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.

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.

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.

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 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.

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 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.