Evolution of extrema features reveals optimal stimuli for biological state transitions

Introduction to Focus Issue: Dynamical disease: A translational approach

The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. Since its introduction, this concept has been applied to a number of physiological systems, most notably cardiac, hematological, and neurological. A quarter century after the inaugural meeting on dynamical diseases held in Mont Tremblant, Québec [Bélair et al., Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods.

Falling off a limit cycle using phase-agnostic stimuli: Applications to clinical oscillopathies

For over a century, physiological studies have shown that precisely timed pulses can switch off a biological oscillator. This empiric finding has shaped our mechanistic understanding of how perturbations start, stop, and reset biological oscillators and has led to treatments that suppress pathological oscillations using electrical pulses given within specified therapeutic phase windows. Here, we present evidence, using numerical simulations of models of epileptic seizures and reentrant tachycardia, that the phase window can be opened to the entire cycle using novel complex stimulus waveforms. Our results reveal that the trajectories are displaced by such phase-agnostic stimuli off the oscillator's limit cycle and corralled into a region where oscillation is suppressed, irrespective of the phase at which the stimulus was applied. Our findings suggest the need for broadening theoretical understanding of how complex perturbing waveforms interact with biological oscillators to access their arrhythmic states. In clinical practice, oscillopathies may be treated more effectively with non-traditional stimulus waveforms that obviate the need for phase specificity.

Falling off a limit cycle using phase-agnostic stimuli: Definitions and conceptual framework

Nearly a half-century of biomedical research has revealed methods and mechanisms by which an oscillator with bistable limit cycle kinetics can be stopped using critical stimuli applied at a specific phase. Is it possible to construct a stimulus that stops oscillation regardless of the phase at which the stimulus is applied? Using a radial isochron clock model, we demonstrate the existence of such stimulus waveforms, which can take on highly complex shapes but with a surprisingly simple mechanism of rhythm suppression. The perturbation, initiated at any phase of the limit cycle, first corrals the oscillator to a narrow range of new phases, then drives the oscillator to its phase singularity. We further constructed a library of waveforms having different durations, each achieving phase-agnostic suppression of rhythm but with varying rates of phase corralling prior to amplitude suppression. The optimal stimulus energy to achieve phase-agnostic suppression of rhythm is dependent on the rate of phase corralling and the configuration of the phaseless set. We speculate that these results are generic and suggest the existence of stimulus waveforms that can stop the rhythm of more complex oscillators irrespective of the applied phase.

Optimizing stimulus waveforms for electroceuticals

There has been a growing interest in the use of electrical stimulation as a therapy across diverse medical conditions. Most electroceutical devices use simple waveforms, for example sinusoidal or rectangular biphasic pulses. Clinicians empirically tune the waveform parameters (e.g. amplitude, frequency) without altering the fundamental shape of the stimulus. In this article, we review computational strategies that have been used to optimize the shape of stimulus waveforms in order to improve clinical outcomes, and we discuss potential directions for future exploration.

Optimizing stimulus waveforms for suppressing epileptic activity reveals a counterbalancing mechanism

Electrical stimulation is used to treat drug- resistant epilepsy, and excessive stimulation can lead to adverse effects for patients. In this article, we use an extrema featured stochastic search algorithm to find energy-efficient stimulus waveforms that suppress seizure activity in two different computational models of epilepsy. We infer general principles that may provide insight into future design of energy efficient stimulus for epilepsy treatments.