Application of micro-computed tomography with iodine staining to cardiac imaging, segmentation, and computational model development

Three-dimensional non-destructive soft-tissue visualization with X-ray staining micro-tomography

Low inherent contrast in soft tissues has been limiting the use of X-ray absorption micro-computed tomography (micro-CT) to access high-resolution structural information of animal organs. The staining agents used in micro-CT to improve the contrast fail in providing high-quality images of whole organs of animals due to diffusion problems of the staining agent into the sample. We demonstrate a staining protocol that incorporates a biochemical conditioning step prior to exposure to the staining agent that succeeds in overcoming the diffusion problems, thus quickly providing high-quality micro-CT images of whole organs of mammals. Besides of yielding non-distorted three-dimensional information at the same spatial resolution accessible in histological sections, micro-CT images of whole organs stained by our method enable easy screening of slices along any direction of the volume thus demonstrating new possibilities of structural analysis in biomedical science.

Three-dimensional histology: tools and application to quantitative assessment of cell-type distribution in rabbit heart

Aims

Cardiac histo-anatomical organization is a major determinant of function. Changes in tissue structure are a relevant factor in normal and disease development, and form targets of therapeutic interventions. The purpose of this study was to test tools aimed to allow quantitative assessment of cell-type distribution from large histology and magnetic resonance imaging- (MRI) based datasets.

Methods and results

Rabbit heart fixation during cardioplegic arrest and MRI were followed by serial sectioning of the whole heart and light-microscopic imaging of trichrome-stained tissue. Segmentation techniques developed specifically for this project were applied to segment myocardial tissue in the MRI and histology datasets. In addition, histology slices were segmented into myocytes, connective tissue, and undefined. A bounding surface, containing the whole heart, was established for both MRI and histology. Volumes contained in the bounding surface (called ‘anatomical volume’), as well as that identified as containing any of the above tissue categories (called ‘morphological volume’), were calculated. The anatomical volume was 7.8 cm³ in MRI, and this reduced to 4.9 cm³ after histological processing, representing an ‘anatomical’ shrinkage by 37.2%. The morphological volume decreased by 48% between MRI and histology, highlighting the presence of additional tissue-level shrinkage (e.g. an increase in interstitial cleft space). The ratio of pixels classified as containing myocytes to pixels identified as non-myocytes was roughly 6:1 (61.6 vs. 9.8%; the remaining fraction of 28.6% was ‘undefined’).

Conclusion

Qualitative and quantitative differentiation between myocytes and connective tissue, using state-of-the-art high-resolution serial histology techniques, allows identification of cell-type distribution in whole-heart datasets. Comparison with MRI illustrates a pronounced reduction in anatomical and morphological volumes during histology processing.

Assessing the three-dimensional collagen network in soft tissues using contrast agents and high resolution micro-CT: Application to porcine iliac veins

The assessment of the three-dimensional architecture of collagen fibers inside vessel walls constitutes one of the bases for building structural models for the description of the mechanical behavior of these tissues. Multiphoton microscopy allows for such observations, but is limited to volumes of around a thousand of microns. In the present work, we propose to observe the collagenous network of vascular tissues using micro-CT. To get a contrast, three staining solutions (phosphotungstic acid, phosphomolybdic acid and iodine potassium iodide) were tested. Two of these stains were showed to lead to similar results and to a satisfactory contrast within the tissue. A detailed observation of a small porcine iliac vein sample allowed assessing the collagen fibers orientations within the medial and adventitial layers of the vein. The vasa vasorum network, which is present inside the adventitia of the vein, was also observed. Finally, the demonstrated micro-CT staining technique for the three-dimensional observation of thin soft tissues samples, like vein walls, contributes to the assessment of their structure at different scales while keeping a global overview of the tissue.

Morphological Characterisation of Unstained and Intact Tissue Micro-architecture by X-ray Computed Micro- and Nano-Tomography

Characterisation and quantification of tissue structures is limited by sectioning-induced artefacts and by the difficulties of visualising and segmenting 3D volumes. Here we demonstrate that, even in the absence of X-ray contrast agents, X-ray computed microtomography (microCT) and nanotomography (nanoCT) can circumvent these problems by rapidly resolving compositionally discrete 3D tissue regions (such as the collagen-rich adventitia and elastin-rich lamellae in intact rat arteries) which in turn can be segmented due to their different X-ray opacities and morphologies. We then establish, using X-ray tomograms of both unpressurised and pressurised arteries that intra-luminal pressure not only increases lumen cross-sectional area and straightens medial elastic lamellae but also induces profound remodelling of the adventitial layer. Finally we apply microCT to another human organ (skin) to visualise the cell-rich epidermis and extracellular matrix-rich dermis and to show that conventional histological and immunohistochemical staining protocols are compatible with prior X-ray exposure. As a consequence we suggest that microCT could be combined with optical microscopy to characterise the 3D structure and composition of archival paraffin embedded biological materials and of mechanically stressed dynamic tissues such as the heart, lungs and tendons.

Optimization of catheter ablation of atrial fibrillation: insights gained from clinically-derived computer models

Atrial fibrillation (AF) is the most common heart rhythm disturbance, and its treatment is an increasing economic burden on the health care system. Despite recent intense clinical, experimental and basic research activity, the treatment of AF with current antiarrhythmic drugs and catheter/surgical therapies remains limited. Radiofrequency catheter ablation (RFCA) is widely used to treat patients with AF. Current clinical ablation strategies are largely based on atrial anatomy and/or substrate detected using different approaches, and they vary from one clinical center to another. The nature of clinical ablation leads to ambiguity regarding the optimal patient personalization of the therapy partly due to the fact that each empirical configuration of ablation lines made in a patient is irreversible during one ablation procedure. To investigate optimized ablation lesion line sets, in silico experimentation is an ideal solution. 3D computer models give us a unique advantage to plan and assess the effectiveness of different ablation strategies before and during RFCA. Reliability of in silico assessment is ensured by inclusion of accurate 3D atrial geometry, realistic fiber orientation, accurate fibrosis distribution and cellular kinetics; however, most of this detailed information in the current computer models is extrapolated from animal models and not from the human heart. The predictive power of computer models will increase as they are validated with human experimental and clinical data. To make the most from a computer model, one needs to develop 3D computer models based on the same functionally and structurally mapped intact human atria with high spatial resolution. The purpose of this review paper is to summarize recent developments in clinically-derived computer models and the clinical insights they provide for catheter ablation.

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

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

The use of nano-computed tomography to enhance musculoskeletal research

Advances in computed tomography (CT) imaging are opening new avenues toward more precise characterization and quantification of connective tissue microarchitecture. In the last two decades, micro-computed tomography (microCT) has significantly augmented destructive methods for the 3D micro-analysis of tissue structure, primarily in the bone research field. Recently, microCT has been employed in combination with contrast agents to generate contrast-enhanced images of soft tissues that are otherwise difficult to visualize due to their native radiodensity. More recent advances in CT technology have enabled ultra-high resolution imaging by utilizing a more powerful nano-focused X-ray source, such as that found in nano-computed tomography (nanoCT) systems. NanoCT imaging has facilitated the expansion of musculoskeletal research by reducing acquisition time and significantly expanding the range of samples that can be imaged in terms of size, age and tissue-type (bone, muscle, tendon, cartilage, vessels and adipose tissue). We present the application and early results of nanoCT imaging in various tissue types and how this ultra-high resolution imaging modality is capable of characterizing microstructures at levels of details previously not possible. Contrast-enhanced imaging techniques to enable soft-tissue visualization and characterization are also outlined.

Role of atrial tissue substrate and electrical activation pattern in fractionation of atrial electrograms: a computational study

Complex fractionated atrial electrograms (CFAEs) are often used as a clinical marker for re-entrant drivers of atrial fibrillation. However, outcomes of clinical ablation procedures based on CFAEs are controversial and the mechanistic links between fractionation, re-entrant activity and the characteristics of the atrial substrate are not completely understood. We explore such links by simulating electrograms arising from both normal and re-entrant electrical activity in atrial tissue models. 2D and 3D tissue geometries with a range of conditions for intracellular coupling and myofiber orientation fields were studied. Electrograms were fractionated in the presence of complex atrial fiber fields and in 3D irregular geometries, due to far-field excitations. The complexity of the local electrical activity was not a strong determinant of the degree of fractionation. These results suggest that electrogram fractionation is more strongly linked to atrial substrate characteristics (including tissue geometry, fiber orientation and degree of intercelullar coupling) than to the electrical activation pattern sustaining atrial fibrillation.

Evolution and pharmacological modulation of the arrhythmogenic wave dynamics in canine pulmonary vein model

Aims

Atrial fibrillation (AF), the commonest cardiac arrhythmia, has been strongly linked with arrhythmogenic sources near the pulmonary veins (PVs), but underlying mechanisms are not fully understood. We aim to study the generation and sustenance of wave sources in a model of the PV tissue.

Methods and results

A previously developed biophysically detailed three-dimensional canine atrial model is applied. Effects of AF-induced electrical remodelling are introduced based on published experimental data, as changes of ion channel currents (I_CaL, I_K1, I_to, and I_Kur), the action potential (AP) and cell-to-cell coupling levels. Pharmacological effects are introduced by blocking specific ion channel currents. A combination of electrical heterogeneity (AP tissue gradients of 5–12 ms) and anisotropy (conduction velocities of 0.75–1.25 and 0.21–0.31 m/s along and transverse to atrial fibres) can results in the generation of wave breaks in the PV region. However, a long wavelength (171 mm) prevents the wave breaks from developing into re-entry. Electrical remodelling leads to decreases in the AP duration, conduction velocity and wavelength (to 49 mm), such that re-entry becomes sustained. Pharmacological effects on the tissue heterogeneity and vulnerability (to wave breaks and re-entry) are quantified to show that drugs that increase the wavelength and stop re-entry (I_K1 and I_Kur blockers) can also increase the heterogeneity (AP gradients of 26–27 ms) and the likelihood of wave breaks.

Conclusion

Biophysical modelling reveals large conduction block areas near the PVs, which are due to discontinuous fibre arrangement enhanced by electrical heterogeneity. Vulnerability to re-entry in such areas can be modulated by pharmacological interventions.

Optimal iodine staining of cardiac tissue for X-ray computed tomography

X-ray computed tomography (XCT) has been shown to be an effective imaging technique for a variety of materials. Due to the relatively low differential attenuation of X-rays in biological tissue, a high density contrast agent is often required to obtain optimal contrast. The contrast agent, iodine potassium iodide (), has been used in several biological studies to augment the use of XCT scanning. Recently was used in XCT scans of animal hearts to study cardiac structure and to generate 3D anatomical computer models. However, to date there has been no thorough study into the optimal use of as a contrast agent in cardiac muscle with respect to the staining times required, which has been shown to impact significantly upon the quality of results. In this study we address this issue by systematically scanning samples at various stages of the staining process. To achieve this, mouse hearts were stained for up to 58 hours and scanned at regular intervals of 6–7 hours throughout this process. Optimal staining was found to depend upon the thickness of the tissue; a simple empirical exponential relationship was derived to allow calculation of the required staining time for cardiac samples of an arbitrary size.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Sine systemate chaos? A versatile tool for earthworm taxonomy: non-destructive imaging of freshly fixed and museum specimens using micro-computed tomography

In spite of the high relevance of lumbricid earthworms ('Oligochaeta': Lumbricidae) for soil structure and functioning, the taxonomy of this group of terrestrial invertebrates remains in a quasi-chaotic state. Earthworm taxonomy traditionally relies on the interpretation of external and internal morphological characters, but the acquisition of these data is often hampered by tedious dissections or restricted access to valuable and rare museum specimens. The present state of affairs, in conjunction with the difficulty of establishing primary homologies for multiple morphological features, has led to an almost unrivaled instability in the taxonomy and systematics of certain earthworm groups, including Lumbricidae. As a potential remedy, we apply for the first time a non-destructive imaging technique to lumbricids and explore the future application of this approach to earthworm taxonomy. High-resolution micro-computed tomography (μCT) scanning of freshly fixed and museum specimens was carried out using two cosmopolitan species, Aporrectodea caliginosa and A. trapezoides. By combining two-dimensional and three-dimensional dataset visualization techniques, we demonstrate that the morphological features commonly used in earthworm taxonomy can now be analyzed without the need for dissection, whether freshly fixed or museum specimens collected more than 60 years ago are studied. Our analyses show that μCT in combination with soft tissue staining can be successfully applied to lumbricid earthworms. An extension of the approach to other families is poised to strengthen earthworm taxonomy by providing a versatile tool to resolve the taxonomic chaos currently present in this ecologically important, but taxonomically neglected group of terrestrial invertebrates.

A mathematical model of the unidirectional block caused by the pulmonary veins for anatomically induced atrial reentry

It is widely believed that the pulmonary veins (PVs) of the left atrium play the central role in the generation of anatomically induced atrial reentry but its mechanism has not been analytically explained. To understand this mechanism, a new analytic approach is proposed by adapting the geometric relative acceleration analysis from spacetime physics based on the hypothesis that a large relative acceleration can translate to a dramatic increase in the curvature of a wavefront and subsequently to conduction failure. By verifying the strong dependency of the propagational direction and the magnitude of anisotropy for conduction failure, this analytic method reveals that a unidirectional block can be generated by asymmetric propagation toward the PVs. This model is validated by computational tests in a T-shaped domain, computational simulations for three-dimensional atrial reentry and previous in-silico reports for anatomically induced atrial reentry.

Three-dimensional imaging of the mouse heart and vasculature using micro-CT and whole-body perfusion of iodine or phosphotungstic acid

Recent studies have investigated histological staining compounds as micro-computed tomography (micro-CT) contrast agents, delivered by soaking tissue specimens in stain and relying on passive diffusion for agent uptake. This study describes a perfusion approach using iodine or phosphotungstic acid (PTA) stains, delivered to an intact mouse, to capitalize on the microvasculature as a delivery conduit for parenchymal staining and direct contact for staining artery walls. Twelve C57BL/6 mice, arterially perfused with either 25% Lugol's solution or 5% PTA solution were scanned intact and reconstructed with 26 µm isotropic voxels. The animals were fixed and the heart and surrounding vessels were excised, embedded and scanned; isolated heart images were reconstructed with 13 µm isotropic voxels. Myocardial enhancement and artery diameters were measured. Both stains successfully enhanced the myocardium and vessel walls. Interestingly, Lugol's solution provided a significantly higher enhancement of the myocardium than PTA [2502 ± 437 vs 656 ± 178 Hounsfield units (HU); p < 0.0001], delineating myofiber architecture and orientation. There was no significant difference in vessel wall enhancement (Lugol's, 1036 ± 635 HU; PTA, 738 ± 124 HU; p = 0.29), but coronary arteries were more effectively segmented from the PTA-stained hearts, enabling segmented imaging of fifth- order coronary artery branches. The combination of whole mouse perfusion delivery and use of heavy metal-containing stains affords high-resolution imaging of the mouse heart and vasculature by micro-CT. The differential imaging patterns of Lugol's- and PTA-stained tissues reveals new opportunities for micro-analyses of cardiac and vascular tissues.

Heterogeneous and anisotropic integrative model of pulmonary veins: computational study of arrhythmogenic substrate for atrial fibrillation

Mechanisms underlying the genesis of re-entrant substrate for the most common cardiac arrhythmia, atrial fibrillation (AF), are not well understood. In this study, we develop a multi-scale three-dimensional computational model that integrates cellular electrophysiology of the left atrium (LA) and pulmonary veins (PVs) with the respective tissue geometry and fibre orientation. The latter is reconstructed in unique detail from high-resolution (approx. 70 μm) contrast micro-computed tomography data. The model is used to explore the mechanisms of re-entry initiation and sustenance in the PV region, regarded as the primary source of high-frequency electrical activity in AF. Simulations of the three-dimensional model demonstrate that an initial break-down of normal electrical excitation wave-fronts can be caused by the electrical heterogeneity between the PVs and LA. High tissue anisotropy is then responsible for the slow conduction and generation of a re-entrant circuit near the PVs. Evidence of such circuits has been seen clinically in AF patients. Our computational study suggests that primarily the combination of electrical heterogeneity and conduction anisotropy between the PVs and LA tissues leads to the generation of a high-frequency (approx. 10 Hz) re-entrant source near the PV sleeves, thus providing new insights into the arrhythmogenic mechanisms of excitation waves underlying AF.

Quantitative analysis of microscopic X-ray computed tomography imaging: Japanese quail embryonic soft tissues with iodine staining

Rapid three-dimensional imaging of embryos to better understand the complex process of morphogenesis has been challenging. Recently introduced iodine staining protocols (I2 KI and alcoholic iodine stains) combined with microscopic X-ray computed tomography allows visualization of soft tissues in diverse small organisms and tissue specimens. I2 KI protocols have been developed specifically for small animals, with a limited number of quantitative studies of soft tissue contrasts. To take full advantage of the low X-ray attenuation of ethanol and retain bound iodine while dehydrating the specimen in ethanol, we developed an ethanol I2 KI protocol. We present comparative microscopic X-ray computed tomography analyses of ethanol I2 KI and I2 KI staining protocols to assess the performance of this new protocol to visualize soft tissue anatomy in late stage Japanese quail embryos using quantitative measurements of soft tissue contrasts and sample shrinkage. Both protocols had only 5% shrinkage compared with the original harvested specimen, supporting the use of whole mounts to minimize tissue shrinkage effects. Discrimination within and among the selected organs with each staining protocol and microscopic X-ray computed tomography imaging were comparable to those of a gray scale histological section. Tissue discrimination was assessed using calibrated computed tomography values and a new discrimination index to quantify the degree of computed tomography value overlaps between selected soft tissue regions. Tissue contrasts were dependent on the depth of the tissue within the embryos before the embryos were saturated with each stain solution, and optimal stain saturations for the entire embryo were achieved at 14 and 28 days staining for I2 KI and ethanol I2 KI, respectively. Ethanol I2 KI provided superior soft tissue contrasts by reducing overstaining of fluid-filled spaces and differentially modulating staining of some tissues, such as bronchial and esophageal walls and spinal cord. Delineating the selected soft tissues using optimal threshold ranges derived from the quantitative analyses of the contrast enhancement in optimally stained embryos is possible. The protocols presented here are expected to be applicable to other organisms with modifications to staining time and contribute toward rapid and more efficient segmentation of soft tissues for three-dimensional visualization.

Arrhythmogenic substrate for atrial fibrillation: insights from an integrative computational model of pulmonary veins

Mechanisms underlying the genesis of re-entrant substrate for atrial fibrillation (AF) in the pulmonary veins (PVs) and left atrium (LA) are not well understood. We develop a biophysically detailed computational model for the PVs and surrounding LA tissue. The model integrates canine PV and LA single cell electrophysiology with the respective 3D tissue geometry and fiber orientation reconstructed from micro-CT data. The model simulations demonstrate that a combination of tissue anisotropy and electrical heterogeneity between the PVs and LA causes a break-down of normal electrical excitation wave-fronts. This leads to the generation of a high-frequency re-entrant source near the PV sleeves. Evidence of such sources have been seen clinically in AF patients. In summary, our modeling results provide new insights into the arrhythmogenic mechanisms of re-entrant excitation waves underlying AF.

The morphology of the mouse masticatory musculature

The mouse has been the dominant model organism in studies on the development, genetics and evolution of the mammalian skull and associated soft-tissue for decades. There is the potential to take advantage of this well studied model and the range of mutant, knockin and knockout organisms with diverse craniofacial phenotypes to investigate the functional significance of variation and the role of mechanical forces on the development of the integrated craniofacial skeleton and musculature by using computational mechanical modelling methods (e.g. finite element and multibody dynamic modelling). Currently, there are no detailed published data of the mouse masticatory musculature available. Here, using a combination of micro-dissection and non-invasive segmentation of iodine-enhanced micro-computed tomography, we document the anatomy, architecture and proportions of the mouse masticatory muscles. We report on the superficial masseter (muscle, tendon and pars reflecta), deep masseter, zygomaticomandibularis (anterior, posterior, infraorbital and tendinous parts), temporalis (lateral and medial parts), external and internal pterygoid muscles. Additionally, we report a lateral expansion of the attachment of the temporalis onto the zygomatic arch, which may play a role in stabilising this bone during downwards loading. The data presented in this paper now provide a detailed reference for phenotypic comparison in mouse models and allow the mouse to be used as a model organism in biomechanical and functional modelling and simulation studies of the craniofacial skeleton and particularly the masticatory system.

Three-dimensional impulse propagation in myocardium: arrhythmogenic mechanisms at the tissue level

Impulse propagation in the heart depends on the excitability of individual cardiomyocytes, impulse transmission between adjacent myocytes, and the 3-dimensional arrangement of those cells. Here, we review the role of each of these factors in normal and aberrant cardiac electric activation, with particular emphasis on the effects of 3-dimensional myocyte architecture at the tissue scale. The analysis draws on findings from in vivo and in vitro experiments, as well as biophysically based computer models that have been used to integrate and interpret these experimental data. It indicates that discontinuous arrangement of myocytes and extracellular connective tissue at the tissue scale can give rise to current source-to-sink mismatch, spatiotemporal distribution of refractoriness, and rate-sensitive electric instability, which contribute to the initiation and maintenance of reentrant cardiac arrhythmia. This exacerbates the risk of rhythm disturbance associated with heart disease. We conclude that structure-based, multiscale computer models that incorporate accurate information about local cellular electric activity provide a powerful platform for investigating the basis of reentrant cardiac arrhythmia. However, it is important that these models capture key features of structure and related electric function at the tissue scale.

Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart

Background

One of the main factors affecting propagation of electrical waves and contraction in ventricles of the heart is anisotropy of cardiac tissue. Anisotropy is determined by orientation of myocardial fibres. Determining fibre orientation field and shape of the heart is important for anatomically accurate modelling of electrical and mechanical function of the heart. The aim of this paper is to introduce a theoretical rule-based model for anatomy and fibre orientation of the left ventricle (LV) of the heart and to compare it with experimental data. We suggest explicit analytical formulae that allow us to obtain the left ventricle form and its fibre direction field. The ventricle band concept of cardiac architecture given by Torrent-Guasp is chosen as the model postulate.

Methods

In our approach, anisotropy of the heart is derived from some general principles. The LV is considered as a set of identical spiral surfaces, each of which can be produced from the other by rotation around one vertical axis. Each spiral surface is filled with non-intersecting curves which represent myocardial fibres.

For model verification, we use experimental data on fibre orientation in human and canine hearts.

Results

LV shape and anisotropy are represented by explicit analytical expressions in a curvilinear 3-D coordinate system. The derived fibre orientation field shows good qualitative agreement with experimental data. The model reveals the most thorough quantitative simulation of fibre angles at the LV middle zone.

Conclusions

Our analysis shows that the band concept can generate realistic anisotropy of the LV. Our model shows good qualitative agreement between the simulated fibre orientation field and the experimental data on LV anisotropy, and the model can be used for various numerical simulations to study the effects of anisotropy on cardiac excitation and mechanical function.

Pro-arrhythmogenic effects of atrial fibrillation-induced electrical remodelling: insights from the three-dimensional virtual human atria

Chronic atrial fibrillation (AF) is associated with structural and electrical remodelling in the atria, which are associated with a high recurrence of AF. Through biophysically detailed computer modelling, this study investigated mechanisms by which AF-induced electrical remodelling promotes and perpetuates AF. A family of Courtemanche–Ramirez–Nattel variant models of human atrial cell action potentials (APs), taking into account of intrinsic atrial electrophysiological properties, was modified to incorporate various experimental data sets on AF-induced changes of major ionic channel currents (I_CaL, I_Kur, I_to, I_K1, I_Ks, I_NaCa) and on intracellular Ca²⁺ handling. The single cell models for control and AF-remodelled conditions were incorporated into multicellular three-dimensional (3D) atrial tissue models. Effects of the AF-induced electrical remodelling were quantified as the changes of AP profile, AP duration (APD) and its dispersion across the atria, and the vulnerability of atrial tissue to the initiation of re-entry. The dynamic behaviour of re-entrant excitation waves in the 3D models was characterised. In our simulations, AF-induced electrical remodelling abbreviated atrial APD non-uniformly across the atria; this resulted in relatively short APDs co-existing with marked regional differences in the APD at junctions of the crista terminalis/pectinate muscle, pulmonary veins/left atrium. As a result, the measured tissue vulnerability to re-entry initiation at these tissue junctions was increased. The AF-induced electrical remodelling also stabilized and accelerated re-entrant excitation waves, leading to rapid and sustained re-entry. Under the AF-remodelled condition, re-entrant scroll waves in the 3D model degenerated into persistent and erratic wavelets, leading to fibrillation. In conclusion, realistic 3D atrial tissue models indicate that AF-induced electrical remodelling produces regionally heterogeneous and shortened APD; these respectively facilitate initiation and maintenance of re-entrant excitation waves.

Concentration-dependent specimen shrinkage in iodine-enhanced microCT

Iodine potassium iodide (I2 KI) solution can be employed as a contrast agent for the visualisation of soft tissue structures in micro-computed tomography studies. This technique provides high resolution images of soft tissue non-destructively but initial studies suggest that the stain can cause substantial specimen shrinkage. The degree of specimen shrinkage, and potential deformation, is an important consideration when using the data for morphological studies. Here we quantify the macroscopic volume changes in mouse skeletal muscle, cardiac muscle and cerebellum as a result of immersion in the common fixatives 10% phosphate-buffered formal saline, 70% ethanol and 3% glutaraldehyde, compared with I2 KI staining solution at concentrations of 2, 6, 10 and 20%. Immersion in the I2 KI solution resulted in dramatic changes of tissue volume, which were far larger than the shrinkage from formalin fixation alone. The degree of macroscopic change was most dependent upon the I2 KI concentration, with severe shrinkage of 70% seen in solutions of 20% I2 KI after 14 days' incubation. When using this technique care needs to be taken to use the lowest concentration that will give adequate contrast to minimise artefacts due to shrinkage.

A three-dimensional finite element model of human atrial anatomy: new methods for cubic Hermite meshes with extraordinary vertices

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.

Studying the microanatomy of the heart in three dimensions: a practical update

The structure and function of the heart needs to be understood in three dimensions. We give a brief historical summary of the methods by which such an understanding has been sought, and some practical details of the relatively new technique of micro-CT with iodine contrast enhancement in samples from rat and rabbit. We discuss how the improved anatomical detail available in fixed cadaveric hearts will enhance our ability to model and to understand the integrated function of the cardiomyocytes, conducting tissues, and fibrous supporting structures that generate the pumping function of the heart.