The non-invasive research of information inside biological tissues can be made by means of setups using continuous, time-dependent or frequency modulated light sources, which emit in the visible or near-infrared range. Moreover, the biological structures such as brain, breast or fruits, can be regarded as closer to a spherical shape than a slab. This paper focus on the retrieval of tissue optical parameters in a spherical geometry using fittings with analytical solutions adapted for semi-infinite geometry. The data were generated using three different optical spectroscopy methods: frequency-resolved, spatially-resolved, and time-resolved modes. Simulations based on a Monte Carlo code were performed on homogeneous spheres, with 18 spaced detectors located on their boundary. First, data are examined in the frequency domain. Second, they are treated with optimization algorithms to assess the optical coefficients. The computations show that the spatially-resolved measurements are often more robust than those related to the frequency-resolved mode. In the temporal domain, errors on the estimates are also exhibited with the fitting by the Fourier transform of a solution based on the semi-infinite geometry. Furthermore, when the analytical solution is modified by taking into account the spherical shape, the retrieval of the coefficients is improved.
The interaction of light with biological materials, such as fruits and vegetables, is a complex process which involves both absorption, and scattering events at different scales. Measuring the optical properties of a fruit allows understanding the physical and chemical characteristics. In this paper, an optical bench based on the use of a continuous laser source and a CCD camera was developed to study the light diffusion inside apple tissue structures. The method refers to the well-known steady-state spatially resolved method. First, the optoelectronics system was tested with a tissue phantom in order to show the optimal sensing range required to obtain the best estimated optical properties. Second, experimental results were obtained using peeled and unpeeled apples as interrogated tissues. The data were confronted with a diffusion model in order to extract the optical properties at two wavelengths of 633, and 852 nm. To better understand the effect of the apple tissue structures, investigations into the propagation of light through a half cut apple were also performed.
The knowledge of the light fluence rate distribution inside a biological tissue irradiated by a Laser (or LED) is fundamental to achieve medical treatments. In this paper, we present a semi-analytical model based on the 2-D Fourier Transform of the diffusion equation. This method can be applied to any irradiation source (cylindrically symmetric or not) at the surface of the tissue. Two particular beam shapes are studied: planar irradiation and flat beam with finite radius. The total fluence rate along the depth in tissues was computed by adding the collimated and the diffuse components. The analytical solution was also used to study the effect of the beam radius on the light attenuation. Measurements were performed using a tank filled with a liquid-simulating medium (Milk), illuminated with a LED array (660 nm, 100mm×100mm). Several circular diaphragms were used to obtain uniform circular beams with well defined radii. An optical fibre (with an isotropic tip) was used to measure the fluence rate inside the medium. Preliminary experimental results are in agreement with theoretical predictions.
Optical imaging of turbid media is a challenging problem mainly due to the scattering process that reduces image
contrast and degrades spatial resolution. The development of fluorescent probes has recently improved the noninvasive
optical technique. In this paper, we are interested in the time gating fluorescence signals. The diffusion approximation is
used in order to describe the light propagation of a laser pulse in a turbid media that mimics breast like biological tissue.
A numerical model based on a finite element method is proposed. Fluorescence time dependent numerical simulations
are performed in order to compute time-gated intensities resulting from line scans across partially absorbing and
scattering slab configurations. Optical properties of embedded objects are chosen to be the same as optical properties of
breast tumor. Tacking into account two hidden objects, we investigate the lateral resolution aimed by fluorescence
modality, and we also compared the results to thus obtained by photon propagation. Different widths of the time gate are
computed and it is demonstrated that both lateral localization of one inclusion, and resolution of two inclusions, are
enhanced when the time-gate width (▵t) is decreased. The overall computations confirm that fluorescent time-gating
technique is very sensitive to local variations in optical properties that are due to breast-like tumors in turbid media.
Optical methods allow investigating biological tissue noninvasively without ionizing radiations. Moreover, considering
low absorption processes in the tissue in the near-infrared wavelengths range, biological tissue can be deeply
investigated. In this field, we studied the resolution limits of the detection of one and two tumour-like heterogeneities
embedded in the middle plane of a slab that mimics a breast enclosed between two transparent plates. We used the
diffusion equation in order to model the photons propagation in such slab. It is solved in the time-domain by means of a
finite element method. We computed time-resolved trans-illumination data based on lateral scan of the slab. The timedependent
transmitted light, received at the opposite of the source, was transformed in the frequency-domain and the
modulation and phase-shift of the signal are then obtained. The resulting phase-shift considering the embedded objects
was analyzed versus the distance between the objects. Then, the resolution limits were estimated considering different
modulation frequencies and a noise level. The overall combinations took into account a set of optical properties that
mimics realistic optical properties for healthy breast tissue and tumours.
In the framework of the depth detection of tumor using the diffusion equation, a finite element method is proposed in
order to solve the time-dependent light propagation in highly scattering media. A tumor-like object is positioned in the
media. The finite element method tacks into account Robin type air-tissue boundary conditions. This study is devoted to
the depth localization of a tumor enclosed into a breast tissue-like slab. Cartesian coordinates are used in order to solve
the time-dependent diffusion approximation. A short laser pulse of 1ps is considered. The transillumination technique is
able to laterally detect the objects when the source and detector are moved together on the same axis. In order to perform
the depth localization of the inclusion, we were interested in a non-coaxial transillumination technique conjugated to
interesting contrast functions based on the mean time of flight of photons. These functions allow to localize axially the
inclusion using the high scattering processes. Thus, we performed first results of a depth indicator of a tumor. We now
perform a parametric study. The optical properties of the slab are varying. Furthermore, different sizes of the objects are
tested. Thus, the influence and the variation of these parameters on the depth indicator are shown. Our study
demonstrates the possibility to deeply localize a tumor enclosed in a breast tissue using the high scattering processes
induced by a tumor. To enhance the scattering processes, an interesting way is then to use recent nanoparticles allowing
to modify the scattering coefficient.
Optical spectroscopy based on the use of fluorescent contrast agents has become an interesting tool to detect and localize
diseased tissues from healthy structures in a harmless way. Herein, we present a numerical model based on the finite
element method that allows to simulate time-resolved reflectance signals from a realistic compartmented two-dimensional
model of a breast bearing a small-sized fluorescent inclusion. Results show that the depth location of the
inclusion can be well inferred from the observation of the time to reach the half maximum intensity of the reflected
signals. Improvements may be obtained if depth localization is provided by a dimensionless indicator based on a twoway
reflectance determination.
KEYWORDS: Absorption, Reflectivity, Diffusion, Monte Carlo methods, Finite element methods, Data modeling, Skin, Tissues, Scattering, Near infrared spectroscopy
This work presents results on the modeling of the photon diffusion in a three-layered model, (skin, fat and muscle). The
Finite Element method was performed in order to calculate the temporal response of the above-mentioned structure. The
thickness of the fat layer was varied from 1 to 15 mm to investigate the effects of increasing fat thickness on the muscle
layer absorption coefficient measurements for a source-detector spacing of 30 mm.
The simulated time-resolved reflectance data, at different wavelengths, were fitted to the diffusion model to yield the
scattering and absorption coefficients of muscle. The errors in estimating muscle absorption coefficients &mgr;α depend on
the thickness of the fat layer and its optical properties. In addition, it was shown that it is possible to recover with a good
precision (~2.6 % of error) the absorption coefficient of muscle and this up to a thickness of the fat layer not exceeding
4mm. Beyond this limit a correction is proposed in order to make measurements coherent. The muscle-corrected
absorption coefficient can be then used to calculate hemoglobin oxygenation.
KEYWORDS: Scattering, Diffusion, Monte Carlo methods, Finite element methods, Head, Brain, Light scattering, Reflectivity, Data modeling, Optical properties
In this work, a Finite Element calculations based on diffusion approximation are compared with Monte Carlo transport
data code in time-resolved reflectance simulations of light propagation in a three-layered head model, which can be seen
as a very simplistic approximation of the adult head. We also address the effects caused by the cerebrospinal fluid (CSF),
filling the space between the skull and the brain, on the accuracy of the diffusion approximation for different values of
CSF reduced scattering coefficients μs' varying between 0.1 and 1 mm-1. Significant differences between transport and
diffusion calculations show that diffusion approximation fails to describe accurately light propagation in voidlike region
such as the cerebrospinal fluid (CSF), in which absorption and scattering are very small compared to the surrounding
media, whereas the Monte Carlo predictions are not greatly affected. However, It is shown that the diffusion equation
should provide reasonable solutions with a CSF reduced scattering coefficient μs' = 0.3 mm-1. The results indicate that a
multi-layered model including CSF is more appropriate for the determination of the optical properties of the human head
and to obtain accurate solutions of the forward problem with diffusion approximation.
In the last few years, the propagation of diffuse photons in scattering media has become an important field of interest. This is mainly due to the possibility offered by the low absorption of light in the range 700 to 900nm. Indeed, this property leads to a potential deep penetration. But a non negligible limitation appears: the scattering processes strongly reduce both the contrast and the resolution. In this paper, the time-dependent light propagation in highly scattering media containing an inclusion is solved by means of a finite element method, tacking into account Robin type air-tissue boundary conditions. This study is devoted to the depth localization of a tumor enclosed into a breast-like slab. The tissue is modeled by a rectangular meshed domain that mimics a breast compressed between two transparent plates. Cartesian coordinates are used in order to solve the time-dependent diffusion approximation. A short laser pulse of 1ps is considered. The transillumination technique is able to laterally detect the object when the source and detector are moved together on the same axis. In order to perform the localization of the inclusion in this study, the optical properties of the object were varied. Knowing the lateral position of the inclusion, we derive interesting temporal contrast functions based on the mean time of flight of photons. These functions allow to localize in depth the inclusion under the assumption that the object is very diffusing. To conclude, our study demonstrates the possibility to detect laterally and axially a tumor-like inclusion enclosed in breast-like tissues.
The present work aims at comparing simulations of photon transport phenomena in biological multi-layered tissues by means of two methods: a finite element code and a Monte Carlo procedure. We apply these codes to model time-dependent light propagation in multi-layered media. The physical situation refers to the case of a narrow incident laser pulse of 1 ps duration acting upon the surface of the media. Time-resolved spectra are reported for different geometries and optical properties for high media. Here, codes are applied to simulate data acquired from measurements on tissues in extremities. The results of the study provide information to calibrate the finite element characteristics for future experiences including fluorescence events in multi-layered complex systems.
The potentialities offered by time-gated transillumination of inhomogeneous tissue slab media are numerically investigated in this paper. A finite element model is firstly presented in order to solve the time-dependent light transport in mutiple-scattering optical media containing different embedded objects. The numerical procedure is based on the Galerkin formulation added to an implicite finite difference scheme (Backward Euler) to integrate the resulting matrix formulation with respect to time. The meshed domain refers to Cartesian-coordinates system (x,y) such that the computational grid can be adapted to scan along the longitudinal coordinate x. It takes into account the boundary conditions relative to air-tissue interfaces. The use of the method is demonstrated by the forward computations of time-gated intensities, resulting from line scans across either partially absorbing or scattering cylindrical objects. The overall computations confirm that time-gating technique is very sensitive to local variations in optical properties that are due to hidden objects in turbid media. It is also shown that the lateral localization of these inclusions is enhanced when the time-gate width (Δt) is decreased to about 30 ps.
The depth-localization of fluorescent objects having different diameters and embedded within semi-infinite turbid tissue is determined with a model based on the finite element method. The work relies on the time to reach half of the maximum fluorescence intensity. The model is based on a set of two-dependent photon diffusion equations: - the transport of the pulsed laser source (duration 1 ps) and - the transport of the induced fluorescent light excited by the source. The coupling between these equations is due to a source term directly proportional to the scattered fluence rate at the same location. To solve this problem, the method proceeds following the Galerkin formulation added to an implicit finite difference scheme (Backward Euler) to integrate the resulting matrix formulation with respect to time. The meshed domain is axi-symmetrical and takes into account the boundary conditions relative to air-tissue interface. The different computational results show that the fluorescent signals can be used to provide time of flight information about the depth localization of a spherical tumor embedded in a turbid medium. These findings are in good agreement with experimental works.
Reactive hyperemia signals obtained with laser Doppler flowmetry are currently used to diagnose peripheral arterial occlusive diseases (PAOD). De-noising of such signals could lead to improved diagnoses. For this purpose, the principal components analysis is applied to signals acquired on PAOD and healthy subjects.
In the biomedical field, the laser Doppler flowmetry (LDF) technique is a non-invasive method to monitor skin perfusion. On the skin of healthy humans, LDF signals present a significant transient increase in response to a local and progressive pressure application. This vasodilatory reflex response may have important implications for cutaneous pathologies involved in various neurological diseases and in the pathophysiology of decubitus ulcers. The present work analyses the dynamic characteristics of these signals on young type 1 diabetic patients, and on healthy age-matched subjects. To obtain accurate dynamic characteristic values, a de-noising wavelet-based algorithm is first applied to LDF signals. All the de-noised signals are then normalised to the same value. The blood flow peak and the time to reach this peak are then calculated on each computed signal. The results show that a large vasodilation is present on signals of healthy subjects. The mean peak occurs at a pressure of 3.2 kPa approximately. However, a vasodilation of limited amplitude appears on type 1 diabetic patients. The maximum value is visualised, on the average, when the pressure is 1.1 kPa. The inability for diabetic patients to increase largely their cutaneous blood flow may bring
explanations to foot ulcers.
A computational model based on finite element method is derived to examine how the recorded time-dependent signals are related to the basic optical properties of a slab at both excitation and emission wavelengths. The model is based on a set of two time-dependent photon diffusion equations: -the transport of the pulsed laser source light (1 ps) and -the transport of the induced fluorescent light excited by the source. The coupling between these equations is due to a source term directly proportional to the scattered fluence rate at the same location. To solve this problem, the method proceeds following the Galerkin formulation, added to implicite finite difference scheme (Backward Euler) to integrate the resulting matrix formulation with respect to time. The meshed domain is two dimensional and takes into account the available boundary conditions relative to air-tissue interface (Robin boundary conditions). The computations are first carried out for a slab in which fluorophores are uniformly distributed, and afterwards devoted to the localization in depth of a fluorescent object (like a tumor) embedded within the slab.
The laser Doppler flowmetry technique has recently been used to report a significant transient increase of the cutaneous blood
flow signal when a local non-noxious pressure is applied progressively on the skin (11.1 Pa/s). The present work analyses the dynamic characteristics of this vasodilatory reflex response on anaesthetised rats. A de-noising algorithm using wavelets is proposed to obtain accurate values of these dynamic characteristics. The blood flow peak and the time to reach this peak are computed on the de-noised recordings. The results show that the mean time to reach the peak of perfusion is 85.3 s (time t = 0 at the beginning of the pressure application). The mean peak value is 188.3 arbitrary units (a.u.), whereas the mean value of the perfusion before the pressure application is 113.4 a.u. The mean minimum value obtained at the end of the experiment is 60.7 a.u. This latter value is, on the average, reached 841.3 s after the beginning of the pressure application. The comparison of the dynamic characteristics, computed with the de-noising algorithm on signals obtained in other situations, will give a better understanding on some cutaneous lesions such as those present on diabetic people.
A detailed investigation of the use of time-resolved reflectance and frequency-resolved reflectance for the optical characterization of scattering medium such as breast tissues based on the diffusion equation has been performed. Two different boundary conditions were imposed at the air-tissue interface : the first use the" zero real surface" (ZRS) , the second refers to the " zero extrapolated surface" (ZES). To simplify the preliminary analysis, the tissues have been assimilated to a semi-infinite geometry or a slab sufficiently thick. Among the results, the computation showed that at low frequency approximation, the determination of the phase angle shift is independent of whatever boundary conditions is applied.
Consequently breast tissue optical properties would be retrieved by means of frequency resolved data (modulation and phase) recorded at two different radial distances. For modulated light at f≈20 MHz, and using a model accounting for simple ZRS formulation. Under thes approximations discrepancies are within 3% for a μa and 0.5% for μ's.
The goal of the present work is to analyse multiple scattering in laser Doppler blood flowmetry reactive hyperaemia experiments. For this purpose, three different kinds of outputs from a laser Doppler flowmeter are studied: the concentration of moving blood cells (CMBC), the linearised unfiltered flux and the unlinerised unfiltered flux. Three vascular occlusion lengths of time are observed on eight healthy volunteers. For each reactive hyperaemia experiment, the difference between the linearised unfiltered flux and the unlinearised unfiltered flux is calculated to examine the multiple scattering. The latter is considered as a function of time and compared to blood flux and concentration of erthrocyte variations. This work shows that, during reactive hyperaemia, the multiple scattering is predominant when the CMBC signal reaches its peak, the latter occurring at the peak of perfusion. However, very rapidly the multiple scattering becomes negligible whereas the CMBC and the linearised flux still take high values. Moreover, the longer the occlusion length of time, the longer the presence of the multiple scattering.
Breast tissues can be investigated by means of the frequency- resolved spectroscopy, using the transmittance data. A model based on the Fourier transform of the time-resolved transmittance is firstly established, by considering the slightly compressed breast tissues as a finite homogeneous slab of different thicknesses. Two methods of determining the optical properties of this arrangement are presented. The former allows to use moderate modulation frequency of about 100 MHz, while the second requires a limited frequency range of 10 - 20 MHz, in accordance with the low frequency approximation. Under these conditions, computations reveal the potential of extracting the main optical tissue properties from the recorded phase angle shift and modulation linked to transmittance data, at fixed operating modulation frequency. In each case, graphical or numerical solutions can provide good estimates of both reduced scattering and absorption coefficients.
A 3-D finite element model of the human eye is developed to study the heat transfers induced by an argon laser absorbed on the iris tissue. The main objective is to explain the appearance of complications inherent to the iridectomy such as corneal burns and lens opacities. Contraction burn preceding the iris opening by photovaporization is studied. The iris temperature threshold fixed as onset for the tissue removal is 300 degrees Celsius. For closed angle glaucoma, the thermal history on the corneal endothelium and lens due to recurrent laser shots with pulse durations of 0.5 sec, 0.05 sec and 0.04 sec are presented and discussed. Typically, an overheating of the lens and cornea endothelium by the side of the iridectomy site is observed. This phenomena is important on the cornea endothelium where the temperature increases to 70 degrees Celsius in case of two recurrent laser pulses of 0.5 sec in duration, 0.43 W in power and 0.5 sec in relaxation time. For irradiation time of 0.05 sec this overheating is much less important and the temperature on the cornea endothelium doesn't exceed 47 degrees Celsius. These computations confirm that short laser pulses decrease the amount of adverse effects and agree well with experiments reported by ophthalmologists.
The purpose of this work was to gain better overall picture to the thermal process involved in ablation of biological media performed by means of both continuous waves (cw) and pulsed laser irradiations. The theoretical analysis is based upon a computerized laser evaporative model. This scheme has been applied in order to clarify the following situations: (1) Ablation of tissue assimilated as water with finite absorption coefficient. (2) Tissue ablation by cw argon laser using gel (tissue-like phantom material) as a model system for tissue. (3) Skin ablation performed by pulsed Er:YAG laser radiation. In each case the role played by optical absorption in the dynamics of the ablation process is depicted. Typically, it appears that the position of the ablation front (or crater depth) and the transient ablation velocity are both influenced by tissue absorption while the steady-state stays independent on this parameter and evolves linearly with power density. Additionally, the ablation temperature beyond the moving front can reach a maximum higher than ablation threshold temperature. The peak temperature and its location are mediated by tissue type. Calculations show that for small absorption coefficients higher temperatures are reached at deeper levels. In contrast, at fixed absorption coefficient, the growing of the power density increases the peak temperature but reduces the penetration depth of the heated volume. The whole of computed data confirms that thermal laser ablation of tissue can be described as an explosive event and that a decrease of water content in the target alters the penetration depth which control the ablation rate.
KEYWORDS: Argon ion lasers, 3D modeling, Finite element methods, Eye, Modeling and simulation, Iris, Tissues, Laser development, Convection, Objectives
A 3D finite element model is developed to study the conduction and convection heat transfer due to an argon laser iridectomy in the human eye. The objective is to explain the appearance of two important postoperative complications reported by ophthalmologists: corneal burns and lens opacities. Contraction burn is studied using simple shot of 1 s in duration, 0.5 mm in size, 0.4 W in power and double laser shot of 0.5 s in duration, 0.5 mm in size, 0.4 W in power and 0.5 s of relaxation time. Iris tissue pyrolisis temperature threshold is included as onset of tissue removal. Two laser spot positions on the iris circumference are considered. The phenomena of cornea and lens overheating for both normal and pathological human eyes are presented and discussed.
Photorefractive keratectomy (PRK) performed by means of the 193 nm excimer laser has stimulated considerable interest in the ophthalmic community because this new procedure has the potential to correct myopia, hyperopia, and astigmatism. The use of a laser beam to remove a controlled amount of tissue from the cornea implies that both the energy density of the laser beam and the target removed rate are accurately known. In addition, the required tissue ablation profile to achieve refractive correction must be predicted by optical calculations. This paper investigates: (1) Optical computations based on raytracing model to determine what anterior profile of cornea is needed postoperatively for ametropia. (2) Maximal depth of the removed corneal tissue against the ablation zone treated. And (3) the thickness of ablated corneal lenticule at any distance from the optical axis. Relationships between these data are well fitted by polynomial regressive curves in order to be useful as an algorithm in the computer-controlled delivery of the ArF laser beam.
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