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Finite growth models

Shakir Bilal, Brajendra K Singh, Awadhesh Prasad, Edwin Michael
We study changes in the bifurcations of seasonally driven compartmental epidemic models, where the transmission rate is modulated temporally. In the presence of periodic modulation of the transmission rate, the dynamics varies from periodic to chaotic. The route to chaos is typically through period doubling bifurcation. There are coexisting attractors for some sets of parameters. However in the presence of quasiperiodic modulation, tori are created in place of periodic orbits and chaos appears via finite torus doublings...
September 2016: Chaos
Shuo Wang, Heinz Schattler
We consider cancer chemotherapy as an optimal control problem with the aim to minimize a combination of the tumor volume and side effects over an a priori specified therapy horizon when the tumor consists of a heterogeneous agglomeration of many subpopulations. The mathematical model, which accounts for different growth and apoptosis rates in the presence of cell densities, is a finite-dimensional approximation of a model originally formulated by Lorz et al. [18,19] and Greene et al. [10,11] with a continuum of possible traits...
December 1, 2016: Mathematical Biosciences and Engineering: MBE
Krzysztof Fujarewicz, Krzysztof Lakomiec
We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth...
December 1, 2016: Mathematical Biosciences and Engineering: MBE
Jie Gao, John L Williams, Esra Roan
Growth plate chondrocytes are responsible for bone growth through proliferation and differentiation. However, the way they experience physiological loads and regulate bone formation, especially during the later developmental phase in the mature growth plate, is still under active investigation. In this study, a previously developed multiscale finite element model of the growth plate is utilized to study the stress and strain distributions within the cartilage at the cellular level when rapidly compressed to 20 %...
October 21, 2016: Biomechanics and Modeling in Mechanobiology
David S Dean, Antonio Iorio, Enzo Marinari, Gleb Oshanin
The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential...
September 2016: Physical Review. E
Jaya Kumar Alageshan, Yashodhan Hatwalne, Murugappan Muthukumar
When an entangled interpenetrating collection of long flexible polymer chains dispersed in a suitable solvent is cooled to low enough temperatures, thin lamellar crystals form. Remarkably, these lamellae are sectored, with several growth sectors that have differing melting temperatures and growth kinetics, eluding so far an understanding of their origins. We present a theoretical model to explain this six-decade-old challenge by addressing the elasticity of fold surfaces of finite-sized lamella in the presence of disclination-type topological defects arising from anisotropic line tension...
September 2016: Physical Review. E
Jong Sang Youn, Janae Csavina, Kyle P Rine, Taylor Shingler, Mark Patrick Taylor, A Eduardo Sáez, Eric A Betterton, Armin Sorooshian
This study examines size-resolved physicochemical data for particles sampled near mining and smelting operations and a background urban site in Arizona with a focus on how hygroscopic growth impacts particle deposition behavior. Particles with aerodynamic diameters between 0.056 - 18 µm were collected at three sites: (i) an active smelter operation in Hayden, AZ, (ii) a legacy mining site with extensive mine tailings in Iron King, AZ, and (iii) an urban site, inner-city Tucson, AZ. Mass size distributions of As and Pb exhibit bimodal profiles with a dominant peak between 0...
October 4, 2016: Environmental Science & Technology
Anders Rosendal Korshoej, Guilherme Bicalho Saturnino, Line Kirkegaard Rasmussen, Gorm von Oettingen, Jens Christian Hedemann Sørensen, Axel Thielscher
OBJECTIVE: The present work proposes a new clinical approach to TTFields therapy of glioblastoma. The approach combines targeted surgical skull removal (craniectomy) with TTFields therapy to enhance the induced electrical field in the underlying tumor tissue. Using computer simulations, we explore the potential of the intervention to improve the clinical efficacy of TTFields therapy of brain cancer. METHODS: We used finite element analysis to calculate the electrical field distribution in realistic head models based on MRI data from two patients: One with left cortical/subcortical glioblastoma and one with deeply seated right thalamic anaplastic astrocytoma...
2016: PloS One
Yichen Lu, Mei Yan Lee, Shu Zhu, Talid Sinno, Scott L Diamond
During clotting under flow, platelets bind and activate on collagen and release autocrinic factors such as ADP and thromboxane, while tissue factor (TF) on the damaged wall leads to localized thrombin generation. Towards patient-specific simulation of thrombosis, a multiscale approach was developed to account for: platelet signalling [neural network (NN) trained by pairwise agonist scanning (PAS), PAS-NN], platelet positions (lattice kinetic Monte Carlo, LKMC), wall-generated thrombin and platelet-released ADP/thromboxane convection-diffusion (partial differential equation, PDE) and flow over a growing clot (lattice Boltzmann)...
September 25, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Peter E Hammer, Erin G Roberts, Sitaram M Emani, Pedro J Del Nido
OBJECTIVES: Neither heart valve repair methods nor current prostheses can accommodate patient growth. Normal aortic and pulmonary valves have 3 leaflets, and the goal of valve repair and replacement is typically to restore normal 3-leaflet morphology. However, mammalian venous valves have bileaflet morphology and open and close effectively over a wide range of vessel sizes. We propose that they might serve as a model for pediatric heart valve reconstruction and replacement valve design...
August 31, 2016: Journal of Thoracic and Cardiovascular Surgery
Naiara Rodriguez-Florez, Alessandra Carriero, Sandra J Shefelbine
This study aimed at using eXtended finite element method (XFEM) to characterize crack growth through bone's intra-cortical pores. Two techniques were compared using Abaqus: (1) void material properties were assigned to pores; (2) multiple enrichment regions with independent crack-growth possibilities were employed. Both were applied to 2D models of transverse images of mouse bone with differing porous structures. Results revealed that assigning multiple enrichment regions allows for multiple cracks to be initiated progressively, which cannot be captured when the voids are filled...
September 22, 2016: Computer Methods in Biomechanics and Biomedical Engineering
Kara E Garcia, Ruth J Okamoto, Philip V Bayly, Larry A Taber
During early vertebrate development, local constrictions, or sulci, form to divide the forebrain into the diencephalon, telencephalon, and optic vesicles. These partitions are maintained and exaggerated as the brain tube inflates, grows, and bends. Combining quantitative experiments on chick embryos with computational modeling, we investigated the biophysical mechanisms that drive these changes in brain shape. Chemical perturbations of contractility indicated that actomyosin contraction plays a major role in the creation of initial constrictions (Hamburger-Hamilton stages HH11-12), and fluorescent staining revealed that F-actin is circumferentially aligned at all constrictions...
August 15, 2016: Journal of the Mechanical Behavior of Biomedical Materials
Fatemeh Sadeghpour, Nasser Fatouraee, Mahdi Navidbakhsh
Aortic valve (AV) stenosis is described as the deposition of calcium within the valve leaflets. With the growth of stenosis, haemodynamic, mechanical performances of the AV and blood flow through the valve are changed. In this study, we proposed two fluid-structure interaction (FSI) finite element (FE) models. The hyperelastic material model was considered for leaflets tissue. The leaflet tissue was considered stiffer in stenotic valve than the healthy leaflets because of its calcium content. Therefore, the valve could not open completely and this led to a decrease in the orifice area of the valve...
September 15, 2016: Journal of Medical Engineering & Technology
Mir Jalil Razavi, Ramana Pidaparti, Xianqiao Wang
Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as their morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases...
August 2016: Physical Review. E
Jakub J Słowiński, Aleksandra Czarnecka
INTRODUCTION: The goal of this numerical study was to identify the results of modulated growth simulation of the mandibular bone during traction in Pierre-Robin Sequence (PRS) treatment. METHODS: Numerical simulation was conducted in the Ansys 16.2 environment. Two FEM (finite elements method) models of a newborn's mandible (a spatial and a flat model) were developed. The procedure simulated a 20-week traction period. The adopted growth measure was mandibular length increase, defined as the distance between the Co-Pog anatomic points used in cephalometric analysis...
October 2016: International Journal of Pediatric Otorhinolaryngology
I González-Valverde, C Semino, J M García-Aznar
Cell clustering and aggregation are fundamental processes in the development of several tissues and the progression of many diseases. The formation of these aggregates also has a direct impact on the oxygen concentration in their surroundings due to cellular respiration and poor oxygen diffusion through clusters. In this work, we propose a mathematical model that is capable of simulating cell cluster formation in 3D cultures through combining a particle-based and a finite element approach to recreate complex experimental conditions...
October 1, 2016: Computers in Biology and Medicine
Viet T Chau, Zdeněk P Bažant, Yewang Su
Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10(5)-10(6) almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model...
October 13, 2016: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
David L Des Marais, Samsad Razzaque, Kyle M Hernandez, David F Garvin, Thomas E Juenger
All plants must optimize their growth with finite resources. Water use efficiency (WUE) measures the relationship between biomass acquisition and transpired water. In the present study, we performed two experiments to understand the genetic basis of WUE and other parameters of plant-water interaction under control and water-limited conditions. Our study used two inbred natural accessions of Brachypodium distachyon, a model grass species with close phylogenetic affinity to temperate forage and cereal crops. First, we identify the soil water content which causes a reduction in leaf relative water content and an increase in WUE...
October 2016: Plant Science: An International Journal of Experimental Plant Biology
Stephen J Elliott, Guangjian Ni, Carl A Verschuur
Preservation of residual hearing after cochlear implantation is now considered an important goal of surgery. However, studies indicate an average post-operative hearing loss of around 20 dB at low frequencies. One factor which may contribute to post-operative hearing loss, but which has received little attention in the literature to date, is the increased stiffness of the round window, due to the physical presence of the cochlear implant, and to its subsequent thickening or to bone growth around it. A finite element model was used to estimate that there is approximately a 100-fold increase in the round window stiffness due to a cochlear implant passing through it...
August 30, 2016: Hearing Research
Umut Akalp, Stephanie J Bryant, Franck J Vernerey
Despite tremendous advances in the field of tissue engineering, a number of obstacles remain that hinder its successful translation to the clinic. One challenge that relates to the use of cells encapsulated in a hydrogel is identifying a hydrogel design that can provide an appropriate environment for cells to successfully synthesize and deposit new matrix molecules while providing a mechanical support that can resist physiological loads at the early stage of implementation. A solution to this problem has been to balance tissue growth and hydrogel degradation...
September 28, 2016: Soft Matter
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