Three-dimensional cardiac computational modelling: methods, features and applications

Accelerating simulations of cardiac electrical dynamics through a multi-GPU platform and an optimized data structure

Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior. Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers. Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms. We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.

Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve

We present a coupled left atrium-mitral valve model based on computed tomography scans with fibre-reinforced hyperelastic materials. Fluid-structure interaction is realised by using an immersed boundary-finite element framework. Effects of pathological conditions, eg, mitral valve regurgitation and atrial fibrillation, and geometric and structural variations, namely, uniform vs non-uniform atrial wall thickness and rule-based vs atlas-based fibre architectures, on the system are investigated. We show that in the case of atrial fibrillation, pulmonary venous flow reversal at late diastole disappears, and the filling waves at the left atrial appendage orifice during systole have reduced magnitude. In the case of mitral regurgitation, a higher atrial pressure and disturbed flows are seen, especially during systole, when a large regurgitant jet can be found with the suppressed pulmonary venous flow. We also show that both the rule-based and atlas-based fibre defining methods lead to similar flow fields and atrial wall deformations. However, the changes in wall thickness from non-uniform to uniform tend to underestimate the atrial deformation. Using a uniform but thickened wall also lowers the overall strain level. The flow velocity within the left atrial appendage, which is important in terms of appendage thrombosis, increases with the thickness of the left atrial wall. Energy analysis shows that the kinetic and dissipation energies of the flow within the left atrium are altered differently by atrial fibrillation and mitral valve regurgitation, providing a useful indication of the atrial performance in pathological situations.

Fast personalized electrophysiological models from computed tomography images for ventricular tachycardia ablation planning

Aims

Clinical application of patient-specific cardiac computer models requires fast and robust processing pipelines that can be seamlessly integrated into clinical workflows. We aim at building such a pipeline from computed tomography (CT) images to personalized cardiac electrophysiology (EP) model. The simulation output could be useful in the context of post-infarct ventricular tachycardia (VT) radiofrequency ablation (RFA) planning for pre-operative targets prediction.

Methods and results

The support for model personalization is a patient-specific virtual three-dimensional heart obtained from CT images. Here, the scar is identified as thinning of the myocardial wall on automatically computed thickness maps. We then use an Eikonal model of wave front propagation with reduced velocity in the damaged areas. An image-based vessel enhancement algorithm can automatically identify VT isthmuses. The personalized model is used for virtual pacing. We obtained a very fast pipeline that enables simulations in only a few minutes. It is fully automated starting from the semi-automated image segmentation phase. The computational time frame is compatible with the construction of a virtual pacing tool. In this tool, onset points and an optional directional block could be interactively selected. The directional block is a simple way to model tissue refractoriness. Output activation maps are compared with EP data acquired pre-operatively. We show that this framework allows the reproduction of recorded re-entrant VT activation patterns.

Conclusion

Our simulation framework has an application in VT RFA intervention planning. It could be used to guide EP explorations and even predict ablation targets pre-operatively. This could reduce intervention duration and improve success rate.

Accelerating cardiac diffusion tensor imaging combining local low-rank and 3D TV constraint

OBJECTIVE

Diffusion tensor magnetic resonance imaging (DT-MRI, or DTI) is a promising technique for invasively probing biological tissue structures. However, DTI is known to suffer from much longer acquisition time with respect to conventional MRI and the problem is worsened when dealing with in vivo acquisitions. Therefore, faster DTI for both ex vivo and in vivo scans is highly desired.

MATERIALS AND METHODS

This paper proposes a new compressed sensing (CS) reconstruction method that employs local low-rank (LLR) model and three-dimensional (3D) total variation (TV) constraint to reconstruct cardiac diffusion-weighted (DW) images from highly undersampled k-space data. The LLR model takes the set of DW images corresponding to different diffusion gradient directions as a 3D image volume and decomposes the latter into overlapping 3D blocks. Then, the 3D blocks are stacked as two-dimensional (2D) matrix. Finally, low-rank property is applied to each block matrix and the 3D TV constraint to the 3D image volume. The underlying constrained optimization problem is finally solved using the first-order fast method. The proposed method is evaluated on real ex vivo cardiac DTI data as a prerequisite to in vivo cardiac DTI applications.

RESULTS

The results on real human ex vivo cardiac DTI images demonstrate that the proposed method exhibits lower reconstruction errors for DTI indices, including fractional anisotropy (FA), mean diffusivities (MD), transverse angle (TA), and helix angle (HA), compared to existing CS-based DTI image reconstruction techniques.

CONCLUSION

The proposed method provides better reconstruction quality and more accurate DTI indices in comparison with the state-of-the-art CS-based DW image reconstruction methods.

Personalized Cardiac Computational Models: From Clinical Data to Simulation of Infarct-Related Ventricular Tachycardia

In the chronic stage of myocardial infarction, a significant number of patients develop life-threatening ventricular tachycardias (VT) due to the arrhythmogenic nature of the remodeled myocardium. Radiofrequency ablation (RFA) is a common procedure to isolate reentry pathways across the infarct scar that are responsible for VT. Unfortunately, this strategy show relatively low success rates; up to 50% of patients experience recurrent VT after the procedure. In the last decade, intensive research in the field of computational cardiac electrophysiology (EP) has demonstrated the ability of three-dimensional (3D) cardiac computational models to perform in-silico EP studies. However, the personalization and modeling of certain key components remain challenging, particularly in the case of the infarct border zone (BZ). In this study, we used a clinical dataset from a patient with a history of infarct-related VT to build an image-based 3D ventricular model aimed at computational simulation of cardiac EP, including detailed patient-specific cardiac anatomy and infarct scar geometry. We modeled the BZ in eight different ways by combining the presence or absence of electrical remodeling with four different levels of image-based patchy fibrosis (0, 10, 20, and 30%). A 3D torso model was also constructed to compute the ECG. Patient-specific sinus activation patterns were simulated and validated against the patient's ECG. Subsequently, the pacing protocol used to induce reentrant VTs in the EP laboratory was reproduced in-silico. The clinical VT was induced with different versions of the model and from different pacing points, thus identifying the slow conducting channel responsible for such VT. Finally, the real patient's ECG recorded during VT episodes was used to validate our simulation results and to assess different strategies to model the BZ. Our study showed that reduced conduction velocities and heterogeneity in action potential duration in the BZ are the main factors in promoting reentrant activity. Either electrical remodeling or fibrosis in a degree of at least 30% in the BZ were required to initiate VT. Moreover, this proof-of-concept study confirms the feasibility of developing 3D computational models for cardiac EP able to reproduce cardiac activation in sinus rhythm and during VT, using exclusively non-invasive clinical data.

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts

Rule-based methods are often used for assigning fiber orientation to cardiac anatomical models. However, existing methods have been developed using data mostly from the left ventricle. As a consequence, fiber information obtained from rule-based methods often does not match histological data in other areas of the heart such as the right ventricle, having a negative impact in cardiac simulations beyond the left ventricle. In this work, we present a rule-based method where fiber orientation is separately modeled in each ventricle following observations from histology. This allows to create detailed fiber orientation in specific regions such as the endocardium of the right ventricle, the interventricular septum, and the outflow tracts. We also carried out electrophysiological simulations involving these structures and with different fiber configurations. In particular, we built a modeling pipeline for creating patient-specific volumetric meshes of biventricular geometries, including the outflow tracts, and subsequently simulate the electrical wavefront propagation in outflow tract ventricular arrhythmias with different origins for the ectopic focus. The resulting simulations with the proposed rule-based method showed a very good agreement with clinical parameters such as the 10 ms isochrone ratio in a cohort of nine patients suffering from this type of arrhythmia. The developed modeling pipeline confirms its potential for an in silico identification of the site of origin in outflow tract ventricular arrhythmias before clinical intervention.

Optimization of Lead Placement in the Right Ventricle During Cardiac Resynchronization Therapy. A Simulation Study

Patients suffering from heart failure and left bundle branch block show electrical ventricular dyssynchrony causing an abnormal blood pumping. Cardiac resynchronization therapy (CRT) is recommended for these patients. Patients with positive therapy response normally present QRS shortening and an increased left ventricle (LV) ejection fraction. However, around one third do not respond favorably. Therefore, optimal location of pacing leads, timing delays between leads and/or choosing related biomarkers is crucial to achieve the best possible degree of ventricular synchrony during CRT application. In this study, computational modeling is used to predict the optimal location and delay of pacing leads to improve CRT response. We use a 3D electrophysiological computational model of the heart and torso to get insight into the changes in the activation patterns obtained when the heart is paced from different regions and for different atrioventricular and interventricular delays. The model represents a heart with left bundle branch block and heart failure, and allows a detailed and accurate analysis of the electrical changes observed simultaneously in the myocardium and in the QRS complex computed in the precordial leads. Computational simulations were performed using a modified version of the O'Hara et al. action potential model, the most recent mathematical model developed for human ventricular electrophysiology. The optimal location for the pacing leads was determined by QRS maximal reduction. Additionally, the influence of Purkinje system on CRT response was assessed and correlation analysis between several parameters of the QRS was made. Simulation results showed that the right ventricle (RV) upper septum near the outflow tract is an alternative location to the RV apical lead. Furthermore, LV endocardial pacing provided better results as compared to epicardial stimulation. Finally, the time to reach the 90% of the QRS area was a good predictor of the instant at which 90% of the ventricular tissue was activated. Thus, the time to reach the 90% of the QRS area is suggested as an additional index to assess CRT effectiveness to improve biventricular synchrony.

Trabecular Architecture Determines Impulse Propagation Through the Early Embryonic Mouse Heart

Most embryonic ventricular cardiomyocytes are quite uniform, in contrast to the adult heart, where the specialized ventricular conduction system is molecularly and functionally distinct from the working myocardium. We thus hypothesized that the preferential conduction pathway within the embryonic ventricle could be dictated by trabecular geometry. Mouse embryonic hearts of the Nkx2.5:eGFP strain between ED9.5 and ED14.5 were cleared and imaged whole mount by confocal microscopy, and reconstructed in 3D at 3.4 μm isotropic voxel size. The local orientation of the trabeculae, responsible for the anisotropic spreading of the signal, was characterized using spatially homogenized tensors (3 × 3 matrices) calculated from the trabecular skeleton. Activation maps were simulated assuming constant speed of spreading along the trabeculae. The results were compared with experimentally obtained epicardial activation maps generated by optical mapping with a voltage-sensitive dye. Simulated impulse propagation starting from the top of interventricular septum revealed the first epicardial breakthrough at the interventricular grove, similar to experimentally obtained activation maps. Likewise, ectopic activation from the left ventricular base perpendicular to dominant trabecular orientation resulted in isotropic and slower impulse spreading on the ventricular surface in both simulated and experimental conditions. We conclude that in the embryonic pre-septation heart, the geometry of the A-V connections and trabecular network is sufficient to explain impulse propagation and ventricular activation patterns.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

Non-contact Quantification of Jugular Venous Pulse Waveforms from Skin Displacements

The jugular venous (JV) pressure waveform is a non-invasive, proven indicator of cardiovascular disease. Conventional clinical methods for assessing these waveforms are often overlooked because they require specialised expertise, and are invasive and expensive to implement. Recently, image-based methods have been used to quantify JV pulsation waveforms on the skin as an indirect way of estimating the pressure waveforms. However, these existing image-based methods cannot explicitly measure skin deformations and rely on the use of photoplethysmography (PPG) devices for identification of the pulsatile waveforms. As a result, they often have limited accuracy and robustness and are unsuitable in the clinical environment. Here, we propose a technique to directly measure skin deformations caused by the JV pulse using a very accurate subpixel registration algorithm. The method simply requires images obtained from the subject’s neck using a commodity camera. The results show that our measured waveforms contained all of the essential features of diagnostic JV waveforms in all of 19 healthy subjects tested in this study, indicating a significantly important capability for a potential future diagnostic device. The shape of our measured JV displacement waveforms was validated using waveforms measured with a laser displacement sensor, where the average correlation score between the two waveforms was 0.93 ± 0.05. In addition, synchronously recorded ECG signals were used to verify the timings of diagnostic features of the measured waveforms. To our knowledge, this is the first use of image registration for direct measurement of JV displacement waveforms. Significant advantages of our novel method include the high precision of our measurements, and the ability to use ordinary cameras, such as those in modern mobile phones. These advantages will enable the development of affordable and accessible devices to measure JV waveforms for cardiac diagnostics in the clinical environment. Future devices based on this technology may provide viable options for telemedicine applications, point of care diagnostics, and mobile-based cardiac health monitoring systems.

Retrieving hidden atrial repolarization waves from standard surface ECGs

BACKGROUND

This study estimates atrial repolarization activities (Ta waves), which are typically hidden most of the time from body surface electrocardiography when diagnosing cardiovascular diseases. The morphology of Ta waves has been proven to be an important marker for the early sign of inferior injury, such as acute atrial infarction, or arrhythmia, such as atrial fibrillation. However, Ta waves are usually unseen except during conduction system malfunction, such as long QT interval or atrioventricular block. Therefore, justifying heart diseases based on atrial repolarization becomes impossible in sinus rhythm.

METHODS

We obtain TMPs in the atrial part of the myocardium which reflects the correct excitation sequence starting from the atrium to the end of the apex.

RESULTS

The resulting TMP shows the hidden atrial part of ECG waves.

CONCLUSIONS

This extraction makes many diseases, such as acute atrial infarction or arrhythmia, become easily diagnosed.

Position Paper Computational Cardiology

Computational cardiology is the scientific field devoted to the development of methodologies that enhance our mechanistic understanding, diagnosis and treatment of cardiovascular disease. In this regard, the field embraces the extraordinary pace of discovery in imaging, computational modeling, and cardiovascular informatics at the intersection of atherogenesis and vascular biology. This paper highlights existing methods, practices, and computational models and proposes new strategies to support a multidisciplinary effort in this space. We focus on the means by that to leverage and coalesce these multiple disciplines to advance translational science and computational cardiology. Analyzing the scientific trends and understanding the current needs we present our perspective for the future of cardiovascular treatment.

Automatic estimation of Purkinje-Myocardial junction hot-spots from noisy endocardial samples: A simulation study

The reconstruction of the ventricular cardiac conduction system (CCS) from patient-specific data is a challenging problem. High-resolution imaging techniques have allowed only the segmentation of proximal sections of the CCS from images acquired ex vivo. In this paper, we present an algorithm to estimate the location of a set of Purkinje-myocardial junctions (PMJs) from electro-anatomical maps, as those acquired during radio-frequency ablation procedures. The method requires a mesh representing the myocardium with local activation time measurements on a subset of nodes. We calculate the backwards propagation of the electrical signal from the measurement points to all the points in the mesh to define a set of candidate PMJs that is iteratively refined. The algorithm has been tested on several Purkinje network configurations, with simulated activation maps, subject to different error amplitudes. The results show that the method is able to build a set of PMJs that explain the observed activation map for different synthetic CCS configurations. In the tests, the average error in the predicted activation time is below the amplitude of the error applied to the data.

Effect of Transmural Differences in Excitation-Contraction Delay and Contraction Velocity on Left Ventricle Isovolumic Contraction: A Simulation Study

Recent studies have shown that left ventricle (LV) exhibits considerable transmural differences in active mechanical properties induced by transmural differences in electrical activity, excitation-contraction coupling, and contractile properties of individual myocytes. It was shown that the time between electrical and mechanical activation of myocytes (electromechanical delay: EMD) decreases from subendocardium to subepicardium and, on the contrary, the myocyte shortening velocity (MSV) increases in the same direction. To investigate the physiological importance of this inhomogeneity, we developed a new finite element model of LV incorporating the observed transmural gradients in EMD and MSV. Comparative simulations with the model showed that when EMD or MSV or both were set constant across the LV wall, the LV contractility during isovolumic contraction (IVC) decreased significantly ((dp/dt)max⁡  was reduced by 2 to 38% and IVC was prolonged by 18 to 73%). This was accompanied by an increase of transmural differences in wall stress. These results suggest that the transmural differences in EMD and MSV play an important role in physiological contractility of LV by synchronising the contraction of individual layers of ventricular wall during the systole. Reduction or enhancement of these differences may therefore impair the function of LV and contribute to heart failure.

3D + time blood flow mapping using SPIM-microPIV in the developing zebrafish heart

We present SPIM-μPIV as a flow imaging system, capable of measuring in vivo flow information with 3D micron-scale resolution. Our system was validated using a phantom experiment consisting of a flow of beads in a 50 μm diameter FEP tube. Then, with the help of optical gating techniques, we obtained 3D + time flow fields throughout the full heartbeat in a ∼3 day old zebrafish larva using fluorescent red blood cells as tracer particles. From this we were able to recover 3D flow fields at 31 separate phases in the heartbeat. From our measurements of this specimen, we found the net pumped blood volume through the atrium to be 0.239 nL per beat. SPIM-μPIV enables high quality in vivo measurements of flow fields that will be valuable for studies of heart function and fluid-structure interaction in a range of small-animal models.

Validation and Trustworthiness of Multiscale Models of Cardiac Electrophysiology

Computational models of cardiac electrophysiology have a long history in basic science applications and device design and evaluation, but have significant potential for clinical applications in all areas of cardiovascular medicine, including functional imaging and mapping, drug safety evaluation, disease diagnosis, patient selection, and therapy optimisation or personalisation. For all stakeholders to be confident in model-based clinical decisions, cardiac electrophysiological (CEP) models must be demonstrated to be trustworthy and reliable. Credibility, that is, the belief in the predictive capability, of a computational model is primarily established by performing validation, in which model predictions are compared to experimental or clinical data. However, there are numerous challenges to performing validation for highly complex multi-scale physiological models such as CEP models. As a result, credibility of CEP model predictions is usually founded upon a wide range of distinct factors, including various types of validation results, underlying theory, evidence supporting model assumptions, evidence from model calibration, all at a variety of scales from ion channel to cell to organ. Consequently, it is often unclear, or a matter for debate, the extent to which a CEP model can be trusted for a given application. The aim of this article is to clarify potential rationale for the trustworthiness of CEP models by reviewing evidence that has been (or could be) presented to support their credibility. We specifically address the complexity and multi-scale nature of CEP models which makes traditional model evaluation difficult. In addition, we make explicit some of the credibility justification that we believe is implicitly embedded in the CEP modeling literature. Overall, we provide a fresh perspective to CEP model credibility, and build a depiction and categorisation of the wide-ranging body of credibility evidence for CEP models. This paper also represents a step toward the extension of model evaluation methodologies that are currently being developed by the medical device community, to physiological models.

Image-based modelling of skeletal muscle oxygenation

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology

The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the initialization of reaction-diffusion systems for numerical simulations of cardiac EP from steady-state conditions. We exploit surface point correspondence to establish volumetric point correspondence. Upon introduction of a new 3D anatomy with surface point correspondence, a prediction of the cell model steady states is derived from the set of earlier biophysical simulations. We show that the prediction error is typically less than 10% for all model variables, with most variables showing even greater accuracy. When initializing simulations with the predicted model states, it is demonstrated that simulation times can be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing. Overall, these results increase the clinical applicability of detailed computational EP studies on personalized anatomies.

Can the Drosophila model help in paving the way for translational medicine in heart failure?

Chronic heart failure is a common consequence of various heart diseases. Mechanical force is known to play a key role in heart failure development through regulating cardiomyocyte hypertrophy. In order to understand the complex disease mechanism, this article discussed a multi-disciplinary approach that may aid the illustration of heart failure molecular process.

Robust cardiac motion estimation using ultrafast ultrasound data: a low-rank topology-preserving approach

Cardiac motion estimation is an important diagnostic tool for detecting heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate cardiac motion using ultrafast ultrasound data. Our solution is based on a variational formulation characterized by the L ²-regularized class. Displacement is represented by a lattice of b-splines and we ensure robustness, in the sense of eliminating outliers, by applying a maximum likelihood type estimator. While this is an important part of our solution, the main object of this work is to combine low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows one to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. The low-rank constraint speeds up the convergence of the optimization problem while topology preservation ensures a more accurate displacement. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that exhibit motion.

Patient-specific CFD simulation of intraventricular haemodynamics based on 3D ultrasound imaging

BACKGROUND

The goal of this paper is to present a computational fluid dynamic (CFD) model with moving boundaries to study the intraventricular flows in a patient-specific framework. Starting from the segmentation of real-time transesophageal echocardiographic images, a CFD model including the complete left ventricle and the moving 3D mitral valve was realized. Their motion, known as a function of time from the segmented ultrasound images, was imposed as a boundary condition in an Arbitrary Lagrangian-Eulerian framework.

RESULTS

The model allowed for a realistic description of the displacement of the structures of interest and for an effective analysis of the intraventricular flows throughout the cardiac cycle. The model provides detailed intraventricular flow features, and highlights the importance of the 3D valve apparatus for the vortex dynamics and apical flow.

CONCLUSIONS

The proposed method could describe the haemodynamics of the left ventricle during the cardiac cycle. The methodology might therefore be of particular importance in patient treatment planning to assess the impact of mitral valve treatment on intraventricular flow dynamics.

Towards estimating cardiac motion using low-rank representation and topology preservation for ultrafast ultrasound data

Estimation of the cardiac motion is very important in order to detect heart diseases. This work presents a cardiac motion estimation approach using ultrafast ultrasound data. We optimize a variational framework which has the benefits of combining low-rank data representation with topology preservation. We show through the analysis of experimental results that this combination offers a radical reduction in computational time and noise while ensuring preservation of the anatomical structure of the heart under complex deformations. Although in this work we use the heart as a study case, our solution is promising to analyze other organs experiencing motion.

Personalized Computer Simulation of Diastolic Function in Heart Failure

The search for a parameter representing left ventricular relaxation from non-invasive and invasive diagnostic tools has been extensive, since heart failure (HF) with preserved ejection fraction (HF-pEF) is a global health problem. We explore here the feasibility using patient-specific cardiac computer modeling to capture diastolic parameters in patients suffering from different degrees of systolic HF. Fifty eight patients with idiopathic dilated cardiomyopathy have undergone thorough clinical evaluation, including cardiac magnetic resonance imaging (MRI), heart catheterization, echocardiography, and cardiac biomarker assessment. A previously-introduced framework for creating multi-scale patient-specific cardiac models has been applied on all these patients. Novel parameters, such as global stiffness factor and maximum left ventricular active stress, representing cardiac active and passive tissue properties have been computed for all patients. Invasive pressure measurements from heart catheterization were then used to evaluate ventricular relaxation using the time constant of isovolumic relaxation Tau (τ). Parameters from heart catheterization and the multi-scale model have been evaluated and compared to patient clinical presentation. The model parameter global stiffness factor, representing diastolic passive tissue properties, is correlated significantly across the patient population with τ. This study shows that multi-modal cardiac models can successfully capture diastolic (dys) function, a prerequisite for future clinical trials on HF-pEF.

Myocyte-fibroblast communication in cardiac fibrosis and arrhythmias: Mechanisms and model systems

Development of cardiac fibrosis and arrhythmias is controlled by the activity of and communication between cardiomyocytes and fibroblasts in the heart. Myocyte-fibroblast interactions occur via both direct and indirect means including paracrine mediators, extracellular matrix interactions, electrical modulators, mechanical junctions, and membrane nanotubes. In the diseased heart, cardiomyocyte and fibroblast ratios and activity, and thus myocyte-fibroblast interactions, change and are thought to contribute to the course of disease including development of fibrosis and arrhythmogenic activity. Fibroblasts have a developing role in modulating cardiomyocyte electrical and hypertrophic activity, however gaps in knowledge regarding these interactions still exist. Research in this field has necessitated the development of unique approaches to isolate and control myocyte-fibroblast interactions. Numerous methods for 2D and 3D co-culture systems have been developed, while a growing part of this field is in the use of better tools for in vivo systems including cardiomyocyte and fibroblast specific Cre mouse lines for cell type specific genetic ablation. This review will focus on (i) mechanisms of myocyte-fibroblast communication and their effects on disease features such as cardiac fibrosis and arrhythmias as well as (ii) methods being used and currently developed in this field.

Segmentation of the left ventricular endocardium from magnetic resonance images by using different statistical shape models

We evaluate in this paper different strategies for the construction of a statistical shape model (SSM) of the left ventricle (LV) to be used for segmentation in cardiac magnetic resonance (CMR) images. From a large database of LV surfaces obtained throughout the cardiac cycle from 3D echocardiographic (3DE) LV images, different LV shape models were built by varying the considered phase in the cardiac cycle and the registration procedure employed for surface alignment. Principal component analysis was computed to describe the statistical variability of the SSMs, which were then deformed by applying an active shape model (ASM) approach to segment the LV endocardium in CMR images of 45 patients. Segmentation performance was evaluated by comparing LV volumes derived by ASM segmentation with different SSMs and those obtained by manual tracing, considered as a reference. A high correlation (r(2)>0.92) was found in all cases, with better results when using the SSM models comprising more than one frame of the cardiac cycle.