Soft tissue structure modelling for use in orthopaedic applications and musculoskeletal biomechanics

We present our methodology for the three-dimensional anatomical and geometrical description of soft tissues, relevant for orthopaedic surgical applications and musculoskeletal biomechanics. The technique involves the segmentation and geometrical description of muscles and neurovascular structures from high-resolution computer tomography scanning for the reconstruction of generic anatomical models. These models can be used for quantitative interpretation of anatomical and biomechanical aspects of different soft tissue structures. This approach should allow the use of these data in other application fields, such as musculoskeletal modelling, simulations for radiation therapy, and databases for use in minimally invasive, navigated and robotic surgery

A Comparison of Interpolation Methods for Sparse Data: Application to Wind and Concentration Fields

In order to produce gridded fields of pollutant concentration data and surface wind data for use in an air quality model, a number of techniques for interpolating sparse data values are compared. The techniques are compared using three data sets. One is an idealized concentration distribution to which the exact solution is known, the second is a potential flow field, while the third consists of surface ozone concentrations measured in the Los Angeles Basin on a particular day. The results of the study indicate that fitting a second-degree polynomial to each subregion (triangle) in the plane with each data point weighted according to its distance from the subregion provides a good compromise between accuracy and computational cost

Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)

Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through routing models. The most important input to debris \ufb02ow routing models are the topographic data, usually in the form of Digital Elevation Models (DEMs). The quality of DEMs depends on the accuracy, density, and spatial distribution of the sampled points; on the characteristics of the surface; and on the applied gridding methodology. Therefore, the choice of the interpolation method affects the realistic representation of the channel and fan morphology, and thus potentially the debris \ufb02ow routing modeling outcomes. In this paper, we initially investigate the performance of common interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor, Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging) in building DEMs with the complex topography of a debris \ufb02ow channel located in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full- waveform Light Detection And Ranging (LiDAR) data. The investigation is carried out through a combination of statistical analysis of vertical accuracy, algorithm robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms on the performance of a Geographic Information System (GIS)-based cell model for simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation between the DEMs heights uncertainty resulting from the gridding procedure and that on the corresponding simulated erosion/deposition depths, both the effect of interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid discharges, and channel morphology after the event. The comparison among the tested interpolation methods highlights that the ANUDEM and ordinary kriging algorithms are not suitable for building DEMs with complex topography. Conversely, the linear triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy and shape reliability. Anyway, the evaluation of the effects of gridding techniques on debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does not signi\ufb01cantly affect the model outcomes

Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing

The workshop successfully brought together researchers from mathematical analysis, numerical mathematics, computer graphics and image processing. The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Correlation length by measuring empty space in simulated aggregates

We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it has a scaled form independent of the concentration phi, for both two- (2D) and three-dimensional (3D) model gels at low phi. The mean remoteness is proportional to the density-density correlation length of the gel, xi, allowing a more precise measurement of xi than by other methods. A simple analytical form for the scaled remoteness distribution is developed, highlighting the geometrical information content of the data. We show that the second moment of the distribution gives a useful estimate of the permeability of porous media.Comment: 4 page

A non-invasive technique for burn area measurement

The need for a reliable and accurate method for assessing the surface area of burn wounds currently exists in the branch of medicine involved with burn care and treatment. The percentage of the surface area is of critical importance in evaluating fluid replacement amounts and nutritional support during the 24 hours of postburn therapy. A noninvasive technique has been developed which facilitates the measurement of burn area. The method we shall describe is an inexpensive technique to measure the burn areas accurately. Our imaging system is based on a technique known as structured light. Most structured light computer imaging systems, including ours, use triangulation to determine the location of points in three dimensions as the intersection of two lines: a ray of light originating from the structured light projector and the line of sight determined by the location of the image point in the camera plane. The geometry used to determine 3D location by triangulation is identical to the geometry of other stereo-based vision system, including the human vision system. Our system projects a square grid pattern from 35mm slide onto the patient. The grid on the slide is composed of uniformly spaced orthogonal stripes which may be indexed by row and column. Each slide also has square markers placed in between time lines of the grid in both the horizontal and vertical directions in the center of the slide. Our system locates intersections of the projected grid stripes in the camera image and determines the 3D location of the corresponding points on the body by triangulation. Four steps are necessary in order to reconstruct 3D locations of points on the surface of the skin: camera and projector calibration; image processing to locate the grid intersections in the camera image; grid labeling to establish the correspondence between projected and imaged intersections; and triangulation to determine three-dimensional position. Three steps are required to segment burned portion in image: edge detection to get the strongest edges of the region; edge following to form a closed boundary; and region filling to identify the burn region. After combining the reconstructed 3D locations and segmented image, numerical analysis and geometric modeling techniques are used to calculate the burn area. We use cubic spline interpolation, bicubic surface patches and Gaussian quadrature double integration to calculate the burn wound area. The accuracy of this technique is demonstrated The benefits and advantages of this technique are, first, that we don’t have to make any assumptions about the shape of the human body and second, there is no need for either the Rule-of-Nines, or the weight and height of the patient. This technique can be used for human body shape, regardless of weight proportion, size, sex or skin pigmentation. The low cost, intuitive method, and demonstrated efficiency of this computer imaging technique makes it a desirable alternative to current methods and provides the burn care specialist with a sterile, safe, and effective diagnostic tool in assessing and investigating burn areas

Pappus-Guldin theorems applied the study of solid modeling with GeoGebra software

In this work, we use Geogebra software to simulate the shape of objects (solids) in three dimensions from their photo and real dimensions using spline interpolation. With the reconstructed object, we analyze its volume and surface area using the Pappus-Guldin Theorems (PGT), the theorems that use mathematical analysis ideas to describe the volume and surface area by the sectional area and by the contour curve of the object. In the simulations, we tested the verification of the modeling for known solids (sphere and torus) and then analyzed some objects used in the industry, such as the packaging of products, pet bottles, yogurt containers, coffee powder packaging, aluminum soda cans, and the packaging of chocolate powder. We also analyzed some objects created by rotating bodies, such as the shape of a jar and an aluminum barrel, and also shapes found in nature, such as the shape of a pear and an egg. Modeling allows us to better understand the packaging used in the industry to minimize manufacturing costs and maximize its utility. Thus, we can modify these packages to obtain the best development of how these products are presented to the public, optimizing its format by analyzing its surface and its volume.In this work, we use Geogebra software to simulate the shape of objects (solids) in three dimensions from their photo and real dimensions using spline interpolation. With the reconstructed object, we analyze its volume and surface area using the Pappus-Guldin Theorems (PGT), the theorems that use mathematical analysis ideas to describe the volume and surface area by the sectional area and by the contour curve of the object. In the simulations, we tested the verification of the modeling for known solids (sphere and torus) and then analyzed some objects used in the industry, such as the packaging of products, pet bottles, yogurt containers, coffee powder packaging, aluminum soda cans, and the packaging of chocolate powder. We also analyzed some objects created by rotating bodies, such as the shape of a jar and an aluminum barrel, and also shapes found in nature, such as the shape of a pear and an egg. Modeling allows us to better understand the packaging used in the industry to minimize manufacturing costs and maximize its utility. Thus, we can modify these packages to obtain the best development of how these products are presented to the public, optimizing its format by analyzing its surface and its volume