Impact of age-selective vs non-selective physical-distancing measures against coronavirus disease 2019: a mathematical modelling study.

BACKGROUND: There is a real possibility of successive COVID-19-epidemic waves with devastating consequences. In this context, it has become mandatory to design age-selective measures aimed at achieving an optimal balance between protecting public health and maintaining a viable economic activity. METHODS: We programmed a Susceptible, Exposed, Infected, Removed (SEIR) model in order to introduce epidemiologically relevant age classes into the outbreak-dynamics analysis. The model was fitted to the official death toll and calculated age distribution of deaths in Wuhan using a constrained linear least-squares algorithm. Subsequently, we used synthetic location-specific and age-structured contact matrices to quantify the effect of age-selective interventions both on mortality and on economic activity in Wuhan. For this purpose, we simulated four different scenarios ranging from an absence of measures to age-selective interventions with stronger physical-distancing measures for older individuals. RESULTS: An age-selective strategy could reduce the death toll by >30% compared with the non-selective measures applied during Wuhan's lockdown for the same workforce. Moreover, an alternative age-selective strategy could allow a 5-fold increase in the population working on site without a detrimental impact on the death toll compared with the Wuhan scenario. CONCLUSION: Our results suggest that age-selective-distancing measures focused on the older population could have achieved a better balance between COVID-19 mortality and economic activity during the first COVID-19 outbreak in Wuhan. However, the implications of this need to be interpreted along with considerations of the practical feasibility and potential wider benefits and drawbacks of such a strategy.

Orthogonality-breaking polarimetric sensing modalities for selective polarization imaging.

Polarimetric sensing/imaging by orthogonality breaking is a microwave-photonics-inspired optical remote sensing technique that was shown to be particularly suited to characterize dichroic samples in a direct and single-shot way. In this work, we expand the scope of this approach in order to gain sensitivity on birefringent and/or purely depolarizing materials by respectively introducing a circular or a linear polarization analyzer in the detection module. We experimentally validate the interest of these two new, to the best of our knowledge, induced orthogonality-breaking modalities in the context of infrared active imaging.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus: erratum.

For J. Opt. Soc. Am. A33, 434 (2016)JOAOD60740-323210.1364/JOSAA.33.000434, a corrected version of Eq. (9) is provided owing to typographical errors in the original article. The original full article text and calculations are unchanged. Another typo is corrected in Eq. (A5) of Appendix A.

Generation of a coherent light beam with precise and fast dynamic control of the state and degree of polarization.

Recent developments of polarized light sources with tunable state and degree of polarization (SOP and DOP) inherently provide a temporally incoherent beam, which makes them unsuitable for applications like interferometry. We present a method for generating a coherent beam with full, precise, and independent control of the SOP and DOP. Our approach is based on an imbalanced dual-frequency dual-polarization light source. We demonstrate that it offers three different working regimes, respectively providing perfectly depolarized light, DOP modulated light, or fully polarized light with a deterministic SOP trajectory. A simple implementation of this versatile approach is described and experimentally validated.

Free-space active polarimetric imager operating at 1.55 µm by orthogonality breaking sensing.

We report the design and optimization of an active polarimetric imaging demonstrator operating at 1.55 µm that is based on the orthogonality breaking technique. It relies on the use of a fibered dual-frequency dual-polarization source raster scanned over the scene. A dedicated opto-electronic detection chain is developed to demodulate the optical signal backscattered at each location of the scene in real time, providing multivariate polarimetric image data in one single scan with limited acquisition time. We experimentally show on a homemade scene that contrast maps can be built to reveal hidden dichroic objects over a depolarizing background, as well as their orientation. Finally, experiments through air turbulence illustrate the benefit of such an imaging architecture over standard polarimetric techniques requiring multiple image acquisitions.

Enhanced depolarization contrast in polarization-sensitive optical coherence tomography.

We demonstrate the first application of the differential depolarization index (DDI) for depolarization imaging in polarization-sensitive optical coherence tomography (PS-OCT). Unlike the widely used degree of polarization uniformity (DOPU), the DDI is independent of the incident polarization state and, therefore, more robust to varying system and sample parameters. Moreover, it can be applied to single-input-polarization-state PS-OCT systems, and it overcomes several limitations of the emerging depolarization index used in multiple-input-polarization-state systems. Our results on tissue phantoms and human skin prove that DDI yields significant depolarization contrast improvements compared to DOPU, which highlights its potential for depolarization imaging in PS-OCT.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus.

Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency-dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic, and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality-breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality-breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.

Generalized Jones matrix method for homogeneous biaxial samples.

The generalized Jones matrix (GJM) is a recently introduced tool to describe linear transformations of three-dimensional light fields. Based on this framework, a specific method for obtaining the GJM of uniaxial anisotropic media was recently presented. However, the GJM of biaxial media had not been tackled so far, as the previous method made use of a simplified rotation matrix that lacks a degree of freedom in the three-dimensional rotation, thus being not suitable for calculating the GJM of biaxial media. In this work we propose a general method to derive the GJM of arbitrarily-oriented homogeneous biaxial media. It is based on the differential generalized Jones matrix (dGJM), which is the three-dimensional counterpart of the conventional differential Jones matrix. We show that the dGJM provides a simple and elegant way to describe uniaxial and biaxial media, with the capacity to model multiple simultaneous optical effects. The practical usefulness of this method is illustrated by the GJM modeling of the polarimetric properties of a negative uniaxial KDP crystal and a biaxial KTP crystal for any three-dimensional sample orientation. The results show that this method constitutes an advantageous and straightforward way to model biaxial media, which show a growing relevance for many interesting applications.

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.

Full characterization of dichroic samples from a single measurement by circular polarization orthogonality breaking.

We report a novel method to unambiguously determine the magnitude and orientation of linear dichroism in a simultaneous way. It is based on the use of a dedicated dual-frequency dual-polarization coherent source providing two orthogonal circularly polarized modes at the output. We show that the interaction of such a beam with dichroic media gives rise to a beatnote signal whose amplitude and phase enable the full determination of the diattenuation coefficient and axis orientation, respectively. The application of this method to polarimetric imaging provides single-shot sample characterization by its diattenuation coefficient and optical axis angle, with potential applications in biomedical imaging.

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.

Generalized Jones matrices for anisotropic media.

The interaction of arbitrary three-dimensional light beams with optical elements is described by the generalized Jones calculus, which has been formally proposed recently [Azzam, J. Opt. Soc. Am. A 28, 2279 (2011)]. In this work we obtain the parametric expression of the 3×3 differential generalized Jones matrix (dGJM) for arbitrary optical media assuming transverse light waves. The dGJM is intimately connected to the Gell-Mann matrices, and we show that it provides a versatile method for obtaining the macroscopic GJM of media with either sequential or simultaneous anisotropic effects. Explicit parametric expressions of the GJM for some relevant optical elements are provided.

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.

Experimental validation of Mueller matrix differential decomposition.

Mueller matrix differential decomposition is a novel method for retrieving the polarimetric properties of general depolarizing anisotropic media [N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011), R. Ossikovski, Opt. Lett. 36, 2330 (2011)]. The method has been verified for Mueller matrices available in the literature. We experimentally validate the decomposition for five different experimental setups with different commutation properties and controlled optical parameters, comparing the differential decomposition with the forward and reverse polar decompositions. The results enable to verify the method and to highlight its advantages for certain experimental applications of high interest.

Mueller matrix differential decomposition for direction reversal: application to samples measured in reflection and backscattering.

Mueller matrix differential decomposition is a novel method for analyzing the polarimetric properties of optical samples. It is performed through an eigenanalysis of the Mueller matrix and the subsequent decomposition of the corresponding differential Mueller matrix into the complete set of 16 differential matrices which characterize depolarizing anisotropic media. The method has been proposed so far only for measurements in transmission configuration. In this work the method is extended to the backward direction. The modifications of the differential matrices according to the reference system are discussed. The method is successfully applied to Mueller matrices measured in reflection and backscattering.

Depolarizing differential Mueller matrices.

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.

Mueller matrix differential decomposition.

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.

Thermal injury models for optical treatment of biological tissues: a comparative study.

The interaction of optical radiation with biological tissues causes an increase in the temperature that, depending on its magnitude, can provoke a thermal injury process in the tissue. The establishment of laser irradiation pathological limits constitutes an essential task, as long as it enables to fix and delimit a range of parameters that ensure a safe treatment in laser therapies. These limits can be appropriately described by kinetic models of the damage processes. In this work, we present and compare several models for the study of thermal injury in biological tissues under optical illumination, particularly the Arrhenius thermal damage model and the thermal dosimetry model based on CEM (Cumulative Equivalent Minutes) 43°C. The basic concepts that link the temperature and exposition time with the tissue injury or cellular death are presented, and it will be shown that they enable to establish predictive models for the thermal damage in laser therapies. The results obtained by both models will be compared and discussed, highlighting the main advantages of each one and proposing the most adequate one for optical treatment of biological tissues.

Photodynamic effects on basal cell carcinoma with topical Photosensitizer.

Photodynamic therapy (PDT) is a potential cancer therapy used in several clinical fields. Its application in dermatology following a fixed protocol usually generates good results. However, some cases of basal cell carcinoma show tumour persistence. The poor response observed in this type of pathology, whose lesions penetrate in the deeper layers of the skin, could be attributed to an insufficient accumulation of the PS (Photosensitizer) in deeper tissues. The development of accurate models could propose the adequate treatment dosimetry for those problematic cases in order to maximize the efficiency of the PDT treatment outcome. In this work we present a PDT model that tries to predict the photodynamic effect on the skin affected by a basal cell carcinoma with a topically administered photosensitizer. The results obtained allow us to know the evolution of the cytotoxic agent in order to estimate the necrotic area adjusting parameters such as the optical power, the photosensitizer concentration, the incubation and exposition time or the diffusivity and permeability of the damaged tissue.

Photochemical approach of photodynamic therapy applied to skin.

Photodynamic Therapy (PDT) is a recent treatment modality that allows malignant tissue destruction. The technique provides a localized effect and good cosmetic results. The application of PDT is based on the inoculation of a photosensitizer and the posterior irradiation by an optical source. This radiation chemically activates the drug and provokes reactions that lead to tissue necrosis. Nowadays there are fixed clinical PDT protocols that make use of a particular optical dose and photosensitizer amount. These parameters are independent of the patient and the lesion. In this work we present a PDT model that tries to predict the effect of the treatment on the tissue. The 3D optical propagation of radiation is calculated by means of the Radiation Transport Theory (RTT) model, solved via a Monte Carlo numerical model. Once the optical energy is obtained, a complex photochemical model is employed. This model takes into account the electronic transitions between molecular levels and particles concentrations. The data obtained allow us to estimate the destroyed area. The optical power of the source, the exposition time and the optochemical characteristics of the tissue can be varied. This implies that these parameters could be adjusted to the particular pathology we are dealing with. As a consequence, the treatment would be more efficient. We apply the model to the skin, due to the fact that PDT is commonly applied on it.