Part II: A new perspective for modeling the bone remodeling process: Biology, mechanics, and pathologies.

In this paper, we explore the effects of biological (pathological) and mechanical damage on bone tissue within a benchmark model. Using the Finite Element Methodology, we analyze and numerically test the model's components, capabilities, and performance under physiologically and pathologically relevant conditions. Our findings demonstrate the model's effectiveness in simulating bone remodeling processes and self-repair mechanisms for micro-damage induced by biological internal conditions and mechanical external ones within bone tissue. This article is the second part of a series, where the first part presented the mathematical model and the biological and physical significance of the terms used in a simplified benchmark model. It explored the bone remodeling model's application, implementation, and results under physiological conditions.

Analysis of the airflow features and ventilation efficiency of an Ultra-Clean-Air operating theatre by qDNS simulations and experimental validation.

Ultra-Clean-Air (UCA) operating theatres aim to minimise surgical instrument contamination and wound infection through high flow rates of ultra-clean air, reducing the presence of Microbe Carrying Particles (MCPs). This study investigates the airflow patterns and ventilation characteristics of a UCA operating theatre (OT) under standard ventilation system operating conditions, considering both empty and partially occupied scenarios. Utilising a precise computational model, quasi-Direct Numerical Simulations (qDNS) were conducted to delineate flow velocity profiles, energy spectra, distributions of turbulent kinetic energy, energy dissipation rate, local Kolmogorov scales, and pressure-based coherent structures. These results were also complemented by a tracer gas decay analysis following ASHRAE standard guidelines. Simulations showed that contrary to the intended laminar regime, the OT's geometry inherently fosters a predominantly turbulent airflow, sustained until evacuation through the exhaust vents, and facilitating recirculation zones irrespective of occupancy level. Notably, the occupied scenario demonstrated superior ventilation efficiency, a phenomenon attributed to enhanced kinetic energy induced by the additional obstructions. The findings underscore the critical role of UCA-OT design in mitigating MCP dissemination, highlighting the potential to augment the design to optimise airflow across a broader theatre spectrum, thereby diminishing recirculation zones and consequently reducing the propensity for Surgical Site Infections (SSIs). The study advocates for design refinements to harness the turbulent dynamics beneficially, steering towards a safer surgical environment.

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.

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.

A dynamical system for the IGF1-AKT signaling pathway in skeletal muscle adaptation.

Physical activity produces a change in skeletal-muscle size by activating synthesis or degradation of protein, which are outcomes of stimulating the IGF1-AKT signaling pathway. In this work, we propose a mathematical model that predicts the variation in muscle size under different activity conditions. The IGF1-AKT pathway was modeled using its 4 main molecules as variables in a dynamical system. We checked the stability of the system; we defined exercise training as a function of intensity, duration, and frequency; and we tested the model under four scenarios: first, we considered the daily low-intensity activity that should not promote atrophy nor hypertrophy (steady state); second, we simulated the effects of physical therapy in spinal cord injury patients (atrophy); third, we simulated exercise training in healthy subjects (hypertrophy); and fourth, we considered the effects of suspending a training program in healthy subjects (recovery after hypertrophy). Results showed that: protein synthesis and degradation are inactive, thus the size of the muscle stays stable in the first scenario; the muscle decreases only 10% of its initial size after 84 days of therapy every two days in the second scenario; training frequency produces rapid hypertrophy (11% after 25 days) when training every day, to no hypertrophy when training every 5 days in the third scenario; and a reduction of 50% the gain of the training program in the fourth scenario. By comparing our results to experimental reports, we found a remarkable agreement; therefore, our model is suitable for the development of training and therapeutic protocols.

Growth Plate Pathology in the Mucopolysaccharidosis Type VI Rat Model-An Experimental and Computational Approach.

BACKGROUND: Mucopolysaccharidoses (MPS) are a group of inherited metabolic diseases caused by impaired function or absence of lysosomal enzymes involved in degradation of glycosaminoglycans. Clinically, MPS are skeletal dysplasias, characterized by cartilage abnormalities and disturbances in the process of endochondral ossification. Histologic abnormalities of growth cartilage have been reported at advanced stages of the disease, but information regarding growth plate pathology progression either in humans or in animal models, as well as its pathophysiology, is limited. METHODS: Histological analyses of distal femur growth plates of wild type (WT) and mucopolysaccharidosis type VI (MPS VI) rats at different stages of development were performed, including quantitative data. Experimental findings were then analyzed in a theoretical scenario. RESULTS: Histological evaluation showed a progressive loss of histological architecture within the growth plate. Furthermore, in silico simulation suggest the abnormal cell distribution in the tissue may lead to alterations in biochemical gradients, which may be one of the factors contributing to the growth plate abnormalities observed, highlighting aspects that must be the focus of future experimental works. CONCLUSION: The results presented shed some light on the progression of growth plate alterations observed in MPS VI and evidence the potentiality of combined theoretical and experimental approaches to better understand pathological scenarios, which is a necessary step to improve the search for novel therapeutic approaches.

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.

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.

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.

Geometrical and mechanical factors that influence slipped capital femoral epiphysis: a finite element study.

Slipped capital femoral epiphysis (SCFE) is an orthopedic pathology in which damage of the growth plate leads to the anterosuperior displacement of the femoral body in respect to the femoral head. Despite being a widely studied disease, its etiology is still unknown. This study was carried out to determine the influence of the physeal-diaphysis angle, body mass, the presence of the perichondrial ring, the type of physical activity, and physeal thickness on SCFE. For this purpose, a finite element analysis of the hip joint and the femur-physis interface was carried out. With the computational model, the Von Mises stresses along the growth plate were calculated and subsequently analyzed statistically to find their correlation with the studied factors. It was found that body mass, the type of physical activity, and the presence of the perichondrial ring had more statistical relevance for the physeal stresses than the physeal-diaphysis angle and the physeal thickness. Thus, our work suggests that changes in growth plate inclination and thickness do not influence the etiology of SCFE.

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.

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.

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 biochemical strategy for simulation of endochondral and intramembranous ossification.

Following the assumption that parathyroid hormone related protein and Indian hedgehog form a biochemical regulatory loop for the endochondral process and bone morphogenetic protein 2 and Noggin in the intramembranous process, this paper implements these regulatory mechanisms. For this purpose, we use a set of reaction-diffusion equations that are widely used in morphogenesis, in which biochemical factors are assumed to be secreted by precursor cells, mesenchymal cells and chondrocytes, in endochondral and intramembranous ossification, respectively. The solution leads to the so-called Turing patterns, which represent these processes of ossification in a very approximate way.

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.

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.