Computational modeling of three-dimensional electrodiffusion in biological systems: application to the node of Ranvier

A computational model is presented for the simulation of three-dimensional electrodiffusion of ions. Finite volume techniques were used to solve the Poisson-Nernst-Planck equation, and a dual Delaunay-Voronoi mesh was constructed to evaluate fluxes of ions, as well as resulting electric potentials. The algorithm has been validated and applied to a generalized node of Ranvier, where numerical results for computed action potentials agree well with cable model predictions for large clusters of voltage-gated ion channels. At smaller channel clusters, however, the three-dimensional electrodiffusion predictions diverge from the cable model predictions and show a broadening of the action potential, indicating a significant effect due to each channel's own local electric field. The node of Ranvier complex is an elaborate organization of membrane-bound aqueous compartments, and the model presented here represents what we believe is a significant first step in simulating electrophysiological events with combined realistic structural and physiological data.     

Computational modeling of the fluid flow in type B aortic dissection using a modified finite element embedded formulation

Biomechanics and Modeling in Mechanobiology - This work explores the use of an embedded computational fluid dynamics method to study the type B aortic dissection. The use of the proposed technique...     

A quasi-incompressible and quasi-inextensible finite element analysis of fibrous soft biological tissues

Biomechanics and Modeling in Mechanobiology - The contribution presents an extension and application of a recently proposed finite element formulation for quasi-inextensible and...     

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.     

Computational modeling reveals inflammation-driven dilatation of the pulmonary autograft in aortic position

Biomechanics and Modeling in Mechanobiology - The pulmonary autograft in the Ross procedure, where the aortic valve is replaced by the patient’s own pulmonary valve, is prone to failure due...     

Molecular modeling of immersion optical clearing of biological tissues

The interaction of six low-molecular tissue-clearing agents (1,2 and 1,3-propanediol, ethylene glycol, glycerol, xylitol, sorbitol) with the collagen mimetic peptide (GPH)₃ was studied by applying the methods of classical molecular dynamics (GROMACS), molecular docking (AutoDock Vina) and quantum chemistry (PM6 and B3LYP). The spatial configurations of intermolecular complexes were determined and interaction energies calculated. The dependence of the volume occupied by the collagen peptide on the clearing agent concentration in an aqueous solution was calculated. This dependence is not linear, and has a maximum for almost all the agents in the study. The correlations between the optical clearing potential and intermolecular interactions parameters, such as the time of an agent being in a hydrogen-bonded state, and the relative probability of formation of double hydrogen bonds and interaction energies, were determined. Using the correlations determined, we predicted the numeric value of the optical clearing potential of dextrose molecules in rat skin, which correlates with experimental data. A molecular mechanism of tissue optical clearing within the post-diffusion stage is suggested.

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Graphical abstract The molecular modeling of the interaction between clearing agents and collagen

     

Computational modeling of healing: an application of the material force method

The basic aim of the present contribution is the qualitative simulation of healing phenomena typically encountered in hard and soft tissue mechanics. The mechanical framework is provided by the theory of open system thermodynamics, which will be formulated in the spatial as well as in the material motion context. While the former typically aims at deriving the density and the spatial motion deformation field in response to given spatial forces, the latter will be applied to determine the material forces in response to a given density and material deformation field. We derive a general computational framework within the finite element context that will serve to evaluate both the spatial and the material motion problem. However, once the spatial motion problem has been solved, the solution of the material motion problem represents a mere post-processing step and is thus extremely cheap from a computational point of view. The underlying algorithm will be elaborated systematically by means of two prototype geometries subjected to three different representative loading scenarios, tension, torsion, and bending. Particular focus will be dedicated to the discussion of the additional information provided by the material force method. Since the discrete material node point forces typically point in the direction of potential material deposition, they can be interpreted as a driving force for the healing mechanism.Blues the healer, John Lee Hooker [1989]     

A top-down approach to mechanistic biological modeling: application to the single-chain antibody folding pathway

A top-down approach to mechanistic modeling of biological systems is presented and exemplified with the development of a hypothesis-driven mathematical model for single-chain antibody fragment (scFv) folding in Saccharomyces cerevisiae by mediators BiP and PDI. In this approach, model development starts with construction of the most basic mathematical model—typically consisting of predetermined or newly-elucidated biological behavior motifs—capable of reproducing desired biological behaviors. From this point, mechanistic detail is added incrementally and systematically, and the effects of each addition are evaluated. This approach follows the typical progression of experimental data availability in that higher-order, lumped measurements are often more prevalent initially than specific, mechanistic ones. It also necessarily provides the modeler with insight into the structural requirements and performance capabilities of the resulting detailed mechanistic model, which facilitates further analysis. The top-down approach to mechanistic modeling identified three such requirements and a branched dependency-degradation competition motif critical for the scFv folding model to reproduce experimentally observed scFv folding dependencies on BiP and PDI and increased production when both species are overexpressed and promoted straightforward prediction of parameter dependencies. It also prescribed modification of the guiding hypothesis to capture BiP and PDI synergy.     

Theoretical analysis of thermal damage in biological tissues caused by laser irradiation

A bioheat transfer approach is proposed to study thermal damage in biological tissues caused by laser radiation. The laser light propagation in the tissue is first solved by using a robust seven-flux model in cylindrical coordinate system. The resulting spatial distribution of the absorbed laser energy is incorporated into the bioheat transfer equation for solving temperature response. Thermal damage to the tissue is assessed by the extent of denatured protein using a rate process equation. It is found that for the tissue studied, a significant protein denaturation process would take place when temperature exceeds about 53 degrees C. The effects of laser power, exposure time and beam size as well as the tissue absorption and scattering coefficients on the thermal damage process are examined and discussed. The laser conditions that cause irreversible damage to the tissue are also identified.     

Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture

Shared random effects joint models are becoming increasingly popular for investigating the relationship between longitudinal and time‐to‐event data. Although appealing, such complex models are computationally intensive, and quick, approximate methods may provide a reasonable alternative. In this paper, we first compare the shared random effects model with two approximate approaches: a naïve proportional hazards model with time‐dependent covariate and a two‐stage joint model, which uses plug‐in estimates of the fitted values from a longitudinal analysis as covariates in a survival model. We show that the approximate approaches should be avoided since they can severely underestimate any association between the current underlying longitudinal value and the event hazard. We present classical and Bayesian implementations of the shared random effects model and highlight the advantages of the latter for making predictions. We then apply the models described to a study of abdominal aortic aneurysms (AAA) to investigate the association between AAA diameter and the hazard of AAA rupture. Out‐of‐sample predictions of future AAA growth and hazard of rupture are derived from Bayesian posterior predictive distributions, which are easily calculated within an MCMC framework. Finally, using a multivariate survival sub‐model we show that underlying diameter rather than the rate of growth is the most important predictor of AAA rupture.     

Computational modeling to predict mechanical function of joints: application to the lower leg with simulation of two cadaver studies

Computational models of musculoskeletal joints and limbs can provide useful information about joint mechanics. Validated models can be used as predictive devices for understanding joint function and serve as clinical tools for predicting the outcome of surgical procedures. A new computational modeling approach was developed for simulating joint kinematics that are dictated by bone/joint anatomy, ligamentous constraints, and applied loading. Three-dimensional computational models of the lower leg were created to illustrate the application of this new approach. Model development began with generating three-dimensional surfaces of each bone from CT images and then importing into the three-dimensional solid modeling software SOLIDWORKS and motion simulation package COSMOSMOTION. Through SOLIDWORKS and COSMOSMOTION, each bone surface file was filled to create a solid object and positioned necessary components added, and simulations executed. Three-dimensional contacts were added to inhibit intersection of the bones during motion. Ligaments were represented as linear springs. Model predictions were then validated by comparison to two different cadaver studies, syndesmotic injury and repair and ankle inversion following ligament transection. The syndesmotic injury model was able to predict tibial rotation, fibular rotation, and anterior/posterior displacement. In the inversion simulation, calcaneofibular ligament extension and angles of inversion compared well. Some experimental data proved harder to simulate accurately, due to certain software limitations and lack of complete experimental data. Other parameters that could not be easily obtained experimentally can be predicted and analyzed by the computational simulations. In the syndesmotic injury study, the force generated in the tibionavicular and calcaneofibular ligaments reduced with the insertion of the staple, indicating how this repair technique changes joint function. After transection of the calcaneofibular ligament in the inversion stability study, a major increase in force was seen in several of the ligaments on the lateral aspect of the foot and ankle, indicating the recruitment of other structures to permit function after injury. Overall, the computational models were able to predict joint kinematics of the lower leg with particular focus on the ankle complex. This same approach can be taken to create models of other limb segments such as the elbow and wrist. Additional parameters can be calculated in the models that are not easily obtained experimentally such as ligament forces, force transmission across joints, and three-dimensional movement of all bones. Muscle activation can be incorporated in the model through the action of applied forces within the software for future studies.     

Beyond the epithelium: cadherin function in fibrous connective tissues

In fibrous connective tissues, fibroblasts are organized into syncytia, cellular networks that enable matrix remodeling and that are interconnected by intercellular adherens junctions (AJs). The AJs of fibroblasts are mediated by N-cadherin, a broadly expressed classical cadherin that is critically involved in developmental processes, wound healing and several diseases of mesenchymal tissues. In contrast to E-cadherin-dependent junctions of epithelia, the formation of AJs in fibrous connective tissues is relatively uncharacterized. Work over the last several years has documented an expanding list of molecules which function to regulate N-cadherin mediated junctions such as: Fer, PTP1B, cortactin, calcium, gelsolin, PIP5KIgamma, PIP2, and the Rho family of GTPases. We present an overview on the regulation of N-cadherin-mediated junction formation that highlights recent molecular advances in the field and rationalizes the roles of N-cadherin in connective tissue function.     

Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics

Biomechanics and Modeling in Mechanobiology - The analysis of tissue mechanics in biomedical applications demands nonlinear constitutive models able to capture the energy dissipation mechanisms,...