RESUMO
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.
Assuntos
Distrofia Muscular de Duchenne , Distrofia Muscular de Duchenne/metabolismo , Distrofia Muscular de Duchenne/patologia , Humanos , Músculo Esquelético/metabolismo , Músculo Esquelético/patologia , Animais , Simulação por Computador , Modelos BiológicosRESUMO
The midpalatal suture (MPS) corresponds to the tissue that joins the two maxillary bones. Understanding the mechanical behavior of this tissue is of particular interest to those patients who require orthodontic treatments such as Rapid Maxillary Expansion (RME). The objective of this research was to observe the influence of interdigitation and collagen fibers on the mechanical response of MPS. To this end, a finite element analysis in two-dimensional models of the bone-suture-bone interface was performed considering the characteristics of the MPS. The geometry of the suture was modeled with 4 different levels of interdigitation: null, moderate, scalloped and fractal. The influence of collagen fibers, aligned transversely along the suture, was considered by incorporating linked structures of the bone fronts. According to the results, the factor that has the greatest impact on the magnitude and distribution of stresses is the interdigitation degree. A higher level of interdigitation produces an increase in tissue stiffness and a lower influence of collagen fibers on the mechanical response of the tissue. Therefore, this research contributes to the understanding of the MPS biomechanics by providing information that may be useful to health staff when evaluating the feasibility of procedures such as RME.
Assuntos
Suturas Cranianas , Maxila , Humanos , Análise de Elementos Finitos , Suturas , ColágenoRESUMO
Cleft lip and palate is a congenital defect that affects the oral cavity. Depending on its severity, alveolar graft surgery and maxillary orthopedic therapies must be carried out as a part of the treatment. It is widely accepted that the therapies should be performed before grafting. Nevertheless, some authors have suggested that mechanical stimuli such as those from the maxillary therapies could improve the success rate of the graft. The aim of this study is to computationally determine the effect of maxillary therapies loads on the biomechanical response of an alveolar graft with different degrees of ossification. We also explore how the transverse width of the cleft affects the graft behavior and compare results with a non-cleft skull. Results suggest that stresses increase within the graft as it ossifies and are greater if maxillary expansion therapy is applied. This has consequences in the bone remodeling processes that are necessary for the graft osseointegration. Maxillary orthopedic therapies after graft surgery could be considered as a part of the treatment since they seem to act as a positive extra stimulus that can benefit the graft.
Assuntos
Biofísica , Fenda Labial/cirurgia , Fissura Palatina/cirurgia , Maxila/cirurgia , Maxila/transplante , Técnica de Expansão Palatina , Fenômenos Biomecânicos , Transplante Ósseo , Criança , Feminino , Análise de Elementos Finitos , Humanos , Osseointegração , Palato Duro , Pressão , Estresse MecânicoRESUMO
Long bone formation starts early during embryonic development through a process known as endochondral ossification. This is a highly regulated mechanism that involves several mechanical and biochemical factors. Because long bone development is an extremely complex process, it is unclear how biochemical regulation is affected when dynamic loads are applied, and also how the combination of mechanical and biochemical factors affect the shape acquired by the bone during early development. In this study, we develop a mechanobiological model combining: (1) a reaction-diffusion system to describe the biochemical process and (2) a poroelastic model to determine the stresses and fluid flow due to loading. We simulate endochondral ossification and the change in long bone shapes during embryonic stages. The mathematical model is based on a multiscale framework, which consisted in computing the evolution of the negative feedback loop between Ihh/PTHrP and the diffusion of VEGF molecule (on the order of days) and dynamic loading (on the order of seconds). We compare our morphological predictions with the femurs of embryonic mice. The results obtained from the model demonstrate that pattern formation of Ihh, PTHrP and VEGF predict the development of the main structures within long bones such as the primary ossification center, the bone collar, the growth fronts and the cartilaginous epiphysis. Additionally, our results suggest high load pressures and frequencies alter biochemical diffusion and cartilage formation. Our model incorporates the biochemical and mechanical stimuli and their interaction that influence endochondral ossification during embryonic growth. The mechanobiochemical framework allows us to probe the effects of molecular events and mechanical loading on development of bone.
Assuntos
Biofísica , Simulação por Computador , Modelos Biológicos , Osteogênese , Animais , Cartilagem/fisiologia , Fêmur/anatomia & histologia , Análise de Elementos Finitos , Lâmina de Crescimento/crescimento & desenvolvimento , Proteínas Hedgehog/metabolismo , Camundongos Endogâmicos BALB C , Morfogênese , Proteína Relacionada ao Hormônio Paratireóideo/metabolismo , Reologia , Estresse MecânicoRESUMO
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.
Assuntos
Cartilagem Articular , Morte Celular , Proliferação de Células , Condrócitos , Modelos Biológicos , Técnicas de Cultura de Células , Humanos , Engenharia TecidualRESUMO
The processes of flat bones growth, sutures formation and interdigitation in the human calvaria are controlled by a complex interaction between genetic, biochemical and environmental factors that regulate bone formation and resorption during prenatal development and infancy. Despite previous experimental evidence accounting for the role of the main biochemical factors acting on these processes, the underlying mechanisms controlling them are still unknown. Therefore, we propose a mathematical model of the processes of flat bone and suture formation, taking into account several biological events. First, we model the growth of the flat bones and the formation of sutures and fontanels as a reaction diffusion system between two proteins: TGF-ß2 and TGF-ß3. The former is expressed by osteoblasts and allows adjacent mesenchymal cells differentiation on the bone fronts of each flat bone. The latter is expressed by mesenchymal cells at the sutures and inhibits their differentiation into osteoblasts at the bone fronts. Suture interdigitation is modelled using a system of reaction diffusion equations that develops spatio-temporal patterns of bone formation and resorption by means of two molecules (Wnt and Sclerostin) which control mesenchymal cells differentiation into osteoblasts at these sites. The results of the computer simulations predict flat bone growth from ossification centers, sutures and fontanels formation as well as bone formation and resorption events along the sutures, giving rise to interdigitated patterns. These stages were modelled and solved by the finite elements method. The simulation results agree with the morphological characteristics of calvarial bones and sutures throughout human prenatal development and infancy.
Assuntos
Simulação por Computador , Suturas Cranianas/anatomia & histologia , Suturas Cranianas/embriologia , Desenvolvimento Embrionário , Modelos Anatômicos , Crânio/anatomia & histologia , Crânio/embriologia , Proteínas Adaptadoras de Transdução de Sinal , Adulto , Proteínas Morfogenéticas Ósseas/metabolismo , Marcadores Genéticos , Humanos , Lactente , Análise Numérica Assistida por Computador , Osteogênese , Fator de Crescimento Transformador beta2/metabolismo , Fator de Crescimento Transformador beta3/metabolismo , Proteínas Wnt/metabolismoRESUMO
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.
Assuntos
Desenvolvimento Ósseo/fisiologia , Simulação por Computador , Lâmina de Crescimento/crescimento & desenvolvimento , Lâmina de Crescimento/fisiologia , Adolescente , Criança , Pré-Escolar , Epífises/embriologia , Epífises/crescimento & desenvolvimento , Epífises/fisiologia , Feminino , Análise de Elementos Finitos , Lâmina de Crescimento/embriologia , Humanos , Lactente , Recém-Nascido , Modelos Lineares , Masculino , Modelos Biológicos , Osteogênese/fisiologia , Gravidez , Estresse MecânicoRESUMO
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF strengths and different configurations of both electrical and chemical stimuli. Accordingly, we found that the cell migration speed is described as the combination of an electrical and a chemical term. Cell migration is faster when both stimuli orient cell migration towards the same direction. In contrast, a reduced speed is obtained when the EF vector is opposed to the direction of the chemical stimulus. Numerical relations were obtained to quantify the cell migration speed at each configuration. Additional calculations for the cell colonization of a substrate also show mediation of the EF strength. Therefore, the term electro-osteoconduction is introduced to account the electrically induced cell colonization. Since numerical results compare favorably with experimental evidence, the model is suitable to be extended to other types of cells, and to numerically explore the influence of EF during wound healing.
Assuntos
Movimento Celular , Eletricidade , Modelos Biológicos , Osteoblastos/citologia , QuimiotaxiaRESUMO
The partial rupture of ligament fibres leads to an injury known as grade 2 sprain. Wound healing after injury consists of four general stages: swelling, release of platelet-derived growth factor (PDGF), fibroblast migration and proliferation and collagen production. The aim of this paper is to present a mathematical model based on reaction-diffusion equations for describing the repair of the medial collateral ligament when it has suffered a grade 2 sprain. We have used the finite element method to solve the equations of this. The results have simulated the tissue swelling at the time of injury, predicted PDGF influence, the concentration of fibroblasts migrating towards the place of injury and reproduced the random orientation of immature collagen fibres. These results agree with experimental data reported by other authors. The model describes wound healing during the 9 days following such injury.
Assuntos
Proliferação de Células , Colágeno/biossíntese , Fibroblastos/citologia , Ligamentos/citologia , Animais , Fibroblastos/metabolismo , Humanos , Ligamentos/metabolismo , Fator de Crescimento Derivado de Plaquetas/metabolismoRESUMO
In this study, a computational model of bone remodelling problem as proposed by Weinans et al. (1992) is described and solved by other temporal integration techniques different from the Euler scheme. This model considers three types of numerical integration schemes of the evolution of the material density during the remodelling: Euler, Heun and Runge-Kutta methods. Also the strain and the density field are obtained inside each element, at Gauss points or at the nodes of the mesh. A square plate with 1.00 m of side subjected to non-uniform pressure is simulated with two meshes of quadrilateral element with size [Formula: see text] and [Formula: see text] m. Two increments time size: [Formula: see text] and [Formula: see text] days are used. The results show that Euler, Heun and Runge-Kutta's methods correctly approached the problem of bone remodelling and that there were no appreciable differences in the patterns obtained by the mesh and time step used. In contrast, using an element-based approach and node-based approach, substantial differences were produced in bone remodelling density pattern. 'Chess board' type discontinuities were found in the element approach near the applied pressure area, as were well-defined columns away from this. The node-based approach showed continuity in density distribution. These patterns were well represented by the methods for resolving the density equation. This study concluded that any method of time integration could be used for these meshes and time steps size.
Assuntos
Remodelação Óssea/fisiologia , Modelos Biológicos , Algoritmos , Fenômenos Biomecânicos/fisiologia , Densidade Óssea/fisiologia , Simulação por Computador , Análise de Elementos Finitos , HumanosRESUMO
Developing bone consists of epiphysis, metaphysis and diaphysis. The secondary ossification centre (SOC) appears and grows within the epiphysis, involving two histological stages. Firstly, cartilage canals appear; they carry hypertrophy factors towards the central area of the epiphysis. Canal growth and expansion is modulated by stress on the epiphysis. Secondly, the diffusion of hypertrophy factors causes SOC growth. Hypertrophy is regulated by biological and mechanical factors present within the epiphysis. The finite element method has been used for solving a coupled system of differential equations for modelling these histological stages of epiphyseal development. Cartilage canal spatial-temporal growth patterns were obtained as well as the SOC formation pattern. This model qualitatively agreed with experimental results reported by other authors.
Assuntos
Epífises/crescimento & desenvolvimento , Modelos Biológicos , Animais , Cartilagem Articular/crescimento & desenvolvimento , Condrócitos/fisiologia , Subunidade alfa 1 de Fator de Ligação ao Core/fisiologia , Epífises/fisiologia , Análise de Elementos Finitos , Lâmina de Crescimento/crescimento & desenvolvimento , Humanos , Metaloproteinase 9 da Matriz/fisiologia , Mecanotransdução Celular/fisiologia , Osteogênese/fisiologia , Proteína Relacionada ao Hormônio Paratireóideo/fisiologia , Estresse MecânicoRESUMO
Articular cartilage (AC) is a biological tissue that allows the distribution of mechanical loads and movement of joints. The presence of these mechanical loads influences the behavior and physiological condition of AC. The loads may cause damaged by fatigue through injuries due to repeated accumulated stresses. The aim of this work is to introduce a phenomenological mathematical model of damage caused by mechanical action. It is considered that tissue failure is a consequence of chondrocyte death and matrix loss, taking into account factors modifying fatigue resistance such as age, body mass index (BMI) and metabolic activity. The model was numerically implemented using the finite elements method and the results obtained allowed us to predict tissue failure at different loading frequencies, different damage sites and variations in damage magnitude. Qualitative concordance between numerical results and experimental data led us to conclude that the model may be useful for physicians and therapists as a prediction tool for prescribing physical exercise and prognosis of joint failure.
Assuntos
Cartilagem Articular/patologia , Modelos Teóricos , Análise de Elementos Finitos , HumanosRESUMO
The aim of this paper is to introduce a new mathematical model using a mechanobiological approach describing the process of osseointegration at the bone-dental implant interface in terms of biological and mechanical factors and the implant surface. The model has been computationally implemented by using the finite element method. The results show the spatial-temporal patterns distribution at the bone-dental implant interface and demonstrate the ability of the model to reproduce features of the wound healing process such as blood clotting, osteogenic cell migration, granulation tissue formation, collagen-like matrix displacements and new osteoid formation. The model might be used as a methodological basis for designing a dental tool useful to predict the degree of osseointegration of dental implants and subsequent formulation of mathematical models associated with different types of bone injuries and different types of implantable devices.
Assuntos
Implantes Dentários , Planejamento de Prótese Dentária/métodos , Análise de Elementos Finitos , Osseointegração/fisiologia , Simulação por Computador , Fibrina/metabolismo , Estresse Mecânico , Trombina/metabolismoRESUMO
The healing of the injured tissues after the insertion of a dental implant begins with the formation of a fibrin clot that detains the blood flow and gives initial support to the osteoprogenitor cells. The adequate formation of this clot determines the direct and stable connection between bone and implant, process known as osseointegration. The aim of this work is to introduce a mathematical model of the coagulation in the bone-dental implant interface based on two reaction-diffusion equations representing the kinetic reaction that leads to the production of fibrin and a transformation equation representing the formation of the fibrillar network compounding the clot. The model also includes a parameter associated to the blood platelets concentration that extends the model framework to the analysis of two hematological disorders well reported: thrombocytosis and thrombocytopenia. The solution of the model is performed using the finite element method, obtaining as results the distribution of spatial-temporal patterns in the bone-dental implant interface. These results are in qualitative concordance with experimental results previously reported by other authors. Although the model is a simplified version of the biological process of coagulation, the results here obtained justify the mathematical formulation implemented. It is concluded that the model can be used as a methodological basis for the formulation of a general model of the osseointegration in the bone-dental implant interface.