Stability of a non-local kinetic model for cell migration with density-dependent speed

The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a d-dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation

Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis

Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. Precisely, several biochemical and biophysical cues give rise to tactic migration in the direction of their specific targets. Thus, this defines a multi-cue environment in which cells have to sort and combine different, and potentially competitive, stimuli. We propose a non-local kinetic model for cell migration in which cell polarization is influenced simultaneously by two external factors: contact guidance and chemotaxis. We propose two different sensing strategies, and we analyze the two resulting transport kinetic models by recovering the appropriate macroscopic limit in different regimes, in order to observe how the cell size, with respect to the variation of both external fields, influences the overall behavior. This analysis shows the importance of dealing with hyperbolic models, rather than drift-diffusion ones. Moreover, we numerically integrate the kinetic transport equations in a two-dimensional setting in order to investigate qualitatively various scenarios. Finally, we show how our setting is able to reproduce some experimental results concerning the influence of topographical and chemical cues in directing cell motility

Modelling physical limits of migration by a kinetic model with non-local sensing

Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell overcrowding may hamper cells from moving in certain directions or even from sensing beyond regions that practically act like physical barriers. We extend the non-local kinetic model proposed by Loy and Preziosi (J Math Biol, 80, 373–421, 2020) to include situations in which the sensing radius is not constant, but depends on position, sensing direction and time as the behaviour of the cell might be determined on the basis of information collected before reaching physically limiting configurations. We analyse how the actual possible sensing of the environment influences the dynamics by recovering the appropriate macroscopic limits and by integrating numerically the kinetic transport equation

Future care: rethinking technology enhanced aged care environments

© 2018, Emerald Publishing Limited. Purpose: Cutting-edge hospital and residential care architecture and interior design aim to address the emotional and practical needs of patients, staff and visitors. Yet, whilst improving on past practice, current approaches to design still rarely recognise or respond to individuals. The purpose of this paper is to provide a review of design-led research into digital technology across disciplines for the personalisation of healthcare environments and is informed by the authors’ ongoing hospital-based research. Design/methodology/approach: This review is based on a design anthropology framework providing insight into designing for changing the experience for older patients in current healthcare contexts and future focused strategies, integrating digital technologies and human-centred design across scale and disciplines. It is informed by ongoing hospital studies based on design-led research methodology, drawing on design anthropology and ethnographical methods. Findings: Technology enhanced, human-centred, assistive devices and environments implemented into healthcare across scale are developing but integration is needed for meaningful experiences. Research limitations/implications: This review is a positioning paper for design-led research into digital technology across scale and medium. Practical implications: This paper provides the basis for practical research including the ongoing hospital-based research of the authors. Social implications: This approach potentially enhances emotional experiences of connected healthcare. Originality/value: Future care scenarios are proposed, with technology and human experience as key drivers. Individualised and personalised solutions better cater for diversity. Within this context, it is strategic to question and test new ways of crafting the older persons care experience. This paper brings new direction to this discussion

Structure preserving schemes for Fokker–Planck equations with nonconstant diffusion matrices

In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker–Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are formulated in a one-dimensional setting, here we consider exclusively the two-dimensional case. We prove that the proposed schemes preserve fundamental structural properties like nonnegativity of the solution without restriction on the size of the mesh and entropy dissipation. Moreover, all the methods presented here are at least second order accurate in the transient regimes and arbitrarily high order for large times in the hypothesis in which the flux vanishes at the stationary state. Suitable numerical tests will confirm the theoretical results

Effect of various characteristics of raw wood on energy saturation of the chipper

Grinding of raw wood into chips is a complex process depending on various factors. Study of a grinding process is complicated not only because of a large number of these factors, but also because of the possibility of many combinations. Cutting power can be considered to be one of the criterion determining the extent and nature of these factors influence on the grinding process

Direction-dependent turning leads to anisotropic diffusion and persistence

Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains

Osteomyelitis Associated with \u3ci\u3eNocardiopsis composta\u3c/i\u3e in a Dog

Osteomyelitis can be caused by bacterial or fungal agents or may be idiopathic. Cocci, bacilli, and filamentous bacteria such as members of the Actinomycetes have all been determined to be causes of osteomyelitis. Differential diagnoses for Gram-positive filamentous rods in the family Actinomycetales causing osteomyelitis in the dog, include members of the more frequently encountered genera Nocardia and Actinomyces. Bacteria gain access to the bone via several routes but are most often associated with direct inoculation (such as percutaneous injuries, compound fractures, or secondary to foreign bodies such as surgical or other material including dirt and wood) and fracture instability. Less frequently, the route is hematogenous, as has been found with Propionibacterium acnes. Agents isolated from osteolytic lesions in dogs and cats have included Gram-positive Staphylococcus spp., Streptococcus spp., Gram-negative Escherichia coli, Proteus spp., Klebsiella spp., Pseudomonas spp., anaerobic Clostridium spp., Peptostreptococcus spp., Actinomyces spp., Bacterioides spp., Fusobacterium spp., and rarely Brucella canis, Nocardia spp., and Mycobacterium avium. Fungal causes include Coccidioides immitis, Blastomyces dermatitidis, Histoplasma capsulatum, Cryptococcus neoformans, and Aspergillus spp. Osteosarcoma with associated cellulitis is a reported noninfectious cause of osteomyelitis in dogs. Our report details the diagnosis, treatment, and resolution of osteomyelitis in a dog caused by a unique agent, Nocardiopsis composta