How to report multiple outcome metrics in virtual reality simulation

Background Virtual reality (VR) simulation is increasingly used in surgical disciplines. Since VR simulators measure multiple outcomes, standardized reporting is needed. Methods We present an algorithm for combining multiple VR outcomes into dimension summary measures, which are then integrated into a meaningful total score. We reanalyzed the data of two VR studies applying the algorithm. Results The proposed algorithm was successfully applied to both VR studies. Conclusions The algorithm contributes to standardized and transparent reporting in VR-related research.

Analysis of space-time environmental data in complex regions

This thesis develops a comprehensive and a flexible statistical framework for the analysis and detection of space, time and space-time clusters of environmental point data. The developed clustering methods were applied in both simulated datasets and real-world environmental phenomena; however, only the cases of forest fires in Canton of Ticino (Switzerland) and in Portugal are expounded in this document. Normally, environmental phenomena can be modelled as stochastic point processes where each event, e.g. the forest fire ignition point, is characterised by its spatial location and occurrence in time. Additionally, information such as burned area, ignition causes, landuse, topographic, climatic and meteorological features, etc., can also be used to characterise the studied phenomenon. Thereby, the space-time pattern characterisa- tion represents a powerful tool to understand the distribution and behaviour of the events and their correlation with underlying processes, for instance, socio-economic, environmental and meteorological factors. Consequently, we propose a methodology based on the adaptation and application of statistical and fractal point process measures for both global (e.g. the Morisita Index, the Box-counting fractal method, the multifractal formalism and the Ripley's K-function) and local (e.g. Scan Statistics) analysis. Many measures describing the space-time distribution of environmental phenomena have been proposed in a wide variety of disciplines; nevertheless, most of these measures are of global character and do not consider complex spatial constraints, high variability and multivariate nature of the events. Therefore, we proposed an statistical framework that takes into account the complexities of the geographical space, where phenomena take place, by introducing the Validity Domain concept and carrying out clustering analyses in data with different constrained geographical spaces, hence, assessing the relative degree of clustering of the real distribution. Moreover, exclusively to the forest fire case, this research proposes two new methodologies to defining and mapping both the Wildland-Urban Interface (WUI) described as the interaction zone between burnable vegetation and anthropogenic infrastructures, and the prediction of fire ignition susceptibility. In this regard, the main objective of this Thesis was to carry out a basic statistical/- geospatial research with a strong application part to analyse and to describe complex phenomena as well as to overcome unsolved methodological problems in the characterisation of space-time patterns, in particular, the forest fire occurrences. Thus, this Thesis provides a response to the increasing demand for both environmental monitoring and management tools for the assessment of natural and anthropogenic hazards and risks, sustainable development, retrospective success analysis, etc. The major contributions of this work were presented at national and international conferences and published in 5 scientific journals. National and international collaborations were also established and successfully accomplished. -- Cette thèse développe une méthodologie statistique complète et flexible pour l'analyse et la détection des structures spatiales, temporelles et spatio-temporelles de données environnementales représentées comme de semis de points. Les méthodes ici développées ont été appliquées aux jeux de données simulées autant qu'A des phénomènes environnementaux réels; nonobstant, seulement le cas des feux forestiers dans le Canton du Tessin (la Suisse) et celui de Portugal sont expliqués dans ce document. Normalement, les phénomènes environnementaux peuvent être modélisés comme des processus ponctuels stochastiques ou chaque événement, par ex. les point d'ignition des feux forestiers, est déterminé par son emplacement spatial et son occurrence dans le temps. De plus, des informations tels que la surface bru^lée, les causes d'ignition, l'utilisation du sol, les caractéristiques topographiques, climatiques et météorologiques, etc., peuvent aussi être utilisées pour caractériser le phénomène étudié. Par conséquent, la définition de la structure spatio-temporelle représente un outil puissant pour compren- dre la distribution du phénomène et sa corrélation avec des processus sous-jacents tels que les facteurs socio-économiques, environnementaux et météorologiques. De ce fait, nous proposons une méthodologie basée sur l'adaptation et l'application de mesures statistiques et fractales des processus ponctuels d'analyse global (par ex. l'indice de Morisita, la dimension fractale par comptage de boîtes, le formalisme multifractal et la fonction K de Ripley) et local (par ex. la statistique de scan). Des nombreuses mesures décrivant les structures spatio-temporelles de phénomènes environnementaux peuvent être trouvées dans la littérature. Néanmoins, la plupart de ces mesures sont de caractère global et ne considèrent pas de contraintes spatiales com- plexes, ainsi que la haute variabilité et la nature multivariée des événements. A cet effet, la méthodologie ici proposée prend en compte les complexités de l'espace géographique ou le phénomène a lieu, à travers de l'introduction du concept de Domaine de Validité et l'application des mesures d'analyse spatiale dans des données en présentant différentes contraintes géographiques. Cela permet l'évaluation du degré relatif d'agrégation spatiale/temporelle des structures du phénomène observé. En plus, exclusif au cas de feux forestiers, cette recherche propose aussi deux nouvelles méthodologies pour la définition et la cartographie des zones périurbaines, décrites comme des espaces anthropogéniques à proximité de la végétation sauvage ou de la forêt, et de la prédiction de la susceptibilité à l'ignition de feu. A cet égard, l'objectif principal de cette Thèse a été d'effectuer une recherche statistique/géospatiale avec une forte application dans des cas réels, pour analyser et décrire des phénomènes environnementaux complexes aussi bien que surmonter des problèmes méthodologiques non résolus relatifs à la caractérisation des structures spatio-temporelles, particulièrement, celles des occurrences de feux forestières. Ainsi, cette Thèse fournit une réponse à la demande croissante de la gestion et du monitoring environnemental pour le déploiement d'outils d'évaluation des risques et des dangers naturels et anthro- pogéniques. Les majeures contributions de ce travail ont été présentées aux conférences nationales et internationales, et ont été aussi publiées dans 5 revues internationales avec comité de lecture. Des collaborations nationales et internationales ont été aussi établies et accomplies avec succès.

Threat Simulation- The Function of Dreaming?

Dreaming is a pure form of phenomenality, created by the brain untouched by external stimulation or behavioral activity, yet including a full range of phenomenal contents. Thus, it has been suggested that the dreaming brain could be used as a model system in a biological research program on consciousness (Revonsuo, 2006). In the present thesis, the philosophical view of biological realism is accepted, and thus, dreaming is considered as a natural biological phenomenon, explainable in naturalistic terms. The major theoretical contribution of the present thesis is that it explores dreaming from a multidisciplinary perspective, integrating information from various fields of science, such as dream research, consciousness research, evolutionary psychology, and cognitive neuroscience. Further, it places dreaming into a multilevel framework, and investigates the constitutive, etiological, and contextual explanations for dreaming. Currently, the only theory offering a full multilevel explanation for dreaming, that is, a theory including constitutive, etiological, and contextual level explanations, is the Threat Simulation Theory (TST) (Revonsuo, 2000a; 2000b). The empirical significance of the present thesis lies in the tests conducted to test this specific theory put forth to explain the form, content, and biological function of dreaming. The first step in the empirical testing of the TST was to define exact criteria for what is a ‘threatening event’ in dreams, and then to develop a detailed and reliable content analysis scale with which it is possible to empirically explore and quantify threatening events in dreams. The second step was to seek answers to the following questions derived from the TST: How frequent threatening events are in dreams? What kind of qualities these events have? How threatening events in dreams relate to the most recently encoded or the most salient memory traces of threatening events experienced in waking life? What are the effects of exposure to severe waking life threat on dreams? The results reveal that threatening events are relatively frequent in dreams, and that the simulated threats are realistic. The most common threats include aggression, are targeted mainly against the dream self, and include simulations of relevant and appropriate defensive actions. Further, real threat experiences activate the threat simulation system in a unique manner, and dream content is modulated by the activation of long term episodic memory traces with highest negative saliency. To sum up, most of the predictions of the TST tested in this thesis received considerable support. The TST presents a strong argument that explains the specific design of dreams as threat simulations. The TST also offers a plausible explanation for why dreaming would have been selected for: because dreaming interacted with the environment in such a way that enhanced fitness of ancestral humans. By referring to a single threat simulation mechanism it furthermore manages to explain a wide variety of dream content data that already exists in the literature, and to predict the overall statistical patterns of threat content in different samples of dreams. The TST and the empirical tests conducted to test the theory are a prime example of what a multidisciplinary approach to mental phenomena can accomplish. Thus far, dreaming seems to have always resided in the periphery of science, never regarded worth to be studied by the mainstream. Nevertheless, when brought to the spotlight, the study of dreaming can greatly benefit from ideas in diverse branches of science. Vice versa, knowledge learned from the study of dreaming can be applied in various disciplines. The main contribution of the present thesis lies in putting dreaming back where it belongs, that is, into the spotlight in the cross-road of various disciplines.

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

A physical model for the simulation of x-ray emission spectra from samples irradiated with kilovolt electron beams is proposed. Inner shell ionization by electron impact is described by means of total cross sections evaluated from an optical-data model. A double differential cross section is proposed for bremsstrahlung emission, which reproduces the radiative stopping powers derived from the partial wave calculations of Kissel, Quarles and Pratt [At. Data Nucl. Data Tables 28, 381 (1983)]. These ionization and radiative cross sections have been introduced into a general-purpose Monte Carlo code, which performs simulation of coupled electron and photon transport for arbitrary materials. To improve the efficiency of the simulation, interaction forcing, a variance reduction technique, has been applied for both ionizing collisions and radiative events. The reliability of simulated x-ray spectra is analyzed by comparing simulation results with electron probe measurements.

Cost Optimisation of Mobile Advertising Client Data Transfer

Data traffic caused by mobile advertising client software when it is communicating with the network server can be a pain point for many application developers who are considering advertising-funded application distribution, since the cost of the data transfer might scare their users away from using the applications. For the thesis project, a simulation environment was built to mimic the real client-server solution for measuring the data transfer over varying types of connections with different usage scenarios. For optimising data transfer, a few general-purpose compressors and XML-specific compressors were tried for compressing the XML data, and a few protocol optimisations were implemented. For optimising the cost, cache usage was improved and pre-loading was enhanced to use free connections to load the data. The data traffic structure and the various optimisations were analysed, and it was found that the cache usage and pre-loading should be enhanced and that the protocol should be changed, with report aggregation and compression using WBXML or gzip.

Ionospheric tomography using GNSS reflections

In this paper, we report a preliminary analysis of the impact of Global Navigation Satellite System Reflections (GNSS-R) data on ionospheric monitoring over the oceans. The focus will be on a single polar Low Earth Orbiter (LEO) mission exploiting GNSS-R as well as Navigation (GNSS-N) and Occultation (GNSS-O) total electron content (TEC) measurements. In order to assess impact of the data, we have simulated GNSS-R/O/N TEC data as would be measured from the LEO and from International Geodesic Service (IGS) ground stations, with an electron density (ED) field generated using a climatic ionospheric model. We have also developed a new tomographic approach inspired by the physics of the hydrogen atom and used it to effectively retrieve the ED field from the simulated TEC data near the orbital plane. The tomographic inversion results demonstrate the significant impact of GNSS-R: three-dimensional ionospheric ED fields are retrieved over the oceans quite accurately, even as, in the spirit of this initial study, the simulation and inversion approaches avoided intensive computation and sophisticated algorithmic elements (such as spatio-temporal smoothing). We conclude that GNSS-R data over the oceans can contribute significantly to a Global/GNSS Ionospheric Observation System (GIOS). Index Terms Global Navigation Satellite System (GNSS), Global Navigation Satellite System Reflections (GNSS-R), ionosphere, Low Earth Orbiter (LEO), tomography.

Real-Time Simulation of Mobile and Industrial Machines Using the Multibody Simulation Approach

This thesis introduces a real-time simulation environment based on the multibody simulation approach. The environment consists of components that are used in conventional product development, including computer aided drawing, visualization, dynamic simulation and finite element software architecture, data transfer and haptics. These components are combined to perform as a coupled system on one platform. The environment is used to simulate mobile and industrial machines at different stages of a product life time. Consequently, the demands of the simulated scenarios vary. In this thesis, a real-time simulation environment based on the multibody approach is used to study a reel mechanism of a paper machine and a gantry crane. These case systems are used to demonstrate the usability of the real-time simulation environment for fault detection purposes and in the context of a training simulator. In order to describe the dynamical performance of a mobile or industrial machine, the nonlinear equations of motion must be defined. In this thesis, the dynamical behaviour of machines is modelled using the multibody simulation approach. A multibody system may consist of rigid and flexible bodies which are joined using kinematic joint constraints while force components are used to describe the actuators. The strength of multibody dynamics relies upon its ability to describe nonlinearities arising from wearing of the components, friction, large rotations or contact forces in a systematic manner. For this reason, the interfaces between subsystems such as mechanics, hydraulics and control systems of the mechatronic machine can be defined and analyzed in a straightforward manner.

Comparison of a deterministic and a data driven model to describe MBR fouling

Membrane bioreactors (MBRs) are a combination of activated sludge bioreactors and membrane filtration, enabling high quality effluent with a small footprint. However, they can be beset by fouling, which causes an increase in transmembrane pressure (TMP). Modelling and simulation of changes in TMP could be useful to describe fouling through the identification of the most relevant operating conditions. Using experimental data from a MBR pilot plant operated for 462days, two different models were developed: a deterministic model using activated sludge model n°2d (ASM2d) for the biological component and a resistance in-series model for the filtration component as well as a data-driven model based on multivariable regressions. Once validated, these models were used to describe membrane fouling (as changes in TMP over time) under different operating conditions. The deterministic model performed better at higher temperatures (>20°C), constant operating conditions (DO set-point, membrane air-flow, pH and ORP), and high mixed liquor suspended solids (>6.9gL-1) and flux changes. At low pH (<7) or periods with higher pH changes, the data-driven model was more accurate. Changes in the DO set-point of the aerobic reactor that affected the TMP were also better described by the data-driven model. By combining the use of both models, a better description of fouling can be achieved under different operating conditions

Adherence and perceptions regarding simulation training in undergraduate health Sciences

BACKGROUND: Simulation techniques are spreading rapidly in medicine. Suc h resources are increasingly concentrated in Simulation Laboratories. The MSRP-USP is structuring such a laboratory and is interested in the prevalence of individual initiatives that could be centralized there. The MSRP-USP currently has five full-curriculum courses in the health sciences: Medicine, Speech Therapy, Physical Therapy, Nutrition, and Occupational Therapy, all consisting of core disciplines. GOAL: To determine the prevalence of simulation techniques in the regular courses at MSRP-USP. METHODS: Coordinators of disciplines in the various courses were interviewed using a specifically designed semi-structured questionnaire, and all the collected data were stored in a dedicated database. The disciplines were grouped according to whether they used (GI) or did not use (GII) simulation resources. RESULTS AND DISCUSSION: 256 disciplines were analyzed, of which only 18.3% used simulation techniques, varying according to course: Medicine (24.7.3%), Occupational Therapy (23.0%), Nutrition (15.9%), Physical Therapy (9.8%), and Speech Therapy (9.1%). Computer simulation programs predominated (42.5%) in all five courses. The resources were provided mainly by MSRP-USP (56.3%), with additional funding coming from other sources based on individual initiatives. The same pattern was observed for maintenance. There was great interest in centralizing the resources in the new Simulation Laboratory in order to facilitate maintenance, but there was concern about training and access to the material. CONCLUSIONS: 1) The MSRP-USP simulation resources show low complexity and are mainly limited to computer programs; 2) Use of simulation varies according to course, and is most prevalent in Medicine; 3) Resources are scattered across several locations, and their acquisition and maintenance depend on individual initiatives rather than central coordination or curricular guidelines

Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

Measurement and simulation of solar radiation availability in relation to the growth of coffee plants in an agroforestry system with rubber trees

Solar radiation is an important factor for plant growth, being its availability to understory crops strongly modified by trees in an Agroforestry System (AFS). Coffee trees (Coffea arabica - cv. Obatã IAC 1669-20) were planted at a 3.4 x 0.9 m spacing inside and aside rows of monocrops of 12 year-old rubber trees (Hevea spp.), in Piracicaba-SP, Brazil (22º42'30" S, 47º38'00" W - altitude: 546m). One-year-old coffee plants exposed to 25; 30; 35; 40; 45; 80; 90; 95 and 100% of the total solar radiation were evaluated according to its biophysical parameters of solar radiation interception and capture. The Goudriaan (1977) adapted by Bernardes et al. (1998) model for radiation attenuation fit well to the measured data. Coffee plants tolerate a decrease in solar radiation availability to 50% without undergoing a reduction on growth and LAI, which was approximately 2m².m-2 under this condition. Further reductions on the availability of solar radiation caused a reduction in LAI (1.5m².m-2), thus poor land cover and solar radiation interception, resulting in growth reduction.

MODELING AND SIMULATION OF RELIEF INFLUENCE ON EUCALYPTUS FORESTS: INTERACTION BETWEEN SOLAR IRRADIANCE AND PRODUCTIVITY

ABSTRACT This study aimed to verify the differences in radiation intensity as a function of distinct relief exposure surfaces and to quantify these effects on the leaf area index (LAI) and other variables expressing eucalyptus forest productivity for simulations in a process-based growth model. The study was carried out at two contrasting edaphoclimatic locations in the Rio Doce basin in Minas Gerais, Brazil. Two stands with 32-year-old plantations were used, allocating fixed plots in locations with northern and southern exposure surfaces. The meteorological data were obtained from two automated weather stations located near the study sites. Solar radiation was corrected for terrain inclination and exposure surfaces, as it is measured based on the plane, perpendicularly to the vertical location. The LAI values collected in the field were used. For the comparative simulations in productivity variation, the mechanistic 3PG model was used, considering the relief exposure surfaces. It was verified that during most of the year, the southern surfaces showed lower availability of incident solar radiation, resulting in up to 66% losses, compared to the same surface considered plane, probably related to its geographical location and higher declivity. Higher values were obtained for the plantings located on the northern surface for the variables LAI, volume and mean annual wood increase, with this tendency being repeated in the 3PG model simulations.

Simulation of moisture profiles in a Latossol in Dourados region, in the State of Mato Grosso do Sul, Brazil

The understanding of unsaturated soil water flow at process-level is essential to develop proper management actions for environmental protection in agricultural systems. One important tool for simulation of soil water flow that has been used worldwide is the SWAP model. The aim of this work was to test and to calibrate the SWAP model by inverse modeling to describe moisture profiles in a Brazilian very clayey Latossol in Dourados, State of Mato Grosso do Sul, Brazil. The SWAP model was tested in an experimental field of 0.09 ha cultivated with soybean and soil profiles were sampled eight times between December 2006 and October 2007. The SWAP input values (i.e. soil water retention curves and meteorological data) were based on in-situ measurements. Simulations with uncalibrated soil water retention curves resulted in moisture profiles that were too wet for almost all sampling dates, in particular between 0-10 cm depth. After calibration of soil water retention curves, there was a good improvement in the simulated moisture profiles, which were within the range of measured values for almost all depths and sampling dates.

Application of simulated annealing in simulation and optimization of drying process of Zea mays malt

Kinetic simulation and drying process optimization of corn malt by Simulated Annealing (SA) for estimation of temperature and time parameters in order to preserve maximum amylase activity in the obtained product are presented here. Germinated corn seeds were dried at 54-76 °C in a convective dryer, with occasional measurement of moisture content and enzymatic activity. The experimental data obtained were submitted to modeling. Simulation and optimization of the drying process were made by using the SA method, a randomized improvement algorithm, analogous to the simulated annealing process. Results showed that seeds were best dried between 3h and 5h. Among the models used in this work, the kinetic model of water diffusion into corn seeds showed the best fitting. Drying temperature and time showed a square influence on the enzymatic activity. Optimization through SA showed the best condition at 54 ºC and between 5.6h and 6.4h of drying. Values of specific activity in the corn malt were found between 5.26±0.06 SKB/mg and 15.69±0,10% of remaining moisture.

Influence of data acquisition geometry on soybean spectral response simulated by the prosail model

View angle and directional effects significantly affect reflectance and vegetation indices, especially when daily images collected by large field-of-view (FOV) sensors like the Moderate Resolution Imaging Spectroradiometer (MODIS) are used. In this study, the PROSAIL radiative transfer model was chosen to evaluate the impact of the geometry of data acquisition on soybean reflectance and two vegetation indices (Normalized Difference Vegetation Index - NDVI and Enhanced Vegetation Index -EVI) by varying biochemical and biophysical parameters of the crop. Input values for PROSAIL simulation were based on the literature and were adjusted by the comparison between simulated and real satellite soybean spectra acquired by the MODIS/Terra and hyperspectral Hyperion/Earth Observing-One (EO-1). Results showed that the influence of the view angle and view direction on reflectance was stronger with decreasing leaf area index (LAI) and chlorophyll concentration. Because of the greater dependence on the near-infrared reflectance, the EVI was much more sensitive to viewing geometry than NDVI presenting larger values in the backscattering direction. The contrary was observed for NDVI in the forward scattering direction. In relation to the LAI, NDVI was much more isotropic for closed soybean canopies than for incomplete canopies and a contrary behavior was verified for EVI.