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Register a new userNovel solutions for a model of wound healing angiogenesis
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We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In this work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime: we construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.
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We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p near 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.
We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions between them. Above a critical value of adhesion and for small proliferation large isolated clusters are formed ahead of the front. This is mapped onto the well-known ferromagnetic phase transition in the Ising model. For large adhesion, and larger proliferation the clusters become connected (at some fixed time). For adhesion below the critical value the results are similar to our previous work which neglected adhesion. The results are compared with experiments, and possible directions of future work are proposed.
The purpose of this study is to find ideal forces for reducing cell stress in wound healing process by micro robots. Because of this aim, we made two simulations on COMSOL Multiphysics with micro robot to find correct force. As a result of these simulation, we created force curves to obtain the minimum force and friction force that could lift the cells from the surface will be determined. As the potential of the system for two micro robots that have 2 mm x 0.25 mm x 0.4 mm dimension SU-8 body with 3 NdFeB that have 0.25 thickness and diameter, simulation results at maximum force in the x-axis calculated with 4.640 mN, the distance between the two robots is 150 um.
This paper studies the following system of differential equations modeling tumor angiogenesis in a bounded smooth domain $Omega subset mathbb{R}^N$ ($N=1,2$): $$label{0} left{begin{array}{ll} p_t=Delta p- ablacdotp p(displaystylefrac alpha {1+c} abla c+rho abla w)+lambda p(1-p),,& xin Omega, t>0, c_t=Delta c-c-mu pc,, &xin Omega, t>0, w_t= gamma p(1-w),,& xin Omega, t>0, end{array}right. $$ where $alpha, rho, lambda, mu$ and $gamma$ are positive parameters. For any reasonably regular initial data $(p_0, c_0, w_0)$, we prove the global boundedness ($L^infty$-norm) of $p$ via an iterative method. Furthermore, we investigate the long-time behavior of solutions to the above system under an additional mild condition, and improve previously known results. In particular, in the one-dimensional case, we show that the solution $(p,c,w)$ converges to $(1,0,1)$ with an explicit exponential rate as time tends to infinity.
Next generation wound care technology capable of diagnosing wound parameters, promoting healthy cell growth and reducing pathogenic infections noninvasively will provide patients with an improved standard of care and an accelerated wound repair. Temperature is one of the indicating biomarkers specific to chronic wounds. This work reports a hybrid, multifunctional optical platform: nanodiamond-silk membranes as bioinspired dressings capable of temperature sensing and wound healing. The hybrid was fabricated through electrospinning and formed sub-micron fibrous membranes with high porosity. The silk fibres are capable of compensating for the lack of extracellular matrix at the wound site, supporting the wound healing. The negatively charged nitrogen vacancy (NV-) color centres in nanodiamonds (NDs) exhibit optically detected magnetic resonance (ODMR) properties and act as fluorescent nanoscale thermometers, capable of sensing temperature variations associated to the presence of infection or inflammation in a wound, without physically removing the dressing. Our results show that the presence of NDs in the hybrid ND-silk membranes improve the thermal stability of silk fibres. The NV- color centres in NDs embedded in silk fibres exhibit well-retained fluorescent and ODMR. Using the NV- centres as fluorescent nanoscale thermometers, we achieved temperature sensing at a range of temperatures, including the biologically relevant temperature window, on cell-cultured ND-silk membranes. Enhancement in the temperature sensitivity of the NV- centres was observed for the hybrids. The membranes were further tested in vivo in a murine wound healing model and demonstrated biocompatibility and equivalent wound closure rates as the control wounds. Additionally, the hybrid ND-silk membranes showed selective antifouling and biocidal propensity toward Gram-negative Pseudomonas aeruginosa and Escherichia coli.
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