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.

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 unified framework of cell population dynamics and mechanical stimulus using a discrete approach in bone remodelling.

Multiphysics models have become a key tool in understanding the way different phenomenon are related in bone remodeling and various approaches have been proposed, yet, to the best of the author's knowledge there is no model able to link a cell population model with a mechanical stimulus model using a discrete approach, which allows for an easy implementation. This article couples two classical models, the cell population model from Komarova and the Nackenhorst model in a 2D domain, where correlations between the mechanical loading and the cell population dynamics can be established, furthermore the effect of different paracrine and autocrine regulators is seen on the overall density of a portion of trabecular bone. A discretization is performed using frame 1D finite elements, representing the trabecular structure. The Nackenhorst model is implemented by using the finite element method to calculate the strain energy as the main mechanical stimulus that determines the bone mass density evolution in time. This density is normalized to be added to the bone mass percentage proposed by the Komarova model, where coupling terms have been added as well that guarantee a stable response. In the simulations, the equations were solved employing the finite element method with a user subroutine implemented in ABAQUS (2017) and by applying a direct formulation. The methodology presented can model the cell dynamics occurring in bone remodelling in accordance with the asynchronous nature of this process, yet allowing to differentiate zones with higher density, the main trabecular groups are obtained for the proximal femur. Finally, the model is tested in pathological cases, such as osteoporosis and osteopetrosis, yielding results similar to the pathology behavior. Furthermore, the discrete modelling technique is shown to be of use in this particular application.

A mathematical model of the process of ligament repair: effect of cold therapy and mechanical stress.

This article proposes a mathematical model that predicts the wound healing process of the ligament after a sprain, grade II. The model describes the swelling, expression of the platelet-derived growth factor (PDGF), formation and migration of fibroblasts into the injury area and the expression of collagen fibers. Additionally, the model can predict the effect of ice treatment in reducing inflammation and the action of mechanical stress in the process of remodeling of collagen fibers. The results obtained from computer simulation show a high concordance with the clinical data previously reported by other authors.

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.

Effect of umbilical cord length on early fetal biomechanics.

The umbilical cord suspends the fetus within the amniotic cavity, where fetal dynamics is one of its many functions. Hence, the umbilical cord is a viable index in determining fetal activity. Fetal movements result in mechanical loads that are fundamental for fetal growth. At present, mechanical environment during early human fetal development is still largely unknown. To determine early fetal movement dynamics at given physiological (0.060 m) and pathological umbilical cord lengths (0.030 m, 0.020 m, 0.017 m and 0.014 m) a 2D computational model was created to simulate dynamic movement conditions. Main findings of this computational model revealed the shortest umbilical cord length (0.014 m) with a 6(10-6)N, twitch force amplitude had a two-fold increase on linear velocity (0.12 m/s) in comparison with other lengths (0.05m/s). Moreover, umbilical cord length effect presented an increasing exponential tension on the fetus body wall from longest to shortest, from 0 N in the control length to 0.05 N for the shortest umbilical cord. Last, tension was always present over a period of time for the shortest cord (0.03 N to 0.08 N). Collectively, for all variables evaluated the shortest umbilical cord (0.014 m) presented remarkable differences with other lengths in particular with the second shortest umbilical cord (0.017 m), suggesting a 0.003 m difference represents a greater biomechanical effect. In conclusion, this computational model brings new insights required by clinicians, where the magnitude of these loads could be associated with different pathologies found in the clinic.

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.

Stress and strain propagation on infant skull from impact loads during falls: a finite element analysis.

Background and Objective: To simulate infant skull trauma after low height falls when variable degrees of ossification of the sutures are present. Methods: A finite elements model of a four-week-old infant skull was developed for simulating low height impact from 30 cm and 50 cm falls. Two impacts were simulated: An occipito-parietal impact on the lambdoid suture and a lateral impact on the right parietal and six cases were considered: unossified and fully ossified sutures, and sagittal, metopic, right lambdoid and right coronal craniosynostosis. Results: 26 simulations were performed. Results showed a marked increase in strain magnitudes in skulls with unossified sutures and fontanels. Higher deformations and lower Von Mises stress in the brain were found in occipital impacts. Fully ossified skulls showed less overall deformation and lower Von Mises stress in the brain. Results suggest that neonate skull impact when falling backward has a higher probability of resulting in permanent damage. Conclusion: This work shows an initial approximation to the mechanisms underlying TBI in neonates when exposed to low height falls common in household environments, and could be used as a starting point in the design and development of cranial orthoses and protective devices for preventing or mitigating TBI.

Computational model of a synovial joint morphogenesis.

Joints enable the relative movement between the connected bones. The shape of the joint is important for the joint movements since they facilitate and smooth the relative displacement of the joint's parts. The process of how the joints obtain their final shape is yet not well understood. Former models have been developed in order to understand the joint morphogenesis leaning only on the mechanical environment; however, the obtained final anatomical shape does not match entirely with a realistic geometry. In this study, a computational model was developed with the aim of explaining how the morphogenesis of joints and shaping of ossification structures are achieved. For this model, both the mechanical and biochemical environments were considered. It was assumed that cartilage growth was controlled by cyclic hydrostatic stress and inhibited by octahedral shear stress. In addition, molecules such as PTHrP and Wnt promote chondrocyte proliferation and therefore cartilage growth. Moreover, the appearance of the primary and secondary ossification centers was also modeled, for which the osteogenic index and PTHrP-Ihh concentrations were taken into account. The obtained results from this model show a coherent final shape of an interphalangeal joint, which suggest that the mechanical and biochemical environments are crucial for the joint morphogenesis process.

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.

Proximal femoral growth plate mechanical behavior: Comparison between different developmental stages.

In long bones the growth plate is a cartilaginous structure located between the epiphysis and the diaphysis. This structure regulates longitudinal growth and helps determine the structure of mature bone through the process of endochondral ossification. During human growth the femur's proximal growth plate experiences changes in its morphology that may be related to its mechanical environment. Thus, in order to test this hypothesis from a computational perspective, a finite element analysis on a proximal femur was performed on which we modeled different physeal geometries corresponding to the shapes acquired for this structure in a child between the ages of five to eleven. Results show augmented Von Mises stress values with increasing irregularities in physeal geometry, whereas displacement decreased with increased irregularities in the growth plate's morphology. Such observations suggest that growth plate's shape changes follows a possible mechanical adaptation on imposed loads to sustain a person's increasing body mass during growth.

A mathematical model for describing the metastasis of cancer in bone tissue.

Metastasis is the rapid proliferation of cancer cells (secondary tumour) at a specific place, generally leading to death. This occurs at anatomical parts providing the necessary environment for vascularity, oxygen and food to hide their actions and trigger the rapid growth of cancer. Prostate and breast cancers, for example, use bone marrow for their proliferation. Bone-supporting cancer cells thus adapt to the environment, mimicking the behaviour of genetic and molecular bone cells. Evidence of this has been given in Cecchini et al. (2005, EAU Update Ser. 3:214-226), providing arguments such as how cancer cell growth is so active during bone reabsorption. This paper simulates metastasis activation in bone marrow. A mathematical model has been developed involving the activation of molecules from bone tissue cells, which are necessary for cancer to proliferate. Here, we simulate two forms of secondary tumour growth depending on the type of metastasis: osteosclerosis and osteolysis.

Spongiosa primary development: a biochemical hypothesis by Turing patterns formations.

We propose a biochemical model describing the formation of primary spongiosa architecture through a bioregulatory model by metalloproteinase 13 (MMP13) and vascular endothelial growth factor (VEGF). It is assumed that MMP13 regulates cartilage degradation and the VEGF allows vascularization and advances in the ossification front through the presence of osteoblasts. The coupling of this set of molecules is represented by reaction-diffusion equations with parameters in the Turing space, creating a stable spatiotemporal pattern that leads to the formation of the trabeculae present in the spongy tissue. Experimental evidence has shown that the MMP13 regulates VEGF formation, and it is assumed that VEGF negatively regulates MMP13 formation. Thus, the patterns obtained by ossification may represent the primary spongiosa formation during endochondral ossification. Moreover, for the numerical solution, we used the finite element method with the Newton-Raphson method to approximate partial differential nonlinear equations. Ossification patterns obtained may represent the primary spongiosa formation during endochondral ossification.

Can the size of the epiphysis determine the number of secondary ossification centers? A mathematical approach.

Previous studies have concluded that the chemical feedback (loop) between two reagent molecular factors through a reaction-diffusion mechanism could explain the stable spatial pattern found in the origin of the secondary ossification centres (SOCs). Furthermore, the emergence of the SOC may depend on the size and shape of the head of the bone, as observed in different animals. In this paper, we develop new computer simulations that study the effect of the size of the epiphysis on the emergence of the SOC. This study determines two or more SOCs, that may appear in the head of long bones, depending on the size of the epiphysis.

A mathematical model of epiphyseal development: hypothesis of growth pattern of the secondary ossification centre.

This paper introduces a 'hypothesis about the growth pattern of the secondary ossification centre (SOC)', whereby two phases are assumed. First, the formation of cartilage canals as an event essential for the development of the SOC. Second, once the canals are merged in the central zone of the epiphysis, molecular factors are released (primarily Runx2 and MMP9) spreading and causing hypertrophy of adjacent cells. In addition, there are two important molecular factors in the epiphysis: PTHrP and Ihh. The first one inhibits chondrocyte hypertrophy and the second helps the cell proliferation. Between these factors, there is negative feedback, which generates a highly localised and stable pattern over time. From a mathematical point of view, this pattern is similar to the patterns of Turing. The spread of Runx2 hypertrophies the cells from the centre to the periphery of the epiphysis until found with high levels of PTHrP to inhibit hypertrophy. This mechanism produces the epiphyseal bone-plate. Moreover, the hypertrophy is inhibited when the cells sense low shear stress and high pressure levels that maintain the articular cartilage structure. To test this hypothesis, we solve a system of coupled partial differential equations using the finite element method and we have obtained spatio-temporal patterns of the growth process of the SOC. The model is in qualitative agreement with experimental results previously reported by other authors. Thus, we conclude that this model can be used as a methodological basis to present a complete mathematical model of the whole epiphyseal development.

A model of cerebral cortex formation during fetal development using reaction-diffusion-convection equations with Turing space parameters.

The cerebral cortex is a gray lamina formed by bodies of neurons covering the cerebral hemispheres, varying in thickness from 1.25 mm in the occipital lobe to 4mm in the anterior lobe. The brain's surface is about 30 times greater that of the skull because of its many folds; such folds form the gyri, sulci and fissures and mark out areas having specific functions, divided into five lobes. Convolution formation may vary between individuals and is an important feature of brain formation; such patterns can be mathematically represented as Turing patterns. This article describes how a phenomenological model was developed by describing the formation pattern for the gyri occurring in the cerebral cortex by reaction diffusion equations with Turing space parameters. Numerical examples for simplified geometries of a brain were solved to study pattern formation. The finite element method was used for the numerical solution, in conjunction with the Newton-Raphson method. The numerical examples showed that the model can represent cerebral cortex fold formation and reproduce pathologies related to gyri formation, such as polymicrogyria and lissencephaly.

A mathematical model of epiphyseal development: hypothesis on the cartilage canals growth.

The role of cartilage canals is to transport nutrients and biological factors that cause the appearance of the secondary ossification centre (SOC). The SOC appears in the centre of the epiphysis of long bones. The canal development is a complex interaction between mechanical and biological factors that guide its expansion into the centre of the epiphysis. This article introduces the 'Hypothesis on the growth of cartilage canals'. Here, we have considered that the development of these canals is an essential event for the appearance of SOC. Moreover, it is also considered to be important for the transport of molecular factors (RUNX2 and MMP9) at the ends of such canals. Once the canals are merged in the centre of the epiphysis, these factors are released causing hypertrophy of adjacent cells. This RUNX2 and MMP9 release occurs due to the action of mechanical loads that supports the epiphysis. In order to test this hypothesis, we use a hybrid approach using the finite element method to simulate the mechanical stresses present in the epiphysis and the cellular automata to simulate the expansion of the canals and the hypertrophy factors pathway. By using this hybrid approach, we have obtained as a result the spatial-temporal patterns for the growth of cartilage canals and hypertrophy factors within the epiphysis. The model is in qualitative agreement with experimental results previously reported by other authors. Thus, we conclude that this model may be used as a methodological basis to present a complete mathematical model of the processes involved in epiphyseal development.

Obtención de un biocompuesto constituido por fosfato tricálcico y quitosana para ser usado como sustituto óseo en un modelo animal / Development of a biocomposite made up of tricalcium phosphate and chitosan to be used as bone substitute in an animal model

La investigación se trata de la obtención de un biocompuesto a partir de una matriz cerámica y un polímero, con el fin de utilizarlo como relleno óseo. Se mezcló la matriz cerámica, fosfato tricálcico Ca (OH)2 y quitosana, polímero de origen natural. En el estudio se realizaron pruebas preliminares de mezclas para escoger 4 tipos de biocompuestos (BC1, BC2, BC3, BC4), con diferentes proporciones de los elementos de la matriz cerámica. Se trabajó en la preparación del biocompuesto con un pH entre 6,5 y 8,5 y un tiempo de secado entre 7 y 20 min. Se seleccionaron las mezclas óptimas para analizar sus propiedades mecánicas a partir de la prueba de la resistencia a la compresión. Se determinaron los valores de pH, los cuales estuvieron en un rango de 7,05 y 7,6. Igualmente se hallaron unos tiempos de secado que oscilaron entre 7 y 15 min, la pasta mantuvo una temperatura constante de 25 ºC y consistencia moldeable, condiciones que son apropiadas para su utilización como sustituto óseo. La muestra que obtuvo mejores propiedades en cuanto a pH, temperatura y tiempo de secado fue seleccionada para ser implantada en tibias de conejo para determinar la respuesta histológica después de 60 días...

The research deals with the development of a biocomposite from a ceramic matrix and a polymer with the purpose of using it as bone filler. A mixture was made of the ceramic matrix, tricalcium phosphate Ca (OH)2 and chitosan, a polymer of natural origin. The mixtures underwent preliminary testing to choose 4 types of biocomposites (BC1, BC2, BC3, BC4) with varying proportions of ceramic matrix elements. The biocomposite was prepared at a pH between 6.5 and 8.5. Drying time ranged between 7 and 20 minutes. Optimal samples were chosen and their mechanical properties analyzed by means of compression resistance testing. PH measurements showed values between 7.05 and 7.6, and drying times ranged between 7 and 15 minutes. The paste remained at a constant temperature of 25 ºC and maintained molding consistency. These properties are required for use as bone substitute. The sample exhibiting the best pH, temperature and drying time values was chosen for implantation in rabbit tibiae to verify the histological response after 60 days...

Una formulación preliminar de tipo electromecánica para la formación de hueso en un proceso de remodelación / Preliminary electromechanical formulation for bone formation in a remodeling process

En este artículo se propone un modelo de remodelación ósea que tiene en cuenta los estímulos mecánicos y eléctricos. Bajo estos supuestos, se obtiene la distribución de masa que depende de las cargas mecánicas y eléctricas. El trabajo coloca de manifiesto la importancia del campo eléctrico en el proceso de remodelación y, propone la cuantificación de sus efectos para obtener un modelo aplicable a nivel clínico...

A bone remodeling model is proposed which takes account of mechanical and electrical stimuli. Under these assumptions, a mass distribution is obtained which depends on mechanical and electrical loads. The paper reveals the importance of the electric field in the remodeling process, and proposes to quantify its effects with a view to obtaining a clinically applicable model...

Representación del desarrollo de la espongiosa primaria por medio de un sistema de reacción-difusión: Una hipótesis sobre el inicio de la formación de hueso inmaduro. Parte 1: Descripción del modelo / Representation of the development of the primary spongiosa by means of a reaction-diffusion system: a hypothesis on the onset of immature bone formation. Part 1: Model description

Se presenta un modelo bioquímico que predice la formación de la arquitectura de la espongiosa primaria, a partir de la interacción de 2 factores moleculares: VEGF (factor de crecimiento endotelial vascular) y MMP13 (metaloproteinasas 13). Se supone que el MMP13 regula la degradación del cartílago y el VEGF permite la vascularización y el avance del frente de osificación mediante la presencia de osteoblastos. El acople de este conjunto de moléculas se representa mediante ecuaciones de reacción-difusión con parámetros en el espacio de Turing, y se obtiene como resultado un patrón espacio-temporal estable que da paso a la formación de las trabéculas presentes en el tejido esponjoso...

A biochemical model is presented which predicts the formation of the architecture of the primary spongiosa, based on the interaction of two molecular factors: VEGF (vascular endothelial growth factor) and MMP-13 (metalloproteinases-13). It is assumed that MMP-13 regulates cartilage degradation, and VEGF allows vascularization and the advance of the ossification front through the presence of osteoblasts. The coupling of this set of molecules is represented by means of reaction-diffusion equations with Turing space parameters, and a stable spatio-temporal pattern is obtained which leads to the formation of the trabeculae present in the spongy tissue...