Left atrial fibrosis is thought to contribute to the manifestation of atrial fibrillation (AF). Late Gadolinium enhancement (LGE) MRI has the potential to image regions of low perfusion, which can be related to fibrosis. We show that a simulation with a patient-specific model including left atrial regional fibrosis derived from LGE-MRI reproduces local activation in the left atrium more precisely than the regular simulation without fibrosis. AF simulations showed a spontaneous termination of the arrhythmia in the absence of fibrosis and a stable rotor center in the presence of fibrosis. The methodology may provide a tool for a deeper understanding of the mechanisms maintaining AF and eventually also for the planning of substrate-guided ablation procedures in the future.
Atrial fibrillation (AF) is the most common cardiac arrhythmia, and the total number of AF patients is constantly increasing. The mechanisms leading to and sustaining AF are not completely understood yet. Heterogeneities in atrial electrophysiology seem to play an important role in this context. Although some heterogeneities have been used in in-silico human atrial modeling studies, they have not been thoroughly investigated. In this study, the original electrophysiological (EP) models of Courtemanche et al., Nygren et al. and Maleckar et al. were adjusted to reproduce action potentials in 13 atrial regions. The parameter sets were validated against experimental action potential duration data and ECG data from patients with AV block. The use of the heterogeneous EP model led to a more synchronized repolarization sequence in a variety of 3D atrial anatomical models. Combination of the heterogeneous EP model with a model of persistent AF-remodeled electrophysiology led to a drastic change in cell electrophysiology. Simulated Ta-waves were significantly shorter under the remodeling. The heterogeneities in cell electrophysiology explain the previously observed Ta-wave effects. The results mark an important step toward the reliable simulation of the atrial repolarization sequence, give a deeper understanding of the mechanism of atrial repolarization and enable further clinical investigations.
Computational atrial models aid the understanding of pathological mechanisms and therapeutic measures in basic research. The use of biophysical models in a clinical environment requires methods to personalize the anatomy and electrophysiology (EP). Strategies for the automation of model generation and for evaluation are needed. In this manuscript, the current efforts of clinical atrial modeling in the euHeart project are summarized within the context of recent publications in this field. Model-based segmentation methods allow for the automatic generation of ready-to-simulate patient-specific anatomical models. EP models can be adapted to patient groups based on a-priori knowledge, and to the individual without significant further data acquisition. ECG and intracardiac data build the basis for excitation personalization. Information from late enhancement (LE) MRI can be used to evaluate the success of radio-frequency ablation (RFA) procedures and interactive virtual atria pave the way for RFA planning. Atrial modeling is currently in a transition from the sole use in basic research to future clinical applications. The proposed methods build the framework for model-based diagnosis and therapy evaluation and planning. Complex models allow to understand biophysical mechanisms and enable the development of simplified models for clinical applications.
Multiscale cardiac modeling has made great advances over the last decade. Highly detailed atrial models were created and used for the investigation of initiation and perpetuation of atrial fibrillation. The next challenge is the use of personalized atrial models in clinical practice. In this study, a framework of simple and robust tools is presented, which enables the generation and validation of patient-specific anatomical and electrophysiological atrial models. Introduction of rule-based atrial fiber orientation produced a realistic excitation sequence and a better correlation to the measured electrocardiograms. Personalization of the global conduction velocity lead to a precise match of the measured P-wave duration. The use of a virtual cohort of nine patient and volunteer models averaged out possible model-specific errors. Intra-atrial excitation conduction was personalized manually from left atrial local activation time maps. Inclusion of LE-MRI data into the simulations revealed possible gaps in ablation lesions. A fast marching level set approach to compute atrial depolarization was extended to incorporate anisotropy and conduction velocity heterogeneities and reproduced the monodomain solution. The presented chain of tools is an important step towards the use of atrial models for the patient-specific AF diagnosis and ablation therapy planing.
BACKGROUND: The prevalence of atrial fibrillation is increased in patients with end-stage renal disease. Previous studies suggested that extracellular electrolyte alterations caused by hemodialysis (HD) therapy could be proarrhythmic. METHODS: Multiscale models were used for a consequent analysis of the effects of extracellular ion concentration changes on atrial electrophysiology. Simulations were based on measured electrolyte concentrations from patients with end-stage renal disease. RESULTS: Simulated conduction velocity and effective refractory period are decreased at the end of an HD session, with potassium having the strongest influence. P-wave is prolonged in patients undergoing HD therapy in the simulation as in measurements. CONCLUSIONS: Electrolyte concentration alterations impact atrial electrophysiology from the action potential level to the P-wave and can be proarrhythmic, especially because of induced hypokalemia. Analysis of blood electrolytes enables patient-specific electrophysiology modeling. We are providing a tool to investigate atrial arrhythmias associated with HD therapy, which, in the future, can be used to prevent such complications.
AIMS: P-wave morphology correlates with the risk for atrial fibrillation (AF). Left atrial (LA) enlargement could explain both the higher risk for AF and higher P-wave terminal force (PTF) in lead V1. However, PTF-V1 has been shown to correlate poorly with LA size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IAC), which both show tremendous variability. METHODS AND RESULTS: Atrial excitation was triggered from seven different EAS in a cohort of eight anatomically personalized computational models. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed and separated by left and right atrial contributions. Mid-septal EAS yielded the highest PTF-V1. More anterior/superior and more inferior EAS yielded lower absolute PTF-V1 values deviating by a factor of up to 2.0 for adjacent EAS. Earliest right-to-left activation was conducted via Bachmann's Bundle (BB) for anterior/superior EAS and shifted towards posterior IACs for more inferior EAS. Non-conducting posterior IACs increased PTF-V1 by up to 150% compared to intact posterior IACs for inferior EAS. LA contribution to the P-wave integral was 24% on average. CONCLUSION: The electrical contributor's site of earliest activation and intactness of posterior IACs affect PTF-V1 significantly by changing LA breakthrough sites independent from LA size. This should be considered for interpretation of electrocardiographical signs of LA abnormality and LA enlargement.
ECG imaging is an emerging technology for the reconstruction of cardiac electric activity from non-invasively measured body surface potential maps. In this case report, we present the first evaluation of transmurally imaged activation times against endocardially reconstructed isochrones for a case of sustained monomorphic ventricular tachycardia (VT). Computer models of the thorax and whole heart were produced from MR images. A recently published approach was applied to facilitate electrode localization in the catheter laboratory, which allows for the acquisition of body surface potential maps while performing non-contact mapping for the reconstruction of local activation times. ECG imaging was then realized using Tikhonov regularization with spatio-temporal smoothing as proposed by Huiskamp and Greensite and further with the spline-based approach by Erem et al. Activation times were computed from transmurally reconstructed transmembrane voltages. The results showed good qualitative agreement between the non-invasively and invasively reconstructed activation times. Also, low amplitudes in the imaged transmembrane voltages were found to correlate with volumes of scar and grey zone in delayed gadolinium enhancement cardiac MR. The study underlines the ability of ECG imaging to produce activation times of ventricular electric activity-and to represent effects of scar tissue in the imaged transmembrane voltages.
The fiber orientation in the atria has a significant contribution to the electrophysiologic behavior of the heart and to the genesis of arrhythmia. Atrial fiber orientation has a direct effect on excitation propagation, activation patterns and the P-wave. We present a rule-based algorithm that works robustly on different volumetric meshes composed of either isotropic hexahedra or arbitrary tetrahedra as well as on 3-dimensional triangular surface meshes in patient-specific geometric models. This method fosters the understanding of general pro-arrhythmic mechanisms and enhances patient-specific modeling approaches.
Numerical and patient-specific models of the human atrial anatomy and electrophysiology have a high potential to enhance our knowledge regarding pathological conditions and to increase the outcome of diagnosis and therapy. This chapter briefly describes the current state of the art in modeling of generalized human atria. Furthermore, the chapter demonstrates ways to personalize human atrial anatomy and electrophysiology based on a variety of measurement data from, e.g. late enhancement magnetic resonance imaging (MRI), patch clamp technique, intracardiac electrograms and body surface potential maps. Wherever patient data cannot be collected, patient-group specific behavior can be integrated. Some examples of the personalization process are described and the validation process is discussed together with future options for personalization, validation and application.
Atrial arrhythmias are frequently treated using catheter ablation during electrophysiological (EP) studies. However, success rates are only moderate and could be improved with the help of personalized simulation models of the atria. In this work, we present a workflow to generate and validate personalized EP simulation models based on routine clinical computed tomography (CT) scans and intracardiac electrograms. From four patient data sets, we created anatomical models from angiographic CT data with an automatic segmentation algorithm. From clinical intracardiac catheter recordings, individual conduction velocities were calculated. In these subject-specific EP models, we simulated different pacing maneuvers and measurements with circular mapping catheters that were applied in the respective patients. This way, normal sinus rhythm and pacing from a coronary sinus catheter were simulated. Wave directions and conduction velocities were quantitatively analyzed in both clinical measurements and simulated data and were compared. On average, the overall difference of wave directions was 15° (8%), and the difference of conduction velocities was 16 cm/s (17%). The method is based on routine clinical measurements and is thus easy to integrate into clinical practice. In the long run, such personalized simulations could therefore assist treatment planning and increase success rates for atrial arrhythmias.
This review article gives a comprehensive survey of the progress made in computa- tional modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple peanut-like structures to very detailed models including atrial wall and fiber di- rection. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.
The loss of cardiac pump function accounts for a significant increase in both mortality and morbidity in Western society, where there is currently a one in four lifetime risk, and costs associated with acute and long-term hospital treatments are accelerating. The significance of cardiac disease has motivated the application of state-of-the-art clinical imaging techniques and functional signal analysis to aid diagnosis and clinical planning. Measurements of cardiac function currently provide high-resolution datasets for characterizing cardiac patients. However, the clinical practice of using population-based metrics derived from separate image or signal-based datasets often indicates contradictory treatments plans owing to inter-individual variability in pathophysiology. To address this issue, the goal of our work, demonstrated in this study through four specific clinical applications, is to integrate multiple types of functional data into a consistent framework using multi-scale computational modelling.
Conduction velocity (CV) and CV restitution are important substrate parameters for understanding atrial arrhythmias. The aim of this work is to (i) present a simple but feasible method to measure CV restitution in-vivo using standard circular catheters, and (ii) validate its feasibility with data measured during incremental pacing. From five patients undergoing catheter ablation, we analyzed 8 datasets from sinus rhythm and incremental pacing sequences. Every wavefront was measured with a circular catheter and the electrograms were analyzed with a cosine-fit method that calculated the local CV. For each pacing cycle length, the mean local CV was determined. Furthermore, changes in global CV were estimated from the time delay between pacing stimulus and wavefront arrival. Comparing local and global CV between pacing at 500 and 300 ms, we found significant changes in 7 of 8 pacing sequences. On average, local CV decreased by 2015% and global CV by 1713%. The method allows for in-vivo measurements of absolute CV and CV restitution during standard clinical procedures. Such data may provide valuable insights into mechanisms of atrial arrhythmias. This is important both for improving cardiac models and also for clinical applications, such as characterizing arrhythmogenic substrates during sinus rhythm.
Deep hypothermic circulatory arrest is necessary for some types of cardiac and aortic surgery. Perfusion of the brain can be maintained using a heart-lung machine and unilateral antegrade cerebral perfusion (ACP). Cooling rates during extracorporeal circulation depend on local perfusion. A core temperature of 24-25 degrees C is aimed at to extend ischemic tolerance of tissues. Information on cerebral perfusion and temperature is important for the safety of patients but hardly accessible to measurement. A combined simulation model of haemodynamics and temperature is presented in this paper. The haemodynamics model employs the transmission line approach and integrates the Circle of Willis. This allows for parametrization of individual aberrations. Simulation results of cerebral perfusion are shown for two configurations of the Circle of Willis. The temperature model provides spatial information on temperature fields. It considers heat transfer in the various tissues retrieving data of local tissue perfusion from the haemodynamics model. The combined model is evaluated by retrospective simulation of two aortic operations.
Simulations of the electrophysiological behavior of the heart improve the comprehension of the mechanisms of the cardiovascular system. Furthermore, the mathematical modeling will support diagnosis and therapy of patients suffering from heart diseases. In this paper, the chain of modeling of the electrical function in the heart is described. The components are explained briefly, namely modeling of cardiac geometry, reconstructing the cardiac electrophysiology and excitation propagation. Additionally, the mathematical methods allowing to implement and solve these models are outlined. The three recently more investigated cases atrial fibrillation, ischemia and long-QT syndrome are described and show how cardiac modeling can support cardiologists in answering their open questions.
In open heart surgery the patient is connected to a heart-lung machine which pumps and oxygenizes the blood. The body core temperature is reduced by cooling the blood in a heat exchanger to reduce oxygen consumption of the tissues and so protect organs from hypoxia. Monitoring of vital parameters is crucial for safety of the patient. However, only little information is available from direct measurement. Models of haemodynamics and heat exchange in the human body are presented in this paper which provide the perfusionist with detailed data on blood flow and temperature in regions of the body which cannot be accessed by measurement devices. Simulation is performed on a real-time hardware platform which receives measured signals from the heart-lung machine via a serial interface.
A modular multichannel SQUID-system, in which every single channel can be optimized or replaced individually, is presented. The DC-SQUIDs based on the materials NbN/MgO are prepared by thin film technology and show noise values below 10μΦ0/√Hz. A simplified way of coupling the modulation and feedback current directly to the coupling coil is realized The complete SQUID module including the superconducting shield was miniaturized down to a diameter of 5mm. The gradiometers are wire wound and an as made balancing better than 10−3 is achieved. The cryogenic system was optimized with respect to low vibrations and low helium boil off rate. Simple conductive paint with precisely adjusted surface resistivity is used for RF-shielding. The complete SQUID-electronic of one channel has been realized on one single board and uses a new bias modulation scheme to completely suppress intrinsic 1/f noise. The noise level of the complete system is below 10fT/√Hz. Biomagnetic measurements of the human heart and brain are presented. Single current dipole reconstructions and current density imaging techniques can be used to find the underlying sources. Using a special coil positioning system an overlay of the functional current images with morphological MR-images can be carried out.
Current sources in the human body can be localized by measuring the biomagnetic fields with multichannel SQUID systems. Important system aspects are the noise level, the ambient field suppression, the dynamic range, the reliability, the number of channels, and the arrangement of gradiometers. From the users point of view the most important quality factor is the accuracy with which a current dipole can be localized. A test procedure is proposed to determine the localization power of the system. A 31-channel-SQUID system is presented together with the results of the test. The crucial parts of the system determining the accuracy are pointed out.
O. Dössel, B. David, M. Fuchs, J. Krüger, W. H. Kullmann, and K. M. Ludeke. A modular approach to multichannel magnetometry. In Clinical Physics and Physiological Measurement : an Official Journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics, vol. 12 Suppl B, pp. 75-79, 1991
A 19-channel SQUID system for biomagnetic measurements has been developed. This system differs from standard instruments in its modular approach. Various gradiometers can be coupled to the SQUIDs, the cryogenic system allows the exchange of single channels and the electronics is based on a cassette system. Problems with thermal insulation, vibrations of the gradiometers and tilted gradiometer geometries are discussed and solutions are presented.
Book Chapters (3)
G. Seemann, M. W. Krueger, and M. Wilhelms. Elektrophysiologische Modellierung und Virtualisierung für die Kardiologie - Methoden und potenzielle Anwendungen. In Der virtuelle Patient, Health Academy, pp. 98-116, 2012
Simulationen des elektrophysiologischen Verhaltens des Herzens fördern das Verständnis über die Mechanismen innerhalb des Herz-Kreislauf-Systems. Darüber hinaus werden diese mathematischen Modelle die Diagnose und Therapie von Patienten, die unter Herzerkrankungen leiden, unterstützen. In dieser Arbeit wird die Vorgehensweise für die Modellierung der elektrischen Funktion des Herzens beschrieben. Hierfür werden die Modellierung der Geometrie, der kardialen Elektrophysiologie, der elektrischen Erregungsausbreitung und der EKG-Berechnung kurz erläutert. Die seit Kurzem mehr und mehr untersuchten Fälle Ischämie und personalisierte Vorhofmodellierung werden beispielhaft beschrieben und zeigen, wie die Modellierung des Herzens dazu benutzt werden kann, um Kardiologen bei der Beantwortung von offenen Fragen zu unterstützen.
O. Dössel, B. David, M. Fuchs, J. Krüger, and H. A. Wischmann. Simple test procedures for multichannel squid systems. In Biomagnetism: fundamental research and clinical applications; proceedings of the 9th International Conference on Biomagnetism (BIOMAG '93 Vienna), Amsterdam, Elsevier/IOS Press, pp. 515-520, 1995
Abstract. Atrial fibrillation (AF) is the most common cardiac arrhyth- mia. Patient-specific computational modeling of the atria can provide a better understanding about mechanisms underlying the arrhythmia and will potentially be used for model-based ablation therapy evaluation and planning. Electrical excitation spreads from the left to the right atrium at discrete locations. The location of the muscular bridges cannot be determined from image data. In the present study, left atrial activation sources were manually identified in local activation time maps of 4 AF patients. This information was used to adjust rule-based placed intera- trial bridges in anatomical atrial models of the patients. Sinus rhythm simulations showed a better qualitative agreement to the measured left atrial activation patterns after the adjustment of the bridges. For one patient, the simulated body surface potential (BSP) pattern after the adjustment correlated better to measured BSP maps. The results show that the fusion of intracardiac electrical measurements of early left atrial activation can be used to refine patient atria models with information of the myocardial structure which cannot be imaged. In future, such personalized atrial models may be used to support EP interventions.
M. W. Krueger. Towards Personalized Clinical in-silico Modeling of Atrial Anatomy and Electrophysiology. In cDEMRIS 2012, 2012
Biophysical models of the human atria have proven to aid the understanding of disease mechanisms and therapeutic measures in basic research. Atrial modeling is currently in a transition from the sole use in basic research to future clinical applications.In order to use biophysical models in a clinical environment, the anatomical and electrophysiological models need to be personalized to the specific patient. The methods for this require to be largely automatic and should also allow for the evaluation of the simulation outcome. A-priori knowledge of the human anatomy and electrophysiology needs to be merged with MRI, ECG and intracardiac electrogram data to achieve such model personalization. Additionally, information from DE-MRI can be transferred into complex atrial models to evaluate ablation therapy outcome for the specific patient.In the future, complex models will continue to allow for a further understanding of pathological mechanisms, but they will also enable the development of simplified models which can be introduced into the clinic. Interactive virtual atria will in such manner pave the way for model-based personalized radio-frequency ablation planning.
M. W. Krueger, O. Dössel, and G. Seemann. Towards personalized biophysical models of atrial anatomy and electrophysiology in clinical environments. In Biomedizinische Technik / Biomedical Engineering, vol. 57(s1) , 2012
Atrial myofiber orientation is complex and has multiple discrete layers and bundles. A novel robust semi-automatic method to incorporate atrial anisotropy and heterogeneities into patient-specific models is introduced. The user needs to provide 22 distinct seed-points from which a network of auxiliary lines is constructed. These are used to define fiber orientation and myocardial bundles. The method was applied to 14 patient-specific volumetric models derived from CT, MRI and photographic data. Initial electrophysiological simulations show a significant influence of anisotropy and heterogeneity on the excitation pattern and P-wave duration (20.7% shortening). Fiber modeling results show good overall correspondence with anatomical data. Minor modeling errors are observed if more than four pulmonary veins exist in the model. The method is an important step towards creating realistic patient-specific atrial models for clinical applications.
Atrial fibre architecture has complex patterns of bundles and layers and is known to impact on atrial electrophysiology, especially in fast-conducting bundles like Crista Terminalis, Bachmanns bundle and pectinate muscles. Based on a priori knowledge of atrial fibre structure, we incorporated rule-based fibre orientation in seven volumetric models of human atria using a semi-automatic approach. We were able to introduce multiple layers of myofibres and regional heterogeneities of ion channels in the models. We evaluated the influence of complete atrial fibre architecture on multiple modelling scales. First, we simulated atrial excitation in the isotropic and anisotropic models using the model of Courtemanche et al. in combination with the monodomain approach. Second, we computed body surface potentials from the simulated transmembrane voltages and compared these to measured ECGs from the respective patients. Temporal behaviour of the atrial excitation sequences was significantly altered in the anisotropic models compared to the sequences in the isotropic models. Complete atrial activation was achieved approximately 20% faster in the anisotropic models mostly due to fast conducting myofibre bundles. Electrophysiological heterogeneities influenced right atrial transmembrane voltage distribution over time due to a less negative action potential plateau in Crista Terminalis cells. P-wave duration was significantly shorted by the introduction of atrial anisotropy and the error to measured P-wave duration was reduced. Furthermore, a pattern change in body surface potential distribution over time was observed. The anisotropic patterns showed a better match to the measurements. Thus, the modelling error by using generalised fibre architecture for patient-specific models was smaller than by using isotropic models. The results highlight the necessity to incorporate atrial anisotropy in personalised models to produce more realistic simulations. The semi-automatic approach allows the use of these models for future clinical applications.
Background: Patients with end-stage renal disease show an increased prevalence of atrial fibrillation. A combined simulation and electrocardio- gram analysis study revealed a correlation between the changes in plasma electrolytes and intra-atrial conduction velocity related to hemodialysis (HD) session. A recognized limitation of the study is that simulations were performed on single-cell level. We present a computer study to investigate the influence of HD-related electrolyte modifications on atrial electrophys- iology in a volumetric environment.Methods: Based on the Courtemanche-Ramirez-Nattel model and its parameterization for different atrial tissues, we studied action potential, effective refractory period, conduction velocity (CV) restitution, and wave length restitution for common atrial myocardium (CAM) and fast conducting Crista Terminalis (CT). We used isotropic, homogeneous tissue patches. External stimuli were applied with 184 different pacing rates (PRs) from 330 to 1250 milliseconds.Results: The effect of temporary HD- related electrolyte changes on the action potential morphology and effective refractory period showed results consistent with the previous single-cell study. Action potential morphology was not significantly altered both in CAM and CT, but resting potential decreased from ␣82.6 to ␣88.2 mV for CAM and from ␣81.7 to ␣87.3 mV for CT. Effective refractory period decreased from 32 (pre-HD) to 308 milliseconds (end-HD). At a PR of 832 milliseconds, CV dropped by ␣6.3% for both types of tissue (CAM: 741 694 mm/s; CT: 746 699 mm/s). Wave length increased slightly with higher PR, but rapidly fell off below a PR of 450 milliseconds. Wave length was ␣30 mm shorter in the end-HD condition.Conclusions: Conduction velocity decrease and consequent wave length shortening increases vulnerability for atrial fibrillation onset, especially in conjunction with structural dilation often present in atria of end-stage renaldisease patients. Temporary HD-caused electrical remodeling has equal effects on regular and fast-conducting tissue. Although there is no biophysical model for fast interatrial condition pathways (eg, Bachmann dundle) available, the HD influence on them should also be similar and therefore slow down interatrial conduction significantly. It has been suggested that constantly repeating alteration of atrial electrophysiology may lead to a longer lasting electrical atrial remodeling; future studies should therefore investigate the long-term HD effects.
IntroductionAtrial fibrillation (AF) is the most common cardiac arrhythmia. Over 4.5 million people in the European Union suffer from AF. The mechanisms leading to AF are still not completely understood although various theories were proposed. Numerical models of the human atria can help to understand these mechanisms. Personalized atrial models may in fu- ture be used to set up patient-specific therapies.MethodsPersonalization of atrial models splits into different tasks. The individual atrial and thorax anatomy are derived from various imaging modalities (CT, MRI). Valuable information is hidden in these data, such as atrial wall thickness and myocardial fiber structure. The missing parts are added to the geometric model using rule-based approaches. Atrial electrophysiology is adapted to different pathologies (e.g. remodeling, genetic defects) and to ECG and intracardiac measurements of the individual patient by tuning model parameters (e.g. conductivity).ResultsPersonalization of atrial anatomy enables a realistic simulation of atrial excitation propagation during sinus rhythm. Ad- justment of the generalized electrophysiology model to the according patient group provides insights into the substrate of the known global effects. Adaption of these model parameters to the individual patient results in a better fit of simu- lated intracardiac and ECG signals to the measurements.ConclusionWith the help of various personalization techniques, generalized atrial models can be adapted to patient data. These models may in future be used for personalized model-based AF-treatment planning.
Current models of the human atria represent geometries of single individuals or base on statistical data. We present a work-flow for the creation of patient-specific atrial models. Furthermore we show a framework to compare simulated P- waves and body surface potential maps (BSPMs) of individual patients with measurements. Models of the atrial and thorax anatomy were segmented from MRI data. Volumetric atrial models were semi-automatically enhanced with electrophys- iologically (EP) relevant structures. Simulations were performed on an anisotropic voxel-based mesh and were forward calculated to obtain simulated BSPMs. BSPMs were acquired using a 64 electrode ECG system. Comparison of simulated and measured P-waves in Einthoven leads showed a general agreement of both, although no personalization of the atrial electrophysiology model was performed. P-wave duration was longer in the simulations, highlighting the need for elec- trophysiological model personalization. Simulated and measured BSPMs revealed similar patterns. The presented method enables realistic simulations of atrial activation on patient-specific volumetric atrial models with EP relevant myocardial structures resulting in computed ECGs (P-wave) and BSPMs with show physiological morphologies
Motivation: Anatomical models of the heart can be used to conduct multi-physics simulations. These simulations can aid basic and clinical research and are being translated into clinical practice nowadays.Problem statement: The human myocardium has very complex fiber structure, which has a strong impact on cardiac physiology. To understand and evaluate 3D fiber orientation in volumetric cardiac models, it is often necessary to project these onto printed pictures.Approach: Images of myocardial fibers using color-coded cylinders, color-coded streamlines and anaglyph methods are compared. Results: Streamlines provide a good distinction of myocardial bundles. Cylinders show the most accurate results. Color-coded representations reveal abrupt changes in fiber direction. Anaglyph visualizations give an illusion of depth in 2D prints and can display overlaying bundles. Conclusions: Streamlines are superior in imaging global fiber orientation, whereas cylinders give better results for local structures. Color-coding increases information where fiber structure is very complex, e.g. in the atria. Anaglyph images cause a loss in color information but help the viewer to understand the 3D object. Overall, it is necessary to choose the appropriate method of picturing fibers for specific tasks.
M. W. Krueger, F. M. Weber, O. Dössel, and G. Seemann. Influence of myocardial structures on electrophysiologic simulations in patient specific atrial models. In The Cardiac Physiome: Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart, 2009
M. W. Krueger, F. M. Weber, O. Dössel, and G. Seemann. Semi-automatic segmentation of sinus node, Bachmann's Bundle and Terminal Crest for patient specific atrial models. In World Congress on Medical Physics and Biomedical Engineering. IFMBE Proceedings, vol. 25/4, pp. 673-676, 2009
The human atria contain fine structures, which can hardly be distinguished with common medical imaging techniques. However, some of these structures play an important role in the electrophysiologic depolarisation sequence of the atria. We present a semi-automatic algorithm to segment the sinus node, Bachmann’s Bundle and the Terminal Crest in given anatomical shape models of the atria. The algorithm bases on anatomical knowledge of the atria and only requires the user to provide few distinct landmarks in the atria as input. Incorporation of these structures into patient individual atrial geometries augments the electrophysiological correctness of the models.
M. W. Krueger, D. L. Weiss, and O. Doessel. Intraventricular outweighs transmural dispersion of repolarization after epicardial pacing in a virtual human left ventricle. In 41. Jahrestagung der DGBMT im VDE. Proceedings BMT 2007, vol. 52, 2007
M. W. Krueger, D. L. Weiss, O. Dössel, and G. Seemann. Die Begrenztheit theoretischer Modelle der menschlichen Biologie und ihr großer Nutzen für das Verständnis des Körpers. In Challenges and Limitations of Models in Science and Theology, 2007
P-wave morphology correlates with the risk for AF. Left atrial (LA) enlargement could explain both the higher risk for AF and higher P-wave terminal force (PTF) in lead V1. However, PTF-V1 has been shown to correlate poorly with LA size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IAC), which both show tremendous variability. Atrial excitation was triggered from seven different EAS on the epicardial surface around the sinus node region in eight anatomically personalized computational models including rule-based myocyte orientation and spatial electrophysiological heterogeneity. EAS1 was located midway between the tip of the right atrial appendage (RAA) and its junction with the superior vena cava (SVC), EAS2 at the superior part of the anterior wall, and EAS3 at the junction of the RAA and the SVC. EAS4 to EAS7 were uniformly distributed along the crista terminalis between EAS3 and orifice of the inferior vena cava (EAS7). IACs connected the atria at Bachmann’s bundle, coronary sinus and posteriorly. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed using realistic, heterogeneous torso models. Mid-septal EAS yielded the highest PTF-V1 measured as the product of the duration and the maximal amplitude of the negative phase of the P-wave in V1. More anterior/superior and more inferior EAS yielded lower absolute values deviating by a factor of up to 2.0 for adjacent EAS. Earliest right-to-left activation was conducted via BB for EAS1-3 and shifted towards posterior IACs for EAS 4-7. Non-conducting posterior IACs increased PTF-V1 by up to 150%. The electrical contributors EAS and intactness of posterior IACs affect PTF-V1 significantly by changing LA breakthrough sites. This should be considered when assessing LA anatomy based on the ECG.
Aim: P-wave morphology correlates with the risk for AF. Left atrial enlargement could explain both the higher risk for AF and higher P-wave terminal force in lead V1 (PTF-V1). However, PTF-V1 has been shown to correlate poorly with left atrial size. We hypothesize that PTF-V1 is also affected by the earliest activated site (EAS) in the right atrium and its proximity to inter-atrial connections (IACs), which both show tremendous variability. Methods: Atrial excitation was triggered from seven different EASs (Fig 1A,B) in eight anatomically personalized computational models including rule-based fiber orientation and spatial electrophysiological heterogeneity. IACs connected the atria at Bachmann’s bundle, coronary sinus, and posteriorly. The posterior IACs were non-conductive in a second set of simulations. Body surface ECGs were computed using realistic, heterogeneous torso models of the same subjects. Results: Mid-septal EASs yielded the highest PTF-V1 measured as the product of the duration and the maximal amplitude of the negative phase of the P-wave in V1. More anterior/superior and more inferior EASs yielded lower absolute values deviating by a factor of up to 2.0 for adjacent EAS (Fig 1C). Earliest right-to-left activation was conducted via BB for EAS1-EAS3 and shifted towards posterior IACs for EAS4-EAS7. Non- conducting posterior IACs increased PTF-V1 by up to 150% (Fig 1D). Conclusions: Location of EAS in the right atrium and its proximity to functioning IACs affect PTF-V1 independently of the left atrial size and further support the caution that needs to be exercised when interpreting electrocardiographically signs of left atrial abnormality, which include PTF-V1.
ECG markers derived from the P-wave are used frequently to assess atrial function and anatomy, e.g. left atrial enlargement. While having the advantage of being routinely acquired, the processes under- lying the genesis of the P-wave are not understood in their entirety. Particularly the distinct contributions of the two atria have not been analyzed mechanistically. We used an in silico approach to simulate P-waves originating from the left atrium (LA) and the right atrium (RA) separately in two realistic models. LA contribution to the P-wave integral was limited to 30% or less. Around 20 % could be attributed to the first third of the P-wave which reflected almost only RA depolarization. Both atria contributed to the second and last third with RA contribution being about twice as large as LA contribution. Our results foster the comprehension of the difficulties related to ECG-based LA assessment.
Atrial fibrillation is a common irregular heart rhythm. Until today there is still a need for research to quantify typical signal characteristics of rotors, which can induce atrial fibrillation. In this work, signal characteristics of a stable and a more unstable rotor in a realistic heart model including fiber orientation were analyzed with the following methods: peak-to-peak amplitude, Hilbert phase, approximate entropy and RS-difference. In this simulation model the stable rotor rotated with a cycle length of 145 ms and stayed in an area of 1.5 mm x 3 mm. Another more unstable rotor with a cycle length of 190 ms moved in an area of 10 mm × 4 mm. In a distance of 2 mm to the rotor tip, the peak-to-peak amplitude decreased significantly, whereas the RS-difference and the approximate entropy were maximal. The rotor center trajectories were detected by phase singularity points determined by the Hilbert transform. We showed that more unstable rotors resulted in more amplitude changes over time and also the cycle length differed more. Furthermore, we presented typical activation time patterns of the Lasso catheter centered at the rotor tip and in different distances to the rotor tip. We suggest that cardiologists use a combination of the described methods to determine a rotor tip position in a more robust manner.
Cardiac computer modeling can help to gain a deeper insight into the physiological processes of the heart. In this work we present a new electromechanical modeling framework which allows to simulate the contraction of the atria in a model of the whole heart with realistic bound- ary conditions. For the active tension development (TD) we used a model, which was originally developed to describe the TD of the ventricles. However, TD in the atria differs significantly from that of the ventricles. On that account, we adapted the TD model to the measurement data of the atria. The modeling framework allows to obtain a realistic motion of the atria during the contraction cycle.
Model-based segmentation approaches have been proven to produce very accurate segmentation results while simultaneously providing an anatomic labeling for the segmented structures. However, variations of the anatomy, as they are often encountered e.g. on the drainage pattern of the pulmonary veins to the left atrium, cannot be represented by a single model. Automatic model selection extends the model-based segmentation approach to handling significant variational anatomies without user interaction. Using models for the three most common anatomical variations of the left atrium, we propose a method that uses an estimation of the local fit of different models to select the best fitting model automatically. Our approach employs the support vector machine for the automatic model selection. The method was evaluated on 42 very accurate segmentations of MRI scans using three different models. The correct model was chosen in 88.1 % of the cases. In a second experiment, reflecting average segmentation results, the model corresponding to the clinical classification was automatically found in 78.0 % of the cases.
Whole organ scale patient specific biophysical simulations contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmia. However, many individual steps are required to bridge the gap from an anatomical scan to a personal- ized biophysical model. In biophysical modeling, differential equations are solved on spatial domains represented by volumetric meshes of high resolution and in model-based segmentation, surface or volume meshes represent the patients geometry. We simplify the personalization pro- cess by representing the simulation mesh and additional relevant struc- tures relative to the segmentation mesh. Using a surface correspondence preserving model-based segmentation algorithm, we facilitate the inte- gration of anatomical information into biophysical models avoiding a complex processing pipeline. In a simulation study, we observe surface correspondence of up to 1.6mm accuracy for the four heart chambers. We compare isotropic and anisotropic atrial excitation propagation in a personalized simulation.
Cardiac electrophysiology procedures are routinely used to treat patients with rhythm disorders. The success rates of ablation procedures and cardiac resynchronization therapy are still sub-optimal. Recent advances in medical imaging, image processing and cardiac biophysical modeling have the potential to improve patient outcome. This manuscript provides an overview of how these advances have been translated into the clinical environment.
Atrial fibrillation (AF) is the most common cardiac arrhythmia, and is mainly sustained by reentrant circuits and rapid ectopic activity. In the present study, we performed computer simulations using a 3D human atrial model including fibre orientation, electrophysiological heterogeneities and tissue anisotropy. Membrane kinetics were described as in the human atrial action potential model by Maleckar et al., including AF-induced ionic remodeling. The impact of ionic changes on reentrant activity was investigated by characterizing arrhythmia stability, rotor dynamics and dominant frequency (DF). Our simulations show that reentrant circuits tend to organize around the pulmonary veins and the right atrial appendage. Simulated IK1 and INa blocks lead to slower DF in the whole atria, expanded wave meandering and reduction of secondary wavelets. INaK block slightly reduces DF and does not notably change the propagation pattern. Regularity and coupling indices of electrograms are usually higher in the right atrium than in the left atrium, entailing a higher likelihood of arrhythmia generation in the latter, as occurs in AF patients.
Anatomically realistic computational models provide a powerful platform for investigating mechanisms that underlie atrial rhythm disturbances. In recent years, novel techniques have been developed to construct structurally-detailed, image-based models of 3D atrial anatomy. However, computational models still do not contain full descriptions of the atrial intramural myofiber architecture throughout the entire atria. To address this, a semi-automatic rule-based method was developed for generating multi-layer myofiber orientations in the human atria. The rules for fiber generation are based on the careful anatomic studies of Ho, Anderson and co-workers using dissection, macrophotography and visual tracing of fiber tracts. Separately, a series of high color contrast images were obtained from sheep atria with a novel confocal surface microscopy method. Myofiber orientations in the normal sheep atria were estimated by eigen-analyis of the 3D image structure tensor. These data have been incorporated into an anatomical model that provides the quantitative representation of myofiber architecture in the atrial chambers. In this study, we attempted to compare the two myofiber generation approaches. We observed similar myo-bundle structure in the human and sheep atria, for example in Bachmann's bundle, atrial septum, pectinate muscles, superior vena cava and septo-pulmonary bundle. Our computational simulations also confirmed that the preferential propagation pathways of the activation sequence in both atrial models is qualitatively similar, largely due to the domination of the major muscle bundles.
The objective of personalised modelling of the atria is to improve comprehension of the etiology of atrial arrhythmias, to enable specific diagnosis and to optimise therapy. We start with CT or MR datasets and use adapted segmentation procedures to build a patient-specific 3D-model of the atria. Then we include fibre direction based on the rules of atrial anatomy. Work in progress is also considering late enhancement MRI in order to add areas of fibrotic tissue. Next we can use BSPM data of the P-wave and solve the inverse problem of ECG to get a hypothesis about the spread of depolarisation. Finally we use intracardiac catheter signals (e.g. using a circular catheter) to measure direction and conduction velocity of depolarisation waves (sinus rhythm, atrial flutter, or following stimulation). All this is integrated into a personalised model of the atria of an individual patient. Our next goal will be to properly add ablation lines into the model.The research leading to these results has partly received funding from the European Communitys Seventh Framework Programme (FP7/2007-2013) under grant agreement n 224495 (euHeart project).
A framework for step-by-step personalization of a computational model of human atria is presented. Beginning with anatomical modeling based on CT or MRI data, next fiber structure is superimposed using a rule-based method. If available, late-enhancement-MRI images can be considered in order to mark fibrotic tissue. A first estimate of individual electrophysiology is gained from BSPM data solving the inverse problem of ECG. A final adjustment of electrophysiology is realized using intracardiac measurements. The framework is applied using several patient data. First clinical application will be computer assisted planning of RF-ablation for treatment of atrial flutter and atrial fibrillation.
The delineation of anatomical structures in medical images can be achieved in an efficient and robust manner using statistical anatomical organ models, which has been demonstrated for an already considerable set of organs, including the heart. While it is possible to provide models with sufficient shape variability to cope, to a large extent, with inter-patient variability, as long as object topology is conserved, it is a fundamental problem to cope with topological organ variability. We address this by creating a set of model variants and selecting the most appropriate model variant for the patient at hand. We propose a hybrid method combining model-based image analysis with a guided region growing approach for automated anatomical variant selection and apply it to the left atrium in cardiac CT images. Concerning the human heart, the left atrium is the most variable sub-structure with a variable number of pulmonary veins draining into it. It is of large clinical interest in the context of atrial fibrillation and related interventions.
Electrophysiological simulations of the atria could improve diagnosis and treatment of cardiac arrhythmia, like atrial fibrillation or flutter. For this purpose, a precise segmentation of both atria is needed. However, the atrial epicardium and the electrophysiological structures needed for electrophysiological simulations are barely or not at all detectable in CT-images. Therefore, a model based segmentation of only the atrial endocardium was developed as a landmark generator to facilitate the registration of a finite wall thickness model of the right and left atrial myocardium. It further incorporates atlas information about tissue structures relevant for simulation purposes like Bachmanns bundle, terminal crest, sinus node and the pectinate muscles. The correct model based segmentation of the atrial endocardium was achieved with a mean vertex to surface error of 0.53 mm for the left and 0.18 mm for the right atrium respectively. The atlas based myocardium segmentation yields physiologically correct results well suited for electrophysiological simulations.
In spite of the considerable medical and technical progress during the last years, catheter ablation of atrial fibrillation is still challenging. For a successful execution of the ablation and the avoidance of intricacies the catheter must be in contact with the endocardium, which is still difficult to assure with existent techniques. It would be desirable to detect the endocardial catheter contact directly from the signal shape and its properties. In this work, significant signal property changes were detected and investigated, which allow an automatic contact detection. Furthermore, atrial electrograms were simulated and compared with a database of measured and annotated signals. During these simulations, the distance between endocardium and the catheter tip could be chosen discretionary. The simulated signals revealed themselves to be very accurate. Simulations can now be used to analyse intracardiac signals more closely. The exact position of the catheter will hereby always be assured, which is not always granted in clinical practice.
# BackgroundMethods for the non-invasive imaging of atrial activation times could provide cardiologists with valuable information on pathological excitation conduction patterns, e.g. for treatment planning.In this study, the source representation functions used in the critical times method (Greensite et al. 1997) are expanded with a range adjustment to generate more accurate activation time maps from ECG measurements.# Materials and methodsExcitation conduction in the atria was simulated for various excitation origins with a cellular automaton. Body surface potential maps were obtained from forward calculations using a bidomain approach.As introduced in Greensite et al. 1995, the method of critical times can be used to quantitatively localize critical point locations and times, and to reconstruct surface activation in a qualitative manner. To this end, all atrial surface nodes were treated as critical points and the corresponding critical times were reconstructed using the zero-crossing method by Greensite, which is the subtraction of the two representation functions.For the heart surface nodes, it was observed that the minuend representation function in the zero-crossing term is often by magnitudes greater than the subtrahend. For the minuend to not dominate the subtrahend before the desired zero-crossing, which is supposed to occur at the time of depolarization, the minuend was therefore weighted with a sigmoid function and normalized to the range of the subtrahend.# ResultsAtrial activation times were reconstructed with both the zero-crossing method by Greensite and the sigmoid-weighted zero-crossing. Two effects were observed. The overall reconstruction quality of the established method improves in the presence of 30dB additive white Gaussian noise. This effect results from a gradual offset that is imposed on the reconstructed critical times under these circumstances (see Huiskamp and Greensite 1997). Second, it could be shown that a significant reduction of reconstruction error can be achieved in the absence of noise with the sigmoid-weighted adaptation of the formula.# ConclusionWith the newly introduced sigmoidal normalization, the quality of reconstruction can be improved significantly if noise levels are below 30dB. Clinical studies need to be made in order to validate the method and assess its performance in a realistic environment.
Background: Catheter ablation of complex atrial arrhythmias, such as atrial fibrillation and atypical atrial flutter, is still challenging. Clinically evaluated ablation methods are leading to moderate success rates. Assessments of intracardiac electrograms are often done subjectively by the physician. Automatic algorithms can therefore improve the analysis of complex atrial electrograms (EGMs). In this work, we demonstrate a quantitative analysis of intracardiac EGMs from circular mapping catheters in humans. Both the wave direction and the local conduction velocity (CV) were calculated from individual wave fronts passing the catheter.Methods: Intracardiac EGMs measured with circular mapping catheters in humans were retrospectively analyzed. Five data sets from 3 patients undergoing catheter ablation of atrial fibrillation or flutter were available. Using a nonlinear energy operator, activation times from 9 bipolar catheter signals were calculated for each atrial activity. The resulting activation pattern was fitted to a cosine-shaped data model that has been validated in a previous simulation study. The cosine phase represented the wave direction. From the cosine amplitude and the catheter radius, the conduction velocity was calculated.Results: The wave directions in all five measurements were stable with a standard deviation below 10°. Calculated CVs were in the range of 70 to 110 cm/s, which is in accordance with published values. In one patient, electrograms were recorded during atrial stimulation. Stimulation cycle length was decreased from 500 to 300 milliseconds. Conduction velocity decreased by approximately 10% at a cycle length of 300 milliseconds compared with the CV at 500 milliseconds.Conclusion: The results show the ability to reliably extract wave direction and conduction velocity from intracardiac EGMs recorded with circular mapping catheters. Detected directions were stable, and the CV values were in a physiological range. As individual beats are analyzed, the method will also enable the quantitative study of singular events such as ectopic beats and facilitate the localization of tachycardia origins. Further, it will help to measure substrate parameters such as the CV and even CV restitution behavior. This way, the method can help to identify patient-specific physiological parameters that can be integrated into patient-specific models. Furthermore, it can directly provide quantitative data of high diagnostic value to the examiner and thereby improve clinical success rates.
Catheter ablation of complex atrial arrhythmias is a frequently applied procedure, but its success rates are only moderate and highly dependent on the experience of the physician. Personalized atrial simulation models could assist the physician in treatment planning and thus increase success rates. In this work we created a personalized anatomical model for a specific patient from CT image data. Left atrial conduction velocity and local wave directions were determined from intracardiac electrogram (EGM) recordings. We simulated normal sinus rhythm and the clinical pacing protocol using a Cellular Automaton. The incidence direction and conduction velocity were extracted from the simulated data and compared to the results of the clinical EGMs of the same patient. We then showed that the incidence angles differed by less than 15% and that the conduction velocity error was below 12 cm/s. This implies that the model has similar electric properties compared to the real atria. In conclusion, we have presented a workflow for model personalization and validation.
Atrial fibrillation (AF) is the most common cardiac arrhythmia in the western world. Genetic variants in the cardiac I Kr channel have been identified to influence ventricular repolarization. The aim of this work is to investigate the effect of the mutation N588K on atrial repolarization and the predisposition to AF. Experimental data of N588K mutated hERG channel were incorporated in an atrial ionic model using parameter fitting. The effects of the mutation were analyzed in cell and tissue. N588K showed a gain of function effect, causing a rapid repolarization and a shortening of the action potential duration. Computer simulations of a schematic right atrial geometry were used to investigate the excitation conduction properties. The effective refractory period of mutant cells were reduced from 317 to 233 ms at 1 Hz. The conduction velocity is not significantly influenced by the mutation. Nevertheless, the wavelength of mutant cells is for all frequencies smaller, indicating that the mutation N588K predisposes the initiation and perpetuation of AF.
Patient-specific cardiac simulations are approaching clinical applications. They could for example improve the treatment of atrial fibrillation (AF). Currently, many patients suffering from AF are treated with minimally-invasive catheter ablation. Using this technique, trigger sources for AF (mainly the pulmonary veins), are electrically isolated from the rest of the atrium. However, a large set of different ablation strategies is currently used in clinical practice. Therefore, the choice of a certain ablation strategy as well as the probability for successful and sustained AF termination are strongly dependent on the experience of the cardiologist. Atrial simulations could assist the cardiologist in the choice of a suitable method for an individual patient. For this, the atrial models have to be adapted to the patient. Besides anatomical modeling, several challenges must be faced in this process. First, an appropriate model of cellular electrophysiology and excitation conduction must be chosen. The model must provide the necessary accuracy and at the same time be fast enough for clinical applications. As a trade-off between accuracy and speed, we propose a minimal model adapted to atrial electrophysiology. Second, a main problem is the adaptation of physiological parameters in the patient-specific model as well as its validation. Therefore, an interface between clinical data and the model is needed. Data collected in standard clinical workflow are mainly intracardiac catheter ECGs. We therefore present techniques to model such catheter measurements. Signals from both circular mapping catheters (such as Lasso or Orbiter) as well as Coronary Sinus catheters can be simulated and compared to clinical signals. These are important steps towards clinical applications of atrial models. The long-term goal then is to assist the cardiologist in the choice of the best treatment for an individual patient.
A modular multichannel superconducting quantum interference device (SQUID) system, in which every channel can be optimized or replaced individually, was further improved. The number of channels was increased to 31. The noise level is better than 10 fT/√Hz. A novel way of RF shielding using conductive paint avoids degradation of the SQUID characteristics due to RF interference without introducing significant extra noise, so that the system works without any Faraday cage. A simplified way of coupling the modulation and feedback signal directly to the SQUID was developed and tested successfully. The SQUID module with superconducting connections to the gradiometer and its superconducting shield was miniaturized to an outer diameter of 5 mm, so that it can be placed near the gradiometer without introducing significant unbalance. Tests have demonstrated that the accuracy of the system with respect to the localization of a single current dipole is better than 2 mm
M. W. Krüger. Personalized Multi-Scale Modeling of the Atria : Heterogeneities, Fiber Architecture, Hemodialysis and Ablation Therapy. KIT Scientific Publishing. Dissertation. 2013
This book targets three fields of computational multi-scale cardiac modeling. First, advanced models of the cellular atrial electrophysiology and fiber orientation are introduced. Second, novel methods to create patient-specific models of the atria are described. Third, applications of personalized models in basic research and clinical practice are presented. The results mark an important step towards the patient-specific model-based atrial fibrillation diagnosis, understanding and treatment.
Student Theses (2)
M. W. Krüger. Modellierung des Einflusses der Hämodynamik auf die Temperaturverteilung während extrakorporaler Zirkulation. Universität Karlsruhe (TH). Diplomarbeit. 2008
M. W. Krüger. Erhöhung der transmuralen Dispersion der Repolarisation durch epikardiale Stimulation eines virtuellen linken Ventrikels. Institut für Biomedizinische Technik, Universität Karlsruhe (TH). . 2007