On the emergence of the Λ{\bf\Lambda}CDM model from self-interacting Brans-Dicke theory in d=5{\bf d= 5}

We investigate whether a self-interacting Brans-Dicke theory in $d=5$ without matter and with a time-dependent metric can describe, after dimensional reduction to $d=4$, the FLRW model with accelerated expansion and non-relativistic matter. By rewriting the effective 4-dimensional theory as an autonomous three-dimensional dynamical system and studying its critical points, we show that the $\Lambda$CDM cosmology cannot emerge from such a model. This result suggests that a richer structure in $d=5$ may be needed to obtain the accelerated expansion as well as the matter content of the 4-dimensional universe.Comment: 7 pages, 7 figure

Heart rate as the level of stimulation is increased from that in Figure 3 (from 0.75 <i>mA</i> to 1.75 <i>mA</i>).

<p>Pronounced bradycardia is observed.</p

A map of neural activity (discharge) at the three levels of the neural network under the model parasympathetic threshold conditions and corresponding to the pattern of heart rate observed in Figure 9.

<p>Here the <i>direct</i> component of the VSC is stimulated, with the level of stimulation of the indirect component being maintained the same as under the sympathetic threshold conditions. The direct component of the VSC dominates, leading to the bradycardia observed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114498#pone-0114498-g009" target="_blank">Figure 9</a>. Legend as in the caption of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114498#pone-0114498-g010" target="_blank">Figure 10</a>.</p

Schematic of mathematical model.

<p>Closed-loop control of cardiac output is shown as a networked 3-level hierarchy.</p

Hierarchical networked model for cardiac control.

<p>Network interactions occur within the local circuit neural (LCN) populations. These integrate activities within and between peripheral ganglia and the central nervous system subserve reflex control of the heart. The intrinsic cardiac nervous system possesses sympathetic (Sympath) and parasympathetic (Parasym) efferent post-ganglionic neurons, local circuit neurons (LCN) and afferent (Aff.) neurons. The intrathoracic extracardiac nervous system is comprised of ganglia containing afferent neurons, LCN and sympathetic efferent post-ganglionic neurons. Cardiovascular heart rate and demand inputs are conveyed centrally via dorsal root (DRG), nodose and petrosal ganglia subserving spinal cord (C-cervical, T-thoracic), brainstem and higher center reflexes for hemostatic maintenance.</p

Recurrent myocardial infarction: Mechanisms of free-floating adaptation and autonomic derangement in networked cardiac neural control - Fig 4

<p>In Fig 4 through <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180194#pone.0180194.g014" target="_blank">Fig 14</a> inclusive the simulation results are depicted as solid lines for four variables: (i) efferent sympathetic activity (red), (ii) heart rate (green), (iii) central drive (black), and (iv) parasympathetic efferent (blue). The simulation timeline definitions described here are further explained in Simulation Design. Each of the red vertical lines <i>E</i>_<i>j</i>, <i>j</i> = 1, 2, 3 indicates the beginning of the <i>j</i>^<i>th</i> episode. Three sub-events within each episode are the red, blue, and black vertical lines that respectively correspond to the onset of infarction (or unstable angina), recovery, and demand. The last vertical dashed line indicates the beginning of the aftermath of the recurrent pathology. In this figure, a stratified network with low neural diversity is shown. Local circuit neurons are affected and remain alive. Neurons that transduce heart rate and blood flow demand are affected and remain alive. There is no autonomic derangement.</p

Model simulation under sympathetic threshold conditions whereby the direct component of the VSC is not being activated but the indirect component is being activated at higher intensity than that in Figure 7.

<p>Pronounced tachycardia is observed, similar to that seen in the experiment under moderate intensity stimulation (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114498#pone-0114498-g003" target="_blank">Figure 3</a>). Red bars indicate time intervals when VNS is on.</p

Model simulation under subthreshold conditions whereby the direct component of the VSC is not being activated but the indirect component and therefore the local circuit elements of the neural network are being activated at low intensity.

<p>Here, as in the experiment (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114498#pone-0114498-g002" target="_blank">Figure 2</a>), there are no discernible changes in heart rate. Red bars indicate time intervals when VNS is on.</p

Model simulation under baseline conditions (zero stimulation).

<p>The oscillatory pattern and the variability in that pattern is similar to that observed in the experiment (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114498#pone-0114498-g001" target="_blank">Figure 1</a>) and is typical at low blood demand and in the presence of low level noise within the system <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114498#pone.0114498-Kember1" target="_blank">[14]</a>. Brief intervals of resonance, whereby the oscillations are subdued, can be observed in both cases.</p

Heart rate in an anesthetized canine under baseline conditions, in the absence of VNS.

<p>Note the variations in heart rate that occur in the normal state.</p