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.

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 Shoulder Musculoskeletal Model with Three-Dimensional Complex Muscle Geometries.

Muscle structure is an essential component in typical computational models of the musculoskeletal system. Almost all musculoskeletal models represent muscle geometry using a set of line segments. The straight-line approach limits models' ability to accurately predict the paths of muscles with complex geometry. This approach needs knowledge of how the muscle changes shape and interacts with fundamental structures like muscles, bones, and joints that move. Moreover, the moment arms are supposed to be equivalent to all the fibers in the muscle. This study aims to create a shoulder musculoskeletal model that includes complex muscle geometries. We reconstructed the shape of fibers in the entire volume of six muscles adjacent to the shoulder using an automated technique. This method generates many fibers from the surface geometry of the skeletal muscle and its attachment areas. Highly discretized muscle representations for all muscles were created and used to simulate different shoulder movements. The moment arms of each muscle were calculated and validated against cadaveric measurements and models of the same muscles from the literature. We found that simulations using the developed musculoskeletal models generated more realistic geometries, which expands the physical representation of muscles compared to line segments. The shoulder musculoskeletal model with complex muscle geometry is created to increase the anatomical reality of models and the lines action of muscle fibers, and to be used for finite element investigations.

Influence of growth plate morphology on bone trabecular groups, a framework computational approach.

The morphology of the growth plate undergoes various transformations during each stage of development, affecting its shape, width, density, and other characteristics. This significantly impacts the distribution of stress in the epiphysis of long bones. To the best of our knowledge, this study represents the first attempt to examine the relationship between growth plate morphology and trabecular bone patterns. Our analysis was conducted using a finite element model and we analyzed two medical cases: trabecular patterns in the femoral epiphysis and the calcaneus bone. Our findings revealed a correlation between the formation of main trabecular groups and growth plate morphology. We investigated how an increased density in high-shear stress zones, which are typically located at the periphery of the growth plate, may occur to prevent failure by shear. This is evident in cases such as slipped capital femoral epiphysis or sever's disease, different simulations align with the clinical data available in the literature from a qualitative and quantitative point of view. Our results suggest that further research should focus on understanding the impact of growth plate morphology on bone remodeling and exploring potential preventive measures for different bone disorders.

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.

A unified framework of cell population dynamics and mechanical stimulus using a discrete approach in bone remodelling.

Multiphysics models have become a key tool in understanding the way different phenomenon are related in bone remodeling and various approaches have been proposed, yet, to the best of the author's knowledge there is no model able to link a cell population model with a mechanical stimulus model using a discrete approach, which allows for an easy implementation. This article couples two classical models, the cell population model from Komarova and the Nackenhorst model in a 2D domain, where correlations between the mechanical loading and the cell population dynamics can be established, furthermore the effect of different paracrine and autocrine regulators is seen on the overall density of a portion of trabecular bone. A discretization is performed using frame 1D finite elements, representing the trabecular structure. The Nackenhorst model is implemented by using the finite element method to calculate the strain energy as the main mechanical stimulus that determines the bone mass density evolution in time. This density is normalized to be added to the bone mass percentage proposed by the Komarova model, where coupling terms have been added as well that guarantee a stable response. In the simulations, the equations were solved employing the finite element method with a user subroutine implemented in ABAQUS (2017) and by applying a direct formulation. The methodology presented can model the cell dynamics occurring in bone remodelling in accordance with the asynchronous nature of this process, yet allowing to differentiate zones with higher density, the main trabecular groups are obtained for the proximal femur. Finally, the model is tested in pathological cases, such as osteoporosis and osteopetrosis, yielding results similar to the pathology behavior. Furthermore, the discrete modelling technique is shown to be of use in this particular application.

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.

In vitro and in vivo proves of concept for the use of a chemically cross-linked poly(ester-urethane-urea) scaffold as an easy handling elastomeric biomaterial for bone regeneration.

Bone loss can occur as a result of various pathologies, traumas and injuries and poor bone healing leads to functionally debilitating condition, loss of self-sufficiency and deterioration in life quality. Given the increasing incidence of facial trauma and the emergence of new procedural techniques, advanced scaffolds are currently developed as substitutes for bone tissue engineering. In this study, we investigated the capability of a chemically cross-linked ε-caprolactone-based poly(ester-urethane-urea) (PCLU) scaffold to support bone regeneration. In vitro assays demonstrated that PCLU scaffolds could be colonized by cells through direct cell seeding and cell migration from outside to scaffold inside. Moreover, PCLU scaffolds could provide a suitable environment for stem cells proliferation in a 3D spatial arrangement, and allowed osteogenic differentiation under appropriate induction. In vivo results revealed the osteogenic properties of PCLU scaffolds through a drilled-hole femoral bone defect repair improvement in rats. Using histology and microtomography analysis, we showed that PCLU scaffolds fit well the bone cavity and were eventually entrapped between the newly formed trabeculae. Finally, no sign of inflammation or rejection was noticed. We envision that PCLU scaffolds can provide the clinicians with a substitute having appropriate characteristics for the treatment of bone defects.

Electrospun Poly(ε-caprolactone) Fiber Scaffolds Functionalized by the Covalent Grafting of a Bioactive Polymer: Surface Characterization and Influence on in Vitro Biological Response.

The purpose of this study is to present the poly(caprolactone) (PCL) functionalization by the covalent grafting of poly(sodium styrene sulfonate) on electrospun scaffolds using the "grafting from" technique and evaluate the effect of the coating and surface wettability on the biological response. The "grafting from" technique required energy (thermal or UV) to induce the decomposition of the PCL (hydro)peroxides and generate radicals able to initiate the polymerization of NaSS. In addition, UV irradiation was used to initiate the radical polymerization of NaSS directly from the surface (UV direct "grafting from"). The interest of these two techniques is their easiness, the reduction of the number of process steps, and its applicability to the industry. The selected parameters allow controlling the grafting rate (i.e., degree of functionalization). The aim of the study was to compare two covalent grafting in terms of surface functionalization and hydrophilicity and their effect on the in vitro biological responses of fibroblasts. The achieved results showed the influence of the sulfonate functional groups on the cell response. In addition, outcomes highlighted that the UV direct "grafting from" method allows to moderate the amount of sulfonate groups and the surface hydrophilicity presents a considerable interest for covalently immobilizing bioactive polymers onto electrospun scaffolds designed for tissue engineering applications using efficient post-electrospinning chemical modification.

The Use of Platelet-Rich Plasma to Promote Cell Recruitment into Low-Molecular-Weight Fucoidan-Functionalized Poly(Ester-Urea-Urethane) Scaffolds for Soft-Tissue Engineering.

Due to their elastomeric behavior, polyurethane-based scaffolds can find various applications in soft-tissue engineering. However, their relatively inert surface has to be modified in order to improve cell colonization and control cell fate. The present study focuses on porous biodegradable scaffolds based on poly(ester-urea-urethane), functionalized concomitantly to the scaffold elaboration with low-molecular-weight (LMW) fucoidan; and their bio-activation with platelet rich plasma (PRP) formulations with the aim to promote cell response. The LMW fucoidan-functionalization was obtained in a very homogeneous way, and was stable after the scaffold sterilization and incubation in phosphate-buffered saline. Biomolecules from PRP readily penetrated into the functionalized scaffold, leading to a biological frame on the pore walls. Preliminary in vitro assays were assessed to demonstrate the improvement of scaffold behavior towards cell response. The scaffold bio-activation drastically improved cell migration. Moreover, cells interacted with all pore sides into the bio-activated scaffold forming cell bridges across pores. Our work brought out an easy and versatile way of developing functionalized and bio-activated elastomeric poly(ester-urea-urethane) scaffolds with a better cell response.

Characterization of elastomeric scaffolds developed for tissue engineering applications by compression and nanoindentation tests, µ-Raman and µ-Brillouin spectroscopies.

In tissue engineering, porous biodegradable scaffolds are developed with morphological, chemical and mechanical properties to promote cell response. Therefore, the scaffold characterization at a (sub)micrometer and (bio)molecular level is paramount since cells are sensitive to the chemical signals, the rigidity, and the spatial structuring of their microenvironment. In addition to the analysis at room temperature by conventional quasi-static (0.1-45 Hz) mechanical tests, the ultrasonic (10 MHz) and µ-Brillouin inelastic light scattering (13 GHz) were used in this study to assess the dynamical viscoelastic parameters at different frequencies of elastomeric scaffolds. Time-temperature superposition principle was used to increase the high frequency interval (100 MHz-100 THz) of Brillouin experiments providing a mean to analyse the viscoelastic behavior with the fractional derivative viscoelastic model. Moreover, the µ-Raman analysis carried out simultaneously during the µ-Brillouin experiment, gave the local chemical composition.