A novel micro-to-macro approach for cardiac tissue mechanics

For studying cardiac mechanics, hyperelastic anisotropic computational models have been developed which require the tissue anisotropic and hyperelastic parameters. These parameters are obtained by tissue samples mechanically testing. The validity of such parameters are limited to the specific tissue sample only. They are not adaptable for pathological tissues commonly associated with tissue microstructure alterations. To investigate cardiac tissue mechanics, a novel approach is proposed to model hyperelasticity and anisotropy. This approach is adaptable to various tissue microstructural constituent’s distributions in normal and pathological tissues. In this approach, the tissue is idealized as composite material consisting of cardiomyocytes distributed in extracellular matrix (ECM). The major myocardial tissue constituents are mitochondria and myofibrils while the main ECM’s constituents are collagen fibers and fibroblasts. Accordingly, finite element simulations of uniaxial and equibiaxial tests of normal and infarcted tissue samples with known amounts of these constituents were conducted, leading to corresponding tissue stress–strain data that were fitted to anisotropic/hyperelastic models. The models were validated where they showed good agreement characterized by maximum average stress-strain errors of 16.17 and 10.01% for normal and infarcted cardiac tissue, respectively. This demonstrate the effectiveness of the proposed models in accurate characterization of healthy and pathological cardiac tissues.     

How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle

The bidomain model, which describes the behavior of many electrically active tissues, is equivalent to a multi-dimensional cable model and can be represented by a network of resistors and capacitors. For a two-dimensional sheet of tissue, the intracellular and extracellular conductivity tensors can be visualized as two ellipses. For any pair of conductivity tensors, a coordinate transformation can be found that reduces the extracellular ellipse to a circle and aligns the intracellular ellipse with the coordinate axes. The eccentricity of the intracellular ellipse in this new coordinate system is an important parameter. It can have two special values: zero (in which case the tissue has equal anisotropy ratios) or one (in which case the tissue is comprised of one-dimensional fibers coupled through the two-dimensional extracellular space). Thus the bidomain model provides a unifying framework within which the electrical behavior of a wide variety of nerve and muscle tissues can be studied.When the anisotropy ratios in the intracellular and extracellular domains are not equal, stimulation with an anode always causes depolarization of some region of tissue. An analogous effect occurs in models that describe one-dimensional fibers, in which an activating function determines the site of stimulation. Experiments indicate that cardiac muscle does not have equal anisotropy ratios. Therefore, models developed to describe stimulation of axons may also help in understanding stimulation of two- or three-dimensional cardiac tissue, and may explain the concept of anodal stimulation of cardiac tissue through a virtual cathode.     

Spatial Graphs: Principles and Applications for Habitat Connectivity

ABSTRACT Well-founded methods to assess habitat connectivity are essential to inform land management decisions that include conservation and restoration goals. Indeed, to be able to develop a conservation plan that maintains animal movement through a fragmented landscape, spatial locations of habitat and paths among them need to be represented. Graph-based approaches have been proposed to determine paths among habitats at various scales and dispersal movement distances, and balance data requirements with information content. Conventional graphs, however, do not explicitly maintain geographic reference, reducing communication capacity and utility of other geo-spatial information. We present spatial graphs as a unifying theory for applying graph-based methods in a geographic context. Spatial graphs integrate a geometric reference system that ties patches and paths to specific spatial locations and spatial dimensions. Arguably, the complete graph, with paths between every pair of patches, may be one of the most relevant graphs from an ecosystem perspective, but it poses challenges to compute, process and visualize. We developed Minimum Planar Graphs as a spatial generalization of Delaunay triangulations to provide a reasonable approximation of complete graphs that facilitates visualization and comprehension of the network of connections across landscapes. If, as some authors have suggested, the minimum spanning tree identifies the connectivity “backbone” of a landscape, then the Minimum Planar Graph identifies the connectivity “network”. We applied spatial graphs, and in particular the Minimum Planar Graph, to analyze woodland caribou habitat in Manitoba, Canada to support the establishment of a national park.     

A modelling approach towards epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.     

Role of matricellular proteins in cardiac tissue remodeling after myocardial infarction

After onset of myocardial infarction (MI), the left ventricle (LV) undergoes a continuum of molecular, cellular, and extracellular responses that result in LV wall thinning, dilatation, and dysfunction. These dynamic changes in LV shape, size, and function are termed cardiac remodeling. If the cardiac healing after MI does not proceed properly, it could lead to cardiac rupture or maladaptive cardiac remodeling, such as further LV dilatation and dysfunction, and ultimately death. Although the precise molecular mechanisms in this cardiac healing process have not been fully elucidated, this process is strictly coordinated by the interaction of cells with their surrounding extracellular matrix (ECM) proteins. The components of ECM include basic structural proteins such as collagen, elastin and specialized proteins such as fibronectin, proteoglycans and matricellular proteins. Matricellular proteins are a class of non-structural and secreted proteins that probably exert regulatory functions through direct binding to cell surface receptors, other matrix proteins, and soluble extracellular factors such as growth factors and cytokines. This small group of proteins, which includes osteopontin, thrombospondin-1/2, tenascin, periostin, and secreted protein, acidic and rich in cysteine, shows a low level of expression in normal adult tissue, but is markedly upregulated during wound healing and tissue remodeling, including MI. In this review, we focus on the regulatory functions of matricellular proteins during cardiac tissue healing and remodeling after MI.     

Solvers for the cardiac bidomain equations

The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue. They are especially important for accurately modeling extracellular stimulation, as evidenced by their prediction of virtual electrode polarization before experimental verification. However, solution of the equations is computationally expensive due to the fine spatial and temporal discretization needed. This limits the size and duration of the problem which can be modeled. Regardless of the specific form into which they are cast, the computational bottleneck becomes the repeated solution of a large, linear system. The purpose of this review is to give an overview of the equations and the methods by which they have been solved. Of particular note are recent developments in multigrid methods, which have proven to be the most efficient.     

Hydrogel based injectable scaffolds for cardiac tissue regeneration

Tissue engineering promises to be an effective strategy that can overcome the lacuna existing in the current pharmacological and interventional therapies and heart transplantation. Heart failure continues to be a major contributor to the morbidity and mortality across the globe. This may be attributed to the limited regeneration capacity after the adult cardiomyocytes are terminally differentiated or injured. Various strategies involving acellular scaffolds, stem cells, and combinations of stem cells, scaffolds and growth factors have been investigated for effective cardiac tissue regeneration. Recently, injectable hydrogels have emerged as a potential candidate among various categories of biomaterials for cardiac tissue regeneration due to improved patient compliance and facile administration via minimal invasive mode that treats complex infarction. This review discusses in detail on the advances made in the field of injectable materials for cardiac tissue engineering highlighting their merits over their preformed counterparts.     

Genetic conservation of Ficus bonijesulapensis R.M. Castro in a dry forest on limestone outcrops

Ficus bonijesulapensis is endemic to a seasonally dry forest on limestone outcrops and it is arranged in disjunct areas in the Cerrado and Caatinga Domains. Species of this genus are considered to be key plants in tropical forests, since they provide resources during periods of scarcity of other resources and, additionally, they contribute in a plant community's restoration. Therefore, the conservation of these species in their natural habitat contributes to the maintenance of the long-term population viability and their genetic diversity. We used nine ISSR primers to analyze the genetic diversity and the genetic spatial patterns of 15 populations of F. bonijesulapensis. We obtained 75 polymorphic bands, the expected heterozygosity (He) was 0.30 and AMOVA showed that most of the genetic diversity was found within populations (77%). The historical gene flow was 1.1 migrants and the Bayesian genetic structure assigned individuals genotypes to eight groups. However, there was not a spatial pattern of genetic variability according to a multivariate correlogram and as confirmed by Mantel's test (r = 0.06, p = 0.68). Eight management units (MU) were proposed and were aiming at the MU's ability to maintain minimally viable populations and a higher genetic variability.     

Considerations for the use of cellular electrophysiology models within cardiac tissue simulations

The use of mathematical models to study cardiac electrophysiology has a long history, and numerous cellular scale models are now available, covering a range of species and cell types. Their use to study emergent properties in tissue is also widespread, typically using the monodomain or bidomain equations coupled to one or more cell models. Despite the relative maturity of this field, little has been written looking in detail at the interface between the cellular and tissue-level models. Mathematically this is relatively straightforward and well-defined. There are however many details and potential inconsistencies that need to be addressed, in order to ensure correct operation of a cellular model within a tissue simulation. This paper will describe these issues and how to address them.Simply having models available in a common format such as CellML is still of limited utility, with significant manual effort being required to integrate these models within a tissue simulation. We will thus also discuss the facilities available for automating this in a consistent fashion within Chaste, our robust and high-performance cardiac electrophysiology simulator.It will be seen that a common theme arising is the need to go beyond a representation of the model mathematics in a standard language, to include additional semantic information required in determining the model’s interface, and hence to enhance interoperability. Such information can be added as metadata, but agreement is needed on the terms to use, including development of appropriate ontologies, if reliable automated use of CellML models is to become common.     

Criterion for stable reentry in a ring of cardiac tissue

We model electrical wave propagation in a ring of cardiac tissue using an mth-order difference equation, where m denotes the number of cells in the ring. Under physiologically reasonable assumptions, the difference equation has a unique equilibrium solution. Applying Jury’s stability test, we prove a theorem concerning the local asymptotic stability of this equilibrium solution. Our results yield conditions for sustained reentrant tachycardia, a type of cardiac arrhythmia.      

An estimate of anisotropic poroelastic constants of an osteon

The anisotropic poroelastic constants of an osteon are estimated by micromechanical analysis. Two extreme cases are examined, the drained and the undrained elastic constants. The drained elastic constants are the porous medium’s effective elastic constants when the fluid in the pores easily escapes and the pore fluid can sustain no pore pressure. The undrained elastic constants are the porous medium’s effective elastic constants when the medium is fully saturated with pore fluid and the fluid cannot escape. The drained and undrained elastic constants at the lacunar and canalicular porosity tissue levels are estimated by using an effective moduli model consisting of the periodic distribution of ellipsoidal cavities. These estimated anisotropic poroelastic constants provide a database for the development of an accurate anisotropic poroelastic model of an osteon.     

Connective tissue growth factor induces cardiac hypertrophy through Akt signaling

In the process of cardiac remodeling, connective tissue growth factor (CTGF/CCN2) is secreted from cardiac myocytes. Though CTGF is well known to promote fibroblast proliferation, its pathophysiological effects in cardiac myocytes remain to be elucidated. In this study, we examined the biological effects of CTGF in rat neonatal cardiomyocytes. Cardiac myocytes stimulated with full length CTGF and its C-terminal region peptide showed the increase in cell surface area. Similar to hypertrophic ligands for G-protein coupled receptors, such as endothelin-1, CTGF activated amino acid uptake; however, CTGF-induced hypertrophy is not associated with the increased expression of skeletal actin or BNP, analyzed by Northern-blotting. CTGF treatment activated ERK1/2, p38 MAPK, JNK and Akt. The inhibition of Akt by transducing dominant-negative Akt abrogated CTGF-mediated increase in cell size, while the inhibition of MAP kinases did not affect the cardiac hypertrophy. These findings indicate that CTGF is a novel hypertrophic factor in cardiac myocytes.     

Biomimetic scaffold combined with electrical stimulation and growth factor promotes tissue engineered cardiac development

Toward developing biologically sound models for the study of heart regeneration and disease, we cultured heart cells on a biodegradable, microfabricated poly(glycerol sebacate) (PGS) scaffold designed with micro-structural features and anisotropic mechanical properties to promote cardiac-like tissue architecture. Using this biomimetic system, we studied individual and combined effects of supplemental insulin-like growth factor-1 (IGF-1) and electrical stimulation (ES). On culture day 8, all tissue constructs could be paced and expressed the cardiac protein troponin-T. IGF-1 reduced apoptosis, promoted cell-to-cell connectivity, and lowered excitation threshold, an index of electrophysiological activity. ES promoted formation of tissue-like bundles oriented in parallel to the electrical field and a more than ten-fold increase in matrix metalloprotease-2 (MMP-2) gene expression. The combination of IGF-1 and ES increased 2D projection length, an index of overall contraction strength, and enhanced expression of the gap junction protein connexin-43 and sarcomere development. This culture environment, designed to combine cardiac-like scaffold architecture and biomechanics with molecular and biophysical signals, enabled functional assembly of engineered heart muscle from dissociated cells and could serve as a template for future studies on the hierarchy of various signaling domains relative to cardiac tissue development.     

A remarkable case of mosaic parapatry in millipedes

The parapatric boundary between Tasmaniosoma compitale Mesibov, 2010 and Tasmaniosoma hickmanorum Mesibov, 2010 (Polydesmida: Dalodesmidae) in northwest Tasmania was mapped in preparation for field studies of parapatry and speciation. Both millipede species can be collected as adults throughout the year, are often abundant in eucalypt forest and tolerate major habitat disturbance. The parapatric boundary between the two species is ca 100 m wide in well-sampled sections and ca 230 km long. It runs from sea level to 600-700 m elevation, crosses most of the river catchments in northwest Tasmania and several major geological boundaries, and one portion of the boundary runs along a steep rainfall gradient. The location of the boundary is estimated here from scattered sample points using a method based on Delaunay triangulation.     

Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle

As an initial step to investigate stimulus–response relations in growth and remodeling (G&R) of cardiac tissue, this study aims to develop a method to simulate 3D-inhomogeneous volumetric growth. Growth is regarded as a deformation that is decomposed into a plastic component which describes unconstrained growth and an elastic component to satisfy continuity of the tissue after growth. In current growth models, a single reference configuration is used that remains fixed throughout the entire growth process. However, considering continuous turnover to occur together with growth, such a fixed reference is unlikely to exist in reality. Therefore, we investigated the effect of tissue turnover on growth by incrementally updating the reference configuration. With both a fixed reference and an updated reference, strain-induced cardiac growth in magnitude of 30% could be simulated. However, with an updated reference, the amplitude of the stimulus for growth decreased over time, whereas with a fixed reference this amplitude increased. We conclude that, when modeling volumetric growth, the choice of the reference configuration is of great importance for the computed growth.     

Evaluation of the contact angle from molecular simulations

An alternative method for determination of the contact angle of droplets at a solid underlay from molecular simulations is proposed. The method is based on a recently developed general method of identification the surface molecules of a molecular system with the interface of an arbitrary shape and on a subsequent parametrisation of the surface of the droplet by a smooth function. The method has been verified first by considering two artificial systems with the exactly known contact angles and then by comparison with literature data for two realistic systems.     

Voltage noise influences action potential duration in cardiac myocytes

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current-voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current-voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.     

A voltage-activated proton current in human cardiac fibroblasts

A voltage-activated proton current in human cardiac fibroblasts, measured using the whole-cell recording configuration of the patch-clamp technique, is reported. Increasing the pH of the bathing solution shifted the current activation threshold to more negative potentials and increased both the current amplitude and its rate of activation. Changing the pH gradient by one unit caused a 51mV shift in the reversal potential of the current, demonstrating a high selectivity for protons of the channel carrying the current. Extracellularly applied Zn(2+) reversibly inhibited the current. Activation of the current contributes to the resting membrane conductance under conditions of intracellular acidosis. It is proposed that this current in cardiac fibroblasts is involved in the regulation of the intracellular pH and the membrane potential under physiological conditions as well as in response to pathological conditions such as ischemia.     

Rapid proteomic remodeling of cardiac tissue caused by total body ionizing radiation

Accidental nuclear scenarios lead to environmental contamination of unknown level. Immediate radiation‐induced biological responses that trigger processes leading to adverse health effects decades later are not well understood. A comprehensive proteomic analysis provides a promising means to identify and quantify the initial damage after radiation exposure. Early changes in the cardiac tissue of C57BL/6 mice exposed to total body irradiation were studied, using a dose relevant to both intentional and accidental exposure (3 Gy gamma ray). Heart tissue protein lysates were analyzed 5 and 24 h after the exposure using isotope‐coded protein labeling (ICPL) and 2‐dimensional difference‐in‐gel‐electrophoresis (2‐D DIGE) proteomics approaches. The differentially expressed proteins were identified by LC‐ESI‐MS‐MS. Both techniques showed similar functional groups of proteins to be involved in the initial injury. Pathway analyses indicated that total body irradiation immediately induced biological responses such as inflammation, antioxidative defense, and reorganization of structural proteins. Mitochondrial proteins represented the protein class most sensitive to ionizing radiation. The proteins involved in the initial damage processes map to several functional categories involving cardiotoxicity. This prompts us to propose that these early changes are indicative of the processes that lead to an increased risk of cardiovascular disease after radiation exposure.