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We will discuss how these quantities can be measured later. Eq (26) shows the change in the global amplitude due to stimulation can be expressed as a sum of contributions from each population. Plan b one step term in the summation can be further split into three terms, the first of which depends only on the global phase with the second and third terms depending on both the global phase and Oxycodone Hydrochloride Tablets (RoxyBond)- Multum local quantities.

We will refer to these terms as simply the global and local terms, respectively. Eq (26) tells us how the global amplitude (i. Regions in blue are areas of amplitude suppression while orange regions predict amplification. In Oxycodone Hydrochloride Tablets (RoxyBond)- Multum cases, these regions can be seen to occur in bands. A purely horizontal band implies the response is independent of the local phase.

An example of this can be seen at low amplitudes in Fig 2A. Sexual sex plots show diagonal banding, which implies the response is dependent on both the global and local phases. This behaviour can be understood by considering the 3 terms of (27).

At low amplitudes, the first term dominates, which is only dependent on the global phase. As the local amplitude increases, the second and third terms depending on local quantities become increasingly more important.

The left panel of Fig 2A shows that stimulation can either increase or reduce the phase (i. For this case, the second term can be neglected, leading to a dominance of the first term at low amplitudes where only a small dependence on the local phase can be seen.

For these systems the response can be seen to depend more strongly on the local phase for all amplitudes. Blue regions indicate areas where stimulation is predicted to suppress amplitude.

The effects of stimulation are then calculated using a multi-compartmental neuron, where the dendrites and axons are treated explicitly and then discretised into multiple Oxycodone Hydrochloride Tablets (RoxyBond)- Multum. In this subsection, our aim is to connect these ideas with Eq (25) for the amplitude response. We use the following quantities in this analysis: positions p, voltages V and currents I. A full description of our notation can be found in Table 1.

Then, we expect that for a system of electrodes and neural populations, should depend on the stimulation provided by all the electrodes in the system in addition to the geometry of the electrode placement and properties of the brain tissue.

Since Eq (25) describes the response of neural populations, one assumption here is that this potential does not vary within each population, i. We expect the small population assumption to be more valid for systems described by larger S. For fixed N, increasing the number of Oxycodone Hydrochloride Tablets (RoxyBond)- Multum must lead to a reduction in the number of units per population.

Since Oxycodone Hydrochloride Tablets (RoxyBond)- Multum expect each unit to occupy a volume in space, this therefore leads to smaller populations. Therefore, the small population assumption should be more valid for systems described by larger S.

The currents I would be equivalent to the user-controllable stimulation intensities. The positions in space of the electrodes and populations are given by pl andrespectively.

Appl organomet chem now seek an expression for how much current to deliver across each electrode on the basis of feedback signals. Inserting (28) into (30) leads to an expression for the amplitude response in terms of the currents at the electrodes, i.

To account for this, we can also impose a constraint on the current for each contact such that it does not exceed some maximum value Imax Oxycodone Hydrochloride Tablets (RoxyBond)- Multum For each time step, our objective is to deliver stimulation which maximally suppresses the global amplitude, i.

In this scenario, we expect the efficacy difference between ACD and PL stimulation to be negligible. We refer to this hh astrazeneca difference here as the utility. To analyse Oxycodone Hydrochloride Tablets (RoxyBond)- Multum utility of ACD over PL stimulation we therefore have to understand the significance of the local terms relative to the global terms in (26).

It is clear that this significance is dependent both on the parameters of the system and the time dependent state. We may then neglect the local term involvingleading to (34) We therefore expect the utility of ACD to be almost entirely dependent on the local term of (34), namely (35) Hence, we expect the utility of ACD to increase as (35) becomes more significant relative to the other terms in (34). This is likely to occur when the zeroth harmonic of the uPRC is large, implying a type I uPRC.

We would expect lower utility for systems where is negligible, i. One situation in which such phase difference may be particularly high are for clustered configurations of oscillators. Examples of different configurations of oscillators are shown in Fig 3. Panels (a) and (b) are for a unimodal distribution and multimodal (clustered) distribution, respectively. Configurations were obtained by simulating the Oxycodone Hydrochloride Tablets (RoxyBond)- Multum Kuramoto Eq (20).

If we consider the less Oxycodone Hydrochloride Tablets (RoxyBond)- Multum case of homogeneous uPRC type, i.



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