Pranay Goel

On the human sensorimotor-cortex beta rhythm: sources and modeling.

Cortical oscillations in the beta band (13-35 Hz) are known to be modulated by the GABAergic agonist benzodiazepine. To investigate the mechanisms generating the approximately 20-Hz oscillations in the human cortex, we administered benzodiazepines to healthy adults and monitored cortical oscillatory activity by means of magnetoencephalography. Benzodiazepine increased the power and decreased the frequency of beta oscillations over rolandic areas. Minimum current estimates indicated the effect to take place around the hand area of the primary sensorimotor cortex. Given that previous research has identified sources of the beta rhythm in the motor cortex, our results suggest that these same motor-cortex beta sources are modulated by benzodiazepine. To explore the mechanisms underlying the increase in beta power with GABAergic inhibition, we simulated a conductance-based neuronal network comprising excitatory and inhibitory neurons. The model accounts for the increase in the beta power, the widening of the spectral peak, and the slowing down of the rhythms with benzodiazepines, implemented as an increase in GABAergic conductance. We found that an increase in IPSCs onto inhibitory neurons was more important for generating neuronal synchronization in the beta band than an increase in IPSCs onto excitatory pyramidal cells.

Synchrony, stability, and firing patterns in pulse-coupled oscillators

We study non-trivial firing patterns in small assemblies of pulse-coupled oscillatory maps. We find conditions for the existence of waves in rings of coupled maps that are coupled bi-directionally. We also find conditions for stable synchrony in general all-to-all coupled oscillators. Surprisingly, we find that for maps that are derived from physiological data, the stability of synchrony depends on the number of oscillators. We describe rotating waves in two-dimensional lattices of maps and reduce their existence to a reduced system of algebraic equations which are solved numerically.

HOMOGENIZATION OF THE CELL CYTOPLASM: THE CALCIUM BIDOMAIN EQUATIONS ∗

All previous models of the dynamics of intracellular calcium concentration have either made the ad hoc assumption that the cytoplasm and the endoplasmic reticulum (ER) coexist at every point in space or have explicitly separated the cytoplasm and the ER into different spatial domains. The former approach is unjustified, and the dependence on the diffusion coefficients on the geometry of the ER is unclear; the latter approach leads to extreme computational difficulties. To avoid the disadvantages of these approaches, we derive a bidomain model of calcium concentration inside the ER network, and outside it, in the cytosol. The homogenized macroscopic behavior is described in a two-concentration field model, a formula is derived for the effective diffusion coefficients of calcium in the ER and in the cytoplasm, and the effective diffusion coefficients are numerically computed for different ER geometries.

Learning Theories Reveal Loss of Pancreatic Electrical Connectivity in Diabetes as an Adaptive Response

Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible for secreting the hormone insulin in response to glucose stimulation. Gap junctions are the only electrical contacts between the beta-cells in the tissue of these excitable islets. It is generally believed that they are responsible for synchrony of the membrane voltage oscillations among beta-cells, and thereby pulsatility of insulin secretion. Most attempts to understand connectivity in islets are often interpreted, bottom-up, in terms of measurements of gap junctional conductance. This does not, however, explain systematic changes, such as a diminished junctional conductance in type 2 diabetes. We attempt to address this deficit via the model presented here, which is a learning theory of gap junctional adaptation derived with analogy to neural systems. Here, gap junctions are modelled as bonds in a beta-cell network, that are altered according to homeostatic rules of plasticity. Our analysis reveals that it is nearly impossible to view gap junctions as homogeneous across a tissue. A modified view that accommodates heterogeneity of junction strengths in the islet can explain why, for example, a loss of gap junction conductance in diabetes is necessary for an increase in plasma insulin levels following hyperglycemia.

The Geometry of Bursting in the Dual Oscillator Model of Pancreatic

We describe an extended fast-slow analysis for the dual oscillator model (DOM) for bursting oscillations in pancreatic

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-cells

-cells, which occur on a wide range of time scales, from seconds to minutes. This wide dynamic range has been suggested to result from the interactions of a very slow metabolic, possibly glycolytic, oscillator and a faster electrical oscillator, itself containing several negative feedback mechanisms with a range of time scales. Although the high dimensionality of the slow subsystem would defeat a straightforward fast-slow analysis, we show that an approximate geometrical analysis that exploits particular features of the DOM and is based on superimposing the bifurcation diagrams of the component oscillators leads to new insights into the functioning of the system.

A neuronal network for the logic of Limax learning

We construct a neuronal network to model the logic of associative conditioning as revealed in experimental results using the terrestrial mollusk Limax maximus. We show, in particular, how blocking to a previously conditioned stimulus in the presence of the unconditional stimulus, can emerge as a dynamical property of the network. We also propose experiments to test the new model.

A Decision Tree Analysis of Diabetic Foot Amputation Risk in Indian Patients

Aim The aim of this study is to create an evidence-based tool that guides the risk of amputation in diabetic foot patients. Materials and methods Hospital records of 301 diabetic foot patients were examined retrospectively for explanatory variables of foot amputation decisions. The study included all patients with a lower limb ulcer with a known history of diabetes mellitus or those diagnosed post-admission. The dataset was analyzed, and a risk scoring system was constructed using the decision tree algorithm, C5.0. Two classifiers, one simple and another complex, were constructed for predicting amputation outcome. Results and discussion Based on our evaluation, the most influential predictors for a decision to amputate are Doppler flow measurements and the Wagner grading of the ulceration. The simple classifier uses just these two parameters in determining risk. The results obtained show an accuracy of 96.4% in the primary group and an accuracy of 94% in the test group. The second classifier is a more complex computer-derived construct that showed 100% accuracy in the principle group and an accuracy of 96% during testing. Conclusion In the present era of precision medicine, these two classifiers act as an accurate guide to the prognosis of the limb in patients with diabetic foot and can predict the risk of future amputation.

Thresholds of oxidative stress in newly diagnosed diabetic patients on intensive glucose-control therapy.

Cellular and animal studies suggest that oxidative stress could be the central defect underlying both beta-cell dysfunction and insulin resistance in type 2 diabetes mellitus. A reduction of glycemic stress in diabetic patients on therapy alleviates systemic oxidative stress and improves insulin resistance and beta-cell secretion. Monitoring oxidative stress systematically with glucose can potentially identify an individuals recovery trajectory. To determine a quantitative model of serial changes in oxidative stress, as measured via the antioxidant glutathione, we followed patients newly diagnosed with diabetes over 8 weeks of starting anti-diabetic treatment. We developed a mathematical model which shows recovery is marked with a quantal response. For each individual the model predicts three theoretical quantities: an estimate of maximal glutathione at low stress, a glucose threshold for half-maximal glutathione, and a rate at which recovery progresses. Individual patients are seen to vary considerably in their response to glucose control. Thus, model estimates can potentially be used to determine whether an individual patients response is better or worse than average in terms of each of these indices; they can therefore be useful in reassessing treatment strategy. We hypothesize that this method can aid the personalization of effective targets of glucose control in anti-diabetic therapy.