94 research outputs found
www.elsevier.com/locate/cam On deflation and singular symmetric positive semi-definite matrices
For various applications, it is well-known that the deflated ICCG is an efficient method for solving linear systems with invertible coefficient matrix. We propose two equivalent variants of this deflated ICCG which can also solve linear systems with singular coefficient matrix, arising from discretization of the discontinuous Poisson equation with Neumann boundary conditions. It is demonstrated both theoretically and numerically that the resulting methods accelerate the convergence of the iterative process. Moreover, in practice the singular coefficient matrix has often been made invertible by modifying the last element, since this can be advantageous for the solver. However, the drawback is that the condition number becomes worse-conditioned. We show that this problem can completely be remedied by applying the deflation technique with just one deflation vector
Automated parameters for troubled-cell indicators using outlier detection
In Vuik and Ryan (2014) we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent parameter is chosen. This parameter is used in a threshold which decides whether or not to detect an element as a troubled cell. Until now, these parameters could not be chosen automatically. The choice of the parameter has impact on the approximation: it determines the strictness of the troubled-cell indicator. An inappropriate choice of the parameter will result in detection (and limiting) of too few or too many elements. The optimal parameter is chosen such that the minimal number of troubled cells is detected and the resulting approximation is free of spurious oscillations. In this paper we will see that for each troubled-cell indicator the sudden increase or decrease of the indicator value with respect to the neighboring values is important for detection. Indication basically reduces to detecting the outliers of a vector (one dimension) or matrix (two dimensions). This is done using Tukey's boxplot approach to detect which coefficients in a vector are straying far beyond others (Tukey, 1977). We provide an algorithm that can be applied to various troubled-cell indication variables. Using this technique the problem-dependent parameter that the original indicator requires is no longer necessary as the parameter will be chosen automatically
Smoothness-Increasing Accuracy-Conserving (SIAC) filters for derivative approximations of discontinuous Galerkin (DG) solutions over nonuniform meshes and near boundaries
Accurate approximations for the derivatives are usually required in many application areas such as biomechanics, chemistry and visualization applications. With the help of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering, one can enhance the derivatives of a discontinuous Galerkin solution. However, current investigations of derivative filtering are limited to uniform meshes and periodic boundary conditions, which do not meet practical requirements. The purpose of this paper is twofold: to extend derivative filtering to nonuniform meshes and propose position-dependent derivative filters to handle filtering near the boundaries. Through analyzing the error estimates for SIAC filtering, we extend derivative filtering to nonuniform meshes by changing the scaling of the filter. For filtering near boundaries, we discuss the advantages and disadvantages of two existing position-dependent filters and then extend them to position-dependent derivative filters, respectively. Further, we prove that with the position-dependent derivative filters, the filtered solutions can obtain a better accuracy rate compared to the original discontinuous Galerkin approximation with arbitrary derivative orders over nonuniform meshes. One- and two-dimensional numerical results are provided to support the theoretical results and demonstrate that the position-dependent derivative filters, in general, enhance the accuracy of the solution for both uniform and nonuniform meshes
A biomechanical mathematical model for the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds
A continuum hypothesis-based, biomechanical model is presented for the simulation of the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds that cover a large surface area. Since wound contraction mainly takes place in the dermal layer of the skin, solely a portion of this layer is included explicitly into the model. This portion of dermal layer is modeled as a heterogeneous, orthotropic continuous solid with bulk mechanical properties that are locally dependent on both the local concentration and the local geometrical arrangement of the collagen bundles. With respect to the dynamic regulation of the geometrical arrangement of the collagen bundles, it is assumed that a portion of the collagen molecules are deposited and reoriented in the direction of movement of (myo)fibroblasts. The remainder of the newly secreted collagen molecules are deposited by ratio in the direction of the present collagen bundles. Simulation results show that the distribution of the collagen bundles influences the evolution over time of both the shape of the wounded area and the degree of overall contraction of the wounded area. Interestingly, these effects are solely a consequence of alterations in the initial overall distribution of the collagen bundles, and not a consequence of alterations in the evolution over time of the different cell densities and concentrations of the modeled constituents. In accordance with experimental observations, simulation results show furthermore that ultimately the majority of the collagen molecules ends up permanently oriented toward the center of the wound and in the plane that runs parallel to the surface of the skin
A mathematical model for the simulation of the contraction of burns
A continuum hypothesis-based model is developed for the simulation of the contraction of burns in order to gain new insights into which elements of the healing response might have a substantial influence on this process. Tissue is modeled as a neo-Hookean solid. Furthermore, (myo)fibroblasts, collagen molecules, and a generic signaling molecule are selected as model components. An overview of the custom-made numerical algorithm is presented. Subsequently, good agreement is demonstrated with respect to variability in the evolution of the surface area of burns over time between the outcomes of computer simulations and measurements obtained in an experimental study. In the model this variability is caused by varying the values for some of its parameters simultaneously. A factorial design combined with a regression analysis are used to quantify the individual contributions of these parameter value variations to the dispersion in the surface area of healing burns. The analysis shows that almost all variability in the surface area can be explained by variability in the value for the myofibroblast apoptosis rate and, to a lesser extent, the value for the collagen molecule secretion rate. This suggests that most of the variability in the evolution of the surface area of burns over time in the experimental study might be attributed to variability in these two rates. Finally, a probabili
Red Flag Signs and Symptoms for Patients With Early-Onset Colorectal Cancer:A Systematic Review and Meta-Analysis
Importance: Early-onset colorectal cancer (EOCRC), defined as a diagnosis at younger than age 50 years, is increasing, and so-called red flag signs and symptoms among these individuals are often missed, leading to diagnostic delays. Improved recognition of presenting signs and symptoms associated with EOCRC could facilitate more timely diagnosis and impact clinical outcomes. Objective: To report the frequency of presenting red flag signs and symptoms among individuals with EOCRC, to examine their association with EOCRC risk, and to measure variation in time to diagnosis from sign or symptom presentation. Data Sources: PubMed/MEDLINE, Embase, CINAHL, and Web of Science were searched from database inception through May 2023. Study Selection: Studies that reported on sign and symptom presentation or time from sign and symptom presentation to diagnosis for patients younger than age 50 years diagnosed with nonhereditary CRC were included. Data Extraction and Synthesis: Data extraction and quality assessment were performed independently in duplicate for all included studies using Preferred Reporting Items for Systematic Reviews and Meta-analyses reporting guidelines. Joanna Briggs Institute Critical Appraisal tools were used to measure risk of bias. Data on frequency of signs and symptoms were pooled using a random-effects model. Main Outcomes and Measures: Outcomes of interest were pooled proportions of signs and symptoms in patients with EOCRC, estimates for association of signs and symptoms with EOCRC risk, and time from sign or symptom presentation to EOCRC diagnosis. Results: Of the 12859 unique articles initially retrieved, 81 studies with 24908126 patients younger than 50 years were included. The most common presenting signs and symptoms, reported by 78 included studies, were hematochezia (pooled prevalence, 45% [95% CI, 40%-50%]), abdominal pain (pooled prevalence, 40% [95% CI, 35%-45%]), and altered bowel habits (pooled prevalence, 27% [95% CI, 22%-33%]). Hematochezia (estimate range, 5.2-54.0), abdominal pain (estimate range, 1.3-6.0), and anemia (estimate range, 2.1-10.8) were associated with higher EOCRC likelihood. Time from signs and symptoms presentation to EOCRC diagnosis was a mean (range) of 6.4 (1.8-13.7) months (23 studies) and a median (range) of 4 (2.0-8.7) months (16 studies). Conclusions and Relevance: In this systematic review and meta-analysis of patients with EOCRC, nearly half of individuals presented with hematochezia and abdominal pain and one-quarter with altered bowel habits. Hematochezia was associated with at least 5-fold increased EOCRC risk. Delays in diagnosis of 4 to 6 months were common. These findings highlight the need to identify concerning EOCRC signs and symptoms and complete timely diagnostic workup, particularly for individuals without an alternative diagnosis or sign or symptom resolution..</p
Red Flag Signs and Symptoms for Patients With Early-Onset Colorectal Cancer:A Systematic Review and Meta-Analysis
Importance: Early-onset colorectal cancer (EOCRC), defined as a diagnosis at younger than age 50 years, is increasing, and so-called red flag signs and symptoms among these individuals are often missed, leading to diagnostic delays. Improved recognition of presenting signs and symptoms associated with EOCRC could facilitate more timely diagnosis and impact clinical outcomes. Objective: To report the frequency of presenting red flag signs and symptoms among individuals with EOCRC, to examine their association with EOCRC risk, and to measure variation in time to diagnosis from sign or symptom presentation. Data Sources: PubMed/MEDLINE, Embase, CINAHL, and Web of Science were searched from database inception through May 2023. Study Selection: Studies that reported on sign and symptom presentation or time from sign and symptom presentation to diagnosis for patients younger than age 50 years diagnosed with nonhereditary CRC were included. Data Extraction and Synthesis: Data extraction and quality assessment were performed independently in duplicate for all included studies using Preferred Reporting Items for Systematic Reviews and Meta-analyses reporting guidelines. Joanna Briggs Institute Critical Appraisal tools were used to measure risk of bias. Data on frequency of signs and symptoms were pooled using a random-effects model. Main Outcomes and Measures: Outcomes of interest were pooled proportions of signs and symptoms in patients with EOCRC, estimates for association of signs and symptoms with EOCRC risk, and time from sign or symptom presentation to EOCRC diagnosis. Results: Of the 12859 unique articles initially retrieved, 81 studies with 24908126 patients younger than 50 years were included. The most common presenting signs and symptoms, reported by 78 included studies, were hematochezia (pooled prevalence, 45% [95% CI, 40%-50%]), abdominal pain (pooled prevalence, 40% [95% CI, 35%-45%]), and altered bowel habits (pooled prevalence, 27% [95% CI, 22%-33%]). Hematochezia (estimate range, 5.2-54.0), abdominal pain (estimate range, 1.3-6.0), and anemia (estimate range, 2.1-10.8) were associated with higher EOCRC likelihood. Time from signs and symptoms presentation to EOCRC diagnosis was a mean (range) of 6.4 (1.8-13.7) months (23 studies) and a median (range) of 4 (2.0-8.7) months (16 studies). Conclusions and Relevance: In this systematic review and meta-analysis of patients with EOCRC, nearly half of individuals presented with hematochezia and abdominal pain and one-quarter with altered bowel habits. Hematochezia was associated with at least 5-fold increased EOCRC risk. Delays in diagnosis of 4 to 6 months were common. These findings highlight the need to identify concerning EOCRC signs and symptoms and complete timely diagnostic workup, particularly for individuals without an alternative diagnosis or sign or symptom resolution..</p
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