Closing the loop of deep brain stimulation

Abstract

High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we consider whether the classical open-loop HFS fulfills these criteria and outline current experimental or theoretical research on the different types of closed-loop DBS that could provide better clinical outcomes. In the first part of the review, the two routes followed by HFS-evoked axonal spikes are explored. In one direction, orthodromic spikes functionally de-afferent the stimulated nucleus from its downstream target networks. In the opposite direction, antidromic spikes prevent this nucleus from being influenced by its afferent networks. As a result, the pathological synchronized activity no longer propagates from the cortical networks to the stimulated nucleus. The overall result can be described as a reversible functional de-afferentation of the stimulated nucleus from its upstream and downstream nuclei. In the second part of the review, the latest advances in closed-loop DBS are considered. Some of the proposed approaches are based on mathematical models, which emphasize different aspects of the parkinsonian basal ganglia: excessive synchronization, abnormal firing-rate rhythms, and a deficient thalamo-cortical relay. The stimulation strategies are classified depending on the control-theory techniques on which they are based: adaptive and on-demand stimulation schemes, delayed and multi-site approaches, stimulations based on proportional and/or derivative control actions, optimal control strategies. Some of these strategies have been validated experimentally, but there is still a large reservoir of theoretical work that may point to ways of improving practical treatment.

Keywords: DBS; antidromic; closed loop; mechanisms; open loop.

Figures

Figure 1

Chronaxy. Deep-brain high-frequency stimulation is applied through an extracellular stimulating electrode. Stimulation usually consists of 60–400 μs pulses applied at a frequency of 100–130 Hz. It activates one or several neuronal elements close to the stimulating electrode: somato-dendritic trees, axons, axon terminals. This depends on stimulation parameters, since each of these elements has a specific chronaxy (Ranck, 1975) which determines whether they are activated by a given stimulation. A single, short-duration, extracellular stimulating pulse preferentially activates axons The link between the intensity of stimulation (Y axis) and the minimal duration of this stimulation (pulse width, X axis) needed to activate a given element (muscle fiber or neuron, soma or axon of a neuron) is hyperbolic and described by the Weiss law: I = Rh (Cr/t +1). When the current intensity of a pulse is decreased, its duration (pulse width) must be increased to produce constant effects i.e., activate the given neuronal element. The asymptote to the X axis defines the rheobase (Rh). It corresponds to the minimal current intensity needed to activate an element (muscular or neuronal). If applied at an intensity lower than rheobase, the stimulus will never activate a given element, whatever its duration (t). The minimum duration required for a constant electric current of twice the rheobase to excite tissue is the Chronaxy (Cr). When I = 2Rh, t = Cr The concepts of “chronaxie” and “rheobase” were introduced in 1909 by the French physiologist L. Lapicque. The root word “rheo” means current and the root word “chron” means time. The chronaxy is used to quantify the excitability of an element. The element is more excitable when its chronaxy is short. Chronaxies of the different elements of the nervous system differ by a factor of 5 to 300. Large myelinated axons of the central nervous system have a chronaxy of 30–300 μs and around 500 μs for non-myelinated axons, whereas that of somas and dendrites is around 1–10 ms (Ranck, 1975). In the cat visual cortex, Nowak and Bullier (1998) found similar results with a chronaxy of around 270 μs for axons of the subcortical white matter and of 15 ms for somas in the cortex. Therefore, a stimulating pulse of 60–400 μs duration preferentially activates axons. Larger axons have a lower threshold of activation because the intracellular resistance to longitudinal ionic flux is low as a result of the higher percentage of ions that carry the current per length unit. Therefore, for a given current applied, the large axons are those most easily depolarized.

Figure 2

The two hypotheses on the effect of STN HFS-evoked orthodromic spikes on the activity of substantia nigra and pallidal neurons. (A) Schematic illustration of the experimental design showing the stimulation and recording sites. (B) HFS-evoked orthodromic spikes in STN axons evoke excitatory (left) and inhibitory (right) responses in SNr neurons recorded in cell-attached (c-a) or whole-cell (w-c) configuration in voltage (top) or current (bottom) clamp mode. Scale bars: 100 pA top, 5 mV bottom, 400 ms. Adapted from Bosch et al. (2011). (C–E) HFS-evoked orthodromic spikes in STN axons evoke low amplitude EPSCs in SNr (C), SNc (D), and GPe (E) neurons. Bottom traces in (C) and (E) are close ups to the top traces at the beginning (C) left and at the end (C) right, (E) of the stimulation. Scale bars are 50 pA, 200 and 20 ms in (C), 50 pA and 5 ms in (D) and 50 pA, 200 and 20 ms in (E). (C) from Ammari and Hammond (personal communication), (D) adapted from Zheng et al. (2011) and (E) adapted from Ammari et al. (2011). (F) Schematic illustration of the possible mechanisms underlying HFS-induced depression of synaptic transmission.

Figure 3

Antidromic spikes. The antidromic propagation of a spike refers to its conduction in a direction opposite from the normal (orthodromic) direction (away from axon terminals to soma instead of propagating from the initial segment of the axon, close to the soma, toward axon terminals). To evoke antidromic spikes, axons are directly stimulated with a suprathreshold stimulus. Evoked spikes propagate in both directions (orthodromic and antidromic). This shows that axons do not have a preferential direction of conduction: the direction of propagation is given by the synapses, which are unidirectional [from the axon terminal (presynaptic element) to the postsynaptic element]. Antidromic activation is often used in a laboratory setting to confirm that a recorded neuron projects to the structure of interest. During HF DBS, antidromic spikes are evoked because an extracellular stimulation preferentially activates axons (axon terminals, passing axons). Criteria for identification of an antidromic spike are: (i) Stability of latency (because there are no synapses between the stimulating and recording sites), (ii) Faithful responses to high rates of stimulation (for the same reason as above), (iii) Collision of the antidromic spike (1) with an orthodromically traveling spike (2) because they meet along the same axon and annihilate each other. As antidromically activated units sometimes do not fire spontaneously, in order to perform a collision test the action potentials are orthodromically evoked by another stimulation or by depolarizing the soma with the recording electrode. (a) Three spikes recorded from the soma (blue recording electrode) in response to three stimuli (arrows) applied at the axon (red stimulating electrode) (three superimposed traces). (b) A spontaneous orthodromic spike (2) does not suppress the evoked spike (1) when it is recorded long before the stimulation but does so (c, *) when it is recorded 10 ms before the stimulation. These results show that spike 1 is an antidromic spike: it has a fixed latency (a), it faithfully follows high frequency stimulation (a) and it collides with spontaneous spikes (c).

Figure 4

Effect of STN HFS-evoked antidromic spikes on cortical activity. (A) Schematic illustration of the experimental design showing the stimulation and recording sites. (B) Antidromic spiking in cortical neurons evoked by STN-HFS (intracellular recording in the motor cortex). Black bar indicates the period of STN-HFS. Stimulation artefacts are removed. Right trace is a close-up of (B) left. Arrow shows a spontaneous spike before stimulation with subsequent loss of an antidromic spike caused by collision. Adapted from Li et al. (2007). (C) Evoked potentials in the ipsilateral motor cortex in response to bipolar stimulation of the dorsal STN. Latencies of the peaks were 4, 13.7, and 24.5 ms. The short-latency negative-evoked potential has a peak latency of 4 ms in bilateral frontal and central leads (C3, C4, Cz). Adapted from Kuriakose et al. (2010). (D) STN-HF DBS induces beta attenuation in motor cortex. Spectrogram of single cortical ECoG channel during HF DBS (top) 1.5 mM dorsal to the dorsal border of the STN and (bottom) within the STN (2.6 mM below dorsal border) from a representative patient. Black bars indicate the full time that HF DBS is on. The bars marked “AEs” indicate the period when HF DBS is increased from 0 to 3 V to test for adverse clinical effects; these segments were not used in analyses. The color scale indicates the level of log beta power on a decibel scale. Note the power rebound when STN DBS is turned off. Adapted from Whitmer et al. (2012). (E) From top to bottom and left to right. Optical HFS (130 Hz, 5-ms pulse width) reduces amphetamine-induced ipsilateral rotations in 6-OHDA Thy1::ChR2 mice (P < 0.01, n = five mice) in contrast to optical LFS (20 Hz, 5-ms pulse width, P > 0.05, n = four mice); t-test with m = 0. Sample paths before, during and after HFS are shown (100 s each, path lengths in cm). Adapted from Gradinaru et al. (2009). (F) Schematic illustration of the possible mechanisms underlying the antidromic effects of HFS. Spontaneous orthodromic spikes are in black and HFS-evoked antidromic spikes in red.

Figure 5

Kuramato oscillator. Periodically spiking neurons are characterized by the existence of an attractive limit cycle in their phase portrait. A classical way to reduce the complexity of analyzing their rhythm is to focus on their instantaneous position along this limit-cycle. Using phase-response curves, this abstraction enables the neuron's dynamics to be reduced to a single scalar variable, referred to as its phase. Phase models: For periodically spiking neurons whose limit cycle results from a Hopf bifurcation, the limit cycle can be abstracted to a periodic circle. A normal form of the resulting dynamics is known as the Andronov-Hopf oscillator, which is ruled by the complex equation: z˙i(t)=(jωi+1−|zi(t)|2)zi(t)+∑i=1Nκij(zi(t)−zi(t)), where ωi denotes the natural frequency of the i-th oscillator and κij are interconnection gains between the N oscillators. When the neuronal interconnection keeps the module of z(t) constant, the dynamics of the resulting phase θi takes an even simpler form, known as the Kuramoto oscillator (Kuramoto, 1984): θ˙i(t)=ωi+∑i=1Nκijsin(θj(t)−θi(t)) Such phase dynamics have been extensively used in the literature to predict synchrony onset in a neuronal population and to derive closed-loop stimulation strategies (Pyragas et al., ; Tukhlina et al., ; Omel chenko et al., ; Franci et al., 2011, 2012).

Figure 6

Model of Rubin and Terman. This scheme represents the synaptic interconnections, both within the basal ganglia and between their afferent and efferent anatomical structures. This type of circuit representation has generated several basal ganglia models, both at the microscopic and at the mesoscopic scales. Microscopic models: Neural activity is described at the level of each neuron. Following the approach of Hodgkin and Huxley (1952), the dynamics of the membrane voltage Vi(t) associated with the i-th neuron is described by a conductance model CmdVi(t)dt=gκni4(t)(EK−Vi(t))+gNami3(t)hi(t)(ENa−Vi(t))                   + gL(EL−Vi(t))+∑j=1nκijIijSyn(t)+IiExt(t) where the variables ni(t), mi(t), and hi(t) describe the opening-closing dynamics of different ion channels. In the work (Rubin and Terman, 2004), the parameters that appear in such conductance models are identified for the thalamus, the STN, the GPe, and the GPi. With these parameters in hand, the influence of (open-loop) DBS on model behavior can be analyzed. The conclusion of Rubin and Terman is that the effect of DBS on the STN/GPe/GPi network restores a normal interaction between the cortex and the thalamus, by breaking the pathological patterns generated by the STN/GPe interconnection. Mesoscopic models: Neural activity is described at the level of small neural populations; for example, the region of the sub-thalamic nucleus that is activated by a particular type of movement. Following the approach of Wilson and Cowan (1972), the activity of the i-th population is characterized by its firing rate ri(t), which satisfies the equation τidri(t)dt=−ri(t)+Fi(∑j ∈ Eκijrj(t−δij)−∑j ∈ Eκijrj(t−δij)+IiExt(t)) where E and I are the set of excitatory and inhibitory populations, respectively. The sigmoid function Fi, called the activation function, characterizes the degree of excitation of the i-th population as a function of the inputs that it receives from all the other populations. (Nevado Holgado et al., 2010) used this equation to derive a model of the STN/GPe network, with E = {Ctx, STN} and I = {Str, GPe}. In this model, the interconnection delays δij play a central role in the mechanism that generates pathological beta-band oscillations.

Figure 7

Illustration of a strategy of closed-loop DBS relying on the measurement y of the mean-field of the targeted neuronal population. Stimulation input u is dynamically established based on measurement y, and takes the form u = G(s)y, where G(s) denotes a filter that can either be proportional (G(s) = K) such as in Wagenaar et al. (2005); Leondopulos (2007); Franci et al. (2011, 2012); Liu et al. (2011), include integral or derivative terms such as in Pyragas et al. (2007), or rely on more involved filtering such as in Tukhlina et al. (2007).

Figure 8

Possible behaviors of a network of phase oscillators. Top left: Phase-locking (all phase differences tend to a constant value). Top right: Full desynchronization (all phases drift away from one another). Bottom left: Inhibition (all phases tend to a constant value, no oscillations persist). Bottom right: Practical phase-locking (phase differences do not tend to a constant value, but instantaneous frequencies remain close to each other).