A mechanobiological model of epiphysis structures formation

Computational model of endochondral ossification: Simulating growth of a long bone

Mechanical loading is a crucial factor in joint and bone development. Using a computational model, we investigated the role of mechanics on cartilage growth rate, ossification of the secondary center, formation of the growth plate, and overall bone shape. A computational algorithm was developed and implemented into finite element models to simulate the endochondral ossification for symmetric and asymmetric motion in a generic diarthrodial joint. Under asymmetric loading condition the secondary center ossifies asymmetrically leaning toward the external load and results in tilted growth plate. Also the mechanics seems to have greater influence in the early onset of the ossification of the secondary center rather than later progression of the center. While previous models have simulated select stages of skeletal development, our model can simulate growth and ossification during the entirety of post-natal development. Such computational models of skeletal development may provide insight into specific loading conditions that cause bone and joint deformities, and the required timing for rehabilitative repair.

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.

DEVELOPMENTAL SCENARIOS OF THE EPIPHYSIS AND GROWTH PLATE UPON MECHANICAL LOADING: A COMPUTATIONAL MODEL

Long bone growth relies on the continuous bone formation from cartilaginous tissue (endochondral ossification). This process starts in the central region (diaphysis) of the forming bone and short before birth, ossification starts in bone extremes (epiphysis). A cartilaginous region known as the growth plate is maintained until adolescence between epiphysis and diaphysis to further contribute to longitudinal growth. Even though there are several biochemical factors controlling this process, there is evidence revealing an important regulatory role of mechanical stimuli. Up to now approaches to understand mechanical effects on ossification have been limited to epiphysis. In this work, based on Carter's mathematical model for epiphyseal ossification, we explored human growth plate response to mechanical loads. We analyzed growth plate stress distribution using finite element method for a generic bone considering different stages of bone development in order to shed light on mechanical contribution to growth plate function. Results obtained revealed that mechanical environment within the growth plate change as epiphyseal ossification progresses. Furthermore, results were compared with physiological behavior, as reported in literature, to analyze the role of mechanical stimulus over development. Our results suggest that mechanical stimuli may play different regulation roles on growth plate behavior through normal long bone development. However, as this approach only took into account mechanical aspects, failed to accurately predict biological behavior in some stages. In order to derive biologically relevant information from computational models it is necessary to consider biological contribution and possible mechanical–biochemical interactions affecting human growth plate physiology. Along these lines, we propose the dilatatorial parameter k used by Carter et al. should assume different values corresponding to the developmental stage in question. Thus, reflecting biochemical contribution changes over time.

Cartilage canals in newborn dogs: histochemical and immunohistochemical findings

Cartilage canals (CCs) are microscopic structures involved in secondary ossification centers (SOCs) development. The features of CCs were investigated in the humeral and femoral proximal epiphyses of small-sized newborn dogs (from premature to 28 days after birth) with histochemical and immunohistochemical approaches. Masson's Trichrome revealed a ring-shaped area around CCs, which changes in colour from green (immature collagen) to red (mature collagen) as ossification progresses; perichondrium staining always matched the ring colour. Safranin-O was always negative. Immunohistochemical analysis revealed immunopositivity for both collagen type I and V around the CCs; collagen type II was negative. CCs count showed a tendency to be higher in the humerus than in the femur. This work enlightened for the first time changes in composition of CCs surrounding matrix during SOCs development in dogs, paving the way to further investigations.

Cell-based articular cartilage repair: the link between development and regeneration

Clinical efforts to repair damaged articular cartilage (AC) currently face major obstacles due to limited intrinsic repair capacity of the tissue and unsuccessful biological interventions. This highlights a need for better therapeutic strategies. This review summarizes the recent advances in the field of cell-based AC repair. In both animals and humans, AC defects that penetrate into the subchondral bone marrow are mainly filled with fibrocartilaginous tissue through the differentiation of bone marrow mesenchymal stem cells (MSCs), followed by degeneration of repaired cartilage and osteoarthritis (OA). Cell therapy and tissue engineering techniques using culture-expanded chondrocytes, bone marrow MSCs, or pluripotent stem cells with chondroinductive growth factors may generate cartilaginous tissue in AC defects but do not form hyaline cartilage-based articular surface because repair cells often lose chondrogenic activity or result in chondrocyte hypertrophy. The new evidence that AC and synovium develop from the same pool of precursors with similar gene profiles and that synovium-derived chondrocytes have stable chondrogenic activity has promoted use of synovium as a new cell source for AC repair. The recent finding that NFAT1 and NFAT2 transcription factors (TFs) inhibit chondrocyte hypertrophy and maintain metabolic balance in AC is a significant advance in the field of AC repair. The use of synovial MSCs and discovery of upstream transcriptional regulators that help maintain the AC phenotype have opened new avenues to improve the outcome of AC regeneration.

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.

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.

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.

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.