Radiofrequency ablation (RFA) therapy is the gold standard in interventional treatment of many cardiac arrhythmias. A major obstacle are non transmural lesions, leading to recurrence of arrhythmias. Recent clinical studies have suggested intracardiac electrogram (EGM) criteria as a promising marker to evaluate lesion development. Seeking for a deeper understanding of underlying mechanisms, we established a simulation approach for acute RFA lesions. Ablation lesions were modeled by a passive necrotic core surrounded by a borderzone with properties of heated myocardium. Herein, conduction velocity and electrophysiological properties were altered. We simulated EGMs during RFA to study the relation between lesion formation and EGM changes using the bidomain model. Simulations were performed on a three dimensional setup including a geometrically detailed representation of the catheter with highly conductive electrodes. For validation, EGMs recorded during RFA procedures in five patients were analyzed and compared to simulation results. Clinical data showed major changes in the distal unipolar EGM. During RFA, the negative peak amplitude decreased up to 104% and maximum negative deflection was up to 88% smaller at the end of the ablation sequence. These changes mainly occurred in the first 10 s after ablation onset. Simulated unipolar EGM reproduced the clinical changes, reaching up to 83% negative peak amplitude reduction and 80% decrease in maximum negative deflection for transmural lesions. In future work, the established model may enable the development of further EGM criteria for transmural lesions even for complex geometries in order to support clinical therapy.
Despite the commonly accepted notion that action potential duration (APD) is distributed heterogeneously throughout the ventricles and that the associated dispersion of repolarization is mainly responsible for the shape of the T-wave, its concordance and exact morphology are still not completely understood. This paper evaluated the T-waves for different previously measured heterogeneous ion channel distributions. To this end, cardiac activation and repolarization was simulated on a high resolution and anisotropic biventricular model of a volunteer. From the same volunteer, multichannel ECG data were obtained. Resulting transmembrane voltage distributions for the previously measured heterogeneous ion channel expressions were used to calculate the ECG and the simulated T-wave was compared to the measured ECG for quantitative evaluation. Both exclusively transmural (TM) and exclusively apico-basal (AB) setups produced concordant T-waves, whereas interventricular (IV) heterogeneities led to notched T-wave morphologies. The best match with the measured T-wave was achieved for a purely AB setup with shorter apical APD and a mix of AB and TM heterogeneity with M-cells in midmyocardial position and shorter apical APD. Finally, we probed two configurations in which the APD was negatively correlated with the activation time. In one case, this meant that the repolarization directly followed the sequence of activation. Still, the associated T-waves were concordant albeit of low amplitude.
Ventricular wall deformation is widely assumed to have an impact on the morphology of the T-wave that can be measured on the body surface. This study aims at quantifying these effects based on an in silico approach. To this end, we used a hybrid, static-dynamic approach: action potential propagation and repolarization were simulated on an electrophysiologically detailed but static 3-D heart model while the forward calculation accounted for ventricular deformation and the associated movement of the electrical sources (thus, it was dynamic). The displacement vectors that describe the ventricular motion were extracted from cinematographic and tagged MRI data using an elastic registration procedure. To probe to what extent the T-wave changes depend on the synchrony/asynchrony of mechanical relaxation and electrical repolarization, we created three electrophysiological configurations, each with a unique QT time: a setup with physiological QT time, a setup with pathologically short QT time (SQT), and pathologically long QT time (LQT), respectively. For all three electrophysiological configurations, a reduction of the T-wave amplitude was observed when the dynamic model was used for the forward calculations. The largest amplitude changes and the lowest correlation coefficients between the static and dynamic model were observed for the SQT setup, followed by the physiological QT and LQT setups.
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.
Catheter ablation has emerged as an effective treatment strategy for atrial fibrillation (AF) in recent years. During AF, complex fractionated atrial electrograms (CFAE) can be recorded and are known to be a potential target for ablation. Automatic algorithms have been developed to simplify CFAE detection, but they are often based on a single descriptor or a set of descriptors in combination with sharp decision classifiers. However, these methods do not reflect the progressive transition between CFAE classes. The aim of this study was to develop an automatic classification algorithm, which combines the information of a complete set of descriptors and allows for progressive and transparent decisions. We designed a method to automatically analyze CFAE based on a set of descriptors representing various aspects, such as shape, amplitude and temporal characteristics. A fuzzy decision tree (FDT) was trained and evaluated on 429 predefined electrograms. CFAE were classified into four subgroups with a correct rate of 81+/-3%. Electrograms with continuous activity were detected with a correct rate of 100%. In addition, a percentage of certainty is given for each electrogram to enable a comprehensive and transparent decision. The proposed FDT is able to classify CFAE with respect to their progressive transition and may allow objective and reproducible CFAE interpretation for clinical use.
Congenital Long-QT Syndrome (LQTS) is a genetic dis- order affecting the repolarization of the heart. The most prevalent subtypes of LQTS are LQT1-3. In this work, we aim to evaluate the differences in the T-waves of simu- lated LQT1-3 in order to identify markers in the ECG that might help to classify patients solely based on ECG mea- surements. For LQT1, mutation S277L was used to char- acterize IKs and mutation S818L in IKr for LQT2. Volt- age clamp data were used to parametrize the ion channel equations of the ten Tusscher and Panfilov model of hu- man ventricular electrophysiology. LQT3 was integrated using an existing mutant INa model. The monodomain model was used in a transmural and apico-basal heteroge- neous model of the ventricles to calculate ventricular exci- tation propagation. The forward calculation on a torso model was performed to determine body surface ECGs. Compared to the physiological case with a QT-time of 375 ms, this interval was prolonged in all LQTS (LQT1 423 ms; LQT2 394 ms; LQT3 405 ms). The T-wave ampli- tude was changed (Einthoven lead II: LQT1 108%; LQT2 91%; LQT3 103%). Also, the width of the T-wave was en- larged (full width at half maximum: LQT1 111%; LQT2 125%; LQT3 109%). At the current state of modeling and data analysis, the three LQTS have not been distinguish- able solely by ECG data.
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.
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.
In this paper, we present an efficient method to estimate changes in forward-calculated body surface potential maps (BSPMs) caused by variations in tissue conductivities. For blood, skeletal muscle, lungs, and fat, the influence of conductivity variations was analyzed using the principal component analysis (PCA). For each single tissue, we obtained the first PCA eigenvector from seven sample simulations with conductivities between ±75% of the default value. We showed that this eigenvector was sufficient to estimate the signal over the whole conductivity range of ±75%. By aligning the origins of the different PCA coordinate systems and superimposing the single tissue effects, it was possible to estimate the BSPM for combined conductivity variations in all four tissues. Furthermore, the method can be used to easily calculate confidence intervals for the signal, i.e., the minimal and maximal possible amplitudes for given conductivity uncertainties. In addition to that, it was possible to determine the most probable conductivity values for a given BSPM signal. This was achieved by probing hundreds of different conductivity combinations with a numerical optimization scheme. In conclusion, our method allows to efficiently predict forward-calculated BSPMs over a wide range of conductivity values from few sample simulations.
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.
D. L. Weiss, D. U. J. Keller, O. Dössel, and G. Seemann. The influence of fibre orientation, extracted from different segments of the human left ventricle, on the activation and repolarization sequence: a simulation study. In Europace, vol. 9(suppl 6) , pp. vi96-vi104, 2007
Aims This computational study examined the influence of fibre orientation on the electrical processes in the heart. In contrast to similar previous studies, human diffusion tensor magnetic resonance imaging measurements were used.Methods The fibre orientation was extracted from distinctive regions of the left ventricle. It was incorporated in a single tissue segment having a fixed geometry. The electrophysiological model applied in the computational units considered transmural heterogeneities. Excitation was computed by means of the monodomain model; the accompanying pseudo-electrocardiograms (ECGs) were calculated.Results The distribution of fibre orientation extracted from the same transversal section showed only small variations. The fibre information extracted from the equal circumferential but different longitudinal positions showed larger differences, mainly in the imbrication angle. Differences of the endocardial myocyte orientation mainly affected the beginning of the activation sequence. The transmural propagation was faster in areas with larger imbrication angles leading to a narrower QRS complex in pseudo-ECGs.Conclusion The model can be expanded to simulate electrophysiology and contraction in the whole heart geometry. Embedded in a torso model, the impact of fibre orientation on body surface ECGs and their relation to local pseudo-ECGs can be identified.
Es wird eine Methode beschrieben, wie medizinische Bilder des Herzens modellbasiert mit EKG-Daten verknüpft werden können, um damit zu einer spezifischen Diagnostik und zu einer besseren Therapieplanung in der Kardiologie zu gelangen. Zunächst wird aus MRT- oder CT-Bildern des Patienten die Geometrie seines Herzens ermittelt. Elektrokardiographische Messungen an der Körperoberfläche (EKG oder Body Surface Potential Mapping) und aus dem Inneren des Herzens (intracardial mapping) werden aufgenommen und die Orte der Messung in den Bilddatensatz eingetragen (registration). Ein elektrophysiologisches Computermodell vom Herzen des Patienten wird mit Hilfe der elektrophysiologischen Messdaten iterativ angepasst. Schließlich entsteht im Computer ein virtuelles Herz des Patienten, welches sowohl die Geometrie als auch die Elektrophysiologie wiedergibt. Ein Modell der Vorhöfe hat beispielsweise das Potenzial, die Ursachen von Vorhofflimmern zu erkennen und die Radiofrequenz-Ablationsstrategie zu optimieren. Ein Modell der Ventrikel des Herzens kann helfen, genetisch bedingte Rhythmusstörungen besser zu verstehen oder auch die Parameter bei der kardialen Resynchronisationstherapie zu optimieren. Die Modellierung des Herzens mit einem Infarktgebiet könnte die elektrophysiologischen Auswirkungen des Infarktes beschreiben und die Risikostratifizierung für gefährliche ventrikuläre Arrhythmien unterstützen oder die Erfolgsrate bei ventrikulären Ablationen erhöhen.
Complex fractionated atrial electrograms (CFAE) are a target for catheter ablation as they coincide with areas of slow conduction. In this study we simulated different vol- ume fractions of diffuse and patchy fibrosis up to 50 %. Catheter signals for different electrode spacings were cal- culated and characteristic features were compared to a clinical database of CFAE-signals. A linear slowing of global conduction velocities was found independent of the type of fibrosis. For patchy fibrosis, electrograms displayed fractionation, which was not seen for diffuse fibrosis of the same degree. In comparison to clinical data, simulated electrograms showed up to 10 zero crossings per electro- gram, which was also seen for clinical EGMs with medium fractionation (class 2 of 3). For both, clinical (84 %) and simulated (88 %) signals, a significant difference in ampli- tude is present between fractionated and non-fractionated signals.
Creating transmural ablation scars in a reliable way is a key issue in improvement of therapeutical pro- cedures for cardiac arrhythmias. About one third of the patients has to undergo several procedures till arrhythmic episodes are successfully treated. Morphological features of intracardiac electrograms might contribute to evaluate scar transmurality during the ablation procedure. We an- alyzed intracardiac signals before, during and after point- wise ablation in patients with atrial flutter. Unipolar elec- trograms of the distal electrode showed a relative decrease in amplitude of the second extremum of up to 99 % with a mean of 84±20.6 % after the endpoint of ablation.
Intracardiac electrograms are the key in under- standing, interpretation and treatment of cardiac arrhythmias. However, electrogram morphologies are strongly variable due to catheter position, orientation and contact. Simulations of intracardiac electrograms can improve comprehension and quantification of influencing parameters and therefore reduce misinterpretations. In this study simulated intracardiac electro- grams are analyzed regarding tilt angles of the catheter relative to the propagation direction, electrode tissue distances as well as clinical filter settings. Catheter signals are computed on a realistic 3D catheter geometry using bidomain simulations of cardiac electrophysiology. Thereby high conductivities of the catheter electrodes are taken into account. For validation, simulated electrograms are compared with in vivo electrograms recorded during an EP-study with direct annotation of catheter orientation and tissue contact. Good agreement was reached regarding timing and signal width of simulated and measured electrograms. Correlation was 0.92±0.07 for bipolar, 0.92±0.05 for unipolar distal and 0.80 ± 0.12 for unipolar proximal electrograms for different catheter orientations and locations.
M. W. Keller, O. Dössel, and G. Seemann. Simulating extracellular microelectrode recordings on cardiac tissue preparations in a bidomain model. In Biomedizinische Technik / Biomedical Engineering, vol. 57(s1) , pp. 814, 2012
M. W. Keller, and O. Dössel. Towards simultaneous optical and electrical characterization of the electrode tissue interface in catheter measurements of atrial electrophysiology. In Biomedizinische Technik / Biomedical Engineering (Proc. BMT 2011), vol. 56(s1) , 2011
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.
D. U. J. Keller, O. Dössel, and G. Seemann. Simulating cardiac excitation in a high resolution biventricular model. In Proceedings BMT 2010, 44. DGBMT Jahrestagung, 3-Länder-Tagung D-A-CH, Rostock, vol. 55(s1) , pp. 205-208, 2010
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.
M. W. Keller, C. Schilling, A. Luik, C. Schmitt, and O. Dössel. Descriptors for a classification of complex fractionated atrial electrograms as a guidance for catheter ablation of atrial fibrillation. In Biomedizinische Technik / Biomedical Engineering, vol. 55(s1) , pp. 100-103, 2010
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
D. U. J. Keller, O. Dössel, and G. Seemann. Evaluation of rule-based approaches for the incorporation of skeletal muscle fiber orientation in patient-specific anatomies. In Proceedings Computers in Cardiology, vol. 36, pp. 181-184, 2009
Muscle anisotropy is important for the realistic solution of the forward problem of electrocardiography. Whenever computer models of patient-specific anatomies are created usually no information about the muscle fiber arrangement in the heart or skeletal muscle is available. As in-vivo imaging techniques that can determine fiber orientation like Diffusion Tensor MRI are time-consuming and susceptible to motion artifacts, cardiac fiber orientation is frequently described using simplified rules. However, for the skeletal muscle there are only few suggestions for a rule-based implementation of fiber orientation into patient-specific models. In this work we evaluated a rule-based approach from the literature together with two new methods by comparing the corresponding forward calculated body surface potential maps (BSPMs) with the BSPM resulting from a reference skeletal muscle fiber distribution extracted from the thin-section photos of the Visible Man dataset (Journal of Computing and Information Technology vol.6, pp. 95-101 1998). The skeletal muscle anisotropy ratio was set to 3:1. The following fiber orientation setups were evaluated: A) the torso is divided into twelve sectors (cross-section perspective) and fiber direction was assumed to be perpendicular to the bisector as proposed by Klepfer et al. (IEEE Trans. Biomed. Eng. vol. 44, no. 8, pp. 706-719 1997); B) A 3D Sobel filter was used on the torso geometry filled with a gradient from inside to outside which generated a vector that was normal to the thoracic surface in every voxel. Fiber orientation was assumed to be perpendicular to the plane formed by these normal vectors and the direction from head to feet (longitudinal torso orientation); C) Same procedure as in B) but additionally, the back muscles which are known to have a longitudinal orientation were integrated accordingly. Potentials were extracted at 64 electrode positions from the BSPMs. The RMS was calculated at these electrode positions between the reference fiber distribution and the respective rule-based approaches. The RMS was comparable between A) and B) (8.8e-5 vs. 8.9e-5) leading to the conclusion that the twelve discrete sectors introduced no significant error. A) and B) performed also well compared to a modified version of the reference dataset where the longitudinal component of the fiber vectors was set to zero (8.3e-5). Including the longitudinal components of the back muscles as done in C) enhances the RMS to 5.5e-5. If the skeletal muscle anisotropy was neglected and only cardiac fiber orientation was taken into account, the RMS improved (!) further to only 4.0e-5. Thus it can be concluded that neglecting the longitudinal component (A) and B)) or accounting for it with a highly simplified approach (C)) is not sufficient. In cases where no detailed information about the skeletal muscle fiber arrangement is available, it is better to entirely neglect its anisotropic influence.
D. U. J. Keller, R. Kalayciyan, O. Dössel, and G. Seemann. Fast creation of endocardial stimulation profiles for the realistic simulation of body surface ECGs. In IFMBE Proceedings World Congress on Medical Physics and Biomedical Engineering, vol. 25/4, pp. 145-148, 2009
The Purkinje network plays a major role for realistically simulating the activation sequence of the ventricles. In this work, we describe a method to create an endocardial stimulation profile that describes the location and time instant of ventricular stimulation, thus mimicking the His-Purkinje conduction system. By adapting model parameters stimulation profiles can be generated for different ventricular anatomies with minimal manual interaction. The stimulation profile parameters are evaluated by analyzing the excitation propagation in a three-dimensional, heterogeneous and anisotropic model of the human ventricles which are embedded in an anatomically detailed torso geometry. The calculated QRS complexes are in good agreement with the corresponding clinical recordings on the same proband.
The congenital long-QT syndrome is commonly associated with a high risk for polymorphic ventricular tachy-cardia and sudden cardiac death. This is probably due to an intensification of the intrinsic heterogeneities present in ventricular myocardium. Increasing the electrophysiological heterogeneities amplifies the dispersion of repolarization which directly affects the morphology of the T wave in the ECG. The aim of this work is to investigate the effects of LQT2, a specific subtype of the long-QT syndrome (LQTS), on the Body Surface Potential Maps (BSPM) and the ECG. In this context a three-dimensional, heterogeneous model of the human ventricles is used to simulate both physiological and pathological excitation propagation. The results are used as input for the forward calculation of the BSPM and ECG. Characteristic QT prolongation is simulated correctly. The main goal of this study is to prepare and evaluate a simulation environment that can be used prospectivley to find features in the ECG or the BSPM that are characteristic for the LQTS. Such features might be used to facilitate the identification of LQTS patients.
D. U. J. Keller, D. L. Weiss, O. Dössel, and G. Seemann. Transferring ventricular myocyte orientation to individual patient data based on diffusion tensor MRI measurements. In Tagungsband 6. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie e. V., pp. 255-258, 2007
D. U. J. Keller, O. Dössel, G. Seemann, and D. L. Weiss. Detailed anatomical modeling of human ventricles based on diffusion tensor MRI. In Gemeinsame Jahrestagung der Deutschen, der Österreichischen und der Schweizerischen Gesellschaft für Biomedizinische Technik, vol. 50/1, 2006
There is still a need for research to understand the co- herences of the origin of arrhythmias such like rotors and possible ablation strategies. The aim of this work was the analysis of typical signal characteristics near a rotor cen- ter. Rotors were simulated on 2D patch geometry (100 mm x 100 mm) with spatial resolution of 0.1mm. Based on extracellular potentials, different features were evalu- ated: Local activation time, peak to peak amplitude, steep- est negative slope and approximate entropy were com- pared regarding their ability to indicate the rotor tip lo- cation. Furthermore, typical signal patterns of different mapping catheters centered at the rotor tip position were analyzed. The determined maximum distances between the focal point of phase singularities and determined centers by the peak to peak amplitudes were maximal 1.7 mm.
Local activation time (LAT) maps help to understand the path of electrical excitation in cardiac arrhythmias. They can be generated automatically from intracardiac electrograms using various criteria provided by commercial electroanatomical mapping systems. This study compares existing criteria and a novel method based on the non-linear energy operator (NLEO) with respect to their precision and robustness.
Intracardiac electrograms are essential for the diagnosis and treatment of various cardiac arrhythmias. To gain reliable information about structural alterations of underlying tissue, it is necessary to interpret these electrograms correctly. Therefore it has to be understood how other parameters influence the signal. Realistic 3D geometries were created and simulated using the bidomain model. Based on these simulations, the influences of catheter orientation, tissue thickness and conduction velocity on the amplitudes of intracardiac electrograms were evaluated.
Heterogeeities of the ventricular electrophysiol- ogy play a major role in the generation of the T-wave mor- phology and amplitude. The exact way of the distribution of electrophysiological differences is not known. In this work, a numerical approach is presented in which the excitation propagation of different heterogeneity distributions of IKs are simulated and the multi-channel ECG is calculated. The ECG data are evaluated against measured ECGs. The most realistic configuration is a combination of transmural and apico-basal heterogeneity with 35% of Endo, 30% of M and 35% of Epi cells and an apico-basal gradient with a factor of 2. This specific setup has a correlation of around 90% and a root mean square error of around 0.0795.
T. Fritz, O. Jarrousse, D. Keller, O. Dössel, and G. Seemann. In silico analysis of the impact of transmural myocardial infarction on cardiac mechanical dynamics for the 17 AHA segments. In Proceedings of the 6th International Conference on Functional Imaging and Modeling of the Heart, vol. LNCS, 6666, pp. 241-249, 2011
The impact of transmural infarctions of the left ventricle on the cardiac mechanical dynamics is evaluated for all 17 AHA segments in a computer model. The simulation framework consists of two parts: an electrophysiological model and an elastomechanical model of the ventricles. The electrophysiological model is used to simulate the electrophysiological processes on cellular level, excitation propagation and the tension development. It is linked to the elastomechanical model, which is based on nonlinear finite element analysis for continuum mechanics. Altogether, 18 simulations of the contraction of the ventricles were performed, 17 with an infarction in the respective AHA segment and one simulation for the control case. For each simulation, the mechanical dynamics as well as the wall thickening of the infarct region were analyzed and compared to the corresponding region of the control case. The simulation revealed details of the impact of the myocardial infarction on wall thickening as well as on the velocity of the infarct region for most of the AHA segments
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.
W. H. W. Schulze, D. U. J. Keller, and O. Dössel. A recursive cellular automaton that reconstructs transmembrane voltages with a range-adjusted Tikhonov-method. In International Journal of Bioelectromagnetism, vol. 13(4) , pp. 184-189, 2011
Tikhonov methods usually lead to solutions of low amplitude that are distributed around zero. When reconstructing transmembrane voltages (TMVs) in the myocardium, the signal is therefore often not in the physiological range of between around -80mV and 10mV. In this article, we propose an adjusted Tikhonov method that reconstructs TMVs in the correct range, given an estimate of one polarized node in the heart and an estimated set of nodes that have depolarized in the preceding time step. It is shown that when feeding the reconstructed TMVs into a simple cellular automaton recursively, and when using the computed excitation propagation as a prior for the Tikhonov method, it is possible to reconstruct the excitation propagation throughout the ventricular myocardium. The method requires an estimate of the region of initial activation.
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.
R. Kalayciyan, D. U. J. Keller, O. Dössel, and G. Seemann. Creation of a realistic endocardial stimulation profile for the visible man dataset. In IFMBE Proceedings World Congress on Medical Physics and Biomedical Engineering, vol. 25/4, pp. 934-937, 2009
C. A. Otto, D. U. J. Keller, O. Dössel, and G. Seemann. Integrating Beta-Adrenergic Signaling into a Computational Model of Human Cardiac Electrophysiology. In IFMBE Proceedings World Congress on Medical Physics and Biomedical Engineering, vol. 25/4, pp. 1033-1036, 2009
High performance computing is required to make feasible simulations of whole organ models of the heart with biophysically detailed cellular models in a clinical setting. Increasing model detail by simulating electrophysiology and mechanical models increases computation demands. We present scaling results of an electro mechanical cardiac model of two ventricles and compare them to our previously published results using an electrophysiological model only. The anatomical data-set was given by both ventricles of the Visible Female data-set in a 0.2 mm resolution. Fiber orientation was included. Data decomposition for the distribution onto the distributed memory system was carried out by orthogonal recursive bisection. Load weight ratios for non tissue vs. tissue elements used in the data decomposition were 1:1, 1:2, 1:5, 1:10, 1:25, 1:38.85, 1:50 and 1:100. The ten Tusscher et al. (2004) electrophysiological cell model was used and the Rice et al. (1999) model for the computation of the calcium transient dependent force. Scaling results for 512, 1024, 2048, 4096, 8192 and 16,384 processors were obtained for 1 ms simulation time. The simulations were carried out on an IBM Blue Gene/L supercomputer. The results show linear scaling from 512 to 16,384 processors with speedup factors between 1.82 and 2.14 between partitions. The most optimal load ratio was 1:25 for on all partitions. However, a shift towards load ratios with higher weight for the tissue elements can be recognized as can be expected when adding computational complexity to the model while keeping the same communication setup. This work demonstrates that it is potentially possible to run simulations of 0.5 s using the presented electro-mechanical cardiac model within 1.5 hours.
Orthogonal recursive bisection (ORB) algorithm can be used as data decomposition strategy to distribute a large data set of a cardiac model to a distributed memory supercomputer. It has been shown previously that good scaling results can be achieved using the ORB algorithm for data decomposition. However, the ORB algorithm depends on the distribution of computational load of each element in the data set. In this work we investigated the dependence of data decomposition and load balancing on different rotations of the anatomical data set to achieve optimization in load balancing. The anatomical data set was given by both ventricles of the Visible Female data set in a 0.2 mm resolution. Fiber orientation was included. The data set was rotated by 90 degrees around x, y and z axis, respectively. By either translating or by simply taking the magnitude of the resulting negative coordinates we were able to create 14 data sets of the same anatomy with different orientation and position in the overall volume. Computation load ratios for non tissue vs. tissue elements used in the data decomposition were 1:1, 1:2, 1:5, 1:10, 1:25, 1:38.85, 1:50 and 1:100 to investigate the effect of different load ratios on the data decomposition. The ten Tusscher et al. (2004) electrophysiological cell model was used in monodomain simulations of 1 ms simulation time to compare performance using the different data sets and orientations. The simulations were carried out for load ratio 1:10, 1:25 and 1:38.85 on a 512 processor partition of the IBM Blue Gene/L supercomputer. The results show that the data decomposition does depend on the orientation and position of the anatomy in the global volume. The difference in total run time between the data sets is 10 s for a simulation time of 1 ms. This yields a difference of about 28 h for a simulation of 10 s simulation time. However, given larger processor partitions, the difference in run time decreases and becomes less significant. Depending on the processor partition size, future work will have to consider the orientation of the anatomy in the global volume for longer simulation runs.
The output data generated in whole heart simula- tions are usually single or multiple parameters at each point in the simulation space. Visualizing data sets of gigabyte size puts great stress on the hardware and can be slow and tedious. Creating animated movies to analyze the excitation propaga- tion can take hours on standard systems. We present two par- allel visualization techniques to improve rendering of large datasets from cardiac simulations.The Scalable Parallel Visualization Networking (SPVN) toolkit provides the ability to assist in optimizing the utility and functionality of the aggregate resources in visualization clusters. Run time visualization offers the opportunity to visu- alize the results of cardiac simulations on the fly on High Per- formance Computers. Parallel visualization techniques enable fast manipulation of high resolution whole heart data sets and simulation results. The SPVN system has the potential to be linked with the simulation environment similar to the run time visualization described.Future efforts will focus on creating a simulation and visu- alization environment with appropriate characteristics for clinical setting. Specifically, speed, intuitive control and the ability to render diverse signals will likely be critical to drive adoption in the clinical setting.
Cisapride is a drug to help gastric problems. It is limited because of reports of the side-effect long QT syndrome which predisposes to arrhythmias. In this computatinal study, the effects of Cisapride on human ventricular myocytes are investigated in-silico. From literature reported effects of the drug on ion channel level are included into a virtual human ventricular cell. Cisapride has the most dominating effect on the rapid delayed rectifier current IKr. A shift in the activation and inactivation and mainly a reduction of conductivity is seen. This leads to the prolongation of the APD comparable to the long QT syndrome. In future studies, the stability of the heart under the influence of this drug will be evaluated
After mathematical modeling of the healthy heart now modeling of diseases comes into the focus of research. Modeling of arrhythmias already shows a large degree of realism. This offers the chance of more detailed diagnosis and computer assisted therapy planning. Options for genetic diseases (channelopathies like Long-QT-syndrome), infarction and infarction-induced ventricular fibrillation, atrial fibrillation (AF) and cardiac resynchronization therapy are demonstrated.
R. Miri, O. Dössel, M. Reumann, D. U. J. Keller, and D. Farina. Comparison of the electrophysiologically based optimization methods with different pacing parameters in patient undergoing resynchronization treatment. In Engineering in Medicine and Biology Society, 2008. EMBS 2008. 30th Annual International Conference of the IEEE, vol. 2008, pp. 1741-1744, 2008
Many studies conducted on patients suffering from congestive heart failure have shown the efficacy of cardiac resynchronization therapy (CRT). The presented research investigates an off-line optimization algorithm based on different electrode positioning and timing delays. A computer model of the heart was used to simulate left bundle branch block (LBBB), myocardial infarction (MI) and reduction of intraventricular conduction velocity in order to customize the patient symptom. The optimization method evaluates the error between the healthy heart and pathology with/without pacing in terms of activation time and QRS length. Additionally, a torso model of the patient is extracted to compute the body surface potential map (BSPM) and to simulate the ECG with Wilson leads to validate the results obtained by the electrophysiological heart model optimization.
Multi-scale, multi-physical heart models have not yet been able to include a high degree of accuracy and resolution with respect to model detail and spatial resolution due to computational limitations of current systems. We propose a framework to compute large scale cardiac models. Decomposition of anatomical data in segments to be distributed on a parallel computer is carried out by optimal recursive bisection (ORB). The algorithm takes into account a computational load parameter which has to be adjusted according to the cell models used. The diffusion term is realized by the monodomain equations. The anatomical data-set was given by both ventricles of the Visible Female data-set in a 0.2 mm resolution. Heterogeneous anisotropy was included in the computation. Model weights as input for the decomposition and load balancing were set to (a) 1 for tissue and 0 for non-tissue elements; (b) 10 for tissue and 1 for non-tissue elements. Scaling results for 512, 1024, 2048, 4096 and 8192 computational nodes were obtained for 10 ms simulation time. The simulations were carried out on an IBM Blue Gene/L parallel computer. A 1 s simulation was then carried out on 2048 nodes for the optimal model load. Load balances did not differ significantly across computational nodes even if the number of data elements distributed to each node differed greatly. Since the ORB algorithm did not take into account computational load due to communication cycles, the speedup is close to optimal for the computation time but not optimal overall due to the communication overhead. However, the simulation times were reduced form 87 minutes on 512 to 11 minutes on 8192 nodes. This work demonstrates that it is possible to run simulations of the presented detailed cardiac model within hours for the simulation of a heart beat.
Electrophysiological modeling of the heart enable quantitative description of electrical processes during normal and abnormal excitation. Cell models describe e.g. the properties of the cell membrane and the gating process of ionic channels. New measurement data is available for these channels for physiological and some pathological states. These data should be included in the models to enhance their features. In this work we describe a framework adapting ion channel models to measurement data by using a particle swarm optimization (PSO). Models of ion channels can be described by Hogdkin-Huxley equations or by Markovian models. They consider rate constants that are complex functions depending on the transmembrane voltage. Each transition has two rate constants described by several parameters. These parameters need to be varied in order to minimize the difference between measured and simulated ion channel kinetics. Since this minimization procedure is multidimensional and the function can have several local minima, conventional optimization strategies like Powells algorithm and conjugate gradient do not ensure to find the global minimum. To overcome this, a PSO was implemented that inserts several dependent particles randomly into the search space. It is based on the social behavior of swarms. As the particles are independent during each iteration the procedure can be calculated in parallel. The measurement data used for this work were current traces of a voltage-clamp protocol of reggae mutant hERG channels. The same protocol as for the measurement was assigned to the model of Lu et al. describing hERG function with a Markovian model. The value to be minimized was the sum of mean square errors between measured and simulated currents at certain time instances. Both Powell and PSO were started several times with random starting values. In 94% of the cases PSO found the minimum compared to 16% for Powell. On the other hand PSO needed approximately 100 times more function evaluations. The parallelization decreased the overall time needed by the PSO to about the same amount Powell needed. Therefore, the parallel PSO is a fast and reliable approach for adapting ion channel models to measured data.
Simulation of cardiac excitation is often a trade-off between accuracy and speed. A promising minimal, time-efficient cell model with four state variables has recently been presented together with parametrizations for ventricular cell behaviour. In this work, we adapt the model parameters to reproduce atrial excitation properties as given by the Courtemanche model. The action potential shape is considered as well as the restitution of action potential duration and conduction velocity. Simulation times in a single cell and a tissue patch are compared between the two models. We further present the simulation of a sinus beat on the atria in a realistic 3D geometry using the fitted minimal model in a monodomain simulation.
R. Miri, O. Dössel, M. Reumann, D. U. J. Keller, and D. Farina. A non-invasive computer based optimization strategy of biventricular pacing. In Tagungsband 6. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie e. V., pp. 133-136, 2007
R. Miri, O. Dössel, M. Reumann, D. Keller, and D. Farina. Computer based optimization of biventricular pacing according to the left ventricular 17 myocardial segments. In Proceedings of the 29th Annual International Conference of the IEEE EMBS, pp. 1418-1421, 2007
Heterogeneity of ion channel properties within human ventricular tissue determines the sequence of repolarization under healthy conditions. In this computational study, the impact of different extend of electrophysiological heterogeneity in both human ventricles on the ECG was investigated by a forward calculation of the cardiac electrical signals on the body surface. The gradients ranged from solely transmural, interventricular and apico-basal up to full combination of these variations. As long interventricular heterogeneities were neglected, the transmural gradient generated a positive T wave that was increased when apico-basal variations were considered. Inclusion of interventricular changes necessitated the incorporation of both transmural and apico-basal heterogeneities to reproduce the positive T wave.
M. Keller. Formation of Intracardiac Electrograms under Physiological and Pathological Conditions. KIT Scientific Publishing. Dissertation. 2014
This work presents methods to advance electrophysiological simulations of intracardiac electrograms (IEGM). An experimental setup is introduced, which combines electrical measurements of extracellular potentials with a method for optical acquisition of the transmembrane voltage in-vitro. Thereby, intracardiac electrograms can be recorded under defined conditions. Using experimental and clinical signals, detailed simulations of IEGMs are parametrized, which can support clinical diagnosis.
D. U. J. Keller. Multiscale modeling of the ventricles: from cellular electrophysiology to body surface electrocardiograms. KIT Scientific Publishing. Dissertation. 2011
This work is focused on different aspects within the loop of multiscale modeling:On the cellular level, effects of adrenergic regulation and the Long-QT syndrome have been investigated.On the organ level, a model for the excitation conduction system was developed and the role of electrophysiological heterogeneities was analyzed.On the torso level a dynamic model of a deforming heart was created and the effects of tissue conductivities on the solution of the forward problem were evaluated.
Student Theses (4)
L. Keller. Influence of Electrical Propagation Patterns on Diffusion Currents. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Bachelorarbeit. 2023
Currently, therapeutic approaches for cardiac arrhythmias like atrial fibrillation are not personalized, leading to more than half of the patients experiencing relapses after ablation treatments. Moreover, the risk of atrial fibrillation increases with age, posing a significant challenge to healthcare systems due to the aging population. Personalization and improving the success rate of arrhythmia treatment could be achieved through the use of mathematical models. Simulating cardiac electrophysiology, these models offer insights into individual aspects of treatment options for each patient. However, existing models are impractical for clinical application either due to their computational demands or limitations in simulating various scenarios. The DREAM presents a mathematical model that aims to circumvent these drawbacks by alternating available models, yet it remains clinically unusable due to existing inaccuracies. One reason for these inaccuracies lies in the computation of the diffusion current, a parameterized function computed independently of electrical wave propagation patterns. The aim of this work is to study the relationships between the diffusion current and propagation patterns, enabling their incorporation into the DREAM and enhancing its precision in simulating cardiac arrhythmias.In order to establish connections between the diffusion current and emerging electrical wave propagation patterns, two novel variables were introduced: the source area and the sink rate. These newly defined variables reflect the ratio of excited to unexcited nodes for each node within a mesh. The monodomain model was applied to simulate both a curved wavefront and colliding waves. When analyzing the effects of different pacing frequencies, the influence of the diastolic interval on the diffusion current was investigated. This involved introducing six stimuli with a constant pacing cycle length in a monodomain model simula- tion. For experiments involving various propagation patterns and varying pacing frequencies, the diffusion current was characterized by its maximum and minimum values, providing insights into the upstroke and downstroke.By examining various source-sink dynamics, it was discovered that the source has an impact on the upstroke, while the sink influences the downstroke of the diffusion current. Connections between the source area and the maximum of the diffusion current, as well as between the sink rate and the minimum of the diffusion current, were established. Further- more, the investigation of pacing frequencies revealed a correlation between the maximum and minimum of the diffusion current and the diastolic interval, manifested as a restitution curve.This work demonstrated, on one hand, the influence of source-sink dynamics on the shape of the diffusion current, and on the other hand, highlighted the distorted results deriving from the underlying scenario of source-sink dynamics correlation. Focusing solely on a curved wavefront, the distribution of data complicated the curve fitting to the extent of making it impossible. Lastly, this study delineates how the acquired insights into existing correlations can be incorporated into the DREAM, offering an approach to optimize its precision.
M. Keller. Charakterisierung und Analyse von räumlich-zeitlichen Erregungsmustern bei Vorhofflimmern. Institut für Biomedizinische Technik, Karlsruher Institut für Technologie (KIT). Diplomarbeit. 2010
D. U. J. Keller. Detailed anatomical and electrophysiological modeling of human ventricles based on diffusion tensor MRI. Institute of Biomedical Engineering, Universität Karlsruhe (TH). Diplomarbeit. 2006
The importance of a detailed model characterizing the fiber orientation of the ventricular my- ocardium is unquestioned when it comes to simulating excitation conduction processes. It was therefore the scope of this work to provide the necessary tools to create rules that describe the fiber orientation in various parts of both left and right ventricle. This was not previously possible, as a single rule was utilized for the complete left ventricle whereas the right ventricle could not be characterized at all. The additional rules were created by subdividing the ventricular anatomy in a certain number of segments. A single rule was now determined for every automatically generated segment that characterizes the course of the fiber orientation. The number of segments can be set depending on the desired density with which the rules, describing the muscle fiber orientation, are determined. A higher number of rules leads to a more realistic description of the genuine fiber orientation. On the other hand however, a large number of rules is more difficult to create and verify.The results presented in chapter 6 underline, that a single rule as it has previously been used is not able to depict the regional differences of the fiber orientation. Especially the transverse an- gle showed variations from apex to base that are in agreement with other literature reports (see [18, 19]). The transmural fluctuations of the transverse angles agreed with the work of Scollan  while the presence of a non-zero transverse angle conflicted with reports from Rijcken, Bovendeerd and Ubbink at the same time [24, 25].The generated results should be confirmed by the investigation of additional DTMRI datasets. An increased spatial resolution of the datasets would furhermore support the extraction of rules from the right ventricle which was very problematic in the dataset at hand, due to the limited number of voxels that constitute the right ventricular wall.Future work should focus on the definition of additional subdivisions in the left ventricular apex. Presently, there is no reasonable allocation implemented and an extraction of fiber orientation rules therefore not possible (see chapter 6). Additionally, the manual segmentation procedure which turned out to be time-consuming and slightly inaccurate can be improved by including the available information inherent in the diffusion data (see chapter 5.5). Finally, it is important to investigate the full impact of the created fiber orientation model which is only possible by simulating the excitation conduction process in the complete ventricle. As a prerequisite for these simulations, the encountered problems described in chapter 7 have to be overcome and the concept of exchanging data based on shared-memory should be extended to allow the handling of datasets with a high spatial resolution.
D. U. J. Keller. Investigating Options for a Low Cost and High Performance Doppler OCT. University of Western Australia. . 2005