Two-dimensional Area Research Articles

Research on inversion and application of failure depth of coal seam roof and floor based on triangular network acoustic CT tomography

Acoustic tomography is an important test method in engineering geology and underground engineering, however, the problems of model parameterization, forward modeling and inversion in the process of tomographic imaging still need further study. In this work, the triangulation method of two-dimensional complex area was studied and the global algorithm of triangular ray tracing in two-dimensional complex area was formulated. Numerical simulation results of triangular acoustic ray tomography show that with the increase of iteration times, the ray tracing becomes increasingly close to the ray-tracing forward from the velocity model; through seven iterations, the low-speed plate with a thickness of only 0.56 m can also be clearly reflected. Besides, based on triangular ray-tracing tomography of the two-dimensional complex structure, the deep acoustic detection of coal seam floor failure zone is carried out. After the initial velocity model is determined by the single-hole acoustic detection results, the velocity distribution of the floor between holes is obtained by triangular network acoustic tomography from the premining, mid-mining and postmining acoustic penetration detection. Field measurements show that the 17-m-span acoustic wave penetration is successfully realized in sandstone and mudstone strata of coal seam floor, with accurate delineation of the development range of water-conducting fissures in floor failure. The triangular acoustic tomography method makes full use of the characteristics of flexible model division and makes the imaging results appear closer to the actual structural morphological characteristics.

Echocardiographic analysis of acute effects of percutaneous mitral annuloplasty on severity of secondary mitral regurgitation.

AimsPercutaneous mitral annuloplasty (PMA) represents a new treatment option for secondary mitral regurgitation (SMR) being associated with higher morbidity and mortality. The present study was aimed to evaluate whether or not acute effects on SMR severity can quantitatively be assessed after PMA.Methods and resultsPMA was performed in 30 patients (mean age 76 ± 9; 37% males) with moderate (n = 14) or severe (n = 16) SMR. Vena contracta (VC), left ventricular (LV) velocity‐time‐integral ratio (VTIMV/LVOT), effective regurgitant orifice area (EROA) by two‐dimensional proximal isovelocity surface area (PISA), regurgitant volume (RVolPISA) and regurgitant fraction (RFPISA) by PISA, RVolvolume and RFvolume by LV volume analyses, and parameters describing LV morphology, function, and cardiac performance were assessed by transthoracic echocardiography prior to and after PMA. According to RFPISA/RFvolume, 14 patients showed mild, 15 moderate, and 1 severe SMR after PMA. Mean RF, RVol, EROA, VC, and VTIMV/LVOT were lower directly after PMA (RFPISA: 49% ± 11 vs. 34% ± 13, P < 0.001; RFvolume: 46% ± 10 vs. 34% ± 13, P < 0.001; RVolPISA: 33 mL ± 13 vs. 25 mL ± 12, P < 0.001; RVolvolume: 28 mL ± 17 vs. 20 mL ± 14, P < 0.05; EROAPISA: 0.24 cm2 ± 0.1 vs. 0.19 cm2 ± 0.1, P < 0.05; VC: 5.2 ± 0.1 vs. 4.1 ± 0.2, P < 0.001; VTIMV/LVOT: 1.9 ± 0.4 vs. 1.6 ± 0.5, P < 0.05). Parameters of LV morphology, function, and cardiac performance did not change directly after PMA.ConclusionsPMA leads to a reduction of MR severity in >80% of SMR patients. Acute effects of PMA can quantitatively be assessed by transthoracic echocardiography.

Research of one interpolation formula at creation of the finite-difference scheme for functions with internal zones of the bigger gradients

In work the method creation of the interpolation formula which is bringing closer function of the smoothing gap, meeting in solutions of one-dimensional tasks with a heatmass transfer is investigated. Interpolation on the basis of the decision for the smoothing gap is used for creation of finite-difference schemes to multidimensional tasks with ruptures of the first sort in boundary and initial and regional conditions. Use of additional knots with the constructed interpolation gives considerable reduction of approximating viscosity in finite-difference schemes for the convective and diffusive equations of transfer. For the constructed interpolation in case of existence of an internal interface which thickness less step of a regular grid is conducted an accuracy research at the asymptotic approximations in small parameters corresponding to changes of required function in the neighborhood of a thin interface.The carried-out numerical calculations on a heat and mass transfer for a test task in two-dimensional rectangular area on the basis of the developed method show increase in an asymptotic order of accuracy of numerical decisions to the second from a grid step at application of the known schemes in the wide range of small parameter of diffusion.

Non-scanning 2-D Laser Cutting of Polyimide by Using a Computer-Generated Hologram

Laser processing is an effective way for precisely and accurately removing a small region of materials without tool wear. Conventional laser processing, which has a limitation on the processing speed, is performed by scanning a single spot on a target material. For improving its speed, a high-power laser beam can be spatially distributed using a hologram to simultaneously process a two-dimensional area. This technique has been used in experiments such as drilling, patterning, etc. However, as far as we know, due to several difficulties, no experiments have been reported that apply the holographic technique to non-scanning cutting with a single hologram. In this research, we experimentally performed non-scanning 2-D laser cutting of a polyimide film by using a single computer-generated hologram (CGH) and a high-power laser of 120 W. To do this, we designed a CGH to reconstruct twelve lines in a 24 mm × 23 mm area. This was then fabricated with fused silica so that it would not be damaged by the high-power laser. This method makes possible the achievement of a high throughput in a material cutting process by utilizing a high-power laser efficiently.

A method for measuring boresight errors for a radioparent radome of arbitrary shape

The previously presented method for measuring and calculating the components of boresight angle errors (BAE) in the “antenna – radioparent radome (RPR)” system in the two-dimensional angular scanning area of the antenna with electronic beam control, which includes a phased-array antenna (PAA), was tested in relation to a system with a drop-shaped radome. Measurements were carried out using an antenna measuring collimator complex (“compact polygon”) with a complex drop-shaped RPR and PAA installed thereunder. To create a BAE matrix on the surface of the RPR, measurements and subsequent calculations were performed at different “roll” angles of the antenna-radome system and different deflection angles of the PAA beam in “oblique planes”. The BAE measurements carried out in several RPR surface sections by the proposed method, show a good reproducibility and correlate well with the results of BAE measurements carried out using the same sections by the conventional difference method, where the BAE component is calculated as the difference between the angular coordinates of the minima of the corresponding PAA tracking pattern (TP), before and after the RPR installation.

Validation of inverse stereology generation of two dimensional area gradations for computational modelling of asphalt mixtures

Over the last few years, several researchers have employed computational methods to model and investigate the overall behaviour of asphalt mixture composites and different factors that influence this behaviour. Two-dimensional models, particularly those with computationally generated geometries, are commonly used in lieu of three-dimensional models due to their computational efficiency. When building these types of models, it is critical to properly determine a two-dimensional area distribution of aggregates in a given cross section, which needs to be generated from a representative three-dimensional volumetric gradation. This can be typically achieved using some form of mathematical transformation; one type of transformation often used for asphalt mixture gradations is inverse stereology. The goal of this study was to determine the effectiveness of the inverse stereology approach when compared with the true two-dimensional area gradation observed in laboratory compacted HMA specimens. The results from this study show that an inverse stereology approach based on a polyhedron shape was effective in replicating the two-dimensional area gradation created by cutting a laboratory specimen. In addition, the aspect ratio of particles was considered based on cutting the specimens vertically and horizontally; it was determined that no substantial difference existed between the vertical and horizontal cut specimens. However, it was also confirmed that the aspect ratios obtained using aggregate imaging are not representative of aspect ratios in a two dimensional cross-section of an asphalt mixture. An inverse stereology approach to converting aspect ratios from 2D to 3D provided better results, but was still not accurately able to represent the distribution of aspect ratios of aggregates.

Comparative Analysis of Early Life Stage Traits in Annual and Perennial Phaseolus Crops and Their Wild Relatives.

Herbaceous perennial species are receiving increased attention for their potential to provide both edible products and ecosystem services in agricultural systems. Many legumes (Fabaceae Lindl.) are of special interest due to nitrogen fixation carried out by bacteria in their roots and their production of protein-rich, edible seeds. However, herbaceous perennial legumes have yet to enter widespread use as pulse crops, and the response of wild, herbaceous perennial species to artificial selection for increased seed yield remains under investigation. Here we compare cultivated and wild accessions of congeneric annual and herbaceous perennial legume species to investigate associations of lifespan and cultivation with early life stage traits including seed size, germination, and first year vegetative growth patterns, and to assess variation and covariation in these traits. We use “cultivated” to describe accessions with a history of human planting and use, which encompasses a continuum of domestication. Analyses focused on three annual and four perennial species of the economically important genus Phaseolus. We found a significant association of both lifespan and cultivation status with seed size (weight, two-dimensional lateral area, length), node number, and most biomass traits (with cultivation alone showing additional significant associations). Wild annual and perennial accessions primarily showed only slight differences in trait values. Relative to wild forms, both cultivated annual and cultivated perennial accessions exhibited greater seed size and larger overall vegetative size, with cultivated perennials showing greater mean trait differences relative to wild accessions than cultivated annuals. Germination proportion was significantly lower in cultivated relative to wild annual accessions, while no significant difference was observed between cultivated and wild perennial germination. Regardless of lifespan and cultivation status, seed size traits were positively correlated with most vegetative traits, and all biomass traits examined here were positively correlated. This study highlights some fundamental similarities and differences between annual and herbaceous perennial legumes and provides insights into how perennial legumes might respond to artificial selection compared to annual species.

Application of One-Dimensional and Two-Dimensional Coupled Overtopping Embankment Flood Model in Wuyi River

Numerical simulation is an effective method to study the law of flood evolution. Adopting a one-dimensional two-dimensional coupling approach, the river flood evolution uses a one-dimensional model and the flood protection areas on both sides of the river adopt a tow-dimensional model. The two-dimensional model is laterally connected to the one-dimensional model, which can simulate the flood evolution process in the two-dimensional flood protection area after the flood of one-dimensional river overtopping the dam. A one-dimensional and two-dimensional coupled overtopping dam flood model in Wuyij River basin is established. The model calculation accuracy is relatively high and the results are overall reasonable.

Validation of Semiautomated Quantification of Mitral Valve Regurgitation by Three-Dimensional Color Doppler Transesophageal Echocardiography

The aim of this study was to evaluate the accuracy of mitral regurgitation (MR) volume quantified on three-dimensional (3D) color Doppler transesophageal echocardiography (TEE) using new semiautomated software compared with conventional two-dimensional (2D) proximal isovelocity surface area (PISA) transthoracic echocardiography (TTE) and TEE and cardiac magnetic resonance imaging (CMR). Fifty-one patients (mean age, 63±16years; 35 men) prospectively underwent TTE, TEE, and CMR for MR evaluation. Regurgitant volume (RVol) by 3D MR flow quantification was compared with 2D TTE, TEE, and CMR, and the accuracy of evaluation of severe MR by 3D MR flow quantification was compared against guideline criteria by TEE. Twenty-nine patients had severe MR, 16 had moderate MR, and six had mild MR. Three-dimensional MR flow quantification was feasible in all patients, including prolapse (n=37), restriction (n=9), functional MR (n=5), and eccentric or multiple jects (n=41). RVol on 3D MR flow quantification correlated well with RVol on 2D PISA TTE (interclass correlation coefficient [ICC]=0.75, P<.001), quantitatively estimated RVol (ICC=0.74, P<.001), and 2D PISA TEE (ICC=0.79, P<.001). Three-dimensional MR flow quantification agreed better with CMR (ICC=0.86, P<.001) than did RVol on 2D PISA TTE (ICC=0.66, P<.001) and 2D PISA TEE (ICC=0.69, P<.001), with narrower limits of agreement on Bland-Altman analysis. Three-dimensional MR flow quantification had high accuracy for diagnosing severe MR using TEE (area under the curve=0.85, 95% CI 0.74-0.96, P<.001) or CMR (area under the curve=0.95; 95% CI, 0.89-1.00; P<.001) as the criterion. The new software enabled semiautomated 3D MR flow quantification in complex MR with multiple and eccentric jets and showed better agreement with CMR than 2D PISA TTE or TEE, suggesting that this method is more accurate than conventional 2D PISA TTE and TEE.

Micro-X-Ray Diffractometer Focused by Polycapillary Optics and Its Applications for Materials

The analysis of small samples and micro areas of large samples are significant in material, environment and geology fields. This work reports the study of a micro-X-ray diffractometer developed by our laboratory and its applications for not only micro-X-ray diffraction (μ-XRD) analysis but also micro energy dispersive X-ray fluorescence (μ-EDXRF) analysis. The accomplishment of the two analysis methods in one instrument makes it possible to characterize micro materials in situ by a very efficient way. In order to demonstrate the feasibility of this diffractometer, the samples difficult to be measured by the conventional diffractometer were studied. Firstly, a cooper wire with a diameter of 140 μm was analysed as a micro sample. Then two different points of a TiN film were analysed to discuss their phase transitions in micro areas. Moreover, the phase distribution of a two-dimensional area on an iPhone mainboard was scanned. The phase mapping was acquired by data processing. These researches highlight the abilities of this diffractometer in the applications on micro material characterizations. As a result, this diffractometer can adapt to the analyses of elemental composition, mineralogical composition and their distributions in the micro materials. It can also provide useful reference information for the micro phase transitions. Therefore, it can be concluded that this micro-X-ray diffractometer has potential prospect in the micro material analysis and any other related fields.

Observations of low-frequency, long-range acoustic propagation in the Philippine Sea and comparisons with mode transport theory.

The year-long Philippine Sea (2010-2011) experiment (PhilSea) was an extensive deep water acoustic propagation experiment in which there were six different sources transmitting to a water column spanning a vertical line array. The six sources were placed in an array with a radius of 330 km and transmitted at frequencies in the 200-300 Hz and 140-205 Hz bands. The PhilSea frequencies are higher than previous deep water experiments in the North Pacific for which modal analyses were performed. Further, the acoustic paths sample a two-dimensional area that is rich in internal tides, waves, and eddies. The PhilSea observations are, thus, a new opportunity to observe acoustic modal variability at higher frequencies than before and in an oceanographically dynamic region. This paper focuses on mode observations around the mid-water depths. The mode observations are used to compute narrowband statistics such as transmission loss and broadband statistics such as peak pulse intensity, travel time wander, time spreads, and scintillation indices. The observations are then compared with a new hybrid broadband transport theory. The model-data comparisons show excellent agreement for modes 1-10 and minor deviations for the rest. The discrepancies in the comparisons are related to the limitations of the hybrid model and oceanographic fluctuations other than internal waves.

Reconstruction of coverage hole model and cooperative repair optimization algorithm in heterogeneous wireless sensor networks

Coverage hole repair not only determines whether the heterogeneous wireless sensor networks (HWSNs) can work normally and effectively, but also determines the network coverage, performance and time to live. The sensor nodes may be covered by random deployment or network failure during the network operation. Therefore, coverage hole repair is a very critical and challenging problem in HWSNs. In this paper, we reconstruct the hole model and proposes a multi-factor collaborative hole repair optimization algorithm (FCH-ROA) between HWSNs nodes. The algorithm considers the distance between the virtual repair node and the mobile node, the energy consumption during the mobile repair process and the confidence of the node to be repaired. A Pearson-like fuzzy matching relationship between the virtual repair node and the mobile node is established to cover the hole repair. Firstly, the hole model is reconstructed, and the Voronoi polygons are randomly divided into the static nodes of the HWSNs in the two-dimensional square monitoring area. Secondly, the key areas of the static nodes are connected in the counterclockwise direction to determine the hole areas. According to the different concave shapes, the convexity is degenerate into a convex hull, and the convex hull center is used as the base point. The Delaunary triangulation is combined with the bulge vertices to calculate the position of the virtual repair node. Finally, based on the relative distance of the nodes, residual energy, and the node of criticality, the multi-factor synergy matching decision table between the virtual repair node and the mobile node, according to the decision table, the mobile node performs the finite distance movement to realize the repair optimization of the coverage hole. Simulation experiments show that compared with the existing coverage hole algorithm, FCH-ROA algorithm improves network coverage and extends network life cycle.

Strengthening of cruciform sample arms for large strains during biaxial stretching

Material-forming abilities are crucial for the optimisation of sheet metal-forming processes. Among the many methods used for the evaluation of forming limits, those based on cruciform samples are very promising, mostly because of their frictionless character and access to a pure two-dimensional stress area. In contrary to punch or tubular test samples, they allow in-situ strain measurements on both sides of the gauge region. Nevertheless, they have some disadvantages. Namely, the arms of the sample crack at the gauge region before reaching the deformation limit. This reduces the mechanical insights that can be gained from a single specimen. The paper describes the development of cruciform specimens in which large strains can be achieved during bi-axial tensile testing. The experiments focus on the application of initial deformation on the cruciform sample arms prior to the test. Strain-induced hardening of the sample arms is shown to increase the maximum achievable strain within the gauge section. This allows the stress strain response of a given material to be characterised following large plastic deformation. The samples used in the bi-axial tensile tests each had one particular pre-deformed shape in the corners, whose degree of pre-deformation differed between them. The results demonstrate the increased strain characterisation capabilities, which can be determined from the addition of initial plastic deformation. Increased cold working was found to increase the maximum plastic deformation, and the associated data collection, which could be achieved within the test area. Selecting the correct degree of pre-deformation in the support region made it possible to increase the strain in the gauge section of the sample from ∼1% to about ∼11% without the need to build up the arms or reduce the thickness of the test area.

Effective sweep-width for barrier missions against an evasive target

An effective sweep-width, to be used in predicting the performance of a barrier patrol against a smart, evasive intruder is defined. Following Washburn’s example for a two-dimensional area search, the nominal sweep-width of the searcher is reduced to account for the target’s evasive ability. The formulation presented here allows for the barrier to be either stationary or advancing. Two different definitions are offered for an effective sweep-width: one that focuses solely on the probability of detecting the intruder and one that includes deterrence as a form of success for the searcher.

Application of building geometry indexes to assess the correlation between buildings and air temperature

The quantitative exploration of the correlation between buildings and air temperature (Tair) is of widespread research concern. Two building geometry indexes (BGIs), a two-dimensional Area Index (2DAI) and a three-dimensional Volume Index (3DVI) were proposed in this study. Furthermore, we constructed multilayer buffer zones around weather stations and used Spearman's rank correlation to assess the correlation between the 2DAI, 3DVI and Tair to explore the buffer zone with the highest correlation coefficient (Optimal Buffer Zone, OBZ) that exists between BGIs and Tair. The results demonstrated the following. (1) The correlation coefficient between the 3DVI and Tair was higher than that of 2DAI, but this coefficient was affected by the season and month. (2) The OBZ between the BGIs and Tair was the 250 m buffer zone, but the OBZ between the 3DVI and Tair could only be concentrated during the high-temperature period. (3) The change mechanisms of the correlation coefficients and the OBZs between the BGIs and Tair were related to the upper limit of the 2DAI that exists in the buffer zone and the stronger thermal sensitivity of the 3DVI in a high-temperature environment. (4) The upper limits of the 2DAI and 3DVI in 500m×500m grids should be determined according to the actual situation of the BGIs in all grids of the study area. This study provides a new perspective from which to explore the correlation between buildings and Tair and identifies the optimal size of grid units that can be used in urban thermal environment planning units.

Software for deformable solid mechanics

Subject of Research. The paper presents a software building method for the tasks of deformable solid mechanics. This software should guarantee high accuracy and speed of calculations, as well as simple preparation of the initial data and data processing even for an inexperienced user. The software was developed using the open source GMSH mesh generator application programming interface (API) and the Eigen mathematical library. Method. The developed software consists of three modules: GMSH_API, InputFile, FEMSolver and a database. The GMSH_API module, which prepares the finite element model, was written using the GMSH mesh generator API. The InputFile module describes methods for interacting with a previously created database, that provides quick and easy preparation of the input file needed to start the calculation. Numerical calculation by the finite element method is implemented in the FEMSolver module. The Eigen mathematical library was actively used for its implementation, and it can build sparse matrices that do not store zero elements in memory. This possibility obviates the need for additional transformations of the global stiffness matrix used in the finite element method. Main Results. The Kirsch task was solved as an example in a plane-stressed setting: a distributed tensile load was applied to the upper edge of a steel plate, with a round hole in the center, the lower edge of the plate was rigidly fixed. After calculating and obtaining the von Mises stress distribution field in the plate, we observe an error of 1.72% relative to the analytical solution. Such error value is considered low, therefore, the developed software not only facilitates the preparation of data for calculation, but also guarantees high accuracy of the obtained results. Practical Relevance. Commercial software for solving the problems of deformable solid mechanics, such as ANSYS Mechanical APDL, Abaqus, etc., is very expensive. Free software is primarily focused on researchers and, as a rule, is difficult for learning by an ordinary user-engineer, and the compromise version of the PDE Toolbox for MATHLAB is applicable only for tasks in a two-dimensional area and only supports a linear triangular finite element. However, the application of GMSH API and the Eigen library provides for creation of an easy-to-use but powerful tool for solving the problems of deformable solid mechanics.

P868Temporal remodeling of coronary arteries during progression of atherosclerosis with serial coronary CT angiography using 3D metrics: results from the PARADIGM study

Abstract Aim To determine compensatory enlargement and luminal reduction of coronary arteries during the progression of atherosclerosis with serial coronary computed tomography angiography (CCTA) by using volumetric measurements. To date, the impact of coronary plaque progression on temporal remodeling, as opposed to the static remodeling, has only been studied with invasive imaging modalities and primarily two-dimensional areas rather than three-dimensional volumes. Methods In total, 1,245 patients with suspected coronary artery disease (CAD) at 13 sites (61±9 years, 39% women) underwent serial CCTA with interscan interval of ≥2 years. The primary objective was to assess volumetric temporal remodeling, defined as the linear association between the change in coronary plaque, lumen and vessel volume at follow-up CCTA on a per-segment level. Temporal remodeling was determined in strata of low and high baseline plaque burden as well as different coronary segments at baseline. Linear regression analysis and Pearson's correlation coefficients were calculated to assess associations. Results Amongst 1,245 patients with 19,920 segments, the median interscan interval was 3.3 (IQR 2.6–4.8) years. For each 1 mm3 increase in plaque volume, the increase in vessel volume was 0.72 mm3 and the decrease in lumen volume was 0.28 mm3 (Figure 1, both p&lt;0.001). Volumetric temporal remodeling was similar in low versus high PAV [0.70 mm3 vs 0.73 mm3 (p for interaction=0.491)] and left-main arteries versus all other segments [0.78 mm3 vs. 0.72 mm3 (p for interaction=0.336)], but not in proximal versus distal segments at baseline [0.75 mm3 vs. 0.61 mm3 (p for interaction=0.020)]. Figure 1. Volumetric temporal remodeling Conclusion In general, coronary plaque grows approximately 70% outward and 30% into the coronary lumen during the progression of atherosclerosis. Volumetric temporal remodeling is not limited by baseline plaque burden, but is potentially dependent on its location within the coronary artery tree. Acknowledgement/Funding NRF of Korea (Grant No. 2012027176); Dalio Institute of Cardiovascular Imaging and Michael J. Wolk Foundation

Mole senses.

Many people are familiar with the meandering tunnels of moles, far fewer are familiar with the creatures that made them. Such secrecy is, of course, one of the great benefits of burrowing through the earth where few predators can follow. But it's not the only benefit. Soil contains a smorgasbord of nutritious invertebrate prey - hence all the tunneling. In fact the richness of the soil niche has given rise to a diversity of mole species that could be said to resemble the evolutionary diversification of bats, though on a smaller scale. In both cases, mammals have evolved a suite of unique anatomical traits (coincidentally involving modification of the forelimb) that allows them to exploit a huge resource of invertebrate prey that is largely inaccessible to their competitors. For bats the thin, delicate wings were the key innovation, for moles the forelimbs have undergone a similarly dramatic structural shift, but in the opposite direction - the bones have become short, stout, and powerful to act as shovels.

Monitoring Wound Healing of Diabetic Foot Ulcers Using Two-Dimensional and Three-Dimensional Wound Measurement Techniques: A Prospective Cohort Study

Objective: Three-dimensional (3D) wound measurements enable the evaluation of wound healing from the wound bed, which may be a more sensitive measure than traditional two-dimensional (2D) area meas...

Sistemas de medición de heridas

Una herida crónica constituye un importante problema asistencial que disminuye la calidad de vida de los pacientes y que también afecta al sistema de salud, por su elevado coste económico y por la dedicación de tiempo de los profesionales sanitarios. La medición de las úlceras es parte importante de su evaluación y representa una herramienta para desarrollar un plan de manejo y predecir el tiempo de cicatrización, dado que la reducción de la superficie de la herida es un buen indicador de cicatrización y eficacia de la terapia empleada.Existen multitud de sistemas para medir las úlceras: simples (lineales), de dos dimensiones (área de la superficie) o de tres dimensiones (volumen de la herida). Sin embargo, aún no hay consenso claro sobre cuál es el mejor método, que sea rápido, práctico, barato y sencillo en la práctica habitual, ya que resulta difícil medir las úlceras debido a su estructura dinámica tridimensional, en la que el área, el volumen y la forma, incluyendo la curvatura natural del cuerpo humano deben ser tenidas en consideración.