Tumor growth for remodeling process: A 2D approach

This paper aims to present a comprehensive framework for coupling tumor-bone remodeling processes in a 2-dimensional geometry. This is achieved by introducing a bio-inspired damage that represents the growing tumor, which subsequently affects the main populations involved in the remodeling process, namely, osteoclasts, osteoblasts, and bone tissue. The model is constructed using a set of differential equations based on the Komarova's and Ayati's models, modified to incorporate the bio-inspired damage that may result in tumor mass formation. Three distinct models were developed. The first two models are based on the Komarova's governing equations, with one demonstrating an osteolytic behavior and the second one an osteoblastic model. The third model is a variation of Ayati's model, where the bio-inspired damage is induced through the paracrine and autocrine parameters, exhibiting an osteolytic behavior. The obtained results are consistent with existing literature, leading us to believe that our in-silico experiments will serve as a cornerstone for paving the way towards targeted interventions and personalized treatment strategies, ultimately improving the quality of life for those affected by these conditions.

Duchenne and Becker muscular dystrophy: Cellular mechanisms, image analysis, and computational models: A review

The muscle is the principal tissue that is capable to transform potential energy into kinetic energy. This process is due to the transformation of chemical energy into mechanical energy to enhance the movements and all the daily activities. However, muscular tissues can be affected by some pathologies associated with genetic alterations that affect the expression of proteins. As the muscle is a highly organized structure in which most of the signaling pathways and proteins are related to one another, pathologies may overlap. Duchenne muscular dystrophy (DMD) is one of the most severe muscle pathologies triggering degeneration and muscle necrosis. Several mathematical models have been developed to predict muscle response to different scenarios and pathologies. The aim of this review is to describe DMD and Becker muscular dystrophy in terms of cellular behavior and molecular disorders and to present an overview of the computational models implemented to understand muscle behavior with the aim of improving regenerative therapy.

Computational model of articular cartilage regeneration induced by scaffold implantation in vivo

Computational models allow to explain phenomena that cannot be observed through an animal model, such as the strain and stress states which can highly influence regeneration of the tissue. For this purpose, we have developed a simulation tool to determine the mechanical conditions provided by the polymeric scaffold. The computational model considered the articular cartilage, the subchondral bone, and the scaffold. All materials were modeled as poroelastic, and the cartilage had linear-elastic oriented collagen fibers. This model was able to explain the remodeling process that subchondral bone goes through, and how the scaffold allowed the conditions for cartilage regeneration. These results suggest that the use of scaffolds might lead the cartilaginous tissue growth in vivo by providing a better mechanical environment. Moreover, the developed computational model demonstrated to be useful as a tool prior experimental in vivo studies, by predicting the possible outcome of newly proposed treatments allowing to discard approaches that might not bring good results.

A coupled mathematical model between bone remodeling and tumors: a study of different scenarios using Komarova's model

This paper aims to construct a general framework of coupling tumor-bone remodeling processes in order to produce plausible outcomes of the effects of tumors on the number of osteoclasts, osteoblasts, and the frequency of the bone turnover cycle. In this document, Komarova's model has been extended to include the effect of tumors on the bone remodeling processes. Thus, we explored three alternatives for coupling tumor presence into Komarova's model: first, using a "damage" parameter that depends on the tumor cell concentration. A second model follows the original structure of Komarova, including the tumor presence in those equations powered up to a new parameter, called the paracrine effect of the tumor on osteoclasts and osteoblasts; the last model is replicated from Ayati and collaborators in which the impact of the tumor is included into the paracrine parameters. Through the models, we studied their stability and considered some examples that can reproduce the tumor effects seen in clinic and experimentally. Therefore, this paper has three parts: the exposition of the three models, the results and discussion (where we explore some aspects and examples of the solution of the models), and the conclusion.

Both network architecture and micro cracks effects on lacuno-canalicular liquid flow efficiency within the context of multiphysics approach for bone remodeling

When physical forces are applied to bone, its mechanical adaptive behaviors change according to the microarchitecture configuration. This leads to changes in biological and physical thresholds in the remodeling cell population, involving sensor cells (osteocytes) interacting with each other and changes in osteocyte shape due to variation in lacunar shape. The resulting alterations in fluid flow leads to changes in the membrane electrical potential and shear stress. Eventual creation of microcracks, may lead in turn to modify cell activity. In contrast, the redundancy in the lacuno canalicular network (LCN) interconnectivity maintains partial flow. Our goal was to investigate the role of fluid flow in LCN by proposing a model of electro-mechanical energy spread through inhomogeneous microarchitectures. We focused on mechano-sensitivity to changes in load-induced flow impacted by neighboring micro cracks and quantifying its critical role in changing, velocity, shear stress and orientation of liquid mass transportation from one cell to another. To enhance the concept of intricacy LCN micro-structure to fluid flow, we provide a new combined effects factor considered as osteocytes sensor efficiency. We customized an influence function for each osteocyte, coupling: in one hand, the spatial distribution within remodeling influence areas, conducting a significant fluid spread, leading hydro-dynamic behavior and impacted further by presence of micro cracks and; in other hand, the fluid electro kinetic behavior. As an attempt to fill the limitations stated by many of the recent studies, we reveal in numerical simulation, some results which cannot be measured in vitro/in vivo studies. Numerical calculations were performed in order to evaluate, among many others, how liquid flow conditions changes between lacunas, how the orientation and the magnitude of the governing flow in LCN can regulate osteocytes efficiency. In addition to be regulated by osteocytes, a direct effects of fluid flow are also acting on osteoblast activity. In summary, this new approach considers mechano-sensitivity in relation to liquid flow dynamic and suggests additional pathway for Osseo integration via osteoblast regulation. However, this novel modeling approach may help improve the mapping and design bone scaffolds and/or selection of scaffold implantation regions.

Multi-scale mechanobiological model for skeletal muscle hypertrophy

Skeletal muscle adaptation is correlated to training exercise by triggering different signaling pathways that target many functions; in particular, the IGF1-AKT pathway controls protein synthesis and degradation. These two functions regulate the adaptation in size and strength of muscles. Computational models for muscle adaptation have focused on: the biochemical description of signaling pathways or the mechanical description of muscle function at organ scale; however, an interrelation between these two models should be considered to understand how an adaptation in muscle size affects the protein synthesis rate. In this research, a dynamical model for the IGF1-AKT signaling pathway is linked to a continuum-mechanical model describing the active and passive mechanical response of a muscle; this model is used to study the impact of the adaptive muscle geometry on the protein synthesis at the fiber scale. This new computational model links the signaling pathway to the mechanical response by introducing a growth tensor, and links the mechanical response to the signaling pathway through the evolution of the protein synthesis rate. The predicted increase in cross sectional area (CSA) due to an 8 weeks training protocol excellently agreed with experimental data. Further, our results show that muscle growth rate decreases, if the correlation between protein synthesis and CSA is negative. The outcome of this study suggests that multi-scale models coupling continuum mechanical properties and molecular functions may improve muscular therapies and training protocols.

The Effect of Pore Directionality of Collagen Scaffolds on Cell Differentiation and In Vivo Osteogenesis

Although many bone substitutes have been designed and produced, the development of bone tissue engineering products that mimic the microstructural characteristics of native bone remains challenging. It has been shown that pore orientation within collagen scaffolds influences bone matrix formation by the endochondral route. In addition, that the unidirectional orientation of the scaffolds can limit the growth of blood vessels. However, a comparison between the amount of bone that can be formed in scaffolds with different pore orientations in addition to analyzing the effect of loading osteogenic and proangiogenic factors is still required. In this work we fabricated uni- and multidirectional collagen sponges and evaluated their microstructural, physicochemical, mechanical and biological characteristics. Although the porosity and average pore size of the uni- and multidirectional scaffolds was similar (94.5% vs. 97.1% and 260 µm vs. 269 µm, respectively) the unidirectional sponges had a higher tensile strength, Young's modulus and capacity to uptake liquids than the multidirectional ones (0.271 MPa vs. 0.478 MPa, 9.623 MPa vs. 3.426 MPa and 8000% mass gain vs. 4000%, respectively). Culturing of rat bone marrow mesenchymal stem cells demonstrated that these scaffolds support cell growth and osteoblastic differentiation in the presence of BMP-2 in vitro, although the pore orientation somehow affected cell attachment and differentiation. The evaluation of the ability of the scaffolds to support bone growth when loaded with BMP-2 or BMP-2 + VEGF in an ectopic rat model showed that they both supported bone formation. Histological analysis and quantification of mineralized matrix revealed that the pore orientation of the collagen scaffolds influenced the osteogenic process.

Simulation of pandemics in real cities: enhanced and accurate digital laboratories

This study develops a modelling framework for simulating the spread of infectious diseases within real cities. Digital copies of Birmingham (UK) and Bogotá (Colombia) are generated, reproducing their urban environment, infrastructure and population. The digital inhabitants have the same statistical features of the real population. Their motion is a combination of predictable trips (commute to work, school, etc.) and random walks (shopping, leisure, etc.). Millions of individuals, their encounters and the spread of the disease are simulated by means of high-performance computing and massively parallel algorithms for several months and a time resolution of 1 minute. Simulations accurately reproduce the COVID-19 data for Birmingham and Bogotá both before and during the lockdown. The model has only one adjustable parameter calculable in the early stages of the pandemic. Policymakers can use our digital cities as virtual laboratories for testing, predicting and comparing the effects of policies aimed at containing epidemics.

Influence of interdigitation and expander type in the mechanical response of the midpalatal suture during maxillary expansion

BACKGROUND AND OBJECTIVE

The orthopedic Maxillary Expansion (ME) procedure is used for treating the transverse maxillary deficiency. This pathology consists in a smaller transverse dimension in the maxilla and leads to malocclusion. The treatment takes advantage of the existence of the midpalatal suture (MPS), which corresponds to the junction at the palatine bones of its horizontal portions. The technique employs a device, conventionally a palatal expander attached to the posterior teeth, to separate the two maxillary bones in the MPS. The objective of this study was to analyze, using the Finite Element Method, the biomechanical behavior of the MPS when an expansion is applied.

METHODS

A Computer Tomography image of the maxilla was reconstructed, the suture geometry was modeled with different interdigitation levels and types of hyrax devices. A total of 12 geometric models (three levels for interdigitation and four types of hyrax devices) were prepared and analyzed taking into account the chewing forces and the expansion displacement. For each case, maximum principal stresses on the maxilla (bone), and equivalent stresses on the expander device (stainless steel) were observed. In the MPS, maximum principal stresses and directional displacement were evaluated.

RESULTS

The results showed that the interdigitation does not have an important influence on the deformation behavior of the maxilla but it affects the stress distribution. In addition, the type of expander device and anchorage have a direct relationship with the treatment effectiveness; larger deformation in the expansion direction was obtained with skeletal when compared to dental anchorage.

CONCLUSIONS

A study that allows a better understanding of the oral biomechanics during the application of ME was presented. To our knowledge, it is the first study based on computational simulations that takes into account bone structures, like maxilla and part of the skull, to analyze the interdigitation influence on the MPS behavior when exposed to a ME.

Biophysical Stimuli: A Review of Electrical and Mechanical Stimulation in Hyaline Cartilage

OBJECTIVE

Hyaline cartilage degenerative pathologies induce morphologic and biomechanical changes resulting in cartilage tissue damage. In pursuit of therapeutic options, electrical and mechanical stimulation have been proposed for improving tissue engineering approaches for cartilage repair. The purpose of this review was to highlight the effect of electrical stimulation and mechanical stimuli in chondrocyte behavior.

DESIGN

Different information sources and the MEDLINE database were systematically revised to summarize the different contributions for the past 40 years.

RESULTS

It has been shown that electric stimulation may increase cell proliferation and stimulate the synthesis of molecules associated with the extracellular matrix of the articular cartilage, such as collagen type II, aggrecan and glycosaminoglycans, while mechanical loads trigger anabolic and catabolic responses in chondrocytes.

CONCLUSION

The biophysical stimuli can increase cell proliferation and stimulate molecules associated with hyaline cartilage extracellular matrix maintenance.

Cellular automata model for human articular chondrocytes migration, proliferation and cell death: An in vitro validation

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.

Morphological changes of physeal cartilage and secondary ossification centres in the developing femur of the house mouse (Mus musculus): A micro-CT based study

In mammals, long bones are formed by ossification of a cartilaginous mould during early stages of development, through the formation of structures called the primary ossification centre, the secondary ossification centres (SOCs) and the physeal cartilages (PCs). The PC is responsible for long bone growth. The morphology of the PC and the SOCs varies during different stages of femoral growth. In this respect, several details involving the process of murine femoral development are lacking. In the present study, a morphological characterization of femur development from the embryonic period to adulthood in mice was studied using micro-computed tomography (micro-CT). To achieve this aim, femora were collected at embryonic day (E) 14.5, E16.5 and E18.5 and at postnatal day (P)1, P7, P14, P35, P46 and P52. CT images were obtained using a micro-CT scanner (X-SkyScan 1172; Micro Photonics) and analysed using the micro-CT 3D visualization software Mimics (Materialise NV, Leuven, Belgium) and NRecon (Micro Photonics). The results of the present study revealed that the femur and its PCs and SOCs undergo morphological changes during different stages of development, including changes in their shape as well as position and thickness. These changes may be due to the response of the femur to mechanical loads imposed by muscle surrounding the bone during these stages of development. The result of the present study is important to improve our knowledge related to ossification and growth patterns of mouse femur during development.

Capacitively coupled electrical stimulation of rat chondroepiphysis explants: A histomorphometric analysis

The growth plate is a cartilaginous layer present from the gestation period until the end of puberty where it ossifies joining diaphysis and epiphysis. During this period several endocrine, autocrine, and paracrine processes within the growth plate are carried out by chondrocytes; therefore, a disruption in cellular functions may lead to pathologies affecting bone development. It is known that electric fields impact the growth plate; however, parameters such as stimulation time and electric field intensity are not well documented. Accordingly, this study presents a histomorphometrical framework to assess the effect of electric fields on chondroepiphysis explants. Bones were stimulated with 3.5 and 7 mV/cm, and for each electric field two exposure times were tested for 30 days (30 min and 1 h). Results evidenced that electric fields increased the hypertrophic zones compared with controls. In addition, a stimulation of 3.5 mV/cm applied for 1 h preserved the columnar cell density and its orientation. Moreover, a pre-hypertrophy differentiation in the center of the chondroepiphysis was observed when explants were stimulated during 1 h with both electric fields. These findings allow the understanding of the effect of electrical stimulation over growth plate organization and how the stimulation modifies chondrocytes morphophysiology.

A Comparison of the Contact Force Distributions on the Acetabular Surface Due to Orthopedic Treatments for Developmental Hip Dysplasia

We used a three-dimensional rigid body spring model (RBSM) to compare the contact force distributions on the acetabular surface of the infant hip joint that are produced by three orthopedic treatments for developmental dysplasia of the hip (DDH). We analyzed treatments using a Pavlik harness, a generic rigid splint, and a spica cast. The joint geometry was modeled from tomography images of a 1-year-old female. The articular cartilage was modeled as linear springs connecting the surfaces of the acetabulum and the femoral head, whereas the femur and the hip bone were considered as rigid bodies. The hip muscles were modeled as tensile-only preloaded springs. The treatments with the Pavlik harness and the generic rigid splint were modeled for an infant in supine position with a hip flexion angle of 90 deg. Also, since rigid splints are often recommended when children are initiating their gait phase, we modeled the treatment with the infant in standing position. For the spica cast, we only considered the infant in standing position with a flexion angle of 0 deg, and the fixation bar at two heights: at the ankle and at the knee. In order to analyze the effect of the hip abduction angle over the contact force distribution, different abduction angles were used for all the treatments modeled. We have found that the treatments with the infant in supine position, with a flexion angle of 90 deg and abduction angles between 60 deg and 80 deg, produce a more homogenous contact force distribution compared to those obtained for the treatments with the infant in standing position.

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.

Growth plate stress distribution implications during bone development: a simple framework computational approach

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.

Numerical investigation into blood clotting at the bone-dental implant interface in the presence of an electrical stimulus

The insertion of a dental implant activates a sequence of wound healing events ending with bone formation and implant osseointegration. This sequence starts with the blood coagulation process and the formation of a fibrin network that detains spilt blood. Fibrin formation can be simplified as the kinetic reaction between thrombin and fibrinogen preceding the conversion of fibrinogen into fibrin. Based on experimental observations of the electrical properties of these molecules, we present a hypothesis for the mechanism of a static electrical stimulus in controlling the formation of the blood clot. Specifically, the electrical stimulus increases the fibrin network formation in such a way that a preferential region of higher fibrin density is obtained. This hypothesis is validated by means of a numerical model for the blood clot formation at the bone-dental implant interface. Numerical results compare favorably to experimental observations for blood clotting with and without the static electrical stimulus. It is concluded that the density of the fibrin network depends on the strength of the static electrical stimulus, and that the blood clot formation has a preferential direction of formation in the presence of the electrical signal.

Growth of the flat bones of the membranous neurocranium: a computational model

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 theoretical model of dentinogenesis: dentin and dentinal tubule formation

INTRODUCTION

Dentinogenesis, odontoblast dentin formation, includes dentinal growth, mineralization and dentinal tubule formation. Odontoblasts synthesize collagen resulting in collagen apposition contributing to dentinogenesis. Furthermore, within the tubule, they express non-collagenous proteins, such as dentin phosphoprotein (DPP), associated with hydroxyapatite crystal formation and growth. The aim of this work was to determine patterns of growth and dentin formation and quantification of its mineralization. Findings from our work are relevant to endodontics for future regenerative treatment.

METHODS

We formulated a 3D domain mathematical model, which recreates the events that lead to dentinal tubule mineralization. As reference we used collagen apposition and DPP activity.

RESULTS

We obtained a model depicting predentin's mineralization distribution during dentin development. Furthermore, we verified different DPP diffusion coefficients to test the model's sensitivity.

CONCLUSIONS

We present a model to shed light on the process of dentin and dentinal tubule formation, and its relation to diffusion and mineralization processes.

Bone tissue formation under ideal conditions in a scaffold generated by a reaction-diffusion system

The design of porous scaffolds for tissue engineering requires methods to generate geometries in order to control the stiffness and the permeability of the implant among others characteristics. This article studied the potential of the reaction-diffusion systems to design porous scaffolds for bone regeneration. We simulate the degradation of the scaffold material and the formation of new bone tissue over canal-like, spherical and ellipsoid structures obtained by this approach. The simulations show that the degradation and growth rates are affected by the form of porous structures. The results have indicated that the proposed method has potential as a tool to generate scaffolds with internal porosities and is comparable with other methodologies to obtain this type of structures.

Computational modeling of the mechanical modulation of the growth plate by sustained loading

This paper presents a computational model that describes the growth of the bone as a function of the proliferation and hypertrophy of chondrocytes in the growth plate. We have included the effects of the mechanical loads on the sizes of the proliferative and hypertrophic areas, the number of proliferative chondrocytes and the final size of the hypertrophic chondrocytes. The validation of the model was performed with experimental data published on other investigations about proximal tibia of rats, subjected to sustained axial stresses of 0.1 MPa, 0.0 MPa, -0.1 MPa and −0.2 MPa. Growth was simulated during 23 days, obtaining numerical errors between 2.77% and 3.73% with respect to experimental growth rates. The results obtained show that the model adequately simulates the behavior of the growth plate and the effect of mechanical loads over its cellular activity.

Numerical test concerning bone mass apposition under electrical and mechanical stimulus

This article proposes a model of bone remodeling that encompasses mechanical and electrical stimuli. The remodeling formulation proposed by Weinans and collaborators was used as the basis of this research, with a literature review allowing a constitutive model evaluating the permittivity of bone tissue to be developed. This allowed the mass distribution that depends on mechanical and electrical stimuli to be obtained. The remaining constants were established through numerical experimentation. The results demonstrate that mass distribution is altered under electrical stimulation, generally resulting in a greater deposition of mass. In addition, the frequency of application of an electric field can affect the distribution of mass; at a lower frequency there is more mass in the domain. These numerical experiments open up discussion concerning the importance of the electric field in the remodeling process and propose the quantification of their effects.

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.

Modeling porous scaffold microstructure by a reaction-diffusion system and its degradation by hydrolysis

One of the most important areas of Tissue Engineering is the research about bone regeneration and the replacement of its function. To meet this requirement, scaffolds have been developed to allow the cell migration, the growth of bone tissue, the transport of growth factors and nutrients and the renovation of the mechanical properties of bone. Scaffolds are made of different biomaterials and manufactured using various techniques that, in some cases, do not allow full control over the size and orientation of the pores that characterize the scaffold microstructure. From this perspective, we propose a novel hypothesis that a reaction-diffusion system can be used to design the geometrical specifications of the bone matrix. The validation of this hypothesis is performed by simulations of the reaction-diffusion system in a representative tridimensional unit cell, coupled with a model of scaffold degradation by hydrolysis. The results show the possibility that a Reaction-Diffusion system can control features such as the percentage of porosity, trabecular size, orientation, and interconnectivity of pores.

A biochemical hypothesis on the formation of fingerprints using a turing patterns approach

BACKGROUND

Fingerprints represent a particular characteristic for each individual. Characteristic patterns are also formed on the palms of the hands and soles of the feet. Their origin and development is still unknown but it is believed to have a strong genetic component, although it is not the only thing determining its formation. Each fingerprint is a papillary drawing composed by papillae and rete ridges (crests). This paper proposes a phenomenological model describing fingerprint pattern formation using reaction diffusion equations with Turing space parameters.

RESULTS

Several numerical examples were solved regarding simplified finger geometries to study pattern formation. The finite element method was used for numerical solution, in conjunction with the Newton-Raphson method to approximate nonlinear partial differential equations.

CONCLUSIONS

The numerical examples showed that the model could represent the formation of different types of fingerprint characteristics in each individual.

A mathematical model of medial collateral ligament repair: migration, fibroblast proliferation and collagen formation

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.

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.