Félix Fanjul-Vélez

Efficient 3D numerical approach for temperature prediction in laser irradiated biological tissues

Temperature prediction in biological tissues irradiated by an optical source is frequently required in some medical applications, like Thermotherapy, Hyperthermia or tissue ablation. In this work we propose a new numerical approach to solve the bio-heat equation. It is based on the two steps 3D modified Du Fort-Frankel algorithm, which allows a better convergence, more accuracy and a faster computation than previous numerical methods developed by other authors. The model also includes adaptive spatial mesh and time step refinement. These improved results for opto-thermal temperature distribution could be used for choosing appropriate laser treatment parameters in medical praxis.

Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography

Corneal polarimetry measurement has been the object of several papers. The results of techniques like polarization-sensitive optical coherence tomography (PS-OCT), scanning laser polarimetry, or polarization microscopy are contradictory. Some studies propose a biaxial-like birefringence pattern, while others postulate that birefringence grows at corneal periphery. Several theoretical approaches were proposed for the interpretation of these measurements, but they usually lack accuracy and an adequate consideration of the nonnormal incidence on the tissue. We analyze corneal polarization effects measured by PS-OCT. In vivo and in vitro PS-OCT images of the human cornea are acquired. PS-OCT measurements are apparently not in agreement with the biaxial-like birefringence pattern. We present a polarimetric model of the human cornea based on the extended Jones matrix formalism applied to multilayered systems. We also apply the Poincaré equivalence theorem to extract optic axis orientation and birefringence. The results show that for a fibrils orientation pattern composed by alternating circular and radial fibrils, the birefringence is biaxial-like at the corneal center, and there is an almost circularly symmetric high-birefringence area at corneal periphery. The model could be useful for diagnosis of corneal diseases or corneal compensation in retinal polarimetric imaging.

Polarimetry of birefringent biological tissues with arbitrary fibril orientation and variable incidence angle

Polarimetric optical techniques such as polarization microscopy or polarization-sensitive optical coherence tomography normally assume that light is perpendicular to the sample surface and that fibrils of a birefringent biological tissue are arranged in a plane parallel to this surface. The approaches that describe quantitatively polarimetric data from tissues with nonparallel fibril orientation and/or off-axis incidence usually lack a rigorous theoretical analysis. We present a polarimetric model with arbitrary fibril orientation and/or variable incidence angle by means of the extended Jones matrix theory, the polar decomposition, and Poincaré equivalence theorem. The model, suitable for diagnosis or tissue structure analysis, is applied to articular cartilage.

Superficial radially resolved fluorescence and 3D photochemical time-dependent model for photodynamic therapy

Photodynamic therapy (PDT) dosimetric tools are crucial for treatment planning and noninvasive monitoring by means of fluorescence. Present approaches consider usually a 1D problem, a simple photochemical process, or a spatially homogeneous photosensitizer. In this work, a radially resolved superficial photosensitizer fluorescence and 3D photochemical time-dependent PDT model are presented. The model provides a time-dependent estimation of tissue fluorescence and the photosensitizer and singlet oxygen 3D concentrations. The model is applied to a basal cell carcinoma treated by Metvix topical photosensitizer protocol. The analysis shows the potentiality in treatment planning and monitoring. The fluorescence results are in agreement with previous measurements.

Frequency up-conversion of coherent images by intracavity nondegenerate four-wave mixing

This work presents theoretical and experimental studies of the processes of light field transformations upon frequency-nondegenerate fourwave mixing (NFWM) in a nonlinear Fabry-Perot interferometer (FPI). The principal aims are the development of a theory for intracavity four-wave mixing in complex molecular media in conditions of scattering from dynamic gratings and resonator feedback; determination of a mechanism of light field transformations in dynamic holograms, and also by nonlinear interferometers; working out and introduction of novel nonlinear-optical methods to control the characteristics of light beams. High diffraction efficiency (up to 13.5%) with simultaneous infrared-to-visible frequency conversion of coherent images has been experimentally obtained by intracavity NFWM.

Polarimetric study of birefringent turbid media with three-dimensional optic axis orientation

Recent approaches to the analysis of biological samples with three-dimensional linear birefringence orientation require numerical methods to estimate the best fit parameters from experimental measures. We present a novel analytical method for characterizing the intrinsic retardance and the three-dimensional optic axis orientation of uniform and uniaxial turbid media. It is based on a model that exploits the recently proposed differential generalized Jones calculus, remarkably suppressing the need for numerical procedures. The method is applied to the analysis of samples modeled with polarized sensitive Monte Carlo. The results corroborate its capacity to successfully characterize 3D linear birefringence in a straightforward way.

Photosensitizer absorption coefficient modeling and necrosis prediction during Photodynamic Therapy.

The development of accurate predictive models for Photodynamic Therapy (PDT) has emerged as a valuable tool to adjust the current therapy dosimetry to get an optimal treatment response, and definitely to establish new personal protocols. Several attempts have been made in this way, although the influence of the photosensitizer depletion on the optical parameters has not been taken into account so far. We present a first approach to predict the spatio-temporal variation of the photosensitizer absorption coefficient during PDT applied to dermatological diseases, taking into account the photobleaching of a topical photosensitizer. This permits us to obtain the photons density absorbed by the photosensitizer molecules as the treatment progresses and to determine necrosis maps to estimate the short term therapeutic effects in the target tissue. The model presented also takes into account an inhomogeneous initial photosensitizer distribution, light propagation in biological media and the evolution of the molecular concentrations of different components involved in the photochemical reactions. The obtained results allow to investigate how the photosensitizer depletion during the photochemical reactions affects light absorption by the photosensitizer molecules as the optical radiation propagates through the target tissue, and estimate the necrotic tumor area progression under different treatment conditions.

Necrosis prediction of photodynamic therapy applied to skin disorders

The great selectivity and the lack of side effects of Photodynamic Therapy make it more advantageous than radiotherapy or chemotherapy. The application of PDT to skin diseases is particularly appropriate, due to the accessibility of this tissue. Common disorders like nonmelanoma skin cancer, that includes basocelullar or squamous cell carcinomas, can be treated with PDT. Conventional procedures, like surgery or radiotherapy, are not so efficient and do not, in general, obtain the same favourable results. PDT in dermatology medical praxis uses fixed protocols depending on the photosensitizer and the optical source used. These protocols are usually provided by the photosensitizer laboratory, and every lesion is treated with the same parameters. In this work we present a photo-chemical model of PDT applied to skin disorders treated with topical photosensitizers. Optical propagation inside the tissue is calculated by means of a 3D diffusion equation, solved via a finite difference numerical method. The photosensitizer degradation or photobleaching is taken into account, as the drug looses efficiency with the irradiation time. With these data the necrosis area is estimated, so this model could be used as a predictive tool to adjust the optical power and exposition time for the particular disease under treatment.

Physically meaningful depolarization metric based on the differential Mueller matrix.

We present a novel depolarization metric for Mueller matrices based on the differential Mueller formalism. The proposed metric relies on the statistical interpretation of the differential Mueller matrix. We show that the differential depolarization index successfully quantifies depolarization even when applied to specific types of Mueller matrices for which some widely used depolarization metrics yield erroneous results. Moreover, the fact that the presented metric is directly linked to the variances and covariances of the elementary anisotropic properties of the sample makes it a valuable tool to quantify depolarization on a physically meaningful basis.

FDTD-based Transcranial Magnetic Stimulation model applied to specific neurodegenerative disorders

Non-invasive treatment of neurodegenerative diseases is particularly challenging in Western countries, where the population age is increasing. In this work, magnetic propagation in human head is modelled by Finite-Difference Time-Domain (FDTD) method, taking into account specific characteristics of Transcranial Magnetic Stimulation (TMS) in neurodegenerative diseases. It uses a realistic high-resolution three-dimensional human head mesh. The numerical method is applied to the analysis of magnetic radiation distribution in the brain using two realistic magnetic source models: a circular coil and a figure-8 coil commonly employed in TMS. The complete model was applied to the study of magnetic stimulation in Alzheimer and Parkinson Diseases (AD, PD). The results show the electrical field distribution when magnetic stimulation is supplied to those brain areas of specific interest for each particular disease. Thereby the current approach entails a high potential for the establishment of the current underdeveloped TMS dosimetry in its emerging application to AD and PD.