Advances in Computational Modeling of Scaffolds for Bone Tissue Engineering: A Narrative Review of the Current Approaches and Challenges

Abstract

Background/Objectives: The process of designing and fabricating bone tissue engineering scaffolds is a multi-faceted and intricate process. The scaffold is designed to attach cells to the required volume of regeneration to subsequently migrate, grow, differentiate, proliferate, and consequently develop tissue within the scaffold which, in time, will degrade, leaving just the regenerated tissue. The fabrication of tissue scaffolds requires adapting the properties of the scaffolds to mimic, to a large extent, the specific characteristics of each type of bone tissue. However, there are some significant limitations due to the constrained scaffolds’ architecture and structural features that inhibit the optimization of bone scaffolds. Methods: To overcome these shortcomings, new computational approaches for scaffold design have been adopted through currently adopted computational methods such as finite element analysis (FEA), computational fluid dynamics (CFD), and fluid–structure interaction (FSI). Results: This paper presents a narrative review of the state of the art in the field of parametric numerical modeling and computational fluid dynamics geometry-based models used in bone tissue engineering. Computational methods for scaffold design improve the process of constructing scaffolds and contribute to tissue engineering. Conclusions: This paper highlights the benefits of computational methods on employing scaffolds with different architectures and inherent characteristics that can potentially contribute to a favorable environment for hosting cells and predict their behavior and response. By recognizing these benefits, researchers can enhance and optimize scaffold properties for future advancements in tissue engineering research that will lead to more accurate and robust outcomes.

1. Introduction

A bone grafting procedure is one of the most widely utilized procedures for transplanting tissues globally, with over 2.2 million of such procedures conducted each year. Various incidents, including injuries and fractures, can give rise to substantial bone defects, potentially leading to enduring deformities such as diminished bone structure and functionality. The vulnerability of human bones to damage from fractures, diseases, and infections is notable. While bones possess an innate ability to regenerate, cases involving severe defects surpassing their natural healing capabilities underscore the imperative for external interventions [1,2,3].

It is noteworthy that the growth of additive manufacturing is closely associated to the increasing use of computational design for scaffolds. Healthcare and tissue engineering are only two of the fields that use additive manufacturing, also referred to as 3D printing, but they have also been transformed by it. Three-dimensional (3D) scaffolds are essential for bone tissue engineering to facilitate the regeneration of damaged or lost bone tissue [3]. Several 3D porous scaffolds are used in tissue engineering, especially in orthopedic surgery. Bone tissue engineering (BTE) strategies (Figure 1) demonstrate greater potential in replacing damaged bone tissue over more traditional bone grafting methods, such as autografts or allografts [4]. A bone scaffold is a three-dimensional matrix, such as an allograft, that allocates and promotes bone regeneration, cell adhesion, and growth to the scaffold surfaces. The scaffolds are designed to mimic host tissue functions and provide an appropriate environment to host cell proliferation and differentiation, as well as the rebuilding of new healthy tissue. Characteristics such as mechanical, biological, and structural properties are considered to be the most significant features of a scaffold. These properties play a critical role in regulating cellular responses, including cell adherence, spreading, proliferation, and differentiation [5]. Pore structure, such as porosity and pore size, scaffold size, surface structure, and, ultimately, unit cell architecture, are the basic properties for scaffold architecture. The porosity of scaffolds does not only allow cell attachment and growth, but also secures nutrition and metabolite transfer [6].

The first step in designing a 3D scaffold for bone regeneration is to select an appropriate material that can support the growth and differentiation of bone cells, as well as provide mechanical stability and structural integrity [7]. Various materials have been examined for this purpose, including metals, ceramics, polymers, and composites. Each material has its pros and cons, depending on factors such as biocompatibility, degradation rate, mechanical properties, and manufacturing process [8]. Another significant characteristic is that scaffolds consist of an interconnected porous network structure with specific unit cells, which is essential for vascular ingrowth as well as the delivery of oxygen and other nutrients to the cells. Scaffolds are frequently designed to mimic the structure of the naturally occurring extracellular matrix (ECM) in order to attain these features. The unit cell serves as the fundamental building block of a scaffold, and it can be categorized into two types: non-parametric and parametric designs. Non-parametric designs are created based on structural and geometric shapes, while parametric designs require the utilization of specific algorithms for production [9]. The mechanical properties and degradation of the scaffold depend on the material properties and the porosity geometry of its structure, while permeability depends on its structure [10]. The mechanical properties of the scaffold must be close to the properties of the replaced bone tissue to prevent stress shielding. Finally, the degradation rate must be as close as possible to the tissue growth rate to maintain stable properties in the tissue–scaffold complex during the regeneration process [11].

Table 1. Scaffold pore size, porosity, and elastic modulus for different tissue applications [12].

Tissue Type	Pore Size (μm)	Porosity (%)	Elastic Modulus (GPa)
Cancellous bone	500–1000	50–90	0.01–0.5
Cortical bone	<500	3–12	3–30
Cartilage	400	80	0.0007–0.0153

depicts the preferred pore size, porosity, and elastic modulus of scaffolds for bone tissue applications [12,13,14,15]. The immune-mediated bone reconstruction driven by the scaffold can be achieved by loading the cells with immunoregulatory function onto the scaffold [15]. In order to achieve a correlation between different scaffold properties, the scaffold has to be designed and tested using computational methods such as computer-aided design (CAD), finite element analysis (FEA), computational fluid dynamics (CFD), and experiments in vivo.

FEA has been evaluated as a significant tool for computational fluid dynamics and an effective alternative to complex and expensive experimental tests. CFD analysis is utilized to investigate the factors that effectively control the pressure, velocity distribution, and wall shear stress (WSS) of scaffolds, as well as other considerable parameters [16,17,18,19]. Computational methods have played a pivotal role in reducing costs and expediting the design process while tailoring the scaffolds to exhibit desired characteristics. By employing these methods, a significant reduction in experimental time can be achieved, leading to a faster assessment of scaffold properties [19]. Furthermore, the computational methods used for scaffold design not only improve the process of creating scaffolds, but, more importantly, open up new horizons in tissue engineering and provide researchers with a wide and flexible range of choices to design and optimize the scaffolds’ architecture.

Through the significant contribution and role of computational approaches in scaffold design and modeling, in this review, various perspectives from recent studies on their application in bone scaffold modeling are compared. A narrative review of the most current computational approaches used in bone tissue engineering scaffold design is presented in this paper. A narrative review was chosen instead of a systematic review because the field is rapidly evolving and highly interdisciplinary, encompassing a range of modeling methods, materials science, and biology research. The research presented herein includes those addressing the design of different scaffold architectures and the simulation of their mechanical response under fluid flow. Furthermore, in order to provide information on the environment of the bone tissue, the review reports simulation studies on fluid flow in perfusion bioreactors.

2. Applications of Computational Methods in Scaffold Modeling and Design

The recent developments in scaffold design in bone tissue engineering include methods such as computational fluid dynamics (CFD) analysis, structural analysis, and fluid–structure interaction (FSI) analysis. The integration of these methods has the capability to provide a new generation of scaffolds with improved tissue regeneration and clinical performance. This review is limited to articles published between 2016 and 2025 and selected based on their computational approaches. Some of the previously mentioned research conducted from 2009 to 2013 has also been added to provide contrasting background and broaden the scope of the review. To ensure a focused and high-quality narrative review, studies were prioritized based on their relevance to computational modeling in scaffold design for bone tissue engineering. To guarantee thorough coverage, an initial literature search was conducted in the PubMed, Scopus, and Google Scholar databases on different combinations of the following terms: “scaffold,” “bone tissue engineering,” “computational modeling,” “finite element analysis,” “computational fluid dynamics,” “CFD,” “FEA,” and “biomechanics.” The search was restricted to papers published between 2010 and 2025 and preferably English-language, peer-reviewed articles. The inclusion criteria for article selection were (1) the use of computational or simulation techniques for scaffold design or analysis, (2) the demonstration of fluidic or mechanical behavior, and (3) the use of approaches for bone tissue engineering. Excluded were purely experimental studies without computational modeling, or non-bone-tissue-related studies. An overview of the literature selection strategy is summarized in

Table 2. Summary of the literature search and study selection criteria used in this narrative review.

Parameter	Description
Review Type	Narrative review
Databases	PubMed, Scopus, Google Scholar
Search Terms	“scaffold”, “bone tissue engineering”, “computational modeling”, “CFD”, “FEA”, “biomechanics”
Publication Years Covered	2010–2025
Language	English only
Inclusion Criteria	Studies applying computational methods (e.g., FEA, CFD) in scaffold design, analysis, or simulation in bone tissue engineering
Total Studies Considered	92

.

2.1. Simulation of Scaffold Fluidic and Mechanical Properties

In the scientific literature, CFD has been used to simulate and model the movement of fluids within a specific domain and calculate various fluid flow parameters within scaffolds. This is achieved by numerically solving the Navier–Stokes equations and continuity equations, which describe fluid flow behavior. In CFD studies, the fluid flow that is being analyzed typically begins at designated inlet surfaces, passes through the scaffold, and then exits at a defined outlet [20]. The parameters that can be calculated include fluid velocity, pressure, permeability, and WSS [21]. Figure 2 presents a workflow that outlines the complete CFD simulation process. The validity of computational modeling results in scaffold design is highly dependent on proper validation. Several of the studies surveyed validated their CFD and FEA simulations with experimental data to test model accuracy. For example, FEA-predicted mechanical properties (e.g., compressive strength and Young’s modulus) were compared with quasi-static compression or tensile test data, as reported in the work of Yu et al. (2020) [22] and Wang et al. (2021) [23]. Similarly, CFD-simulated permeability and WSS were compared with experimental perfusion bioreactor measurements or falling head permeability tests. Scocozza et al. (2023) [24] conducted experimental compression tests and demonstrated the predictive ability of their finite element simulation through a comparison of structural stiffness. These methods illustrate the quality of experimental validation in simulation-based scaffold design.

Bone scaffold porosity and stiffness play a critical role in the success of critical-size bone defect healing. Bártolo et al. (2013) [25] simulated the fluid behavior inside the scaffolds with different pore sizes and found that a larger pore size leads to a lower difference of shear strain rate and WSS between the outer and inner regions of scaffolds. They attributed this to the decreased difficulty of fluid flow entering the interior region due to the larger pore size. Abraham et al. (2019) [26] performed a fluid flow analysis to determine the fluid behavior of implant scaffolds under fluid flow conditions with different materials and pore shapes. A static structural analysis was used to calculate the stresses and deformations in bone scaffolds when a force was applied on it. Taking into account the static structural loading condition and material comparison, the study indicates that the equivalent stress produced in the pores of the scaffold model plays an important role in the selection of the material. In addition, the study of Deng et al. (2021) [27], based on computational fluid dynamics analysis, used four common porous scaffolds with a porosity 65% and a pore size of approximately 650 μm but with different architecture. The permeability, velocity, and flow trajectory inside the scaffold structure were calculated. They depicted the fluid trajectories inside the four different scaffold structures, which were analyzed through CFD analysis. Among the four structures, the DIA structure exhibits low internal flow rates and internal flow speeds allowing cells to attach more easily to the surface of the scaffold, thus promoting bone growth. They concluded that the internal fluid velocity of the diamond structure is the smallest, and the trajectory of fluid flow inside the scaffold is the longest, which is beneficial for blood vessel growth, nutrient transport, and bone formation. Moreover, Gomez et al. (2016) [28] used the Voronoi method to design new 3D porous scaffolds. The fluid flow calculation was performed in Rhinoceros 3D after the Boolean subtraction of the scaffold geometry from the volume of interest. The CFD analysis of the scaffolds was conducted with a laminar flow and a steady Navier–Stokes model. The authors used linear FEA to investigate the scaffold properties, with a modeling assumption that the scaffold material behaves in a linear manner, which may not accurately capture non-linear material behaviors under realistic conditions. This assumption could be considered a limitation of their study. The results showed that the final properties of the scaffolds can be controlled during the initial design of their microstructure. It was also demonstrated that these properties can be further adjusted during the design stage to closely match those of natural trabecular bone. The calculated average permeability values indicate isotropic behavior across the scaffold models, with an observed increase in permeability correlating with higher porosity levels within each respective scaffold model.

Moreover, current studies have also investigated how the surface roughness influences the fluidic properties of a given scaffold. Ali et al. (2018) [29] investigated how surface roughness affects bone scaffold permeability and fluid-flow-induced WSS using CFD analysis. This study was conducted to address the limitation of most numerical models that treat blood as a simplified Newtonian fluid, despite it being a non-Newtonian fluid. The research establishes a clear distinction between these models, with the non-Newtonian model showing significantly lower permeability and higher WSS. These findings highlight the importance of conducting further numerical studies using a non-Newtonian blood model in designing tissue engineering scaffolds. Additionally, regarding the impact of surface roughness on permeability and WSS, it was observed that surface roughness had a minimal effect on permeability compared to pore sizes. However, in scaffolds with the smallest pore sizes (300 µm), surface roughness had a significant impact on permeability. On the other hand, surface roughness had a more substantial effect on WSS. In scaffolds with larger pore sizes, rough surfaces promoted favorable conditions for cell attachment. However, in scaffolds with smaller pores, rough surfaces led to channel occlusion, hindering cell differentiation and proliferation. Liu et al. (2020) [30] investigated the effect of the meso-structure on scaffolds’ mechanical and transport properties using FEA and CFD. They found that the gradient (G) and gradient and staggered (GS) meso-structure designs led to a higher scaffold permeability, to a more homogeneous flow inside the scaffold, and to a lower wall shear stress (WSS) in comparison with the basic (B) meso-structure design. Their CFD results demonstrated that the meso-structure influenced the scaffold’s permeability, as well as the distribution of flow-induced WSS and velocity. While the design parameters had delicate influences on WSS and flow velocity, the scaffold permeability is only determined by the porosity. Given a fixed pressure drop over the scaffold, the porosity determines the flow rate through the scaffold, and thus also the permeability, which is affected to some degree by the ratio between the flow rate and the pressure drop. Another approach to determine the scaffold permeability and WSS is presented by Ali et al. (2017) [31]. Six levels of porosity (65%, 70%, 75%, 80%, 85%, and 90%) were assigned to the scaffold architectures, and 12 models were developed. The scaffold model was enclosed in a domain where a unidirectional flow was passing through with a defined inlet and outlet flow rate or pressure. Scaffold deformation under static loading, compressive strength based on von Mises criteria, pressure drop, and fluid-flow-induced WSS in the scaffolds were also determined by finite element analysis. In all scaffold types, models with higher porosity exhibited lower mechanical properties. Under the same porosity, the lattice-based scaffolds exhibited a Young’s modulus and a compressive strength higher than those achieved by the gyroid scaffolds and exhibited higher permeability and lower WSS than the gyroid models. Liu et al. (2024) [32] explored the use of auxetic structures in bone scaffolds, focusing on their influence on mechanical behavior and shear stress during deformation. Using finite element modeling, the authors analyzed how negative Poisson’s ratio designs affect mass transport and wall shear stress under compression. Their findings indicate that auxetic scaffolds can enhance stress distribution and fluid flow, potentially promoting more effective bone tissue formation compared to conventional designs. Another study by Channasanon et al. (2024) [33] investigated how different scaffold geometries influence bone cell differentiation and proliferation within a dynamic perfusion bioreactor. Three distinct scaffold designs (Woodpile, LC-1000, and LC-1400) were fabricated and analyzed. Computational fluid dynamics (CFD) simulations were employed to predict fluid flow and WSS, which were found to significantly affect osteogenic responses. The study concluded that the LC-1000 scaffold had the optimal balance of flow shear stress and permeability, promoting the highest levels of calcium deposition and osteogenic differentiation over 21 days. Deng et al. (2025) [34] also investigated the role of pore architecture in scaffold design for bone tissue engineering. The authors developed gradient porous scaffolds using additive manufacturing and evaluated their influence on mass transport, mechanical integrity, and biological compatibility. By varying the porosity gradients, they demonstrated improved mechanical performance and nutrient diffusion while maintaining scaffold stability. The study concluded that optimized gradient porosity can significantly enhance scaffold functionality for bone regeneration applications. The study by Jusoh et al. (2022) [35] gives more insights on how the variations in pore sizes significantly affect the scaffold permeability. In this study, the permeability of hexagonal unit cells at different pore sizes and at different inlet velocities was simulated using CFD analysis. The results showed that as the pore diameter of the unit cell decreases, the pressure drop from the inlet to the outlet increases. Conversely, increasing the flow velocity, a greater pressure drop across the unit cell is observed. The pressure drops at the three different inlet velocities were 1.40 × 10⁻⁴ Pa, 7.02 × 10⁻² Pa, and 1.41 × 10⁻¹ Pa, respectively, for a 1.0mm pore size. They also calculated the permeability for each unit cell, and based on the upper limit of human bone permeability, the value of the parameter of permeability was inside the range. The variation in velocities did not affect the permeability of the scaffold. However, the difference in pore sizes affected the scaffold permeability. The permeability values for pore sizes of 1.0 mm, 1.5 mm, and 2.0 mm were 2.900 × 10⁻⁸ m², 4.863 × 10⁻⁸ m², and 8.529 × 10⁻⁸ m², respectively, with a flow rate of 0.001 mm/s.

Compressive strength and Young’s modulus are the mechanical properties that are regularly assessed in a scaffold. For any scaffold intended for in vivo use, it is crucial to possess suitable compressive strength and Young’s modulus to provide the necessary mechanical support [36]. Yu et al. (2020) [22] investigated the compressive and tensile properties of porous scaffolds using quasi-static compression and tensile tests, respectively, in three different types of porous Ti64 scaffolds with the same porosity (65%). The deformation behaviors of porous structures were analyzed using finite element analysis (FEA) simulation at different compression strains and loading conditions. The results of this study show that gyroid scaffolds have the highest compressive strength and tensile strength at 392.1 MPa and 321.3 MPa, respectively, almost two times higher than that of body-centered cubic (BCC) scaffolds. The permeability of the scaffolds was measured using the falling head method and compared with the results from the computational fluid dynamics simulations. The outcomes demonstrated that the gyroid scaffolds’ permeability was almost 20% less than that of the BCC scaffolds. A study by Wang et al. (2021) [23] included a more thorough approach to the overall process of creating a honeycomb scaffold structure and used the static compression test to evaluate the properties and permeability of each group of scaffolds, matched to the characteristics of human bone tissue. The model was placed between an upper and a lower steel plate. The lower steel plate was fixed, which imposed fixed constraints on the whole lower surface, and the upper steel plate was a movable steel plate, which played the role of loading. From the mechanical compression experiment, it was found that the shape of the scaffold is about 6% in a complete compression process. Therefore, in the process of simulation, they applied the same displacement deformation to the scaffold. Scocozza et al. (2023) [24] presented a validated computational framework to support the design of hybrid scaffolds. They conducted a structural FEA of the hybrid scaffold under compression by comparing the numerical results with the corresponding experimental data. The impact of alginate inclusion and infill pattern on scaffold stiffness was investigated. In this study, Ferguson et al. (2025) [37] developed a biomimetic scaffold combining hard and soft phases with a gradient irregular pore structure to replicate the mechanical and biological characteristics of natural bone. The scaffold was fabricated using a hybrid 3D printing approach and tested for structural integrity, porosity, and in vitro biocompatibility. The results showed improved mechanical performance and favorable cell proliferation, indicating the scaffold’s potential for effective bone repair and regeneration. Temiz et al. (2022) [38] developed a biodegradable structure with a gyroid-type triply periodic minimal surface (TPMS) to generate a porous framework. Comparative compression tests were conducted on the resulting gyroid structure and on sheep bone. Additionally, a finite element model of the gyroid structure was developed using ANSYS (NASDAQ 2022 R1, ANSYS Inc., Canonsburg, PA, USA). According to the results obtained from the FEA, when the circular cross-sectional beam model was examined, the fractures were seen to start in the inner regions. The circular cross-sectional beam model exhibited less bending of the cell walls and outward convexity in the central part compared to the results of the FEA gyroid model. The study of Ye et al. (2025) [39] focuses on the fabrication and mechanical characterization of 3D-printed titanium scaffolds with hierarchical porous structures for bone regeneration. The researchers used a combined experimental and numerical approach to analyze how micro- and macro-pore integration affects mechanical strength and biological viability. The results showed that the hierarchical design improved load-bearing capacity while ensuring sufficient permeability for cell ingrowth, highlighting its potential for orthopedic implant applications. Shahid et al. (2024) [40] focused on evaluating the fluid dynamics of triply periodic minimal surface (TPMS)-based scaffolds, specifically comparing diamond and gyroid structures with varying porosity levels (50–80%). The study employed CFD to analyze the pressure, velocity distribution, permeability, and WSS within the scaffolds. The CFD results revealed that as the porosity increases, the pressure drop decreases in both scaffold types, with the diamond structure showing a higher pressure drop compared to the gyroid due to its more complex geometry and higher stiffness. Permeability increased with porosity, and gyroid structures exhibited better permeability than diamond structures, making them more favorable for nutrient transport and waste removal. The wall shear stress (WSS) decreased as the porosity increased, with gyroid structures showing higher WSS than diamond structures, which could have implications for cell proliferation and tissue regeneration.

The study by Yang et al. (2024) [41] explored the design and mechanical behavior of porous titanium scaffolds intended for bone defect repair. The study employed FEA to simulate and optimize the mechanical properties, particularly the elastic modulus, of scaffolds with varying strut lengths and cross-section diameters. Using the ANSYS Workbench (NASDAQ), the FEA simulations provided insights into how different geometries of scaffold units (such as tetrahedral, octahedral, and inverted-V structures) influence the strength and stiffness of the scaffold. By applying pressures ranging from 3 to 10 MPa, the elastic modulus for each scaffold design was calculated, demonstrating how porosity and rod dimensions impact overall mechanical performance. The FEA models helped determine that the regular tetrahedral structure achieved the highest compressive strength while maintaining a balance between porosity and stiffness. Additionally, the simulations showed that the scaffolds could be optimized for specific applications, such as a femoral implant, by adjusting parameters like rod length and diameter, resulting in a calculated elastic modulus that closely matches the mechanical properties of human bone. In another study, Shuai Ma et al. (2019) [42] employed numerical analysis methods to investigate the mechanical behaviors and mass transport properties of gyroid-based scaffolds. The study utilized computational simulations to assess the structural reliability and the characteristics of these biomimetic scaffolds, providing valuable insights into their potential applications in bone tissue engineering. The outcomes derived from their CFD simulations indicated that gyroid structures exhibit favorable fluidic characteristics, resulting in enhanced fluid flow within the central region of the channel. This accelerated fluid movement proves beneficial for the efficient transport of nutrients, highlighting the suitability of gyroid structures for facilitating nutrient transportation. Moreover, Montazerian et al. (2017) [43] performed FEA and CFD simulations for a group of TPMS-based unitary structural units to investigate the role of pore characteristics in determining the normalized stiffness, strength, and permeability values. Numerical models revealed that the highest elastic properties and permeability were observed at an approximately 30% relative design density, which has previously been shown to be desirable for cell penetration in bone tissue engineering.

Naghieh et al. (2016) [44] developed a finite element model to predict the elastic mechanical response of porous polymeric bone scaffold fabricated by the fused deposition modeling process. Their aim was to predict the mechanical response of the fabricated bone scaffold to generate parametric finite elements through the ABAQUS 6.11-1 (Dassault Systèmes). The numerical calculated modulus of elasticity of the scaffold bone was about 213.21 MPa, which was around 16.11% higher than that obtained experimentally. This indicates that the model that was developed could predict the elastic modulus of post-heated bone scaffolds more accurately compared to the fabricated ones. Rosa et al. (2023) [45] determined the mechanical properties of a composite scaffold material, and 3D-printed structures were analyzed using computer simulations. The evaluation of the elastic mechanical properties of the composite materials was achieved by validating the finite element models against the experimental results from the two types of 3D-printed scaffold models. Scaffolds were modeled using linear quadratic elements. From the results obtained in this paper, by considering simultaneously the morphology of the scaffolds, their mechanical behavior, and the mechanical stimulus, it was concluded that two types of the designed scaffolds had the highest potential for bone replacement and regeneration. Furthermore, in the study by Uth et al. (2017) [46] conducted to validate CAD scaffold design, COMSOL Multiphysics software (COMSOL, v5.6, AB, Stockholm, Sweden) was used to optimize the topology of scaffolds made of PLGA–nHA–collagen. The results of the numerical optimization were compared to an optimized statistical model generated via a designed experiment (DE). It was hypothesized that both the experimental (DE) and COMSOL (FE) models should result in similar optimal topologies. Both models were expected to yield an optimal topology within the design space while satisfying the recommended porosity for use in (trabecular) bone regeneration. A compressive modulus of 10 MPa was targeted in this study and seven 30% nHA scaffolds were printed to validate the predictions of the DE and COMSOL models. Moreover, Page et al. (2021) [47] characterized the mechanical behavior of a common fibrin hydrogel and implemented this hydrogel as the composite matrix material within their previously developed model. A compressible second-order reduced polynomial hyperelastic model gave the best fit to the experimental data. However, the boundary conditions did exhibit an appreciable influence on ROI mechanics for a two-bilayer unit cell. In general, the constructed unit cell model enables the simulation of the mechanical conditions experienced by a cell-containing hydrogel within a tissue engineering scaffold when subjected to predetermined loads. Furthermore, Almeida et al. (2013) [48] presented a numerical simulation strategy to study the compressive behavior of scaffolds with different pore sizes. Two models were used at once, with a linear elastic behavior model for small strains within the elastic region, and a compressible foam behavior model for the high strains in the plastic region. The results revealed that as the pore size increases, the compressive strength of the scaffold decreases. Additionally, they noted that the numerical model cannot accurately predict the compaction phenomenon, leading to a minor difference between the numerical predictions and the experimental findings observed in the compression test results.

In contrast, Liang et al. (2019) [49] primarily focused on investigating the in vitro structural mechanics of 3D-printed scaffolds. They integrate various methodologies to characterize the mechanical properties of porous scaffolds, which could significantly influence the design and potential clinical applications of such scaffolds in replacing, repairing, or regenerating load-bearing tissues. The finite element method was used to determine the theoretical compressive singularities of computer-aided design scaffold models with square, hexagonal, and wheeled structures. Compression was applied with the confinement region and loading region being the bottom surface and the top surface of the cylindrical scaffold, respectively. The loading force was 500 N. Under those forces, the scaffold models were loaded within the linear elastic region. The findings were illustrated schematically, and a nephogram of stress distribution was depicted using various pseudo colors to represent different stress intensities. Across scaffold models featuring square, hexagonal, and orbital structures, predominantly high stress intensity was observed, suggesting a generally homogeneous transmission of stress within these structures. A numerical investigation by Geng et al. (2025) [50] evaluated auxetic scaffolds—structures with a negative Poisson’s ratio—and their ability to generate fluid flow and shear stress under mechanical deformation. Using fluid–structure interaction models, the study quantified the internal wall shear stress and transport efficiency as the scaffold undergoes compression. They concluded that auxetic scaffolds provide a mechanically responsive environment that enhances biophysical cues such as shear stress, which are beneficial for bone cell stimulation and tissue ingrowth.

Perier-Metz et al. (2021) [51] used computational modeling to investigate the mechanobiological principles behind scaffold-guided bone regeneration and the influence of scaffold design on the regeneration process. The predictions of the computational model were compared with experimental data from the regeneration of large bone defects in sheep. They identified three main key factors in scaffold-driven regeneration: (a) the scaffold surface direction of cell migration, (b) tissue formation processes, and (c) the stimulation of progenitor cell activity by the composition of the scaffold material. The study revealed that a reduced scaffold surface area to volume ratio is advantageous for bone regeneration as it facilitates enhanced cell migration. Gupta et al. (2025) [52] proposed a data-driven approach for scaffold design using deep learning and topological optimization. The researchers trained a neural network model on simulation data to predict scaffold performance under varying design parameters. Integrating this with a topology optimization framework, they generated novel scaffold designs tailored for optimal stress distribution and permeability. The approach demonstrates strong potential for accelerating scaffold development through AI-assisted, performance-guided design pipelines. Gortsas et al. (2022) [53] presented their findings by numerically assessing two distinct fields developed within the bodies of two compressed scaffolds. These fields appear to be conducive to facilitating cell detecting and enhancing cell viability and seeding. These two fields concern the surface octahedral strains that the cells attached to the scaffold can experience and the internal strain gradients that create electrical pathways due to the flexoelectric phenomenon. Both surface octahedral strains and strain gradient fields have been evaluated for 0/90 and 0/90 offset scaffolds. In their results, higher displacements appeared on the 0/90 offset scaffold. This was obviously due to the supporting columns at the crossing points of the 0/90 scaffold and the structural bending occurring on the suspended filaments of the 0/90 offset scaffold. In the study by Drakoulas et al. (2024) [54], a full computational model was developed to simulate the mechanical and fluidic behavior of a multilayered PLA–steel composite scaffold in bending and fluid flow. Surface shear strain and wall shear stress were calculated and incorporated into a mechanobioregulatory model with boundary element and finite volume methods to simulate early-stage cell differentiation. To reduce computational cost, a machine learning-based reduced-order model (ROM) was introduced to enable fast simulations and support sensitivity analysis and optimization. The results highlighted the dominance of fluid-induced stresses on cell behavior and demonstrated the effectiveness of ROMs for scaffold design optimization.

Table 3. Summary of reviewed studies on the simulation of scaffold properties.

Study	Methodology	Outcome
Bártolo et al. (2013) [25]	CFD simulations were used to analyze fluid behavior in scaffolds with different pore sizes, focusing on shear strain rate and wall shear stress (WSS).	Larger pore sizes resulted in a smaller difference in shear strain rate and WSS between the scaffold’s outer and inner regions, improving fluid flow toward the center.
Abraham et al. (2019) [26]	Fluid flow and static structural analysis using CFD and FEA. Compared scaffold materials and pore shapes under static loading.	Equivalent stress in scaffold pores was identified as a critical factor for material selection; mechanical behavior varied with shape and material.
Deng et al. (2021) [27]	CFD analysis on four scaffold architectures with the same porosity (65%) and pore size (~650 µm). Measured permeability, velocity, and flow trajectory.	Diamond (DIA) structure had the slowest internal flow and longest fluid path, enhancing cell attachment, nutrient transport, and bone formation.
Gomez et al. (2016) [28]	Used Voronoi method to design 3D scaffolds, simulated fluid flow with Rhinoceros 3D and steady Navier–Stokes CFD model. Linear FEA applied for scaffold analysis.	Scaffold properties could be tailored at the design stage to mimic natural bone; higher porosity correlated with increased permeability and isotropic behavior.
Ali et al. (2018) [29]	CFD analysis of fluid flow and WSS with varying surface roughness; compared Newtonian vs. non-Newtonian blood models.	Non-Newtonian modeling showed lower permeability and higher WSS; roughness had minimal impact on permeability but significantly influenced WSS, especially in small-pore scaffolds.
Liu et al. (2020) [30]	Used FEA and CFD to study the effect of meso-structure designs (Basic, Gradient, Gradient-Staggered) on mechanical and transport properties.	Gradient and Gradient-Staggered structures showed higher permeability, more uniform flow, and lower WSS. Porosity was the main determinant of permeability.
Ali et al. (2017) [31]	Created 12 scaffold models with varying (65–90 porosity %) and analyzed them using FEA to assess deformation, compressive strength, pressure drop, and WSS.	Higher porosity decreased mechanical strength. Lattice scaffolds had better mechanical properties and permeability but lower WSS than gyroid scaffolds.
Liu et al. (2024) [32]	Designed radial gradient scaffolds using a tree-like fractal model and dual-material 3D printing. Characterized mechanical strength and tested biocompatibility in vitro and in vivo.	Gradient scaffolds showed improved strength (1.00 ± 0.19 MPa), supported cell proliferation, and had good biocompatibility.
Channasanon et al. (2024) [33]	Fabricated three scaffold designs (Woodpile, LC-1000, LC-1400) and used CFD to assess fluid flow and WSS in a dynamic perfusion bioreactor.	LC-1000 scaffold had optimal balance of WSS and permeability, resulting in the highest calcium deposition and osteogenic differentiation over 21 days.
Deng et al. (2025) [34]	Used Voronoi algorithm to generate conformal scaffold geometries. Fabricated using Ti6Al4V and tested via mechanical, CFD, and geometric evaluations.	Voronoi scaffolds had optimal WSS distribution, better mass transport, and matched bone mechanical properties.
Jusoh et al. (2022) [35]	CFD simulation of hexagonal unit cells with various pore sizes and inlet velocities to measure pressure drop and permeability.	Permeability increased with pore size but was minimally affected by flow velocity. Pressure drop increased with velocity and smaller pores.
Yu et al. (2020) [22]	Mechanical tests (compression and tensile) combined with FEA simulation; compared three porous Ti64 scaffolds with same porosity (65%).	Gyroid scaffolds had highest mechanical strength (392.1 MPa compressive, 321.3 MPa tensile), but ~20% lower permeability than BCC scaffolds.
Wang et al. (2021) [23]	Designed honeycomb scaffold structures; used static compression tests and simulations applying displacement deformation to match experimental setup.	Found ~6% deformation under full compression. Scaffold properties were aligned with human bone characteristics.
Scocozza et al. (2023) [24]	Developed a validated computational framework using FEA to analyze hybrid scaffolds under compression and compared with experimental data.	Alginate inclusion and infill pattern significantly affected scaffold stiffness; simulations matched experimental behavior well.
Ferguson et al. (2025) [37]	Employed multi-objective optimization on TPMS structures (Schwarz P) to enhance mechanobiological stimulation and permeability.	Optimized scaffold improved bone ingrowth by 18.5% and balanced stimulus with transport properties.
Temiz et al. (2022) [38]	Fabricated gyroid-type TPMS biodegradable scaffolds; compared mechanical behavior using compression tests and FEA (ANSYS).	FEA showed fractures starting in inner regions. Circular beam models showed less wall bending and more central stiffness than other configurations.
Ye et al. (2025) [39]	Created gradient scaffolds by combining pore geometry variations. Conducted CFD and mechanical testing to evaluate shear stress and flow.	Gradient scaffolds showed controlled increases in shear stress and velocity, supporting region-specific cell response.
Shahid et al. (2024) [40]	CFD study comparing diamond and gyroid TPMS scaffolds with porosities from 50–80%; analyzed pressure, velocity, permeability, and WSS.	As porosity increased, permeability increased and pressure drop decreased. Gyroid had higher permeability and WSS, suggesting better nutrient transport but differing cellular responses.
Yang et al. (2024) [41]	FEA in ANSYS to simulate and optimize porous titanium scaffold geometries (tetrahedral, octahedral, inverted-V) for bone repair.	Regular tetrahedral structure provided highest compressive strength and elastic modulus. Geometries could be tuned to mimic bone for implants.
Shuai Ma et al. (2019) [42]	Employed CFD and structural simulations to analyze gyroid-based scaffolds’ mechanical behaviors and mass transport properties.	Gyroid structures showed favorable fluid dynamics, with enhanced central fluid flow, improving nutrient transport efficiency.
Montazerian et al. (2017) [43]	Performed FEA and CFD on TPMS-based unit structures to assess stiffness, strength, and permeability across pore designs.	At ~30% design density, scaffolds exhibited optimal elastic properties and permeability, supporting effective cell penetration for tissue engineering.
Naghieh et al. (2016) [44]	Used FEA (ABAQUS) to model elastic mechanical response of polymeric bone scaffolds fabricated via fused deposition modeling.	Numerically predicted elastic modulus (213.21 MPa) was ~16% higher than experimental, showing strong correlation and model accuracy.
Rosa et al. (2023) [45]	Simulated mechanical properties of 3D printed composite scaffolds using linear quadratic FEA, validated against experiments.	Identified two scaffold types with high potential for bone regeneration, combining optimal morphology and mechanical behavior.
Uth et al. (2017) [46]	Used COMSOL Multiphysics and design of experiments (DE) to optimize scaffold topology (PLGA-nHA-collagen); validated with printed scaffolds.	Both COMSOL and DE predicted similar topologies. Aimed for 10 MPa compressive modulus; 30% nHA scaffolds matched predictions closely.
Page et al. (2021) [47]	Characterized mechanical behavior of fibrin hydrogel using experimental data and hyperelastic modeling; implemented within a unit cell scaffold model.	A second-order reduced polynomial hyperelastic model best fit the data. Boundary conditions influenced mechanical response, enabling accurate simulation of cell environments in scaffolds.
Almeida et al. (2013) [48]	Numerical simulation using linear elastic and compressible foam models to study scaffold compressive behavior at various pore sizes.	Larger pores decreased compressive strength. The model could not fully capture compaction, causing slight differences from experimental data.
Liang et al. (2019) [49]	Combined FEA and compression testing of 3D-printed scaffolds with square, hexagonal, and wheeled geometries under 500 N load.	All designs exhibited mostly homogeneous stress distribution. High-stress regions were visualized using stress nephograms, confirming structural robustness.
Geng et al. (2025) [50]	Simulated mass transport and WSS in deforming auxetic scaffolds using FEA and transient CFD.	Deformation enhanced local flow and shifted WSS distribution, suggesting dynamic control of mechanical cues.
Perier-Metz et al. (2021) [51]	Computational modeling to analyze scaffold-guided bone regeneration; compared simulation results to experimental data from sheep bone defects.	Identified key regeneration factors: scaffold surface direction, tissue formation, and progenitor cell stimulation. Lower surface-to-volume ratio improved cell migration and regeneration.
Gupta et. al. (2025) [52]	Analyzed gyroid scaffolds with CFD under non-Newtonian perfusion to find optimal pore and strut dimensions.	Identified pore/strut combo (~600/200 µm) that balanced permeability and osteogenic WSS (~35 mPa).
Gortsas et al. (2022) [53]	Numerical evaluation of strain fields in two scaffold designs (0/90 and 0/90 offset) under compression to study mechanobiological effects.	0/90 offset scaffold showed higher displacement due to bending and support column arrangement. Strain gradients linked to enhanced cell seeding and viability.
Drakoulas et al. (2024) [54]	Developed a computational framework combining FEA, fluid dynamics, and a mechanobioregulatory model to simulate scaffold-induced cell differentiation. Implemented a machine learning-based reduced-order model for efficient optimization	Fluid-induced stresses had a dominant role in guiding early cell differentiation. The ROM significantly reduced simulation time, enabling scaffold design optimization for enhanced bone regeneration.

summarizes the reviewed research on the simulation of scaffold fluidic and mechanical properties, while the board presents the study methodology and outcomes.

In most of the CFD works reviewed here, simulations were conducted under steady-state laminar flow conditions using packages such as ANSYS Fluent and COMSOL Multiphysics. Standard boundary conditions included specified inlet velocities (typically between 0.5 and 5 mm/s), outlet pressure defined as atmospheric pressure (0 Pa), and no-slip for the scaffold walls. Computational domains were discretized with tetrahedral or hybrid elements to accommodate the complex scaffold geometries. FEA simulations were generally carried out using linear elastic material models to solve for stress distributions and deformation under static or dynamic loads.

2.2. Fluid–Structure Interaction

Several studies also integrate fluid–structure interaction (FSI) analysis to investigate the characteristics of a scaffold. This computational method allows researchers to gain a more comprehensive understanding of how variations in scaffold properties, such as different geometries or pore sizes, directly influence the distribution of shear stress on the scaffold surfaces. By examining the shear stress patterns, researchers can discern how cells interact and adhere to these surfaces, providing valuable insights into the mechanical environment that cells experience within the scaffold. This knowledge is crucial for optimizing scaffold design to promote better cell attachment, proliferation, and tissue regeneration in bone tissue engineering (BTE) applications. Through the combination of CFD and FSI analyses, researchers can gain a deeper understanding of the complex interplay between fluid dynamics, mechanical forces, and cellular responses. While these simulations provide valuable insights into scaffold performance, biocompatibility ultimately depends on a range of fundamental and extrinsic factors, including material properties, surface chemistry, and in vivo interactions. Specifically, shear stress in the range of 0.1–2 Pa has been shown to promote osteogenic differentiation, while lower levels may support proliferation and migration. Malvè et al. (2018) [55] considered nine different scaffolds that are classified based on their properties. The computational model of this study was implemented using the commercial software package Adina R&D with the aim of estimating the WSS, stresses and strains, and mass transport within the porous scaffold structure, taking into consideration the fluid–structure interaction. For the FSI model, they considered the structure of the scaffold to be made of a homogeneous, isotropic, and elastic material. The FSI simulations were performed, assuming quasi-steady conditions for the flow model and static conditions for the solid model. The scaffold structure was considered deformable. They performed a CFD analysis of the fluid domain, imposing the flow at both inflow and outflow. Once the pressure was determined, they used its value as an outlet condition for the FSI model. The velocity trajectories derived from the FSI model reveal the fluid flow patterns within the scaffold. The calculated results indicated that the fluid flows into the scaffold from its top surface, exiting not only from the bottom surface, but also through the side pores. This flow behavior leads to significant perfusion within the microstructure of the tissue scaffold. Especially in the regions near the bottom surface, due to the separation of the flow from the construct strands, the WSS was particularly high. The researchers concluded that the value of the strand diameter and horizontal span influences the WSS generated on the scaffold. It was shown that by increasing the diameter, the maximum WSS was increased and by increasing the horizontal span, the WSS was decreased.

Suffo et al. (2021) [56] carried out a comparative analysis to determine the most adequate turbulence method for the design of a 3D scaffold through an FSI method. Two 3D scaffold models were designed and imported into finite element–CFD software to investigate the fluid properties of scaffolds with three different pore sizes (300, 400, and 500 µm). The two-way FSI method was used to evaluate the fluid equivalent von Mises stress on the 3D geometric models. For the CFD study, a steady problem based on pressure was proposed, with the gravitational stress being neglected. The results of the CFD–structural analysis allowed the PLA material with the 400 µm model to be chosen due to the improvement seen in the mechanical properties, particularly the von Mises maximum stress caused by the viscous friction as an external load, which was reduced by 51% compared to other scaffold configurations. The obtained results revealed that the detached eddy simulation (DES) model exhibits better performance for the use of 3D scaffolds in its normal operating regime. Majumder et al. (2024) [57] depicted detailed simulations to compare mechanical stimuli experienced by osteoblasts within trabecular bone and gyroid scaffolds. These simulations used fluid–structure interaction (FSI) models and computational fluid dynamics (CFD) to evaluate fluid shear stress (FSS) and strain energy density (SED)—two key parameters for bone regeneration. The fluid flow through both the trabecular bone and gyroid scaffold was modeled using ANSYS Fluent. This simulation calculated the FSS exercised by the interstitial fluid on the cells. The trabecular bone and the scaffold were subjected to a constant inlet velocity, and no-slip boundary conditions were applied at the walls. FSS values were compared across various porosities and locations to optimize scaffold design for promoting osteogenic differentiation. After the CFD analysis, the resulting fluid pressure was applied to the solid components (trabecular bone and scaffold) in ANSYS structural analysis software to compute this mechanical deformation. A uniaxial load was applied to simulate physiological compressive strain, focusing on how the bone/scaffold responds mechanically under stress. These simulations allowed for a comparative analysis, showing that the gyroid scaffold had higher FSS and SED in most cases, especially at specific positions, which makes it more favorable for bone regeneration.

Chen et al. (2020) [58] studied the biomechanical properties of the scaffold through the FSI method. Permeabilities and fluid velocities from different coordinates of the scaffold were evaluated using the reconstructed mesh models derived from micro-CT images. The shear stress and compressive loading on the scaffold surface exerted by the two-way coupled FSI method evaluated the fluid behavior within the pores and the strain on the scaffold. The results of the permeability analysis indicate that the computational streamlines of the fluid flow were homogenously isolated within the pores of the scaffold, and a higher flow velocity was observed inside the scaffold. This high flow velocity can enhance the liquid transport within each portion of the scaffold. Moreover, the FSI merged maps showed that the WSS of the outer surface was greater than that of the inner facet and central area. This fluid movement and the relevant trajectories cause fluid shear stress (FSS) on the cell surface, and this is something that it is thought to be a trigger for biochemical signaling. Thus, it can be assumed that a larger WSS of 0.5–2 Pa can stimulate osteoblast proliferation and matrix accumulation, and a WSS less than 0.5 Pa seems to promote a proliferative and osteogenic state [59].

Table 4. Summary of reviewed studies on fluid–structure interaction (FSI) in scaffolds.

Study	Methodology	Outcome
Malvè et al. (2018) [55]	Performed CFD and FSI simulations on 9 scaffold models using Adina R&D software. Assumed quasi-steady flow and static solid conditions; scaffold modeled as homogeneous, isotropic, and elastic. Pressure from CFD used as input for FSI. Analyzed velocity trajectories and wall shear stress (WSS).	Found that fluid entered from top and exited through sides and bottom. High WSS observed near bottom surface due to flow separation. Larger strand diameter increased WSS; larger horizontal span decreased WSS.
Suffo et al. (2021) [56]	Comparative FSI analysis of 3D-printed scaffolds with pore sizes of 300, 400, and 500 µm using FEA-CFD tools. Used steady CFD with pressure-based setup and evaluated equivalent von Mises stress through two-way FSI. Tested turbulence models including detached eddy simulation (DES).	Identified 400 µm pore PLA scaffold as optimal due to 51% reduction in von Mises stress. DES model showed best turbulence performance.
Majumder et al. (2024) [57]	Used FSI and CFD in ANSYS Fluent to compare trabecular bone and gyroid scaffold. Simulated constant inlet flow and no-slip boundary; evaluated FSS and SED. Applied pressure output to ANSYS software for deformation under compressive strain.	Gyroid scaffold showed higher FSS and SED compared to trabecular bone, indicating better performance for bone regeneration, especially at certain locations.
Chen et al. (2020) [58]	Used FSI method with meshes reconstructed from micro-CT scans. Evaluated permeabilities, flow velocities, and surface strain from shear stress and compressive loading using two-way FSI.	High flow velocity and homogenized fluid trajectories observed. WSS on outer surface > inner regions. WSS range of 0.5–2 Pa linked to osteoblast proliferation and matrix accumulation; lower WSS (<0.5 Pa) associated with osteogenic behavior.

summarizes the reviewed research on fluid–structure interaction (FSI) in scaffolds, while the board presents the study methodology and outcomes. As shown in Table 4, variations in scaffold geometry, flow velocity, and material properties lead to significant differences in predicted shear stress and deformation values, highlighting the sensitivity of FSI outcomes to modeling assumptions and boundary conditions.

2.3. Computational Modeling of Media Flow Through Perfusion Bioreactors

Bioreactor systems have been used in bone tissue engineering to simulate the dynamic nature of bone tissue environments. Perfusion bioreactors have been reported as the most efficient types of shear-loading bioreactor [60]. Moreover, the combination of forces, such as rotation plus perfusion, has been reported to enhance cell growth and osteogenic differentiation. Mathematical modeling using infrastructure processes could be helpful and streamline the development of functional grafts by estimating and defining an effective range of bioreactor settings for better augmentation of the tissue engineering process [61]. In the study by Hanieh et al. (2016) [62], a computational modeling method for newly designed bioreactors was evaluated in order to improve the time and material consumption for estimating bioreactor parameters and the effect of fluid flow hydrodynamics on osteogenesis. FEA was used to investigate the effect of fluid flow hydrodynamics inside the bioreactor. In the study by Zhao et al. (2019) [63], a multiscale CFD approach was developed to quantify the micro-fluidic environment in highly irregular scaffolds, test its accuracy and feasibility, and examine the WSS and its influence on cell behavior inside various scaffolds with either rectangular or circular pores. To test the feasibility for modeling realistic sample sizes, a multiscale analysis based on multiple microstructural regions of interest within a larger scaffold was used to evaluate the homogeneity of the WSS in a complex scaffold under medium perfusion. The researchers concluded that the flow rate within the range 0.5–5 mL min⁻¹ was deemed optimal. Flow rates below this range were found to be inadequate in inducing mineralization, while higher flow rates led to cellular death. Reza et al. (2020) [64] used computational modeling to examine how fluid flows through 3D-printed scaffolds in a bioreactor. They observed different angles between the strands in the scaffolds and examined various flow rates. Their analysis showed that the flow rate at the bioreactor’s inlet directly influenced the velocity of the fluid and the value of shear stress that is experienced within the scaffolds. Specifically, scaffolds with strands angled at 30° showed higher fluid velocity and shear stress compared to those with angles of 45°, 60°, and 90°, regardless of the flow rate used. To investigate what reduction in the external flow rate applied to the bioreactor during culturing is needed to keep the WSS in the optimal range, Zhao et al. (2020) [65] conducted a computational study that simulated the formation of extracellular matrix (ECM), and in which they investigated the effect of constant fluid flow and different fluid flow reduction scenarios on the WSS. It was found that for both constant and reduced fluid flow scenarios, the WSS did not exceed the critical value, which was set to 60 mPa. The conservation of a constant flow velocity led to a notable decline in the percentage of the cell/ECM surface experiencing WSS within the optimal range, diminishing from an initial 50% to 18.6% by day 21. The modulation of fluid flow rates over time could effectively mitigate this decline, resulting in the preservation of optimal WSS conditions for 40.9% of the surface area at the 21-day mark. In a recent study, Capuana et al. (2022) [66] implemented a numerical simulation at the pore level of the scaffold for fluid flow through porous media during perfused culture. A CFD simulation was used to define the velocity profile inside the bioreactor in the presence of multi-grid support during the perfusion flow. After optimization, a uniform velocity field distribution was obtained when the boundary conditions were adjusted to mimic the cell experiments. The flow velocity and shear stress profiles were calculated at the surface of the scaffold using the single-phase laminar flow model based on the Navier–Stokes equation. In a study by Keshtiban et al. (2024) [67], the authors utilized CFD to simulate the fluid flow and WSS on 3D-printed scaffolds. The CFD simulations were performed using ANSYS Fluent (NASDAQ), and the goal was to evaluate how different scaffold geometries (TPMS structures with varying porosities) impacted fluid behavior within a perfusion bioreactor. The study employed a custom-designed perfusion bioreactor to replicate dynamic cell culture conditions. This bioreactor was designed with a cylindrical scaffold chamber, matching the scaffold’s dimensions to ensure stable positioning during fluid flow. Three different scaffold geometries were tested with various flow rates (0.4, 0.6, and 0.8 mL/min). The simulations revealed that scaffolds with smaller pore sizes led to higher velocity magnitudes and shear stress, which are crucial for stimulating cell proliferation. The CFD analysis helped in selecting the optimal geometry that maximized WSS, enhancing biological outcomes like cell attachment. Previously, Yan et al. [68] investigated the effects of scaffold pore size, fiber diameter, and flow rate on the shear stress distribution within the scaffold in a perfusion bioreactor and found that scaffolds with larger pore sizes allow for better fluid velocity and flow rates, leading to improved nutrient transport and waste removal within the scaffold structure. From the simulations, they obtained results for the perfusion bioreactor case and presented their findings. The streamlines pass through the tissue scaffold, indicating that there is robust perfusion within the scaffold. They also illustrated from their results that fluid mobility is low in other parts of the bioreactor. As a result, perfusion causes significant shear stresses on the surfaces of the strands in certain regions of the scaffold. Across the reviewed studies, certain trends emerge. Most bioreactor simulations focus on flow-induced shear stress or nutrient transport, using idealized scaffold geometries. However, there is limited consensus on optimal flow rates or bioreactor configurations, making cross-comparison challenging. Despite differences in methodology, studies consistently suggest that dynamic culture conditions enhance tissue development compared to static culture, supporting the relevance of in silico bioreactor modeling in scaffold design.

Table 5. Summary of reviewed studies on computational modeling of media flow through perfusion bioreactors.

Study	Methodology	Outcome
Hanieh et al. (2016) [62]	Computational modeling using FEA to analyze fluid flow hydrodynamics in a newly designed bioreactor.	Identified ways to reduce time and material costs when estimating bioreactor parameters affecting osteogenesis.
Zhao et al. (2019) [63]	Multiscale CFD approach applied to scaffolds with rectangular and circular pores to analyze WSS and microfluidic environments.	Determined optimal flow rate range (0.5β€”5 mL/min)
Reza et al. (2020) [64]	Computational modeling of fluid flow through 3D-printed scaffolds with various strand angles and flow rates.	Found that 30Β° angled strands produced higher velocity and shear stress, regardless of flow rate.
Zhao et al. (2020) [65]	CFD simulations studying ECM formation under constant vs. reduced flow scenarios in bioreactors.	Modulated flow helped maintain optimal WSS longer, improving WSS exposure from 18.6% to 40.9% by day 21.
Capuana et al. (2022) [66]	CFD simulation at scaffold pore level using Navier–Stokes equation to model flow with multi-grid support.	Achieved uniform velocity field
Keshtiban et al. (2024) [67]	CFD in ANSYS Fluent to analyze effects of TPMS scaffold geometries with varying porosities and flow rates.	Smaller pores increased velocity and shear stress, enhancing cell proliferation and attachment.
Yan et al. (2012) [68]	Simulation study examining effects of pore size, fiber diameter, and flow rate on shear stress distribution.	Larger pores improved flow and nutrient transport

summarizes the reviewed research on computational modeling of media flow through perfusion bioreactors, while the board presents the study methodology and outcomes

2.4. Modeling the Tissue Regeneration Within Scaffolds

CFD results can indicate the locations where the culture environment may be harmful to cells, either due to excessive shear stress or inadequate nutrient concentration. Moreover, the stress and strain distribution revealed by FEA and CFD may act as mechanical stimuli to predict cell differentiation [69]. Cell seeding, behavior, and response are also found to be significantly influenced by the architectural properties of the scaffold. It has been shown that the scaffolds used in bone tissue regeneration must possess optimum pore size, pore shape, porosity, interconnectivity, and fiber orientation.

Olivares et al. [70] modeled scaffold behavior under both fluid flow and compression and compared the two conditions, concluding that cell differentiation is more sensitive to fluid flow than axial compression. This study provides a computational approach to determine the mechanical stimuli at the cellular level when cells are cultured in a bioreactor and to relate mechanical stimuli with cell differentiation. To generate the desired level of mechanical stimulation in fluid shear stress (FSS), Zhao et al. (2016) [71] combined the CFD and the finite element (FE) methods to quantitatively evaluate the influence of scaffold geometry (structure, pore size, and porosity) on FSS. Hendrikson et al. (2017) [72] employed a combination of CFD and FEA to investigate the impact of various lattice scaffold geometries on shear stresses and strains within the structures. These mechanical characteristics were then integrated with Prendergast mechano-regulation theory, enabling the assessment of how these different scaffold geometries influence cell differentiation. The findings of the study revealed a significant correlation between the scaffold’s geometry and the cell differentiation process. Specifically, they observed that certain scaffold geometries promoted a higher level of bone formation compared to others. Among the tested geometries, the “0–90 offset geometry” demonstrated superior performance in terms of encouraging bone formation. This research provides valuable insights into the influence of scaffold design on cell behavior and tissue formation. The researchers demonstrated the prediction of the cell differentiation stimulus based on the surface shear strain with mechanical compression alone that shows a profile similar to the strain distribution. By combining numerical simulations with mechano-regulation theory, the study offers a comprehensive understanding of how scaffold properties can be optimized to enhance bone formation and potentially improve the effectiveness of tissue engineering applications. Moreover, scaffold structure with higher porosity and pore interconnectivity are favorable for fluid flow and vasculature formation. Since the scaffold properties and behavior under fluid flow are so significant for the 3D perfusion cell culture, it is necessary to adopt the CFD method to investigate the scaffolds properties and behavior in the presence of fluid [73].

More recently, Mirkhalaf et al. (2020) [74] also highlighted the importance of the architecture of the scaffold and the relevance of the geometric parameters in its selection. In their study, the shear stress on tissues caused by loads from the mechanical properties was found to play a potential role on the scaffolds. Since cells are very sensitive to their surrounding environment, they can sense shear stresses as mechanical stimuli through mechanotransduction. The mechanical stimuli can influence cell growth, differentiation, and tissue formation [69]. A finite element model was used to determine the mechano-regulation of stem cells with regard to tissue differentiation and growth. Simulations suggested that high porosities (70%), higher stiffness (1000 MPa), and medium dissolution rates (0.5%/iteration) provided the greatest amount of bone growth. Recent use of the mechanobiological model has demonstrated tissue growing to form curved surfaces and has suggested optimal beam diameters for varied lattice architectures to promote tissue growth [75]. The work of Zhang et al. (2024) [76] presents a novel framework for optimizing bone scaffold geometries that enhance mechanobiological stimulation and nutrient transport. Through a multi-objective optimization strategy, the authors simultaneously targeted the mechanical stimulation of bone cells and efficient biotransport. Computational simulations identified scaffold geometries that promote bone ingrowth by balancing fluid shear stress and nutrient distribution. The approach offers a practical pathway for designing patient-specific scaffolds with enhanced biological performance. Another in silico study by Minku et al. (2024) [77] focused on evaluating different porous lattice structures in orthopedic implants, emphasizing their role in promoting bone ingrowth. The research used FEA to simulate bone ingrowth in five lattice structures. A mechanobiological approach was applied to assess tissue differentiation at the bone–implant interface under various micromotion conditions. The results demonstrate that cubic lattice structures exhibit the highest bone tissue ingrowth, while X-shape structures perform the poorest. The study provides a significant computational framework to optimize implant design for better osseointegration, potentially influencing future implant development in terms of porosity, stiffness, and mechanical compatibility with human bone. The results show the superior bone ingrowth for cubic and FCC lattices, and the poorer performance of the X-shape structure, aligned with mechanical properties like stiffness, which could also be modeled using CFD to understand how fluid flow (e.g., blood or nutrient delivery) interacts with these structures.

In a review by Bobbert et al. [78] on the architecture of bone replacement materials, it was shown that scaffolds with small pores (200–300 µm) present a better environment for the seeding of cells; however, they limit cell sustainability, proliferation, and differentiation. The authors also concluded that designing what they referred to as a “tortuous void network” would, in fact, help control the passage of the cell suspension through the scaffold, thus increasing the surface area and available time for cell attachment. Based on that, another study by Ali et al. (2019) [79] focused on the effect of scaffold architecture on the adhesion of the cells, which was computationally investigated. For this purpose, four scaffold models, including double-diamond, gyroid, FR-D, and Schwarz primitive, were designed using triply periodic minimal surface (TPMS) geometry with a constant porosity of 80%. An inlet velocity of zero to simulate static cell culture and three different inlet velocities for modeling the dynamic cell culture conditions were selected. The results showed that the cell culture efficiency of scaffolds could be increased sevenfold from architecture to architecture under the same conditions. The efficiency of cell culture in scaffolds with tortuous architecture was also reported to be higher than those with relatively straight microchannels. Marin et al. (2018) [80] created a computational model that can predict where cells may be located within a scaffold over both time and space under bioreactor conditions. This computational model was designed to replicate the process of cell seeding in vitro, allowing researchers to understand how varying flow rates affect the movement and placement of cells on the scaffold surface. The cells suspended in the culture medium were described as a discrete phase of sphere particles with 10 µm diameter. Three different flow rates were tested, and the cells tracked along the fluid streamlines, with their velocities matching those of the fluid. At a flow rate of 12 µL/min, where the flow reverses only twice and the secondary flow is weaker compared to the other two cases, very few cells attached to the scaffold surface. Unexpectedly, despite anticipating a stronger secondary flow and, consequently, higher cell deposition on the scaffold surface at a flow rate of 600 µL/min, the deposition of cells on the scaffold was higher at a flow rate 120 µL/min and achieved the best results.

In the CFD simulation of scaffolds, a bioreactor set-up is usually used to mimic the in vivo fluid environment. A bioreactor, as referred to previously, is a device in which biological or biochemical processes develop under closely monitored and closely controlled environmental and operating conditions. In the study by Paz et al. (2019) [81], a numerical model of osteocyte growth was utilized. The model includes the oxygen and nutrient consumption of biomass, the effect of shear stress on cell proliferation, and the specific growth rate of osteocytes. The implementation of the model was evaluated in two 3D realistic scaffolds of different porosity, and four input velocities of the culture medium in the bioreactor. Through diagrams, the researchers illustrated the effect that velocity has on cell growth when it is limited by the shear stress exerted by the culture medium on the wall of the scaffold. In the proposed model, it was considered that there is cell adhesion and cell growth when the shear value was between 5 × 10⁻⁵ and 0.056 Pa. The results obtained showed that the numerical model was implemented correctly because the cellular molar concentration increases with time according to the exponential growth phase of the cells for all of the cases simulated. It has also been proven that cell proliferation is conditioned by the WSS. For all of these cases, the results obtained show a cell growth rate with a positive slope, without rises and falls, and sustained over time. A paper by Li et al. (2024) [82] presents a computational study of conically graded porous bone scaffolds, assessing their mechanical strength, failure patterns, and permeability. The authors used finite element analysis (FEA) and computational fluid dynamics (CFD) to evaluate how conical gradients in porosity influence both structural and transport behavior. Their results revealed that scaffolds with a conical porosity gradient provide enhanced stress distribution and more favorable fluid dynamics, making them suitable candidates for improving both mechanical support and nutrient flow in bone tissue engineering. In the study by Nguyen et al. (2018) [83], a numerical method based on a multiscale approach and CFD analysis was proposed. The aim of their work was to determine the optimal flow rate of a direct perfusion bioreactor to enhance cell proliferation and to advance future bone reconstruction. Through CFD analysis, the study provided insights into the flow patterns of the culture media within the scaffold. From their results, they determined the growth rate of cell colonization as a function of the inlet flow rate after a 7-day cell culture. They concluded that the best result is given for a flow rate of Q = 0.69 mL·min⁻¹, which corresponds to a growth rate above 325% for a 7-day cell culture. Kozaniti et al. (2023) [84] employed fluid mechanics models to determine the fluid behavior in a bioreactor system, and to describe the characteristics of the fluid–dynamic systems. They solved equations related to the flow of an incompressible and laminar substance through the bioreactor’s tube. Their results yield valuable insight indicating that the distribution of cells within layers 2–5 tends to be either random or constrained due to physical factors. Higher inlet velocities result in a more efficient distribution of cells. It may be observed that, in all cases, the initial number of cells that are distributed in the first layer reduces to half of the cells in the fifth layer. Jungreuthmayer et al. (2009) [85] quantified the deformation of cells seeded on a collagen– glycosaminoglycans (GAG) scaffold, which was perfused by culture medium inside a flow perfusion bioreactor. The WSS and the hydrostatic wall pressure on the cell surface were computed using a CFD simulation and were input into a linear elastostatics model to calculate the deformation of the cells. The model used numerically seeded cells of two common morphologies, where cells are either attached flatly on the scaffold wall or bridging two struts of the scaffold. Their study showed that cell displacement is primarily guided by cell morphology.

Moradkhani et al. (2021) [86] applied CFD analysis to analyze the hydrodynamic aspects of scaffold surfaces. FSI methods were employed to examine how fluid flow influences stem cells attached to the surface of the scaffold. Their findings revealed that the microstructure and pore architecture of the scaffold significantly influenced the fluid’s accessibility to various parts of the scaffold. This led to the optimization of shear stress and hydrodynamic pressure across different scaffold surfaces, facilitating improved transport of oxygen and growth factors. Moreover, it enhanced the mechano-regulatory responses in interactions between cells and the scaffold. The results suggested that the Hexagonal Prism (HP) scaffold offered more optimized surfaces for culturing stem cells compared to gyroid and I-graph-Wrapped Package (IWP) scaffolds. Tajsoleiman et al. (2018) [87] utilized computational modeling techniques to design and optimize the scaffold structure. The first part of their work focuses on the mathematical modeling and CFD simulation of a 3D scaffold-based cartilage cell culture within a perfusion bioreactor. Their work then focuses on the effect of nutrient and metabolite concentrations, and the possible influence of fluid-induced shear stress on a targeted cell (cartilage) culture. The simulation set-up gives the possibility of predicting the cell culture behavior under various operating conditions and scaffold designs. Zhang et al. (2020) [88] investigated a numerical model to study the perfusion cell seeding process that incorporates cell mechanics, cell–fluid interaction, and cell–scaffold adhesion. The individual cells were modeled as deformable spherical capsules capable of adhering to the scaffold surface as well as to other cells’ bond formation and rupture. The mechanical deformation of the cells was also calibrated with the stretching of mouse mesenchymal stem cells induced by optical tweezers. The effects of the perfusion pressure and initial cell concentration on the seeding kinetics were studied in terms of adhesion rates, cell cluster formation, seeding uniformity, and efficiency, as well as scaffold permeability. The researchers also measured the distribution of shear stress on the surfaces of the firm-adhesion cells as well as the mean shear stress on each individual one. It was observed that small shear stresses take up a large portion of the cell surfaces. The applied perfusion pressure in their study provides shear stresses less than 20 mPa in 96% of the cell surface, while the mean shear stress on one cell ranges from 2.5 to 10 mPa for 86% of the FA cells. This level of WSS is within the reported values varying from 5 to 100 mPa, a range that has been shown to enhance the proliferation and osteoblastic differentiation of mesenchymal stem cells (MSCs). The results highlight the importance of cell–fluid interaction and adhesion dynamics in modeling the dynamic seeding process.

Table 6. Summary of reviewed studies on modeling tissue regeneration within scaffolds.

Study	Methodology	Outcome
Olivares et al. (2009) [70]	Combined CFD and compression simulations to model scaffold behavior; compared mechanical stimuli under fluid flow vs. axial compression.	Found that cell differentiation is more sensitive to fluid flow than to axial compression; provided a computational method to relate mechanical stimuli to differentiation.
Zhao et al. (2016) [71]	Combined CFD and finite element (FE) methods to evaluate scaffold geometry (pore size, porosity) and their influence on fluid shear stresses (FSS).	Demonstrated how scaffold structure affects the magnitude and distribution of FSS, helping to inform design for optimal mechanical stimulation in bioreactors.
Hendrikson et al. (2017) [72]	Used CFD and FEA along with Prendergast mechano-regulation theory to analyze different lattice scaffold geometries.	Found a strong correlation between scaffold geometry and bone cell differentiation; “0–90 offset geometry” promoted the most bone formation.
Mirkhalaf et al. (2020) [74]	Applied finite element modeling to examine mechano-regulation in stem cell differentiation and tissue growth under mechanical stimuli (stress, stiffness, porosity).	Identified optimal scaffold parameters (70% porosity, 1000 MPa stiffness, 0.5%/iteration dissolution rate) for enhanced bone formation; also highlighted curved tissue formation patterns.
Zhang et al. (2024) [76]	Simulated fluid flow in uniform and gradient scaffolds with varying geometrical parameters using CFD.	Gradient structures gradually increased velocity and WSS, mimicking osteochondral interfaces.
Minku et al. (2024) [77]	Used FEA and a mechanobiological model to evaluate bone ingrowth in five porous lattice structures under micromotion conditions.	Cubic and FCC lattice structures showed the highest bone tissue ingrowth; X-shape performed worst; provided a computational framework to optimize implant geometry for osseointegration.
Bobbert et al. (2017) [78]	Literature review analyzing scaffold architecture, particularly pore size and void network design, in bone tissue engineering.	Concluded that small pores (200–300 µm) aid cell seeding but hinder sustainability and proliferation; proposed “tortuous void networks” to improve cell suspension flow and surface interaction.
Ali et al. (2019) [79]	Designed four TPMS-based scaffold models (double-diamond, gyroid, FR-D, Schwarz primitive) and used CFD to assess cell adhesion under static and dynamic flow conditions.	Found that tortuous architectures significantly improved cell culture efficiency—up to 7× higher—compared to straight-channel designs.
Marin et al. (2018) [80]	Developed a CFD-based computational model simulating cell seeding over time and space within a scaffold under different bioreactor flow rates.	Determined that moderate flow rate (120 µL/min) resulted in the highest cell attachment, outperforming both lower and higher flow conditions.
Paz et al. (2019) [81]	Created a numerical model incorporating oxygen/nutrient consumption, shear stress, and cell proliferation in two 3D scaffolds with varying porosity and inlet velocities.	Demonstrated that wall shear stress (WSS) strongly influences cell proliferation; cell growth occurred consistently within optimal shear range (5 × 10−5 to 0.056 Pa).
Li et al. (2024) [82]	Evaluated Voronoi scaffold with mechanical, CFD, in vitro, and in vivo studies. Linked simulations with biological results.	Voronoi scaffold showed highest bone growth and WSS alignment with osteogenesis, outperforming other designs.
Nguyen et al. (2018) [83]	Used CFD with a multiscale approach to identify optimal flow rate in a direct perfusion bioreactor over a 7-day culture period.	Found that a flow rate of 0.69 mL/min maximized cell proliferation (~325% growth), providing a benchmark for optimizing bioreactor conditions.
Kozaniti et al. (2023) [84]	Applied fluid mechanics modeling to study incompressible, laminar fluid flow in a bioreactor system; analyzed cell distribution across scaffold layers.	Found that higher inlet velocities improved cell distribution efficiency; noted reduction in cell numbers from layer 1 to layer 5, highlighting effects of physical constraints.
Jungreuthmayer et al. (2009) [85]	Combined CFD simulation with linear elastostatics model to evaluate cell deformation on a collagen-GAG scaffold in a perfusion bioreactor.	Showed that cell displacement depends heavily on morphology—cells bridging struts deformed differently than flat-attached cells; WSS and pressure influenced deformation.
Moradkhani et al. (2021) [86]	Used CFD and fluid–structure interaction (FSI) methods to analyze hydrodynamics and mechano-regulation in different scaffold microstructures.	Found that Hexagonal Prism (HP) scaffold had better performance in terms of optimized shear stress, nutrient delivery, and mechano-regulation compared to Gyroid and IWP designs.
Tajsoleiman et al. (2018) [87]	Conducted CFD simulations and mathematical modeling to study nutrient/metabolite transport and shear stress in cartilage culture within a perfusion bioreactor.	Enabled prediction of culture behavior under varied scaffold designs and conditions; highlighted importance of scaffold geometry for nutrient delivery and mechanical stimulation.
Zhang et al. (2020) [88]	Developed a numerical model incorporating cell mechanics, cell–fluid interaction, and adhesion dynamics in scaffold perfusion seeding.	Showed that shear stress levels (mostly < 20 mPa) matched optimal ranges for MSC proliferation and differentiation; model emphasized importance of adhesion and cell deformation in seeding.

summarizes the reviewed research on modeling tissue regeneration within scaffolds and presents the study methodology and outcomes.

2.5. Limitations and Future Trends of Bone Tissue Engineering (BTE) Scaffolds

While there is a growing interest in this field of research, the body of work currently available is relatively limited. The current literature on computational methods presents a general limitation regarding the usage of a single generic bone type and not patient-specific bone structures. This limitation needs to be addressed since we need to consider how the selection of a specific scaffold affects different tissues or bone segments. Without taking into consideration individual differences in bone density, mechanical characteristics, and anatomical features, computational models may fail to effectively anticipate how specific patients would respond to alternative treatment strategies, resulting in unsatisfactory outcomes. Hence, in the context of numerical applications, it becomes imperative to carefully contemplate how diverse scaffold characteristics can exert distinct influences on various tissues or specific sections of bone. For example, a study could involve gathering information from a wide group of patients, such as bone density, mechanical qualities, and anatomical deviations. Researchers can use this data to create computational models that reflect the personalized nature of bone formations. Recognizing the intricacies of these interactions is vital for advancing the precision and applicability of CFD studies in BTE. By acknowledging the requirements of different tissues or bone segments, researchers can design their numerical simulations to better associate with the specific needs and challenges posed by diverse applications within the field of regenerative medicine. This consideration ensures that the outcomes of different types of analyses not only contribute to the broader understanding of scaffold behavior, but also provide valuable insights applicable to the intricacies of tissue engineering, fostering advancements that address the specificities of each application within the broader framework of bone regeneration. Additionally, future advancements in computational modeling should aim for stronger integration with clinical practice by enabling real-time predictions and simulation-based treatment planning, which can assist clinicians in selecting optimal scaffold designs for individual patients. Emerging data-driven approaches, such as machine learning, can complement traditional modeling by enabling pattern recognition in large experimental datasets and supporting the development of adaptive, self-improving models.

Additionally, most research studies only simulate the behavior of scaffolds under simple uniaxial loads. However, in real-world scenarios, scaffolds can experience a variety of complex loadings that are more diverse than uniaxial loads. Although several researchers have examined the impact of filament position and orientation on cell seeding and proliferation, few have taken into account long-term performance. As a result, optimizing scaffold design for tissue creation remains a challenge. Long-term in vitro and in vivo studies are complex and expensive, which may explain the scarcity of such studies. Another significant limitation derives from the gap between numerical and experimental results in current CFD studies. This discrepancy may be due to certain factors such as surface roughness not being considered in the simulations, making it difficult to accurately determine scaffold characteristics. Across CFD analyses, differences in fluid modeling approaches (Newtonian vs. non-Newtonian assumptions) led to variations in predicted wall shear stress, suggesting that fluid properties can significantly influence simulation outcomes. Moreover, most of the studies do not include sensitivity analyses and model uncertainty handling, which could significantly affect the predictions’ reliability. The inclusion of uncertainty quantification methods would increase confidence in simulation outcomes and result in more robust models. Many existing computational studies focus on either the micro or macro scale, ignoring the complexity between different scales within bone tissue. The size of the scaffolds significantly impacts the properties and behavior of the scaffold. The predominance of a micro-scale dimension in the examined studies highlights a constraint focused primarily on correcting minor flaws. Constructing scaffolds at the micro scale is useful in some cases, but it may not adequately capture the complexities associated with greater tissue abnormalities or more extensive bone damage. Overcoming the challenges associated with multiscale modeling will be fundamental for advancing BTE. While there have been some in vitro degradation studies [89], the effect of scaffold geometry on degradation and resorption have not been extensively researched yet. Nonetheless, the most important aspect in the BTE area is to ensure the reliability of computational models with extensive validation against experimental data. A major limitation is the lack of established processes for model validation. The validation of tissue regeneration models remains a challenge, as many rely on assumed cell behavior without direct experimental confirmation. While some studies compare simulated cell growth with histological or imaging data, systematic validation remains limited. Incorporating biological variability and long-term follow-up is needed to strengthen model reliability. The establishment of uniform criteria and validation processes would improve the validity and comparability of various computing approaches in this field. In addition, the development and use of open-source platforms could foster reproducibility and data sharing among re-searchers. Lastly, technological limitations additionally restrict the capability of existing computational approaches. While computer capacity has increased significantly in recent years, modeling software may still lack the level of accuracy required to effectively simulate the complex processes involved in bone regeneration. Furthermore, the scalability and practicality of such models for widespread use in clinical practice are questionable, as simulations are computationally intensive and time-consuming. A key challenge is translating in silico findings into clinically viable products. Most models do not yet account for patient-specific variability, biological remodeling, or manufacturing scalability. The interdisciplinary collaboration between clinicians, bioengineers, and computational scientists will be necessary to ensure that models are technically sound but also representative of the clinical practice of patient care and treatment planning. Moving forward, integrating multiscale models and experimental validation will be crucial to bridge the gap between simulation and clinical application. At the same time, making modeling tools more accessible and easier to use will be extremely important to ensure adoption by non-specialist users, especially in a clinical environment. Overcoming such practical constraints will be important in connecting numerical modeling to practical use. Future computational studies are expected to shed more light on the combination of numerical applications for investigating how cells interact with the scaffold and consider scaffold degradation and tissue regeneration in time-dependent simulations as a notably promising area in BTE.

3. Conclusions

Bone tissue engineering is a rapidly developing field, and researchers are focusing on developing and improving new materials to imitate the biological environment of the body as realistically as possible [90]. Tissue engineering is a field that presents an appealing approach that employs scaffolds, cells, and signaling factors to facilitate the repair and restoration of damaged tissues [91]. This article reviewed the research of combining computational methods and 3D scaffolds for bone regeneration through bone tissue engineering. A number of studies focused on computational modeling and simulation methods, and their applications in scaffold modeling have been reviewed to better understand the properties of scaffolds and their characteristics. The capabilities of several computational methods have been depicted, addressing how we can predict the scaffold properties and behavior under different conditions and experiments and highlight the significant advancements made in the field of scaffold modeling through CFD analysis, structural analysis, FSI, and a combination of these methods to shed more light on cell growth and how it is affected. Adapting these computational techniques provides the opportunity for researchers to focus on valuable insights into the behavior, design, and optimization of scaffolds, offering potential for diverse applications in tissue engineering, regenerative medicine, and biomedical research [92]. Finally, our review demonstrates that the proposed computational methods have proven vital in scaffold modeling, fostering a paradigm shift in tissue engineering and regenerative medicine research. These approaches offer solutions for specific tissue types, resulting in a greatly accelerated pace of scaffold development in this field. As computational methods continue to evolve, we can anticipate even more exciting breakthroughs and promising applications. However, the extended study of the current literature also highlighted the limitations of the current state of the art, mainly revolving around the lack of patient-specific bone geometries and adequate validation strategies in order to establish the described methods as solid, well-validated tools to address the intricacies of bone regeneration. Researchers must focus their efforts on collecting and integrating accurate patient-specific data, developing more complete multiscale models, and implementing accurate validation processes. Only through these advancements can computational methods truly fulfill their potential as reliable predictors and guides in the field of BTE, leading to personalized and efficient regenerative solutions.