Modified Reaction-diffusion Model Research Articles

Geospatial analysis of contagious infection growth and cross-boundary transmission in non-vaccinated districts of North-East Indian states during the COVID-19 pandemic

During the initial phase of the COVID-19 pandemic, the Government of India implemented a nationwide lockdown, sealing borders across states and districts. The northeastern region of India, surrounded by three international borders and connected to mainland India by a narrow passage, faced particular isolation. This isolation resulted in these states forming a relatively closed population. Consequently, the availability of population-based data from Indian Council of Medical Research, tracked through national identification cards, offered a distinctive opportunity to understand the spread of the virus among non-vaccinated and non-exposed populations. This research leverages this dataset to comprehend the repercussions within isolated populations. The inter-district variability was visualized using geospatial analysis. The patterns do not follow any established grounded theories on disease spread. Out of 7.1 million total data weekly 0.35 million COVID-19-positive northeast data was taken from April 2020 to February 2021 including "date, test result, population density, area, latitude, longitude, district, and state" to identify the spread pattern using a modified reaction-diffusion model (MRD-Model) and Geographic Information System. The analysis of the closed population group revealed an initial uneven yet rapidly expanding geographical spread characterized by a high diffusion rate α approximately 0.4503 and a lower reaction rate β approximately 0.0256, which indicated a slower growth trajectory of case numbers rather than exponential escalation. In the latter stages, COVID-19 incidence reached zero in numerous districts, while in others, the reported cases did not exceed100. The MRD-Model effectively captured the disease transmission dynamics in the abovementioned setting. This enhanced understanding of COVID-19 spread in remote, isolated regions provided by the MRD modelling framework can guide targeted public health strategies for similar isolated areas. This study is Funded by Indian Council of Medical Research (ICMR).

Free energy dissipation enhances spatial accuracy and robustness of self-positioned Turing pattern in small biochemical systems.

Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Turing proposed a general mechanism for pattern formation exemplified by a reaction-diffusion model with two chemical species in a large system. However, in small biological systems such as a cell, the existence of multiple Turing patterns and strong noise can lower the spatial order. Recently, a modified reaction-diffusion model with an additional chemical species is shown to stabilize the Turing pattern. Here, we study non-equilibrium thermodynamics of this three-species reaction-diffusion model to understand the relationship between energy cost and the performance of self-positioning. By using computational and analytical approaches, we show that beyond the onset of pattern formation the positioning error decreases as energy dissipation increases. In a finite system, we find that a specific Turing pattern exists only within a finite range of total molecule number. Energy dissipation broadens this range, which enhances the robustness of Turing pattern against molecule number fluctuations in living cells. The generality of these results is verified in a realistic model of the Muk system underlying DNA segregation in Escherichia coli, and testable predictions are made for the dependence of the accuracy and robustness of the spatial pattern on the ATP/ADP ratio.

A full contraction-reaction-diffusion model for pattern formation in geometrically confined microtissues

The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Mechanical cues, such as the cellular stresses and strains, have been found to dictate the pattern formation in human stem cell differentiation. As a result, the traditional reaction-diffusion models are modified by adding mechanically related terms to consider the role played by the mechanical cues during the very early stage of embryogenesis. However, these models either do not consider the activeness of the cellular tissues or neglect their poroelastic nature that biological tissues are made by both cells and interstitial fluid. Here we propose a modified reaction-diffusion model that couples with the active contraction of cellular tissues. The cellular tissue is modelled as a piece of biphasic poroelastic material, where mechanical forces naturally regulate the transport of chemical cues. Such chemical cues direct cell fate and hence yield certain types of pattern formations observed in previous experiments.

An optimized generic cerebral tumor growth modeling framework by coupling biomechanical and diffusive models with treatment effects

Mathematical modeling of cerebral tumor growth is of great importance in clinics. It can help in understanding the physiology of tumor growth, future prognosis of tumor shape and volume, quantify tumor aggressiveness, and the response to therapy. This can be achieved at macroscopic level using medical imaging techniques (particularly, magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI)) and complex mathematical models which are either diffusive or biomechanical. We propose an optimized generic modeling framework that couples tumor diffusivity and infiltration with the induced mass effect. Tumor cell diffusivity and infiltration are captured using a modified reaction-diffusion model with logistic proliferation term. On the other hand, tumor mass effect is modeled using continuum mechanics formulation. In addition, we consider the treatment effects of both radiotherapy and chemotherapy. The efficacy of chemotherapy is included via an adaptively modified log-kill method to consider tissue heterogeneity while the efficacy of radiotherapy is considered using the linear quadratic model. Moreover, our model efficiently utilizes the diffusion tensor of the diffusion tensor imaging. Furthermore, we optimize the tumor growth parameters to be patient-specific using bio-inspired particle swarm optimization (PSO) algorithm. Our model is tested on an atlas and real MRI scans of 8 low grade gliomas subjects. Experimental results show that our model efficiently incorporates both treatment effects in the growth modelingprocess. In addition, simulated growths of our model have high accuracy in terms of Dice coefficient (average 87.1%) and Jaccard index (77.14%) when compared with the follow up scans (ground truth) and other models as well.

A Coupled Modified Reaction Diffusion and Biomechanical Models for Cerebral Tumor Growth Modeling in Presence of Treatment.

Tumor growth modeling at macroscopic level from multimodal images can help in predicting the future evolution of tumor and the treatment planning. This can be achieved using mathematical models where multi time-point images are available. In this paper, we propose a coupled modified reaction diffusion model that measures tumor invasion and infiltration with biomechanical model to consider tumor mass effect. In addition, our model considers treatment effects from radiotherapy and/or chemotherapy if any. The chemotherapy effect is included via a modified log-kill method to consider tissue heterogeneity while radiotherapy effect is considered using the linear quadratic model. We test the proposed model on both synthetic and 6 real datasets of low grade glioma cases with and without treatments. Experimental results of the proposed model on the clinical magnetic resonance images show that our model can simulate the tumor growth with good accuracy and effectively include the treatment effects.

Quantifying the strength of quorum sensing crosstalk within microbial communities.

In multispecies microbial communities, the exchange of signals such as acyl-homoserine lactones (AHL) enables communication within and between species of Gram-negative bacteria. This process, commonly known as quorum sensing, aids in the regulation of genes crucial for the survival of species within heterogeneous populations of microbes. Although signal exchange was studied extensively in well-mixed environments, less is known about the consequences of crosstalk in spatially distributed mixtures of species. Here, signaling dynamics were measured in a spatially distributed system containing multiple strains utilizing homologous signaling systems. Crosstalk between strains containing the lux, las and rhl AHL-receptor circuits was quantified. In a distributed population of microbes, the impact of community composition on spatio-temporal dynamics was characterized and compared to simulation results using a modified reaction-diffusion model. After introducing a single term to account for crosstalk between each pair of signals, the model was able to reproduce the activation patterns observed in experiments. We quantified the robustness of signal propagation in the presence of interacting signals, finding that signaling dynamics are largely robust to interference. The ability of several wild isolates to participate in AHL-mediated signaling was investigated, revealing distinct signatures of crosstalk for each species. Our results present a route to characterize crosstalk between species and predict systems-level signaling dynamics in multispecies communities.

Spatially explicit control of invasive species using a reaction–diffusion model

Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.

Strain-gradient dependent fatigue behavior of micron-thick copper single crystal foils

The experimental observations on dislocation structures in the micron-thick cantilever beam-type samples of copper single crystals subjected to symmetrically-reversed bending load and the theoretical simulations using the modified reaction–diffusion model were conducted. It was found that strain-gradient introduced by inhomogeneous deformation has a strong influence on dislocation patterning behavior, cyclic deformation response and fatigue life of the micron-thick copper single crystal beams. The simulation results provide a deep insight into the effects of the geometrical scale and the strain gradient on fatigue behaviors in micron-thick metal foils subjected to symmetrically-reversed bending load.

Mathematical modeling of brain glioma growth using modified reaction–diffusion equation on brain MR images

In this paper, a modified reaction–diffusion model is proposed for modeling the diffusion of brain glioma cells. Unlike the other models, a weighted parameter is introduced, which balances the diffusion coefficient of the grey and white matters. Anisotropic characteristics of the model are represented. A local region similarity measure (local Bhattacharyya distance) determines the weighted parameter. Experimental results demonstrate the effectiveness and accuracy of the modified reaction diffusion equation with a weighted parameter for real brain glioma MR images.

Effect of Grain Orientation on NBTI Variation and Recovery in Emerging Metal-Gate Devices

This letter identifies and investigates the effect of grain orientation (GO) on negative-bias temperature instability (NBTI) characteristics of emerging metal-gate devices. A modified reaction-diffusion model is presented for estimating the effect of GO on NBTI. It is shown that neglecting the GO effect leads to substantial underestimation of the impact of the gate-oxide electric field (EOX) on the threshold voltage degradation (ΔVTH). Moreover, GO results in significant fluctuation in EOX and, hence, fluctuation in NBTI for ultrascaled CMOS devices. In addition, in FinFETs, stand-alone GO-induced gate-oxide electric field not only results in ΔVTH fluctuation but also decelerates the recovery process.

Spontaneously periodic wave generation in coupled excitable media

We studied a modified reaction-diffusion model theoretically by coupling two ideal excitable media systems. In the simulated homogeneous system, we observed the propagation of reaction-diffusion wave trains that required no external force after the initial stimulation. We investigated the dependence of the system's oscillation patterns on model parameters, and we discussed the influence of the different dynamic constants of the individual coupled systems on the dynamics of the coupled systems. Some complex two-dimensional patterns generated by our model are shown. We also found similar phenomena in the models for catalytic CO oxidation on Pt(110), and for cardiac tissue.

Mechanogenetic Coupling of Hydra Symmetry Breaking and Driven Turing Instability Model

The freshwater polyp Hydra can regenerate from tissue fragments or random cell aggregates. We show that the axis-defining step (“symmetry breaking”) of regeneration requires mechanical inflation-collapse oscillations of the initial cell ball. We present experimental evidence that axis definition is retarded if these oscillations are slowed down mechanically. When biochemical signaling related to axis formation is perturbed, the oscillation phase is extended and axis formation is retarded as well. We suggest that mechanical oscillations play a triggering role in axis definition. We extend earlier reaction-diffusion models for Hydra regrowth by coupling morphogen transport to mechanical stress caused by the oscillations. The modified reaction-diffusion model reproduces well two important experimental observations: 1), the existence of an optimum size for regeneration, and 2), the dependence of the symmetry breaking time on the properties of the mechanical oscillations.

A unification of interface-state generation and hole-injection for hot-carrier-injection stress in low and high-voltage NMOSFET

To characterize hot-carrier-injection degradation, a typical reaction–diffusion model has been used in low-voltage NMOSFETs with only hot-electron-injection. In this paper, an improved reaction–diffusion model of hole-injection and electron-injection induced interface-state generation, with a lower time exponent, is proposed in high-voltage NMOSFETs. The dynamics of hot-carrier-injection are considered with simulation, experiment and theory. Hole-injection induced by an additional high-electric-field outside the gate is found to be also responsible for degradation mechanism. Based on a better understanding of the mechanism of HV NMOSFETs, the modified reaction–diffusion model for hot-carrier-injection stress involves hole-injection.

Mechanism of Static and Dynamic Bias Temperature Instability in p- and n-MOSFETs

The BTI-induced degradation of device performance has been ascribed to interface trap generation (ΔNit) and oxide charge buildup (ΔNot) at or near the SiO2/Si interface. Moreover, it has been widely recognized that degradation under dynamic BTI stressing may differ from that under static stressing. In this paper, our recent studies on BTI are reviewed. First, a modified direct-current current-voltage (DCIV) method is proposed, which can monitor ΔNit and ΔNot separately, and is independent on the measurement temperature. Second, negative BTI in pMOSFETs with ultrathin plasma-nitrided SiON gate dielectrics is systematically studied, as well as the effect of nitrogen concentration, using the modified DCIV method. Third, dynamic BTI with is studied at various stressing configurations. A transient degradation enhancement is observed upon quick gate voltage reversal from the accumulation bias to the inversion bias. Finally, a modified reaction-diffusion model is proposed to consistently explain the observed static and dynamic BTI behavior.

Photo-induced travelling waves in condensed Langmuirmonolayers

We report the detailed properties of photo-induced travellingwaves in liquid crystalline Langmuir monolayers composed ofazobenzene derivatives. When the monolayer, in which theconstituent rodlike molecules are coherently tilted from thelayer normal, is weakly illuminated to undergo the trans-cisphoto-isomerization, spatio-temporal periodic oscillations ofthe molecular azimuth begin over the entire excited area andpropagate as a two-dimensional orientational wave. The waveformation takes place only when the film is formed at anasymmetric interface with broken up-down symmetry and whenthe chromophores are continuously excited near thelong-wavelength edge of absorption to induce repeatedphoto-isomerizations between the trans and cis forms. Underproper illumination conditions, Langmuir monolayers composed ofa wide variety of azobenzene derivatives have been confirmed toexhibit similar travelling waves with velocity proportional tothe excitation power irrespective of the degree ofamphiphilicity. The dynamics can be qualitatively explained bythe modified reaction-diffusion model proposed by Reigada,Sagués and Mikhailov.