Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

The relationship between eating behavior and psychological distress among overweight and obese people: is there a role for mindfulness?

This research based on 3 indipendent studies, sought to explore the nature of the relationship between overweight/obesity, eating behaviors and psychological distress; the construct of Mindful eating trough the validation of the Italian adaptation of the Mindful Eating Questionnaire (MEQ); the role of mindfulnessand mindful eating as respectively potential mediator and moderator between overeating behavior (binge eating and emotional overeating) and negative outcomes (psychological distress, body dissatisfaction). All the samples were divided in normal weight, overweight and obese according to BMI categories. STUDY1: In a sample of 691 subjects (69.6% female, mean aged 39.26 years) was found that BMI was not associated with psychological distress, whereas binge eating increases the psychopathological level. BMI and male gender represent negative predictors of psychological distress, but certain types of overeating (i.e., NES/grazing, overeating during or out of meals, and guilt/restraint) result as positive predictors.. STUDY 2 : A sample of 1067 subjects (61.4% female, mean aged 34 years) was analized. The Italian MEQ resulted in a 26-item 4-factor model measuring Disinhibition, Awareness, Distraction, and Emotional response. Internal consistency and test-retest reliability were acceptable MEQ correlated positively with mindfulness (FMI) and it was associated with sociodemographic variables, BMI, meditation. type of exercise and diet. STUDY 3, based on a sample of 502 subjects (68.8% female, mean aged 39.42 years) showed that MEQ and FMI negatively correlated with BES, EOQ, SCL-90-R, and BIAQ. Obese people showed lower level of mindful eating and higher levels of binge eating, emotional overeating, and body dissatisfaction, compared to the other groups Mindfulness resulted to partially mediates the relationship between a) binge eating and psychological distress, b) emotional overeating and psychological distress, c) binge eating and mental well-being, d) emotional overeating and menal well-being. Mindful eating was a moderator only in the relationship between emotional overeating and body dissatisfaction.

Wet and dry model granulates under mechanical load : a confocal microscopy study

Granular matter, also known as bulk solids, consists of discrete particles with sizes between micrometers and meters. They are present in many industrial applications as well as daily life, like in food processing, pharmaceutics or in the oil and mining industry. When handling granular matter the bulk solids are stored, mixed, conveyed or filtered. These techniques are based on observations in macroscopic experiments, i.e. rheological examinations of the bulk properties. Despite the amply investigations of bulk mechanics, the relation between single particle motion and macroscopic behavior is still not well understood. For exploring the microscopic properties on a single particle level, 3D imaging techniques are required.rnThe objective of this work was the investigation of single particle motions in a bulk system in 3D under an external mechanical load, i.e. compression and shear. During the mechanical load the structural and dynamical properties of these systems were examined with confocal microscopy. Therefor new granular model systems in the wet and dry state were designed and prepared. As the particles are solid bodies, their motion is described by six degrees of freedom. To explore their entire motion with all degrees of freedom, a technique to visualize the rotation of spherical micrometer sized particles in 3D was developed. rnOne of the foci during this dissertation was a model system for dry cohesive granular matter. In such systems the particle motion during a compression of the granular matter was investigated. In general the rotation of single particles was the more sensitive parameter compared to the translation. In regions with large structural changes the rotation had an earlier onset than the translation. In granular systems under shear, shear dilatation and shear zone formation were observed. Globally the granular sediments showed a shear behavior, which was known already from classical shear experiments, for example with Jenike cells. Locally the shear zone formation was enhanced, when near the applied load a pre-diluted region existed. In regions with constant volume fraction a mixing between the different particle layers occurred. In particular an exchange of particles between the current flowing region and the non-flowing region was observed. rnThe second focus was on model systems for wet granular matter, where an additional binding liquid is added to the particle suspension. To examine the 3D structure of the binding liquid on the micrometer scale independently from the particles, a second illumination and detection beam path was implemented. In shear and compression experiments of wet clusters and bulk systems completely different dynamics compared to dry cohesive models systems occured. In a Pickering emulsion-like system large structural changes predominantly occurred in the local environment of binding liquid droplets. These large local structural changes were due to an energy interplay between the energy stored in the binding droplet during its deformation and the binding energy of particles at the droplet interface. rnConfocal microscopy in combination with nanoindentation gave new insights into the single particle motions and dynamics of granular systems under a mechanical load. These novel experimental results can help to improve the understanding of the relationship between bulk properties of granular matter, such as volume fraction or yield stress and the dynamics on a single particle level.rnrn

Modeling and simulation of fibrinogen and its adsorption behavior

In this thesis different approaches for the modeling and simulation of the blood protein fibrinogen are presented. The approaches are meant to systematically connect the multiple time and length scales involved in the dynamics of fibrinogen in solution and at inorganic surfaces. The first part of the thesis will cover simulations of fibrinogen on an all atom level. Simulations of the fibrinogen protomer and dimer are performed in explicit solvent to characterize the dynamics of fibrinogen in solution. These simulations reveal an unexpectedly large and fast bending motion that is facilitated by molecular hinges located in the coiled-coil region of fibrinogen. This behavior is characterized by a bending and a dihedral angle and the distribution of these angles is measured. As a consequence of the atomistic detail of the simulations it is possible to illuminate small scale behavior in the binding pockets of fibrinogen that hints at a previously unknown allosteric effect. In a second step atomistic simulations of the fibrinogen protomer are performed at graphite and mica surfaces to investigate initial adsorption stages. These simulations highlight the different adsorption mechanisms at the hydrophobic graphite surface and the charged, hydrophilic mica surface. It is found that the initial adsorption happens in a preferred orientation on mica. Many effects of practical interest involve aggregates of many fibrinogen molecules. To investigate such systems, time and length scales need to be simulated that are not attainable in atomistic simulations. It is therefore necessary to develop lower resolution models of fibrinogen. This is done in the second part of the thesis. First a systematically coarse grained model is derived and parametrized based on the atomistic simulations of the first part. In this model the fibrinogen molecule is represented by 45 beads instead of nearly 31,000 atoms. The intra-molecular interactions of the beads are modeled as a heterogeneous elastic network while inter-molecular interactions are assumed to be a combination of electrostatic and van der Waals interaction. A method is presented that determines the charges assigned to beads by matching the electrostatic potential in the atomistic simulation. Lastly a phenomenological model is developed that represents fibrinogen by five beads connected by rigid rods with two hinges. This model only captures the large scale dynamics in the atomistic simulations but can shed light on experimental observations of fibrinogen conformations at inorganic surfaces.

FaSSIF-C, a Cholesterol containing biorelevant intestinal model medium for development and test of oral drug formulations

Biorelevante Medien sind entwickelt worden, um die Bedingungen im Magen-Darm-Trakt vor und nach der Mahlzeit zu imitieren. Mit FaSSIF und FeSSIF wurden Medien eingeführt, die nicht nur die pH- und Puffer-Kapazität des Dünndarms widerspiegeln, sondern auch Lipid und physiologische Tensid-Arten enthalten. Diese Medien (FaSSIF-V2 und FaSSlFmod6.5) wurden für Bioverfügbarkeitstudien in der Medikamentenentwicklung im Laufe der Jahre kontinuierlich weiterentwickelt. Dennoch sind die auf dem Markt verfügbaren Medien immer noch nicht in der Lage, die realen physiologischen Bedingungen zu simulieren. In der jetzigen Zusammensetzung sind nicht alle Kompetenten enthalten, welche natürlicher Weise im Duodenum vorkommen. Darüber hinaus wird nur eine 1:5 Verdünnung von FeSSIF zu FaSSIF angenommen, die individuelle Wasserzufuhr bei Medikamentengabe wird hierdurch jedoch nur eingeschränkt simuliert, obwohl diese von Patient zu Patient schwanken kann. rnZiel dieser Dissertation war die Verbesserung der Vorhersage der Auflösung und Absorption lipophiler Arzneistoffe durch Simulation der Bedingungen im zweiten Teil des Zwölffingerdarms mit neuen biorelevanten Medien, sowie unter Einwirkung zusätzlicher Detergention als Wirkstoffträger. rnUm den Effekt der Verdünnungsrate und Zeit im Dünndarm zu untersuchen, wurde die Entwicklung der Nanopartikel in der Magen-Darm-Flüssigkeit FaSSIFmod6.5 zu verschiedenen Zeitpunkten und Wassergehalten untersucht. Dafür wurden kinetische Studien an verschieden konzentrierten Modellmedien nach Verdünnungssprung untersucht. Das Modell entspricht der Vermischung der Gallenflüssigkeit mit dem Darminhalt bei variablem Volumen. Die Ergebnisse zeigen, dass Art und Größe der Nanopartikel stark von Verdünnung und Einirkungszeit abhängen. rnrnDie menschliche Darmflüssigkeit enthält Cholesterin, welches in allen früheren Modellmedien fehlt. Daher wurden biokompatible und physiologische Modellflüssigkeiten, FaSSIF-C, entwickelt. Der Cholesteringehalt von FaSSIF - 7C entspricht der Gallenflüssigkeit einer gesunden Frau, FaSSIF - 10C der einer gesunden männlichen Person und FaSSIF - 13C der in einigen Krankheitszuständen. Die intestinale Teilchen-Struktur-Untersuchung mit dynamische Lichtstreuung (DLS) und Neutronen-Kleinwinkelstreuung (SANS) ergab, dass die Korngröße von Vesikeln mit zunehmender Cholesterin-Konzentration abnahm. Zu hohe Cholesterin-Konzentration bewirkte zusätzlich sehr große Partikel, welche vermutlich aus Cholesterin-reichen “Disks“ bestehen. Die Löslichkeiten einiger BCS Klasse II Wirkstoffe (Fenofibrat, Griseofulvin, Carbamazepin, Danazol) in diesen neuen Medien zeigten, dass die Löslichkeit in unterschiedlicher Weise mit der Cholesteringehalt zusammen hing und dieser Effekt selektiv für die Droge war. rnDarüber hinaus wurde die Wirkung von einigen Tensiden auf die kolloidale Struktur und Löslichkeit von Fenofibrat in FaSSIFmod6.5 und FaSSIF -7C untersucht. Struktur und Löslichkeit waren Tensid- und Konzentrations-abhängig. Im Falle von FaSSIFmod6.5 zeigten die Ergebnisse eine dreifache Verzweigung der Lösungswege. Im Bereich mittlerer Tensidkonzentration wurde eine Löslichkeitslücke der Droge zwischen der Zerstörung der Galle-Liposomen und der Bildung von Tensid-reichen Mizellen beobachtet. In FaSSIF - 7C, zerstörten Tenside in höherer Konzentration die Liposomenstruktur trotz der allgemeinen Stabilisierung der Membranen durch Cholesterin. rnDie in dieser Arbeit vorgestellten Ergebnisse ergeben, dass die Anwesenheit von Cholesterin als eine fehlende Komponente der menschlichen Darmflüssigkeit in biorelevanten Medien wichtig ist und dazu beitragen kann, das in vivo Verhalten schwerlöslicher Arzneistoffe im Körper besser vorhersagen zu können. Der Verdünnungsgrad hat einen Einfluss auf die Nanopartikel-Struktur und Tenside beeinflussen die Löslichkeit von Medikamenten in biorelevanten Medien: Dieser Effekt ist sowohl von der Konzentration das Tensids abhängig, als auch dessen Typ.rnrn

A 2-dimensional computational model to analyze the effects of cellular heterogeinity on cardiac pacemaking

The mechanical action of the heart is made possible in response to electrical events that involve the cardiac cells, a property that classifies the heart tissue between the excitable tissues. At the cellular level, the electrical event is the signal that triggers the mechanical contraction, inducing a transient increase in intracellular calcium which, in turn, carries the message of contraction to the contractile proteins of the cell. The primary goal of my project was to implement in CUDA (Compute Unified Device Architecture, an hardware architecture for parallel processing created by NVIDIA) a tissue model of the rabbit sinoatrial node to evaluate the heterogeneity of its structure and how that variability influences the behavior of the cells. In particular, each cell has an intrinsic discharge frequency, thus different from that of every other cell of the tissue and it is interesting to study the process of synchronization of the cells and look at the value of the last discharge frequency if they synchronized.

Tor network forensics and hidden service deanonymization

The cybernetics revolution of the last years improved a lot our lives, having an immediate access to services and a huge amount of information over the Internet. Nowadays the user is increasingly asked to insert his sensitive information on the Internet, leaving its traces everywhere. But there are some categories of people that cannot risk to reveal their identities on the Internet. Even if born to protect U.S. intelligence communications online, nowadays Tor is the most famous low-latency network, that guarantees both anonymity and privacy of its users. The aim of this thesis project is to well understand how the Tor protocol works, not only studying its theory, but also implementing those concepts in practice, having a particular attention for security topics. In order to run a Tor private network, that emulates the real one, a virtual testing environment has been configured. This behavior allows to conduct experiments without putting at risk anonymity and privacy of real users. We used a Tor patch, that stores TLS and circuit keys, to be given as inputs to a Tor dissector for Wireshark, in order to obtain decrypted and decoded traffic. Observing clear traffic allowed us to well check the protocol outline and to have a proof of the format of each cell. Besides, these tools allowed to identify a traffic pattern, used to conduct a traffic correlation attack to passively deanonymize hidden service clients. The attacker, controlling two nodes of the Tor network, is able to link a request for a given hidden server to the client who did it, deanonymizing him. The robustness of the traffic pattern and the statistics, such as the true positive rate, and the false positive rate, of the attack are object of a potential future work.

The influence of infill walls on seismic behavior of a historical building in Shanghai

Seismic assessment and seismic strengthening are the key issues need to be figured out during the process of protection and reusing of historical buildings. In this thesis the seismic behaviors of the hinged steel structure, a typical structure of historical buildings, i.e. hinged steel frames in Shanghai, China, were studied based on experimental investigations and theoretic analysis. How the non-structural members worked with the steel frames was analyzed thoroughly. Firstly, two 1/4 scale hinged steel frames were constructed based on the structural system of Bund 18, a historical building in Shanghai: M1 model without infill walls, M2 model with infill walls, and tested under the horizontal cyclic loads to investigate their seismic behavior. The Shaking Table Test and its results indicated that the seismic behavior of the hinged steel frames could be improved significantly with the help of non-structural members, i.e., surrounding elements outside the hinged steel frames and infilled walls. To specify, the columns are covered with bricks, they consist of I shape formed steel sections and steel plates, which are clenched together. The steel beams are connected to the steel column by steel angle, thus the structure should be considered as a hinged frame. And the infilled wall acted as a compression diagonal strut to withstand the horizontal load, therefore, the seismic capacity and stiffness of the hinged steel frames with infilled walls could be estimated by using the equivalent compression diagonal strut model. A SAP model has been constructed with the objective to perform a dynamic nonlinear analysis. The obtained results were compared with the results obtained from Shaking Table Test. The Test Results have validated that the influence of infill walls on seismic behavior can be estimated by using the equivalent diagonal strut model.

An fMRI study on mental pain and suicidal behavior

Suicide is a poorly understood phenomenon. A clinical model of suicide conceptualizes suicidal behavior as a solution to an unbearable state of mind, experienced as mental pain.

Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

Adsorption behavior of redox-active suppressor additives: Combined electrochemical and STM studies

The redox chemistry and the related surface phase behavior of Safranine (SAF) and Janus Green B (JGB) have been studied by means of cyclic voltammetry in combination with in situ Scanning Tunneling Microscopy using HOPG (Highly Oriented Pyrolytic Graphite) and single crystalline Cu(1 0 0) as model substrates, both revealing different widths of the accessible potential windows. JGB and SAF serve as prototypical heterocyclic suppressor/leveler additives that are used for the metallization of 3D-TSVs (3D Through Silicon Vias) following a classical "leveling" concept. SAF can be considered as the reductive decomposition product of JGB that is formed at the copper/electrolyte interface upon electroplating. Both additives reveal a pronounced pH-dependent redox-chemistry with redox-transitions lying close to or even beyond the anodic limit of the copper potential window. Affected by these redox-processes are in particular the aromatic cores of those heterocycles that can be (quasi)reversibly reduced by a two electron transfer process within the potential window of copper. Therefore we identify the reduced form of those dyes as the active components for the suppressing/leveling effect in copper plating. STM data clearly shows a dye surface phase behavior that is crucially determined by its potential-dependent redox-chemistry. This will be exemplarily discussed for the SAF dye. On chloride-modified Cu(1 0 0) mono-reduced SAF forms a structurally well-defined monolayer of cationic stacking polymers. However, this coupled anion/cation layer reveals only minor suppressing capabilities with respect to the copper dissolution and deposition processes. Complete reduction of the aromatic heterocycle finally leads to the 3D precipitation of hydrophobic reaction products. 3D clusters of this SAF precipitate are discussed as the active structural motif for the suppressing effect of these dyes. (C) 2011 Elsevier Ltd. All rights reserved.

An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

A dedicated animal model for mechanical thrombectomy in acute stroke

BACKGROUND: Recent studies have focused on mechanical thrombectomy as a means to reduce the time required for revascularization and increase the revascularization rate in acute stroke. To date no systematic evaluation has been made of the different mechanical devices in this novel and fast-developing field of endovascular interventions. To facilitate such evaluations, we developed a specific in vivo model for mechanical thrombectomy that allows visualization of dislocation or fragmentation of the thrombus during angiographic manipulation. METHODS: Angiography and embolization with a preformed thrombus was performed in 8 swine. The thrombus was generated by mixing 25 IU bovine thrombin and 10 mL autologous blood. For visualization during angiography, 1 g barium sulfate was added. RESULTS: The preformed thrombus exhibited mechanical stability, reproducibility, and high radiographic absorption, providing excellent visibility during angiography. The setting allowed selective embolization of targeted vessels without thrombus fragmentation. Despite the application of barium sulfate no local or systemic reaction occurred. Histologic evaluation revealed no intimal damage caused by the thrombus or contrast agent washout. CONCLUSION: The model presented here allows selective and reliable thromboembolization of vessels that reproduce the anatomic and hemodynamic situation in acute cerebrovascular stroke. It permits visualization of the thrombus during angiography and intervention, providing unique insight into the behavior of both thrombus and device, which is potentially useful in the development and evaluation of mechanical clot retrieval in acute cerebrovascular stroke.

Behavioral and anatomical abnormalities in a sodium iodate-induced model of retinal pigment epithelium degeneration

We characterized changes in the visual behavior of mice in which a loss of the retinal pigment epithelium (RPE) was experimentally induced with intravenous (i.v.) administration of sodium iodate (NaIO3). We compared and correlated these changes with alterations in neural retinal structure and function. RPE loss was induced in 4-6 week old male C57BL/6 mice with an i.v. injection of 1% NaIO3 at three concentrations: 35, 50, or 70 mg/kg. At 1, 3, 7, 14, 21, and 28 days (d) as well as 6 months post injection (PI) a behavioral test was performed in previously trained mice to evaluate visual function. Eye morphology was then assessed for changes in both the RPE and neural retina. NaIO3-induced RPE degeneration was both dose and PI time dependent. Our low dose showed no effects, while our high dose caused the most damage, as did longer PI times at our intermediate dose. Using the intermediate dose, no changes were detectable in either visual behavior or retinal morphology at 1 d PI. However, at 3 d PI visual behavior became abnormal and patchy RPE cell loss was observed. From 7 d PI onward, changes in retinal morphology and visual behavior became more severe. At 6 months PI, no recovery was seen in any of these measures in mice administered the intermediate dose. These results show that NaIO3 dosage and/or time PI can be varied to produce different, yet permanent deficits in retinal morphology and visual function. Thus, this approach should provide a unique system in which the onset and severity of RPE damage, and its consequences can be manipulated. As such, it should be useful in the assessment of rescue or mitigating effects of retinal or stem cell transplantation on visual function.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.