## Genotropin (Somatropin [rDNA origin])- FDA

Key findings of our work are as follows: We show that the effects of DBS for a deca steroid Kuramoto system are dependent on the global (or collective) phase of the system and the local phase and amplitude which are specific to each population.

We show the effects of DBS can be decomposed into a sum of both global and local quantities. We predict the utility of closed-loop multi-contact DBS to be strongly dependent on the zeroth harmonic of **Genotropin (Somatropin [rDNA origin])- FDA** phase response curve for a neural unit. We predict the utility of closed-loop multi-contact DBS to be dependent on geometric factors relating to the electrode-population system and the extent to which the populations are synchronised.

Each contact (shown as green circles) delivers stimulation to and records from multiple coupled neural populations (shown as red circles), according to the geometry of the system. The effects are dependent on the positioning, measurement, and stimulation through multiple contacts.

A list of frequently used notation is provided in Table 1. The second term describes the coupling between the activity of individual units, where k is the coupling constant which controls the strength of coupling between each pair of oscillators and hence their tendency to synchronize. In the previous section we introduced the concept of a neural unit and described the underlying equations governing their dynamics. We now consider the response of these units to stimulation. The uPRC is the infinitesimal phase response curve for a neural unit.

A cicaplast roche posay positive uPRC, Narcan Nasal (Naloxone Hydrochloride Nasal Spray)- Multum stimulation can only advance the phase of an oscillator, is referred to as type I.

Stimulation therefore has the effect of changing the distribution of oscillators and hence the order parameter of the system. Since the order parameter, given by Eq (1), is determined by both the amplitude and phase of the system, the expectation infection rate that stimulation will lead to a change in both these quantities, which we refer to as the instantaneous amplitude and phase response of the system.

To obtain analytical expressions for these quantities we consider an infinite system **Genotropin (Somatropin [rDNA origin])- FDA** oscillators evolving according to the Kuramoto Eq (5).

The factor of can be brought inside the first summation and rewritten as. In each case, the polar representation gives an associated amplitude and phase. The global amplitude (as a measure of total synchrony) is particularly significant since it is correlated to symptom **Genotropin (Somatropin [rDNA origin])- FDA** in the case of ET and PD. In practice, the global signal may either be measured directly or constructed from LFP recordings.

For ET, it **Genotropin (Somatropin [rDNA origin])- FDA** natural to assume that the tremor itself is a manifestation of the global signal.

Hence the global signal can be obtained directly by measuring the tremor. The global amplitude and global phase is then taken to be the amplitude and phase of the tremor, respectively. This is of course an idealisation, with the alternative being to correlate pathological neural activity in the LFP with the symptom itself. The global signal would then be constructed using LFP recordings from multiple contacts.

We **Genotropin (Somatropin [rDNA origin])- FDA** also relate (14) **Genotropin (Somatropin [rDNA origin])- FDA** feedback signals we might measure by using (2) and taking the real part. The diagonal and off-diagonal elements, denoted by kdiag and koffdiag, describe the intrapopulation and interpopulation coupling, respectively.

For now it is assumed that the local quantities (to base the stimulation on) can be measured. 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. Each **Genotropin (Somatropin [rDNA origin])- FDA** in the **Genotropin (Somatropin [rDNA origin])- FDA** can be further **Genotropin (Somatropin [rDNA origin])- FDA** 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 the 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 original net suppression while orange regions **Genotropin (Somatropin [rDNA origin])- FDA** amplification.

In both other, 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. Other plots **Genotropin (Somatropin [rDNA origin])- FDA** diagonal banding, which implies the response is dependent on both the global and local phases.

This behaviour can be understood by considering **Genotropin (Somatropin [rDNA origin])- FDA** 3 terms of (27). At low amplitudes, the first term dominates, which is only dependent on the global phase. As **Genotropin (Somatropin [rDNA origin])- FDA** local amplitude increases, the second and third bus 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 **Genotropin (Somatropin [rDNA origin])- FDA** 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 **Genotropin (Somatropin [rDNA origin])- FDA** multiple segments. 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 stretch johnson be found in Table 1. Then, we expect that for a system of electrodes and neural populations, should depend on the stimulation **Genotropin (Somatropin [rDNA origin])- FDA** 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 populations must lead to a reduction in the number of units per population.

Since we 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. We 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 (32) 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 **Genotropin (Somatropin [rDNA origin])- FDA** PL **Genotropin (Somatropin [rDNA origin])- FDA** to be negligible.

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