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.

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.

The Role of Mechanical Properties and Structure of Type I Collagen Hydrogels on Colorectal Cancer Cell Migration.

Mechanical interactions between cells and their microenvironment play an important role in determining cell fate, which is particularly relevant in metastasis, a process where cells invade tissue matrices with different mechanical properties. In vitro, type I collagen hydrogels have been commonly used for modeling the microenvironment due to its ubiquity in the human body. In this work, the combined influence of the stiffness of these hydrogels and their ultrastructure on the migration patterns of HCT-116 and HT-29 spheroids are analyzed. For this, six different types of pure type I collagen hydrogels by changing the collagen concentration and the gelation temperature are prepared. The stiffness of each sample is measured and its ultrastructure is characterized. Cell migration studies are then performed by seeding the spheroids in three different spatial conditions. It is shown that changes in the aforementioned parameters lead to differences in the mechanical stiffness of the matrices as well as the ultrastructure. These differences, in turn, lead to distinct cell migration patterns of HCT-116 and HT-29 spheroids in either of the spatial conditions tested. Based on these results, it is concluded that the stiffness and the ultrastructural organization of the matrix can actively modulate cell migration behavior in colorectal cancer spheroids.

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. Therefore, the present review article presents a conceptual framework that summarizes the anatomical, molecular structure and biochemical properties of hyaline cartilage located in long bones: articular cartilage and growth plate. Moreover, the importance of preparation and application of hyaluronic acid - gelatin hydrogels for cartilage tissue engineering are included. Hydrogels possess benefits of stimulating the production of Agc1, Col2α1-IIa, and SOX9, molecules important for the synthesis and composition of the extracellular matrix of cartilage. Accordingly, they are believed to be promising biomaterials of therapeutic alternatives to treat cartilage damage.

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 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.

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 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.

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.

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.

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.

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. In fact, there is a lack of evidence regarding the calculation and distribution when biophysical stimuli are applied. This protocol is focused on the design and manufacture of devices to generate EFs and MFs and implementation of a computational methodology to predict biophysical stimuli distribution inside and outside of biological samples. The EF device was composed of two parallel stainless-steel electrodes located at the top and bottom of biological cultures. Electrodes were connected to an oscillator to generate voltages (50, 100, 150 and 200 Vp-p) at 60 kHz. The MF device was composed of a coil, which was energized with a transformer to generate a current (1 A) and voltage (6 V) at 60 Hz. A polymethyl methacrylate support was built to locate the biological cultures in the middle of the coil. The computational simulation elucidated the homogeneous distribution of EFs and MFs inside and outside of biological tissues. This computational model is a promising tool that can modify parameters such as voltages, frequencies, tissue morphologies, well plate types, electrodes and coil size to estimate the EFs and MFs to achieve a cellular response.

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.

Multiple regression analysis predicts the dynamic of chondrocytes stimulated by magnetic and electric fields.

PURPOSE: The aim of this study was to implement a multiple regression analysis to find mathematical models that estimate the proliferative rate and the molecular synthesis of chondrocytes when these cells are stimulated either by magnetic or electric fields. METHODS: Data derived from previous studies performed in our laboratory were used for statistical analyses, which consisted of applying magnetic fields (1 and 2 mT) and electric fields (4 and 8 mV/cm) to chondrocytes. Data from cell proliferation and glycosaminoglycan expression were used to adjust and to validate each mathematical model. RESULTS: The root square model efficiently predicted the chondrocyte dynamics, evidencing determination coefficients of R² = 92.04 for proliferation and R² = 70.95 for glycosaminoglycans when magnetic fields were applied, and R² = 88.19 for proliferation and R² = 74.79 for glycosaminoglycans when electric fields were applied. CONCLUSIONS: The reduced, interactive, quadratic and combined models exhibited lower R2 values, nevertheless, they were useful to predict proliferation and glycosaminoglycan synthesis, as the right-skewed distribution, determined by the F parameter, evidenced a Frejected < Fcomputed. The models are efficient since the prediction of chondrocyte dynamics is comparable to the cell growth and to the molecular synthesis observed experimentally. This novel formulation may be dynamic because the variables that fit the models may be modified to improve in vitro procedures focused on cartilage recovery.

Effect of umbilical cord length on early fetal biomechanics.

The umbilical cord suspends the fetus within the amniotic cavity, where fetal dynamics is one of its many functions. Hence, the umbilical cord is a viable index in determining fetal activity. Fetal movements result in mechanical loads that are fundamental for fetal growth. At present, mechanical environment during early human fetal development is still largely unknown. To determine early fetal movement dynamics at given physiological (0.060 m) and pathological umbilical cord lengths (0.030 m, 0.020 m, 0.017 m and 0.014 m) a 2D computational model was created to simulate dynamic movement conditions. Main findings of this computational model revealed the shortest umbilical cord length (0.014 m) with a 6(10-6)N, twitch force amplitude had a two-fold increase on linear velocity (0.12 m/s) in comparison with other lengths (0.05m/s). Moreover, umbilical cord length effect presented an increasing exponential tension on the fetus body wall from longest to shortest, from 0 N in the control length to 0.05 N for the shortest umbilical cord. Last, tension was always present over a period of time for the shortest cord (0.03 N to 0.08 N). Collectively, for all variables evaluated the shortest umbilical cord (0.014 m) presented remarkable differences with other lengths in particular with the second shortest umbilical cord (0.017 m), suggesting a 0.003 m difference represents a greater biomechanical effect. In conclusion, this computational model brings new insights required by clinicians, where the magnitude of these loads could be associated with different pathologies found in the clinic.

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.

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. Mechanical properties of hydrogels were higher if the precursors were dissolved in Calcium-Free Krebs Ringer Buffer (G' = 1141 ± 23 Pa) compared to those diluted in culture media (G' = 213 ± 19 Pa). Cells within stimulated hydrogels were rounder (55%) than non-stimulated cultures (32%) (p = 0.005). Chondrogenic markers such as SOX-9 and aggrecan were higher in stimulated hydrogels compared to controls. The ES demonstrated that normalized content of glycosaminoglycans and collagen to DNA was slightly higher in stimulated samples. Additionally, collagen type II normalized to total collagen was 2.43 times higher in stimulated hydrogels. These findings make ES a promising tool for enhancing articular cartilage tissue engineering outcomes by combining hydrogels and MSCs.

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. In this work, a stimulation device, which produces homogeneous MFs to stimulate cell culture surfaces was designed and manufactured using a computational model. Furthermore, an in vitro culture of primary rat chondrocytes was established and stimulated with two MF schemes to measure both proliferation and ECM synthesis. The best proliferation rate was obtained with an MF of 2 mT applied for 3 h, every 6 h for 8 days. In addition, the increase in the synthesis of glycosaminoglycans was statistically significant when cells were stimulated with an MF of 2 mT applied for 5 h, every 6 h for 8 days. These findings suggest that a stimulation with MFs is a promising tool that could be used to improve in vitro treatments such as autologous chondrocyte implantation, either to increase cell proliferation or stimulate molecular synthesis. Bioelectromagnetics. 2020;41:41-51 © 2019 Bioelectromagnetics Society.

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.