Modeling of the mechano-chemical behavior of the nuclear pore complex: current research and perspectives

Recent evidence suggests that mechanical deformation of the cell nucleus regulates the nuclear import of the transcriptional activators of genes involved in primary physiological cell responses such as stem cell differentiation. In addition, this nuclear mechanosensing response is de-regulated in pathological states, such as cancer and neurodegeneration. One hypothesis that could greatly advance the field is that the deformation of the nuclear envelope activates nuclear pore complexes through a direct mechanical link. The understanding of this possible mechanism for nuclear pore complex stretch-activation entails studying the mechanical connection of this complex to the nuclear envelope at the nanoscale. The nanomechanics of the nuclear pore complex is thus emerging as a novel research field, bridging nanoscience with nanotechnology. This review examines the frontier of research methodologies that are potentially useful for building a computational model of this interaction. This includes, for example, electron tomography to assess the geometrical features of the nuclear pore complex and nanoindentation to estimate its mechanical properties and that of the nuclear envelope. In order to summarize the state-of-the-art and perspectives in the field of NPC nanomechanics, this review covers highly interdisciplinary experimental and theoretical research methodologies pertaining to the fields of physics, chemistry, biology, materials and mechanics

New Methodologies for the Development and Validation of Electrophysiological Models

De acuerdo a los datos de la Organización Mundial de la Salud, se estima que 17,7 millones de personas murieron de enfermedades cardiacas en 2015, lo que supone el 31% de las muertes, haciendo de estas patologías la primera causa de muerte en el mundo. El corazón es un sistema complejo que trabaja gracias a la interacción de un gran número de elementos en diferentes escalas espaciales y temporales. La función principal del corazón es bombear sangre en todo el cuerpo, siendo esta acción mecánica activada por la estimulación eléctrica. La aparición de problemas en el funcionamiento eléctrico o mecánico del corazón en cualquiera de las escalas involucradas, temporal o espacial, puede dar lugar a un mal funcionamiento cardiaco. El modelado matemático y la simulación de la actividad eléctrica del corazón (denominada electrofisiología cardiaca) y el procesado de señales bioeléctricas proporcionan un marco ideal para unir la información clínica y los estudios experimentales con la comprensión de los mecanismos que subyacen a estos problemas. Debido al gran número de factores que se deben tener en cuenta a la hora de desarrollar y validar un modelo computacional de electrofisiología cardiaca, asi como las complejas interacciones que existen entre ellos, hacen que nuevas metodologías que facilitan la concepción, la actualización y la validación de nuevos modelos sean de gran valor. Estas metodologías pueden enfocarse sea en la definición de las compuertas iónicas de los modelos, como en la propagación del impulso eléctrico en modelos multiescala. Esta tesis pretende mejorar el conocimiento existente sobre electrofisiología cardiaca proponiendo nuevas técnicas para desarrollar y validar modelos computacionales cardiacos, a través de la evaluación de los efectos de los eventos modelados mediante la consideración de las interacciones entre los diferentes componentes del modelo y la simulación de un rango de escalas espacio-temporales.En el capítulo 2, se introdujo un nuevo paradigma para desarrollar un nuevo modelo de potencial de acción de cardiomiocito humano, el modelo CRLP, partiendo de un modelo previamente publicado e incorporando nuevas mediciones experimentales de corrientes de potasio y reformulando la corriente de calcio tipo L. El paradigma introducido se basó en el análisis de la capacidad del modelo para replicar un conjunto de marcadores electrofisiológicos bien establecidos y en un análisis de sensibilidad de esos marcadores a las variaciones en los parámetros del modelo. Una de las ventajas del paradigma propuesto fue la posibilidad de identificar parámetros del modelo que no dependen directamente de las mediciones individuales de corrientes o concentraciones y que comúnmente se establecen ad hoc. El modelo CRLP se validó y se midió su rendimiento en la capacidad para predecir marcadores relacionados con la arritmia ventricular en comparación con el modelo cellular en el que se había basado.En el capítulo 3, se actualizó el modelo CRLP desarrollado en el capítulo 2 para introducir la formulación de la dinámica de potasio intracelular ([K+]i). Esta es una característica importante para la investigación de arritmias ventriculares que surgen en condiciones de hiperpotasemia, uno de los componentes de la isquemia de miocardio. La introducción directa de la dinámica de [K+]i en el modelo generó un desequilibrio en las corrientes de potasio que condugeron a una deriva en [K+]i. Para corregir tal desequilibrio, se propuso un algoritmo de optimización que permitía estimar las conductancias de las corrientes iónicas del modelo CRLP al tiempo que garantizaba valores fisiológicamente plausibles de una selección de propiedades electrofisiológicas, algunas de ellas muy relevantes en el estudio de arritmias ventriculares.Como se mencionó anteriormente, al proponer un nuevo modelo o al actualizar un modelo existente, la coherencia entre los datos simulados y experimentales debe verificarse considerando todos los efectos y escalas involucradas. Cuanto mejor se reproduzcan las condiciones experimentales en las simulaciones, más robusto será el proceso de desarrollo y validación del modelo. En el capítulo 4, se propuso la simulación de protocolos experimentales in silico para analizar cómo las interacciones entre los componentes del modelo afectan el desarrollo y la validación de los modelos matemáticos de canales iónicos; y cómo la propagación afecta los marcadores basados en el potencial de acción cuando son simulados en células aisladas o en preparaciones tisulares, identificando cómo contribuye cada corriente iónica en cada caso. y con los modelos de células ventriculares humanas más recientes publicados en laliteratura.El capítulo 7 resume las principales conclusiones de la tesis y presenta nuevas líneas de investigación que podrían emprenderse en futuros estudios. En conclusión, diferentes técnicas para mejorar el desarrollo y la validación de modelos electrofisiológicos cardíacos han sido propuestos y analizados en esta tesis. Basándose en el aumento de potencia computacional, se han considerado nuevas estrategias para reducir el número de hipótesis y/o supuestos al construir un modelo de potencial de acción de cardiomiocito ventricular. La aplicación de un algoritmo de optimización junto con la simulación in silico de los protocolos experimentales han ayudado a encontrar un modelo que represente mejor los resultados experimentales de los marcadores electrofisiológicos de riesgo arrítmico.El modelo CRLP, desarrollado en el capítulo 2 y actualizado en el capítulo 3, presentaba una forma más bien atípica al final de la fase de despolarización del potencial de acción (fase 1). La simulación in silico de los protocolos experimentales descritos en el capítulo 4 y la metodología de optimización presentada en el capítulo 3 se utilizaron para mejorar la forma del potencial de acción al tiempo que validaba el modelo ajustado a escalas iónicas, celulares y de tejido.En el capítulo 6 se integraron todas las formulaciones iniciales y actualizaciones subsiguientes del modelo CRLP propuestas en los capítulos anteriores y se reajustaron las conductancias iónicas del modelo para mejorar el comportamiento del modelo con respecto a medidas electrofisiológicas experimentales. Todas las metodologías introducidas a lo largo de la tesis se utilizaron para obtener un nuevo modelo de potencial de acción ventricular humano. Para la validación del modelo, se consideró un rango de datos experimentales disponibles a diferentes escalas y destinados a evaluar diferentes propiedades electrofisiológicas. Las condiciones subyacentes a cada uno de los estudios experimentales se replicaron tan fielmente como fue posible. Los resultados simulados con la versión final del modelo CRLP se compararon en todos los casos con todas las evidencias experimentales disponiblesAccording to data from the World Health Organization (WHO), 17.7 million people were estimated to have died of cardiovascular diseases (CVDs) in 2015. This represents 31 of all global deaths, making CVDs the leading cause of death worldwide. The heart is a complex system that works due to the interaction of a large number of elements at different temporal and spatial scales. The main function of the heart is to pump blood throughout the body, with this mechanical action being triggered by electrical impulses. Issues arising in the electrical or mechanical actions of the heart at any of the involved temporal and spatial scales can lead to cardiac malfunctioning. Mathematical modeling and simulation of the heart's electrical activity (so-called cardiac electrophysiology) combined with signal processing of bioelectrical signals provide an ideal framework to join the information from clinical and experimental studies with the understanding of the mechanisms underlying them. Due to the high number of factors involved in the development and validation of cardiac computational electrophysiological models and the intricate interrelationships between them, novel methodologies that help to control the design, update and validation of new models become of great advantage. These methodologies can target from the definition of ionic gating in the simulated cells to the propagation of the electrical impulse in multi-scale models. This thesis aims to improve the existing knowledge on heart's electrophysiology by proposing novel techniques to develop and validate cardiac computational models while accounting for the interactions between model components and including simulations of a range of spatio-temporal scales. In chapter 2, a new paradigm was introduced to develop a novel human ventricular cell model, the CRLP model, by departing from a previously published model, the Grandi-Pasqualini-Bers model (Grandi et al., 2009). Novel experimental measurements of potassium currents were incorporated and the L-type calcium current was reformulated. The introduced paradigm was based on the analysis of the model's ability to replicate a set of well-established electrophysiological markers and on a sensitivity analysis of those markers to variations in model parameters (Romero et al., 2008). A major advantage of the proposed paradigm was the possibility to identify model parameter values that do not directly depend on individual current measurements or concentrations, which are commonly set in an ad hoc manner. The developed CRLP model was validated and its improved capacity to investigate arrhythmia-related properties, as compared to the cell model it was based on, was corroborated. In chapter 3, the CRLP model developed in chapter 2 was updated to introduce the formulation of intracellular potassium ([K+]i) dynamics. This is an important characteristic for investigation of ventricular arrhythmias arising under conditions of hyperkalemia, one of the components of myocardial ischemia (Coronel et al. 1988). Direct introduction of [K+]i dynamics into the model generated an imbalance in the potassium currents leading to a drift in [K+]i. To correct for such an imbalance, an optimization framework was proposed that allowed estimating the ionic current conductances of the CRLP model while guaranteeing physiologically plausible values of selected electrophysiological properties, many of them highly relevant for investigation of ventricular arrhythmias. As mentioned above, when proposing a new model, or when updating an existing model, consistency between simulated and experimental data should be verified by considering all involved effects and scales. The closer the experimental conditions are reproduced in the computer simulations, the more robust the process of model development and validation can be. In chapter 4, in silico simulation of experimental protocols was proposed to analyze: how interactions between model components affect the development and validation of mathematical ion channel models; and how propagation affects action potential (AP)-based markers simulated in isolated cells and in tissue preparations, with identification of the ionic contributors in each case. The CRLP model, developed in chapter 2 and updated in chapter 3, presented a rather atypical shape at the end of the depolarization phase of the AP (phase 1). In chapter 5, the in silico simulations of experimental protocols described in chapter and the optimization methodology introduced in chapter 3 were used to improve the AP shape, while validating the adjusted model at ionic, cell and tissue scales. In chapter 6, all the initial formulations and subsequent updates of the CRLP model proposed in previous chapters were integrated and the ionic conductances of the integrated model were readjusted to improve replication of experimental electrophysiological measures. All the methodologies introduced throughout the thesis were thus used to build a novel human ventricular AP model. For model validation, a range of available experimental data at different scales targetting different electrophysiological properties was considered. Conditions underlying each of the experimental studies were replicated as faithfully as possible. Results simulated with the final version of the CRLP model were in all cases compared with all available experimental evidences and with the most recent human ventricular cell models published in the literature. Chapter 7, summarizes the main conclusions of the thesis and presents new lines of research that could be undertaken in future studies. <br /

A detailed methodology to model the Non Contact Tonometry: a Fluid Structure Interaction study

Understanding the corneal mechanical properties has great importance in the study of corneal pathologies and the prediction of refractive surgery outcomes. Non-Contact Tonometry (NCT) is a non-invasive diagnostic tool intended to characterize the corneal tissue response in vivo by applying a defined air-pulse. The biomarkers inferred from this test can only be considered as indicators of the global biomechanical behaviour rather than the intrinsic biomechanical properties of the corneal tissue. A possibility to isolate the mechanical response of the corneal tissue is the use of an inverse finite element method, which is based on accurate and reliable modelling. Since a detailed methodology is still missing in the literature, this paper aims to construct a high-fidelity finite-element model of an idealized 3D eye for in silico NCT. A fluid-structure interaction (FSI) simulation is developed to virtually apply a defined air-pulse to a 3D idealized eye model comprising cornea, limbus, sclera, lens and humors. Then, a sensitivity analysis is performed to examine the influence of the intraocular pressure (IOP) and the structural material parameters on three biomarkers associated with corneal deformation. The analysis reveals the requirements for the in silico study linked to the correct reproduction of three main aspects: the air pressure over the cornea, the biomechanical properties of the tissues, and the IOP. The adoption of an FSI simulation is crucial to capture the correct air pressure profile over the cornea as a consequence of the air-jet. Regarding the parts of the eye, an anisotropic material should be used for the cornea. An important component is the sclera: the stiffer the sclera, the lower the corneal deformation due to the air-puff. Finally, the fluid-like behavior of the humors should be considered in order to account for the correct variation of the IOP during the test which will, otherwise, remain constant. The development of a strong FSI tool amenable to model coupled structures and fluids provides the basis to find the biomechanical properties of the corneal tissue in vivo

On the need of a scale-dependent material characterization to describe the mechanical behavior of 3D printed Ti6Al4V custom prostheses using finite element models

Additive manufacturing is widely used in the orthopaedic industry for the high freedom and flexibility in the design and production of personalized custom implants made of Ti6Al4V. Within this context, finite element modeling of 3D printed prostheses is a robust tool both to guide the design phase and to support clinical eval-uations, possibly virtually describing the in-vivo behavior of the implant. Given realistic scenarios, a suitable description of the overall implant's mechanical behavior is unavoidable. Considering typical custom prostheses' designs (i.e. acetabular and hemipelvis implants), complex designs involving solid and/or trabeculated parts, and material distribution at different scales hinder a high-fidelity modeling of the prostheses.Moreover, uncertainties in the production and in the material characterization of small parts approaching the accuracy limit of the additive manufacturing technology still exist.While recent works suggest that the mechanical properties of thin 3D-printed parts may be peculiarly affected by specific processing parameters (i.e. powder grain size, printing orientation, samples' thickness) as compared to conventional Ti6Al4V alloy, the current numerical models make gross simplifications in describing the complex material behavior of each part at different scales.The present study focuses on two patient-specific acetabular and hemipelvis prostheses, with the aim of experimentally characterizing and numerically describing the dependency of the mechanical behavior of 3D printed parts on their peculiar scale, therefore, overcoming one major limitation of current numerical models. Coupling experimental activities with finite element analyses, the authors initially characterized 3D printed Ti6Al4V dog-bone samples at different scales, representative of the main material components of the investigated prostheses. Afterwards, the authors implemented the characterized material behaviors into finite element models to compare the implications of adopting scale-dependent vs. conventional scaleindependent approaches in predicting the experimental mechanical behavior of the prostheses in terms of their overall stiffness and the local strain distribution. The material characterization results highlighted the need for a scale-dependent reduction of the elastic modulus for thin samples compared to the conventional Ti6Al4V, which is fundamental to properly describe the overall stiffness and local strain distribution on the prostheses.The presented works demonstrate how an appropriate material characterization and a scale-dependent ma-terial description is needed to develop reliable FE models of 3D printed implants characterized by a complex material distribution at different scales

Validation and Verification of High-Fidelity Simulations of Thoracic Stent-Graft Implantation

Thoracic Endovascular Aortic Repair (TEVAR) is the preferred treatment option for thoracic aortic pathologies and consists of inserting a self-expandable stent-graft into the pathological region to restore the lumen. Computational models play a significant role in procedural planning and must be reliable. For this reason, in this work, high-fidelity Finite Element (FE) simulations are developed to model thoracic stent-grafts. Experimental crimp/release tests are performed to calibrate stent-grafts material parameters. Stent pre-stress is included in the stent-graft model. A new methodology for replicating device insertion and deployment with explicit FE simulations is proposed. To validate this simulation, the stent-graft is experimentally released into a 3D rigid aortic phantom with physiological anatomy and inspected in a computed tomography (CT) scan at different time points during deployment with an ad-hoc set-up. A verification analysis of the adopted modeling features compared to the literature is performed. With the proposed methodology the error with respect to the CT is on average 0.92 +/- 0.64%, while it is higher when literature models are adopted (on average 4.77 +/- 1.83%). The presented FE tool is versatile and customizable for different commercial devices and applicable to patient-specific analyses

A simplified mesoscale 3D model for characterizing fibrinolysis under flow conditions

One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient’s bloodstream, which breaks down the thrombi’s fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or embolism that can be fatal. Improvement in patient management drastically reduced these risks, and patients who benefited from thrombolysis soon after the onset of the stroke have a significantly better 3-month prognosis, but treatment success is highly variable. The causes of this variability remain unclear, and it is likely that some fundamental aspects still require thorough investigations. For that reason, we conducted in vitro flow-driven fibrinolysis experiments to study pure fibrin thrombi breakdown in controlled conditions and observed that the lysis front evolved non-linearly in time. To understand these results, we developed an analytical 1D lysis model in which the thrombus is considered a porous medium. The lytic cascade is reduced to a second-order reaction involving fibrin and a surrogate pro-fibrinolytic agent. The model was able to reproduce the observed lysis evolution under the assumptions of constant fluid velocity and lysis occurring only at the front. For adding complexity, such as clot heterogeneity or complex flow conditions, we propose a 3-dimensional mesoscopic numerical model of blood flow and fibrinolysis, which validates the analytical model’s results. Such a numerical model could help us better understand the spatial evolution of the thrombi breakdown, extract the most relevant physiological parameters to lysis efficiency, and possibly explain the failure of the clinical treatment. These findings suggest that even though real-world fibrinolysis is a complex biological process, a simplified model can recover the main features of lysis evolution.</p

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study

Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world. Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231. Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001). Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication

Cellular heterogeneity and repolarisation across the atria: an in silico study

Mechanisms of atrial fibrillation and the susceptibility to reentries can be impacted by the repolarization across the atria. Studies into atrial fibrillation ignore cell-to-cell heterogeneity due to electrotonic coupling. Recent studies show that cellular variability may have a larger impact on electrophysiological behaviour than assumed. This paper aims to determine the impact of cellular heterogeneity on the repolarization phase across the AF remodelled atria. Using a population of models approach, 10 anatomically identical atrial models were created to include cellular heterogeneity. Atrial models were compared with an equivalent homogenous model. Activation, APD90, and repolarization maps were used to compare models. The impact of electrotonic coupling in the tissue was determined through a comparison of RMP, APD20, APD50, APD90, and triangulation between regional atrial tissue and the single cell populations. After calibration, cellular heterogeneity does not impact atrial depolarization. Repolarization patterns were significantly impacted by cellular heterogeneity, with the APD90 across the LA increasing due to heterogeneity and the reverse occurring in the RA. Electrotonic coupling caused a reduction in variability across all biomarkers but did not fully remove variability. Electrotonic coupling resulted in an increase in APD20 and APD50, and reduced triangulation compared to isolated cell populations. Heterogeneity also caused a reduction in triangulation compared with regionally homogeneous atria