biblio.bib

% [ON08]
@article{OOI2008252,
  title    = {Simulation of aqueous humor hydrodynamics in human eye heat transfer},
  journal  = {Computers in Biology and Medicine},
  volume   = {38},
  number   = {2},
  pages    = {252-262},
  year     = {2008},
  issn     = {0010-4825},
  doi      = {https://doi.org/10.1016/j.compbiomed.2007.10.007},
  url      = {https://www.sciencedirect.com/science/article/pii/S001048250700176X},
  author   = {Ean-Hin Ooi and Eddie Yin-Kwee Ng},
  keywords = {Anterior chamber, Temperature, Aqueous humor, Human eye, Heat transfer},
  abstract = {The need to develop accurate representation of the human eye for the purpose of physiological studies is important to ensure that the predicted results are reliable. The presence of natural circulation of aqueous humor (AH) is evident from clinical, experimental and simulated observations. Most of the thermal models of the human eye that are found in the literature, however, had assumed a stagnant AH inside the anterior chamber. In this paper, a two-dimensional model of the human eye is developed where the circulation of AH inside the anterior chamber is included. The effects of the AH flow on the temperature distribution inside the eye are investigated. The natural circulation of AH is found to increase the temperature and distorts the temperature profile in the cornea and anterior chamber. Further investigations, where an artificial heat source is introduced inside the human eye suggest that AH flow plays a role in the heat transfer at the anterior region of the eye although this has yet to be quantified experimentally.}
}


@article{li2010,
  author   = {Li, Eric and Liu, G. R. and Tan, Vincent and He, Z. C.},
  title    = {Modeling and simulation of bioheat transfer in the human eye using the 3D alpha finite element method ($\alpha$FEM)},
  journal  = {International Journal for Numerical Methods in Biomedical Engineering},
  volume   = {26},
  number   = {8},
  pages    = {955-976},
  keywords = {bioheat transfer, numerical method, mesh-free method, finite element method (FEM), alpha finite element method ($\alpha$FEM)},
  doi      = {https://doi.org/10.1002/cnm.1372},
  url      = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.1372},
  abstract = {Abstract Computational modeling is an effective tool for the detection of eye abnormalities and a valuable assistant to hyperthermia treatments. In all these diagnoses and treatments, predicting the temperature distribution accurately is very important. However, the standard finite element method (FEM) currently used for such purposes has strong reliance on element meshes and the discretized system exhibits the so-called ‘overly stiff’ behavior. To overcome this shortcoming, this paper formulates an alpha finite element method ($\alpha$FEM) to compute two-dimensional (2D) and three-dimensional (3D) bioheat transfer in the human eyes. The $\alpha$FEM can produce much more accurate results using triangular (2D) and tetrahedron (3D) elements that can be generated automatically for complicated domains and hence is particularly suited for modeling human eyes. In the $\alpha$FEM, a scaling factor $\alpha$∈[0, 1] is introduced to combine the ‘overly stiff’ FEM model and ‘overly soft’ node-based finite element method (NS-FEM) model. With a properly chosen $\alpha$, the $\alpha$FEM can produce models with very ‘close-to-exact’ stiffness of the continuous system. Numerical results have shown that the present method gives much more accurate results compared with the standard FEM and the NS-FEM. Copyright 2010 John Wiley \& Sons, Ltd.},
  year     = {2010}
}


@article{NG2007829,
  title    = {Ocular surface temperature: A 3D FEM prediction using bioheat equation},
  journal  = {Computers in Biology and Medicine},
  volume   = {37},
  number   = {6},
  pages    = {829-835},
  year     = {2007},
  issn     = {0010-4825},
  doi      = {https://doi.org/10.1016/j.compbiomed.2006.08.023},
  url      = {https://www.sciencedirect.com/science/article/pii/S0010482506001557},
  author   = {E.Y.K. Ng and E.H. Ooi},
  keywords = {Ocular, Temperature, FEM, Bioheat, EM waves},
  abstract = {Computational and mathematical human eye models from previous studies which were constructed in two-dimensions (2D) did not give a precise representation of the actual human eye. This work is an extension from an earlier published work on the 2D model. In this paper, a 3D FEM model of the human eye is simulated for the steady state temperature distribution during normal condition and during electromagnetic (EM) wave radiation. Results show a discrepancy of 0.49\% for a normal condition as opposed to 1.9\% of a 2D model when compared to experimental results from open literatures. Investigations on the EM wave radiations found an average power absorption density of 15,151 and 22,145Wm-3 for the 750 and 1500MHz radiation, respectively. A peak temperature of 38.18°C was predicted for the 750MHz radiation while 41.19°C was computed for the 1500MHz radiation. These temperatures are in reasonable agreement with the simulated results computed by another report in the past.}
}

%% Parameters
% Permissivity = ε and T_amb
@article{MAPSTONE1968237,
  title    = {Measurement of corneal temperature},
  journal  = {Experimental Eye Research},
  volume   = {7},
  number   = {2},
  pages    = {237-IN29},
  year     = {1968},
  issn     = {0014-4835},
  doi      = {https://doi.org/10.1016/S0014-4835(68)80073-9},
  url      = {https://www.sciencedirect.com/science/article/pii/S0014483568800739},
  author   = {R. Mapstone},
  abstract = {Measuring the surface temperature of the cornea by contact thermometry has the disadvantages that anaesthesia and sterility are necessary and that temperature is measured at a point. A method of measuring corneal temperature using a bolometer that does not have these disadvantages is described, together with the results obtained. In addition the theoretical and practical considerations in its use are discussed. A value for the emissivity of the corneal surface of between 0·97 and 1 is derived.}
}

% h_amb
@incollection{KOSKY2013259,
  title     = {Chapter 12 - Mechanical Engineering},
  editor    = {Philip Kosky and Robert Balmer and William Keat and George Wise},
  booktitle = {Exploring Engineering (Third Edition)},
  publisher = {Academic Press},
  edition   = {Third Edition},
  address   = {Boston},
  pages     = {259-281},
  year      = {2013},
  isbn      = {978-0-12-415891-7},
  doi       = {https://doi.org/10.1016/B978-0-12-415891-7.00012-1},
  url       = {https://www.sciencedirect.com/science/article/pii/B9780124158917000121},
  author    = {Philip Kosky and Robert Balmer and William Keat and George Wise}
}

@misc{engeneer-edge,
  title        = {Convective Heat Transfer Coefficients Table Chart},
  author       = {Engineers Edge},
  howpublished = {\url{https://www.engineersedge.com/heat_transfer/convective_heat_transfer_coefficients__13378.htm}},
  note         = {Accessed: 2022-12-28}
}

% h_bl
@article{Lagendijk_1982,
  doi       = {10.1088/0031-9155/27/11/001},
  url       = {https://doi.org/10.1088/0031-9155/27/11/001},
  year      = 1982,
  month     = {11},
  publisher = {{IOP} Publishing},
  volume    = {27},
  number    = {11},
  pages     = {1301--1311},
  author    = {J J W Lagendijk},
  title     = {A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment},
  journal   = {Physics in Medicine and Biology},
  abstract  = {A mathematical model based on the finite difference method has been developed to calculate transient and steady state temperature distributions in normal unexposed human and rabbit eyes, and human and rabbit eyes heated by various heating techniques. The normal steady state temperature distributions in human and rabbit eyes are given. The model has been experimentally fitted to data obtained from measurements on rabbit eyes. The heat transfer from the choroid to the body core temperature of the rabbit is described by the heat transfer coefficient hs=65 W m-2 degrees C-1, and from the cornea to the surrounding air temperature by hc=20W m-2 degrees C-1. The thermal conductivity and the specific heat of the lens of the rabbit eye were determined empirically to be 0.40 W m-1 degrees C-1 and 3.0 J g-1 degrees C-1 respectively. The thermal properties of the vitreous humour were taken to be equal to the thermal properties of water.}
}

% E [Sco88]
@article{Scott_1988,
  doi       = {10.1088/0031-9155/33/2/003},
  url       = {https://doi.org/10.1088/0031-9155/33/2/003},
  year      = 1988,
  publisher = {{IOP} Publishing},
  volume    = {33},
  number    = {2},
  pages     = {227--242},
  author    = {Scott, J.A.},
  title     = {A finite element model of heat transport in the human eye},
  journal   = {Physics in Medicine and Biology},
  abstract  = {A mathematical model of the human eye based on the bioheat transfer equation is developed. The intraocular temperature distribution is calculated using the Galerkin finite element method. A difficulty associated with the development of an accurate model of the human eye is the lack of reliable biological data available on the constants and parameters that are used in the model. These parameters include the thermal conductivities of the ocular tissues, the heat loss from the anterior corneal surface to the surroundings by convection and evaporation, and the convective heat loss from the sclera to the body core. The different values for the parameters reported in the ophthalmic literature are employed in the model, and the sensitivity of the temperature distribution to uncertainties in the parameters is investigated. A set of control parameter values is suggested for the normal human eye. The effect of the ambient temperature and the body-core temperature on the temperature distribution in the human eye is considered.}
}

% [Efr89]
@article{Efron1989OcularST,
  title   = {Ocular surface temperature.},
  author  = {Nathan Efron and Graeme Young and Noel A Brennan},
  journal = {Current eye research},
  year    = {1989},
  volume  = {8 9},
  pages   = {901-6}
}


% [Ng 06]
@article{NG2006268,
  author   = {{Ng, E.Y.K. and Ooi, E.H.}},
  title    = {FEM simulation of the eye structure with bioheat analysis},
  journal  = {Computer Methods and Programs in Biomedicine},
  volume   = {82},
  number   = {3},
  pages    = {268-276},
  year     = {2006},
  issn     = {0169-2607},
  doi      = {https://doi.org/10.1016/j.cmpb.2006.04.001},
  url      = {https://www.sciencedirect.com/science/article/pii/S0169260706000708},
  keywords = {Bioheat, FEM, Eye temperature profile, Physiological simulation},
  abstract = {Computer simulation on medical sciences has gain increasing popularity as computational technology advances. Successful thermal modeling of the human eye will assist in enabling early detections of eye abnormalities such as inflammatory. However, validity of every computer simulated results must be benchmarked with experimental measurement and this can be a daunting task especially in biomedical fields where experimental data is not in abundance. This paper presents a 2D finite element (FE) human eye model developed to simulate its thermal steady state conditions based on the properties and parameters reported in the open literatures. The results are verified with experimental and computational results obtained by previous studies on human as well as animal eyes. Results show discrepancy of only 0.33\% when compared to images from infrared (IR) screening and a difference of only 0.127\% compared to another finite element model. The sensitivity analysis also provides good agreement with results by previous studies. This promising simulation allows new possibility in computational methods for eye health care.}
}

% Evaporation rate E
% https://archive.org/details/physiologyofeyece2adle/page/450/mode/2up
@book{adler53,
  author    = {Adler, Francis Heed},
  editor    = {},
  publisher = {St. Louis Mosby},
  title     = {Physiology of the eye, clinical applications},
  year      = {1953}
}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Eye2brain
@misc{eye2brain,
  author       = {Sala, Lorenzo},
  title        = {Eye2brain},
  howpublished = {\url{http://www.cemosis.fr/projects/eye2brain/}},
  year         = {2016}
}

@article{omvs2023,
  title   = {The Ocular Mathematical Virtual Simulator: a validated multiscale model for hemodynamics and biomechanics in the human eye},
  journal = {International Journal for Numerical Methods in Biomedical Engineering},
  author  = {Sala, Lorenzo and Prud’homme, Christophe and Guidoboni, Giovanna and Szopos, Marcela and Harris, Alon},
  note    = {To appear}
}


@inproceedings{10.1007/978-3-030-63591-6_45,
  author    = {Abdelhafid, Farah
               and Guidoboni, Giovanna
               and Okumura, Naoki
               and Koizumi, Noriko
               and Srinivas, Sangly P.},
  editor    = {Kilgour, D. Marc
               and Kunze, Herb
               and Makarov, Roman
               and Melnik, Roderick
               and Wang, Xu},
  title     = {Operator Splitting for the Simulation of Aqueous Humor Thermo-Fluid-Dynamics in the Anterior Chamber},
  booktitle = {Recent Developments in Mathematical, Statistical and Computational Sciences},
  year      = {2021},
  publisher = {Springer International Publishing},
  address   = {Cham},
  pages     = {489--499},
  abstract  = {This work presents a numerical scheme based on operator splitting for the thermo-fluid-dynamical simulation of aqueous humor flow in the anterior chamber of the human eye. The stability properties of the scheme are investigated theoretically. Numerical results are presented for different postures and different external temperatures.},
  isbn      = {978-3-030-63591-6}
}



@article{BHANDARI2020286,
  title    = {Effect of aging on heat transfer, fluid flow and drug transport in anterior human eye: A computational study},
  journal  = {Journal of Controlled Release},
  volume   = {328},
  pages    = {286-303},
  year     = {2020},
  issn     = {0168-3659},
  doi      = {https://doi.org/10.1016/j.jconrel.2020.08.044},
  url      = {https://www.sciencedirect.com/science/article/pii/S0168365920304855},
  author   = {Ajay Bhandari and Ankit Bansal and Niraj Sinha},
  keywords = {Aging human eye, Anterior chamber, Primary open-angle glaucoma, Heat transfer, Fluid flow},
  abstract = {There are a lot of geometrical and morphological changes that happen in the human eye with age. Primary open-angle glaucoma, which is caused by the increase in intraocular pressure inside the anterior chamber of the eye is also associated with the physiological aging of the eye. Therefore, it is crucial to understand the effects of aging on drug delivery in the human eye when applied topically. Consequently, a numerical model of topical drug delivery for an aging human eye has been developed using commercial software COMSOL Multiphysics in the current study. Three different age groups (young, middle and old) have been considered and the changes in geometrical and tissue properties of different domains of the eye with age have been included in the numerical model. The effect of aging on heat transfer, aqueous humor flow, intraocular pressure and drug concentration in different domains and orientations of the eye have been investigated. Additionally, an attempt has been made to predict the best class of anti-glaucomatic treatment in silico that should be preferred to treat primary open-angle glaucoma effectively. Results illustrate that there is a decrease in the average corneal temperature and an increase in the temperature deviation across the cornea with age. Further, there is a decrease in the aqueous humor flow magnitude in the anterior chamber of the eye and an increase in intraocular pressure in the anterior chamber of older age groups, which leads to primary open-angle glaucoma. The reduced aqueous humor flow leads to increased drug concentration in the anterior chamber as well as iris and reduced drug concentration in the trabecular mesh of the older age groups, thereby affecting the treatment efficacy. Additionally, our simulated results demonstrate that anti-glaucomatic treatments should be more focused on treating the trabecular mesh rather than the ciliary body of the eye.}
}


@article{ROSENBLUTH1977325,
  title    = {Temperature measurements in the eye},
  journal  = {Experimental Eye Research},
  volume   = {25},
  number   = {4},
  pages    = {325-341},
  year     = {1977},
  issn     = {0014-4835},
  doi      = {https://doi.org/10.1016/0014-4835(77)90100-2},
  url      = {https://www.sciencedirect.com/science/article/pii/0014483577901002},
  author   = {Robert F. Rosenbluth and Irving Fatt},
  keywords = {temperature measurement, heat transfer, ocular temperature},
  abstract = {An experimental and theoretical study shows that a metallic needle temperature probe reads in vivo eye temperatures significantly lower than the actual temperatures. In this study an epoxy-encased fine wire thermocouple probe was used to obtain in vivo ocular temperatures in rabbits. Radiometric surface temperatures were obtained over a range of wind velocities. The results obtained from a mathematical model were compared with the data obtained from the needle and fine wire temperature probes placed in the rabbit eye. The comparison suggests that intraocular temperature measurements are in error due to heat conduction losses from the probe and trauma to the eye. The errors are smaller for probes of fine wire than for needle-type probes. Results from the mathematical model can be used to predict intraocular temperatures in rabbits and humans for various air temperatures and wind velocities.}
}


@article{Purslow2005-ky,
  title    = {Ocular surface temperature: a review},
  author   = {Purslow, Christine and Wolffsohn, James S},
  abstract = {PURPOSE: To review the evolution in ocular temperature
              measurement during the last century and examine the advantages
              and applications of the latest noncontact techniques. The
              characteristics and source of ocular surface temperature are also
              discussed. METHODS: The literature was reviewed with regard to
              progress in human thermometry techniques, the parallel
              development in ocular temperature measurement, the current use of
              infrared imaging, and the applications of ocular thermography.
              RESULTS: It is widely acknowledged that the ability to measure
              ocular temperature accurately will increase the understanding of
              ocular physiology. There is a characteristic thermal profile
              across the anterior eye, in which the central area appears
              coolest. Ocular surface temperature is affected by many factors,
              including inflammation. In thermometry of the human eye, contact
              techniques have largely been superseded by infrared imaging,
              providing a noninvasive and potentially more accurate method of
              temperature measurement. Ocular thermography requires high
              resolution and frame rate: features found in the latest
              generation of cameras. Applications have included dry eye,
              contact lens wear, corneal sensitivity, and refractive surgery.
              CONCLUSIONS: Interest in the temperature of the eye spans almost
              130 years. It has been an area of research largely driven by
              prevailing technology. Current instrumentation offers the
              potential to measure ocular surface temperature with more
              accuracy, resolution, and speed than previously possible. The use
              of dynamic ocular thermography offers great opportunities for
              monitoring the temperature of the anterior eye.},
  journal  = {Eye Contact Lens},
  volume   = 31,
  number   = 3,
  pages    = {117--123},
  month    = may,
  year     = 2005,
  language = {en}
}


@article{10.1115/1.3450259,
  author   = {Emery, A. F. and Kramar, P. and Guy, A. W. and Lin, J. C.},
  title    = {{Microwave Induced Temperature Rises in Rabbit Eyes in Cataract Research}},
  journal  = {Journal of Heat Transfer},
  volume   = {97},
  number   = {1},
  pages    = {123-128},
  year     = {1975},
  month    = {02},
  abstract = {{Microwave power deposition patterns and temperature distributions were measured for rabbit eyes exposed to localized near zone 2450 MHz radiation and good agreement was obtained between the measured and predicted transient temperature fields. The lenses were biomicroscopically examined to determine the minimum exposure times necessary to produce posterior lens opacity (cataracts) and these times are correlated with the temperature calculations to suggest that a threshold temperature level exists.}},
  issn     = {0022-1481},
  doi      = {10.1115/1.3450259},
  url      = {https://doi.org/10.1115/1.3450259},
  eprint   = {https://asmedigitalcollection.asme.org/heattransfer/article-pdf/97/1/123/5744217/123\_1.pdf}
}



@article{https://doi.org/10.1002/cnm.3791,
  author   = {Sala, Lorenzo and Prud'homme, Christophe and Guidoboni, Giovanna and Szopos, Marcela and Harris, Alon},
  title    = {The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye},
  journal  = {International Journal for Numerical Methods in Biomedical Engineering},
  % volume   = {n/a},
  % number   = {n/a},
  pages    = {e3791},
  keywords = {hybridizable discontinuous Galerkin method, mathematical and computational ophthalmology, multiphysics and multiscale modeling, ocular hemodynamics and biomechanics, validation},
  doi      = {https://doi.org/10.1002/cnm.3791},
  url      = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3791},
  eprint   = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.3791},
  abstract = {Abstract We present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called Ocular Mathematical Virtual Simulator (OMVS). The OMVS aims to solve problems arising in biomechanics and hemodynamics within the human eye. We discuss our contribution towards improving the reliability and reproducibility of computational studies by performing a thorough validation of the numerical predictions against experimental data. The OMVS proved capable of simulating complex multiphysics and multiscale scenarios motivated by the study of glaucoma. Furthermore, its modular design allows the continuous integration of new models and methods as the research moves forward, and supports the utilization of the OMVS as a promising non-invasive clinical investigation tool for personalized research in ophthalmology.}
}


@ARTICLE{Guidoboni2020-vr,
  title     = "Neurodegenerative disorders of the eye and of the brain: A
               perspective on their fluid-dynamical connections and the
               potential of mechanism-driven modeling",
  author    = "Guidoboni, Giovanna and Sacco, Riccardo and Szopos, Marcela and
               Sala, Lorenzo and Verticchio Vercellin, Alice Chandra and
               Siesky, Brent and Harris, Alon",
  abstract  = "Neurodegenerative disorders (NDD) such as Alzheimer's and
               Parkinson's diseases are significant causes of morbidity and
               mortality worldwide. The pathophysiology of NDD is still
               debated, and there is an urgent need to understand the
               mechanisms behind the onset and progression of these
               heterogenous diseases. The eye represents a unique window to the
               brain that can be easily assessed via non-invasive ocular
               imaging. As such, ocular measurements have been recently
               considered as potential sources of biomarkers for the early
               detection and management of NDD. However, the current use of
               ocular biomarkers in the clinical management of NDD patients is
               particularly challenging. Specifically, many ocular biomarkers
               are influenced by local and systemic factors that exhibit
               significant variation among individuals. In addition, there is a
               lack of methodology available for interpreting the outcomes of
               ocular examinations in NDD. Recently, mathematical modeling has
               emerged as an important tool capable of shedding light on the
               pathophysiology of multifactorial diseases and enhancing
               analysis and interpretation of clinical results. In this
               article, we review and discuss the clinical evidence of the
               relationship between NDD in the brain and in the eye and explore
               the potential use of mathematical modeling to facilitate NDD
               diagnosis and management based upon ocular biomarkers.",
  journal   = "Front. Neurosci.",
  publisher = "Frontiers Media SA",
  volume    =  14,
  pages     = "566428",
  month     =  nov,
  year      =  2020,
  keywords  = "cerebrospinal fluid pressure; fluid-dynamics; glaucoma;
               intraocular pressure; mathematical modeling; neurodegenerative
               disorders",
  copyright = "https://creativecommons.org/licenses/by/4.0/",
  language  = "en"
}


%% SA
@inproceedings{Sobol1993SensitivityEF,
  title={Sensitivity Estimates for Nonlinear Mathematical Models},
  author={Ilya M. Sobol},
  year={1993}
}

@article{MBE2021,
  title    = {Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator},
  journal  = {Mathematical Biosciences and Engineering},
  volume   = {18},
  number   = {3},
  pages    = {2010-2032},
  year     = {2021},
  issn     = {1551-0018},
  doi      = {10.3934/mbe.2021105},
  url      = {https://www.aimspress.com/article/doi/10.3934/mbe.2021105},
  author   = {Christophe Prud'homme and Lorenzo Sala and Marcela Szopos},
  keywords = {predictive ocular vascular dynamics, computational model, sensitivity analysis, ocular mathematical virtual simulator, Sobol index analysis, uncertainty quantification}
}


%% RBM
@article{10.1115/1.1448332,
  author   = {Prud’homme , C.  and Rovas , D. V.  and Veroy , K.  and Machiels, L.  and Maday, Y.  and Patera, A. T.  and Turinici, G. },
  title    = {{Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods }},
  journal  = {Journal of Fluids Engineering},
  volume   = {124},
  number   = {1},
  pages    = {70-80},
  year     = {2001},
  month    = {11},
  abstract = {{We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations—Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation—relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. }},
  issn     = {0098-2202},
  doi      = {10.1115/1.1448332},
  url      = {https://doi.org/10.1115/1.1448332},
  eprint   = {https://asmedigitalcollection.asme.org/fluidsengineering/article-pdf/124/1/70/5902394/70\_1.pdf}
}

@book{Quarteroni2016,
  doi       = {10.1007/978-3-319-15431-2},
  url       = {https://doi.org/10.1007/978-3-319-15431-2},
  year      = {2016},
  publisher = {Springer International Publishing},
  author    = {Alfio Quarteroni and Andrea Manzoni and Federico Negri},
  title     = {Reduced Basis Methods for Partial Differential Equations}
}

@article{Rozza2007,
  author   = {Rozza, G.
              and Huynh, D. B. P.
              and Patera, A. T.},
  title    = {Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations},
  journal  = {Archives of Computational Methods in Engineering},
  year     = {2007},
  month    = {09},
  day      = {01},
  volume   = {15},
  number   = {3},
  pages    = {1-47},
  abstract = {In this paper we consider (hierarchical, La-grange)reduced basis approximation anda posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equa-tions. The essential ingredients are (primal-dual)Galer-kin projection onto a low-dimensional space associated with a smooth ``parametric manifold'' - dimension re-duction; efficient and effective greedy sampling meth-ods for identification of optimal and numerically stable approximations - rapid convergence;a posteriori er-ror estimation procedures - rigorous and sharp bounds for the linear-functional outputs of interest; and Offine-Online computational decomposition strategies - min-imummarginal cost for high performance in the real-time/embedded (e.g., parameter-estimation, control)and many-query (e.g., design optimization, multi-model/ scale)contexts. We present illustrative results for heat conduction and convection-diffusion,inviscid flow, and linear elasticity; outputs include transport rates, added mass,and stress intensity factors.},
  issn     = {1886-1784},
  doi      = {10.1007/BF03024948},
  url      = {https://doi.org/10.1007/BF03024948}
}

@article{Rozza2008-hx,
  title     = {Reduced basis approximation and a posteriori error estimation
               for affinely parametrized elliptic coercive partial differential
               equations},
  author    = {Rozza, G and Huynh, D B P and Patera, A T},
  journal   = {Arch. Comput. Methods Eng.},
  publisher = {Springer Science and Business Media LLC},
  volume    = 15,
  number    = 3,
  pages     = {229--275},
  month     = sep,
  year      = 2008,
  language  = {en}
}

@article{buffa2012,
  author  = {{Buffa, Annalisa} and {Maday, Yvon} and {Patera, Anthony T.} and {Prud\'{}homme, Christophe} and {Turinici, Gabriel}},
  title   = {A priori convergence of the Greedy algorithm  for the parametrized reduced basis method},
  doi     = {10.1051/m2an/2011056},
  url     = {https://doi.org/10.1051/m2an/2011056},
  journal = {ESAIM: M2AN},
  year    = 2012,
  volume  = 46,
  number  = 3,
  pages   = {595-603},
  month   = {}
}



%%
@book{Ern2021-mi,
  title     = {Finite elements {II}},
  author    = {Ern, Alexandre and Guermond, Jean-Luc},
  publisher = {Springer International Publishing},
  series    = {Texts in applied mathematics},
  year      = 2021,
  address   = {Cham}
}

@article{Milka1993,
  abstract  = {In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space $H^1 (\Omega )$ are examined.},
  author    = {Milka, Zden\v{e}k},
  journal   = {Applications of Mathematics},
  keywords  = {heat conduction; heat radiation; finite elements; Stefan-Boltzmann boundary condition; stationary heat conduction; Stefan-Boltzmann boundary condition; stationary heat conduction; finite element},
  language  = {eng},
  number    = {1},
  pages     = {67-79},
  publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
  title     = {Finite element solution of a stationary heat conduction equation with the radiation boundary condition},
  url       = {http://eudml.org/doc/15737},
  volume    = {38},
  year      = {1993}
}




%%
@software{christophe_prud_homme_2023_8272196,
  author       = {Christophe Prud'homme and
                  Vincent Chabannes and
                  StephaneVeys and
                  Thibaut Metivet and
                  Alexandre Ancel and
                  Romain Hild and
                  jbwahl and
                  Cécile Daversin-Catty and
                  Thomas Saigre and
                  Guillaume Dollé and
                  Tarabay and
                  lsala and
                  LANTZT and
                  Doyeux and
                  Trophime and
                  Abdoulaye SAMAKE and
                  Luca Berti and
                  Benjamin Vanthong and
                  Mourad ISMAIL and
                  Vincent Huber and
                  Kyoshe Winstone and
                  schenone and
                  Philippe and
                  Daniele Prada and
                  Céline Van Landeghem and
                  alixkien and
                  Pierre Jolivet and
                  Denis Barbier and
                  clayrc},
  title        = {feelpp/feelpp: Feel++ Release V111 alpha.5},
  month        = aug,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v0.111.0-alpha.5},
  doi          = {10.5281/zenodo.8272196},
  url          = {https://doi.org/10.5281/zenodo.8272196}
}

@software{salome,
  author = {Open CASCADE},
  title  = {SALOME: The Open Source Integration Platform for Numerical Simulation.},
  year   = {2022},
  url    = {https://salome-project.org}
}

@software{mmg,
  author = {MMG tools},
  title  = {MMG: a mesh-based finite element library},
  year   = {2022},
  url    = {https://www.mmgtools.org/}
}

@inbook{Baudin2016,
  author    = {Baudin, Micha{\"e}l
               and Dutfoy, Anne
               and Iooss, Bertrand
               and Popelin, Anne-Laure},
  editor    = {Ghanem, Roger
               and Higdon, David
               and Owhadi, Houman},
  title     = {OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation},
  booktitle = {Handbook of Uncertainty Quantification},
  year      = {2016},
  publisher = {Springer International Publishing},
  address   = {Cham},
  pages     = {1--38},
  isbn      = {978-3-319-11259-6},
  doi       = {10.1007/978-3-319-11259-6_64-1},
  url       = {https://doi.org/10.1007/978-3-319-11259-6_64-1}
}



%% LASER
@article{Masters2004,
  title     = {Franz Frankhauser and Sylwia Kwasniewska (eds): Lasers in Ophthalmology—Basic,  Diagnostic and Surgical Aspects: A Review: Kugler Publications,  The Hague,  The Netherlands,  2003,  pp. 450 (ISBN 90-6299-189-0)},
  volume    = {242},
  issn      = {1435-702X},
  url       = {http://dx.doi.org/10.1007/s00417-004-0873-3},
  doi       = {10.1007/s00417-004-0873-3},
  number    = {5},
  journal   = {Graefe’s Archive for Clinical and Experimental Ophthalmology},
  publisher = {Springer Science and Business Media LLC},
  author    = {Masters, Barry R.},
  year      = {2004},
  month     = apr,
  pages     = {446–447}
}

% Electromagnetic waves
@article{Hirata2007,
  title     = {Temperature elevation in the eye of anatomically based human head models for plane-wave exposures},
  volume    = {52},
  issn      = {1361-6560},
  url       = {http://dx.doi.org/10.1088/0031-9155/52/21/003},
  doi       = {10.1088/0031-9155/52/21/003},
  number    = {21},
  journal   = {Physics in Medicine and Biology},
  publisher = {IOP Publishing},
  author    = {Hirata, A and Watanabe, S and Fujiwara, O and Kojima, M and Sasaki, K and Shiozawa, T},
  year      = {2007},
  month     = oct,
  pages     = {6389–6399}
}

@article{doi:10.1142/S0219519409002936,
  author   = {Ooi, E. H. and Ng, E. Y. K.},
  title    = {Ocular Temperature Distribution: a Mathematical Perspective},
  journal  = {Journal of Mechanics in Medicine and Biology},
  volume   = {09},
  number   = {02},
  pages    = {199-227},
  year     = {2009},
  doi      = {10.1142/S0219519409002936},
  abstract = {Mathematical modeling has proven to be a viable alternative for investigating the temperature distribution inside the human eye. This is due to its ability to overcome the limitations infrared (IR) thermography; the leading method in ocular temperature measurement. A wide range of mathematical studies on the ocular temperature distribution during various conditions have been published in the literature. In this paper, we carry out an in-depth review of the various mathematical models of the eye that have been developed in the past. Various problems and the implications from the mathematical predictions of these studies are discussed. The future directions of studies in ocular temperature distribution are deliberated. }
}


@article{Wang2016,
  author   = {Wang, Wenjia
              and Qian, Xiuqing
              and Song, Hongfang
              and Zhang, Mindi
              and Liu, Zhicheng},
  title    = {Fluid and structure coupling analysis of the interaction between aqueous humor and iris},
  journal  = {BioMedical Engineering OnLine},
  year     = {2016},
  month    = {12},
  day      = {28},
  volume   = {15},
  number   = {2},
  pages    = {133},
  abstract = {Glaucoma is the primary cause of irreversible blindness worldwide associated with high intraocular pressure (IOP). Elevated intraocular pressure will affect the normal aqueous humor outflow, resulting in deformation of iris. However, the deformation ability of iris is closely related to its material properties. Meanwhile, the passive deformation of the iris aggravates the pupillary block and angle closure. The nature of the interaction mechanism of iris deformation and aqueous humor fluid flow has not been fully understood and has been somewhat a controversial issue. The purpose here was to study the effect of IOP, localization, and temperature on the flow of the aqueous humor and the deformation of iris interacted by aqueous humor fluid flow.},
  issn     = {1475-925X},
  doi      = {10.1186/s12938-016-0261-3},
  url      = {https://doi.org/10.1186/s12938-016-0261-3}
}

@inproceedings{saigre:hal-04558924,
  TITLE = {{A coupled fluid-dynamics-heat transfer model for 3D simulations of the aqueous humor flow in the human eye}},
  AUTHOR = {Saigre, Thomas and Prud'Homme, Christophe and Szopos, Marcela and Chabannes, Vincent},
  URL = {https://www.compbiomed.net/2024/cmbe-proceedings.htm},
  BOOKTITLE = {{8th International Conference on Computational and Mathematical Biomedical Engineering – CMBE2024 Proceedings}},
  EDITOR = {P. Nithiarasu and R. Löhner},
  ADDRESS = {Arlington (Virginia), United States},
  YEAR = {2024},
  MONTH = Jun,
  KEYWORDS = {mathematical and computational ophthalmology ; finite element method ; thermo-fluid dynamics ; mathematical and computational ophthalmology ; Thermo-fluid dynamics},
  PDF = {https://hal.science/hal-04558924/file/CMBE24Abstract.pdf},
  HAL_ID = {hal-04558924},
  HAL_VERSION = {v1},
}


%% SA
@article{DODIG201448,
  title    = {Stochastic sensitivity of the electromagnetic distributions inside a human eye modeled with a 3D hybrid BEM/FEM edge element method},
  journal  = {Engineering Analysis with Boundary Elements},
  volume   = {49},
  pages    = {48-62},
  year     = {2014},
  note     = {Special issue on Bioelectromagnetics},
  issn     = {0955-7997},
  doi      = {https://doi.org/10.1016/j.enganabound.2014.04.005},
  url      = {https://www.sciencedirect.com/science/article/pii/S0955799714000708},
  author   = {H. Dodig and S. Lalléchère and P. Bonnet and D. Poljak and K. {El Khamlichi Drissi}},
  keywords = {Boundary element method, Finite element technique, Hybrid method, Bio-electromagnetism, Uncertainty, Stochastic collocation, Sensitivity analysis},
  abstract = {This contribution was dedicated to the assessment of the electromagnetic (EM) distributions inside a 3D modeled human eye. Since the use of accurate and efficient electromagnetic tools is crucial to obtain such results, an original hybrid boundary element method (BEM)/finite element method (FEM) is presented through the example of an EM wave impinging on the eye corneal region. Due to the variability inherent to the characterizing of living parameters (regarding our frequency range of interest about a few GHz), an accurate modeling of those mostly electrical data is necessary. A simple formalism based upon a “philosophy” close to Monte Carlo requirements is proposed in this paper in order to integrate efficiently and precisely uncertainties in the proposed results. The analysis of the sensitivity of different electrical parameters aims to increase a better knowledge of the EM fields distribution inside an eye. Obviously, both the deterministic EM modeling and the stochastic theoretical basis will be presented. The whole model will be illustrated on numerical examples including different random variables.}
}

@article{SUSNJARA20221,
  title    = {Uncertainty quantification and sensitivity analysis of transcranial electric stimulation for 9-subdomain human head model},
  journal  = {Engineering Analysis with Boundary Elements},
  volume   = {135},
  pages    = {1-11},
  year     = {2022},
  issn     = {0955-7997},
  doi      = {https://doi.org/10.1016/j.enganabound.2021.10.026},
  url      = {https://www.sciencedirect.com/science/article/pii/S0955799721003192},
  author   = {Anna Šušnjara and Ožbej Verhnjak and Dragan Poljak and Mario Cvetković and Jure Ravnik},
  keywords = {Analysis of variance, Boundary element method, Stochastic collocation, Transcranial electric stimulation, 9-subdomain head model},
  abstract = {This paper deals with uncertainty quantification of transcranial electric stimulation (TES) of realistic human head model. The head model taken from Visible Human Project consists of 9 subdomains: scalp, skull, CSF, grey matter, white matter, cerebellum, ventricles, jaw and tongue. The deterministic computation of quasi-static induced electric scalar potential features boundary element method (BEM). Conductivities of each subdomain are modelled as uniformly distributed random variables and stochastic analysis features a non-intrusive stochastic collocation method (SCM). The input uncertainties impact only the magnitude of the electric scalar potential and not the position of the potential extrema. Skin and brain conductivities play the most important role, while CSF conductivity has negligible impact on the output potential variance. The significance of the skull conductivity is not high for the chosen input parameter setup. In the previous work authors considered 3-compartment head model which consisted of scalp, skull and brain compartments. The presented model is a step forward in SCM+BEM TES analysis, primarily in terms of model complexity. Comparing the results of the two analyses it can be concluded that the uncertainty in the added tissues’ conductivities do not impact the variation of the output electric potential.}
}

@article{9522096,
  author   = {Šušnjara, Anna and Dodig, Hrvoje and Poljak, Dragan and Cvetković, Mario},
  journal  = {IEEE Transactions on Electromagnetic Compatibility},
  title    = {Stochastic-Deterministic Thermal Dosimetry Below 6 GHz for 5G Mobile Communication Systems},
  year     = {2021},
  volume   = {63},
  number   = {5},
  pages    = {1667-1679},
  keywords = {Stochastic processes;Heating systems;Dosimetry;Mathematical model;Computational modeling;Thermal conductivity;Blood;Deterministic and stochastic models;fifth generation (5G) frequency range;sensitivity analysis (SA);stochastic collocation (SC);thermal dosimetry},
  doi      = {10.1109/TEMC.2021.3098431}
}