Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

The role of sweet and savoury taste in food intake and food preferences

Background and aim The sensory attributes of food play a key role in the selection and termination of meals and their rewarding properties. The majority of our foods are either sweet or savoury tasting. In addition, within our food range, savoury-tasting foods contain in general higher levels of protein. The effect of specific taste modalities on human food intake, however, requires further clarification. The primary aim of this thesis was to investigate the role of sweet and savoury taste in food intake and food preferences. The secondary aim was to provide more insight into the processes of explicit and implicit liking and wanting, to be able to identify underlying reward mechanisms involved in food intake behaviour. Methods We conducted series of experiments where healthy young adults participated. We started by investigating the difference between a sweet and savoury taste on satiation, independent of palatability, texture, energy density, and macronutrient composition (n=64). Next, the effect of sweet and savoury taste of a single meal on subsequent satiety and food preferences was investigated (n=61). To further explore the effect of taste in the context of a complete diet on satiety and food preferences, the effect of three 24-h diets that differed only in taste (predominantly sweet tasting, predominantly savoury tasting, or a mixture of sweet and savoury tasting) were compared (n=39). Next, we separated the influence of taste from within-meal protein content on satiety and food preferences, by comparing the effect of sweet and savoury high and low protein single meals (n=60). Finally, the effect of long-term protein status on satiety and food preferences was investigated by comparing the effect of two 14-d diets that differed in protein content (a low protein diet vs. a high protein diet) (n=37). Results Sweet and savoury taste, independent of palatability, texture, energy density, and macronutrient composition, did not differ in their effect on satiation and satiety in terms of subsequent ad libitum intake. Sweet and savoury taste did differ in their effect on subsequent food preferences. In general, after eating a food with a certain taste, appetite for foods with a similar taste was lower than for foods with a dissimilar taste, hence, a clear transfer effect of sensory specific satiety was demonstrated. This transfer effect was not equipotent for sweet and savoury taste; after eating a sweet single meal or sweet 24-h diet, preferences for sweet and savoury foods did not differ. Eating a savoury single meal or savoury 24-h diet, however, led to a clear preference for sweet foods. Neither sweet or savoury tasting single meals nor sweet or savoury 24-h diets shifted food preferences towards high or low protein foods. It was shown that protein content of a meal, independent of taste, did not have an effect on satiety and food preference. We did observe, however, an effect of protein status: after a 14-d low protein diet, there was an increase in ad libitum protein intake, compared to after a 14-d high protein diet, while total energy intake was not different. In addition, food preference for savoury high protein foods was increased. Regarding the different components of food reward it was demonstrated that in all studies both explicit and implicit measures correlated with several aspects of eating. It appeared that in a controlled setting, i.e. in the sensory booths, explicit processes played a stronger determining role in satiation (meal size) than implicit processes. Food choices appeared to be made on a more unconscious level. In a setting where subjects could behave more naturally (i.e. self-selection and serving of foods in a relaxed environment where subjects could sit and eat together), implicit, unconscious processes seemed to explain food intake behaviour more than explicit processes. When subjects experienced protein shortage, after the 14-d low protein diet, it appeared that implicit processes of wanting played a stronger determining role in decisions about what to eat. Conclusion Sweet and savoury taste do not differ in their effect on satiation or satiety in terms of subsequent ad libitum intake. The taste of a meal or diet does have a large effect on subsequent food preferences, thereby showing a clear transfer effect which is not equipotent for sweet and savoury taste. Savoury taste exerts a stronger modulating effect on subsequent food preferences than sweet taste. Sweet and savoury taste of a single meal or 24-h diet do not differ in their effect on food preferences for high or low protein foods. In addition, within-meal protein content seems not to influence satiety or food preferences. A low protein status, however, through selective reduction of dietary protein intake, elicits compensatory changes in food intake and food preferences to restore adequate protein status. It appears that both conscious (explicit) and unconscious (implicit) processes are involved in satiation and food choice. The role implicit motivational processes play in driving food choice is not static, but appears to vary. This is especially the case when homeostasis is challenged (by depleting macronutrient stores), where implicit processes of wanting appear to play a stronger determining role in decisions about what to eat. </p

Assessing the influence of the rhizosphere on soil hydraulic properties using X-ray Computed Tomography and numerical modelling

Understanding the dynamics of water distribution in soil is crucial for enhancing our knowledge of managing soil and water resources. The application of X-ray Computed Tomography (CT) to the plant and soil sciences is now well established. However, few studies have utilised the technique for visualising water in soil pore spaces. Here we utilise this method to visualise the water in soil in situ and in three-dimensions at successive reductive matric potentials in bulk and rhizosphere soil. The measurements are combined with numerical modelling to determine the unsaturated hydraulic conductivity, providing a complete picture of the hydraulic properties of the soil. The technique was performed on soil cores that were sampled adjacent to established roots (rhizosphere soil) and from soil that had not been influenced by roots (bulk soil). A water release curve was obtained for the different soil types using measurements of their pore geometries derived from CT imaging and verified using conventional methods e.g. pressure plates. The water, soil and air phases from the images were segmented and quantified using image analysis. The water release characteristics obtained for the contrasting soils showed clear differences in hydraulic properties between rhizosphere and bulk soil, especially in clay soil. The data suggests that soils influenced by roots (rhizosphere soil) are less porous due to increased aggregation when compared to bulk soil. The information and insights obtained on the hydraulic properties of rhizosphere and bulk soil will enhance our understanding of rhizosphere biophysics and improve current water uptake models

Challenges in imaging and predictive modeling of rhizosphere processes

Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes

A synthesis on the assessment of an alternative disposal strategy to serve sustainability in the Scheldt estuary

The Scheldt estuary is characterised by a valuable multiple-channel system consisting of sandbars in between primary and secondary channels. Within the framework of the Long Term Vision (LTV) for the Scheldt estuary the conservation of this multiple-channel system is defined as the key goal to achieve morphological sustainability.Dredging is one of the human activities having an impact on morphology, hence dredging and disposal should be optimised by minimising the negative impact on morphology. The current disposal strategy for maintenance dredging consists mainly of disposing sediment into the secondary channels. As a consequence of the sustainability goal a maximum dumping capacity is assigned to each secondary channel in order not to exceed the natural bearing capacity of the multiple-channel Scheldt estuary.The assigned yearly disposal capacity for all secondary channels together is sufficient to counter the yearly sediment volume arising from maintenance dredging operations. However, if the total sediment volume that is produced by the deepening of the navigation channel towards Antwerp would be disposed into the secondary channels, the conservation of the multiple-channel system would not be guaranteed. To anticipate on this expectation, shallow water sandbar slopes have been proposed as an alternative disposal location. The use of these alternative disposal locations provides an increase in the estuary’s disposal capacity without increasing the disposal intensity in the secondary channels and is expected to enlarge the area of shallow water habitats, creating opportunities for ecosystem development.The feasibility of this proposal has been investigated by desk studies on historical maps, by field measurements, by physical scale model tests and by numerical simulations and has been confirmed by two in situ experiments. Consequently, the alternative disposal locations will be used during the deepening of the navigation channel towards the port of Antwerp. As a result of the adaptation of the disposal strategy, the conservation of the valuable multiple-channel system in the Scheldt estuary is not endangered by dredging and disposal operations

Major depression with ischemic heart disease: Effects of paroxetine and nortriptyline on long-term heart rate variability measures

Background: Studies have linked depression to sudden death and serious cardiovascular events in patients with preexisting cardiac illness. Recent studies have shown decreased vagal function in cardiac patients with depression and depressed patients without cardiac illness. Methods: We compared 20-hour, sleeping, and awake heart period variability measures using spectral analysis, fractal dimension, and symbolic dynamics in two patient groups with major depression and ischemic heart disease (mean age 59-60 years) before and after 6 weeks of paroxetine or nortriptyline treatment. Results: Spectral measures showed decreases in awake and sleeping total power (TP: 0.0-0.5 Hz), ultra low frequency power (ULF: 0-0.0033 Hz), very low frequency power (VLF: 0.0033-0.04 Hz), and low-frequency power (LF: 0.04-0.15 Hz) for nortriptyline condition and a decrease in high-frequency power (HF: 0.15-0.5 Hz) for the awake condition in patients who received nortriptyline. A measure of nonlinear complexity, WC-100, significantly increased after paroxetine during the awake condition. Conclusions: These findings suggest that nortriptyline has stronger vagolytic effects on cardiac autonomic function compared with paroxetine, which is in agreement with previous clinical and preclinical reports. Paroxetine may have some cardio-protective effects, especially in cardiac patients

STIM1, PKC-δ and RasGRP set a threshold for proapoptotic Erk signaling during B cell development.

Clonal deletion of autoreactive B cells is crucial for the prevention of autoimmunity, but the signaling mechanisms that regulate this checkpoint remain undefined. Here we characterize a previously unrecognized Ca(2+)-driven pathway for activation of the kinase Erk, which was proapoptotic and biochemically distinct from Erk activation induced by diacylglycerol (DAG). This pathway required protein kinase C-δ (PKC-δ) and the guanine nucleotide-exchange factor RasGRP and depended on the concentration of the Ca(2+) sensor STIM1, which controls the magnitude of Ca(2+) entry. Developmental regulation of these proteins was associated with selective activation of the pathway in B cells prone to negative selection. This checkpoint was impaired in PKC-δ-deficient mice, which developed B cell autoimmunity. Conversely, overexpression of STIM1 conferred a competitive disadvantage to developing B cells. Our findings establish Ca(2+)-dependent Erk signaling as a critical proapoptotic pathway that mediates the negative selection of B cells

Major depression with ischemic heart disease: Effects of paroxetine and nortriptyline on measures of nonlinearity and chaos of heart rate

Depression is associated with increased cardiovascular mortality in patients with preexisting cardiac illness. A decrease in cardiac vagal function as suggested by a decrease in heart rate variability (HRV) or heart period variability has been linked to sudden death in patients with cardiac disease as well as in normal controls. Recent studies have shown decreased vagal function in cardiac patients with depression as well as in depressed patients without cardiac illness. In this study, we compared 20 h awake and sleep heart period nonlinear measures using quantification of nonlinearity and chaos in two groups of patients with major depression and ischemic heart disease (mean age 59-60 years) before and after 6 weeks of treatment with paroxetine or nortriptyline. Patients received paroxetine, 20-30 mg/day or nortriptyline targeted to 190-570 nmol/l for 6 weeks. For HRV analysis, 24 patients were included in the paroxetine treatment study and 20 patients in the nortriptyline study who had at least 20,000 s of awake data. The ages of these groups were 60.4 +/- 10.5 years for paroxetine and 60.8 +/- 13.4 years for nortriptyline. There was a significant decrease in the largest Lyapunov exponent (LLE) after treatment with nortriptyline but not paroxetine. There were also significant decreases in nonlinearity scores on S-netPR and S-netGS after nortriptyline, which may be due to a decrease in cardiac vagal modulation of HRV. S-netGS and awake LLE were the most significant variables that contributed to the discrimination of postparoxetine and postnortriptyline groups even with the inclusion of time and frequency domain measures. These findings suggest that nortriptyline decreases the measures of chaos probably through its stronger vagolytic effects on cardiac autonomic function compared with paroxetine, which is in agreement with previous clinical and preclinical reports. Nortriptyline was also associated with a significant decrease in nonlinearity scores, which may be due to anticholinergic and/or sympatholytic effects. As depression is associated with a strong risk factor for cardiovascular mortality, one should be careful about using any drug that adversely affects cardiac vagal function. Copyright (C) 2002 S. Karger AG, Basel

Stable isotope paleoecology (d¹³C and d¹⁸O) of early Eocene <i>Zeauvigerina aegyptiaca</i> from the North Atlantic (DSDP Site 401)

Within the expanded and clay-enriched interval following the Paleocene-Eocene Thermal Maximum (PETM; ~55.8 Ma) at Deep Sea Drilling Project (DSDP) Site 401 (eastern North Atlantic), high abundances of well-preserved biserial planktic foraminifera such as Zeauvigerina aegyptiaca and Chiloguembelina spp. occur. The paleoecological preferences of these taxa are only poorly constrained, largely because existing records are patchy in time and space. The thin-walled Z. aegyptiaca is usually rather small (13C and d18O) study of well-preserved specimens of Z. aegyptiaca and several planktic foraminiferal species (Morozovella subbotinae, Subbotina patagonica, Chiloguembelina wilcoxensis) enabled us to determine the preferred depth habitat and mode of life for Z. aegyptiaca. Oxygen isotope values of Z. aegyptiaca range from -1.57‰ to -2.07‰ and overlap with those of M. subbotinae indicating that their habitat is (1) definitely planktic, which has been questioned by some earlier isotopic studies, and (2) probably within the lower surface mixed layer. Carbon isotope ratios range from 0.99‰ to 1.34‰ and are distinctly lower than values for non-biserial planktic species. This may indicate isotopic disequilibrium between ambient seawater and the calcareous tests of Z. aegyptiaca, which we relate to vital effects and to its opportunistic behavior. The observed isotopic signal of Z. aegyptiaca relative to the other planktic foraminiferal species is highly similar to many other microperforate bi- and triserial planktic genera that have appeared through geological time such as Heterohelix, Guembelitria, Chiloguembelina, Streptochilus and Gallitellia and we suggest that Z. aegyptiaca shares a similar ecology and habitat. Thus, in order for the opportunistic Z. aegyptiaca to bloom during the aftermath of the PETM, we assume that at that time, the surface waters at Site 401 were influenced by increased terrestrial run-off and nutrient availability