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]     

Simulation modeling of the origin of multicellular animals

A simulation model of the evolution of a free-living bilayered animal is proposed. The model object developed two layers of cells. The inner layer was able to produce digestive enzymes, to split and absorb organic substances. The evolution of these model objects was accompanied by mutations resembling real adaptations in some coelenterates and placozoans. It was observed that the outer layer of the model produced cells capable of secretion of digestive ferments. This mutation was a principal apomorphy leading to the appearance of organisms with extraorganismal digestion. Visual Basic and STELLA modeling software were used for simulations.     

Simulation of soft tissue failure using the material point method

Understanding the factors that control the extent of tissue damage as a result of material failure in soft tissues may provide means to improve diagnosis and treatment of soft tissue injuries. The objective of this research was to develop and test a computational framework for the study of the failure of anisotropic soft tissues subjected to finite deformation. An anisotropic constitutive model incorporating strain-based failure criteria was implemented in an existing computational solid mechanics software based on the material point method (MPM), a quasi-meshless particle method for simulations in computational mechanics. The constitutive model and the strain-based failure formulations were tested using simulations of simple shear and tensile mechanical tests. The model was then applied to investigate a scenario of a penetrating injury: a low-speed projectile was released through a myocardial material slab. Sensitivity studies were performed to establish the necessary grid resolution and time-step size. Results of the simple shear and tensile test simulations demonstrated the correct implementation of the constitutive model and the influence of both fiber family and matrix failure on predictions of overall tissue failure. The slab penetration simulations produced physically realistic wound tracts, exhibiting diameter increase from entrance to exit. Simulations examining the effect of bullet initial velocity showed that the anisotropy influenced the shape and size of the exit wound more at lower velocities. Furthermore, the size and taper of the wound cavity was smaller for the higher bullet velocity. It was concluded that these effects were due to the amount of momentum transfer. The results demonstrate the feasibility of using MPM and the associated failure model for large-scale numerical simulations of soft tissue failure.     

Computational modeling of dendrites

Computational methods have been part of neuroscience for many years. For example, models developed with these methods have provided a theory that helps explain the action potential. More recently, as experimental patch-electrode techniques have revealed new biophysics related to dendritic function and synaptic integration, computational models of dendrites have been developed to explain and further illuminate these results, and to predict possible additional behavior. Here, a collection of computational models of dendrites is reviewed. The goal is to help explain how such computational techniques work, some of their limitations, and what one can hope to learn about dendrites by modeling them.     

Spatio-temporal modeling of nanoparticle delivery to multicellular tumor spheroids

The inefficiency of nanoparticle penetration in tissues limits the therapeutic efficacy of such formulations for cancer applications. Recent work has indicated that modulation of tissue architecture with enzymes such as collagenase significantly increases macromolecule delivery. In this study we developed a mathematical model of nanoparticle penetration into multicellular spheroids that accounts for radially dependent changes in tumor architecture, as represented by the volume fraction of tissue accessible to nanoparticle diffusion. Parameters such as nanoparticle binding, internalization rate constants, and accessible volume fraction were determined experimentally. Unknown parameters of nanoparticle binding sites per cell in the spheroid and pore shape factor were determined by fitting to experimental data. The model was correlated with experimental studies of the penetration of 40 nm nanoparticles in SiHa multicellular spheroids with and without collagenase treatment and was able to accurately predict concentration profiles of nanoparticles within spheroids. The model was also used to investigate the effects of nanoparticle size. This model contributes toward the understanding of the role of tumor architecture on nanoparticle delivery efficiency.     

Computational modeling of membrane proteins

The determination of membrane protein (MP) structures has always trailed that of soluble proteins due to difficulties in their overexpression, reconstitution into membrane mimetics, and subsequent structure determination. The percentage of MP structures in the protein databank (PDB) has been at a constant 1–2% for the last decade. In contrast, over half of all drugs target MPs, only highlighting how little we understand about drug‐specific effects in the human body. To reduce this gap, researchers have attempted to predict structural features of MPs even before the first structure was experimentally elucidated. In this review, we present current computational methods to predict MP structure, starting with secondary structure prediction, prediction of trans‐membrane spans, and topology. Even though these methods generate reliable predictions, challenges such as predicting kinks or precise beginnings and ends of secondary structure elements are still waiting to be addressed. We describe recent developments in the prediction of 3D structures of both α‐helical MPs as well as β‐barrels using comparative modeling techniques, de novo methods, and molecular dynamics (MD) simulations. The increase of MP structures has (1) facilitated comparative modeling due to availability of more and better templates, and (2) improved the statistics for knowledge‐based scoring functions. Moreover, de novo methods have benefited from the use of correlated mutations as restraints. Finally, we outline current advances that will likely shape the field in the forthcoming decade. Proteins 2015; 83:1–24. © 2014 Wiley Periodicals, Inc.     

Computational modeling of extracellular mechanotransduction

Mechanotransduction may occur through numerous mechanisms, including potentially through autocrine signaling in a dynamically changing extracellular space. We developed a computational model to analyze how alterations in the geometry of an epithelial lateral intercellular space (LIS) affect the concentrations of constitutively shed ligands inside and below the LIS. The model employs the finite element method to solve for the concentration of ligands based on the governing ligand diffusion-convection equations inside and outside of the LIS, and assumes idealized parallel plate geometry and an impermeable tight junction at the apical surface. Using the model, we examined the temporal relationship between geometric changes and ligand concentration, and the dependence of this relationship on system characteristics such as ligand diffusivity, shedding rate, and rate of deformation. Our results reveal how the kinetics of mechanical deformation can be translated into varying rates of ligand accumulation, a potentially important mechanism for cellular discrimination of varying rate-mechanical processes. Furthermore, our results demonstrate that rapid changes in LIS geometry can transiently increase ligand concentrations in underlying media or tissues, suggesting a mechanism for communication of mechanical state between epithelial and subepithelial cells. These results underscore both the plausibility and complexity of the proposed extracellular mechanotransduction mechanism.     

Computational biomechanical analysis of postoperative inferior tibiofibular syndesmosis: a modified modeling method

To analyze the biomechanical effect of syndesmotic screw through three and four cortices, a total of 12 finite element models simulating healthy ankles, tibiofibular syndesmosis injured ankles, and post-operative ankles by screw fixations through three or four cortices were built. A set of biomechanical data were obtained to find that screw fixation methods for inferior tibiofibular syndesmosis can help recover most of the biomechanical relations of the ankle especially the tricortical fixation, while the screw of quadricortical fixation bear more stress than the tricortical fixation. The modeling method for finite element models was also modified for saving more time and realizing personalized modeling for clinical application.     

Computational challenges of tumor spheroid modeling

The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we put forward general considerations that apply to any fine-grained numerical model of tumors. We discuss ways to bypass computational limitations and discuss our incremental approach, where each step is validated by experimental observations on a quantitative basis. We present a few results on the growth of tumor cells in closed and open environments and of tumor spheroids. This study suggests new ways to explore the initial growth phase of solid tumors and to optimize antitumor treatments.     

Computational modeling of acute myocardial infarction

Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.     

Computational modeling of evolutionary learning processes in the brain

The evolutionary selection circuits model of learning has been specified algorithmically. The basic structural components of the selection circuits model are enzymatic neurons, that is, neurons whose firing behavior is controlled by membrane-bound macromolecules called excitases. Learning involves changes in the excitase contents of neurons through a process of variation and selection. In this paper we report on the behavior of a basic version of the learning algorithm which has been developed through extensive interactive experiments with the model. This algorithm is effective in that it enables single neurons or networks of neurons to learn simple pattern classification tasks in a number of time steps which appears experimentally to be a linear function of problem size, as measured by the number of patterns of presynaptic input. The experimental behavior of the algorithm establishes that evolutionary mechanisms of learning are competent to serve as major mechanisms of neuronal adaptation. As an example, we show how the evolutionary learning algorithm can contribute to adaptive motor control processes in which the learning system develops the ability to reach a target in the presence of randomly imposed disturbances.     

Computational modeling of the catalytic reaction in triosephosphate isomerase

We present a comprehensive analysis of the catalytic cycle of the enzyme triosephosphate isomerase (TIM), including both the reactive chemistry and the catalytic loop and side-chain motions. Combining accurate mixed quantum mechanics/molecular mechanics (QM/MM) and protein structure prediction methods, we have modeled both the structural and chemical aspects of the reversible isomerization of dihydroxyacetone phosphate (DHAP) to d-glyceraldehyde 3-phosphate (GAP), for which there is a wealth of experimental data. The conjunction of this novel computational approach with the use of the recent near-atomic resolution TIM-DHAP Michaelis complex PDB structure, 1NEY.pdb, has enabled us to obtain robust qualitative and, where available, quantitative agreement with a wide range of experimental data. Among the principal conclusions that we are able to draw are the importance of the monoanionic (as opposed to dianioic) form of the substrate phosphate group in the catalytic cycle, detailed positioning and energetics of the key catalytic residues in the active-site, the flexible nature of Glu165, which favors its direct involvement in the formation of the enediol intermediate, energetics of the open and closed form of the catalytic loop region in the presence and absence of substrate, and quantitative reproduction of various experimentally measured reaction rates, typically to within approximately 1 kcal/mol. Our results are consistent with the available experimental data, and provide an initial picture as to why loop opening when GAP is the product has a higher barrier than when DHAP is the product.