Abstract
Detailed fibre architecture plays a crucial role in myocardial mechanics both passively and actively. Strong interest has been attracted over decades in mathematical modelling of fibrous tissue (arterial wall, myocardium, etc.) by taking into account realistic fibre structures, i.e. from perfectly aligned one family of fibres, to two families of fibres, and to dispersed fibres described by probability distribution functions. It is widely accepted that the fibres, i.e. collage, cannot bear the load when compressed, thus it is necessary to exclude compressed fibres when computing the stress in fibrous tissue. In this study, we have focused on mathematical modelling of fibre dispersion in myocardial mechanics, and studied how different fibre dispersions affect cardiac pump function. The fibre dispersion in myocardium is characterized by a non-rotationally symmetric distribution using a pi -periodic Von Mises distribution based on recent experimental studies. In order to exclude compressed fibres for passive response, we adopted the discrete fibre dispersion model for approximating a continuous fibre distribution with finite fibre bundles, and then the general structural tensor was employed for describing dispersed active tension. We first studied the numerical accuracy of the integration of fibre contributions using the discrete fibre dispersion approach, then compared different mechanical responses in a uniaxially stretched myocardial sample with varied fibre dispersions. We finally studied the cardiac pump functions from diastole to systole in two heart models, a rabbit bi-ventricle model and a human left ventricle model. Our results show that the discrete fibre model is preferred for excluding compressed fibres because of its high computational efficiency. Both the diastolic filling and the systolic contraction will be affected by dispersed fibres depending on the in-plane and out-of-plane dispersion degrees, especially in systolic contraction. The in-plane dispersion seems affecting myocardial mechanics more than the out-of-plane dispersion. Despite different effects in the rabbit and human models caused by the fibre dispersion, large differences in pump function exist when fibres are highly dispersed at in-plane and out-of-plane. Our results highlight the necessity of using dispersed fibre models when modelling myocardial mechanics, especially when fibres are largely dispersed under pathological conditions, such as fibrosis.
Highlights
Computational models have been developed over decades aiming to better understand the mechanism of the heart function under physiological and pathological conditions, ranging from lumped parameter models [1,2] to single ventricles [3], to bi-ventricles and whole heart [4], and towards multiphysics personalized models for treatment planning and risk stratification [5], etc
In a recent study [31], we have studied dispersed active tension in a bi-ventricular model using a non-symmetric fibre distribution derived from an ex vivo diffusion tensor (DT)-magnetic resonance imaging (MRI) dataset, the dispersed active tension was derived by following the generalized structure tensor (GST) approach, the results showed that with rule-based myofibre structure, there is a need to employ a dispersed fibre model when simulating cardiac contraction, but fibre dispersion in the passive response of myocardium was not considered
This study systematically investigates the impact of fibre dispersions on myocardial mechanics both passively and actively, first on a myocardial strip, a rabbit bi-ventricle model, and a human left ventricle (LV) model
Summary
Computational models have been developed over decades aiming to better understand the mechanism of the heart function under physiological and pathological conditions, ranging from lumped parameter models [1,2] to single ventricles [3], to bi-ventricles and whole heart [4], and towards multiphysics personalized models for treatment planning and risk stratification [5], etc. One of the essential parts in computational cardiac modelling is the strain energy function, accurate and reliable stress/strain prediction essentially relies on the constitutive modelling of myocardium. The current common practice is to use fibre-reinforced hyperelastic material models by taking into account layered myofibre structures, such as the widely used strain-invariant-based function proposed by Holzapfel and Ogden [6], the so-called HO model. Micro-structurally informed constitutive modelling in soft tissue has attracted tremendous interest in this area since its introduction in the 1970s [7]. Constitutive modelling of soft tissue with dispersed fibres have found that dispersed collagen fibres can have a significant effect on the overall mechanical response of the soft tissue [11,12]
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