The impact of osteoporosis and diabetes on fracture healing under different loading conditions.

BACKGROUND: Osteoporosis and diabetes are two prevalent conditions among the elderly population. Each of these conditions can profoundly influence the fracture healing process by disturbing the associated inflammatory process. However, the combined effects of osteoporosis and diabetes on fracture healing remain unclear. Therefore, the purpose of the present study is to investigate the role of osteoporosis and diabetes in fracture healing and the underlying mechanisms by developing numerical models. METHOD: This study introduces a numerical model that consists of a three-dimensional model of a tibia fracture stabilized by a Locking Compression Plate (LCP), coupled with a two-dimensional axisymmetric model which illustrates the transport and reactions of cells and cytokines throughout the inflammatory phase in early fracture healing. First, the model parameters were calibrated using available experimental data. The model was then implemented to predict the healing outcomes of fractures under five varied conditions, consisting of both osteoporotic and non-osteoporotic bones, each subjected to different physiological loads. RESULTS: The instability of the fracture callus can significantly escalate in osteoporotic fractures (e.g., when a 150 N physiological load is applied, the unstable region of the osteoporotic fracture callus can reach 26 %, in contrast to 12 % in non-osteoporotic fractures). Additionally, the mesenchymal stem cells (MSCs) proliferation and differentiation can be disrupted in osteoporotic fracture compared to non-osteoporotic fractures (e.g., on the 10th day post-fracture, the decrease in the concentration of MSCs, osteoblasts, and chondrocytes in osteoporotic fractures is nearly double that in non-osteoporotic fractures under a 150 N). Finally, the healing process of fractures can suffer significant impairment when osteoporosis coexists with diabetes (e.g., the concentration of MSCs can be drastically reduced by nearly 37 % in osteoporotic fractures under diabetic conditions when subjected to a load of 200 N) CONCLUSIONS: Fracture calluses destabilized by osteoporosis can negatively affect the fracture healing process by disrupting the proliferation and differentiation of mesenchymal stem cells (MSCs). Moreover, when osteoporosis coexists with diabetes, the fracture healing process can severely impair the fracture healing outcomes.

Effect of uncertain clinical conditions on the early healing and stability of distal radius fractures.

BACKGROUND AND OBJECTIVES: The healing outcomes of distal radius fracture (DRF) treated with the volar locking plate (VLP) depend on surgical strategies and postoperative rehabilitation. However, the accurate prediction of healing outcomes is challenging due to a range of certainties related to the clinical conditions of DRF patients, including fracture geometry, fixation configuration, and physiological loading. The purpose of this study is to investigate the influence of uncertainty and variability in fracture/fixation parameters on the mechano-biology and biomechanical stability of DRF, using a probabilistic numerical approach based on the results from a series of experimental tests performed in this study. METHODS: Six composite radius sawboneses fitted with titanium VLP (VLP 2.0, Austofix) were loaded to failure at a rate of 2 N/s. The testing results of the elastic and plastic behaviour of the VLP were used as inputs for a probabilistic-based computational model of DRF, which simulated mechano-regulated tissue differentiation and fixation elastic capacity at the fracture site. Finally, the probability of success in early indirect healing and fracture stabilisation was predicted. RESULTS: The titanium VLP is a strong and ductile fixation whose flexibility and elastic capacity are governed by flexion working length and bone-to-plate distance, respectively. A fixation with optimised designs and configurations is critical to mechanically stabilising the early fracture site. Importantly, the uncertainty and variability in fracture/fixation parameters could compromise early DRF healing. The physiological loading uncertainty is the most adverse factor, followed by the negative impact of uncertainty in fracture geometry. CONCLUSIONS: The VRP 2.0 fixation made of grade II titanium is a desirable fixation that is strong enough to resist irreparable deformation during early recovery and is also ductile to deform plastically without implant failure at late rehabilitation.

Computational Modelling for Managing Pathways to Cartilage Failure.

Over several decades the perception and therefore description of articular cartilage changed substantially. It has transitioned from being described as a relatively inert tissue with limited repair capacity, to a tissue undergoing continuous maintenance and even adaption, through a range of complex regulatory processes. Even from the narrower lens of biomechanics, the engagement with articular cartilage has changed from it being an interesting, slippery material found in the hostile mechanical environment between opposing long bones, to an intriguing example of mechanobiology in action. The progress revealing this complexity, where physics, chemistry, material science and biology are merging, has been described with increasingly sophisticated computational models. Here we describe how these computational models of cartilage as an integrated system can be combined with the approach of structural reliability analysis. That is, causal, deterministic models placed in the framework of the probabilistic approach of structural reliability analysis could be used to understand, predict, and mitigate the risk of cartilage failure or pathology. At the heart of this approach is seeing cartilage overuse and disease processes as a 'material failure', resulting in failure to perform its function, which is largely mechanical. One can then describe pathways to failure, for example, how homeostatic repair processes can be overwhelmed leading to a compromised tissue. To illustrate this 'pathways to failure' approach, we use the interplay between cartilage consolidation and lubrication to analyse the increase in expected wear rates associated with cartilage defects or meniscectomy.

Development of numerical model-based machine learning algorithms for different healing stages of distal radius fracture healing.

BACKGROUND AND OBJECTIVES: Early therapeutic exercises are vital for the healing of distal radius fractures (DRFs) treated with the volar locking plate. However, current development of rehabilitation plans using computational simulation is normally time-consuming and requires high computational power. Thus, there is a clear need for developing machine learning (ML) based algorithms that are easy for end-users to implement in daily clinical practice. The purpose of the present study is to develop optimal ML algorithms for designing effective DRF physiotherapy programs at different stages of healing. METHOD: First, a three-dimensional computational model for the healing of DRF was developed by integrating mechano-regulated cell differentiation, tissue formation and angiogenesis. The model is capable of predicting time-dependant healing outcomes based on different physiologically relevant loading conditions, fracture geometries, gap sizes, and healing time. After being validated using available clinical data, the developed computational model was implemented to generate a total of 3600 clinical data for training the ML models. Finally, the optimal ML algorithm for each healing stage was identified. RESULTS: The selection of the optimal ML algorithm depends on the healing stage. The results from this study show that cubic support vector machine (SVM) has the best performance in predicting the healing outcomes at the early stage of healing, while trilayered ANN outperforms other ML algorithms in the late stage of healing. The outcomes from the developed optimal ML algorithms indicate that Smith fractures with medium gap sizes could enhance the healing of DRF by inducing larger cartilaginous callus, while Colles fractures with large gap sizes may lead to delayed healing by bringing excessive fibrous tissues. CONCLUSIONS: ML represents a promising approach for developing efficient and effective patient-specific rehabilitation strategies. However, ML algorithms at different healing stages need to be carefully chosen before being implemented in clinical applications.

Osteochondral junction leakage and cartilage joint lubrication.

BACKGROUND AND OBJECTIVES: Previous studies have shown that there is potentially interstitial fluid exchange between cartilage tissue and the subarticular spongiosa region in the case of injury or disease (e.g., osteoarthritis and osteoporosis). Interstitial flow is also required for cartilage lubrication under joint load. A key question then is how cartilage lubrication is modified by increased interstitial fluid leakage across the osteochondral junction. Thus, the purpose of this study is to develop a numerical model to investigate changes in cartilage lubrication with changes in osteochondral junction leakage. METHODS: The multi-phase coupled model includes domains corresponding to the contact gap, cartilage tissue and subchondral bone plate region (ScBP). Each of these domains are treated as poroelastic systems, with their coupling implemented through mass and pressure continuity. The effects of osteochondral junction leakage on lubrication were investigated with a parametric study on the relative permeability between the ScBP and cartilage tissue. RESULTS: Significant effects of ScBP permeability were predicted, especially during the early stage of the junction leakage development (early stage of the disease). There is a significant reduction in mixed-mode lubrication duration under the effect of increased junction leakage (the cartilage tissue mixed-mode lubrication duration is about 33% decrease for a relative permeability ratio of 0.1 between ScBP and cartilage tissue, and about 52% decrease under the osteoarthritis condition). In addition, the time for cartilage to reach steady-state consolidation is significantly reduced when ScBP permeability increases (the consolidation time reduces from roughly 2 h to 1.2 h when the relative permeability ratio increases from 0.001 to 0.1, and it reduces to 0.8 h for an advanced osteoarthritis condition). It is predicted that the initial friction coefficient could increase by over 60% when the ScBP permeability is consistent with an advanced osteoarthritis (OA) condition. CONCLUSION: Increased osteochondral junction leakage induced by joint injury and disease could result in increased cartilage surface wear rates due to more rapid interstitial fluid depressurization within articular cartilage.

Influence of muscle loading on early-stage bone fracture healing.

Designing weight-bearing exercises for patients with lower-limb bone fractures is challenging and requires a systematic approach that accounts for patient-specific loading conditions. However, 'trial-and-error' approaches are commonplace in clinical settings due to the lack of a fundamental understanding of the effect of weight-bearing exercises on the bone healing process. Whilst computational modelling has the potential to assist clinicians in designing effective patient-specific weight-bearing exercises, current models do not explicitly account for the effects of muscle loading, which could play an important role in mediating the mechanical microenvironment of a fracture site. We combined a fracture healing model involving a tibial fracture stabilised with a locking compression plate (LCP) with a detailed musculoskeletal model of the lower limb to determine interfragmentary strains in the vicinity of the fracture site during both full weight-bearing (100% body weight) and partial weight-bearing (50% body weight) standing. We found that muscle loading significantly altered model predictions of interfragmentary strains. For a fractured bone with a standard LCP configuration (bone-plate distance = 2 mm, working length = 30 mm) subject to full weight-bearing, the predicted strains at the near and far cortices were 23% and 11% higher when muscle loading was included compared to the case when muscle loading was omitted. The knee and ankle muscles accounted for 38% of the contact force exerted at the knee joint during quiet standing and contributed significantly to the strains calculated at the fracture site. Thus, models of bone fracture healing ought to account explicitly for the effects of muscle loading. Furthermore, the study indicated that LCP configuration parameters play a crucial role in influencing the fracture site microenvironment. The results highlighted the dominance of working length over bone-plate distance in controlling the flexibility of fracture sites stabilised with LCP devices.

The effects of mechanical instability on PDGF mediated inflammatory response at early stage of fracture healing under diabetic condition.

BACKGROUND AND OBJECTIVE: Mechanical stability plays an important role in fracture healing process. Excessive interfragmentary movement will continuously damage the tissue and newly formed capillaries at the fracture site, which leads to overproduction of platelet-derived growth factor (PDGF) that attracts more macrophages into fracture callus, ultimately persistent and enhanced inflammatory response happens. For diabetic condition, the impact of mechanical instability of fracture site on inflammatory response could be further compliciated and the relevant research in this field is relatively limited. METHODS: Building on previous experimental studies, this study presents a numerical model consisting of a system of reactive-transport equations representing the transport as well as interactions of different cells and cytokines within the fracture callus. The model is initially validated by available experimental data, and then implemented to investigate the role of mechanical stability of fracture site in inflammatory response during early stage of healing. It is assumed that there is an increased release of PDGF due to the rupture of blood vessels resulting from mechanical instability, which leads to increased production of inflammatory cytokines (i.e., TNF-α). The bone healing process under three different conditions were investigated, i.e., mechanically stable condition with normal inflammatory response (Control, Case 1), mechanically unstable condition with normal inflammatory response (Case 2) and mechanically unstable condition with diabetes (Case 3). RESULTS: Mechanical instability can promote the macrophage infiltration and thus induce an enhanced and prolonged inflammatory response, which could impede the MSCs proliferation during the early fracture healing stage (e.g., compared with the control condition, the MSCs concentration in unstable fracture with normal inflammatory response can be reduced by 3.2% and 5.2% on day 2 and day 10 post-fracture, respectively). Under diabetic condition, the mechanical instability of fracture site could lead to a significant increase of TNF-α concentration in fracture callus (Case 3) in comparison to control (Case 1) (e.g., three-fold increase in TNF-α concentration compared to control). In addition, the results show that the mechanical instability affects the cell differentiation and proliferation in fracture callus in a spatially dependent manner, e.g., for diabetic fracture patients, the mechanical instability could potentially decrease the concentration of MSCs, osteoblasts and chondrocytes by around 39%, 30% and 29% in cortical callus, respectively, in comparison to control. CONCLUSION: The mechanical instability together with diabetic condition can significantly affect the natural resolution of inflammation during early stage of healing by turning acute inflammation into chronic inflammation which is characterized by a continuously upregulated TNF-α pathway.

Influences of variability and uncertainty in vertical and horizontal surface roughness on articular cartilage lubrication.

BACKGROUND AND OBJECTIVES: Cartilage surface roughness has significant implications on joint lubrication. However, the effects of the variability in surface roughness in different directions (especially in horizontal direction) in mixed-mode lubrication have not been fully investigated and relevant research work in this field is limited. This study presents a probabilistic numerical approach to investigate the influence of variability and uncertainty of Root-Mean-Square (RMS) roughness heights (vertical roughness) and roughness correlation lengths (horizontal roughness) on cartilage lubrication. METHODS: The synthetic surface topographies with typical ranges of vertical and horizontal roughness characteristics were firstly input to a coupled cartilage contact model. A response surface was then constructed using the input roughness parameters and the output coefficient of friction (CoF). Finally, a large number of independent or correlated roughness samples were generated for computing the probability of mixed-mode lubrication failure (PoF), which was defined as CoF > 0.27 (corresponding to a 90% loss of fluid support in the contact interface). RESULTS: Both independent RMS roughness heights and correlation lengths are correlated positively with CoF. This indicates that the increase of the vertical surface roughness could exacerbate cartilage wear, whereas increasing surface roughness in horizontal direction (i.e., reducing correlation lengths) could retain gap fluid that aids mixed-mode lubrication. Importantly, it shows that CoF is dominant by RMS roughness height. The uncertainty in the independent correlation lengths may lead to the underestimation of PoF. By simulating osteoarthritic surface roughness with a strong correlation between RMS roughness heights and correlation lengths, the value of PoF could reach 70-99%. CONCLUSION: This study highlights the significance of incorporating the mutual relations between the surface roughness in vertical and horizontal directions into research, and the findings could potentially contribute to the design of biomimetic cartilage surfaces for the treatment of osteoarthritis.

Influence of therapeutic grip exercises induced loading rates in distal radius fracture healing with volar locking plate fixation.

BACKGROUND AND OBJECTIVE: Therapeutic exercises could potentially enhance the healing of distal radius fractures (DRFs) treated with volar locking plate (VLP). However, the healing outcomes are highly dependant on the patient-specific fracture geometries (e.g., gap size) and the loading conditions at the fracture site (e.g., loading frequency) resulted from different types of therapeutic exercises. The purpose of this study is to investigate the effects of different loading frequencies induced by therapeutic exercises on the biomechanical microenvironment of the fracture site and the transport of cells and growth factors within the fracture callus, ultimately the healing outcomes. This is achieved through numerical modelling and mechanical testing. METHODS: Five radius sawbones specimens (Pacific Research Laboratories, Vashon, USA) fixed with VLP (VRP2.0+, Austofix) were mechanically tested using dynamic test instrument (INSTRON E3000, Norwood, MA). The loading protocol used in mechanical testing involved a series of cyclic axial compression tests representing hand and finger therapeutic exercises. The relationship between the dynamic loading rate (i.e., loading frequency) and dynamic stiffness of the construct was established and used as inputs to a developed numerical model for studying the dynamic loading induced cells and growth factors in fracture site and biomechanical stimuli required for healing. RESULTS: There is a strong positive linear relationship between the loading rate and axial stiffness of the construct fixed with VLP. The loading rates induced by the moderate frequencies (i.e., 1-2 Hz) could promote endochondral ossification, whereas relatively high loading frequencies (i.e., over 3 Hz) may hinder the healing outcomes or lead to non-union. In addition, a dynamic loading frequency of 2 Hz in combination of a fracture gap size of 3 mm could produce a better healing outcome by enhancing the transport of cells and growth factors at the fracture site in comparison to free diffusion (i.e. without loading), and thereby produces a biomechanical microenvironment which is favourable for healing. CONCLUSION: The experimentally validated numerical model presented in this study could potentially contribute to the design of effective patient-specific therapeutic exercises for better healing outcomes. Importantly, the model results demonstrate that therapeutic grip exercises induced dynamic loading could produce a better biomechanical microenvironment for healing without compromising the mechanical stability of the overall volar locking plate fixation construct.

Role of TNF-α in early-stage fracture healing under normal and diabetic conditions.

BACKGROUND AND OBJECTIVE: Inflammatory response plays a crucial role in the early stage of fracture healing. Immediately after fracture, the debris and immune cells (e.g., macrophages), recruited into the fracture callus, lead to the secretion of inflammatory cytokines, such as tumor necrosis factor-alpha (TNF-α), which governs the mesenchymal stem cells (MSCs) mediated healing processes. However, it is still unclear how chronic inflammatory diseases (e.g., diabetes) affect the level of TNF-α in fracture callus, ultimately the healing outcomes at the early stage of healing. Therefore, the purpose of this study is to develop a numerical model for investigating TNF-α mediated bone fracture healing. METHODS: A mathematical model consisting of a system of partial differential equations that represent the reactive transport of cells and cytokines in the fracture callus is developed in this study. The model is first calibrated by using available experimental data and then implemented to study the effect of TNF-α on the early stage of fracture healing under normal and diabetic conditions. RESULTS: There is a significant elevation of TNF-α level in facture callus during the first 24 h post-fracture in normal condition, and its influence in the concentration of MSCs and cell differentiation becomes significant three days post-fracture (e.g., the absence of TNF-α signaling could reduce the concentration of MSCs more than 20% in cortical callus). In addition, the excessive secretion of TNF-α induced by diabetes could decrease the concentration of MSCs at the initial stage of healing, particularly reduce the concentration of MSCs in cortical callus by around 25%. CONCLUSION: The model predictions suggested that there should be an optimal concentration of TNF-α in fracture callus, which enhances the early stage of healing, and excessive or insufficient secretion of TNF-α might significantly hinder the healing process.

Optimal time-dependent levels of weight-bearing for bone fracture healing under Ilizarov circular fixators.

It is known that weight-bearing exercises under Ilizarov circular fixators (ICF) could enhance bone fracture healing by mechano-regulation. However, interfragmentary movements at the fracture site induced by weight-bearing may inhibit angiogenesis and ultimately delay the healing process. To tackle this challenge, a computational model is presented in this study which considers the spatial and temporal changes in mechanical properties of fracture callus to predict optimal levels of weight-bearing during fracture healing under ICF. The study takes sheep fractures as example and shows that the developed model has the capability of predicting patient specific, time-dependent optimal levels of weight-bearing which enhances mechano-regulation mediated healing without hindering the angiogenesis process. The results demonstrate that allowable level of weight-bearing and timings depend on fracture gap size. For normal body weights (BW) and moderate fracture gap sizes (e.g. 3 mm), weight-bearing with 30% BW could start by week 4 post-operation and gradually increase to 100% BW by week 11. In contrast, for relatively large fracture gap sizes (i.e. 6 mm), weight-bearing is recommended to commence in later stages of healing (e.g. week 11 post-operation). Furthermore, increasing ICF stiffness (e.g. using half pins instead of pretension wires) can increase the level of weight-bearing significantly in the early stages up to a certain time point (e.g. week 8 post-operation) beyond which no noticeable benefits could be achieved. The findings of this study have potential applications in designing post-operative weight bearing exercises.

Balance Between Mechanical Stability and Mechano-Biology of Fracture Healing Under Volar Locking Plate.

The application of volar locking plate (VLP) is promising in the treatment of dorsally comminuted and displaced fracture. However, the optimal balance between the mechanical stability of VLP and the mechanobiology at the fracture site is still unclear. The purpose of this study is to develop numerical models in conjunction with experimental studies to identify the favourable mechanical microenvironment for indirect healing, by optimizing VLP configuration and post-operative loadings for different fracture geometries. The simulation results show that the mechanical behaviour of VLP is mainly governed by the axial compression. In addition, the model shows that, under relatively large gap size (i.e., 3-5 mm), the increase of FWL could enhance chondrocyte differentiation while a large BPD could compromise the mechanical stability of VLP. Importantly, bending moment produced by wrist flexion/extension and torsion moment produced from forearm rotation could potentially hinder endochondral ossification at early stage of healing. The developed model could potentially assist orthopaedic surgeons in surgical pre-planning and designing post-operation physical therapy for treatment of distal radius fractures.

A probabilistic approach for modelling bone fracture healing under Ilizarov circular fixator.

Bone fracture treatments using Ilizarov circular fixator (ICF) involve dealing with uncertainties about a range of critical factors that control the mechanical microenvironment of the fracture site such as ICF configuration, fracture gap size, physiological loading etc. To date, the effects of the uncertainties about these critical factors on the mechanical microenvironment of the fracture site have not been fully understood. The purpose of this study is to tackle this challenge by using computational modelling in conjunction with engineering reliability analysis. Particularly, the effects of uncertainties in fracture gap size (GS), level of weight-bearing (P), ICF wire pretension (T) and wire diameter (WD) on the fracture site mechanical microenvironment at the beginning of the reparative phase of healing was investigated in this study. The results show that the mechanical microenvironment of fracture site stabilised with ICF is very sensitive to the uncertainties in P and GS. For example, an increase in the coefficient of variation of P (COVP ) from 0.1 to 0.9 (i.e., an increase in the uncertainty in P) could reduce the probability of achieving a favourable mechanical microenvironment within the fracture site (i.e., Probability of Success, PoS) by more than 50%, while an increase in the coefficient of variation of GS (COVGS ) from 0.1 to 0.9 could decrease PoS by around 30%. In contrast, an increase in the uncertainties in T and WD (COV increase from 0.1 to 0.9) has little influence on the fracture site mechanical microenvironment (PoS changes <5%).

A Probabilistic Failure Risk Approach to The Problem of Articular Cartilage Lubrication.

BACKGROUND AND OBJECTIVE: The geometrical and mechanical properties that characterise the cartilage contact gap are uncertain and spatially varied. To date the effects of such uncertainties on cartilage lubrication have not been explored. Using a probabilistic approach, the purpose of this study is to numerically investigate the influence of surficial cartilage glycoaminoglycan (GAG) content on joint lubrication behaviour. Gap asperity stiffness and polymer brush border (PBB) thickness are affected by the uncertainty of surficial GAG concentration, and so their correlated effects in maintaining hydrodynamic joint lubrication are investigated. METHODS: Correlated sampling data are first generated by Monte Carlo simulation. These data are used as inputs for the cartilage contact model, which includes three distinctive features of cartilage tissue (tension-compression nonlinearity, aggrecan dependent permeability and compressive modulus) and fluid flow resistance effects of PBB on cartilage surface. The degree of hydrodynamic lubrication after thirty minutes of constant loading is used as an indicator for assessing the lubrication performance at the contact interface. RESULTS: The increase of PBB thickness with GAG concentration enhances the hydrodynamic lubrication component in the cartilage contact gap, whereas increasing the asperity stiffness with GAG concentration impairs hydrodynamic lubrication. GAG loss rate increases with the rise of GAG concentration. More aggrecan shedding through the surface could result in a thicker and denser PBB, and therefore enhance the lubrication performance in mixed-mode regime. On the other hand, higher GAG content makes the asperities stiffer, which may impede contact gap closure, and thus encourage gap fluid loss and impair the lubrication performance of cartilage. CONCLUSION: The lubrication performance of cartilage varies with the physiological conditions of the joint. Since a range of variables are internally related, the outcomes on joint lubrication are difficult to predict. A probabilistic approach accounting for the uncertainties can potentially result in more accurate evaluations of joint lubrication performance.

The investigation of bone fracture healing under intramembranous and endochondral ossification.

After trauma, fractured bone starts healing directly through bone union or indirectly through callus formation process. Intramembranous and endochondral ossification are two commonly known mechanisms of indirect healing. The present study investigated the bone fracture healing under intramembranous and endochondral ossification by developing theoretical models in conjunction with performing a series of animal experiments. Using experimentally determined mean bone densities in sheep tibia stabilized by the Locking Compression Plate (LCP) fixation system, the research outcomes showed that intramembranous and endochondral ossification can be described by Hill Function with two unique sets of function parameters in mechanical stimuli mediated fracture healing. Two different thresholds exist within the range of mechanical simulation index which could trigger significant intramembranous and endochondral ossification, with a relatively higher bone formation rate of endochondral ossification than that of intramembranous ossification. Furthermore, the increase of flexibility of the LCP system and the use of titanium LCP could potentially promote uniform bone formation across the fracture gap, ultimately better healing outcomes.

Computational study on synovial fluid flow behaviour in cartilage contact gap under osteoarthritic condition.

This study numerically investigates the pathological changes of fluid flow in cartilage contact gap due to the changes in cartilage surface roughness and synovial fluid characteristics in osteoarthritic (OA) condition. First, cartilage surface topographies in both healthy and OA conditions are constructed using a numerical approach with consideration of both vertical and horizontal roughness. Then, constitutive equations for synovial fluid viscosity are obtained through calibration against previous experimental data. Finally, the roughness and synovial fluid information are input into the gap flow model to predict the gap permeability. The results show that the rougher surface of OA cartilage tends to decrease gap permeability by around 30%-60%. More importantly, with the reduction in gap size, the decrease in gap permeability becomes more significant, which could result in an early fluid ultrafiltration into the tissue. Moreover, it is demonstrated that the pathological synovial fluid has more deleterious effects on the gap permeability than the OA cartilage surface, as it could potentially increase the gap permeability by a few hundred times for pressure gradients less than 106 Pa/m, which could inhibit the fluid ultrafiltration into the tissue. The outcomes from this research indicate that the change in fluid flow behaviour in contact gap in OA condition could significantly affect the function of articular joints.

The status and challenges of replicating the mechanical properties of connective tissues using additive manufacturing.

The ability to fabricate complex structures via precise and heterogeneous deposition of biomaterials makes additive manufacturing (AM) a leading technology in the creation of implants and tissue engineered scaffolds. Connective tissues (CTs) remain attractive targets for manufacturing due to their "simple" tissue compositions that, in theory, are replicable through choice of biomaterial(s) and implant microarchitecture. Nevertheless, characterisation of the mechanical and biological functions of 3D printed constructs with respect to their host tissues is often limited and remains a restriction towards their translation into clinical practice. This review aims to provide an update on the current status of AM to mimic the mechanical properties of CTs, with focus on arterial tissue, articular cartilage and bone, from the perspective of printing platforms, biomaterial properties, and topological design. Furthermore, the grand challenges associated with the AM of CT replacements and their subsequent regulatory requirements are discussed to aid further development of reliable and effective implants.

A probabilistic-based approach for computational simulation of bone fracture healing.

BACKGROUND AND OBJECTIVE: It is widely known that bone fracture healing is affected by mechanical factors such as fracture geometry, fixation configuration and post-operative weight bearing loading. However, there are several uncertainties associated with the magnitude of the mechanical factors affecting bone healing as it is challenging to adjust and control them in clinical practice. The current bone fracture healing investigations mainly adopt a deterministic approach for identifying the optimal mechanical conditions for a favourable bone healing outcome. However, a probabilistic approach should be used in the analysis to incorporate such uncertainties for prediction of bone healing. METHODS: In this study we developed a probabilistic-based computational model to predict the probability of delayed healing or non-union under different fracture treatment mechanical conditions for fractures stabilised by locking plates. RESULTS: The results show that there is a strong positive linear correlation between the mechanical stimulations (S) in the fracture gap and the magnitude of weight bearing, the bone-plate distance (BPD) and the plate working length (WL), whereas the fracture gap size has a highly negative and nonlinear correlation with S. While the results show that fracture mechanical microenvironment is more sensitive to the uncertainties in WL compared to BPD, the uncertainty associated with the magnitude of WL is very low and can be resulted from implant manufacturing tolerance. However, there is a high uncertainty associated with the magnitude of BPD as it cannot be accurately adjusted during the surgery. The results show that the tissue differentiation at the far cortex of fracture gap is more sensitive to the variation of BPD compared with that at the near cortex. The probability of delayed healing (fibrous tissue formation) at far cortex is increased from 0% to 40% when coefficient of variation (COV) of BPD rises from 0.1 to 0.9 (for average BPD = 2 mm, WL = 65 mm, fracture gap size = 3 mm and Weight bearing = 150 N). Further, both near and far cortex of fracture site are sensitive to the variation in weight bearing loading. CONCLUSIONS: The developed probabilistic model may lead to useful guidelines that could help orthopaedic surgeons identify how reliable a specific fracture treatment strategy is.

The investigation of fluid flow in cartilage contact gap.

Synovial fluid flow in articular joint capsule plays an important role during mixed mode lubrication. However, the actual fluid flow behaviour during cartilage contact has not been fully understood so far. This is due to the difficulties in measuring the gap permeability using conventional experimental techniques. The problem becomes further complicated with consideration of the cartilage surface roughness. Here a validated numerical study was developed to quantify the gap permeability of lateral synovial fluid flow. Both macro- and micro-scale gap flow models were created based on Darcy's law at the macro-scale and the Navier-stokes equation at the micro-scale. To generate model inputs, the cartilage topography was numerically synthesised based on the experimental measurements of bovine medial tibia cartilage surface roughness using Dektak Stylus Profilers. The experimental results show that the average roughness height Ra is 1.97 µm and root-mean-square roughness height Rq is 2.44 µm, while the correlation lengths of the secondary and tertiary undulations are round 100 µm and 20 µm, respectively. The numerical results indicate that the contact gap height and fluid pressure gradient are two critical parameters which significantly affect the gap permeability. As the contact gap closes, there is a decrease in gap permeability, and most importantly, the gap permeability is also very sensitive to the fluid pressure gradient. Furthermore, with gap closure, the permeability of the contact gap gradually approaches that of the cartilage tissue, at which point the contact gap is functional closed. This occurs at a contact gap height around 1 µm and fluid pressure gradient below 5 × 105 Pa/m in this study.

The Effects of Dynamic Loading on Bone Fracture Healing Under Ilizarov Circular Fixators.

Early weight bearing appears to enhance bone fracture healing under Ilizarov circular fixators (ICFs). However, the role of early weight bearing in the healing process remains unclear. This study aims to provide insights into the effects of early weight bearing on healing of bone fractures stabilized with ICFs, with the aid of mathematical modeling. A computational model of fracture site was developed using poro-elastic formulation to simulate the transport of mesenchymal stem cells (MSCs), fibroblasts, chondrocytes, osteoblasts, osteogenic growth factor (OGF), and chondrogenic growth factor (CGF) and MSC differentiation during the early stage of healing, under various combinations of fracture gap sizes (GS), ICF wire pretension forces, and axial loads. 1 h of physiologically relevant cyclic axial loading followed by 23 h of rest in the post-inflammation phase (i.e., callus with granulation tissue) was simulated. The results show that physiologically relevant dynamic loading could significantly enhance cell and growth factor concentrations in the fracture site in a time and spatially dependent manner. 1 h cyclic loading (axial load with amplitude, PA, of 200 N at 1 Hz) increased the content of chondrocytes up to 37% (in all zones of callus), CGF up to 28% (in endosteal and periosteal callus) and OGF up to 50% (in endosteal and cortical callus) by the end of the 24 h period simulated. This suggests that the synergistic effect of dynamic loading-induced advective transport and mechanical stimuli due to early weight bearing is likely to enhance secondary healing. Furthermore, the study suggests that relatively higher PA values or lower ICF wire pretension forces or smaller GS could result in increased chondrocyte and GF content within the callus.