A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions.

In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction-diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs.

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.

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.

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

: To simulate infant skull trauma after low height falls when variable degrees of ossification of the sutures are present. : 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.

Maxillary suture expansion: A mouse model to explore the molecular effects of mechanically-induced bone remodeling.

The aim of this study was to analyze the effect of rapid maxillary expansion (RME) on hard tissues. Opening loops bonded to the first and second maxillary molars on both sides were used to apply distracting forces of 0.28 N, 0.

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.

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.

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.

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.

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.

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

This article proposes a mathematical model that predicts the wound healing process of the ligament after a sprain, grade II. The model describes the swelling, expression of the platelet-derived growth factor (PDGF), formation and migration of fibroblasts into the injury area and the expression of collagen fibers. Additionally, the model can predict the effect of ice treatment in reducing inflammation and the action of mechanical stress in the process of remodeling of collagen fibers.

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

The cerebral cortex is a gray lamina formed by bodies of neurons covering the cerebral hemispheres, varying in thickness from 1.25 mm in the occipital lobe to 4mm in the anterior lobe. The brain's surface is about 30 times greater that of the skull because of its many folds; such folds form the gyri, sulci and fissures and mark out areas having specific functions, divided into five lobes.

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

Metastasis is the rapid proliferation of cancer cells (secondary tumour) at a specific place, generally leading to death. This occurs at anatomical parts providing the necessary environment for vascularity, oxygen and food to hide their actions and trigger the rapid growth of cancer. Prostate and breast cancers, for example, use bone marrow for their proliferation.

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.

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

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

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.