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The bending strength of silicon nitride (Si3N4) plays a vital role in its application and is influenced by various process factors. Current experimental methods for investigating Si3N4 ceramics exhibiting low efficiency and high cost are incapable of systematically analysing the effect of process factors on the bending strength of Si3N4 ceramics and quantitatively predicting the optimum process parameters. In this study, machine learning (ML) approaches based on extreme gradient boosting (XGBoost) were applied to predict and analyse the bending strength of Si3N4 ceramics. Because the classification model of XGBoost is easily interpretable, the factors affecting the bending strength could be quantitatively evaluated. The current model can provide a suitable order of adding sintering additives to obtain excellent bending strength in Si3N4 ceramics. Although this study focuses on the bending strength of Si3N4 ceramics, the new approach reported herein is applicable for the in silico design and analysis of other ceramic materials.

Wampee fruit is a popular fruit cultivar in South‐East Asia due to its high levels of nutrients and antioxidants; however, pericarp browning leads to a short storage life with great economic loss during years. The purpose of this work was to determine whether postharvest ethanol fumigation affected pericarp browning development of wampee fruit during 12 days of storage at 8 ± 0.5°C, and if so, how it is related to phenol metabolism and how it affects quality attributes and antioxidant systems during storage. After fruits were fumigated with 100, 300, 500, and 800 μl/L for 5 hr at 22 ± 0.5°C, ethanol significantly reduced the development of pericarp browning by increasing total phenolics (TP) content and decreasing the activity of polyphenol oxidase (PPO), especially in 500 μl/L ethanol treatment. Additionally, ethanol delayed the losses in fruit firmness (FF), soluble solid content (SSC), and titratable acidity (TA), retarded weight loss and accumulation of malondialdehyde (MDA) content and maintained relatively high contents of ascorbic acid (AsA), total flavonoids (TF), and total antioxidant capacity (TAC) and activities of superoxide dismutase (SOD), catalase (CAT), and peroxidase (POD). In conclusion, results demonstrated that postharvest ethanol fumigation in wampee fruit has ability to reduce pericarp browning development by regulating phenol metabolism and enhancing antioxidant systems., Ethanol fumigation reduced the development of pericarp browning; ethanol fumigation delayed the losses in firmness, the degradation of TSS, TA, and VC of wampee fruit. Ethanol fumigation maintained high contents of AsA, TF, and TAC and activities of SOD, CAT, POD in wampee fruit.

Objectives The purpose of this study was to evaluate the effect of combined postharvest use of Bacillus siamensis strain and chlorogenic acid on quality maintenance and disease control in wax apple fruit. Materials and Methods Wax apple fruit were treated with Bacillus siamensis strain (N1), chlorogenic acid (CHA) and N1+CHA and preserved at 25 °C for 12 d. The appearance and quality parameters were evaluated, along with the disease index, content of total soluble solids (TSS), total acid (TA), vitamin C (Vc), total phenolic, and flavonoids during cold storage. Meanwhile, the activities of β-1,3-glucanase (GLU), phenylalanine ammonialyase (PAL), polyphenol oxidase (PPO), and peroxidase (POD) were determined. Furthermore, the transcriptome and the expression level of key defense enzyme genes were analyzed by RNA-seq and real-time quantitative reverse transcription polymerase chain reaction. Results N1+CHA treatment significantly lowered DI and delayed fruit quality deterioration by slowing TSS and TA loss and enhancing antioxidant capacity, including Vc, total phenolic, and flavonoids content. Meanwhile, the activities of GLU, PAL, PPO, and POD were dramatically increased by N1+CHA treatment. Additionally, N1+CHA treatment modulated several metabolic pathways, including those involved in plant–hormone signal transduction and plant–pathogen interaction. The expression levels of key defense enzyme genes were significantly upregulated in stored wax apple fruit by the N1+CHA treatment, which were well coincided with the transcriptome data. Conclusions The combined use of N1+CHA significantly prevents disease and maintains fruit quality of wax apple during storage. These findings indicate that it could serve as a promising biological technique for preserving wax apple fruit.

This study develops a multifunctional molecular optical nanoprobe (SiO2@Gd2O3: Yb3+/Er3+/Li+@Ce6/MC540) with a unique core-satellite form. The rare-earth doped nanodots with good crystallinity are uniformly embedded on the surface of a hydrophilic silica core, and the nanoprobe can emit near-infrared-IIb (NIR-IIb) luminescence for imaging as well as visible light that perfectly matches the absorption bands of two included photosensitizers under 980 nm irradiation. The optimal NIR-IIb emission and upconversion efficiency are attainable via regulating the doping ratios of Yb3+, Er3+ and Li+ ions. The relevant energy transfer mechanism was addressed theoretically that underpins rare-earth photoluminescence where energy back-transfer and cross relaxation processes play pivotal roles. The nanoprobe can achieve an excellent dual-drive photodynamic treatment performance, verified by singlet oxygen detections and live-dead cells imaging assays, with a synergistic effect. And a brightest NIR-IIb imaging was attained in tumoral site of mouse. The nanoprobe has a high potential to serve as a new type of optical theranostic agent for tumor.

Lanthanide fluorescence nanoprobe is versatile in multicolor cell imaging, although it still faces a great challenge in improving its luminescent efficiency. Herein, we validated the feasibility of lanthanide ions co-doped gadolinium phosphate nanocrystals serving as a safe, effective and color-tunable fluorescence probe for live cell imaging. Well-crystallized hexagonal phase GdPO4 nanoparticles with multi-morphologies such as nanowires, nanorods, tetragonal nanocubes and hexagonal nanoprisms were synthesized via a typical hydrothermal method. We have systematically investigated the synthesis of different morphologies of GdPO4 nanoparticles through adjusting their processing parameters. The nanoparticles can gain a bright color-tunable photoluminescence from red, orange, yellow to green region when the GdPO4 nanoparticles are co-doped with Eu3+ and Tb3+ ions. The Tb3+ doping significantly enhances the characteristic 4f → 4f transitions of Eu3+ owing to a specific cross-relaxation process from Tb3+ to Eu3+ ions; the mechanism underlying the cross relaxation was exposited in detail. Further biological experiments in vitro proved that the prepared nanoprisms could exhibit a favourable biocompatibility with negligible toxicity. The current investigation manifests a high potential of the nanoparticles applicable to fluorescence imaging probe for live cells.

The development of upconversion nanoparticles (UCNs) for theranostics application is a new strategy toward the accurate diagnosis and efficient treatment of cancer. Here, magnetic and fluorescent lanthanide-doped gadolinium oxide (Gd2O3) UCNs with bright upconversion luminescence (UCL) and high longitudinal relaxivity (r1) are used for simultaneous magnetic resonance imaging (MRI)/UCL dual-modal imaging and photodynamic therapy (PDT). In vitro and in vivo MRI studies show that these products can serve as good MRI contrast agents. The bright upconversion luminescence of the products allows their use as fluorescence nanoprobes for live cells imaging. We also utilized the luminescence-emission capability of the UCNs for the activation of a photosensitizer to achieve significant PDT results. To the best of our knowledge, this study is the first use of lanthanide-doped Gd2O3 UCNs in a theranostics application. This investigation provides a useful platform for the development of Gd2O3-based UCNs for clinical diagnosis, treatment, and imaging-guided therapy of cancer.

Uniform and well-crystallized NaGd(MoO4)2: Yb3+/Er3+ microcrystals with tetragonal plate morphology were synthesized by a facile hydrothermal method. The structure and phase purity of the samples were identified by powder XRD analysis. The steady-state and transient luminescence spectra were measured and analyzed. Under 980 nm excitation, intense green luminescence at 531 and 553 nm, and red luminescence at 657 and 670 nm were observed. The optimum doping concentrations for Yb3+ and Er3+ are determined to be 20% and 1% in NaGd(MoO4)2 tetragonal plate microcrystals. With increasing Yb3+ doping concentrations, the total integral emission intensities increase first and then decrease. The red/green intensity ratio of NaGd(MoO4)2: Yb3+/Er3+ microcrystals increases from 0.4 to 1.0 with the increase in Yb3+ concentrations. Based on the energy level diagram, the energy-transfer mechanisms are investigated in detail according to the double logarithmic plot of upconversion intensities versus pump powers. The energy-transfer mechanisms for green and red upconversion luminescence are ascribed to two-photon processes at lower Yb3+ concentrations, and involve high-Yb3+-induced one-photon processes at higher Yb3+ concentrations. For the red upconversion luminescence, energy back-transfer process, that is, 4S3/2 (Er3+) + 2F7/2 (Yb3+) → 4I13/2 (Er3+) + 2F5/2 (Yb3+), is dominant at higher Yb3+ concentrations. Theoretical model of the energy-transfer mechanisms based on rate equations is established, which agrees well with the experimental results.

Herein, hollow-structured Gd2O3:RE3+/Yb3+ (RE = Er, Ho, Tm) nanoparticles (NPs) were prepared via a urea-based chemical coprecipitation method followed by subsequent calcination and etching. Under 980 nm near-infrared (NIR) irradiation, upconversion (UC) emission gains the highest intensity of red, green and blue peaks for Gd2O3:Er3+/Yb3+, Gd2O3:Ho3+/Yb3+ and Gd2O3:Tm3+/Yb3+ NPs respectively. The corresponding fluorescence in-cell images exhibit bright visible light. The continuous color-tunable UC emission of each spectrum was investigated by increasing the concentration of the sensitizer Yb3+ ions from 0 to 20 mol% with the most intense red, green and blue emission achieved. The structure, morphology, components and magnetic property of Gd2O3:Ho3+/Yb3+ NPs were investigated intensively. The results show that the NPs possess a distinctly hollow structure and uniform spherical shape, and are well-crystallized and highly monodispersed with a mean diameter of 118 nm. Due to the designed hollow structure which is of benefit to water contact of a large number of Gd3+ on the surface, the measured T1 relaxivity of the NPs is nearly 5 times larger than the relaxivity of the commercial gadolinium diethylenetriaminepentaacetate (Gd-DTPA). The relaxation enhancement in the hollow-structured Gd2O3:RE3+/Yb3+ (RE = Er, Ho, Tm) NPs is addressed in the framework of Solomon–Bloembergen–Morgan theory. The biocompatibility studies in 293 and HeLa cells indicate that the hollow NPs have no observable cytotoxicity at a concentration up to 200 μg ml−1. All these results demonstrate that the hollow-structured nanocomposite has the potential to be developed into a safe and highly efficient magnetic resonance and fluorescence nanoprobe for in-cell molecular imaging of cancer.

This study aimed to determine the effects of Metschnikowia pulcherrima yeast on storage quality of 'Tainong' mango, and elucidate it's possible anti-disease mechanism. The results showed that M. pulcherrima could inhibit the changes in peel colour, fruit firmness, the contents of total soluble solids, total acid and vitamin C, and maintain the storage quality of mango fruits. An investigation of the mechanism showed that M. pulcherrima competed not only for the primary carbon source, but also for living space with Colletotrichum gloeosporioides. In addition, M. pulcherrima promoted the activities of defence-related enzymes, including s-1,3-glucanase(GLU) and chitinase (CHT), and secreted a small amount of antimicrobial substances composed of volatile and nonvolatile anti-fungal compounds. The results strongly demonstrated that antagonistic yeast M. pulcherrima could be applied as a biocontrol agent for deducing the spoilage and decay of mango fruit.

Well-crystallized and uniform NaGd(MoO4)2 microcrystals with morphologies of bipyramids, truncated bipyramids, quasi-cubes and tetragonal plates were selectively synthesized via a facile hydrothermal method without any additives under mild conditions. The effects of Na2MoO4/Gd(NO3)3 molar ratios and pH values of precursor solutions on the phase and morphology of the as-synthesized microcrystals were systematically investigated. The molar ratios and pH values played key roles in the selective synthesis of pure phase NaGd(MoO4)2 microcrystals with regular morphology. With increasing Na2MoO4/Gd(NO3)3 molar ratios in the appropriate pH range, the morphology of the products changed from bipyramids, truncated bipyramids, quasi-cubes to tetragonal plates, namely, the morphological truncation degree increased gradually. NaGd(MoO4)2 tetragonal microplates could be synthesized at the molar ratio of 9 : 1. A possible morphological formation mechanism of NaGd(MoO4)2 tetragonal microplates was proposed, i.e. nucleation-Ostwald ripening growth process. Color tunable photoluminescence properties of NaGd(MoO4)2:Eu3+,Tb3+ microcrystals were studied in detail. Among the different morphologies of NaGd(MoO4)2:5% Eu3+ microcrystals, tetragonal microplates had a broadened, red-shifted and enhanced charge transfer band in the excitation spectrum. What's more, the full-width at half-maximum for the charge transfer band of the tetragonal plates was highest (58 nm), which favored efficient excitation and absorption in the ultraviolet region. The introduction of a small amount of Tb3+ into NaGd(MoO4)2 microplates doped with Eu3+ would enhance the 5D0 → 7FJ transition of Eu3+ at 616 nm due to the energy transfer process of cross-relaxation from Tb3+ to Eu3+. Multicolor tunable luminescence from deep red, red, orange, yellow to green under 291 nm ultraviolet excitation and from red, reddish orange to pink under 380 nm near-ultraviolet excitation could be obtained in NaGd(MoO4)2 tetragonal microplates by simply adjusting the doping concentrations of Eu3+ and Tb3+, suggesting NaGd(MoO4)2:Eu3+,Tb3+ microcrystals might have practical application in optoelectronic devices, such as light emitting diodes and color display systems. This facile morphology-controlled hydrothermal synthesis strategy was simple, low-cost and environment-friendly, and might be extended to other inorganic materials.

Yingying Shen,1,2,* Yuanzhi Shao,3,* Haoqiang He,1 Yunpu Tan,4 Xiumei Tian,2 Fukang Xie,2 Li Li11Imaging Diagnostic and Interventional Center, Sun Yat-sen University Cancer Center, Guangzhou, Guangdong, China; 2Department of Histology and Embryology, Zhongshan School of Medicine, Sun Yat-sen University, Guangzhou, Guangdong, China; 3Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou, Guangdong, China; 4Department of Gastrointestinal Surgery, Sun Yat-sen University, Guangzhou, Guangdong, China *These authors contributed equally to this workAbstract: We investigated the tracking potential of a magnetic resonance imaging (MRI) probe made of gadolinium-doped mesoporous silica MCM-41 (Gd2O3@MCM-41) nanoparticles for transplanted bone mesenchymal stem cells (MSCs) and neural stem cells (NSCs) in vivo. The nanoparticles, synthesized using a one-step synthetic method, possess hexagonal mesoporous structures with appropriate assembly of nanoscale Gd2O3 clusters. They show little cytotoxicity against proliferation and have a lower effect on the inherent differentiation potential of these labeled stem cells. The tracking of labeled NSCs in murine brains was dynamically determined with a clinical 3T MRI system for at least 14 days. The migration of labeled NSCs identified by MRI corresponded to the results of immunofluorescence imaging. Our study confirms that Gd2O3@MCM-41 particles can serve as an ideal vector for long-term MRI tracking of MSCs and NSCs in vivo.Keywords: nanoparticles, gadolinium, magnetic resonance imaging, stem cells

Introduction . Rambutan (Nephelium lappaceum L.) is a kind of tropical fruit with high commercial value in international trade. However, harvested rambutan fruits suffer from a short shelf life and show rapid postharvest deterioration problems due to spintern browning and flesh decay. Materials and methods . Rambutan fruit (cv. ‘Baoyan 5’) were harvested in 2009 and 2010. Changes in some chemical components and the physiology of fruits were investigated at different storage temperatures (25 °C and 10 °C) and with different packing materials (regular low-density polyethylene and anti-moisture polyethylene bags). Results and discussion . Changes in the development of the browning index, and contents of total soluble solids, titratable acidity and vitamin C greatly decreased during low temperature storage (10 °C); moreover, low temperature storage (10 °C) could maintain a significantly higher level of superoxide dismutase activity and lower values of malondialdehyde and cell membrane permeability. The effects of packing material were different according to the different storage temperatures. At 10 °C, the beneficial effects of anti-moisture polyethylene bags on fruit quality and physiology were observed. However, at 25 °C, fruit packed with regular low-density polyethylene proved to be of better quality than those packed with anti-moisture polyethylene bags. Conclusion . The overall results suggest that packing with anti-moisture polyethylene bags and storage at 10 °C were the most suitable conditions to maintain quality and to extend the storage life of rambutan fruit.

Nanoprobes for combined optical and magnetic resonance imaging have tremendous potential in early cancer diagnosis. Gold nanoparticles (AuNPs) co-doped with Gd2O3 mesoporous silica nanocomposite (Au/Gd@MCM-41) can produce pronounced contrast enhancement for T1 weighted image in magnetic resonance imaging (MRI). Here, we show the remarkably high sensitivity of Au/Gd@MCM-41 to the human poorly differentiated nasopharyngeal carcinoma (NPC) cell line (CNE-2) using fluorescence lifetime imaging (FLIM). The upconversion luminescences from CNE-2 and the normal nasopharyngeal (NP) cells (NP69) after uptake of Au/Gd@MCM-41 show the characteristic of two-photon-induced-radiative recombination of the AuNPs. The presence of the Gd3+ ion induces a much shorter luminescence lifetime in CNE-2 cells. The interaction between AuNPs and Gd3+ ion clearly enhances the optical sensitivity of Au/Gd@MCM-41 to CNE-2. Furthermore, the difference in the autofluorescence between CNE-2 and NP69 cells can be efficiently demonstrated by the emission lifetimes of Au/Gd@MCM-41 through the Forster energy transfers from the endogenous fluorophores to AuNPs. The results suggest that Au/Gd@MCM-41 may impart high optical resolution for the FLIM imaging that differentiates normal and high-grade precancers.

We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.

Pure tetragonal phase, uniform and well-crystallized sodium gadolinium molybdate (NaGd(MoO4)2) nanocrystals with diverse morphologies, e.g. nanocylinders, nanocubes and square nanoplates have been selectively synthesized via oleic acid-mediated hydrothermal method. The phase, structure, morphology and composition of the as-synthesized products are studied. Contents of both sodium molybdate and oleic acid of the precursor solutions are found to affect the morphologies of the products significantly and oleic acid plays a key role in the morphology-controlled synthesis of NaGd(MoO4)2 nanocrystals with diverse morphologies. Growth mechanism of NaGd(MoO4)2 nanocrystals is proposed based on time-dependent morphology evolution and X-ray diffraction analysis. Morphology-dependent down-shifting photoluminescence properties of NaGd(MoO4)2: Eu3+ nanocrystals and upconversion photoluminescence properties of NaGd(MoO4)2: Yb3+/Er3+ and Yb3+/Tm3+ nanoplates are investigated in detail. Charge transfer band in the down-shifting excitation spectra shows a slight blue-shift and the luminescence intensities and lifetimes of Eu3+ are decreased gradually with the morphology of the nanocrystals varying from nanocubes to thin square nanoplates. Upconversion energy transfer mechanisms of NaGd(MoO4)2: Yb3+/Er3+, Yb3+/Tm3+ nanoplates are proposed based on the energy level scheme and power dependence of upconversion emissions. Thermometric properties of NaGd(MoO4)2: Yb3+/Er3+ nanoplates are investigated and the maximum sensitivity is determined to be 0.01333 K−1 at 285 K.

This study established a fully automated computer-aided diagnosis (CAD) system for the classification of malignant and benign masses via breast magnetic resonance imaging (BMRI). A breast segmentation method consisting of a preprocessing step to identify the air-breast interfacing boundary and curve fitting for chest wall line (CWL) segmentation was included in the proposed CAD system. The Chan-Vese (CV) model level set (LS) segmentation method was adopted to segment breast mass and demonstrated sufficiently good segmentation performance. The support vector machine (SVM) classifier with ReliefF feature selection was used to merge the extracted morphological and texture features into a classification score. The accuracy, sensitivity, and specificity measurements for the leave-half-case-out resampling method were 92.3%, 98.2%, and 76.2%, respectively. For the leave-one-case-out resampling method, the measurements were 90.0%, 98.7%, and 73.8%, respectively.

We report the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subject to the joint application of a deterministic external field and the stochastic mutually correlated noises simultaneously. A time-dependent Ginzburg-Landau stochastic differential equation, including an oscillating modulation and the correlated multiplicative and additive white noises, was addressed and the numerical solution to the relevant Fokker-Planck equation was presented on the basis of an average-period approach of driven field. The correlated white noises and the deterministic modulation induce a kind of dynamic symmetry-breaking order, analogous to the stochastic resonance in trend, in the kinetic ISS, and the reentrant transition has been observed between the dynamic disorder and order phases when the intensities of multiplicative and additive noises were changing. The dependencies of a dynamic order parameterQ upon the intensities of additive noiseA and multiplicative noiseM, the correlation λ between two noises, and the amplitude of applied external fieldh were investigated quantitatively and visualized vividly. Here a brief discussion is given to outline the underlying mechanism of the NDPT in a kinetic ISS driven by an external force and correlated noises.

The feasibility of the gadolinium-doped mesoporous silica nanocomposite Gd2O3@MCM-41 as a safe, effective MRI nanoprobe has been validated in the current investigation systematically from atomistic and molecular modeling to its synthesis and characterization on in vivo MR imaging and biocompatibility. The first-principles calculation indicates that it is nearly impossible for toxic Gd ions to dissociate freely from silica. The biocompatibility studies confirm that the nanocomposite is lack of any potential toxicity; the biodistribution studies reveal a greater accumulation of the nanocomposite in liver, spleen, lung and tumor than in kidney, heart and brain; the excretion studies show that the nanocomposite can be cleared nearly 50% via the hepatobiliary transport mechanism after 1.5 months of injection. A larger water proton relaxivity r1 and a better T1-weighted phantom MR imaging capability were detected in the nanocomposite than in the commercially available gadolinium diethylenetriaminepentaacetate. The results demonstrate that the nanocomposite is superior to the commercial counterpart in terms of contrast enhancement with a satisfactory biocompatibility, and it has a high potential to be developed into a safe and effective targeted probe for in vivo molecular imaging of cancer.

On the basis of two universal power-law scaling laws, i.e. the scaling dynamic hysteresis in physics and the allometric scaling metabolism in biosystem, we studied the dynamic response and the evolution of an immunosurveillant anti-tumor system subjected to a periodic external intervention, which is equivalent to the scheme of a radiotherapy or chemotherapy, within the framework of the growth dynamics of tumor. Under the modulation of either an abrupt or a gradual change external intervention, the population density of tumors exhibits a dynamic hysteresis to the intervention. The area of dynamic hysteresis loop characterizes a sort of dissipative-therapeutic relationship of the dynamic responding of treated tumors with the dose consumption of accumulated external intervention per cycle of therapy. Scaling the area of dynamic hysteresis loops against the intensity of an external intervention, we deduced a characteristic quantity which was defined as the theoretical therapeutic effectiveness of treated tumor and related with the destructive metabolism of tumor under treatment. The calculated dose-effectiveness profiles, namely the dose cumulant per cycle of intervention versus the therapeutic effectiveness, could be well scaled into a universal quadratic formula regardless of either an abrupt or a gradual change intervention involved. We present a new concept, i.e., the therapy-effect matrix and the dose cumulant matrix, to expound the new finding observed in the growth and regression dynamics of a modulated anti-tumor system.

Pure multiplicative noise-induced stochastic resonance, which appears in an anti-tumor system modulated by a seasonal external field, is studied by using theoretical analyses of the generalized potential and numerical simulations. For optimally selected values of the multiplicative noise intensity stochastic resonance is observed, which is manifested by the quasisymmetry of two potential minima. Theoretical results and numerical simulations are in good quantitative agreement.

Multiplicative noise is found to divide the growth law of tumors into two parts in a logistic model, which is driven by additive and multiplicative noises simultaneously. The Fokker-Planck equation was also derived to explain the fact that the influence of the intensity of multiplicative noise on the growth of tumor cells has a stochastic resonance-like characteristic. An appropriate intensity of multiplicative noise is benefit to the growth of the tumor cells. The correlation between two sorts of noises weakens the stochastic resonance-like characteristic. Homologous noises promote the growth of the tumor cells., Comment: 8 pages, 3 figures

We simulated the invasion of a proliferating, diffusing tumor within different surrounding tissue conditions using a hybrid mathematical model. The in silico invasion of a tumor was addressed systematically for the first time within the framework of a generalized diffusion theory. Our results reveal that a tumor not only migrates using typical Fickian diffusion, but also migrates more generally using subdiffusion, superdiffusion, and even ballistic diffusion, with increasing mobility of the tumor cell when haptotaxis and chemotaxis toward the host tissue surrounding the proliferative tumor are involved. Five functional terms were included in the hybrid model and their effects on a tumor's invasion were investigated quantitatively: haptotaxis toward the extracellular matrix tissue that is degraded by matrix metalloproteinases; chemotaxis toward nutrients; cell-cell adhesion; the proliferation of the tumor; and the immune response toward the tumor. Haptotaxis and chemotaxis, which are initiated by extracellular matrix and nutrient supply (i.e., glucose) respectively, as well as cell-cell adhesions all drastically affect a tumor's diffusion mode when a tumor invades its surrounding host tissue and proliferates. We verified the in silico invasive behavior of a tumor by analyzing experimental data gathered from the in vitro culturing of different tumor cells and clinical imaging observations that used the same approach as was used to process the simulation data. The different migration modes of a tumor suggested by the simulations generally conform to the results observed in cell cultures and in clinical imaging. Our study not only discloses some migration modes of a tumor that proliferates and invades under different host tissues conditions, but also provides a heuristic method to characterize the invasion of a tumor in clinical medical imaging analysis.