Abstract:

In this work, a new framework is presented that is suitable to solve the cardiac bidomain equation efficiently using the scientific computing library PETSc. Furthermore, the framework is able to modularly combine different ionic channels and is flexible enough to include arbitrary heterogeneities in ionic or coupling channel density. The ability of this framework is demonstrated in an example simulation in which the three-dimensional electrophysiological heterogeneity was adjusted in order to get a positive T-wave in the body electrocardiogram (ECG).

Abstract:

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.

Abstract:

Purpose: Three-dimensional (3-D) reconstruction of the coronary arteries during a cardiac catheter-based intervention can be performed from a C-arm based rotational x-ray angiography sequence. It can support the diagnosis of coronary artery disease, treatment planning, and intervention guidance. 3-D reconstruction also enables quantitative vessel analysis, including vessel dynamics from a time-series of reconstructions.Methods: The strong angular undersampling and motion effects present in gated cardiac reconstruction necessitate the development of special reconstruction methods. This contribution presents a fully automatic method for creating high-quality coronary artery reconstructions. It employs a sparseness-prior based iterative reconstruction technique in combination with projection-based motion compensation.Results: The method is tested on a dynamic software phantom, assessing reconstruction accuracy with respect to vessel radii and attenuation coefficients. Reconstructions from clinical cases are presented, displaying high contrast, sharpness, and level of detail.Conclusions: The presented method enables high-quality 3-D coronary artery imaging on an interventional C-arm system.

Abstract:

This paper examined the effects that different tissue conductivities had on forward-calculated ECGs. To this end, we ranked the influence of tissues by performing repetitive forward calculations while varying the respective tissue conductivity. The torso model included all major anatomical structures like blood, lungs, fat, anisotropic skeletal muscle, intestine, liver, kidneys, bone, cartilage, and spleen. Cardiac electrical sources were derived from realistic atrial and ventricular simulations. The conductivity rankings were based on one of two methods: First, we considered fixed percental conductivity changes to probe the sensitivity of the ECG regarding conductivity alterations. Second, we set conductivities to the reported minimum and maximum values to evaluate the effects of the existing conductivity uncertainties. The amplitudes of both atrial and ventricular ECGs were most sensitive for blood, skeletal muscle conductivity and anisotropy as well as for heart, fat, and lungs. If signal morphology was considered, fat was more important whereas skeletal muscle was less important. When comparing atria and ventricles, the lungs had a larger effect on the atria yet the heart conductivity had a stronger impact on the ventricles. The effects of conductivity uncertainties were significant. Future studies dealing with electrocardiographic simulations should consider these effects.

Abstract:

Biventricular pacing (BVP) could be improved by identifying the patient-specific optimal electrode positions. Body surface potential map (BSPM) is a non-invasive technique for obtaining the electrophysiology and pathology of a patient. The study proposes the use of BSPM as input for an automated non-invasive strategy based on a personalized computer model of the heart, to identify the patient pathology and specific optimal treatment with BVP devices. The anatomy of a patient suffering from left bundle branch block and myocardial infarction is extracted from a series of MR data sets. The clinical measurements of BSPM are used to parameterize the computer model of the heart to represent the individual pathology. Cardiac electrophysiology is simulated with ten Tusscher cell model and excitation propagation is calculated with adaptive cellular automaton, at physiological and pathological conduction levels. The optimal electrode configurations are identified by evaluating the QRS error between healthy and pathology case with/without pacing. Afterwards, the simulated ECGs for optimal pacing are compared to the post-implantation clinically measured ECGs. Both simulation and clinical optimization methods identified the right ventricular (RV) apex and the LV posterolateral regions as being the optimal electrode configuration for the patient. The QRS duration is reduced both in measured and simulated ECG after implantation with 20 and 14%, respectively. The optimized electrode positions found by simulation are comparable to the ones used in hospital. The similarity in QRS duration reduction between measured and simulated ECG signals indicates the success of the method. The computer model presented in this work is a suitable tool to investigate individual pathologies. The personalized model could assist therapy planning of BVP in patients with congestive heart failure. The proposed method could be used as prototype for further clinically oriented investigations of computerized optimization of biventricular pacing.

Abstract:

OBJECT: Most functional magnetic resonance imaging (fMRI) experiments use gradient-echo echo planar imaging (GE EPI) to detect the blood oxygenation level-dependent (BOLD) effect. This technique may fail in the presence of anatomy-related susceptibility-induced field gradients in the human head. In this work, we present a novel 3D compensation method in combination with a template-based correction that can be optimized over particular regions of interest to recover susceptibility-induced signal loss without acquisition time penalty. MATERIALS AND METHODS: Based on an evaluation of B(0) field maps of eight subjects, slice-dependent gradient compensation moments are derived for maximal BOLD sensitivity in two compromised regions: the orbitofrontal cortex and the amygdala areas. A modified EPI sequence uses these additional gradient moments in all three imaging directions. The method is compared to non-compensated, template-based and subject-specific correction gradients and also in a breath-holding experiment. RESULTS: The slice-dependent gradient compensation method significantly improves signal intensity/BOLD sensitivity by about 35/43% in the orbitofrontal cortex and by 17/30% in the amygdala areas compared to a conventional acquisition. Template-based correction and subject-specific correction perform equally well. The BOLD sensitivity in the breath hold experiment is effectively increased in compensated regions. CONCLUSION: The new method addresses the problem of susceptibility-induced signal loss, without compromising temporal resolution. It can be used for event-related functional experiments without requiring additional subject-specific calibration or calculation time.

Abstract:

This work presents a new approach toward a fast, simultaneous amplitude of radiofrequency field (B(1)) and T(1) mapping technique. The new method is based on the "actual flip angle imaging" (AFI) sequence. However, the single pulse repetition time (TR) pair used in the standard AFI sequence is replaced by multiple pulse repetition time sets. The resulting method was called "multiple TR B(1)/T(1) mapping" (MTM). In this study, MTM was investigated and compared to standard AFI in simulations and experiments. Feasibility and reliability of MTM were proven in phantom and in vivo experiments. Error propagation theory was applied to identify optimal sequence parameters and to facilitate a systematic noise comparison to standard AFI. In terms of accuracy and signal-to-noise ratio, the presented method outperforms standard AFI B(1) mapping over a wide range of T(1). Finally, the capability of MTM to determine T(1) was analyzed qualitatively and quantitatively, yielding good agreement with reference measurements. Magn Reson Med, 2010. (c) 2010 Wiley-Liss, Inc.

Abstract:

Atrial arrhythmias, such as atrial flutter or fibrillation, are frequent indications for catheter ablation. Recorded intracardiac electrograms (EGMs) are, however, mostly evaluated subjectively by the physicians. In this paper, we present a method to quantitatively extract the wave direction and the local conduction velocity from one single beat in a circular mapping catheter signal. We simulated typical clinical EGMs to validate the method. We then showed that even with noise, the average directional error was below 10(°) and the average velocity error was below 5.4 cm/s. In a realistic atrial simulation, the method could clearly distinguish between stimuli from different pulmonary veins. We further analyzed eight clinical data segments from three patients in normal sinus rhythm and with stimulation. We obtained stable wave directions for each segment and conduction velocities between 70 and 115 cm/s. We conclude that the method allows for easy quantitative analysis of single macroscopic wavefronts in intracardiac EGMs, such as during atrial flutter or in typical clinical stimulation procedures after termination of atrial fibrillation. With corresponding simulated data, it can provide an interface to personalize electrophysiological (EP) models. Furthermore, it could be integrated into EP navigation systems to provide quantitative data of high diagnostic value to the physician

Abstract:

This article presents three success stories that show how the coaction of mathematics and medicine has pushed a development towards patient specific models on the basis of modern medical imaging and virtual labs, which, in the near future, will play an increasingly important role. Thereby the interests of medicine and mathematics seem to be consonant: either discipline wants the results fast and reliably. As for the medical side, this means that the necessary computations must run in shortest possible times on a local PC in the clinics and that their results must be accurate and resilient enough so that they can serve as a basis for medical decisions. As for the mathematical side, this means that highest level requirements for the efficiency of the applied algorithms and the numerical and visualization software have to be met. Yet there is still a long way to go, until anatomically correct and medically useful individual functional models for the essential body parts and for the most frequent.

Abstract:

Atrial fibrillation (AF) is a common pathology. AF modifies the electrophysiological properties of cells (remodeling) promoting the occurrence and maintenance of AF.Electrical remodeling includes changes in ICa,L, Ito, IK1 and IK,ACh. These effects were integrated in a human atrial computer model. Gap junction remodeling was considered in the conductivity of the monodomain equation calculating excitation. Specific features were calculated to determine the risk of AF initiation and perpetuation.ERP was reduced from 330ms to 103ms. CV was lowered from 755mm/s to 608mm/s. The WL reduction was even higher (from 249mm to 63mm) leading to a higher probability of occurrence and maintenance of AF. A maximum of 7 spirals waves were initiated leading to a peak in the power spectrum at 10.32Hz.The computer model underlines the relevance of remodeling in AF chronification. The results add to the knowledge of AF maintenance. Our model might prove to be a tool for the development of novel therapeutic strategies.

Abstract:

Simultaneous recording of ECG, Atrial Blood Pressure (ABP) and respiration is possible and sometimes done to investigate cardiovascular and respiration coupling. But analysis most often concentrates on Heart Rate Variability (HRV) and Blood Pressure Variability (BPV). Although analysis of HRV and BPV has lead to important clinical information in the past, an investigation of the morphology of the time course of ECG and ABP could reveal additional diagnostic information.To analyse the morphology of the Blood Bressure (PB) wave a detection of characteristic points, outliers and boundaries is necessary. A wavelet based algorithm for blood pressure segmentation with outlier detection is presented in this paper. It is tested on 108 records with durations of 30 minutes each.

Abstract:

There is a large interest in analysing the QT-interval, as a prolonged QT-interval can cause the development of ventricular tachyarrhythmias such as Torsade de Pointes. One major part of QT-analysis is T-end detection. Three automatic T-end delineation methods based on wavelet fil- terbanks (WAM), correlation (CORM) and Principal Com- ponent Analysis PCA (PCAM) have been developed and applied to Physionet QT database. All algorithms tested on Physionet QT database showed good results, while PCAM produced better results than WAM and CORM achieved best results. Standard de- viation in sampling points (fs=250Hz) have been 33.3 (WAM), 8.0 (PTDM) and 7.8 (CORM). It could be shown that WAM is prone to interference while CORM is the most stable method even under bad conditions. Further- more it was possible to detect significant QT-prolongation caused by Moxifloxacin in Thorough QT Study # 2 us- ing CORM. QT-prolongation is significantly correlated to blood plasma concentration of Moxifloxacin.

Abstract:

Prolongation of the ECG QT-interval is a risk factor as it can cause the development of ventricular tachyarrhythmias such as Torsade de Points and ventricular fibrillation often leading to sudden cardiac death. Thus there is a large interest in analysing the QT-interval in the ECG. One major part of ECG QT-analysis is T-end detection. A method for automatic T-end detection is presented and validated by the Physionet QT-database. The delineation algorithm presented here is based on a correlation method. Results have been compared to hand marked T-waves in the Physionet QT-database. The algorithm produced significantly better results than using the standard wavelet method.

Abstract:

In Magnetic Particle Imaging (MPI) the human body is exposed to magnetic fields of the lower kHz-range. The effects of those fields to biological tissue are yet to be determined. According to Faraday's Law, time-varying magnetic fields induce rotating electric fields. In body tissues, the induced electric field may cause an electric current, the formation of electric dipoles or the reorientation of present dipoles, depending on the strength of the magnetic field, the frequency and the properties of the body tissue, i.e. electrical conductivity and permittivity. Both electrical conductivity and permittivity vary with the frequency of the applied field. In case of a circular loop, the induced current density is proportional to the radius, the rate of change of the magnetic flux density and the conductivity of the tissue. Low frequency electric currents are able to stimulate skeletal muscles. Because of the capacitive characteristic of the cell membrane, the stimulating effect decreases with rising frequency. Furthermore, very short impulses (t ≪ 1 ms) cannot open the Na-ion channels involved in nerve stimulation as effectively as longer ones. At higher frequencies, energy absorption becomes an issue. Exposure to electro-magnetic fields can lead to local temperature increase. The amount of absorbed energy per tissue weight is expressed by the specific absorption rate (SAR). The aim of this work is to calculate and evaluate the effects of the magnetic fields applied in MPI and propose ways to minimize them. At the same time, the risk of painful muscle stimulation should be minimized, even if MPI satisfies the requirements related to patient safety. In order to fulfill this task, simulation studies as well as experiments are being carried out. The following sections give an overview about the projects that are running or will be started in the near future.

Abstract:

Since the idea of Magnetic Particle Imaging (MPI) has been initially published in 2005, a lot of effort has been invested to improve temporal and spatial resolution. Most recently, first in vivo 3D real-time MPI scans were presented revealing details of a beating mouse heart [1]. In MPI, besides a strong time-constant field gradient, an alternating magnetic field of about 25 kHz frequency is applied to the patient. For the development of a new imaging technique, it is important to investigate the effects of the induced fields with respect to current densities and specific absorption rates (SAR) to ensure safe operation. This work presents simulations of the fields induced by a typical MPI laboratory setup and an MPI system scaled up to whole body dimensions.

Abstract:

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.

Abstract:

There is a large number of published studies analyzing the inhomogeneously distributed electrophysiological properties of the ventricles in a computer model. However only few of them deal with the impact on the hearts mechanics. In 2003 Cordeiro and colleagues [1] analyzed the influence of the transmural left ventricular electrophysiological heterogeneity on the myocardial mechanics. Therefore, they examined the unloaded cell shortening of sub-epicardial cells, sub-endocardial cells, and cells from the middle of the wall, isolated from canine left ventricle.In this work a heterogenous electromechanical model was used to reconstruct these experiments of Cordeiro et al. in the computer. A simulation framework, which is consisting of an electrophysiological cell model, a tension development model and an elastomechanical model was used to simulate the cell shortening. Two experiments with different heterogeneities had been conducted. The first experiment examined, how the heterogeneity of the membrane channels influences the cell shortening. In the second experiment the additional impact of the heterogeneity of the intracellular calcium handling was analyzed. The results of the simulations were compared qualitatively to the findings of Cordeiro et al.

Abstract:

Alternating magnetic fields induce AC currents in conductive materials. These currents can depolarize the cell-membrane, causing an action potential. In current literature stimulation thresholds for alternating magnetic fields were published up to a frequency of 1 kHz only. Beyond 1 kHz there are thresholds for electrode stimulation only. To convey these thresholds for magnetic fields the current densities caused by the alternating magnetic fields in an anatomical model were calculated. With these current densities the necessary flux densities were reevaluated. The intention of this paper was the development of a system for inductive stimulation of peripheral muscles to validate the simulation in the frequency range from 1 kHz to 50kHz.

Abstract:

A volumetric mass-spring system, originally developed for myocardial mechanics modeling [1], is used to simulate the elasto-mechanical deformation of several breast datasets from prone to supine positions. Segmented MRI datasets of pa- tients in prone position, available from the online repository provided by Susan C. Hagness at the University of Wisconsin- Madison [2] were used in the biomechanical simulations. These models were considered to be consisting of two materi- als, fat and fibroconnective/glandular tissues. Each tissue is represented as a nearly incompressible Neo-Hookean elastic isotropic material. Each simulation was conducted in two steps: in the first step, the unloaded model is generated by apply- ing gravity forces to the original model pointing toward the body. The unloaded model is then used in the second step, by applying gravity forces. Eventually, the breast model in supine position is obtained.

Abstract:

Patients suffering from the congenital Long-QT syndrome have been reported to react highly sensitive to the presence of beta-adrenergic agents that are produced by the sympathetic nervous system. In this work we used an anisotropic and electrophysiologically heterogeneous in- silico model to reproduce wedge experiments in which the Long-QT syndrome was induced pharmacologically. The integration of an intracellular signaling cascade allowed the prediction of the effects of adrenergic agents on the different subtypes of the Long-QT syndrome. For LQT1 the in-silico model predicted a QT prolongation in the transmural pseudo ECG without an increase in transmural dispersion of repolarization. For LQT2 and LQT3 the QT prolongation was accompanied by an increased transmural dispersion of repolarization. beta-adrenergic tonus shortened the QT interval and increased transmural dispersion of repolarization. These findings were consistent with the experimental reports.

Abstract:

The shape of a simulated excitation wavefront depends on the underlying spatial resolution. The aim of this work is twofold: On the one hand we investigated the dependency of the wavefront on spatial resolution by simulating the excitation spread in three virtual patches of ventricular tissue that have different resolutions. On the other hand we simulate a realistic excitation sequence in an anisotropic and electrophysiologically heterogeneous biventricular model. Our patch experiments with different spatial resolutions demonstrated that resolutions below 0.2 mm led to a deformation of the excitation wavefront to non-elliptical shapes. The biventricular model with 0.2 mm grid size shows realistic excitation spread and conduction velocities. Similar biventricular models in conjunction with a computational representation of the thorax will be used in future to predict the effects of changes on the ion-channel level on the ECG.

Abstract:

Atrial fibrillation (AFib) is a frequent and serious cardiac arrhythmia. A successful method to treat AFib is catheter ab- lation. Areas with complex fractionated atrial electrograms (CFAE) are ideal targets for catheter ablation. Concerning the ablation strategy and the search for CFAEs the physician is mainly dependent on his own judgment. For this reason ablation strategies are highly operator dependent. In this work a set of seven descriptors is presented which show promising results concerning a classification of measured atrial electrograms. The descriptors are evaluated on a database of 25 CFAE sig- nals. The results reveal a possible discrimination between CFAE classes which could be a valuable support for physicians curing AFib

Abstract:

Following the ICH E14 clinical evaluation guideline [1], the measurement of QT/QTc interval prolongation has become the standard surrogate biomarker for cardiac drug safety assessment and the faith of a drug development. In Thorough QT (TQT) study, a so-called positive control is employed to assess the ability of this study to detect the endpoint of interest, i.e. the QT prolongation by about five milliseconds. In other words the lower bound of the one- sided 95% confidence interval (CI) must be above 0 [ms]. Fully automated detection of ECG fiducial points and mea- surement of the corresponding intervals including QT in- tervals and RR intervals vary between different computer- ized algorithms. In this work we demonstrate the ability and reliability of Hannover ECG System (HES) to as- sess drug effects by detecting QT/QTc prolongation effects that meet the threshold of regulatory concern as mentioned by using THEW database studies namely TQT studies one and two.

Abstract:

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

Abstract:

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.

Abstract:

Session: Translating Computer Models of the Heart into theClinics: Are We There Yet?

Abstract:

Catheter ablation of atrial fibrillation (AF), especially persistent AF, is still challenging. The underlying mechanisms are not yet completely understood and are discussed very controversially. Automated detection and analysis of complex frac- tionated atrial electrograms is essential in supporting the electrophysiologists during ablation therapy. Signal analysis of atrial signals works better the less noise and unwanted signals superimpose the signal to be analysed. As for catheter ablation of persistent AF the atrial signals play the most important role, ventricular activity is unwanted to be seen. For catheter positions in close proximity to the ventricles, i.e. the coronary sinus catheter, those ventricular far fields are taint- ing the atrial signals. For this reason we present a method to cancel the ventricular far field from atrial electrograms. Atrial segments synchronized to the ventricular activity are extracted and the ventricular far field is cancelled by use of a PCA approach. Signal processing of the sole atrial electrogram leads to better results and therefore can better support the abla- tion therapy.

Abstract:

A framework for the automatic extraction and generation of patient-specific organ models from different image modalities is presented. These models can be used to extract and represent diagnostic information about the heart and its function. Furthermore, the models can be used for treatment planning and an overlay of the models onto X-ray fluoroscopy images can support navigation when performing an intervention in the CathLab.

Abstract:

During acute cardiac ischemia, electrophysiological properties of the affected tissue are altered in the subendocardium firstly. If the occlusion worsens, the effects spread transmurally. Diagnosis of cardiac ischemia, which should be improved by computer simulations, is based on shifts of the ST segment. In this work, we simulated heterogeneous ischemic regions with varying transmural extent. The excitation propagation and ECGs were calculated for the different setups. We showed that ST segment polarity can be dependent on the transmural extent of the ischemic region. In case of subendocardial ischemia, short action potentials were initiated in the ischemic zone causing a slight transmural gradient of the transmembrane voltage. Therefore, the ST segment was depressed in leads near the ischemic region in the chosen case. During transmural ischemia, this gradient showed in the opposite direction from epicardium to endocardium leading to ST segment elevation.

Abstract:

The monodomain model is a mathematical description of the electrical excitation propagation in the heart. The numerical solution of this reaction-diffusion equation is a computationally demanding task. Aspects that have to be considered are the accuracy and stability of the solution on the one hand and the computing time on the other hand. Two first order methods an explicit and a semi-implicit scheme solving the monodomain equation were compared in this work. For the benchmark of the solvers, three cell models with different computational complexity were used. Thus, the contribution of the solvers to the total computing time could be analyzed. Generally, if the same time step was used, the semi-implicit was slower than the explicit one, since an additional linear system of equations had to be solved. However, the semi-implicit solver was more accurate and showed better stability behavior than the explicit one, especially at high spatial resolutions. Therefore, larger time steps could be used, achieving the same accuracy and a shorter total computing time as the explicit solver. However, this effect was present only, if the additional calculations of the semi-implicit solver contributed less to the total computing time, i.e. the cell model had to be computationally complex.