Myocardial segment-specific model generation for simulating the electrical action of the heart

A modified approach to determine the six cardiac bidomain conductivities

Accurate values for the six cardiac bidomain conductivities are crucial for meaningful computational studies of conduction in cardiac tissue, and are yet to be determined by experimental means. Although previous studies have proposed an approach using a multi-electrode array to measure potentials, from which the conductivities can be determined, it has been found that the conductivities cannot be retrieved consistently when the noise in the potentials varies. This paper presents a protocol, which not only has been shown to retrieve the conductivities to a reasonable accuracy, but does so under the presence of a more appropriate additive Gaussian noise model, while using fewer computational resources. Through repetitions of the protocol, a comparison of two pre-fabricated 128 electrode arrays, one array with a square arrangement of electrodes and the other with a rectangular arrangement, was made against a 75-electrode array proposed in previous studies. Results indicated that the two pre-fabricated arrays were generally more capable of obtaining the cardiac conductivities to a higher degree of accuracy than the 75-electrode array. The 128-electrode rectangular array was orientated such that the length of the array first ran along the direction of the fibres, then was reorientated such that the length of the array ran perpendicular to the direction of the fibres. The 128-electrode rectangular array, when orientated in this manner, was more capable of retrieving the conductivities than the remainder of the arrays tested, and thus we suggest this arrangement be used during experimental trials.

Approaches for determining cardiac bidomain conductivity values: progress and challenges

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of four experimentally determined conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around 40 years ago, often produce different results in simulations and do not fully represent the three-dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques. Graphical abstract Epicardial potential distributions, arising from a subendocardial ischaemic region, modelled using conductivity data from the indicated studies.

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.

Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia

Reduced blood flow in the coronary arteries can lead to damaged heart tissue (myocardial ischaemia). Although one method for detecting myocardial ischaemia involves changes in the ST segment of the electrocardiogram, the relationship between these changes and subendocardial ischaemia is not fully understood. In this study, we modelled ST-segment epicardial potentials in a slab model of cardiac ventricular tissue, with a central ischaemic region, using the bidomain model, which considers conduction longitudinal, transverse and normal to the cardiac fibres. We systematically quantified the effect of uncertainty on the input parameters, fibre rotation angle, ischaemic depth, blood conductivity and six bidomain conductivities, on outputs that characterise the epicardial potential distribution. We found that three typical types of epicardial potential distributions (one minimum over the central ischaemic region, a tripole of minima, and two minima flanking a central maximum) could all occur for a wide range of ischaemic depths. In addition, the positions of the minima were affected by both the fibre rotation angle and the ischaemic depth, but not by changes in the conductivity values. We also showed that the magnitude of ST depression is affected only by changes in the longitudinal and normal conductivities, but not by the transverse conductivities.

Quantitative comparison of myocardial fiber structure between mice, rabbit, and sheep using diffusion tensor cardiovascular magnetic resonance

BACKGROUND

Accurate interpretations of cardiac functions require precise structural models of the myocardium, but the latter is not available always and for all species. Although scaling or substitution of myocardial fiber information from alternate species has been used in cardiac functional modeling, the validity of such practice has not been tested.

METHODS

Fixed mouse (n = 10), rabbit (n = 6), and sheep (n = 5) hearts underwent diffusion tensor imaging (DTI). The myocardial structures in terms of the left ventricular fiber orientation helix angle index were quantitatively compared between the mouse rabbit and sheep hearts.

RESULTS

The results show that significant fiber structural differences exist between any two of the three species. Specifically, the subepicardial fiber orientation, and the transmural range and linearity of fiber helix angles are significantly different between the mouse and either rabbit or sheep. Additionally, a significant difference was found between the transmural helix angle range between the rabbit and sheep. Across different circumferential regions of the heart, the fiber orientation was not found to be significantly different.

CONCLUSIONS

The current study indicates that myocardial structural differences exist between different size hearts. An immediate implication of the present findings for myocardial structural or functional modeling studies is that caution must be exercised when extrapolating myocardial structures from one species to another.

The presence of two local myocardial sheet populations confirmed by diffusion tensor MRI and histological validation

PURPOSE

To establish the correspondence between the two histologically observable and diffusion tensor MRI (DTMRI) measurements of myolaminae orientation for the first time and show that single myolaminar orientations observed in local histology may result from histological artifact.

MATERIALS AND METHODS

DTMRI was performed on six sheep left ventricles (LV), then corresponding direct histological transmural measurements were made within the anterobasal and lateral-equatorial LV. Secondary and tertiary eigenvectors of the diffusion tensor were compared with each of the two locally observable sheet orientations from histology. Diffusion tensor invariants were calculated to compare differences in microstructural diffusive properties between histological locations with one observable sheet population and two observable sheet populations.

RESULTS

Mean difference ± 1SD between DTMRI and histology measured sheet angles was 8° ± 27°. Diffusion tensor invariants showed no significant differences between histological locations with one observable sheet population and locations with two observable sheet populations.

CONCLUSION

DTMRI measurements of myolaminae orientations derived from the secondary and tertiary eigenvectors correspond to each of the two local myolaminae orientations observed in histology. Two local sheet populations may exist throughout LV myocardium, and one local sheet population observed in histology may be a result of preparation artifact.

Three-dimensional transmural organization of perimysial collagen in the heart

There is strong support for the view that the ventricular myocardium has a laminar organization in which myocytes are grouped into branching layers separated by cleavage planes. However, understanding of the extent and functional implications of this architecture has been limited by the lack of a systematic three-dimensional description of the organization of myocytes and associated perimysial collagen. We imaged myocytes and collagen across the left ventricular wall at high resolution in seven normal rat hearts using extended volume confocal microscopy. We developed novel reconstruction and segmentation techniques necessary for the quantitative analysis of three-dimensional myocyte and perimysial collagen organization. The results confirm that perimysial collagen has an ordered arrangement and that it defines a laminar organization. Perimysial collagen is composed of three distinct forms: extensive meshwork on laminar surfaces, convoluted fibers connecting adjacent layers, and longitudinal cords. While myolaminae are the principal form of structural organization throughout most of the wall, they are not seen in the subepicardium, where perimysial collagen is present only as longitudinal cords.

Construction and validation of a plunge electrode array for three-dimensional determination of conductivity in the heart

The heart's response to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. Analysis of the microstructure of the heart predicts that three unique intracellular electrical conductances can be defined at any point in the ventricular wall; however, to date, there has been no experimental confirmation of this concept. We report the design, fabrication, and validation of a novel plunge electrode array capable of addressing this issue. A new technique involving nylon coating of 24G hypodermic needles is performed to achieve nonconductive electrodes that can be combined to give moderate-density multisite intramural measurement of extracellular potential in the heart. Each needle houses 13 silver wires within a total diameter of 0.7 mm, and the combined electrode array gives 137 sites of recording. The ability of the electrode array to accurately assess conductances is validated by mapping the potential field induced by a point current source within baths of saline of varying concentration. A bidomain model of current injection in the heart is then used to test an approximate relationship between the monodomain conductivities measured by the array, and the full set of bidomain conductivities that describe cardiac tissue.