Color alteration, hydrogen peroxide diffusion, and cytotoxicity caused by in-office bleaching protocols

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Diffusion of laser polarized gases in MRI

The use of Magnetic Resonance Imaging (MRI) as a diagnostic tool is increasingly employing functional contrast agents to study or contrast entire mechanisms. Contrast agents in MRI can be classified in two categories. One type of contrast agents alters the NMR signal of the protons in its surrounding, e.g. lowers the T1 relaxation time. The other type enhances the Nuclear Magnetic Resonance (NMR) signal of specific nuclei. For hyperpolarized gases the NMR signal is improved up to several orders of magnitude. However, gases have a high diffusivity which strongly influences the NMR signal strength, hence the resolution and appearance of the images. The most interesting question in spatially resolved experiments is of course the achievable resolution and contrast by controlling the diffusivity of the gas. The influence of such diffusive processes scales with the diffusion coefficient, the strength of the magnetic field gradients and the timings used in the experiment. Diffusion may not only limit the MRI resolution, but also distort the line shape of MR images for samples, which contain boundaries or diffusion barriers within the sampled space. In addition, due to the large polarization in gaseous 3He and 129Xe, spin diffusion (different from particle diffusion) could play a role in MRI experiments. It is demonstrated that for low temperatures some corrections to the NMR measured diffusion coefficient have to be done, which depend on quantum exchange effects for indistinguishable particles. Physically, if these effects can not change the spin current, they can do it indirectly by modifying the velocity distribution of the different spin states separately, so that the subsequent collisions between atoms and therefore the diffusion coefficient can eventually be affected. A detailed study of the hyperpolarized gas diffusion coefficient is presented, demonstrating the absence of spin diffusion (different from particle diffusion) influence in MRI at clinical conditions. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. The experimental measured diffusion agrees with theoretical simulations. Therefore, the molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this allows for images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Restricted or severely hindered diffusion of intramyocellular lipids in human skeletal muscle shown by in vivo proton MR spectroscopy

Although magnetic resonance spectroscopy can be used as a unique tool to study molecular diffusion, it is rarely used to measure the diffusion properties of intramyocellular and extramyocellular lipids. Lipids have very low apparent diffusion coefficients (ADCs), which make these measurements difficult and necessitate strong diffusion gradients and long diffusion times. Consequence is that these measurements have inherently low signal-to-noise ratio and are prone to artifacts. The addition of physiological triggering and individual storage and processing of the spectra is seen to be a possible approach to maximize signal intensity and achieve high reproducibility of the experiments. Thus, the optimized measurement protocol was used to investigate the diffusion properties of lipids in human skeletal muscle in vivo. At a diffusion time of about 110 ms, intramyocellular lipids show a significantly lower ADC (2.0 × 10(-6) mm(2)/s, 95% confidence interval 1.10 × 10(-6) to 2.94 × 10(-6) mm(2)/s) than extramyocellular lipids (1.58 × 10(-5) mm(2)/s, 95% confidence interval 1.41 × 10(-5) to 1.75 × 10(-5) mm(2)/s). Because the chemical properties of both lipid pools can be assumed to be similar, the difference can only be attributed to restricted or severely hindered diffusion in the intramyocellular droplets.

Apparent diffusion coefficient in the aging mouse brain: a magnetic resonance imaging study

Novel magnetic resonance imaging sequences have and still continue to play an increasing role in neuroimaging and neuroscience. Among these techniques, diffusion-weighted imaging (DWI) has revolutionized the diagnosis and management of diseases such as stroke, neoplastic disease and inflammation. However, the effects of aging on diffusion are yet to be determined. To establish reference values for future experimental mouse studies we tested the hypothesis that absolute apparent diffusion coefficients (ADC) of the normal brain change with age. A total of 41 healthy mice were examined by T2-weighted imaging and DWI. For each animal ADC frequency histograms (i) of the whole brain were calculated on a voxel-by-voxel basis and region-of-interest (ROI) measurements (ii) performed and related to the animals' age. The mean entire brain ADC of mice <3 months was 0.715(+/-0.016) x 10(-3) mm2/s, no significant difference to mice aged 4 to 5 months (0.736(+/-0.040) x 10(-3) mm2/s) or animals older than 9 months 0.736(+/-0.020) x 10(-3) mm2/s. Mean whole brain ADCs showed a trend towards lower values with aging but both methods (i + ii) did not reveal a significant correlation with age. ROI measurements in predefined areas: 0.723(+/-0.057) x 10(-3) mm2/s in the parietal lobe, 0.659(+/-0.037) x 10(-3) mm2/s in the striatum and 0.679(+/-0.056) x 10(-3) mm2/s in the temporal lobe. With advancing age, we observed minimal diffusion changes in the whole mouse brain as well as in three ROIs by determination of ADCs. According to our data ADCs remain nearly constant during the aging process of the brain with a small but statistically non-significant trend towards a decreased diffusion in older animals.

Origin and evolution of reactive and noble gases dissolved in matrix pore water

Reactive and noble gases dissolved in matrix pore water of low permeable crystalline bedrock were successfully extracted and characterized for the fist time based on drillcore samples from the Olkiluoto investigation site (SW Finland). Interaction between matrix pore water and fracture groundwater occurs predominately by diffusion. Changes in the chemical and isotopic composition of gases dissolved in fracture groundwater are transmitted and preserved in the pore water. Absolute concentrations, their ratios and the stable carbon isotope signature of hydrocarbon gases dissolved in pore water give valuable indications about the evolution of these gases in the nearby-flowing fracture groundwaters. Inert noble gases dissolved in matrix pore water and their isotopes combined with their in-situ production and accumulation rates deliver information about the residence time of pore water.

Matrix pore water in low-permeable crystalline bedrock: An archive for the palaeohydrogeological evolution of the Olkiluoto Investigation Site

Matrix pore water in the connected inter- and intragranular pore space of low-permeable crystalline bedrock interacts with flowing fracture groundwater predominately by diffusion. Based on the slow exchange between the two water reservoirs, matrix pore water acts as an archive of past changes in fracture groundwater compositions and thus of the palaeohydrological history of a site. Matrix pore water of crystalline bedrock from the Olkiluoto investigation site (SW Finland) was characterised using the stable water isotopes (δ18O, δ2H), combined with the concentrations of dissolved chloride and bromide as natural tracers. The comparison of tracer concentrations in pore water and present-day fracture groundwater suggest for the pore water the presence of old, dilute meteoric water components that infiltrated into the fractures during various warm climate stages. These different meteoric components can be discerned based on the diffusion distance between the two reservoirs and be brought into context with the palaeohydrological evolution of the site.

A re-examination of petrogenesis and 40Ar/39Ar systematics in the the Chain of Ponds K-feldspar: "diffusion domain" archetype versus polyphase hygrochronology

K-feldspar (Kfs) from the Chain of Ponds Pluton (CPP) is the archetypal reference material, on which thermochronological modeling of Ar diffusion in discrete “domains” was founded. We re-examine the CPP Kfs using cathodoluminescence and back-scattered electron imaging, transmission electron microscopy, and electron probe microanalysis. 40Ar/39Ar stepwise heating experiments on different sieve fractions, and on handpicked and unpicked aliquots, are compared. Our results reproduce the staircase-shaped age spectrum and the Arrhenius trajectory of the literature sample, confirming that samples collected from the same locality have an identical Ar isotope record. Even the most pristine-looking Kfs from the CPP contains successive generations of secondary, metasomatic/retrograde mineral replacements that post-date magmatic crystallization. These chemically and chronologically distinct phases are responsible for its staircase-shaped age spectra, which are modified by handpicking. While genuine within-grain diffusion gradients are not ruled out by these data, this study demonstrates that the most important control on staircase-shaped age spectra is the simultaneous presence of heterochemical, diachronous post-magmatic mineral growth. At least five distinct mineral species were identified in the Kfs separate, three of which can be traced to external fluids interacting with the CPP in a chemically open system. Sieve fractions have size-shifted Arrhenius trajectories, negating the existence of the smallest “diffusion domains”. Heterochemical phases also play an important role in producing non-linear trajectories. In vacuo degassing rates recovered from Arrhenius plots are neither related to true Fick’s Law diffusion nor to the staircase shape of the age spectra. The CPP Kfs used to define the "diffusion domain" model demonstrates the predominance of metasomatic alteration by hydrothermal fluids and recrystallization in establishing the natural Ar distribution amongst different coexisting phases that gives rise to the staircase-shaped age spectrum. Microbeam imaging of textures is as essential for 40Ar-39Ar hygrochronology as it is for U-Pb geochronology.

Relation between acid back -diffusion and luminal surface hydrophobicity in canine gastric mucosa: Effects of salicylate and prostaglandin

The stomach is thought to be protected from luminal acid by a gastric mucosal barrier that restricts the diffusion of acid into tissue. This study tested the hypothesis that the hydrophobic luminal surface of canine gastric mucosa incubated in Ussing chambers, impedes the back-diffusion of luminal acid into the tissue. Isolated sheets of mucosa were treated with cimetidine to inhibit spontaneous acid secretion, and incubated under conditions that prevented significant secretion of luminal bicarbonate. By measuring acid loss from the luminal compartment using the pH-stat technique, acid back-diffusion was continuously monitored; potential difference (PD) was measured as an index of tissue viability. Tissue luminal surface hydrophobicity was estimated by contact angle analysis at the end of each experiment. Addition of 16,16-dimethyl prostaglandin E$\sb2$ to the nutrient compartment enhanced luminal surface hydrophobicity, but did not reduce acid back-diffusion in tissues that maintained a constant PD. 10 mM salicylate at pH 4.00 in the luminal compartment reduced surface hydrophobicity, but this decrease did not occur if 1 ug/ml prostaglandin was present in the nutrient solution. Despite possessing relatively hydrophilic and relatively hydrophobic surface properties, respectively, acid back-diffusion in the absence of salicylate was not significantly different between these two groups. Neither group maintained a PD after incubation with salicylate. Lastly, radiolabelled salicylate was used to calculate the free (non-salicylate associated) acid loss in tissues incubated with salicylate and/or prostaglandin. No significant correlation was found between free acid back-diffusion and luminal surface hydrophobicity. These data do not support the hypothesis that acid back-diffusion in impeded by the hydrophobic surface presented by isolated canine gastric mucosa. ^

Diffusion Issues of Heat and Light Species in Laser Fusion Devices

There are several heat and mass diffusion problems which affect to the IFC chamber design. New simulation models and experiments are needed to take into account the extreme conditions due to ignition pulses and neutron flux

Role of tumor–host interactions in interstitial diffusion of macromolecules: Cranial vs. subcutaneous tumors

The large size of many novel therapeutics impairs their transport through the tumor extracellular matrix and thus limits their therapeutic effectiveness. We propose that extracellular matrix composition, structure, and distribution determine the transport properties in tumors. Furthermore, because the characteristics of the extracellular matrix largely depend on the tumor–host interactions, we postulate that diffusion of macromolecules will vary with tumor type as well as anatomical location. Diffusion coefficients of macromolecules and liposomes in tumors growing in cranial windows (CWs) and dorsal chambers (DCs) were measured by fluorescence recovery after photobleaching. For the same tumor types, diffusion of large molecules was significantly faster in CW than in DC tumors. The greater diffusional hindrance in DC tumors was correlated with higher levels of collagen type I and its organization into fibrils. For molecules with diameters comparable to the interfibrillar space the diffusion was 5- to 10-fold slower in DC than in CW tumors. The slower diffusion in DC tumors was associated with a higher density of host stromal cells that synthesize and organize collagen type I. Our results point to the necessity of developing site-specific drug carriers to improve the delivery of molecular medicine to solid tumors.

Nucleation of voids in metals during diffusion and creep /

Experimental evidence is presented which proves that voids formed during diffusion in brass are heterogeneously nucleated. The nuclei appear to be oxide particles, probably ZnO. When these are removed by re-melting, voids practically do not form upon subsequent dezincification. Brass which had been freed of void nucleation catalysts exhibited a considerably reduced tendency for grain boundary cracking during creep, and increased stress-rupture life.

Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications

Soft tissue engineering presents significant challenges compared to other tissue engineering disciplines such as bone, cartilage or skin engineering. The very high cell density in most soft tissues, often combined with large implant dimensions, means that the supply of oxygen is a critical factor in the success or failure of a soft tissue scaffold. A model is presented for oxygen diffusion in a 15-60 mm diameter dome-shaped scaffold fed by a blood vessel loop at its base. This model incorporates simple models for vascular growth, cell migration and the effect of cell density on the effective oxygen diffusivity. The model shows that the dynamic, homogeneous cell seeding method often employed in small-scale applications is not applicable in the case of larger scale scaffolds such as these. Instead, we propose the implantation of a small biopsy of tissue close to a blood supply within the scaffold as a technique more likely to be successful. Crown Copyright (c) 2005 Published by Elsevier Ltd. All rights reserved.

Do foreign direct investment (FDI) and trade openness explain the disparity in ICT diffusion between Asia-Pacific and the Islamic Middle Eastern countries?

This study investigates the impact of FDI and trade openness on ICT diffusion in the Asia-Pacific and Middle East regions from 1996-2005. The results indicate that while dissimilarities exist between the economies included in this study in terms of their level of socio-economic and political development, education and the growth of GDP have had a positive impact on ICT diffusion in both regions. However, while FDI has generally had a positive and significant impact on ICT diffusion in Asia-Pacific economies, its impact on Middle Eastern economies has been detrimental. The results of this study also show that trade-openness has had, in general, a positive and significant impact on ICT diffusion. Copyright © 2010, IGI Global.