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.

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.

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.

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.

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.

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.

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.

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.

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...

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 2: Implementación numérica / 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 2: Numerical implementation

Se presenta la implementación numérica del modelo bioquímico descrito mediante el sistema de reacción-difusión de la parte 1. De los resultados obtenidos se puede concluir que la retroalimentación química de los 2 factores moleculares a través de un sistema de reacción-difusión (RD) con parámetros en el espacio de Turing, puede explicar la aparición de los patrones espacio-temporales encontrados en la arquitectura de la espongiosa primaria. Para la solución numérica fue usado el método de los elementos finitos junto con el método de Newton-Raphson para aproximar las ecuaciones diferenciales parciales lineales. Los patrones de osificación obtenidos pueden representar la formación de la espongiosa primaria durante la osificación endocondral...

A presentation is made of the numerical implementation of the biochemical model described by means of the reaction-diffusion system in Part 1. Based on the results obtained it may be concluded that the chemical feedback of the two molecular factors by means of a reaction-diffusion (RD) system with Turing space parameters may explain the appearance of the spatio-temporal patterns found in the architecture of the primary spongiosa. For the numerical solution, use was made of the finite element method in combination with the Newton-Raphson method to approximate the linear partial differential equations. The ossification patterns obtained may represent the formation of the primary spongiosa during endochondral ossification...

Modelado computacional del desarrollo óseo humano en la placa de crecimiento del fémur distal / Computational modeling of human bone development in the distal femoral growth plate

La elongación de los huesos largos se produce principalmente por la proliferación e hipertrofia de los condrocitos presentes en las placas de crecimiento. Bajo la hipótesis que el comportamiento de estas células depende de factores bioquímicos y mecánicos, este artículo presenta un modelo computacional por elementos finitos que simula el comportamiento de la placa de crecimiento del fémur distal humano. Se emplea un dominio bidimensional en el que se identifican las regiones de hueso trabecular metafisial y episifial que encierran a la placa de crecimiento y las regiones de cartílago inerte y columnar. La validación del modelo se realiza a partir de la histología correspondiente a la placa de crecimiento del fémur distal de un niño de dos años. Los resultados obtenidos demuestran que el modelo simula el crecimiento y el comportamiento de la placa metafisiaria regulada por su actividad celular y las cargas mecánicas...

Long bone elongation is mainly due to proliferation and hypertrophy of the chondrocytes in growth plates. Under the assumption that the behavior of these cells depends on biochemical and mechanical factors, a presentation is made of a computational finite element model simulating the behavior of the human distal femoral growth plate. A two-dimensional domain is used to identify the regions of metaphyseal and epiphyseal trabecular bone covering the growth plate and the inert and columnar cartilage regions. Model validation was based on the histology corresponding to the distal femoral growth plate of a two-year old boy. The results obtained show that the model simulates the growth and behavior of the metaphyseal plate as regulated by its cellular activity and mechanical loads...

Modelado de la degradación hidrolítica de un implante óseo / Modeling of the hydrolytic degradation of a bone implant

Una de las áreas más importantes de la ingeniería de tejidos es la investigación sobre la regeneración y sustitución del tejido óseo. Para cumplir con estos requisitos, los implantes óseos han sido desarrollados para permitir la migración de las células, el crecimiento del tejido, el transporte de los factores de crecimiento y nutrientes y la renovación de las propiedades mecánicas. Los implantes están hechos de diferentes biomateriales y se han fabricado utilizando varias técnicas que, en algunos casos, no permiten un control total sobre el tamaño y la orientación de los poros que caracterizan a la microestructura del andamio. Desde esta perspectiva, se propone el uso de un sistema de reacción difusión para lograr las características geométricas de la matriz ósea. La validación de esta hipótesis se realiza a través de simulaciones de la geometría obtenida por un sistema de reacción-difusión junto con un modelo de degradación por hidrólisis en elementos tridimensionales representativos...

Research into bone tissue regeneration and substitution is one of the most important components of tissue engineering. In compliance with these requirements, bone implants have been developed which allow cell migration, tissue growth, the transport of growth factors and nutrients, and the renewal of mechanical properties. Implants are made of various biomaterials, and they have been manufactured using techniques which not always allow total control of the size and orientation of the pores involved in the microstructure of the scaffold. From this standpoint, a reaction-diffusion system is proposed for the achievement of appropriate geometric features in the bone matrix. The hypothesis is validated through simulations of the geometry obtained with a reaction-diffusion system and a model of hydrolytic degradation in three-dimensional representative elements...

Método para el cálculo de las medidas angulares de la articulación del radio distal / Method to calculate angular measures of the distal radial articulation

La fractura del radio distal se puede presentar cuando se produce una compresión axial sobre la muñeca. Entre los tratamientos más comunes se encuentran el conservador (inmovilización con yeso) y el quirúrgico. Este último emplea placas y tornillos para la fijación de la fractura después de la reducción, sin embargo, debido a la anatomía compleja de la superficie articular, determinar la posición relativa de los tornillos con respecto a esta puede llegar a ser com,plicado. Para solucionar esto, se han empleado imágenes radiológicas estándar, en las cuales se determina la inclinación palmar y radial de la superficie articular. Con base en los ángulos obtenidos se inclina el antebrazo, de modo que al tomar la radiografía, los labios de la superficie articular queden superpuestos. Sin embargo, este método para determinar las inclinaciones resulta poco efectivo debido a que no se considera en su análisis la anatomía biplana simultáneamente con la bicóncava, del área articular. En este artículo se propone una metodología para hallar los ángulos que determinan la orientación de la superficie articular, empleando reconstrucción tridimensional a partir de imágenes de tomografía axial. Con estas inclinaciones será posible visualizar tangencialmente la superficie articular del radio distal, y así determinar la posición relativa de los tornillos de fijación respecto a esta superficie. Mediante el estudio de un caso, se encontró que la inclinación radial de la superficie articular en su totalidad era de 13° y la palmar de 6° con respecto a una línea perpendicular al eje central del radio. Esto difiere de lo hallado por otros autores que proponen un ángulo radial de 22° a 24° y palmar de 9° a 12°. Por otra parte, para la superficie que articula con el hueso semilunar se encontró una inclinación radial de 7° y una palmar de 10°; en tanto la fosa que está en contacto con el hueso escafoides se inclina radialmente 21° y palmarmente 8°, en el caso analizado...

A distal radial fracture may occur as a result of axial compression of the wrist. The most common treatments include the conservative approach (plaster cast immobilization) and surgery. In the latter procedure, plates and screws are used to fix the fracture after reduction. However, it may be difficult to determine the relative position of the screws with respect to the articular surface, due to the complex anatomy of this structure. To solve this problem, standard radiological imaging has been used to determine the palmar and radial tilt of the articular surface. Based on the angles obtained, the forearm is tilted in such a way that when the radiograph is taken the articular surface labia overlap. However, this method is not very effective to determine tilt, since the biplane and biconcave anatomy of the articular zone are not considered simultaneously. A methodology is proposed to find the angles determining articular surface orientation by means of three-dimensional reconstruction based on axial tomography imaging. Such tilt measurements will make it possible to obtain a tangential view of the distal radial articular surface and determine the relative position of fixation screws with respect to it. In a case study it was found that total radial tilt of the articular surface was 13° and palmar tilt was 6° with respect to a line perpendicular to the central axis of the radius. This outcome differs from findings by other authors, who propose a radial angle of 22° to 24° and a palmar angle of 9° to 12°. Additionally, for the surface articulating with the semilunar bone, radial tilt was found to be 7° and palmar tilt 10°, whereas in the fossa which is in contact with the scaphoid bone, radial tilt is 21° and palmar tilt 8° in the case analyzed...

Morfogénesis de los túbulos dentinales: un modelo matemático / Morphogenesis of dentinal tubules: a mathematical model

La diferenciación mesenquimal a odontoblasto es un proceso complejo que determina la formación de los túbulos dentinales. Este proceso involucra una cuidadosa y regulada secuencia de cambios en el comportamiento de las células mesenquimales, coordinados por la expresión de diferentes factores moleculares, entre ellos, principalmente, el Noggin y BMP2. En este artículo se simula la formación de los túbulos dentinales a partir de un modelo matemático de reacción difusión que es solucionado por el método de los elementos finitos...

Mesenchymal differentiation into odontoblasts is a complex process determining the formation of dentinal tubules. The process involves a carefully regulated sequence of changes in the behavior of mesenchymal cells, coordinated by the expression of various molecular factors, particularly Noggin and BMP2. In this paper the formation of dentinal tubules is simulated using a reaction-diffusion mathematical model solved by the finite element method...

Sobre la osificación intramembranosa: un modelo de aproximación para la calvaria / On intramembranous ossification: an approach model for the calvaria

En este artículo se ha desarrollado un modelo de la aparición y ubicación de los centros primarios de osificación en la calvaria. Este es el primer modelo computacional que determina la ubicación de estas estructuras óseas del cráneo. Se describe un modelo de reacción-difusión de dos moléculas (BMP y Noggins) cuyo comportamiento es del tipo activador-sustrato y su solución produce patrones de Turing, que representan los centros primarios de osificación. Una vez más, el uso de ecuaciones de este tipo posibilita la explicación de fenómenos de morfogénesis antes no dilucidados por otro tipo de teorías, en este caso, teorías de osificación del cráneo. Este tema es de constante investigación, especialmente en la medicina ortopédica y pediátrica...

The paper deals with the development of a model for the appearance and location of primary ossification centers in the calvaria. This is the first computational model intended to determine the location of these cranial bone structures. A reaction-diffusion model is described of two molecules (BMP y Noggin) which behave as substrate activators. The solution produces Turing patterns representing primary ossification centers. Once again the use of these equations makes it possible to explain morphogenesis phenomena not elucidated by other theories, in this case cranial ossification theories. The topic is under permanent research, especially in the fields of orthopedic and pediatric medicine...