Ulrich Parlitz

Stimulated Emission Depletion Live-Cell Super-Resolution Imaging Shows Proliferative Remodeling of T-Tubule Membrane Structures After Myocardial Infarction

Rationale: Transverse tubules (TTs) couple electric surface signals to remote intracellular Ca2+ release units (CRUs). Diffraction-limited imaging studies have proposed loss of TT components as disease mechanism in heart failure (HF). Objectives: Objectives were to develop quantitative super-resolution strategies for live-cell imaging of TT membranes in intact cardiomyocytes and to show that TT structures are progressively remodeled during HF development, causing early CRU dysfunction. Methods and Results: Using stimulated emission depletion (STED) microscopy, we characterized individual TTs with nanometric resolution as direct readout of local membrane morphology 4 and 8 weeks after myocardial infarction (4pMI and 8pMI). Both individual and network TT properties were investigated by quantitative image analysis. The mean area of TT cross sections increased progressively from 4pMI to 8pMI. Unexpectedly, intact TT networks showed differential changes. Longitudinal and oblique TTs were significantly increased at 4pMI, whereas transversal components appeared decreased. Expression of TT-associated proteins junctophilin-2 and caveolin-3 was significantly changed, correlating with network component remodeling. Computational modeling of spatial changes in HF through heterogeneous TT reorganization and RyR2 orphaning (5000 of 20 000 CRUs) uncovered a local mechanism of delayed subcellular Ca2+ release and action potential prolongation. Conclusions: This study introduces STED nanoscopy for live mapping of TT membrane structures. During early HF development, the local TT morphology and associated proteins were significantly altered, leading to differential network remodeling and Ca2+ release dyssynchrony. Our data suggest that TT remodeling during HF development involves proliferative membrane changes, early excitation-contraction uncoupling, and network fracturing.

Phase-resolved analysis of the susceptibility of pinned spiral waves to far-field pacing in a two-dimensional model of excitable media

Life-threatening cardiac arrhythmias are associated with the existence of stable and unstable spiral waves. Termination of such complex spatio-temporal patterns by local control is substantially limited by anchoring of spiral waves at natural heterogeneities. Far-field pacing (FFP) is a new local control strategy that has been shown to be capable of unpinning waves from obstacles. In this article, we investigate in detail the FFP unpinning mechanism for a single rotating wave pinned to a heterogeneity. We identify qualitatively different phase regimes of the rotating wave showing that the concept of vulnerability is important but not sufficient to explain the failure of unpinning in all cases. Specifically, we find that a reduced excitation threshold can lead to the failure of unpinning, even inside the vulnerable window. The critical value of the excitation threshold (below which no unpinning is possible) decreases for higher electric field strengths and larger obstacles. In contrast, for a high excitation threshold, the success of unpinning is determined solely by vulnerability, allowing for a convenient estimation of the unpinning success rate. In some cases, we also observe phase resetting in discontinuous phase intervals of the spiral wave. This effect is important for the application of multiple stimuli in experiments.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Synchronization based system identification of an extended excitable system

A basic state and parameter estimation scheme for an extended excitable system is presented, where time series from a spatial grid of sampling points are used to drive and synchronize corresponding model equations. Model parameters are estimated by minimizing the synchronization error. This estimation scheme is demonstrated using data from generic models of excitable media exhibiting spiral wave dynamics and chaotic spiral break-up that are implemented on a graphics processing unit.

Local observability of state variables and parameters in nonlinear modeling quantified by delay reconstruction

Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using a measured time series. Relevant concepts of this approach are introduced and illustrated for discrete and continuous time systems employing a filtered Hénon map and a Rössler system.

Features of chaotic transients in excitable media governed by spiral and scroll waves

In excitable media, chaotic dynamics governed by spiral or scroll waves is often not persistent but transient. Using extensive simulations employing different mathematical models we identify a specific type-II supertransient by an exponential increase of transient lifetimes with the system size in 2D and an investigation of the dynamics (number and lifetime of spiral waves, Kaplan-Yorke dimension). In 3D, simulations exhibit an increase of transient lifetimes and filament lengths only above a critical thickness. Finally, potential implications for understanding cardiac arrhythmias are discussed.

Modelling far field pacing for terminating spiral waves pinned to ischaemic heterogeneities in cardiac tissue

In cardiac tissue, electrical spiral waves pinned to a heterogeneity can be unpinned (and eventually terminated) using electric far field pulses and recruiting the heterogeneity as a virtual electrode. While for isotropic media the process of unpinning is much better understood, the case of an anisotropic substrate with different conductivities in different directions still needs intensive investigation. To study the impact of anisotropy on the unpinning process, we present numerical simulations based on the bidomain formulation of the phase I of the Luo and Rudy action potential model modified due to the occurrence of acute myocardial ischaemia. Simulating a rotating spiral wave pinned to an ischaemic heterogeneity, we compare the success of sequences of far field pulses in the isotropic and the anisotropic case for spirals still in transient or in steady rotation states. Our results clearly indicate that the range of pacing parameters resulting in successful termination of pinned spiral waves is larger in anisotropic tissue than in an isotropic medium. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

Stabilization of three-dimensional scroll waves and suppression of spatiotemporal chaos by heterogeneities.

Scroll waves in a three-dimensional medium with negative filament tension may break up and display spatiotemporal chaos. The presence of heterogeneities can influence the evolution of the medium, in particular scroll waves may pin to such heterogeneities. We show that as a result the medium may be stabilized by heterogeneities of a suitably chosen geometry. Thin rodlike heterogeneities suppress otherwise developing spatiotemporal chaos and additionally clear out already existing chaotic excitation patterns.

Changes of sleep-stage transitions due to ageing and sleep disorder

Transition patterns between different sleep stages are analysed in terms of probability distributions of symbolic sequences for young and old subjects with and without sleep disorder. Changes of these patterns due to ageing are compared with variations of transition probabilities due to sleep disorder.

Nonlinear system identification employing automatic differentiation

Abstract An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost function and provides exact values of the derivatives. In contrast to numerical differentiation it is not suffering from approximation errors and compared to symbolic differentiation it is more convenient to use, because no closed analytic expressions are required. Furthermore, we demonstrate how to generalize the parameter estimation scheme to delay differential equations, where estimating the delay time requires attention.