Transmural ultrasound-based visualization of patterns of action potential wave propagation in cardiac tissue

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Estimating cardiac active tension from wall motion-An inverse problem of cardiac biomechanics

The contraction of the human heart is a complex process as a consequence of the interaction of internal and external forces. In current clinical routine, the resulting deformation can be imaged during an entire heart beat. However, the active tension development cannot be measured in vivo but may provide valuable diagnostic information. In this work, we present a novel numerical method for solving an inverse problem of cardiac biomechanics-estimating the dynamic active tension field, provided the motion of the myocardial wall is known. This ill-posed non-linear problem is solved using second order Tikhonov regularization in space and time. We conducted a sensitivity analysis by varying the fiber orientation in the range of measurement accuracy. To achieve RMSE <20% of the maximal tension, the fiber orientation needs to be provided with an accuracy of 10°. Also, variation was added to the deformation data in the range of segmentation accuracy. Here, imposing temporal regularization led to an eightfold decrease in the error down to 12%. Furthermore, non-contracting regions representing myocardial infarct scars were introduced in the left ventricle and could be identified accurately in the inverse solution (sensitivity >0.95). The results obtained with non-matching input data are promising and indicate directions for further improvement of the method. In future, this method will be extended to estimate the active tension field based on motion data from clinical images, which could provide important insights in terms of a new diagnostic tool for the identification and treatment of diseased heart tissue.

Ultrafast four-dimensional imaging of cardiac mechanical wave propagation with sparse optoacoustic sensing

Propagation of electromechanical waves in excitable heart muscles follows complex spatiotemporal patterns holding the key to understanding life-threatening arrhythmias and other cardiac conditions. Accurate volumetric mapping of cardiac wave propagation is currently hampered by fast heart motion, particularly in small model organisms. Here we demonstrate that ultrafast four-dimensional imaging of cardiac mechanical wave propagation in entire beating murine heart can be accomplished by sparse optoacoustic sensing with high contrast, ∼115-µm spatial and submillisecond temporal resolution. We extract accurate dispersion and phase velocity maps of the cardiac waves and reveal vortex-like patterns associated with mechanical phase singularities that occur during arrhythmic events induced via burst ventricular electric stimulation. The newly introduced cardiac mapping approach is a bold step toward deciphering the complex mechanisms underlying cardiac arrhythmias and enabling precise therapeutic interventions.

Reconstructing Cardiac Wave Dynamics From Myocardial Motion Data

Various models exist to predict the active stresses and membrane potentials within cardiac muscle tissue. However, there exist no methods to reliably measure active stresses, nor do there exist ways to measure transmural membrane potentials that are suitable for in vivo usage. Prior work has devised a linear model to map from the active stresses within the tissue to displacements [1]. In situations where measurements of tissue displacements are entirely precise, we are able to naively solve for the active stresses from the measurements with ease. However, real measurement processes always carry some associated random error and, in the presence of this error, our naive solution to this inverse problem fails. In this work we propose the use of the Ensemble Transform Kalman Filter to more reliably solve this inverse problem. This technique is faster than other related Kalman Filter techniques while still generating high quality estimates which improve on our naive solution. We demonstrate, using in silico simulations, that the Ensemble Transform Kalman Filter produces errors whose standard deviation is an order of magnitude smaller than the least-squares solution.

Toward Quantification and Visualization of Active Stress Waves for Myocardial Biomechanical Function Assessment

Estimating and visualizing myocardial active stress wave patterns is crucial to understanding the mechanical activity of the heart and provides a potential non-invasive method to assess myocardial function. These patterns can be reconstructed by analyzing 2D and/or 3D tissue displacement data acquired using medical imaging. Here we describe an application that utilizes a 3D finite element formulation to reconstruct active stress from displacement data. As a proof of concept, a simple cubic mesh was used to represent a myocardial tissue "sample" consisting of a 10 × 10 × 10 lattice of nodes featuring different fiber directions that rotate with depth, mimicking cardiac transverse isotropy. In the forward model, tissue deformation was generated using a test wave with active stresses that mimic the myocardial contractile forces. The generated deformation field was used as input to an inverse model designed to reconstruct the original active stress distribution. We numerically simulated malfunctioning tissue regions (experiencing limited contractility and hence active stress) within the healthy tissue. We also assessed model sensitivity by adding noise to the deformation field generated using the forward model. The difference image between the original and reconstructed active stress distribution suggests that the model accurately estimates active stress from tissue deformation data with a high signal-to-noise ratio.

Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media

The heart is an elastic excitable medium, in which mechanical contraction is triggered by nonlinear waves of electrical excitation, which diffuse rapidly through the heart tissue and subsequently activate the cardiac muscle cells to contract. These highly dynamic excitation wave phenomena have yet to be fully observed within the depths of the heart muscle, as imaging technology is unable to penetrate the tissue and provide panoramic, three-dimensional visualizations necessary for adequate study. As a result, the electrophysiological mechanisms that are associated with the onset and progression of severe heart rhythm disorders such as atrial or ventricular fibrillation remain insufficiently understood. Here, we present a novel synchronization-based data assimilation approach with which it is possible to reconstruct excitation wave dynamics within the volume of elastic excitable media by observing spatiotemporal deformation patterns, which occur in response to excitation. The mechanical data are assimilated in a numerical replication of the measured elastic excitable system, and within this replication, the data drive the intrinsic excitable dynamics, which then coevolve and correspond to a reconstruction of the original dynamics. We provide a numerical proof-of-principle and demonstrate the performance of the approach by recovering even complicated three-dimensional scroll wave patterns, including vortex filaments of electrical excitation from within a deformable bulk tissue with fiber anisotropy. In the future, the reconstruction approach could be combined with high-speed imaging of the heart's mechanical contractions to estimate its electrophysiological activity for diagnostic purposes.

Cardiac electrophysiological activation pattern estimation from images using a patient-specific database of synthetic image sequences

While abnormal patterns of cardiac electrophysiological activation are at the origin of important cardiovascular diseases (e.g., arrhythmia, asynchrony), the only clinically available method to observe detailed left ventricular endocardial surface activation pattern is through invasive catheter mapping. However, this electrophysiological activation controls the onset of the mechanical contraction; therefore, important information about the electrophysiology could be deduced from the detailed observation of the resulting motion patterns. In this paper, we present the study of this inverse cardiac electrokinematic relationship. The objective is to predict the activation pattern knowing the cardiac motion from the analysis of cardiac image sequences. To achieve this, we propose to create a rich patient-specific database of synthetic time series of the cardiac images using simulations of a personalized cardiac electromechanical model, in order to study this complex relationship between electrical activity and kinematic patterns in the context of this specific patient. We use this database to train a machine-learning algorithm which estimates the depolarization times of each cardiac segment from global and regional kinematic descriptors based on displacements or strains and their derivatives. Finally, we use this learning to estimate the patient’s electrical activation times using the acquired clinical images. Experiments on the inverse electrokinematic learning are demonstrated on synthetic sequences and are evaluated on clinical data with promising results. The error calculated between our prediction and the invasive intracardiac mapping ground truth is relatively small (around 10 ms for ischemic patients and 20 ms for nonischemic patient). This approach suggests the possibility of noninvasive electrophysiological pattern estimation using cardiac motion imaging.

Dependence of scroll-wave dynamics on the orientation of a gradient of excitability

The dynamics of scroll waves with a variable orientation to a vertically oriented gradient of excitability is studied by optical tomography in the ferroin-catalyzed Belousov-Zhabotinsky reaction. An almost perpendicular orientation between the scroll wave and gradient induces a pair of twists of opposite handedness on the scroll wave. The position of the nodal plane formed between the twists is governed by the time delay of the twist formation and therefore leads to a symmetric or asymmetric twisted scroll wave. Larger inclinations between scroll wave and gradient cause a drift of the filament along the reactor wall until it reaches the bottom of the reaction container. In this case, the scroll wave does not twist, suggesting that a drift acts as an alternative mechanism of responding to the gradient.

Twists of opposite handedness on a scroll wave

The dynamic interaction of scroll waves in the Belousov-Zhabotinsky reaction with a vertically orientated gradient of excitability is studied by optical tomography. This study focuses on scroll waves, whose filaments were oriented almost perpendicular to the gradient. Whereas scroll waves with filaments exactly perpendicular to the gradient remain unaffected, filaments with a component parallel to the gradient develop a twist. Scroll waves with U-shaped filaments exhibit twists starting from both of its ends, resulting in scroll waves whose filaments display a pair of twists of opposite handedness. These twists are separated by a nodal plane where the filament remains straight and untwisted. The experimental findings were reproduced by numerical simulations using the Oregonator model and a linear gradient of excitability almost perpendicular to the orientation of the filament.