44 research outputs found
A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells
Cardiac myocytes are the fundamental cells composing the heart muscle. The
propagation of electric signals and chemical quantities through them is
responsible for their nonlinear contraction and dilatation. In this study, a
theoretical model and a finite element formulation are proposed for the
simulation of adhesive contact interactions between myocytes across the
so-called gap junctions. A multi-field interface constitutive law is proposed
for their description, integrating the adhesive and contact mechanical response
with their electrophysiological behavior. From the computational point of view,
the initial and boundary value problem is formulated as a structure-structure
interaction problem, which leads to a straightforward implementation amenable
for parallel computations. Numerical tests are conducted on different couples
of myocytes, characterized by different shapes related to their stages of
growth, capturing the experimental response. The proposed framework is expected
to have impact on the understanding how imperfect mechano-transduction could
lead to emergent pathological responses.Comment: 31 pages, 17 figure
A note on stress-driven anisotropic diffusion and its role in active deformable media
We propose a new model to describe diffusion processes within active
deformable media. Our general theoretical framework is based on physical and
mathematical considerations, and it suggests to use diffusion tensors directly
coupled to mechanical stress. A proof-of-concept experiment and the proposed
generalised reaction-diffusion-mechanics model reveal that initially isotropic
and homogeneous diffusion tensors turn into inhomogeneous and anisotropic
quantities due to the intrinsic structure of the nonlinear coupling. We study
the physical properties leading to these effects, and investigate mathematical
conditions for its occurrence. Together, the experiment, the model, and the
numerical results obtained using a mixed-primal finite element method, clearly
support relevant consequences of stress-assisted diffusion into anisotropy
patterns, drifting, and conduction velocity of the resulting excitation waves.
Our findings also indicate the applicability of this novel approach in the
description of mechano-electrical feedback in actively deforming bio-materials
such as the heart
Phase field modelling and simulation of damage occurring in human vertebra after screws fixation procedure
The present endeavor numerically exploits the use of a phase-field model to
simulate and investigate fracture patterns, deformation mechanisms, damage, and
mechanical responses in a human vertebra after the incision of pedicle screws
under compressive regimes. Moreover, the proposed phase field framework can
elucidate scenarios where different damage patterns, such as crack nucleation
sites and crack trajectories, play a role after the spine fusion procedure,
considering several simulated physiological movements of the vertebral body. A
convergence analysis has been conducted for the vertebra-screws model,
considering several mesh refinements, which has demonstrated good agreement
with the existing literature on this topic. Consequently, by assuming different
angles for the insertion of the pedicle screws and taking into account a few
vertebral motion loading regimes, a plethora of numerical results
characterizing the damage occurring within the vertebral model has been
derived. Overall, the phase field results may shed more light on the medical
community, which will be useful in enhancing clinical interventions and
reducing post-surgery bone failure and screw loosening.Comment: 23 pages, 9 figures. arXiv admin note: text overlap with
arXiv:2207.0936
A numerical model of the human cornea accounting for the fiber-distributed collagen microstructure
We present a fiber-distributed model of the reinforcing collagen of the human
cornea. The model describes the basic connections between the components of the
tissue by defining an elementary block (cell) and upscaling it to the physical
size of the cornea. The cell is defined by two sets of collagen fibrils running
in sub-orthogonal directions, characterized by a random distribution of the
spatial orientation and connected by chemical bonds of two kinds. The bonds of
the first kind describe the lamellar crosslinks, forming the ribbon-like
lamellae; while the bonds of the second kind describe the stacking crosslinks,
piling up the lamellae to form the structure of the stroma. The spatial
replication of the cell produces a truss structure with a considerable number
of degrees of freedom. The statistical characterization of the collagen fibrils
leads to a mechanical model that reacts to the action of the deterministic
intraocular pressure with a stochastic distribution of the displacements, here
characterized by their mean value and variance. The strategy to address the
solution of the heavy resulting numerical problem is to use the so-called
stochastic finite element improved perturbation method combined with a fully
explicit solver. Results demonstrate that the variability of the mechanical
properties affects in a non-negligible manner the expected response of the
structure to the physiological action.Comment: 18 pages, 6 figure
Osteolytic vs. Osteoblastic Metastatic Lesion: Computational Modeling of the Mechanical Behavior in the Human Vertebra after Screws Fixation Procedure
Metastatic lesions compromise the mechanical integrity of vertebrae, increasing the fracture risk. Screw fixation is usually performed to guarantee spinal stability and prevent dramatic fracture events. Accordingly, predicting the overall mechanical response in such conditions is critical to planning and optimizing surgical treatment. This work proposes an image-based finite element computational approach describing the mechanical behavior of a patient-specific instrumented metastatic vertebra by assessing the effect of lesion size, location, type, and shape on the fracture load and fracture patterns under physiological loading conditions. A specific constitutive model for metastasis is integrated to account for the effect of the diseased tissue on the bone material properties. Computational results demonstrate that size, location, and type of metastasis significantly affect the overall vertebral mechanical response and suggest a better way to account for these parameters in estimating the fracture risk. Combining multiple osteolytic lesions to account for the irregular shape of the overall metastatic tissue does not significantly affect the vertebra fracture load. In addition, the combination of loading mode and metastasis type is shown for the first time as a critical modeling parameter in determining fracture risk. The proposed computational approach moves toward defining a clinically integrated tool to improve the management of metastatic vertebrae and quantitatively evaluate fracture risk
Mathematical modelling of active contraction in isolated cardiomyocytes
We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarizatio
Role of temperature on nonlinear cardiac dynamics.
Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed
Mathematical modelling of active contraction in isolated cardiomyocytes
We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarization