Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds

Understanding the ideal wound healing mechanistic behavior using in silico modelling perspectives: A review

Complexity of the entire body precludes an accurate assessment of the specific contributions of tissues or cells during the healing process, which might be expensive and time consuming. Because of this, controlling the wound's size, depth, and dimensions may be challenging, and there is not yet an efficient and reliable chronic wound model representation. Furthermore, given the inherent challenges associated with conducting non-invasive in vivo investigations, it becomes peremptory to explore alternative methodologies for studying wound healing. In this context, biologically-realistic mathematical and computational models emerge as a valuable framework that can effectively address this need. Therefore, it might improve our approach to understanding the process at its core. This article will examines all facets of wound healing, including the kinds, pathways, and most current developments in wound treatment worldwide, particularly in silico modelling utilizing both mathematical and structure-based modelling techniques. It may be helpful to identify the crucial traits through the feedback loop of computer models and experimental investigations in order to build innovative therapies to cure wounds. Hence the effectiveness of personalised medicine and more targeted therapy in the healing of wounds may be enhanced by this interdisciplinary expertise.

Advances in non-invasive biosensing measures to monitor wound healing progression

Impaired wound healing is a significant financial and medical burden. The synthesis and deposition of extracellular matrix (ECM) in a new wound is a dynamic process that is constantly changing and adapting to the biochemical and biomechanical signaling from the extracellular microenvironments of the wound. This drives either a regenerative or fibrotic and scar-forming healing outcome. Disruptions in ECM deposition, structure, and composition lead to impaired healing in diseased states, such as in diabetes. Valid measures of the principal determinants of successful ECM deposition and wound healing include lack of bacterial contamination, good tissue perfusion, and reduced mechanical injury and strain. These measures are used by wound-care providers to intervene upon the healing wound to steer healing toward a more functional phenotype with improved structural integrity and healing outcomes and to prevent adverse wound developments. In this review, we discuss bioengineering advances in 1) non-invasive detection of biologic and physiologic factors of the healing wound, 2) visualizing and modeling the ECM, and 3) computational tools that efficiently evaluate the complex data acquired from the wounds based on basic science, preclinical, translational and clinical studies, that would allow us to prognosticate healing outcomes and intervene effectively. We focus on bioelectronics and biologic interfaces of the sensors and actuators for real time biosensing and actuation of the tissues. We also discuss high-resolution, advanced imaging techniques, which go beyond traditional confocal and fluorescence microscopy to visualize microscopic details of the composition of the wound matrix, linearity of collagen, and live tracking of components within the wound microenvironment. Computational modeling of the wound matrix, including partial differential equation datasets as well as machine learning models that can serve as powerful tools for physicians to guide their decision-making process are discussed.

A mechanistic protrusive-based model for 3D cell migration

Cell migration is essential for a variety of biological processes, such as embryogenesis, wound healing, and the immune response. After more than a century of research-mainly on flat surfaces-, there are still many unknowns about cell motility. In particular, regarding how cells migrate within 3D matrices, which more accurately replicate in vivo conditions. We present a novel in silico model of 3D mesenchymal cell migration regulated by the chemical and mechanical profile of the surrounding environment. This in silico model considers cell's adhesive and nuclear phenotypes, the effects of the steric hindrance of the matrix, and cells ability to degradate the ECM. These factors are crucial when investigating the increasing difficulty that migrating cells find to squeeze their nuclei through dense matrices, which may act as physical barriers. Our results agree with previous in vitro observations where fibroblasts cultured in collagen-based hydrogels did not durotax toward regions with higher collagen concentrations. Instead, they exhibited an adurotactic behavior, following a more random trajectory. Overall, cell's migratory response in 3D domains depends on its phenotype, and the properties of the surrounding environment, that is, 3D cell motion is strongly dependent on the context.

Estimation of the effects of inset heights and slit configurations in an acetabular cup on the pull-out behavior of an artificial hip joint with a structure for preventing dislocation using finite element analysis

Joint dislocation is a critical problem of total hip replacement. We have newly proposed an artificial hip joint with a structure that prevents dislocation. The proposed joint has a simple form with a femoral head partially covered with an acetabular cup. In the present study, the effects of inset heights and slit configurations of the cup on the pull-out forces of the joint were evaluated using finite element analysis. Joint models with different inset heights and those with or without a slit in the cup were used for the analyses to estimate the pull-out forces of the joint. In the case without the slit, the maximum pull-out force of the joint with 1.0 and 1.5 mm of the inset height was approximately 12 and 40 N, respectively. In the case of 1.0-mm inset height, the maximum force of the joint with and without the slit was approximately 9 and 12 N, respectively. These results reveal that the maximum force is markedly changed by the inset height and is moderately affected by the slit. Thus, we can gain insights into a strategy to optimally design an artificial joint in which dislocation does not occur easily. Graphical abstract.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

Biomedical implications from a morphoelastic continuum model for the simulation of contracture formation in skin grafts that cover excised burns

A continuum hypothesis-based model is developed for the simulation of the (long term) contraction of skin grafts that cover excised burns in order to obtain suggestions regarding the ideal length of splinting therapy and when to start with this therapy such that the therapy is effective optimally. Tissue is modeled as an isotropic, heterogeneous, morphoelastic solid. With respect to the constituents of the tissue, we selected the following constituents as primary model components: fibroblasts, myofibroblasts, collagen molecules, and a generic signaling molecule. Good agreement is demonstrated with respect to the evolution over time of the surface area of unmeshed skin grafts that cover excised burns between outcomes of computer simulations obtained in this study and scar assessment data gathered previously in a clinical study. Based on the simulation results, we suggest that the optimal point in time to start with splinting therapy is directly after placement of the skin graft on its recipient bed. Furthermore, we suggest that it is desirable to continue with splinting therapy until the concentration of the signaling molecules in the grafted area has become negligible such that the formation of contractures can be prevented. We conclude this study with a presentation of some alternative ideas on how to diminish the degree of contracture formation that are not based on a mechanical intervention, and a discussion about how the presented model can be adjusted.

A mathematical model for the simulation of the contraction of burns

A continuum hypothesis-based model is developed for the simulation of the contraction of burns in order to gain new insights into which elements of the healing response might have a substantial influence on this process. Tissue is modeled as a neo-Hookean solid. Furthermore, (myo)fibroblasts, collagen molecules, and a generic signaling molecule are selected as model components. An overview of the custom-made numerical algorithm is presented. Subsequently, good agreement is demonstrated with respect to variability in the evolution of the surface area of burns over time between the outcomes of computer simulations and measurements obtained in an experimental study. In the model this variability is caused by varying the values for some of its parameters simultaneously. A factorial design combined with a regression analysis are used to quantify the individual contributions of these parameter value variations to the dispersion in the surface area of healing burns. The analysis shows that almost all variability in the surface area can be explained by variability in the value for the myofibroblast apoptosis rate and, to a lesser extent, the value for the collagen molecule secretion rate. This suggests that most of the variability in the evolution of the surface area of burns over time in the experimental study might be attributed to variability in these two rates. Finally, a probabilistic analysis is used in order to investigate in more detail the effect of variability in the values for the two rates on the healing process. Results of this analysis are presented and discussed.