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.

Part II: A new perspective for modeling the bone remodeling process: Biology, mechanics, and pathologies.

In this paper, we explore the effects of biological (pathological) and mechanical damage on bone tissue within a benchmark model. Using the Finite Element Methodology, we analyze and numerically test the model's components, capabilities, and performance under physiologically and pathologically relevant conditions. Our findings demonstrate the model's effectiveness in simulating bone remodeling processes and self-repair mechanisms for micro-damage induced by biological internal conditions and mechanical external ones within bone tissue. This article is the second part of a series, where the first part presented the mathematical model and the biological and physical significance of the terms used in a simplified benchmark model. It explored the bone remodeling model's application, implementation, and results under physiological conditions.

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.

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.

Electric and Magnetic Field Devices for Stimulation of Biological Tissues.

Electric fields (EFs) and magnetic fields (MFs) have been widely used by tissue engineering to improve cell dynamics such as proliferation, migration, differentiation, morphology, and molecular synthesis. However, variables such stimuli strength and stimulation times need to be considered when stimulating either cells, tissues or scaffolds. Given that EFs and MFs vary according to cellular response, it remains unclear how to build devices that generate adequate biophysical stimuli to stimulate biological samples. In fact, there is a lack of evidence regarding the calculation and distribution when biophysical stimuli are applied. This protocol is focused on the design and manufacture of devices to generate EFs and MFs and implementation of a computational methodology to predict biophysical stimuli distribution inside and outside of biological samples. The EF device was composed of two parallel stainless-steel electrodes located at the top and bottom of biological cultures. Electrodes were connected to an oscillator to generate voltages (50, 100, 150 and 200 Vp-p) at 60 kHz. The MF device was composed of a coil, which was energized with a transformer to generate a current (1 A) and voltage (6 V) at 60 Hz. A polymethyl methacrylate support was built to locate the biological cultures in the middle of the coil. The computational simulation elucidated the homogeneous distribution of EFs and MFs inside and outside of biological tissues. This computational model is a promising tool that can modify parameters such as voltages, frequencies, tissue morphologies, well plate types, electrodes and coil size to estimate the EFs and MFs to achieve a cellular response.

Effect of electrical stimulation on chondrogenic differentiation of mesenchymal stem cells cultured in hyaluronic acid - Gelatin injectable hydrogels.

Electrical stimulation (ES) has provided enhanced chondrogenesis of mesenchymal stem cells (MSCs) cultured in micro-mass without the addition of exogenous growth factors. In this study, we demonstrate for the first time that ES of MSCs encapsulated in an injectable hyaluronic acid (HA) - gelatin (GEL) mixture enhances the chondrogenic potential of the hydrogel. Samples were stimulated for 21 days with 10 mV/cm at 60 kHz, applied for 30 min every 6 h a day. Mechanical properties of hydrogels were higher if the precursors were dissolved in Calcium-Free Krebs Ringer Buffer (G' = 1141 ± 23 Pa) compared to those diluted in culture media (G' = 213 ± 19 Pa). Cells within stimulated hydrogels were rounder (55%) than non-stimulated cultures (32%) (p = 0.005). Chondrogenic markers such as SOX-9 and aggrecan were higher in stimulated hydrogels compared to controls. The ES demonstrated that normalized content of glycosaminoglycans and collagen to DNA was slightly higher in stimulated samples. Additionally, collagen type II normalized to total collagen was 2.43 times higher in stimulated hydrogels. These findings make ES a promising tool for enhancing articular cartilage tissue engineering outcomes by combining hydrogels and MSCs.