Tumor growth for remodeling process: A 2D approach

This paper aims to present a comprehensive framework for coupling tumor-bone remodeling processes in a 2-dimensional geometry. This is achieved by introducing a bio-inspired damage that represents the growing tumor, which subsequently affects the main populations involved in the remodeling process, namely, osteoclasts, osteoblasts, and bone tissue. The model is constructed using a set of differential equations based on the Komarova's and Ayati's models, modified to incorporate the bio-inspired damage that may result in tumor mass formation. Three distinct models were developed. The first two models are based on the Komarova's governing equations, with one demonstrating an osteolytic behavior and the second one an osteoblastic model. The third model is a variation of Ayati's model, where the bio-inspired damage is induced through the paracrine and autocrine parameters, exhibiting an osteolytic behavior. The obtained results are consistent with existing literature, leading us to believe that our in-silico experiments will serve as a cornerstone for paving the way towards targeted interventions and personalized treatment strategies, ultimately improving the quality of life for those affected by these conditions.

Duchenne and Becker muscular dystrophy: Cellular mechanisms, image analysis, and computational models: A review

The muscle is the principal tissue that is capable to transform potential energy into kinetic energy. This process is due to the transformation of chemical energy into mechanical energy to enhance the movements and all the daily activities. However, muscular tissues can be affected by some pathologies associated with genetic alterations that affect the expression of proteins. As the muscle is a highly organized structure in which most of the signaling pathways and proteins are related to one another, pathologies may overlap. Duchenne muscular dystrophy (DMD) is one of the most severe muscle pathologies triggering degeneration and muscle necrosis. Several mathematical models have been developed to predict muscle response to different scenarios and pathologies. The aim of this review is to describe DMD and Becker muscular dystrophy in terms of cellular behavior and molecular disorders and to present an overview of the computational models implemented to understand muscle behavior with the aim of improving regenerative therapy.

Anatomy, molecular structures, and hyaluronic acid - Gelatin injectable hydrogels as a therapeutic alternative for hyaline cartilage recovery: A review

Cartilage damage caused by trauma or osteoarthritis is a common joint disease that can increase the social and economic burden in society. Due to its avascular characteristics, the poor migration ability of chondrocytes, and a low number of progenitor cells, the self-healing ability of cartilage defects has been significantly limited. Hydrogels have been developed into one of the most suitable biomaterials for the regeneration of cartilage because of its characteristics such as high-water absorption, biodegradation, porosity, and biocompatibility similar to natural extracellular matrix. Therefore, the present review article presents a conceptual framework that summarizes the anatomical, molecular structure and biochemical properties of hyaline cartilage located in long bones: articular cartilage and growth plate. Moreover, the importance of preparation and application of hyaluronic acid - gelatin hydrogels for cartilage tissue engineering are included. Hydrogels possess benefits of stimulating the production of Agc1, Col2α1-IIa, and SOX9, molecules important for the synthesis and composition of the extracellular matrix of cartilage. Accordingly, they are believed to be promising biomaterials of therapeutic alternatives to treat cartilage damage.

A coupled mathematical model between bone remodeling and tumors: a study of different scenarios using Komarova's model

This paper aims to construct a general framework of coupling tumor-bone remodeling processes in order to produce plausible outcomes of the effects of tumors on the number of osteoclasts, osteoblasts, and the frequency of the bone turnover cycle. In this document, Komarova's model has been extended to include the effect of tumors on the bone remodeling processes. Thus, we explored three alternatives for coupling tumor presence into Komarova's model: first, using a "damage" parameter that depends on the tumor cell concentration. A second model follows the original structure of Komarova, including the tumor presence in those equations powered up to a new parameter, called the paracrine effect of the tumor on osteoclasts and osteoblasts; the last model is replicated from Ayati and collaborators in which the impact of the tumor is included into the paracrine parameters. Through the models, we studied their stability and considered some examples that can reproduce the tumor effects seen in clinic and experimentally. Therefore, this paper has three parts: the exposition of the three models, the results and discussion (where we explore some aspects and examples of the solution of the models), and the conclusion.

Multiple regression analysis predicts the dynamic of chondrocytes stimulated by magnetic and electric fields

PURPOSE

The aim of this study was to implement a multiple regression analysis to find mathematical models that estimate the proliferative rate and the molecular synthesis of chondrocytes when these cells are stimulated either by magnetic or electric fields.

METHODS

Data derived from previous studies performed in our laboratory were used for statistical analyses, which consisted of applying magnetic fields (1 and 2 mT) and electric fields (4 and 8 mV/cm) to chondrocytes. Data from cell proliferation and glycosaminoglycan expression were used to adjust and to validate each mathematical model.

RESULTS

The root square model efficiently predicted the chondrocyte dynamics, evidencing determination coefficients of R² = 92.04 for proliferation and R² = 70.95 for glycosaminoglycans when magnetic fields were applied, and R² = 88.19 for proliferation and R² = 74.79 for glycosaminoglycans when electric fields were applied.

CONCLUSIONS

The reduced, interactive, quadratic and combined models exhibited lower R2 values, nevertheless, they were useful to predict proliferation and glycosaminoglycan synthesis, as the right-skewed distribution, determined by the F parameter, evidenced a Frejected < Fcomputed. The models are efficient since the prediction of chondrocyte dynamics is comparable to the cell growth and to the molecular synthesis observed experimentally. This novel formulation may be dynamic because the variables that fit the models may be modified to improve in vitro procedures focused on cartilage recovery.

In Vitro Evaluation of the Effect of Stimulation with Magnetic Fields on Chondrocytes

Magnetic fields (MFs) have been used as an external stimulus to increase cell proliferation in chondrocytes and extracellular matrix (ECM) synthesis of articular cartilage. However, previously published studies have not shown that MFs are homogeneous through cell culture systems. In addition, variables such as stimulation times and MF intensities have not been standardized to obtain the best cellular proliferative rate or an increase in molecular synthesis of ECM. In this work, a stimulation device, which produces homogeneous MFs to stimulate cell culture surfaces was designed and manufactured using a computational model. Furthermore, an in vitro culture of primary rat chondrocytes was established and stimulated with two MF schemes to measure both proliferation and ECM synthesis. The best proliferation rate was obtained with an MF of 2 mT applied for 3 h, every 6 h for 8 days. In addition, the increase in the synthesis of glycosaminoglycans was statistically significant when cells were stimulated with an MF of 2 mT applied for 5 h, every 6 h for 8 days. These findings suggest that a stimulation with MFs is a promising tool that could be used to improve in vitro treatments such as autologous chondrocyte implantation, either to increase cell proliferation or stimulate molecular synthesis. Bioelectromagnetics. 2020;41:41-51 © 2019 Bioelectromagnetics Society.

Cellular automata model for human articular chondrocytes migration, proliferation and cell death: An in vitro validation

Articular cartilage is characterized by low cell density of only one cell type, chondrocytes, and has limited self-healing properties. When articular cartilage is affected by traumatic injuries, a therapeutic strategy such as autologous chondrocyte implantation is usually proposed for its treatment. This approach requires in vitro chondrocyte expansion to yield high cell number for cell transplantation. To improve the efficiency of this procedure, it is necessary to assess cell dynamics such as migration, proliferation and cell death during culture. Computational models such as cellular automata can be used to simulate cell dynamics in order to enhance the result of cell culture procedures. This methodology has been implemented for several cell types; however, an experimental validation is required for each one. For this reason, in this research a cellular automata model, based on random-walk theory, was devised in order to predict articular chondrocyte behavior in monolayer culture during cell expansion. Results demonstrated that the cellular automata model corresponded to cell dynamics and computed-accurate quantitative results. Moreover, it was possible to observe that cell dynamics depend on weighted probabilities derived from experimental data and cell behavior varies according to the cell culture period. Thus, depending on whether cells were just seeded or proliferated exponentially, culture time probabilities differed in percentages in the CA model. Furthermore, in the experimental assessment a decreased chondrocyte proliferation was observed along with increased passage number. This approach is expected to having other uses as in enhancing articular cartilage therapies based on tissue engineering and regenerative medicine.

Capacitively coupled electrical stimulation of rat chondroepiphysis explants: A histomorphometric analysis

The growth plate is a cartilaginous layer present from the gestation period until the end of puberty where it ossifies joining diaphysis and epiphysis. During this period several endocrine, autocrine, and paracrine processes within the growth plate are carried out by chondrocytes; therefore, a disruption in cellular functions may lead to pathologies affecting bone development. It is known that electric fields impact the growth plate; however, parameters such as stimulation time and electric field intensity are not well documented. Accordingly, this study presents a histomorphometrical framework to assess the effect of electric fields on chondroepiphysis explants. Bones were stimulated with 3.5 and 7 mV/cm, and for each electric field two exposure times were tested for 30 days (30 min and 1 h). Results evidenced that electric fields increased the hypertrophic zones compared with controls. In addition, a stimulation of 3.5 mV/cm applied for 1 h preserved the columnar cell density and its orientation. Moreover, a pre-hypertrophy differentiation in the center of the chondroepiphysis was observed when explants were stimulated during 1 h with both electric fields. These findings allow the understanding of the effect of electrical stimulation over growth plate organization and how the stimulation modifies chondrocytes morphophysiology.

Growth plate stress distribution implications during bone development: a simple framework computational approach

Mechanical stimuli play a significant role in the process of long bone development as evidenced by clinical observations and in vivo studies. Up to now approaches to understand stimuli characteristics have been limited to the first stages of epiphyseal development. Furthermore, growth plate mechanical behavior has not been widely studied. In order to better understand mechanical influences on bone growth, we used Carter and Wong biomechanical approximation to analyze growth plate mechanical behavior, and explore stress patterns for different morphological stages of the growth plate. To the best of our knowledge this work is the first attempt to study stress distribution on growth plate during different possible stages of bone development, from gestation to adolescence. Stress distribution analysis on the epiphysis and growth plate was performed using axisymmetric (3D) finite element analysis in a simplified generic epiphyseal geometry using a linear elastic model as the first approximation. We took into account different growth plate locations, morphologies and widths, as well as different epiphyseal developmental stages. We found stress distribution during bone development established osteogenic index patterns that seem to influence locally epiphyseal structures growth and coincide with growth plate histological arrangement.