Contact lens fitting and changes in the tear film dynamics: mathematical and computational models review

PURPOSE

This review explores mathematical models, blinking characterization, and non-invasive techniques to enhance understanding and refine clinical interventions for ocular conditions, particularly for contact lens wear.

METHODS

The review evaluates mathematical models in tear film dynamics and their limitations, discusses contact lens wear models, and highlights computational mechanical models. It also explores computational techniques, customization of models based on individual blinking dynamics, and non-invasive diagnostic tools like high-speed cameras and advanced imaging technologies.

RESULTS

Mathematical models provide insights into tear film dynamics but face challenges due to simplifications. Contact lens wear models reveal complex ocular physiology and design aspects, aiding in lens development. Computational mechanical models explore eye biomechanics, often integrating tear film dynamics into a Multiphysics framework. While different computational techniques have their advantages and disadvantages, non-invasive tools like OCT and thermal imaging play a crucial role in customizing these Multiphysics models, particularly for contact lens wearers.

CONCLUSION

Recent advancements in mathematical modeling and non-invasive tools have revolutionized ocular health research, enabling personalized approaches. The review underscores the importance of interdisciplinary exploration in the Multiphysics approach involving tear film dynamics and biomechanics for contact lens wearers, promoting advancements in eye care and broader ocular health research.

Non-uniform fuel distribution and thermo-mechanical analysis of a 1 MW thermal power micronuclear heat pipe reactor

One of the goals in improving the design of compact portable micronuclear heat pipe reactors is to enhance their operating life so that they can generate maximum power within safe nuclear, thermal, and mechanical limits and with minimal human intervention. This work carries out an analysis to estimate the effect of non-uniform fuel enrichment and thermo-mechanical performance of a 1 MW thermal power uranium nitride fueled Micro Nuclear Heat Pipe Reactor (MNHPR). For neutronic and thermo-mechanical analyses, the open-source Monte Carlo code OpenMC and the COMSOL Multiphysics codes are used. The neutron flux distribution and subsequent fuel temperature, heat transport, stresses and strains are estimated. The analysis of core power distribution shows an uneven power distribution resulting in hot spots. The maximum fuel centerline temperature of 1353 K at the highest peaking factor 1.22 is within the safety limit. However, the high temperature results in higher thermal stress and subsequent displacement of 119 μ m that exceeds the 100 μ m fuel-clad gap. Power peaking thus significantly limits the maximum allowed operating power. In this study it is found that non-uniform placement of the fuel reduces power peaking and enhances the overall core performance. It is recommended to consider each fuel ring as a separate zone and gradually change the fuel enrichment in each zone. The non-uniform distribution of the fuel follows the gradual increase of enrichment from ring 1 to ring 5 with max enrichment in ring 5, and then a drop in the enrichment to mitigate any peaking in ring 6 due to its proximity to the reflector. From ring 1 to ring 6 fuel of 60-62-70-70-75-65 percent enrichment is recommended. The proposed fuel strategy mitigates power peaking in the core and enhances the maximum safe operating power level by 15 % from 775 kW to 893 kW without physical design change.

Dataset of a parameterized U-bend flow for deep learning applications

This dataset contains 10,000 fluid flow and heat transfer simulations in U-bend shapes. Each of them is described by 28 design parameters, which are processed with the help of Computational Fluid Dynamics methods. The dataset provides a comprehensive benchmark for investigating various problems and methods from the field of design optimization. For these investigations supervised, semi-supervised and unsupervised deep learning approaches can be employed. One unique feature of this dataset is that each shape can be represented by three distinct data types including design parameter and objective combinations, five different resolutions of 2D images from the geometry and the solution variables of the numerical simulation, as well as a representation using the cell values of the numerical mesh. This third representation enables considering the specific data structure of numerical simulations for deep learning approaches. The source code and the container used to generate the data are published as part of this work.

A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation

Development of in silico models that capture progression of diseases in soft biological tissues are intrinsic in the validation of the hypothesized cellular and molecular mechanisms involved in the respective pathologies. In addition, they also aid in patient-specific adaptation of interventional procedures. In this regard, a fully-coupled high-fidelity Lagrangian finite element framework is proposed within this work which replicates the pathology of in-stent restenosis observed post stent implantation in a coronary artery. Advection-reaction-diffusion equations are set up to track the concentrations of the platelet-derived growth factor, the transforming growth factor-β, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of volumetric growth involved in the restenotic process, coupled to the evolution of the previously defined vessel wall constituents, is presented. Further, the finite element implementation of the model is discussed, and the behavior of the computational model is investigated via suitable numerical examples. Qualitative validation of the computational model is presented by emulating a stented artery. Patient-specific data are intended to be integrated into the model to predict the risk of in-stent restenosis, and thereby assist in the tuning of stent implantation parameters to mitigate the risk.

A review on reactive transport model and porosity evolution in the porous media

This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and continuum scale. For each of these approaches, the different numerical schemes for solving the coupled advection-diffusion-reactions equations are presented. The parameters influenced by coupled biological and chemical reactions in evolving porous media are emphasised and defined from a pore-scale perspective. Recent pore-scale studies, which have enhanced the basic understanding of processes that affect and control porous media parameters, are discussed. Subsequently, a summary of the common methods used to describe the transport process, fluid flow, reactive surface area and reaction parameters such as porosity, permeability and tortuosity are reviewed.

Computational analysis of vincristine loaded silk fibroin hydrogel for sustained drug delivery applications: Multiphysics modeling and experiments

In this paper, silk fibroin hydrogel is used as a drug carrier for vincristine. To optimize drug delivery, a multi-physics model is proposed that couples the deformation and diffusion fields. We applied inverse analysis and general continuum mechanics to define material parameters and mechanical properties. To examine the mass transport and chemical behavior, an affinity-based diffusion and degradation of a drug-loaded polymer matrix is employed. Some experiments are carried out to examine the capability of the presented model. After preparing the vincristine loaded silk hydrogel syringes, they were injected into PBS and enzyme solutions to monitor the drug release rate for 40 days. Obtained results from the computational simulation and laboratory tests showed that the silk fibroin hydrogel was deswelled after about 40 days in enzyme solution. Degradation led to faster and higher doses of vincristine drug release in comparison to the case of PBS solution. Results revealed that more than 80% of the drug was released in the first 5 days in the enzyme solution, but in PBS solution only 10% of the drug was released during 40 days. The model predictions of deswelling behavior and drug release rate were in good agreement with those of experimental results. Therefore, it can be employed as a reliable tool for further predictions.

Mathematical modeling of surface deformation during vitrification

Mathematical modeling of surface deformation during cryopreservation by vitrification is presented in this study. The specific problem under consideration is of a cryoprotective agent (CPA) solution vitrifying in a vial, following previously obtained cryomacroscopy observations. A multiphysics solution is proposed in this study, combining coupled effects associated with heat transfer, fluid mechanics, and solid mechanics. Consistent with previous investigations, this study demonstrates that surface deformation is the result of material flow, which is the combined outcome of temperature gradients developed during the inward cooling process, the tendency of the material to change its volume with temperature, and the exponential increase in material viscosity with the decreasing temperature. During this process, the behavior of the CPA changes from liquid to a solid-like amorphous material, where the arrested flow in the vitrified state results in mechanical stresses. Results of this study show a good qualitative agreement of surface deformation with previously obtained experimental data, and support prior investigations to explain fracture tendencies propagating from the deformed surface. Results of this study also highlight the effect of heat convection in the CPA at the early stage of cooling.

Effects of a brain tumor in a dispersive human head on SAR and temperature rise distributions due to RF sources at 4G and 5G frequencies

In this paper, effects of a brain tumor located in a dispersive human head model on specific absorption rate (SAR) and temperature rise distributions due to different types of RF sources at 4G and 5G cellular frequencies are investigated with the use of a multiphysics model. This multiphysics model analyzes the dispersive human head with the brain tumor and provides the SAR and temperature rise distributions in the head due to the RF source operated at 4G and 5G cellular frequencies in a single finite-difference time-domain simulation. An adjacent antenna operated at 4G and 5G cellular frequencies to the human head is considered as the RF source for near-field exposure, while a plane wave field radiated by base stations operated at 4G and 5G cellular frequencies is considered as the RF source for far-field exposure. Numerical results show that the brain tumor in the head slightly affects the SAR and temperature rise distributions due to different RF sources at 4G and 5G cellular frequencies.

A multiphysics approach for modeling early atherosclerosis

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid-structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endothelium is considered by a coupled set of advection-diffusion-reaction equations. Thereby, the permeability of the endothelium is wall-shear stress modulated resulting in a locally varying accumulation of foam cells triggering a novel growth and remodeling formulation. The model is calibrated and applied to an murine-specific case study, and a qualitative validation of the computational results is performed. The model is utilized to further investigate the influence of the pulsatile blood flow and the compliance of the artery wall to the atherosclerotic process. The computational results imply that the pulsatile blood flow is crucial, whereas the compliance of the aorta has only a minor influence on atherosclerosis. Further, it is shown that the novel model is capable to produce a narrowing of the vessel lumen inducing an adaption of the endothelial permeability pattern.

Consistent trilayer biomechanical modeling of aortic valve leaflet tissue

Aortic valve tissue exhibits highly nonlinear, anisotropic, and heterogeneous material behavior due to its complex microstructure. A thorough understanding of these characteristics permits us to develop numerical models that can shed insight on the function of the aortic valve in health and disease. Herein, we take a closer look at consistently capturing the observed physical response of aortic valve tissue in a continuum mechanics framework. Such a treatment is the first step in developing comprehensive multiscale and multiphysics models. We highlight two important aspects of aortic valve tissue behavior: the role of the collagen fiber microstructure and the native prestressing. We propose a model that captures these two features as well as the heterogeneous layer-scale topology of the tissue. We find the model can reproduce the experimentally observed multiscale mechanical behavior in a manner that provides intuition on the underlying mechanics.

Effects of Biowastes Released by Mechanically Damaged Muscle Cells on the Propagation of Deep Tissue Injury: A Multiphysics Study

Deep tissue injuries occur in muscle tissues around bony prominences under mechanical loading leading to severe pressure ulcers. Tissue compression can potentially compromise lymphatic transport and cause accumulation of metabolic biowastes, which may cause further cell damage under continuous mechanical loading. In this study, we hypothesized that biowastes released by mechanically damaged muscle cells could be toxic to the surrounding muscle cells and could compromise the capability of the surrounding muscle cells to withstand further mechanical loadings. In vitro, we applied prolonged low compressive stress (PLCS) and short-term high compressive stress to myoblasts to cause cell damage and collected the biowastes released by the damaged cells under the respective loading scenarios. In silico, we used COMSOL to simulate the compressive stress distribution and the diffusion of biowastes in a semi-3D buttock finite element model. In vitro results showed that biowastes collected from cells damaged under PLCS were more toxic and could compromise the capability of normal myoblasts to resist compressive damage. In silico results showed that higher biowastes diffusion coefficient, higher biowastes release rate, lower biowastes tolerance threshold and earlier timeline of releasing biowastes would cause faster propagation of tissue damage. This study highlighted the importance of biowastes in the development of deep tissue injury to clinical pressure ulcers under prolonged skeletal compression.

Computational prediction of strain-dependent diffusion of transcription factors through the cell nucleus

Nuclear spreading plays a crucial role in stem cell fate determination. In previous works, we reported evidence of multipotency maintenance for mesenchymal stromal cells cultured on three-dimensional engineered niche substrates, fabricated via two-photon laser polymerization. We correlated maintenance of multipotency to a more roundish morphology of these cells with respect to those cultured on conventional flat substrates. To interpret these findings, here we present a multiphysics model coupling nuclear strains induced by cell adhesion to passive diffusion across the cell nucleus. Fully three-dimensional reconstructions of cultured cells were developed on the basis of confocal images: in particular, the level of nuclear spreading resulted significantly dependent on the cell localization within the niche architecture. We assumed that the cell diffusivity varies as a function of the local volumetric strain. The model predictions indicate that the higher the level of spreading of the cell, the higher the flux across the nucleus of small solutes such as transcription factors. Our results point toward nuclear spreading as a primary mechanism by which the stem cell translates its shape into a fate decision, i.e., by amplifying the diffusive flow of transcriptional activators into the nucleus.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.