Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations

Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.

Nonlinear stability and numerical simulations for a reaction–diffusion system modelling Allee effect on predators

A reaction–diffusion system governing the prey–predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

Dynamic diabetes solutions: physiologic insulin resensitization

Diabetes is a disease currently affecting over 30 million Americans and is a leading cause of amputation, blindness, and chronic kidney disease. Treatment of diabetes with medications and lifestyle modifications alone have not eliminated these complications, because in part they lack the ability to restore the periodic cycles and rest periods of insulin that exist in healthy physiology. Insulin is excreted in a cyclical and oscillatory pattern by the pancreas, that is critical to maintain adequate insulin sensitivity at the insulin receptor level. Administration of exogenous insulin bio identically matching this physiologic profile is more effective at controlling blood glucose level and reducing complications of diabetes than standard drug therapy and lifestyle modifications alone. This matching of physiological insulin helps reduce inflammatory cascades responsible for a number of diabetic complications. In this article, we will review how insulin is secreted and functions physiologically and highlight a dynamic insulin delivery modality that mimics normal secretion profiles. This biomimicry reduces insulin exposure, which appears to reduce the progression to or worsening of insulin resistance. We will review how administration of insulin in this manner has been associated with reduction of diabetic complications.

ELASTIC AND INELASTIC ALPHA TRANSFER IN THE 16O+12C SCATTERING

The elastic scattering cross section measured at energies $E\lesssim 10$ MeV/nucleon for some light heavy-ion systems having two identical cores like \oc exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic $\alpha$ transfer has been shown to originate directly from the core-exchange symmetry in the elastic \oc scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar $\alpha$ transfer process (or inelastic $\alpha$ transfer) to take place in the inelastic \oc scattering. The present work provides a realistic coupled channel description of the $\alpha$ transfer in the inelastic \oc scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the $\alpha$ transfer to the inelastic \oc scattering cross section at the backward angles. These results suggest that the explicit coupling to the $\alpha$ transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.\Keywords{optical potential, coupled reaction channels, inelastic $\alpha$ transfer

Elastic and Inelastic Alpha Transfer in the \(^{16}\)O+\(^{12}\)C Scattering

The elastic scattering cross section measured at energies \(E\lesssim 10\) MeV/nucleon for some light heavy-ion systems having two identical cores like \(^{16}\)O+\(^{12}\)C exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic \(\alpha\) transfer has been shown to originate directly from the core-exchange symmetry in the elastic \(^{16}\)O+\(^{12}\)C scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar \(\alpha\) transfer process (or inelastic \(\alpha\) transfer) to take place in the inelastic \(^{16}\)O+\(^{12}\)C scattering. The present work provides a realistic coupled channel description of the \(\alpha\) transfer in the inelastic \(^{16}\)O+\(^{12}\)C scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the \(\alpha\) transfer to the inelastic \(^{16}\)O+\(^{12}\)C scattering cross section at the backward angles. These results suggest that the explicit coupling to the \(\alpha\) transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.

Brain Functional Correlates of Intelligence Score in ADHD Based on EEG

It has been shown that intelligence as a general mental ability is related to structure and function of the brain regions. However, specificity of this regional dependencies to the intelligence scores in the typical and atypical developed individuals needs to be well understood. In this study, we hypothesized that neural correlates of IQ should not have a fixed pattern rather it must follow a dynamic pattern to compensate the functional deficits caused by a neurodevelopmental disorder. Therefore, EEG correlates of normal IQ in various subtypes of attention deficit hyperactive disorder (ADHD) were compared to a group of healthy controls. Sixty-three ADHD subjects comprising of combined, inattentive, and hyperactive individuals diagnosed by a psychiatrist using structural clinical interview for DSM-V, and 46 healthy controls with similar normal IQ scores were recruited in this study. The subjects’ EEG data were then recorded during an eye-closed resting condition. The subjects’ intelligence level was measured by the Raven’s standard progressive matrices. Then, association between IQ and power of EEG signal were computed in the conventional frequency bands. Subsequently, topographical representations of these associations were compared between the groups. Our results demonstrated that association between IQ score and EEG power is not the same in various ADHD subtypes, and healthy controls. This finding suggests a compensatory mechanism in ADHD individuals for changing the regional oscillatory pattern to maintain the IQ within a normal range.

Scattering of flexural gravity waves by a pair of submerged vertical porous barriers located above a porous sea-bed

An analytical study is presented to investigate the scattering of oblique flexural gravity waves by a pair of totally submerged vertically placed porous barriers, located at some distance from each other, for a homogenous fluid flowing over a porous sea-bed. A thin ice-sheet, replacing the usual free surface, is considered as the upper surface where it is treated as a thin elastic plate. The complete analytical solution, under the assumption of small-amplitude theory and structural response, is acquired by employing eigenfunction expansion and least square method. Subsequently, computation for the reflection and transmission coefficients, energy loss and wave forces is carried out and discussed for different parameter values corresponding to the ice-sheet, porous sea-bed and porous barriers. This study establishes that the oscillatory behavior exhibited by the reflection of the waves. The vertical porous barriers are found to dissipate a significant portion of the wave energy when an increase in the inertial effect of the porous barriers takes place. The hydrodynamic force on the barriers also follows an oscillatory pattern and it increases when the length of the barrier is increased. It is demonstrated that, corresponding to various structural parameters, almost no reflection and full transmission take place for an impermeable sea-bed and also when only real porosity parameter of the porous sea-bed is considered. Further, variation in the elastic parameter of the floating ice-sheet is observed to command a considerable influence when the wave impinges upon the submerged vertical porous barriers.

Brain Density Clustering Analysis: A New Approach to Brain Functional Dynamics

BackgroundA number of studies in recent years have explored whole-brain dynamic connectivity using pairwise approaches. There has been less focus on trying to analyze brain dynamics in higher dimensions over time.MethodsWe introduce a new approach that analyzes time series trajectories to identify high traffic nodes in a high dimensional space. First, functional magnetic resonance imaging (fMRI) data are decomposed using spatial ICA to a set of maps and their associated time series. Next, density is calculated for each time point and high-density points are clustered to identify a small set of high traffic nodes. We validated our method using simulations and then implemented it on a real data set.ResultsWe present a novel approach that captures dynamics within a high dimensional space and also does not use any windowing in contrast to many existing approaches. The approach enables one to characterize and study the time series in a potentially high dimensional space, rather than looking at each component pair separately. Our results show that schizophrenia patients have a lower dynamism compared to healthy controls. In addition, we find patients spend more time in nodes associated with the default mode network and less time in components strongly correlated with auditory and sensorimotor regions. Interestingly, we also found that subjects oscillate between state pairs that show opposite spatial maps, suggesting an oscillatory pattern.ConclusionOur proposed method provides a novel approach to analyze the data in its native high dimensional space and can possibly provide new information that is undetectable using other methods.

Oscillatory pattern of glycemic control in patients with diabetes mellitus

Daily glucose variability is higher in diabetic mellitus (DM) patients which has been related to the severity of the disease. However, it is unclear whether glycemic variability displays a specific pattern oscillation or if it is completely random. Thus, to determine glycemic variability pattern, we measured and analyzed continuous glucose monitoring (CGM) data, in control subjects and patients with DM type-1 (T1D). CGM data was assessed for 6 days (day: 08:00–20:00-h; and night: 20:00–08:00-h). Participants (n = 172; age = 18–80 years) were assigned to T1D (n = 144, females = 65) and Control (i.e., healthy; n = 28, females = 22) groups. Anthropometry, pharmacologic treatments, glycosylated hemoglobin (HbA1c) and years of evolution were determined. T1D females displayed a higher glycemia at 10:00–14:00-h vs. T1D males and Control females. DM patients displays mainly stationary oscillations (deterministic), with circadian rhythm characteristics. The glycemia oscillated between 2 and 6 days. The predictive model of glycemia showed that it is possible to predict hyper and hypoglycemia (R2 = 0.94 and 0.98, respectively) in DM patients independent of their etiology. Our data showed that glycemic variability had a specific oscillation pattern with circadian characteristics, with episodes of hypoglycemia and hyperglycemia at day phases, which could help therapeutic action for this population.