Diego Alexander Garzón-Alvarado

Design, Materials, and Mechanobiology of Biodegradable Scaffolds for Bone Tissue Engineering

A review about design, manufacture, and mechanobiology of biodegradable scaffolds for bone tissue engineering is given. First, fundamental aspects about bone tissue engineering and considerations related to scaffold design are established. Second, issues related to scaffold biomaterials and manufacturing processes are discussed. Finally, mechanobiology of bone tissue and computational models developed for simulating how bone healing occurs inside a scaffold are described.

A finite element method approach for the mechanobiological modeling of the osseointegration of a dental implant

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.

Growth of the flat bones of the membranous neurocranium

This article assumes two stages in the formation of the bones in the calvaria, the first one takes into account the formation of the primary centers of ossification. This step counts on the differentiation from mesenchymal cells into osteoblasts. A molecular mechanism is used based on a system of reaction-diffusion between two antagonistic molecules, which are BMP2 and Noggin. To this effect we used equations whose behavior allows finding Turing patterns that determine the location of the primary centers. In the second step of the model we used a molecule that is expressed by osteoblasts, called Dxl5 and that is expressed from the osteoblasts of each flat bone. This molecule allows bone growth through its borders through cell differentiation adjacent to each bone of the skull. The model has been implemented numerically using the finite element method. The results allow us to observe a good approximation of the formation of flat bones of the membranous skull as well as the formation of fontanelles and sutures.

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 brains 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 phenomenological mathematical model of the articular cartilage damage

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.

A computational model of clavicle bone formation: a mechano-biochemical hypothesis.

Clavicle development arises from mesenchymal cells condensed as a cord extending from the acromion towards the sternal primordium. First two primary ossification centers form, extending to develop the body of the clavicle through intramembranous ossification. However, at its ends this same bone also displays endochondral ossification. So how can the clavicle be formed by both types of ossification? Developmental events associated with clavicle formation have mainly used histological studies as supporting evidence. Nonetheless, mechanisms of biological events such as molecular and mechanical effects remain to be determined. The objective of this work was to provide a mathematical explanation of embryological events based on two serial phases: first formation of an ossified matrix by intramembranous ossification based on three factors: systemic, local biochemical, and mechanical factors. After this initial phase expansion of the ossified matrix follows with mesenchymal cell differentiation into chondrocytes for posterior endochondral ossification. Our model provides strong evidence for clavicle formation integrating molecules and mechanical stimuli through partial differentiation equations using finite element analysis.

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.

Theoretical distribution of load in the radius and ulna carpal joint

PURPOSE The purpose of this study is to validate a model for the analysis of the load distribution through the wrist joint, subjected to forces on the axes of the metacarpals from distal to proximal for two different mesh densities. METHOD To this end, the Rigid Body Spring Model (RBSM) method was used on a three-dimensional model of the wrist joint, simulating the conditions when making a grip handle. The cartilage and ligaments were simulated as springs acting under compression and tension, respectively, while the bones were considered as rigid bodies. At the proximal end of the ulna the movement was completely restricted, and the radius was allowed to move only in the lateral/medial direction. RESULTS With these models, we found the load distributions on each carpal articular surface of radius. Additionally, the results show that the percentage of the applied load transmitted through the radius was about 86% for one mesh and 88% for the coarser one; for the ulna it was 21% for one mesh and 18% for the coarser. CONCLUSIONS The obtained results are comparable with previous outcomes reported in prior studies. The latter allows concluding that, in theory, the methodology can be used to describe the changes in load distribution in the wrist.

Growth plate stress distribution implications during bone development

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.