To establish a pharmacological treatment for clinical use, in humans typically a 4-phase sequence of clinical trials is performed (Friedman et al., 2010). In pre-clinical studies pharmacokinetic, toxicity and efficacy are studied in non-human subjects. In first in human-studies (phase I) safety and tolerability of a drug are studied in healthy volunteers. Proof of concept studies (phase IIA) determine whether a drug can have any efficacy, whereas dose-finding studies (phase IIB) are performed to reveal optimum dose at which a drug has biological activity with minimal side-effects. Effectiveness and the clinical value of a new intervention are studied in a randomized controlled trial (phase III), compared with state of the art treatment, if available. Finally, post-marketing surveillance trials (phase IV) are performed to detect rare or long-term adverse effects within a much larger patient population and over longer time periods. There might also be combinations of different phases.

In principle, this 4-phase pattern is also valid for medical technology, e.g., neuromodulation technologies. However, if neuromodulation technologies aim at the control of complex dynamics of e.g., neural networks, different parameters and dosage regimens may have complex, non-linear and even counterintuitive effects, (see e.g., Gao et al., 2014; Popovych et al., 2015; Gates and Rocha, 2016; Zañudo et al., 2017; Zhang et al., 2017). This computational paper illustrates how computational modeling can be used to generate hypotheses for dose-finding studies. In general, performing dose-finding studies simply by trial and error may be impossible because of the substantial parameter space to be tested, with trial durations and related costs getting out of hands.

The development of proper dosage strategies and regimens enables favorable compromises between therapeutic efficacy and detrimental factors such as side-effects or treatment duration. This is relevant, e.g., for the development of pharmaceutical (Williams, 1992; Bertau et al., 2008; Peters, 2012; Dash et al., 2014) or radiation therapy (Symonds et al., 2012). Deep brain stimulation (DBS) is the standard treatment of medically refractory movement disorders (Benabid et al., 1991; Krack et al., 2003; Deuschl et al., 2006). The clinical (Temperli et al., 2003) and electrophysiological (Kühn et al., 2008; Bronte-Stewart et al., 2009) effects of standard high-frequency (HF) DBS occur only during stimulation and cease after stimulation offset.

Coordinated reset (CR) stimulation (Tass, 2003a,b) was computationally developed to specifically counteract abnormal neuronal synchrony by desynchronization. CR stimulation uses sequences of stimuli delivered to neuronal sub-populations engaged in abnormal neuronal synchronization (Tass, 2003a,b). As shown computationally, in neuronal populations with spike-timing-dependent plasticity (STDP) (Gerstner et al., 1996; Markram et al., 1997; Bi and Poo, 1998) CR stimulation may have long-lasting, sustained effects (Tass and Majtanik, 2006; Hauptmann and Tass, 2007; Popovych and Tass, 2012). This is because in the presence of STDP, CR stimulation reduces the rate of coincidences. Accordingly, the network may be shifted from an attractor with abnormal synaptic connectivity and abnormal neuronal synchrony to an attractor with weak connectivity and synchrony (Tass and Majtanik, 2006; Hauptmann and Tass, 2007; Popovych and Tass, 2012). This process was termed anti-kindling (Tass and Majtanik, 2006).

Abnormal neuronal synchronization has been shown to be associated with a number of brain diseases, for example, Parkinson's disease (PD) (Lenz et al., 1994; Nini et al., 1995; Hammond et al., 2007), tinnitus (Ochi and Eggermont, 1997; Llinás et al., 1999; Weisz et al., 2005; Eggermont and Tass, 2015), migraine (Angelini et al., 2004; Bjørk and Sand, 2008). In parkinsonian non-human primates it was shown that electrical CR stimulation of the subthalamic nucleus (STN) has sustained, long-lasting after-effects on motor function (Tass et al., 2012b; Wang et al., 2016). In contrast, long-lasting after-effects were not observed with standard HF DBS (Tass et al., 2012b; Wang et al., 2016). For instance, unilateral CR stimulation of the STN of parkinsonian MPTP monkeys, delivered for only 2 h per day during 5 consecutive days led to significant and sustained bilateral therapeutic after-effects for at least 30 days, whereas standard HF DBS had no after-effects (Tass et al., 2012b). By the same token, cumulative and lasting after-effects of electrical CR stimulation of the STN were also observed in PD patients (Adamchic et al., 2014).

HF DBS may not only cause side effects by electrical current spreading outside of the target region, but also by chronic stimulation of the target itself or by functional disconnection of the stimulated structure (Ferraye et al., 2008; Moreau et al., 2008; van Nuenen et al., 2008). Accordingly, it is key to reduce the integral stimulation current. Electrical CR stimulation of the STN employs significantly less current compared to HF DBS (Tass et al., 2012b; Adamchic et al., 2014; Wang et al., 2016). However, to further improve the CR approach, in a previous computational study the spacing principle (Ebbinghaus et al., 1913) was used to achieve an anti-kindling at subcritical intensities, i.e., particularly weak intensities rendering permanently delivered CR stimulation ineffective (Popovych et al., 2015). According to the spacing principle (Ebbinghaus et al., 1913), learning effects can be improved by repeated stimuli spaced by pauses as opposed to delivering a massed stimulus in a single long stimulation session. The spacing principle was investigated on different levels, ranging from behavioral and cognitive (Cepeda et al., 2006, 2009; Pavlik and Anderson, 2008; Xue et al., 2011; Kelley and Whatson, 2013) to neuroscientific and molecular (Itoh et al., 1995; Frey and Morris, 1997; Menzel et al., 2001; Scharf et al., 2002; Naqib et al., 2012). Computationally it was demonstrated that the spacing principle can also be applied to unlearn unwanted, upregulated synaptic connectivity at subcritical stimulation intensities (Popovych et al., 2015). In principle, the results were intriguing, but required rather long pauses and total stimulation durations (Popovych et al., 2015). Spaced CR stimulation at subcritical intensities might possibly be applied to CR DBS. However, for clinical applications, in particular, for non-invasive applications of CR stimulation (Popovych and Tass, 2012), such as acoustic CR stimulation for tinnitus (Tass et al., 2012a) or vibrotactile stimulation for PD (Tass, 2017; Syrkin-Nikolau et al., 2018), it is crucial to achieve therapeutic effects within a reasonable amount of time. Applications of non-invasive medtech devices typically rely on the patients' compliance and should favorably require short stimulation durations. Accordingly, we here set out to apply the spacing principle to CR stimulation at supercritical intensities, i.e., intensities that enable an anti-kindling for moderate stimulation duration and properly selected stimulation frequencies. The overall goal of this study is to design short-term dosage regimen that improve CR stimulation efficacy, while keeping the integral amount of stimulation as well as the overall duration of the protocols at comparably low levels.

In Manos et al. (in review) we studied the influence of the CR stimulation frequency and the intensity on the outcome of CR stimulation with Rapidly Varying Sequences (RVS) and Slowly Varying Sequences SVS (Zeitler and Tass, 2015). CR stimulation consists of sequences of stimuli delivered to each sub-population (Tass, 2003a,b). For RVS CR stimulation, the CR sequence is randomly varied from one CR stimulation period to another (Tass and Majtanik, 2006). Conversely, SVS CR stimulation is characterized by repeating a sequence for a number of times before randomly switching to the next sequence (Zeitler and Tass, 2015). In Manos et al. (in review) we demonstrated that the efficacy of singleshot CR stimulation with moderate stimulation duration depends on the stimulation parameters, in particular, on the intensity as well as the relationship between CR stimulation frequency and intrinsic firing rates. RVS CR stimulation turned out to induce pronounced long-lasting desynchronization, e.g., at weak intensities and CR stimulation frequencies in a certain range around the neurons' intrinsic firing frequencies. In contrast, SVS CR stimulation enabled even more pronounced anti-kindling, however, at the cost of a significantly stronger dependence of the stimulation outcome on the CR stimulation frequency.

Dosage regimen design is an integral part of pharmacokinetic methodology, aiming at an optimization of drug delivery and effects (Williams, 1992). By a similar token, we hypothesize that appropriate dosage regimens might further enhance the efficacy of RVS and SVS CR stimulation. To probe different dosage regimens, we here consider different stimulation singleshot and multishot CR stimulation protocols. Protocols A and B have identical integral stimulation duration, whereas Protocols C and D may require less stimulation.

By comparing spaced CR stimulation with fixed stimulation parameters (Protocol A) and massed, continuous CR stimulation with equal integral duration (Protocol B) with a flexible spaced CR stimulation with demand-controlled variation of CR stimulation frequency and intensity (Protocol C), and with a flexible non-spaced CR stimulation with demand-controlled variation of CR stimulation frequency and intensity (Protocol D), we demonstrated that Protocol C enables to significantly improve the long-term desynchronization outcome of both RVS and SVS CR stimulation, even at comparatively short integral stimulation duration. Remarkably, spacing alone (Protocol A) is not sufficient to provide an efficient short-term dosage regimen (Figures 2, 3). In fact, in particular cases fivefold longer stimulation duration might even be more efficient than five consecutive single CR shots with identical integral stimulation duration, at least for RVS CR stimulation (Figure 2B vs. Figure 4B). The low performance of pure spacing (Protocol A) might be due to the low number of single CR shots, here five, as opposed to slightly larger numbers of CR shots, say eight, tested for the case of subcritical CR stimulation before (Popovych et al., 2015). However, more important might be the approximately fifty-fold longer stimulation and pause duration used for the spaced subcritical CR stimulation protocol (Popovych et al., 2015). The long spaced subcritical CR stimulation protocol might be beneficial for invasive application, such as DBS, and help reduce side-effects by substantially reducing stimulation current intake of the issue.

However, computationally we show that a spacing with rigid five-shot timing structure, but flexible, demand-controlled variation of stimulation frequency and intensity (Protocol C) provides a short-term dosage regimen that significantly improves the long-term desynchronization outcome of RVS and SVS CR stimulation (Figures 6–9). At the end of each pause between CR shots, the stimulus after-effect is assessed. If the desynchronization is considered to be insufficient, a mild variation of the CR stimulation frequency is performed to possibly provide a better fit between network and CR stimulation frequency, without actually adapting the stimulation frequency to frequency characteristics of the network stimulated. If desynchronization is considered to be moderate, the subsequent CR shot is delivered with parameters unchanged. If desynchronization is sufficient, CR stimulation is suspended during the subsequent shot. Intriguingly, in the vast majority of parameters and networks tested, this short-term dosage regimen induces a robust and reliable long-lasting desynchronization (Figures 6–9). This protocol might be a candidate especially for non-invasive, e.g., acoustic (Tass et al., 2012a) or vibrotactile (Tass, 2017; Syrkin-Nikolau et al., 2018), applications of CR stimulation to increase desynchronization efficacy, while keeping the stimulation duration at moderate levels.

Demand-controlled variation of CR stimulation frequency and intensity (Protocol D) alone (i.e., without inserting pauses) is not sufficient to significantly improve the outcome of RVS and SVS stimulation (Figures 11, 12). Hence, introducing pauses significantly improves the effect of the demand-controlled variation of CR stimulation frequency and intensity.

In principle, stimulation parameters other than the CR stimulation frequency might be varied depending on the stimulation outcome. However, in this study we have chosen to vary the CR stimulation frequency, since the latter turned out to be a sensitive parameter, especially for SVS CR stimulation (see Manos et al., in review). In fact, the short-term dosage regimen with demand-controlled variation of stimulation parameters (Protocol C) might help to turn SVS CR stimulation in a method that causes a particularly strong anti-kindling in a robust and reliable manner.

Protocol C does not require a direct adaption of the CR stimulation frequency to measured quantities reflecting frequency characteristics of the network. We have chosen this design, since it might be an advantage not to rely on specific biomarker-type of information. For instance, in the case of PD a number of relevant studies were devoted to closed-loop DBS (Graupe et al., 2010; Rosin et al., 2011; Carron et al., 2013; Little et al., 2013; Priori et al., 2013; Yamamoto et al., 2013; Hosain et al., 2014; Rosa et al., 2015). A relevant issue in this context is the availability of a biomarker adequately reflecting the individual patient's extent of symptoms (Beudel and Brown, 2016; Kühn and Volkmann, 2017). In fact, it is not clear whether low or high frequency beta band oscillations might be more appropriate as biomarker-type of feedback signal (Beudel and Brown, 2016). For several reasons, beta band oscillations might possibly not be an optimal feedback signal (Johnson et al., 2016; Kühn and Volkmann, 2017). Enhanced beta band oscillations are not consistently found in all PD patients (Kühn et al., 2008; Kühn and Volkmann, 2017). The clinical score of PD patients might more appropriately be reflected by the power ratio of two distinct bands of high frequency oscillations around 250 and 350 Hz (Özkurt et al., 2011). Appropriate biomarkers might depend on the patient phenotype (Quinn et al., 2015): In tremor dominant (compared to akinetic rigid) PD patients resting state beta power may decrease during tremor epochs (Bronte-Stewart et al., 2009; Quinn et al., 2015). By a similar token, theta and beta oscillations interact with high-frequency oscillations under physiological (Yanagisawa et al., 2012) as well as pathological (Yang et al., 2014) conditions. Also, quantities assessing the interaction of brain oscillation, e.g., phase amplitude coupling (PAC) might be used as biomarker to represent the amount of symptoms (Beudel and Brown, 2016). Also, activity in the beta band might be relevant for compensatory purposes, as recently shown in a parkinsonian monkey study with sensorimotor rhythm neurofeedback (Philippens et al., 2017).

It might be another potential advantage for clinical applications that the three-stage control of the proposed short-term dosage regimen (Protocol C) could possibly be approximated by scores reflecting the patient's state or the amount symptoms. A simple three-stage rating of the patient's state (bad, medium, and good) might replace the feedback signal-based stages (i), (ii), and (iii). Assessments of the patient's state might be performed in a pause after a CR shot. Depending on the rating, the CR stimulation frequency or intensity of the subsequent CR shot may be varied. In particular, for non-invasive application of CR stimulation a non-invasive assessment of the stimulation effect might straightforwardly be realized.

In realistic biological systems intrinsic (model) parameters typically vary over time. These variations may be of complex dynamical nature (see e.g., Timmer et al., 2000; Yulmetyev et al., 2006). To obtain some indication as to whether Protocol C is robust against low-amplitude intrinsic variations of the neuronal firing rates, we added a low-amplitude term I_var = A · sin(2π · f · t) to the right-hand side of Equation 1a. In the stimulation-free case, I_var causes variations of the neurons' firing rates in the order of ±3% and no qualitative changes of the network dynamics (data not shown). For different frequencies f this type of variation does not significantly affect the long-term desynchronization outcome of Protocol C (f = 0.004, 4, and 20 Hz in Supplementary Figure 1). By the same token, the neuronal firing rates are not significantly altered by the additional periodic force (data not shown).

Note, this is not intended to be a comprehensive study of the impact of periodic forcing of arbitrary frequency on the spontaneous or stimulation-induced dynamics of the model network under consideration. Rather, the slow oscillatory forcing is meant to model slow physiological modulatory processes in an illustrative manner. In the extreme case of f = 0.004 Hz the slow oscillatory modulation acts on the same time scale as a cycle comprising shot and pause and, hence smoothly emulates the step-wise modulation of the CR stimulation frequency in Protocol C.

Conversely, intrinsic variations of sufficient size might naturally mimic variations of the relationship between CR stimulation frequency and intrinsic neuronal firing rates as introduced on purpose in Protocol C. Accordingly, already the purely spaced stimulation without demand-controlled variability (Protocol A) might display some variability of the relationships between intrinsic firing rates and CR stimulation frequency simply due to the intrinsic variability. However, at least with the frequencies 0.004, 4, and 20 Hz in the low-amplitude term I_var = A · sin(2π · f · t) added to the right-hand side of Equation 1a, we were not able to observe any substantial improvement of the desynchronizing outcome of Protocol A (Supplementary Figure 2). However, more physiological patterns of firing rate modulations might have a more significant impact on the stimulation outcome of Protocol A. In future studies typical variations of the signals relevant to a particular pre-clinical or clinical application might be taken into account to further improve desynchronizing short-term dosage regimen. The additional periodic forcing considered here was meant to illustrate the stability of the suggested control approach. However, future studies could also provide a detailed analysis of the interplay of one or more periodic inputs and noise, thereby focusing on stochastic resonance and related phenomena (e.g., Pikovsky and Kurths, 1997; Gammaitoni et al., 1998; Manjarrez et al., 2002; Torres et al., 2011; Bordet et al., 2015; Yu et al., 2016; Guo et al., 2017; Uzuntarla et al., 2017 and references therein). The number of stimulation sites and CR stimulation spatial decay was based on Lysyansky et al. (2011). In accordance to that study, adding more stimulation sites does neither lead to qualitatively different results nor does it improve the stimulation outcome (see Supplementary Figure 3).

The short-term dosage regimen proposed here provides a closed-loop CR stimulation concept that enables to significantly increase the robustness and reliability of the stimulation outcome. Our results motivate to further improve the CR approach by closed loop or feedback-based dosage regimen. Compared to the computationally developed initial concept of demand-controlled CR-induced desynchronization of networks with fixed coupling constants (Tass, 2003a,b), the focus will now be on a feedback-adjusted modulation of synaptic patterns to induce long-lasting therapeutic effects. Currently, clinical proof of concept (phase IIa) is available for deep brain CR stimulation for the therapy of Parkinson's disease (Adamchic et al., 2014) and acoustic CR stimulation for the treatment of chronic subjective tinnitus (Tass et al., 2012a). In addition, promising first in human (phase I) data are available for vibrotactile CR stimulation for the treatment of Parkinson's disease showing pronounced and highly significant sustained therapeutic effects (Syrkin-Nikolau et al., 2018). For the clinical development of these treatments it is mandatory to perform dose-finding studies (phase IIb) to reveal optimal stimulation parameters and dosage regimens, for comparison (see Friedman et al., 2010). The latter are required to get properly prepared for large efficacy (phase III) trials (Friedman et al., 2010). Since CR stimulation modulates complex neuronal dynamics, dose-finding studies are sophisticated, since stimulation parameters as well as dosage patterns have to be chosen appropriately. Selecting appropriate stimulation parameters and dosage regimens by trial and error may neither be effective nor affordable, since it would require a huge number of patients. In contrast, our manuscript illustrates the important role of computational medicine in generating hypotheses for dose-finding studies. Specifically, we show that spacing (i.e., adding pauses in between stimulation epochs) as well as moderate and unspecific parameter variations adapted in the course of the therapy are not sufficient to overcome limitations of CR stimulation. Intriguingly, the combination of both, spacing plus adaptive moderate parameter variation increases the robustness of the stimulation outcome in a significant manner. This computational prediction can immediately be tested in dose-finding studies and, hence, help to optimize the CR therapy, shorten the development time and reduce related costs.

TM, MZ, and PT: Conceived and designed the experiments; TM: Performed the experiments; TM, MZ, and PT: Analyzed the data; TM and MZ: Contributed reagents, materials, and analysis tools; TM, MZ, and PT: Wrote the paper.