A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.

Fast three dimensional r-adaptive mesh redistribution

This paper describes a fast and reliable method for redistributing a computational mesh in three dimensions which can generate a complex three dimensional mesh without any problems due to mesh tangling. The method relies on a three dimensional implementation of the parabolic Monge–Ampère (PMA) technique, for finding an optimally transported mesh. The method for implementing PMA is described in detail and applied to both static and dynamic mesh redistribution problems, studying both the convergence and the computational cost of the algorithm. The algorithm is applied to a series of problems of increasing complexity. In particular very regular meshes are generated to resolve real meteorological features (derived from a weather forecasting model covering the UK area) in grids with over 2×107 degrees of freedom. The PMA method computes these grids in times commensurate with those required for operational weather forecasting.

Mapping Educational Specialist knowHow (MESH): the building of a knowledge management system for research informed practice

In this invited article the authors present an evaluative report on the development of the MESHGuides project (http://www.meshguides.org/). MESHGuides’ objective is to provide education with an international knowledge management system. MESHGuides were conceived as research summaries for supporting teachers’ in developing evidence-based practice. Their aim is to enhance teachers’ capacity to engage actively with research in their own classrooms. The original thinking for MESH arose from the work of UK-based academics Professor Marilyn Leask and Dr Sarah Younie in response to a desire, which has recently gathered momentum in the UK, for the development of a more research-informed teaching profession and for the establishment of an on-line platform to support evidence-based practice (DfE, 2015; Leask and Younie 2001; OECD 2009). The focus of this article is on how the MESHGuides project was conceived and structured, the technical systems supporting it and the practical reality for academics and teachers of composing and using MESHGuides. The project and the guides are in the early stages of development, and discussion indicates future possibilities for more global engagement with this knowledge management system.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

Evaluation of in vitro resistance of titanium and resorbable (poly-L-DL-lactic acid) fixation systems on the mandibular angle fracture

The purpose of this study was to compare, by mechanical in vitro testing, a 2.0-mm system made with poly-L-DL-lactide acid with an analogue titanium-based system. Mandible replicas were used as a substrate and uniformly sectioned on the left mandibular angle. The 4-hole plates were adapted and stabilized passively in the same site in both groups using four screws, 6.0 mm long. During the resistance-to-load test, the force was applied perpendicular to the occlusal plane at three different points: first molar at the plated side; first molar at the contralateral side; and between the central incisors. At 1 mm of displacement, no statistically significant difference was found. At 2 mm displacement, a statistically significant difference was observed when an unfavourable fracture was simulated and the load was applied in the contralateral first molar and when a favourable fracture was simulated and the load was applied between the central incisors. At the failure displacement, a statistically significant difference was observed only when the favourable fracture was simulated and the load was applied on the first molar at the plated side. In conclusion, despite more failure, the poly-L-DL-lactic acid-based system was effective.

Template-based quadrilateral mesh generation from imaging data

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.

Análise cintilográfica da deposição pulmonar de radioaerossol após associação da nebulização através dos dispositivos mesh e jato com a ventilação não invasiva em indivíduos normais e com pneumopatias obstrutivas crônicas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Comparative study between two techniques of incisional hernia repair with polypropylene mesh in rabbits

OBJETIVO: Comparar duas técnicas de tratamento da hérnia incisional em coelhos utilizando a tela de polipropileno apoiando um reforço peritônio - aponeurótico ou suturada nas bordas do anel herniário 'em ponte . MÉTODOS: Foram operados 60 coelhos para a produção de hérnia incisional, em uma incisão mediana de 4 centímetros. Após 30 dias, metade dos animais foram operados com o fechamento primário da parede, com colocação de uma tela de polipropileno apoiando o reforço e a outra metade dos animais com a colocação da tela suturada nas bordas do anel herniárioem ponte . Os animais foram avaliados com 30 (M1), 60 (M2)e 90 (M3) dias de pós-operatório. Os parâmetros analisados foram a evolução clínica, análise da força de ruptura da cicatriz, estudo macroscópico, análise microscópica e morfométrica. RESULTADOS: Não foram observadas diferenças significantes com relação a força de ruptura e estudos histológicos nos dois grupos e vários momentos estudados. Não houve diferença estatística com relação às complicações, embora os animais que receberam a telaem ponte tiveram aderências mais firmes e intensas à parede abdominal. CONCLUSÕES: As duas técnicas utilizadas para correção da hérnia incisional em coelhos não mostraram diferenças significantes quanto a força de ruptura, análise histológica e morfométrica. O número de complicações foi semelhante, porém a aderência de órgãos da cavidade abdominal à área de cicatriz foi muito mais intensa no grupo em que a tela foi colocadaem ponte .

Use of Titanium Mesh for Reconstruction of Extensive Defects in Fronto-orbito-ethmoidal Fracture

Traumatic injuries treatment of the fronto-naso-orbito-ethmoidal region has been one of the most challenging treatments within maxillofacial surgery, particularly of extensive orbital defects, very common in this type of pathologic condition. A 48-year-old man involved in a car collision presented an extensive bilateral fracture of the orbit medial wall, nasal bones, the nasal septum, and the frontal anterior table. The clinical and tomographic findings concluded the diagnosis of a maxilla and fronto-naso-orbito-ethmoidal fracture. Among the variety of biomaterials, the titanium mesh was elected because of the extension and magnitude of the bone defect, obtaining this way esthetic and functional results with better prognosis.

Biomechanical and histologic evaluation of non-washed resorbable blasting media and alumina-blasted/acid-etched surfaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of different types of non-resorbable suture material on the healing of extraction wounds--a histological study in rats.

The influence of different non-resorbable suture materials on the healing of tooth extraction wounds was examined in 120 adult male albino rats. Nylon gave the best biological results for healing of the mucosa and dental socket. Silk and cotton produced considerable delay of socket healing. Healing was only mildly delayed by polyester suture, with a short moderate inflammatory reaction at the initial stage.