A computational model for the joint onset and development.

Joints connect the skeletal components and enable movement. The appearance and development of articulations is due to different genetic, biochemical, and mechanical factors. In the embryonic stage, controlled biochemical processes are critical for organized growth. We developed a computational model, which predicts the appearance, location, and development of joints in the embryonic stage. Biochemical events are modeled with reaction diffusion equations with generic molecules representing molecules that 1) determine the site where the articulation will appear, 2) promote proliferation, and matrix synthesis, and 3) define articular cartilage. Our model accounts for cell differentiation from mesenchymal cells to pre-cartilaginous cells, then cartilaginous cells, and lastly articular cartilage. These reaction-diffusion equations were solved using the finite elements method. From a mesenchymal 'bud' of a phalanx, the model predicts growth, joint cleavage, joint morphology, and articular cartilage formation. Our prediction of the gene expression during development agrees with molecular expression profiles of joint development reported in literature. Our computational model suggests that initial rudiment dimensions affect diffusion profiles result in Turing patterns that dictate sites of cleavage thereby determining the number of joints in a rudiment.

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.

Elbow dimensions in quadrupedal mammals driven by lubrication regime.

Synovial joints, such as the elbow, experience different lubrication regimes, ranging from fluid film to boundary lubrication, depending on locomotion conditions. We explore the relationship between the elbow lubrication regime and the size of quadrupedal mammals. We use allometry to analyze the dimensions, contact stress, and sliding speed of the elbow in 110 quadrupedal mammals. Our results reveal that the average diameter and width of the distal humerus are scaled [Formula: see text], which allowed us to estimate a consistent contact pressure and sliding speed across mammals. This consistency likely promotes fluid film lubrication regardless of body mass. Further, the ratio between the diameter and width is about 0.5 for all analyzed taxa, which is a good compromise between loading capacity and size. Our study deepens our understanding of synovial joints and their adaptations, with implications for the development of treatments, prostheses, and bioinspired joint designs.

A simple and effective 1D-element discrete-based method for computational bone remodeling.

In-silico models applied to bone remodeling are widely used to investigate bone mechanics, bone diseases, bone-implant interactions, and also the effect of treatments of bone pathologies. This article proposes a new methodology to solve the bone remodeling problem using one-dimensional (1D) elements to discretize trabecular structures more efficiently for 2D and 3D domains. An Euler integration scheme is coupled with the momentum equations to obtain the evolution of material density at each step. For the simulations, the equations were solved by using the finite element method, and two benchmark tests were solved varying mesh parameters. Proximal femur and calcaneus bone were selected as study cases given the vast research available on the topology of these bones, and compared with the anatomical features of trabecular bone reported in the literature. The presented methodology has proven to be efficient in optimizing topologies of lattice structures; It can predict the trend of formation patterns of the main trabecular groups from two different cancellous bones (femur and calcaneus) using domains set up by discrete elements as a starting point. Preliminary results confirm that the proposed approach is suitable and useful in bone remodeling problems leading to a considerable computational cost reduction. Characteristics similar to those encountered in topological optimization algorithms were identified in the benchmark tests as well, showing the viability of the proposed approach in other applications such as bio-inspired design.

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.

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.

Computational model for the patella onset.

The patella is a sesamoid bone embedded within the quadriceps tendon and the patellar tendon that articulates with the femur. However, how is it formed is still unknown. Therefore, here we have evaluated, computationally, how three theories explain, independently, the patella onset. The first theory was proposed recently, in 2015. This theory suggested that the patella is initially formed as a bone eminence, attached to the anterodistal surface of the femur, while the quadriceps tendon is forming. Thereafter, a joint develops between the eminence and the femur, regulated by mechanical load. We evaluated this theory by simulating the biochemical environment that surrounds the tendon development. As a result, we obtained a patella-like structure embedded within the tendon, especially for larger flexion angles. The second and third theories are the most accepted until now. They state that the patella develops within tendons in response to the mechanical environment provided by the attaching muscles. The second theory analyzed the mechanical conditions (high hydrostatic stress) that (according to previous Carter theories) lead to the differentiation from tendon to fibrocartilage, and then, to bone. The last theory was evaluated using the self-optimizing capability of biological tissue. It was considered that the development of the patella, due to tissue topological optimization of the developing quadriceps tendon, is a feasible explanation of the patella appearance. For both theories, a patella onset was obtained as a structure embedded within the tendon. This model provided information about the relationship between the flexion angle and the patella size and shape. In conclusion, the computational models used to evaluate and analyze the selected theories allow determining that the patella onset may be the result of a combination of biochemical and mechanical factors that surround the patellar tendon development.

Load distribution on the radio-carpal joint for carpal arthrodesis.

BACKGROUND AND OBJECTIVE: Carpal fusions are useful for treating specific carpal disorders, maximizing postoperative wrist motion, hand strength, reducing pain and instability of the joint. The surgeon selects the appropriate treatment by considering the degree of stability, the chronicity of the injury, functional demands of the patient and former patient's outcomes as well. However there are not many studies regarding the load distribution provided by the treatment. So, the purpose of this study is to analyze the load distribution through the wrist joint with an arthrodesis treatment and compare the results with a normal wrist. METHOD: To this end the rigid body spring model (RBSM) method was used on a three-dimensional model of the wrist joint. The cartilage and ligaments were simulated as springs acting under compression and tension, respectively, while the bones were considered as rigid bodies. To simulate the arthrodesis, the fused bones were considered as a single rigid body. RESULTS: The changes on the load distribution for each arthrodesis agree with the treatment objective, reducing load transmission through a specific articular surface. For example, for SLAC/SNAC II most of the treatments reduced the load transmitted through the radioscaphoid fossae, almost by 8%. However, the capitolunate (CL) arthrodesis was the treatment that managed to keep the load transmitted through the radiolunate joint closer to normal conditions. Also, in treatments where the scaphoid was excised (3-corner, 4-corner and capitolunate arthrodesis), the joint surface between the lunate surface compensates by doubling the transmitted force to the radius. CONCLUSIONS: The common arthrodesis for treating SLAC/SNAC II-III, reduces, in fact, the load on the radioscaphoid joint. Alternative treatments that reduce load distribution on the radiocarpal joint should be three corner and capitolunate arthrodesis for treating SLAC/SNAC-II; and for SLAC/SNAC-III four corners with scaphoid excision. On Kienbock's disease. Scaphocapitate (SC) arthrodesis is more effective on reducing the load transmission through the radiolunate and ulnolunate joints. All arthrodesis treatment should consider changes on the load transmission, and also bones' fusion rates and pain reduction on patient's outcomes.

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.

Método para el cálculo de las medidas angulares de la articulación del radio distal / Method to calculate angular measures of the distal radial articulation

La fractura del radio distal se puede presentar cuando se produce una compresión axial sobre la muñeca. Entre los tratamientos más comunes se encuentran el conservador (inmovilización con yeso) y el quirúrgico. Este último emplea placas y tornillos para la fijación de la fractura después de la reducción, sin embargo, debido a la anatomía compleja de la superficie articular, determinar la posición relativa de los tornillos con respecto a esta puede llegar a ser com,plicado. Para solucionar esto, se han empleado imágenes radiológicas estándar, en las cuales se determina la inclinación palmar y radial de la superficie articular. Con base en los ángulos obtenidos se inclina el antebrazo, de modo que al tomar la radiografía, los labios de la superficie articular queden superpuestos. Sin embargo, este método para determinar las inclinaciones resulta poco efectivo debido a que no se considera en su análisis la anatomía biplana simultáneamente con la bicóncava, del área articular. En este artículo se propone una metodología para hallar los ángulos que determinan la orientación de la superficie articular, empleando reconstrucción tridimensional a partir de imágenes de tomografía axial. Con estas inclinaciones será posible visualizar tangencialmente la superficie articular del radio distal, y así determinar la posición relativa de los tornillos de fijación respecto a esta superficie. Mediante el estudio de un caso, se encontró que la inclinación radial de la superficie articular en su totalidad era de 13° y la palmar de 6° con respecto a una línea perpendicular al eje central del radio. Esto difiere de lo hallado por otros autores que proponen un ángulo radial de 22° a 24° y palmar de 9° a 12°. Por otra parte, para la superficie que articula con el hueso semilunar se encontró una inclinación radial de 7° y una palmar de 10°; en tanto la fosa que está en contacto con el hueso escafoides se inclina radialmente 21° y palmarmente 8°, en el caso analizado...

A distal radial fracture may occur as a result of axial compression of the wrist. The most common treatments include the conservative approach (plaster cast immobilization) and surgery. In the latter procedure, plates and screws are used to fix the fracture after reduction. However, it may be difficult to determine the relative position of the screws with respect to the articular surface, due to the complex anatomy of this structure. To solve this problem, standard radiological imaging has been used to determine the palmar and radial tilt of the articular surface. Based on the angles obtained, the forearm is tilted in such a way that when the radiograph is taken the articular surface labia overlap. However, this method is not very effective to determine tilt, since the biplane and biconcave anatomy of the articular zone are not considered simultaneously. A methodology is proposed to find the angles determining articular surface orientation by means of three-dimensional reconstruction based on axial tomography imaging. Such tilt measurements will make it possible to obtain a tangential view of the distal radial articular surface and determine the relative position of fixation screws with respect to it. In a case study it was found that total radial tilt of the articular surface was 13° and palmar tilt was 6° with respect to a line perpendicular to the central axis of the radius. This outcome differs from findings by other authors, who propose a radial angle of 22° to 24° and a palmar angle of 9° to 12°. Additionally, for the surface articulating with the semilunar bone, radial tilt was found to be 7° and palmar tilt 10°, whereas in the fossa which is in contact with the scaphoid bone, radial tilt is 21° and palmar tilt 8° in the case analyzed...