Journal of Thoracic and Cardiovascular Surgery, ; , 1: Lytle, Pettersson, et al. Reoperative cryopreserved root and ascending aorta replacement for acute aortic prosthetic valve endocarditis. The Annals of Thoracic Surgery, ; Pettersson, Coselli, et al. Journal of Thoracic and Cardiovascular Surgery, ; Kirklin et al. Ann Thorac Surg , June Tuna et al. Ann Thorac Surg ; Philpott and Zemlin. Verveer, P. Methods 4 , — Preibisch, S. Methods 7 , — Barry, A. Garita, B. Heart Circ.
Liu, J. Arrenberg, A. Fahrbach, F. Express 21 , — Zebrafish Oxford University Press, Traver, D.
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High-resolution reconstruction of the beating zebrafish heart
USA , — Langheinrich, U. Schindelin, J. Methods 9 , — Download references. We thank H. Otsuna for assistance with FluoRender and A. Reade, T. Op't Hof, R. Coronel, D. Stainier and members of the Huisken laboratory for their comments. Initial work on this project was performed by J. Stelzer, J. Wittbrodt and D. Correspondence to Jan Huisken. Image of a 48 h. Tg myl7:GFP embryo with segmented outlines pink dotted lines of the heart over a full cardiac cycle. Three synchronized planes of a movie stack of a 48 h. The primary focus of the study was to develop an approach to overcome the challenges inherent in the construction of such a detailed model and to demonstrate the suitability of the model for future research, which was achieved through application of the model in normal and arrhythmic excitation conditions.
The intention of the model is for future studies to incorporate multiple datasets, including those describing multiple disease conditions, to fully assess the role of variability in intracellular structure in determining potentially pro-arrhythmic dynamics; such detailed analysis was therefore beyond the scope of this study.
Comparison with the semi-idealised model revealed similarities and differences between the two levels of detail included in the model. The similarities of whole-cell characteristics and gross spatio-temporal dynamics between the two models during normal structure highlights the suitability of idealised models for general and mechanistic modelling of spatio-temporal dynamics associated with normal structure.
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Second, the degree of disorder associated with alternans dynamics was significantly reduced in the structurally detailed model compared to the idealised model; dyad distribution significantly affects recruitment patterns and therefore spatially constrains the probabilistic nature of recruitment, with real structure reducing the phase variance associated with multiple small-amplitude cycles. Similarly, reduced density of dyad distribution led to significant failure to recruit and very small transients associated with the small amplitude cycle.
These results thus add further insight to those gained in previous studies [ 20 , 25 , 27 ]. These results highlight the necessity for integrated multi-scale models which can capture realistic structure of both the intracellular and SR spaces as well as heterogeneity in dyad properties and flux distribution. For example, a combination of increased heterogeneity in dyad properties with remodelling of dyad distribution may result in highly unpredictable constraints on dynamics. TT structure, dyad distribution and SR structure have all been shown to be perturbed in both animal models of disease and patients [ 7 — 14 ].
Whereas many previous modelling studies have investigated remodelling in proteins and flux dynamics in the single cell e. Application and analysis of structurally accurate models such as the one presented in this study will therefore allow mechanistic evaluation of the role of structural remodelling in determining arrhythmogenic electrical and perturbed contractile dynamics at the cellular scale as well as structure-function relationships underlying normal cardiac excitation.
To demonstrate the generalisability of these approaches, the structural model was integrated with the independent mathematical model of Nivala et al. The whole-cell characteristics of the integrated model were comparable to that of the Nivala et al. This therefore demonstrates the generalisability of the approaches for integration with independent mathematical models and further supports the suitability for future research. For the purpose of the methodological development of the model, only a portion of the myocyte was reconstructed at high resolution and processed to form the computational grids and mapping functions used for simulation.
However, it should be noted that this does not affect the fundamental model itself nor the methodological approaches for structural data processing. In the model, the membrane and SR fluxes were spatially distributed according to maps created from the reconstructions.
Within this structure, the fluxes were distributed evenly and continuously. Incorporation of immuno-labelling data describing the realistic distribution of the proteins responsible for these fluxes would provide a further degree of accuracy in the cell model as well as a tool for investigation of the functional impact of changes to the distribution of these flux-carrying proteins; arbitrary heterogeneity could have been introduced into the present model but this was avoided due to the inherent uncertainty in such an approach—the purpose of this model being to remove this necessity for future research.
In further simulations, we also demonstrate that redistribution of I NaCa primarily to the TTs, as has been performed in other studies [ 24 ], results in preferential flux in the TTs without significant perturbation to whole-cell dynamics S6 Fig. The model includes a restricted buffering subspace which functionally couples neighbouring dyads. We, however, note that similar constructs are present in previously developed models from other groups: in both Gaur-Rudy [ 28 ] and Voigt et al. The present model contains this functional coupling but also preserves the restricted local spaces of individual dyads.
This construct is not critical to the primary novelty of the developed approach—in processing and modelling with the structural datasets—as demonstrated by integration with the independent mathematical model of Nivala et al. Whereas heterogeneity was incorporated through functionality to vary dyadic cleft volume and protein numbers NRyR and NLTCC , the spatial structure of the dyad, including local RyR distribution, is not accounted for in the present model. A multi-scale integration method could feasibly be implemented to integrate previously developed super-resolution models of single dyads [ 37 , 53 ], though this was beyond the scope of the present study.
Similarly, the RyR dynamic model is primarily functional rather than rigorously based on experimental data describing RyR kinetics. Incorporation of a more accurate RyR model, such as the recent induction decay models [ 40 ] would also improve the accuracy and suitability for future studies. Furthermore, the contractile system could also be segmented for simulation of spatially localised troponin buffering and force generation, for application to understand reduced contractile force associated with heart failure, for example.
Full model code is provided S1 Code to facilitate realisation of the potential of future applications of these approaches. Documentation is provided on use of and updating the code. Contains all equations, variables and parameters describing the developed model. Colours are according to the colour bars in Figs 7 and 9. Colours are according to the colour bar in Figs 11 and Video corresponds to the condition illustrated in Fig 14B.
Abstract Intracellular calcium cycling is a vital component of cardiac excitation-contraction coupling. Author summary The organisation of the membrane and sub-cellular structures of cells in the heart closely controls the coupling between its electrical and mechanical function. Download: PPT. Fig 1. Reconstructing intracellular structure for numerical simulation The resolution at which the images were acquired, Bulk cytoplasm geometry.
Reconstruction of a portion of the cytoplasm and TT structure for computational modelling. Surface sarcolemma and t-tubule membranes. Fig 4. Incorporating processed structure datasets. Eq 4 is thus updated to solve the reaction terms only at voxels defined by the mapping functions: 17 And Eqs 5 and 6 are also updated similarly: 18 19 Where volume balances have been implicitly incorporated for clarity and p and q are given by the inverse mapping functions of n.
Coupling to an ionic model. Creating a whole cell model. Fig 6. Whole-cell average characteristics during control pacing. Fig 7. Fig 8. Fig 9. Evaluation of spatial distribution of fluxes in the cytoplasm Fluxes acting on the cytoplasm in a single portion of the 3-D cell were analysed Fig Fig Evaluation of J up and J NaCa fluxes in the cytoplasm.
Spontaneous release events during rapid pacing. Reproducing dynamics under different conditions The suitability of the model for future research was demonstrated by its application under multiple conditions. The role of structure underlying calcium dynamics The primary focus of the study was to develop an approach to overcome the challenges inherent in the construction of such a detailed model and to demonstrate the suitability of the model for future research, which was achieved through application of the model in normal and arrhythmic excitation conditions. Limitations of and future extensions to the model For the purpose of the methodological development of the model, only a portion of the myocyte was reconstructed at high resolution and processed to form the computational grids and mapping functions used for simulation.
Supporting information. S1 Code.
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Code and documentation. S1 Text. Model description. S1 Fig. Comparison between full-sized and cross-sectional portion models. S2 Fig. S3 Fig. S4 Fig. J rel and single-dyad dynamics. S5 Fig. Spatio-temporal dynamics in a model without a subspace. S6 Fig. S1 Video. Spatio-temporal dynamics during a single beat of cardiac excitation. S2 Video. S3 Video. References 1. Bers DM. Calcium cycling and signaling in cardiac myocytes. Annu Rev Physiol.
From the ryanodine receptor to cardiac arrhythmias. View Article Google Scholar 3. Nattel S, Dobrev D. The multidimensional role of calcium in atrial fibrillation pathophysiology: mechanistic insights and therapeutic opportunities. Eur Heart J. Calcium flux balance in the heart.
J Mol Cell Cardiol. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. Three-dimensional distribution of ryanodine receptor clusters in cardiac myocytes. Biophys J. Three-dimensional reconstruction of cardiac sarcoplasmic reticulum reveals a continuous network linking transverse-tubules: this organization is perturbed in heart failure. Circ Res.
View Article Google Scholar 9. A functional role for transverse t- tubules in the atria. Emerging mechanisms of T-tubule remodelling in heart failure. Cardiovasc Res.