab of ex vivo human breast tissue
M. Alrubaiee, M. Xu, S. K. Gayen, et al.
An innovative approach for three-dimensional localization and characterization of a fluorescent target embedded in a turbid medium is presented. The target was a ~4-mm diameter glass sphere with a solution of indocyanine green placed within a 50-mm thick tissuelike phantom with mean free path of ~1-mm at 784-nm and a ~ 26-mm thick ex vivo breast tissue slab. The experimental approach uses a multi-source illumination, and a multi-detector signal acquisition scheme. An analysis scheme based on the independent component analysis from information theory is used for target localization and characterization. Independent component analysis of the perturbation in the spatial intensity distribution of the fluorescent signal measured on the exit plane of the turbid medium locates the embedded objects. The location and size, of the embedded objects are obtained from a Green's function analysis and back-projection Fourier transform of the retrieved independent components.
Crosstalk in the measurement of focal brain activation by near-infrared topography
Crosstalk between oxy- and deoxy-haemoglobin observed in near-infrared topography is investigated. The light propagation in an adult head model is predicted by Monte Carlo simulation to obtain the change in intensity detected with source-detector pairs on the scalp caused by a focal absorption change in the brain. The topographic images of changes in oxy- and deoxy-haemoglobin are obtained from the changes in intensity detected with source-detector pairs on the scalp. The crosstalk depends on the relative position of the focal absorption change to source-detector pairs. The crosstalk is minimised when the focal absorption change is located below a measurement point that is the midpoint between a source and a detector. Appropriate selection of wavelength pair is effective to reduce the crosstalk in the topographic image.
Experimental study of time-resolved measurements on turbid media: determination of optical properties and fluorescent inclusions characterization
Aurelie Laidevant, Anabela da Silva, Michel Berger, et al.
Among the different existing techniques in optical molecular imaging, time-domain approaches can supply information on the probe concentration or localization, in case of specific fluorescent labelling. We present an experimental validation of an analytical solution to the time-domain fluorescence diffusion equation in an infinite medium. A fitting method issued from frequency domain calculations is also presented. The instrumentation employs a pulsed laser diode as light source, optical fibres, and a photomultiplier as the detector in a time correlated single photon counting (TCSPC) system. Measurements were performed on tissue simulating phantoms containing a small fluorescent inclusion, with the fibres either imbedded deep within the volume or placed at the surface, above the inclusion. Good adequacy was found between the simulations and the within medium measurements. We also demonstrate good performances of the method to recover the fluorophore localization.
Frequency-domain optical diffusion tomography of fluorescent proteins
We present preliminary results of the frequency domain fluorescent diffuse tomography (FD FDT) method in application to fluorescent proteins. For first step in the experimental setup we utilized light-emitting diode (530 nm wavelength) modulated with low frequency (18 kHz). A model experiments with capsules containing DsRed suspension in scattering medium has been conducted. The results of post mortem experiments with capsules containing DsRed, introduced into abdominal cavity of mice to simulate tumors inside animal body, are presented. An algorithm of processing fluorescent image based on calculating zero of maximum curvature has been applied to detect fluorescent inclusions boundaries on the image.
Goniometric measurement of the phase function of different fat emulsions
Fat emulsions like Intralipid are frequently used in research of light propagation in turbid media as tissue phantoms. We investigated the phase functions of different major brands and concentrations (10% and 20%) of these fat emulsions at 633nm and 543nm. A theoretical phase function for fat emulsions was calculated using Mie theory. Only small differences of the phase function of the investigated fat emulsions were found.
Dual channel photoplethysmography studies of cardio-vascular response to the body position changes
R. Erts, I. Kukulis, J. Spigulis, et al.
The dual-channel photoplethysmography studies of physiological responses during 3-stage orthostatic test were performed. Clear differences in heartbeat rate, pulse wave transit time and blood pressure variations of healthy volunteers and diabetic patients have been observed.
Evaluation of a segmentation-based reconstruction scheme for fluorescence-enhanced diffusion optical tomography
A. Da Silva, J. Boutet, A. Planat-Chretien, et al.
In the framework of Fluorescence-enhanced Diffuse Optical Tomography, a numerical approach (usually the Finite Element Method) is often required because of the complexity of the geometry of the diffusing systems studied. This approach is appropriate for handling problems modelled by elliptic coupled partial differential equations but is known to be time and memory consuming. The resolution of the adjoint problem considerably speeds up the treatment and allows a full 3D resolution. Nevertheless, because of the ill-posedness of the problem, the reconstruction scheme is sensitive to a priori knowledge on the parameters to be reconstructed. In the present work, a multiple step, self-regularized, reconstruction algorithm for the spatial distribution of the fluorescent regions is presented. The prior knowledge of the regions of interest is introduced via a segmentation. This one is performed on the results obtained with a first rough reconstruction. The results are then refined along iterations of the segmentation/reconstruction scheme. The technique is tested on experiments performed with a home made tomographer. A phantom study is presented.
Combined pulse-oximeter-NIRS system for biotissue diagnostics
Multi-wavelength (670, 805, 848 and 905 nm), multi-detector device for non-invasive measurement of biochemical components concentration in human or animal tissues, combining the methods of conventional pulse-oximetry and near infrared spectroscopy, is developed. The portable and clinically applicable system allows to measure heart pulse rate, oxygen saturation of arterial hemoglobin (pulse-oximetry method) and local absolute concentration of oxyhemoglobin, deoxyhemoglobin and oxidized cytochrome aa3 or other IR absorbed compounds (NIRS method). The system can be applied in monitoring of oxygen availability and utilization by the brain in neonatal and adults, neuro- traumatology, intensive care medicine, transplantation and plastic surgery, in sport, high-altitude and aviation medicine.
Coupled radiative transfer equation and diffusion approximation
Tanja Tarvainen, Marko Vauhkonen, Ville Kolehmainen, et al.
A coupled radiative transfer equation and diffusion approximation model for photon migration in tissues is proposed. The light propagation is modeled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid and the diffusion approximation is used elsewhere in the domain. The coupled equations are solved using the finite element method. The proposed method is tested with simulations. The results of the coupled radiative transfer equation and diffusion approximation model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation. The results show that the coupled radiative transfer equation and diffusion approximation model can be used to describe photon migration in tissues more accurately than the conventional diffusion model.