Mechano-regulation Theory Research Articles

Impacts of post-operation loading and fixation implant on the healing process of fractured tibia.

Healing of tibia demonstrates a complex mechanobiological process as it is stimulated by the major factor of strains applied by body weight. The effect of screw heads and bodies as well as their pressure distribution is often overlooked. Hence, effective mechanical conditions of the healing process of tibia can be categorized into the material of the plate and screws, post-operation loadings, and screw type and pressure. In this paper, a mathematical biodegradation model was used to simulate the PGF/PLA plate-screw device over 8 weeks. The effect of different post-operation loading patterns was studied for both locking and non-locking screws. The aim was to reach the best configuration for the most achievable healing using FEA by computing the healing pattern, trend, and efficiency with the mechano-regulation theory based on deviatoric strain. The biodegradation process of the plate and screws resulted in 82% molecular weight loss and 1.05 GPa decrease in Young's modulus during 8 weeks. The healing efficiency of the cases ranged from 4.72% to 14.75% in the first week and 18.64% to 63.05% in the eighth week. Finally, an optimal case was achieved by considering the prevention of muscle erosion, bone density reduction, and nonunion, according to the obtained results.

Comparative analysis of mechanical conditions in bone union following first metatarsophalangeal joint arthrodesis with varied locking plate positions: A finite element analysis.

First metatarsophalangeal joint arthrodesis is a typical medical treatment performed in cases of arthritis or joint deformity. The gold standard for this procedure is arthrodesis stabilisation with the dorsally positioned plate. However, according to the authors' previous studies, medially positioned plate provides greater bending stiffness. It is worth to compare the mechanical conditions for bone formation in the fracture callus for both placements of the locking plate. Two finite element models of the first metatarsophalangeal joint with the dorsally and medially positioned plate were defined in the Abaqus software to simulate differentiation of the fracture callus. A simplified load application, i.e. one single step per each day and the diffusion of the mesenchymal stem cells into the fracture region were assumed in an iterative hardening process. The changes of the mesenchymal stem cells into different phenotypes during the callus stiffening were governed by the octahedral shear strain and interstitial fluid velocity according to Prendergast mechanoregulation theory. Basing on the obtained results the progress of the cartilage and bone tissues formation and their distribution within the callus were compared between two models. The obtained results suggest that after 6 weeks of simulation the healing progress is in general comparable for both plates. However, earlier closing of external callus was observed for the medially positioned plate which had greater vertical bending stiffness. This process enables faster internal callus hardening and promotes symmetrical bridging.

Mature bone mechanoregulation modelling for the characterization of the osseointegration performance of periodic cellular solids

Osseointegration is an essential process for the clinical success of some orthopedic implants. Delayed osseointegration can lead to post-operative complications and implant failure, which may require revision surgery. Advances in additive manufacturing allow 3D printing cellular solids to provide a favourable biomechanical environment that stimulates bone formation. Thus, this study aimed to simulate the performance of Ti-6Al-4 V strut-based lattice structures for mature bone growth. Mechano-regulation theory is applied to evaluate the osseointegration performance of six lattice topologies, including Diamond, BCC, Tetrahedron, Octet, Cubic, and Rhombic Dodecahedron, taking into consideration their horizontal and vertical orientations. The effect of the lattice relative density is also considered where the lattice topologies are simulated at ten discrete relative densities (5%:5%:50%) subjected to pressures of 0.5 MPa: 1 MPa: 1.5 MPa: 2 MPa. Results showed that Diamond, BCC, Tetrahedron, and Rhombic Dodecahedron with horizontal orientation provide an ideal biomechanical environment for bone growth. Between 10% and 30% relative density, most topologies had 100% of their void space within the optimal biomechanical stimulation for bone growth. The amplitude of the applied load had a substantial influence on the results. This data may help select the best lattice topology with the optimum microscopic attributes for the best biomechanical environment for a specific implant design.

Bone fracture healing under external fixator: Investigating impacts of several design parameters using Taguchi and ANOVA

In this paper we aim to improve the understanding of the relationship between unilateral-uniplanar external fixator design parameters and their influences on fixator performance. Stability and strength of bone-fixator construct as well as the quality of healing were defined as our major concerns in order to evaluate the performance of fixator. The roles of six key design parameters were assessed during the early stage of healing by using finite element models. Tissue differentiation within the callus was predicted through the implementation of a mechanoregulation theory of bone healing. Taguchi and ANOVA methods were used to achieve optimal design sets for outputs and to determine contribution percentage of each design parameter on outputs. For improving overall fixator performance, optimal set of design parameters consisting of 2 mm, 8 mm, 120 mm, 20 GPa, 50 mm and 20 mm were determined by Taguchi for pin diameter, rod diameter, rod elevation, fixator Young’s modulus, distance of the nearest pin to fracture site and distance between adjacent pins, respectively. Also, results of ANOVA revealed that rod elevation is the most important design parameter, with 43 % effectiveness on overall fixator performance, which was followed by fixator material and pin diameter with 28 % and 19 %, respectively. Results of this study can assist orthopedic surgeons to achieve an optimal fixator device with respect to the patient’s condition and give insight into the importance of different design parameters.

The effect of the degradation pattern of biodegradable bone plates on the healing process using a biphasic mechano-regulation theory.

Bone plates are used to treat bone fractures by stabilizing the fracture site and allowing treatments to take place. Mechanical properties of the applied bone plate determine the stability of the fracture site and affect the endochondral ossification process and the healing performance. In recent years, biodegradable bone plates have been used in demand for the elimination of a second surgery to remove the plate. The degradation of these plates into the body environment is commonly accompanied by alterations in the mechanical properties of the bone plate and a shift in the healing performance of the bone. In the present study, the effects of using biodegradable plates with various elastic moduli and degradation patterns, including linear and nonlinear, on the healing process are investigated. A three-dimensional finite element model of the radius bone along with a mechano-regulation theory was used to study the healing performance. Two mechanical stimuli of octahedral shear strain and interstitial fluid flow are considered as the propelling factors of healing. The results of this study indicated that increasing the bone plate's initial elastic modulus accelerates the healing process. However, by increasing the initial Young's modulus of the plate more than 100 GPa, no noticeable alteration is observed. The degradation time period of the plate was seen to be directly related to the speed of the healing process. It is shown, however, that by increasing the degradation time period to more than 8weeks, the healing performance remains almost unchanged. The results of this work showed that the application of plates with a high enough initial elastic modulus and degradation period can prevent the healing process from decelerating.

Optimal mechanical properties of a scaffold for cartilage regeneration using finite element analysis

The development of successful scaffolds for bone tissue engineering requires concurrent engineering that combines different research fields. In previous studies, phenomenological computational models predicted the mechanical properties of a scaffold in a simple loading condition using the mechano-regulation theory. Therefore, the aim of this study is to predict the mechanical properties of an optimum scaffold required for cartilage regeneration using three-dimensional knee joint developed from medical imaging and mechano-regulation theory. It was predicted that the scaffold with optimal mechanical properties would result in greater amounts of cartilage tissue formation than without a scaffold. The results demonstrated the ability of the algorithms to design optimized scaffolds with target properties and confirmed the applicability of set techniques for bone tissue engineering. The scaffolds were optimized to suit the site-specific loading requirements, and the results reveal a new approach for computational simulations in tissue engineering.

Flow rates in perfusion bioreactors to maximise mineralisation in bone tissue engineering in vitro

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5–5 mL/min (or in terms of fluid velocity: 0.166–1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments.

Micromechanical study of the load transfer in a polycaprolactone\u2013collagen hybrid scaffold when subjected to unconfined and confined compression

Scaffolds are used in diverse tissue engineering applications as hosts for cell proliferation and extracellular matrix formation. One of the most used tissue engineering materials is collagen, which is well known to be a natural biomaterial, also frequently used as cell substrate, given its natural abundance and intrinsic biocompatibility. This study aims to evaluate how the macroscopic biomechanical stimuli applied on a construct made of polycaprolactone scaffold embedded in a collagen substrate translate into microscopic stimuli at the cell level. Eight poro-hyperelastic finite element models of 3D printed hybrid scaffolds from the same batch were created, along with an equivalent model of the idealized geometry of that scaffold. When applying an 8% confined compression at the macroscopic level, local fluid flow of up to 20 upmu m/s and octahedral strain levels mostly under 20% were calculated in the collagen substrate. Conversely unconfined compression induced fluid flow of up to 10 upmu m/s and octahedral strain from 10 to 35%. No relevant differences were found amongst the scaffold-specific models. Following the mechanoregulation theory based on Prendergast et al. (J Biomech 30:539–548, 1997. https://doi.org/10.1016/S0021-9290(96)00140-6), those results suggest that mainly cartilage or fibrous tissue formation would be expected to occur under unconfined or confined compression, respectively. This in silico study helps to quantify the microscopic stimuli that are present within the collagen substrate and that will affect cell response under in vitro bioreactor mechanical stimulation or even after implantation.

Mechano-regulation theory-based finite element analysis on the effects of driving strain history on cellular differentiation

The aim of this study was to determine the appropriate driving strain history of a dynamic cell culture device for inducing accelerated cell differentiation. Silicone rubber film is an electroactive polymer and was used as a flexible cell stimulator to transfer mechanical strains to developing cells. Mechano-regulation theory with a deviatoric strain was used to estimate tissue differentiation under strain conditions during iterative calculations by means of finite element analysis. Various driving strain histories comprising 4%, 5%, and 6% strains were introduced to determine the correlation between the strain history and the development of cell phenotypes. The simulation results revealed that driving strain conditions mainly comprising low levels of strain (4%) provided appropriate conditions for differentiating mesenchymal cells into osteoblasts.

SIMULATION ON TISSUE DIFFERENTIATIONS FOR DIFFERENT ARCHITECTURE DESIGNS IN BONE TISSUE ENGINEERING SCAFFOLD BASED ON CELLULAR STRUCTURE MODEL

In bone tissue engineering, mechanical stimuli are among the key factors affecting cell proliferation and differentiation. This study aimed to investigate the effects of different inlet fluid velocities and axial strains on the differentiation of bone marrow mesenchymal stem cells (BMSCs) on the surface of scaffolds with different morphologies. Five three-dimensional bone scaffold architectures with 65% porosity were designed using typical cellular structural models of trabecular bone. Apparent compressive strains between 0% and 5% were applied to simulate an unconfined compression test. Strain distributions were analyzed on the wall surface of the solid model. The interstitial fluid flow at inlet velocities ranging between 0.01 mm/s and 1 mm/s was applied to interconnected pores, simulating a steady state flow in the scaffold. The shear stress distributions on the surface of the scaffolds were calculated. The differentiation of BMSCs on the surface of the scaffolds with different morphologies was predicted according to mechanoregulation theory. This study shows that different levels of mechanical stimuli can be generated as a result of different scaffold morphologies under compressive loading and fluid flow to satisfy the mechanical requirements for different bone defect sites.

Evaluation of the development of tissue phenotypes: Bone fracture healing using functionally graded material composite bone plates

Long bone fractures are conventionally treated using metallic implants that may be accompanied by complications such as stress shielding, corrosion, poor fatigue life, and loosening. Flexible fixations by reducing the structural stiffness of prostheses or using low modulus materials are promising alternatives to overcome these problems. In this study, different configurations of bone plates developed from functionally graded material (FGM) composites were considered to investigate the effect of bending stiffness on bone fracture healing while maintaining an equivalent bone plate modulus. The healing performance and development of tissue phenotypes were estimated using mechano-regulation theory with deviatoric strain, which was implemented and analyzed with the commercial software ABAQUS 6.10 and a user’s subroutine program. The most effective configuration of FGM layers was proposed based on the healing performance.

Modeling mechanical signals on the surface of µCT and CAD based rapid prototype scaffold models to predict (early stage) tissue development.

In the field of tissue engineering, mechano-regulation theories have been applied to help predict tissue development in tissue engineering scaffolds in the past. For this, finite element models (FEMs) were used to predict the distribution of strains within a scaffold. However, the strains reported in these studies are volumetric strains of the material or strains developed in the extracellular matrix occupying the pore space. The initial phase of cell attachment and growth on the biomaterial surface has thus far been neglected. In this study, we present a model that determines the magnitude of biomechanical signals on the biomaterial surface, enabling us to predict cell differentiation stimulus values at this initial stage. Results showed that magnitudes of the 2D strain--termed surface strain--were lower when compared to the 3D volumetric strain or the conventional octahedral shear strain as used in current mechano-regulation theories. Results of both µCT and CAD derived FEMs from the same scaffold were compared. Strain and fluid shear stress distributions, and subsequently the cell differentiation stimulus, were highly dependent on the pore shape. CAD models were not able to capture the distributions seen in the µCT FEM. The calculated mechanical stimuli could be combined with current mechanobiological models resulting in a tool to predict cell differentiation in the initial phase of tissue engineering. Although experimental data is still necessary to properly link mechanical signals to cell behavior in this specific setting, this model is an important step towards optimizing scaffold architecture and/or stimulation regimes.

Simulation of the bone healing process of fractured long bones applied with a composite bone plate with consideration of the blood vessel growth

The healing process of long bones such as the tibia was simulated on the basis of a mechanoregulation theory by taking blood vessel growth into consideration. The tissue differentiation process of calluses by taking into consideration blood vessel growth was simulated by a user subroutine program based on the mechanoregulation model and a diffusion equation. Composite bone plates made of a plain weave carbon/epoxy composite (WSN3k) and a plain weave glass/polypropylene composite (Twintex) were applied to the fracture site to investigate the effect of plate modulus on the healing performance. The simulation results revealed that the flexible composite bone plate made of Twintex [0]18, which had a slightly higher Young’s modulus than a cortical bone, provided the highest healing performance. Moreover, it was found that the effect of the plate modulus on the healing performance reduced when the blood vessel growth at the fracture site was considered, which reflected a more realistic bone healing process.

The finite element analysis for endochondral ossification process of a fractured tibia applied with a composite IM-rod based on a mechano-regulation theory using a deviatoric strain

The bone healing process of fractured tibias applied with various composite IM rods, respectively, was analyzed using finite element analysis. Based on a mechano-regulation theory with a deviatoric strain as a mechanical stimulation the process of tissue differentiation was simulated by a user’s subroutine programmed by a Python code for an iterative calculation. Several representative composite IM rods (fabric composites made of a carbon/epoxy and a glass/polypropylene) were investigated to find the rod modulus appropriate for healing bone fractures. It was found that the initial loading condition was the most sensitive factor of healing performance and that the flexible composite IM rod (WSN3k [±45]nT) was able to accelerate tissue differentiation under a reasonable initial loading condition (3 point gait after surgery), resulting in early bone union.

메카노 규제 이론에 기초한 복합재료 IM-rod가 적용된 골절부의 세포분화과정의 유한요소해석

본 논문에서는 복합재료 IM rod가 적용된 골절부의 세포 분화과정을 모사하기 위해 유한요소해석을 실시하였다. 세포의 골화과정을 해석하기 위해 편향 변형률을 이용한 메카노 규제 이론을 사용하였으며, 반복 계산을 위해 Python 코드를 이용하여 서브루틴을 구현하였다. 치료에 가장 적절한 복합재료 IM rod의 강성을 찾기 위해 직물 탄소섬유/에폭시 복합재료 (WSN3k)의 적층각도를 바꾸어 해석을 실시하였다. 골절부에 가해지는 기계적 자극에 따른 치료효율을 비교하기 위해 두 가지 초기 하중 조건을 적용하였다. 그 결과 치료효율은 강성의 차이보다 하중에 의해 큰 영향을 받았으며, 초기 하중이 몸무게의 10%이고, 적층순서가 <TEX>$[{\pm}45]_{nT}$</TEX>일 때 치료효율이 가장 높았다. This paper describes the bone healing process of fractured long bones such as a tibia applied by composite IM rods using finite element analysis. To simulated tissue differentiation process mechano-regulation theory with a deviatoric strain was implemented and a user's subroutine programmed by a Python code for an iterative calculation was used. To broadly find the appropriate rod modulus for healing bone fractures, composite IM rods were analyzed considering the stacking sequence. To compare mechanical stimulation at fracture gap, two kinds of initial loading conditions were applied. As a result, it was found that the initial loading condition was the most sensitive factor for the healing performance. In case a composite IM rod made of a plain weave carbon fiber/epoxy (WSN3k) had a stacking sequence of <TEX>$[{\pm}45]_{nT}$</TEX>, the healing efficiency was the most effective under a initial load of 10%BW.

The simulation of bone healing process of fractured tibia applied with composite bone plates according to the diaphyseal oblique angle and plate modulus

This paper presents the simulation of the bone healing process of a fractured tibia with oblique angles according to plate modulus and initial loading condition by FE analysis. To simulate tissue differentiation and the pathway of development of the curing cells during the healing process, a mechano-regulation theory on deviatoric strain is introduced. For the iterative calculation to determine cell phenotype during the healing period, a user subroutine was programmed by Python code. The analysis result revealed that the healing efficiency was strongly affected by the initial loading condition and the coupling of the plate’s modulus with the oblique angle. By FE analysis, the most appropriate plate modulus for each initial load condition and oblique angle was suggested.

The simulation of tissue differentiation at a fracture gap using a mechano-regulation theory dealing with deviatoric strains in the presence of a composite bone plate

The endochondral ossification process of fractured long bones was simulated using a three-dimensional finite element model when various composite bone plates were applied to the fracture site. To simulate time-varying cell phenotypes and the corresponding deviatoric strains in the calluses, a user’s subroutine was programmed for iterative calculations. Three representative initial loading conditions were investigated to find a relationship between the initial loading condition and tissue differentiation. Through finite element analysis, the trends in tissue differentiation and healing efficiency in the calluses were evaluated according to the plate modulus and loading conditions; further, the most appropriate plate modulus under each initial loading condition was suggested.

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

A number of mechano-regulation theories have been proposed that relate the differentiation pathway of mesenchymal stem cells (MSCs) to their local biomechanical environment. During spontaneous repair processes in skeletal tissues, the organisation of the extracellular matrix is a key determinant of its mechanical fitness. In this paper, we extend the mechano-regulation theory proposed by Prendergast et al. (J Biomech 30(6):539-548, 1997) to include the role of the mechanical environment on the collagen architecture in regenerating soft tissues. A large strain anisotropic poroelastic material model is used in a simulation of tissue differentiation in a fracture subject to cyclic bending (Cullinane et al. in J Orthop Res 20(3):579-586, 2002). The model predicts non-union with cartilage and fibrous tissue formation in the defect. Predicted collagen fibre angles, as determined by the principal decomposition of strain- and stress-type tensors, are similar to the architecture seen in native articular cartilage and neoarthroses induced by bending of mid-femoral defects in rats. Both stress and strain-based remodelling stimuli successfully predicted the general patterns of collagen fibre organisation observed in vivo. This provides further evidence that collagen organisation during tissue differentiation is determined by the mechanical environment. It is envisioned that such predictive models can play a key role in optimising MSC-based skeletal repair therapies where recapitulation of the normal tissue architecture is critical to successful repair.

Finite element study of scaffold architecture design and culture conditions for tissue engineering

Tissue engineering scaffolds provide temporary mechanical support for tissue regeneration and transfer global mechanical load to mechanical stimuli to cells through its architecture. In this study the interactions between scaffold pore morphology, mechanical stimuli developed at the cell microscopic level, and culture conditions applied at the macroscopic scale are studied on two regular scaffold structures. Gyroid and hexagonal scaffolds of 55% and 70% porosity were modeled in a finite element analysis and were submitted to an inlet fluid flow or compressive strain. A mechanoregulation theory based on scaffold shear strain and fluid shear stress was applied for determining the influence of each structures on the mechanical stimuli on initial conditions. Results indicate that the distribution of shear stress induced by fluid perfusion is very dependent on pore distribution within the scaffold. Gyroid architectures provide a better accessibility of the fluid than hexagonal structures. Based on the mechanoregulation theory, the differentiation process in these structures was more sensitive to inlet fluid flow than axial strain of the scaffold. 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.

Corroboration of mechanobiological simulations of tissue differentiation in an in vivo bone chamber using a lattice‐modeling approach

It is well established that the mechanical environment modulates tissue differentiation, and a number of mechanoregulatory theories for describing the process have been proposed. In this study, simulations of an in vivo bone chamber experiment were performed that allowed direct comparison with experimental data. A mechanoregulation theory for mesenchymal stem cell differentiation based on a combination of fluid flow and shear strain (computed using finite element analysis) was implemented to predict tissue differentiation inside mechanically controlled bone chambers inserted into rat tibae. To simulate cell activity, a lattice approach with stochastic cell migration, proliferation, and selected differentiation was adopted; because of its stochastic nature, each run of the simulation gave a somewhat different result. Simulations predicted the load-dependency of the tissue differentiation inside the chamber and a qualitative agreement with histological data; however, the full variability found between specimens in the experiment could not be predicted by the mechanoregulation algorithm. This result raises the question whether tissue differentiation predictions can be linked to genetic variability in animal populations.