A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells

Thyroid function in elderly people: The role of subclinical thyroid disorders in cognitive function and mood alterations

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Carotid beta stiffness association with thyroid function

Background: Thyroid hormone modulation of cardiovascular function has been associated with cardiovascular disease. Recent evidence suggests that free thyroxine (FT4) levels are associated with an increase in systemic arterial stiffness, but little is known about the effects of FT4 at the local level of the common carotid artery. β-stiffness index is a local elastic parameter usually determined by carotid ultrasound imaging. Methods: We conducted a cross-sectional analysis in the ProgeNIA cohort, including 4846 subjects across a broad age range. For the purpose of this study, we excluded subjects with increased thyrotropin (TSH) levels and those treated with levothyroxine or thyrostatic. We assessed β stiffness, strain, wall–lumen ratio, carotid cross-sectional area (CSA), and stress and flow in the right common carotid artery. We tested whether FT4, heart rate, and their interactions were associated with carotid parameters. Results: FT4 was positively and independently associated with β stiffness index (β = 0.026, p = 0.041), and had a negative association with strain (β = −0.025, p = 0.009). After adding heart rate and the interaction between FT4 and heart rate to the model, FT4 was still associated with the β stiffness index (β = 0.186, p = 0.06), heart rate was positively associated with the stiffness index (β = 0.389, p < 0.001) as well as their interaction (β = 0.271, p = 0.007). Conclusion: This study suggests that higher FT4 levels increase arterial stiffness at the common carotid level, consistent with a detrimental effect on elastic arteries. The effect of FT4 is likely to be primarily attributable to its effect on heart rate

Spontaneous nocturnal growth hormone secretion in anorexia nervosa

In anorexia nervosa, serum GH levels are increased under basal conditions and respond abnormally to provocative stimuli. We report here, for the first time, an analysis of pulsatile GH secretion in these patients performed by Cluster algorithm. Seven anorectic and six normal weight, healthy women underwent serial blood sampling at 20-min intervals form 2030-0830 h for GH estimation. The total area under the curve (AUC; micrograms per L/min) was elevated 4-fold in anorectic patients compared to controls (4743.0 +/- 1520.09 vs. 1148.6 +/- 519.27; P < 0.01), largely due to an increase in the non-pulsatile fraction (3212.5 +/- 990.45 vs. 378.7 +/- 123.27; P < 0.01). Accordingly, the valley mean value was higher in anorectic than in control subjects (5.9 +/- 2.25 vs. 1.0 +/- 1.30 micrograms/L; P < 0.01). Furthermore, pulsatile AUC was also greater in anorectic patients (1530.4 +/- 654.72 vs. 769.8 +/- 404.02; P < 0.01) due to a significant increase in GH peak frequency (5.0 +/- 0.81 vs. 3.0 +/- 0.89; P < 0.01). No correlations were observed in these patients between body mass index and any of the parameters of spontaneous GH release, whereas a positive correlation was found between insulin-like growth factor I levels and pulsatile AUC (r2 = 0.583; P < 0.05), peak height (r2 = 0.743; P = 0.01), peak increment (r2 = 0.801; P < 0.01), and GH valley mean (r2 = 0.576; P < 0.05). In conclusion, it appears that the enhanced GH secretion in anorexia nervosa is the result of an increased frequency of secretory pulses superimposed on enhanced tonic GH secretion. Although this latter is consistent with a reduction of hypothalamic SRIH tone, the former may be accounted for by an increased number of GHRH discharges. Considering that in normal weight and obese subjects parameters of GH release are negatively correlated with adiposity indexes, the lack of such a negative correlation in our patients suggests that the enhancement of spontaneous GH release in anorectic patients is not merely the consequence of malnutrition-dependent impairment of insulin-like growth factor I production, but reflects a more complex hypothalamic dysregulation of GH release

In vitro human growth hormone increases human chorionic gonadotropin and progesterone secretion by human placenta at term: evidence of a modulatory role by opioids

We examined the in vitro effect of human growth hormone (hGH) on hormone placental production and the modulation by opioids of this function. Small placental fragments from 12 term placentas were incubated at 37 degrees C in a 95% air and 5% CO2 atmosphere for 4 h with various concentrations of hGH (1-1000 ng/ml) or naloxone (3-500 ng/ml). Both hGH and naloxone increased the concentrations of human chorionic gonadotropin (hCG) and progesterone in the media. The effect of the hGH was dose-dependent and statistically significant at 10 ng/ml, while naloxone was able to increase hCG and progesterone production only at the highest doses (250-500 ng/ml). The concomitant treatment with ineffective doses of naloxone and hGH was able to enhance hCG and progesterone secretion reaching levels similar to those obtained with the highest doses of hGH alone. High naloxone concentrations significantly decreased both hCG and progesterone secretion induced by high doses of hGH. This study confirms the relevance of growth hormone in sustaining placental endocrine activities and indicates an effect of opioids in modulating these function

Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects

In this paper we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments

A kinetic equation for economic value estimation with irrationality and herding

A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value problem is proved. Numerical experiments for the Boltzmann equation highlight the importance of the reliability of public information in the formation of bubbles and crashes. The use of Bollinger bands in the simulations shows how herding may lead to strong trends with low volatility of the asset prices, but eventually also to abrupt corrections

Variants of ADRA2A are associated with fasting glucose, blood pressure, body mass index and type 2 diabetes risk: meta-analysis of four prospective studies

AIMS/HYPOTHESIS: We quantified the effect of ADRA2A (encoding α-2 adrenergic receptor) variants on metabolic traits and type 2 diabetes risk, as reported in four studies. METHODS: Genotype data for ADRA2A single nucleotide polymorphisms (SNPs) rs553668 and rs10885122 were analysed in >17,000 individuals (1,307 type 2 diabetes cases) with regard to metabolic traits and type 2 diabetes risk. Two studies (n = 9,437), genotyped using the Human Cardiovascular Disease BeadChip, provided 12 additional ADRA2A SNPs. RESULTS: Rs553668 was associated with per allele effects on fasting glucose (0.03 mmol/l, p = 0.016) and type 2 diabetes risk (OR 1.17, 95% CI 1.04-1.31; p = 0.01). No significant association was observed with rs10885122. Of the 12 SNPs, several showed associations with metabolic traits. Overall, after variable selection, rs553668 was associated with type 2 diabetes risk (OR 1.38, 95% CI 1.09-1.73; p = 0.007). rs553668 (per allele difference 0.036 mmol/l, 95% CI 0.008-0.065) and rs17186196 (per allele difference 0.066 mmol/l, 95% CI 0.017-0.115) were independently associated with fasting glucose, and rs17186196 with fasting insulin and HOMA of insulin resistance (4.3%, 95% CI 0.6-8.1 and 4.9%, 95% CI 1.0-9.0, respectively, per allele). Per-allele effects of rs491589 on systolic and diastolic blood pressure were 1.19 mmHg (95% CI 0.43-1.95) and 0.61 mmHg (95% CI 0.11-1.10), respectively, and those of rs36022820 on BMI 0.58 kg/m(2) (95% CI 0.15-1.02). CONCLUSIONS/INTERPRETATION: Multiple ADRA2A SNPs are associated with metabolic traits, blood pressure and type 2 diabetes risk. The α-2 adrenergic receptor should be revisited as a therapeutic target for reduction of the adverse consequences of metabolic trait disorders and type 2 diabetes

Relationship between low Ankle-Brachial Index and rapid renal function decline in patients with atrial fibrillation: A prospective multicentre cohort study

OBJECTIVE: To investigate the relationship between Ankle-Brachial Index (ABI) and renal function progression in patients with atrial fibrillation (AF). DESIGN: Observational prospective multicentre cohort study. SETTING:Atherothrombosis Center of I Clinica Medica of 'Sapienza' University of Rome; Department of Medical and Surgical Sciences of University Magna Græcia of Catanzaro; Atrial Fibrillation Registry for Ankle-Brachial Index Prevalence Assessment-Collaborative Italian Study. PARTICIPANTS: 897 AF patients on treatment with vitamin K antagonists. MAIN OUTCOME MEASURES: The relationship between basal ABI and renal function progression, assessed by the estimated Glomerular Filtration Rate (eGFR) calculated with the CKD-EPI formula at baseline and after 2 years of follow-up. The rapid decline in eGFR, defined as a decline in eGFR >5 mL/min/1.73 m(2)/year, and incident eGFR<60 mL/min/1.73 m(2) were primary and secondary end points, respectively. RESULTS: Mean age was 71.8±9.0 years and 41.8% were women. Low ABI (ie, ≤0.90) was present in 194 (21.6%) patients. Baseline median eGFR was 72.7 mL/min/1.73 m(2), and 28.7% patients had an eGFR60 mL/min/1.73 m(2), 153 (23.9%) had a reduction of the eGFR <60 mL/min/1.73 m(2). ABI ≤0.90 was also an independent predictor for incident eGFR<60 mL/min/1.73 m(2) (HR 1.851, 95% CI 1.205 to 2.845, p=0.005). CONCLUSIONS: In patients with AF, an ABI ≤0.90 is independently associated with a rapid decline in renal function and incident eGFR<60 mL/min/1.73 m(2). ABI measurement may help identify patients with AF at risk of renal function deterioration