Search

In this paper, we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the incompressibility of the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor density exhibits regularizing dynamics thanks to an unexpected comparison principle. Using the comparison principle, we provide quantitative L 1 L^1 -contraction estimates and establish the C 1 , α C^{1,\alpha } -boundary regularity of the tumor patch. Furthermore, whenever the initial nutrient n 0 n_0 either lies entirely above or entirely below the critical value n 0 = 1 n_0=1 , we are able to give a complete characterization of the long-time behavior of the system. When n 0 n_0 is constant, we can even describe the dynamics of the full system in terms of some simpler nutrient-free and parameter-free model problems. These results are in sharp contrast to the observed behavior of the models either with nutrient diffusion or with death rate in tumor cells.

The Eden cell growth model is a simple discrete stochastic process which produces a "blob" in $\mathbb{R}^d$: start with one cube in the regular grid, and at each time step add a neighboring cube uniformly at random. This process has been used as a model for the growth of aggregations, tumors, and bacterial colonies and the healing of wounds, among other natural processes. Here, we study the topology and local geometry of the resulting structure, establishing asymptotic bounds for Betti numbers. Our main result is that the Betti numbers grow at a rate between the conjectured rate of growth of the site perimeter and the actual rate of growth of the site perimeter. We also present the results of computational experiments on finer aspects of the geometry and topology, such as persistent homology and the distribution of shapes of holes., 34 pages, 11 figures, 5 tables; revisions in response to referee reports

In this paper, we introduce and deal with the delayed nutrient-microorganism model with a random network structure. By employing time delay τ as the main critical value of the Hopf bifurcation, we investigate the direction of the Hopf bifurcation of such a random network nutrient-microorganism model. Noticing that the results of the direction of the Hopf bifurcation in a random network model are rare, we thus try to use the method of multiple time scales (MTS) to derive amplitude equation and determine the direction of the Hopf bifurcation. It is showed that the delayed random network nutrient-microorganism model can exhibit a supercritical or subcritical Hopf bifurcation. Numerical experiments are performed to verify the validity of the theoretical analysis.

Migrating cells exhibit various motility patterns, resulting from different migration mechanisms, cell properties, or cell-environment interactions. The complexity of cell dynamics is reflected, e.g., in the diversity of the observed forms of velocity autocorrelation function -- that has been widely served as a measure of diffusivity and spreading -- . By analyzing the dynamics of migrating dendritic cells in vitro, we disentangle the contributions of direction and speed to the velocity autocorrelation. We find that the ability of cells to maintain their speed or direction of motion is unequal, reflected in power-law decays of speed and direction autocorrelation functions with different exponents. The larger power-law exponent of the speed autocorrelation function indicates that the cells lose their speed memory considerably faster than the direction memory. Using numerical simulations, we investigate the influence of speed and direction memories as well as the direction-speed cross-correlation on the search time of a persistent random walker to find a randomly located target in confinement. Although the direction memory and direction-speed coupling play the major roles, we find that the speed autocorrelation can be also tuned to minimize the search time. Adopting an optimal speed memory can reduce the search time even up to 10% compared to uncorrelated spontaneous speeds. Our results suggest that migrating cells can improve their search efficiency, especially in crowded environments, through the directional or speed persistence or the speed-direction correlation., Comment: 10 pages, 9 figures

Fractal fractional operators in Caputo and Caputo-Fabrizio sense are being used in this manuscript to explore the interaction between the immune system and cancer cells. The tumour-immune model has been investigated numerically and theoretically by the singular and non-singular fractal fractional operators. Via fixed point theorems, the existence and uniqueness of the model under the Caputo fractal fractional operator have been demonstrated. Using the fixed point theory, the existence of a unique solution has been derived under the Caputo-Fabrizio case. Through nonlinear analysis, the Ulam-Hyres stability of the model has been derived. For the singular and nonsingular fractal fractional operators, numerical results have been developed by Lagrangian-piece wise interpolation. We simulate the numerical results for the various sets of fractional and fractal orders to describe the relationship between immune and cancer cells under the novel operators with two different kernels. We compared the dynamics of the tumor-immune model using a power law and an exponential-decay kernel to explore that the nonsingular fractal fractional operator provides better dynamics for the considered model.

Context Prostate-specific membrane antigen (PSMA) positron emission tomography/magnetic resonance imaging (PET/MRI) is a novel imaging technique with several potential applications in the prostate cancer (PCa) setting. Objective To perform a systematic review of the current evidence regarding the diagnostic performance of PSMA PET/MRI in patients with primary and recurrent PCa. Evidence acquisition A comprehensive bibliographic search on the MEDLINE and Cochrane Library databases was performed in October 2020. The review was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) statement. Studies were deemed eligible if they assessed patients with primary or recurrent PCa (P) undergoing PSMA PET/MRI (I) with or without comparison with other imaging techniques (C) in order to evaluate its diagnostic performance (O). Retrospective and prospective primary clinical studies were included. Results of previous meta-analyses were reported. Evidence synthesis A total of 23 original articles and three meta-analyses were included. Limited evidence on PSMA PET/MRI is available, especially in the setting of partial gland ablation. PET/MRI can be an effective imaging modality for detecting primary PCa, showing higher accuracy than multiparametric MRI alone. It provides accurate local staging of primary PCa; however, there are contradictory results in this context when its performance is compared with other imaging techniques. PET/MRI also shows high performance for restaging and detecting tumor recurrence, even at low prostate-specific antigen levels. Conclusions PSMA PET/MRI could represent a valuable tool in the management of patients with primary and recurrent PCa. No specific recommendations can be provided. Patient summary Encouraging data regarding the benefits of prostate-specific membrane antigen positron emission tomography/magnetic resonance imaging in patients with prostate cancer are emerging from the literature.

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise diffusion Markov process (PDifMP) at the cellular level, we derive an equation for the density of the transition probability of this Markov process based on the generalised Fokker–Planck equation. Then, a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.

Knowledge graphs have received intensive research interests. When the labels of most nodes or datapoints are missing, anchor graph and hierarchical anchor graph models can be employed. With an anchor graph or hierarchical anchor graph, we only need to optimize the labels of the coarsest anchors, and the labels of datapoints can be inferred from these anchors in a coarse-to-fine manner. The complexity of optimization is therefore reduced to a cubic cost with respect to the number of the coarsest anchors. However, to obtain a high accuracy when a data distribution is complex, the scale of this anchor set still needs to be large, which thus inevitably incurs an expensive computational burden. As such, a challenge in scaling up these models is how to efficiently estimate the labels of these anchors while keeping classification performance. To address this problem, we propose a novel approach that adds an anchor label predictor in the conventional anchor graph and hierarchical anchor graph models. In the proposed approach, the labels of the coarsest anchors are not directly optimized, and instead, we learn a label predictor which estimates the labels of these anchors with their spectral representations. The predictor is optimized with a regularization on all datapoints based on a hierarchical anchor graph, and we show that its solution only involves the inversion of a small-size matrix. Built upon the anchor hierarchy, we design a sparse intra-layer adjacency matrix over these anchors, which can simultaneously accelerate spectral embedding and enhance effectiveness. Our approach is named Faster Learning6 on Anchor Graph (FLAG) as it improves conventional anchor-graph-based methods in terms of efficiency. Experiments on a variety of publicly available datasets with sizes varying fromthousands to millions of Q1 samples demonstrate the effectiveness of our approach.

The influence of the plasmonic of three spherical metal nanoparticles (MNPs) on the semiconductor quantum dot (SQD) having three external fields, is analyzed. The density matrix equations are modified for the description of the optical properties of the SQD-MNPs nanosystem. We study theoretically the role of the plasmon-exciton dipole coupling in the SQD-MNPs nanosystem. We investigate the dependence of the plasmon-exciton dipole coupling of the SQD-MNPs nanosystem on the position of three spherical MNPs with respect to SQD as well as on the material parameters of the hybrid nanosystem. The direction and detunings of the three external fields play an important role on the characterization of the SQD-MNPs nanosystem.

Mathematical modeling of a cancer treatment and drug delivery at the macroscale requires evaluating the leakage of solute flux into the targeted tumor or healthy tissue. This study provides a 2D model for the blood and nanoparticle transport in a single vessel surrounded by a tumor. In the vessel, the blood flow is described by Navier-Stokes equations which are coupled to advection–diffusion equation and energy equation for the fluid and nanoparticle transport. Impacts of the Brownian motion and thermophores parameters together with a thermal radiation are examined. Constant vascular fluid velocity across the vessel walls are assumed, and two phase nanofluid model is considered to represent the nanoparticle concentration. The solution methodology is depending on the finite volume method and features of the blood velocity, temperature and nanoparticle concentration are presented graphically. The major outcomes reveal that the blood temperature within the vessel is enhanced as the nanoparticle extravasation coefficient is increasing, while the concentration of the nanoparticles around the tumor is reduced.

This manuscript deliberates on thermal radiation and viscous dissipation possessions on magneto-hydrodynamic (MHD) bioconvection stream of a new variety of water established the upper-convected Maxwell, Nanoliquid covering Nanoparticles and motile gyrotactic microorganisms over an absorptive vertical moving plate. Nanoliquid bio convective is developed through the mutual possessions of buoyant forces and magnetic field on the collaboration of motile microorganisms and Nanoparticles. The leading nonlinear PDE of the problem are transforming into a structure of nonlinear ODE over suitable similarity conversion and shooting method procedure joined with Runge–Kutta–Fehlberg integration pattern, the exemplary BVP is attempted numerically. A parametric investigation of the complete stream regime is supported out to demonstrate the possessions of the leading constraints, specifically bioconvection Lewis quantity Lb, traditional Lewis quantity Le, bioconvection Peclet quantity Pe, buoyancy quotient constraint Nr, bioconvection Rayleigh quantity Rb, Brownian motion constraint Nb, thermophoresis constraint Nt, Hartmann quantity Ha, Grashof quantity Gr, radiation constraint R Eckert quantity Ec, microorganisms concentration variance constraint Ω and a suction/injection constraint fw on the flow, temperature, volume fraction of nanoparticles and motile microorganisms density outlines as well as the friction quantity, the local Nusselt quantity, the local Sherwood quantity and the local density quantity of the motile microorganisms.

Adherent cells seeded on substrates spread and evolve their morphology while simultaneously displaying motility. Phenomena such as contact guidance, viz. the alignment of cells on patterned substrates, are strongly linked to the coupling of morphological evolution with motility. Here, we employ a recently developed statistical thermodynamics framework for modelling the non-thermal fluctuating response of cells to probe this coupling. This thermodynamic framework is first extended via a Langevin style model to predict temporal responses of cells to unpatterned and patterned substrates. The Langevin model is then shown to not only predict the different experimentally observed temporal scales for morphological observables such as cell area and elongation but also the interplay of morphology with motility that ultimately leads to contact guidance.

Wet adhesion phenomenon of the soap bubble bridge is widespread in the climbing behaviors of geckos and insects, and the surface shapes generally have important impact on the adhesion behavior of soap bubble bridge. In order to focus on the effect of the shape on the wet adhesion, we study the adhesion behavior between two rigid surfaces containing different shapes such as concave, flat, and convex. For a given soap bubble bridge, the relationship between adhesion force and separation is numerically calculated, and the corresponding configuration of soap bubble bridge is also given. The results show that the adhesion force of soap bubble bridge decreases with the increase of separation. This trend is the same as the case of liquid bridge, although the volume of liquid bridge is constant while the volume of soap bubble bridge varies. The adhesion force with concave rigid surfaces is bigger than that of the other two kinds of rigid surfaces at the same separation. The wetting radius of the soap bubble bridge decreases with the increase of separation. The appearance of this phenomenon results from the equation of state for the gas in the soap bubble bridge. This research may improve the understanding of the mechanical mechanism of wet adhesion.

A process simulator has been developed to model and predict the performance of spiral-wound membrane modules in pressure retarded osmosis processes. This has involved automation of generalized protocols for the numerical integration of the solvent and solute flux equations (in conjunction with a suitable electrolyte equation of state) along the surface area of a spiral-wound membrane leaf. Performance equations are solved for discrete area elements and the spiral-wound character of the module as a whole is realized through the programmed sequence in which discrete elements are evaluated. This arrangement allows for mirroring the parabolic flow pattern of the feed stream in the spiral-wound membrane leaf. The total permeation (and, by extension, power density) is thus calculated in a manner that accounts for the driving force profile consistent with flow patterns specific to spiral-wound membranes. This effective treatment of each discrete element as a flat-sheet membrane enables the transferability of membrane parameters characterized in standard, coupon-scale experiments to the simulation of spiral-wound modules. This transferability is illustrated through comparisons of model predictions with published pilot-scale PRO data.

This paper presents a nanoscale-inspired continuum model to capture the coupling of adhesion and friction in contact-mechanics problems. The method relies on Green's function molecular dynamics to calculate the elastic body fields and on a phenomenological mixed-mode coupled cohesive-zone model to describe the interplay between normal and tangential tractions, i.e. adhesion and friction. While the presented formulation is applicable to linearly elastic solids with generic surface roughness, the focus of our analysis is on the indentation of an array of circular rigid punches into a flat, deformable solid. Our results show that the coupling between adhesion and friction leads to an increase in the contact size and a decrease in the pull-off load.

Active matter systems provide fascinating examples of pattern formation and collective motility without counterparts in equilibrium systems. Here, we employ Brownian dynamics simulations to study the collective motion and self-organization in systems of self-propelled semiflexible filaments, inspired by the gliding motility of \textit{filamentous Cyanobacteria}. Specifically, we investigate the influence of stochastic direction reversals on the patterns. We explore pattern formation and dynamics by modulating three relevant physical parameters, the bending stiffness, the activity, and the reversal rate. In the absence of reversals, our results show rich dynamical behavior including spiral formation and collective motion of aligned clusters of various sizes, depending on the bending stiffness and self-propulsion force. The presence of reversals diminishes spiral formation and reduces the sizes of clusters or suppresses clustering entirely. This homogenizing effect of direction reversals can be understood as reversals providing an additional mechanism to either unwind spirals or to resolve clusters., Comment: 15 pages, 11 figures

We consider a spherical swimmer that undergoes helical motion due to the existence of a propulsive torque which is not parallel to a propulsive force that pulls the cell through the fluid. In addition, the cell is bottom-heavy; the centre of gravity is offset from the centre of buoyancy which generates a gravitational torque. In the presence of shear, fluid viscosity generates a further torque. Because cells swim at low Reynolds number, these torques are balanced. This thesis extends the model developed in Bearon (2013) in two distinct directions. Firstly, we consider an extension to the case of a flow where the shear varies with position. We consider a downward flow in a vertical channel. We observe that depending on the parameters, cells may exhibit the classical accumulation towards the centre of the channel or display a new focussing away from the centre. Secondly, we develop the model to describe randomness associated with changes in cell orientation. This is done by developing a Fokker-Planck equation for helical swimmers in terms of Euler angles. The classical Fokker-Planck equation obtained by Pedley and Kessler (1992) is a special case of the equation derived in this thesis. To implement this model numerically as an individual based model, we derive the corresponding stochastic differential equations. The Fokker-Planck equation and stochastic differential equation are extended to examine the spatial-temporal distribution of helical swimmers. We explore in detail how the horizontal distribution of cells in channel flow evolves to an equilibrium state, and how the evolution depends on the model parameters. For non-helical swimmers, we compare the result of the model to the recent experiments of Croze et al (2017).

This paper studies the similarities and the differences between natural aggregate concrete (NAC) beams and recycled aggregate concrete (RAC) beams in terms of concrete material properties, bearing capacity, and crack resistance and further proposes correction formulas for cracking moment calculation of RAC beams that consider different recycled aggregate substitution ratios. First, the basic mechanical properties (e.g., cube compressive strength, axial compressive strength, and elastic modulus) of RAC blocks were tested; second, comparative bending tests of RAC beams and natural aggregate concrete beams were conducted, in order to obtain the cracking moments, yield bending moments, ultimate bending moments, mid-span deflections and crack development forms; finally, numerical simulations were performed to investigate the cracking performances of RAC beams. Through analyzing the experimental results, it is found that the crack development pattern of RAC beams resembles that of natural aggregate concrete beams, while the cracking performance of RAC beams significantly deviates from that of NAC beams. Finally, the correction formulas for the cracking moment calculation of RAC beams are proposed based on the numerical simulation results and verified by data from other researchers, which can be regarded as a correction for the cracking moment calculation formulas in the current code for RAC beams with respect to varied recycled concrete aggregate substitution ratios.

The present paper concerns the formulation and the evolution of the non symmetrical growth of an avascular cancerous cell colony in an analytical mathematical fashion. Although most of the existing research considers spherical tumours, here we work in the frame of a more general case of the prolate spheroidal geometry. The tumour lies inside a host spheroidal shell which provides vital nutrients, receives the debris of the dead cells and also transmittes to the tumour the pressure imposed by the surrounding on its exterior boundary. Under the aim of studying the evolution of the exterior tumour boundary, we focus on the exterior conditions under which such a geometrical structure can be sustained. To that purpose, the corresponding nutrient concentration, the inhibitor concentration and the pressure field are calculated analytically providing the necessary data for the evolution equation to be solvable. It turns out that an avascular tumour can exhibit a prolate spheroidal growth only if the external conditions for the nutrient supply and the transversally isotropic pressure field have a specific form, which is consistent with the tumour evolution. Additionally, our model exhibits a geometrical reduction to special cases and, mainly, to the spherical geometry in order to recover the existing results for the sphere.

In the current study, a mathematical model is developed to visualize the mixed convection boundary layer flow of a nanofluid containing gyrotactic microorganisms past a permeable vertical surface saturated in a porous medium with variable viscosity and velocity slip effects. Suction/injection impact is taken into detail through the flow with heat and mass transfer analysis. Appropriate transformations are applied to transform the governing partial differential equations into non-linear ordinary differential equations, before being solved numerically using Runge-Kutta procedure is used with shooting technique. A parametric study focusing the influence of involved parameters on various fields such as the local skin friction coefficient, local Nusselt number are graphed via plots along with the local Sherwood number and motile microorganisms density number. The present results indicate that the motile microorganism number is enhanced for increasing Peclet number estimations. Moreover, the growing in the thermophoresis parameter leads to sufficient enhancement in the skin friction coefficient, Sherwood number and the density of the motile microorganism number for injection case, while the opposite behavior occurred with suction case.

This paper presents the results of a numerical study of the effects of swirling flow in coolant jets on film cooling performance. Some combined-hole designs with swirling coolant flow entering the delivery hole are proposed and analyzed. Adiabatic film cooling effectiveness values for cases with various blowing ratios are compared. Detailed flow structures and underlying mechanisms are discussed. The results show that film cooling effectiveness is improved with jet swirl at high blowing ratios, and that swirl strength has significant influence on film cooling performance. Combined-hole designs can further improve film cooling performance using swirling jets due to mixing of coolant flows and interaction of vortices. The largest improvements of area-averaged film cooling effectiveness for a single-hole swirl case and a combined-hole swirl case over corresponding non-swirling case results are 157% and 173%, respectively.

In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for the (possible) solutions of the model. In particular, under some conditions on the parameters, we obtain that the system does not develop blow-up at finite time. In addition, we design a fully discrete finite element scheme for the model which preserves some pointwise estimates of the continuous problem. Later, we make an adimensional study in order to reduce the number of parameters. Finally, we detect the main parameters determining different width of the ring formed by proliferative and necrotic cells and different regular/irregular behaviour of the tumor surface., Comment: 25 pages, 20 figures

This paper presents the buckling behavior of the grid stiffened composite conical shell subjected to the lateral pressure. A smeared method is employed to equivalent grid structure into a layer. For this purpose, a typical unit cell is chosen for analyzing forces and moments on it. Therefore equivalent stiffness parameters due to the grid structure are determined. By determining the stiffness parameters of the shell and superimposing with those of the stiffeners, equivalent stiffness of the whole structure is obtained. Governing equations are established based on the Donnell shell theory. The power series method is used to extract the buckling load of the stiffened shell. To validate obtained results, a 3 D finite element model is built using ABAQUS software. The comparison showed that the analytical solution is qualified enough to study the buckling behavior of the grid stiffened composite conical shell. Through this study, the effect of a set of important parameters due to stiffeners like stiffener orientation angle, the number of stiffeners, and due to due to shell like lamination angle and semi-vertex angle are investigated, and finally are presented based on this study results.

We study stationary solutions to the Keller--Segel equation on curved planes. We prove the necessity of the mass being $8 \pi$ and a sharp decay bound. Notably, our results do not require the solutions to have a finite second moment, and thus are novel already in the flat case. Furthermore, we provide a correspondence between stationary solutions to the static Keller--Segel equation on curved planes and positively curved Riemannian metrics on the sphere. We use this duality to show the nonexistence of solutions in certain situations. In particular, we show the existence of metrics, arbitrarily close to the flat one on the plane, that do not support stationary solutions to the static Keller--Segel equation (with any mass). Finally, as a complementary result, we prove a curved version of the logarithmic Hardy--Littlewood--Sobolev inequality and use it to show that the Keller--Segel free energy is bounded from below exactly when the mass is $8 \pi$, even in the curved case., Comment: 15 pages, no figures. Accepted by Proceedings of the Royal Society of Edinburgh Section A

The transport of motile microorganisms is strongly influenced by fluid flows that are ubiquitous in biological environments. Here we demonstrate the impact of fluid inertia. We analyze the dynamics of a microswimmer in pressure-driven Poiseuille flow, where fluid inertia is small but non-negligible. Using perturbation theory and the reciprocal theorem, we show that in addition to the classical inertial lift of passive particles, the active nature generates a ‘swimming lift’, which we evaluate for neutral and pusher/puller-type swimmers. Accounting for fluid inertia engenders a rich spectrum of complex dynamics including bistable states, where tumbling coexists with stable centerline swimming or swinging. The dynamics is sensitive to the swimmer’s hydrodynamic signature and goes well beyond the findings at vanishing fluid inertia. Our work will have non-trivial implications on the transport and dispersion of active suspensions in microchannels.

We have calculated the radiological parameters such as computerized tomography (CT) numbers effective atomic number (Zeff) and electron density (Nel) of newborn tissue and adult tissue of lung, kidney, heart and brain. Effective atomic number is computed by calculating the molecular, atomic and electronic cross section in the wide energy range of 1 keV–100 keV using WinXCOM. The new born tissue and adult tissue a very similar, but their atomic number, CT number and electron densities differs. This fact helps in the radiography and radiotherapy.

The study of stiffened plates and shells subjected to free vibration is the aim of this work. The effect of radius of curvature on the natural frequency of a stiffened cylindrical and spherical shell is studied using ANSYS Parametric Design Language for different boundary conditions. The effect of the orientation of stiffener on natural frequency for the cylindrical shell is analysed. The frequency response of bare plates is estimated theoretically and verified using ANSYS simulation software for various boundary conditions. Also, the effect of a different cross-section of stiffener on the natural frequency of stiffened plates is analysed. Variation of the natural frequency of stiffened plates for various parameters like aspect ratio and thickness ratio with CCCC (C – clamped) boundary condition is studied. Stiffened structures are often utilised in structural engineering, marine works, aircraft, locomotives etc.

According to the Warburg effect, there are some significant differences between metabolisms, products and process of respirations of cancer cells and normal cells. For example, normal cells absorb oxygen and glucose and give water molecules, carbon dioxide, ATP molecules and some number of spinors; while cancer cells take glucose and give lactate, less number of ATP molecules and different number of spinors. Using this property, we can design a system from two graphene sheets that are connected by pairing the fourth free electrons of carbons. Then, we can break some pairs and produce some holes. The number of these holes should be equal to the number of radiated spinors by normal cells. Near a normal cell, all holes are filled and the graphene system doesn't emit any electrical current or wave. However, near a cancer cell, some extra holes or spinors remain that their motions produce some electrical currents. These currents force on cancer cell membranes and destroy them and consequently, cause the cell death. Also, these currents emit some electromagnetic waves which detectors could take them out of the human's body and consequently, they could play the main role in imaging.

A tumor-immune system with diffusion and delays is proposed in this paper. First, we investigate the impact of delay on the stability of nonnegative equilibrium for the model with a single delay, and the system undergoes Hopf bifurcation when delay passes through some critical values. We obtain the normal form of Hopf bifurcation by applying the multiple time scales method for determining the stability and direction of bifurcating periodic solutions. Then, we study the tumor-immune model with two delays, and show the conditions under which the nontrivial equilibria are locally asymptotically stable. Thus, we can restrain the diffusion of tumor cells by controlling the time delay associated with the time of tumor cell proliferation and the time of immune cells recognizing tumor cells. Finally, numerical simulations are presented to illustrate our analytic results.

In this article, we present a critical discussion of the parametric regimes required for reaching the functionality of the two-electron square-planar tetrameric mixed-valence (MV) complexes as molecular cells in quantum cellular automata (QCA). Previous studies on molecular QCA were restricted by the limit case of strong Coulomb interaction that was supposed to be the only way to ensure such two key requirements for functioning QCA cells as bistability and switchability. It was thus assumed that the site-to-site electron transfer energy

Automatic cell counting in pathology images is challenging due to blurred boundaries, low-contrast, and overlapping between cells. In this paper, we train a convolutional neural network (CNN) to predict a two-dimensional direction field map and then use it to localize cell individuals for counting. Specifically, we define a direction field on each pixel in the cell regions (obtained by dilating the original annotation in terms of cell centers) as a two-dimensional unit vector pointing from the pixel to its corresponding cell center. Direction field for adjacent pixels in different cells have opposite directions departing from each other, while those in the same cell region have directions pointing to the same center. Such unique property is used to partition overlapped cells for localization and counting. To deal with those blurred boundaries or low contrast cells, we set the direction field of the background pixels to be zeros in the ground-truth generation. Thus, adjacent pixels belonging to cells and background will have an obvious difference in the predicted direction field. To further deal with cells of varying density and overlapping issues, we adopt geometry adaptive (varying) radius for cells of different densities in the generation of ground-truth direction field map, which guides the CNN model to separate cells of different densities and overlapping cells. Extensive experimental results on three widely used datasets (i.e., VGG Cell, CRCHistoPhenotype2016, and MBM datasets) demonstrate the effectiveness of the proposed approach.

This paper proposes a concept of soil shear strength exertion around an anchorage section to analyze and calculate the anchor’s force and displacement. First, based on the Mohr stress circle, the numerical relationship between the value of the internal friction angle exertion, the value of the cohesion exertion, and the displacement are established under the non-limit active state. According to the interaction mechanism between the anchorage section and the surrounding soil, this paper obtains the corresponding relationship between the value of the soil’s shear strength exertion and displacement under the non-limit active state. Then, according to the load transfer principle of the anchorage section, the basic differential equation is established. The differential equation of the relative displacement distribution along the length of the anchorage section under the non-limit active state is further derived. And the calculation and analysis formula of the shear stress and relative displacement in the anchorage section considering the process of the soil shear strength exertion is also obtained. Finally, this paper compares the calculation method with the hyperbolic model calculation method for the same example. The results verify the accuracy of the calculation method.

Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems. This raises the question of whether the optimization of mixing through the emergence of active turbulent motion in bacterial swarms played a role in the evolution of bacterial shapes. Here, to address this question, we solve the hydrodynamic equation for active nematics coupled with an advection-diffusion equation for the nutrients. The latter models a conserved activity field and mimics the conservation of nutrients in bacterial swarms. At the interface between active and passive nematic phases, in addition to diffusion, the activity is transported by interfacial flows and in turn modifies them through active stresses. We find that the interfacial dispersion of the conserved activity is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects. Furthermore, we observe a non-monotonic dependence of the generalized diffusion coefficient on the aligning parameter, which is related to the shape of the particles. Our simulations suggest that there is an optimal shape that maximizes the dispersion of conserved activity at the active-passive nematic interface.

In development and homeostasis, multi-cellular systems exhibit spatial and temporal heterogeneity in their biochemical and mechanical properties. Nevertheless, it remains unclear how spatiotemporally heterogeneous forces affect the dynamical and mechanical properties of confluent tissue. To address this question, we study the dynamical behavior of the two-dimensional cellular vertex model for epithelial monolayers in the presence of fluctuating cell-cell interfacial tensions, which is a biologically relevant source of mechanical spatiotemporal heterogeneity. In particular, we investigate the effects of the amplitude and persistence time of fluctuating tension on the tissue dynamics. We unexpectedly find that the long-time diffusion constant describing cell rearrangements depends non-monotonically on the persistence time, while it increases monotonically as the amplitude increases. Our analysis indicates that at low and intermediate persistence times tension fluctuations drive motion of vertices and promote cell rearrangements, while at the highest persistence times the tension in the network evolves so slowly that rearrangements become rare., Comment: 16 pages, 14 figures

Curvature induced sorting of lipid membrane bound proteins has been widely studied through experiments that induce curvature variation in a giant unilamellar lipid-bilayer vesicle with adsorbed proteins by pulling thin cylindrical tethers. In the theoretical space, this has been supplemented with models that capture curvature dependent interaction between membrane and idealized protein particles, through free energy contributions. Many membrane proteins such as the BAR domain proteins are known to have extremely anisotropic shapes and soft interacting potentials, whereas the idealizations of protein particles explored in models have only assumed them as hard disk-like particles with curvature anisotropy. Here, we present a model of sorting of the proteins while including the effects of softness in their interaction potentials, shape anisotropy in the protein structure, and curvature anisotropy in the interactions with the membrane. This is based on a clean separation of free energy contributions from non-ideal fluid behavior of soft anisotropic particles and curvature interactions between proteins and membranes. We probe the behavior of the sorting function under limiting conditions and show that it converges to the previously derived models. In addition to this, we present a comparison of the variation in sorting ratio due to the observed variation in the shape parameter values in known membrane proteins. Finally, using published experimental data for membrane proteins, we perform fitting and derive model parameters. We observe that shape anisotropy adversely affects the sorting of proteins to a high curvature region, whereas curvature anisotropy and softer interaction between proteins favor sorting.

Wave-propelled mechanisms are applied to propel unmanned marine vehicles such as Wave Glider and wave-powered boats, which can convert wave energy directly into propulsion. In this paper, a fluid-rigid body coupled dynamic model is utilized to investigate the propulsion performance of the wave-propelled mechanism. Firstly, the coupled dynamic model of the wave-propelled mechanism is developed based on relative motion principle by combining rigid body dynamics model and CFD method. Then, the motion responses of wave-propelled mechanism are calculated. The relationship between the propulsion force, heave and pitch motion of hydrofoil are analyzed by using phase diagrams and the actual operation conditions of propulsion mechanism are obtained. Besides, the effects of restoring spring stiffness and wave heights on the propulsion performance are also investigated, and the vortex evolution is illustrated at different moments of movement and different restoring stiffness. These works can be helpful for the design and optimization of different kinds of wave-propelled vehicles.

In this study, we introduce microwave-induced membrane distillation (MIMD) where microwave radiation is applied not only to heat water but also to enhance the biocidal effects of nanocarbon immobil...

This paper is concerned with the stability of traveling waves for a Keller-Segel model with singular chemotactic term and zero chemo-attractant diffusion, where the model and the waves are established to explain the propagation of bacteria pulses along a capillary tube observed in Adler's experiment [1] . By applying the detailed spectral analysis, Evans function method and special transformations and combining with some numerical simulations, in some range of the parameters all the waves are shown to be spectrally stable in some exponentially weighted spaces, and in other range of parameters all the waves are shown to be unstable in any exponentially weighted spaces. The local well-posedness of the classical positive solution to the Cauchy problem of the model is also obtained by applying semigroup argument and some special transformations.

This manuscript considers the homogeneous Neumann initial-boundary value problem for a three-component chemotaxis system describing the spatio-temporal Alopecia Areata dynamics. The model addresses the complex interactions between CD4+ T cells, CD8+ T cells and interferon-gamma (IFN-γ): Both types of immune cells secrete the chemical that diffuses and degrades; conversely, the T cells are activated by the chemical but decay due to density-dependent death. In addition to random motion, the T cells bias their movement toward the concentration gradient of IFN-γ. To compare with previous chemotaxis models, a distinctive feature of this system is that CD8+ T cells additionally proliferate in a nonlinear manner with the help of CD4+ T cells. Given suitably regular initial data, it is shown that either small logistic damping in the two-dimensional case or strong logistic damping in the three-dimensional setting can prevent any blow-up of classical solutions to the problem. Moreover, we find a specific parameter regime for which the unique coexistence equilibrium is globally convergent.

Organ and tissue growth result from an integration of biophysical communication across biological scales, both in time and space. In this review, we highlight new insight into the dynamic connections between control mechanisms operating at different length scales. First, we consider how the dynamics of chemical and electrical signaling in the shape of gradients or waves affect spatiotemporal signal interpretation. Then, we discuss the mechanics underlying dynamic cell behavior during oriented tissue growth, followed by the connections between signaling at the tissue and organismal levels.

Swirling flows are widely used to enhance heat and mass transfer in energy conversion devices, and predicting the swirl decay rate is important in several applications. This study investigates the ...

Magnetic filaments driven by external magnetic field are an interesting topic of research in-terms of the possible bio-medical applications. In this paper, we investigated the applicability of using ferromagnetic filaments as micro swimmers both experimentally and numerically. It was found that applying a pulse wave field profile with a duty cycle of 30$$\%$$ % induced experimentally observable swimming, which is similar to the breast stroke of micro algae. Good agreement with numerical simulations was found. Moreover, for stable continuous swimming, an initial filament shape is required to avoid transition to the structurally preferred non-swimming S-like mode.

Off-lattice models are a well-established approach in multicellular modeling, where cells are represented as points that are free to move in space. The representation of cells as point objects is useful in a wide range of settings, particularly when large populations are involved; however, a purely point-based representation is not naturally equipped to deal with objects that have length, such as cell boundaries or external membranes. Here we introduce an off-lattice modeling framework that exploits rigid body mechanics to represent objects using a collection of conjoined one-dimensional edges in a viscosity-dominated system. This framework can be used to represent cells as free moving polygons, to allow epithelial layers to smoothly interact with themselves, to model rod-shaped cells such as bacteria and to robustly represent membranes. We demonstrate that this approach offers solutions to the problems that limit the scope of current off-lattice multicellular models. The authors present a framework for modeling cell interactions using rigid bodies, which can used to represent cells as free moving polygons, to allow epithelial layers to smoothly interact, to model bacteria and to robustly represent membranes.

Previous research on the identification of fungi by means of their Raman spectra (i.e. spectra based on the inelastic scattering of light) of their spores indicates that this approach could be a fa...

In this paper, we study the global dynamics of a fractional-order Ebola model with delayed immune response on complex networks. The model describes the interaction of Ebola virus with the immune cells. A time delay is introduced in the cytotoxic T-lymphocyte term to ensure the response period taken against the virus. By constructing a suitable Lyapunov function the global stability of the equilibrium points has been investigated with help of basic reproduction. The analysis shows that the fractional-order time-delay can effectively enrich the dynamics and strengthen the stability condition of the fractional-order infection model. Finally, the derived theoretical results are justified by some numerical simulations.

To investigate the proton exchange membrane fuel cell stack performance heterogeneity, a pseudo two-dimensional stack model integrating non-uniform flow distributions is developed. The frictional a...

Thyristor Controlled Reactor (TCR) has been used to improve power quality through firing angle control by parallel connection to the system in the form of ∆-connection. The inductances of three-phase TCR are assumed to be a same value, but a difference is generated in the inductance value of each phase in the manufacturing process. Due to the difference in three-phase inductance, a conventional TCR control algorithm causes the imbalance of phase voltage. So, this paper proposes a method to solve the phase imbalance problem of TCR using a modified firing angle control scheme, and the performance of the proposed method was verified through Matlab simulation.

The influence of magnetic fields and natural geomagnetic storms on biological circadian rhythms are actively studied. This study reveals an impact of local natural perturbations in the geomagnetic field that occurred at different times of the day on circadian patterns of locomotor activity of zebrafish. A decrease in zebrafish swimming speed was observed during the geomagnetic disturbances before or after the fluctuations of diurnal geomagnetic variation. However, if the geomagnetic perturbations coincided with the fluctuations of diurnal geomagnetic variation, the decrease in zebrafish swimming speed was insignificant. This result suggests that the biological effects of geomagnetic disturbances may depend on synchronization with the diurnal geomagnetic variation. It implies that the previously published correlations between geomagnetic activity and medical or biological parameters could result from a disruption in circadian biorhythms.

BACKGROUND Primary soft tissue giant cell tumor (GCT-ST) is rare and has relatively low malignant potential. Most reports are pathological and clinical studies, while imaging studies have only been reported in cases of adjacent bone or with atypical cystic degeneration. With regard to the findings on magnetic resonance imaging (MRI) or ultrasonography, superficial masses can be further identified based on facial edema, skin thickening, skin contact, internal hemorrhage or necrosis and lobulation of the mass. Unlike deep-seated masses, MRI features do not always provide an accurate diagnosis for benign and malignant patients with superficial soft-tissue lesions. Thus, the application of diffusion-weighted imaging (DWI) to evaluate superficial soft tissue tumors is necessary. CASE SUMMARY A 36-year-old woman who had a suspected malignant tumor in the upper limb on ultrasound and computed tomography is reported. The signal intensity of the suspected tumor was heterogeneous on plain MRI; nodular and heterogeneous enhancement was observed in the tumor with irregular shapes and blurred margins on dynamic contrast-enhanced MRI. The lesion on DWI was hyperintense with a higher mean apparent diffusion coefficient (ADC) value. Finally, a GCT-ST was confirmed by pathology. This case suggests that GCT-ST should be distinguished as a benign soft tissue mass from giant cell-rich soft tissue neoplasms or malignant tumors. CONCLUSION The MRI features of the superficial GCT-ST in the upper limb included heterogeneous signal intensity within the lesion on T2-weighted image (T2WI) and T1-weighted fat-saturation spoiled gradient recalled echo (T1 FSPGR), nodular enhancement with blurred margins, irregular shapes, and a slow-increased enhancement. DWI could be used to differentiate a benign soft tissue mass from a malignant mass by the mean ADC value and provide more radiologic-pathologic information for the diagnosis of GCT-ST. Comprehensive imaging of primary GCT-ST could help complete tumor resection, and in turn likely prolong survival after surgery.

Boundary reflection derivation method has been proposed in order to clarify intracellular structure change among the cell wall, membrane, and cytoplasm in the frequency range from 1 MHz to 3 GHz. This method is composed of three steps, which are 1) dielectric properties extraction of dispersed medium $\varepsilon _{\mathrm {dis}}^{\ast }$ and yeast cells $\varepsilon _{\mathrm {cell}}^{\ast }$ ; 2) dielectric properties fitting of cell wall $\varepsilon _{\mathrm {wall}}^{\ast }$ , membrane $\varepsilon _{\mathrm {mem}}^{\ast }$ , cytoplasm $\varepsilon _{\mathrm {cyto}}^{\ast }$ , and intracellular components $\varepsilon _{\mathrm {IC}}^{\ast }$ by a multishelled sphere model; and 3) reflection coefficients calculation at boundaries between cell wall and membrane $\Gamma _{\text {wm}}^{\ast }$ , and between membrane and cytoplasm $\Gamma _{\text {mc}}^{\ast }$ . With this method, $\Gamma _{\text {wm}}^{\ast }$ and $\Gamma _{\text {mc}}^{\ast }$ in living (LC) and dead (DC) yeast cell solutions with various volume concentrations are calculated from experimental impedances. $\Gamma _{\text {wm}}^{\ast \text {DC}}$ shows a difference as compared with $\Gamma _{\text {wm}}^{\ast \text {LC}}$ in GHz range. $\Gamma _{\text {wm}}^{\ast \text {LC}}$ and $\Gamma _{\text {mc}}^{\ast \text {LC}}$ illustrate electromagnetic waves penetrate yeast cell membrane and cytoplasm in GHz range nevertheless they are reflected in MHz range.