On the role of diffusible binding partners in modulating the transport and concentration of proteins in tissues

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.

Influence of knee flexion on early femoral fracture healing: A combined analysis of musculoskeletal dynamics and finite elements

BACKGROUND AND OBJECTIVES

Knee flexion causes a certain amount of misalignment and relative movement of the fractured ends of the femur fracture, and if the flexion angle is too large it will affect the stability of the fracture and the healing process, making it challenging to design a safe range of flexion. However, due to a lack of basic understanding of the effect of knee flexion on the mechanical environment at the fracture site, clinicians are often unable to provide an objective and safe range of motion in flexion based on subjective experience. The aim of this study was to evaluate the effect of knee flexion on plate and fracture healing using finite element analysis (FEA).

METHODS

A human musculoskeletal model was constructed based on CT scan data, and the mechanical properties of the fracture site were changed by adjusting the knee flexion angle. The joint forces, muscle forces and moments acting on the femur were obtained by inverse dynamics analysis, and the biomechanical properties of the fracture-plate system were analyzed using finite elements. A finite element model of the fracture-plate system without muscle loading was also constructed. The effect of knee flexion on the safety of plate fixation and fracture healing was evaluated in terms of the biomechanical properties of the plate and the interfragmentary motion of the fracture.

RESULTS

As the knee flexion angle increases, the von Mises stress of the locked compression plate (LCP) first increases, then decreases, then increases again. The deformation from compression bending to tension twisting occurs simultaneously. At 30° of flexion, shear interfragmentary motion (SIM) was dominant and inhibited fracture healing; at more than 45° of flexion, the plate was twisted and deformed to the lateral side of the body, and the fracture site underwent greater misalignment and relative motion, with destructive effects on bone scabs and healing tissues. If muscle loading is not taken into account, the plate will undergo predominantly bending deformation and will overestimate the interfragmentary strain in the far and near cortex.

CONCLUSIONS

Knee flexion causes the plate to deform from compression bending to extension and torsion, which has an important impact on the safety and healing process of the fracture, and this study provides a biomechanical basis to guide the clinician in the post-operative rehabilitation of femoral fractures in the clinical setting.

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.

Depth camera-based model for studying the effects of muscle loading on distal radius fracture healing

BACKGROUND

Distal radius fractures (DRFs) treated with volar locking plates (VLPs) allows early rehabilitation exercises favourable to fracture recovery. However, the role of rehabilitation exercises induced muscle forces on the biomechanical microenvironment at the fracture site remains to be fully explored. The purpose of this study is to investigate the effects of muscle forces on DRF healing by developing a depth camera-based fracture healing model.

METHOD

First, the rehabilitation-related hand motions were captured by a depth camera system. A macro-musculoskeletal model is then developed to analyse the data captured by the system for estimating hand muscle and joint reaction forces which are used as inputs for our previously developed DRF model to predict the tissue differentiation patterns at the fracture site. Finally, the effect of different wrist motions (e.g., from 60° of extension to 60° of flexion) on the DRF healing outcomes will be studied.

RESULTS

Muscle and joint reaction forces in hands which are highly dependent on hand motions could significantly affect DRF healing through imposed compressive and bending forces at the fracture site. There is an optimal range of wrist motion (i.e., between 40° of extension and 40° of flexion) which could promote mechanical stimuli governed healing while mitigating the risk of bony non-union due to excessive movement at the fracture site.

CONCLUSION

The developed depth camera-based fracture healing model can accurately predict the influence of muscle loading induced by rehabilitation exercises in distal radius fracture healing outcomes. The outcomes from this study could potentially assist osteopathic surgeons in designing effective post-operative rehabilitation strategies for DRF patients.

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.

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.

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.

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.

Computational Modeling Intervertebral Disc Pathophysiology: A Review

Lower back pain is a medical condition of epidemic proportion, and the degeneration of the intervertebral disc has been identified as a major contributor. The etiology of intervertebral disc (IVD) degeneration is multifactorial, depending on age, cell-mediated molecular degradation processes and genetics, which is accelerated by traumatic or gradual mechanical factors. The complexity of such intertwined biochemical and mechanical processes leading to degeneration makes it difficult to quantitatively identify cause–effect relationships through experiments. Computational modeling of the IVD is a powerful investigative tool since it offers the opportunity to vary, observe and isolate the effects of a wide range of phenomena involved in the degenerative process of discs. This review aims at discussing the main findings of finite element models of IVD pathophysiology with a special focus on the different factors contributing to physical changes typical of degenerative phenomena. Models presented are subdivided into those addressing role of nutritional supply, progressive biochemical alterations stemming from an imbalance between anabolic and catabolic processes, aging and those considering mechanical factors as the primary source that induces morphological change within the disc. Limitations of the current models, as well as opportunities for future computational modeling work are also discussed.

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.

Osteoarthritis: New Strategies for Transport and Drug Delivery Across Length Scales

Osteoarthritis (OA) is the fourth leading cause of disability in adults. Yet, few viable pharmaceutical options exist for pain abatement and joint restoration, aside from joint replacement at late and irreversible stages of the disease. From the first onset of OA, as joint pain increases, individuals with arthritis increasingly reach for drug delivery solutions, from taking oral glycosaminoglycans (GAGs) bought over the counter from retail stores (e.g., Costco) to getting injections of viscous, GAG-containing synovial fluid supplement in the doctor's office. Little is known regarding the efficacy of delivery mode and/or treatment by such disease-modulating agents. This Review addresses the interplay of mechanics and biology on drug delivery to affected joints, which has profound implications for molecular transport in joint health and (patho)physiology. Multiscale systems biology approaches lend themselves to understand the relationship between the cell and joint health in OA and other joint (patho)physiologies. This Review first describes OA-related structural and functional changes in the context of the multilength scale anatomy of articular joints. It then summarizes and categorizes, by size and charge, published molecular transport studies, considering changes in permeability induced through inflammatory pathways. Finally, pharmacological interventions for OA are outlined in the context of molecular weights and modes of drug delivery. Taken together, the current state-of-the-art points to a need for new drug delivery strategies that harness systems-based interactions underpinning molecular transport and maintenance of joint structure and function at multiple length scales from molecular agents to cells, tissues, and tissue compartments which together make up articular joints. Cutting edge and cross-length and -time scale imaging represents a key discovery enabling technology in this process.

Tuning the selective permeability of polydisperse polymer networks

We study the permeability and selectivity ('permselectivity') of model membranes made of polydisperse polymer networks for molecular penetrant transport, using coarse-grained, implicit-solvent computer simulations. In our work, permeability P is determined on the linear-response level using the solution-diffusion model, P = KDin, i.e., by calculating the equilibrium penetrant partition ratio K and penetrant diffusivity Din inside the membrane. We vary two key parameters, namely the network-network interaction, which controls the degree of swelling and collapse of the network, and the network-penetrant interaction, which tunes the selective penetrant uptake and microscopic energy landscape for diffusive transport. We find that the partitioning K covers four orders of magnitude and is a non-monotonic function of the parameters, well interpreted by a second-order virial expansion of the free energy of transferring one penetrant from a reservoir into the membrane. Moreover, we find that the penetrant diffusivity Din in the polydisperse networks, in contrast to highly ordered membrane structures, exhibits relatively simple exponential decays. We propose a semi-empirical scaling law for the penetrant diffusion that describes the simulation data for a wide range of densities and interaction parameters. The resulting permeability P turns out to follow the qualitative behavior (including maximization and minimization) of partitioning. However, partitioning and diffusion are typically anti-correlated, yielding large quantitative cancellations, controlled and fine-tuned by the network density and interactions, as rationalized by our scaling laws. We finally demonstrate that even small changes of network-penetrant interactions, e.g., by half a kBT, modify the permselectivity by almost one order of magnitude.

The particle in the spider's web: transport through biological hydrogels

Biological hydrogels such as mucus, extracellular matrix, biofilms, and the nuclear pore have diverse functions and compositions, but all act as selectively permeable barriers to the diffusion of particles. Each barrier has a crosslinked polymeric mesh that blocks penetration of large particles such as pathogens, nanotherapeutics, or macromolecules. These polymeric meshes also employ interactive filtering, in which affinity between solutes and the gel matrix controls permeability. Interactive filtering affects the transport of particles of all sizes including peptides, antibiotics, and nanoparticles and in many cases this filtering can be described in terms of the effects of charge and hydrophobicity. The concepts described in this review can guide strategies to exploit or overcome gel barriers, particularly for applications in diagnostics, pharmacology, biomaterials, and drug delivery.

A computational model for investigating the effects of changes in bioavailability of insulin-like growth factor-1 on the homeostasis of the intervertebral disc

Insulin-like growth factor-1 (IGF-1) is well-known for upregulating cell proliferation and biosynthesis of the extracellular matrix in the intervertebral disc (IVD). Pathological conditions, such as obesity or chronic kidney disease cause IGF-1 deficiency in plasma. How this deficiency impacts disc homeostasis remains unknown. Pro-anabolic approaches for the treatment of disc degeneration based on enhancing IGF-1 bioavailability to tissue-cells are considered, but knowledge of their effectiveness in enhancing cellular anabolism of a degenerated disc is limited. In this study, we developed a computational model for disc homeostasis specifically addressing the role of IGF-1 in modulating both extracellular matrix biosynthesis and cellularity in the IVD. This model was applied to investigate how changes in IGF-1 bioavailability, namely deficiency or enhancement of growth factor, affect disc health. In this study, it was found that IGF-1 deficiency mainly affects the biosynthesis of ECM components, especially in the most external regions of the IVD such as the cartilage endplates and the outer portion of annulus fibrosus. Also, a total of three approaches for increasing IGF-1 bioavailability as a therapy for degenerated IVDs were investigated. It was found that all these strategies are only beneficial to those disc regions receiving sufficient nutritional supply (i.e., the outmost IVD regions), while they exacerbate tissue degradation in malnourished regions (i.e., inner portion of the disc). This suggests that pro-anabolic growth factor-based therapies are limited in that their success strongly depends on an adequate nutritional supply to the IVD tissue, which is not guaranteed in degenerated discs.

Bone-cartilage crosstalk: a conversation for understanding osteoarthritis

Although cartilage degradation is the characteristic feature of osteoarthritis (OA), it is now recognized that the whole joint is involved in the progression of OA. In particular, the interaction (crosstalk) between cartilage and subchondral bone is thought to be a central feature of this process. The interface between articular cartilage and bone of articulating long bones is a unique zone, which comprises articular cartilage, below which is the calcified cartilage sitting on and intercalated into the subchondral bone plate. Below the subchondral plate is the trabecular bone at the end of the respective long bones. In OA, there are well-described progressive destructive changes in the articular cartilage, which parallel characteristic changes in the underlying bone. This review examines the evidence that biochemical and biomechanical signaling between these tissue compartments is important in OA disease progression and asks whether such signaling might provide possibilities for therapeutic intervention to halt or slow disease development.

Effects of Tobacco Smoking on the Degeneration of the Intervertebral Disc: A Finite Element Study

Tobacco smoking is associated with numerous pathological conditions. Compelling experimental evidence associates smoking to the degeneration of the intervertebral disc (IVD). In particular, it has been shown that nicotine down-regulates both the proliferation rate and glycosaminoglycan (GAG) biosynthesis of disc cells. Moreover, tobacco smoking causes the constriction of the vascular network surrounding the IVD, thus reducing the exchange of nutrients and anabolic agents from the blood vessels to the disc. It has been hypothesized that both nicotine presence in the IVD and the reduced solute exchange are responsible for the degeneration of the disc due to tobacco smoking, but their effects on tissue homeostasis have never been quantified. In this study, a previously presented computational model describing the homeostasis of the IVD was deployed to investigate the effects of impaired solute supply and nicotine-mediated down-regulation of cell proliferation and biosynthetic activity on the health of the disc. We found that the nicotine-mediated down-regulation of cell anabolism mostly affected the GAG concentration at the cartilage endplate, reducing it up to 65% of the value attained in normal physiological conditions. In contrast, the reduction of solutes exchange between blood vessels and disc tissue mostly affected the nucleus pulposus, whose cell density and GAG levels were reduced up to 50% of their normal physiological levels. The effectiveness of quitting smoking on the regeneration of a degenerated IVD was also investigated, and showed to have limited benefit on the health of the disc. A cell-based therapy in conjunction with smoke cessation provided significant improvements in disc health, suggesting that, besides quitting smoking, additional treatments should be implemented in the attempt to recover the health of an IVD degenerated by tobacco smoking.

The pro-inflammatory cytokine 14-3-3ε is a ligand of CD13 in cartilage

Osteoarthritis is a whole-joint disease characterized by the progressive destruction of articular cartilage involving abnormal communication between subchondral bone and cartilage. Our team previously identified 14-3-3ε protein as a subchondral bone soluble mediator altering cartilage homeostasis. The aim of this study was to investigate the involvement of CD13 (also known as aminopeptidase N, APN) in the chondrocyte response to 14-3-3ε. After identifying CD13 in chondrocytes, we knocked down CD13 with small interfering RNA (siRNA) and blocking antibodies in articular chondrocytes. 14-3-3ε-induced MMP-3 and MMP-13 was significantly reduced with CD13 knockdown, which suggests that it has a crucial role in 14-3-3ε signal transduction. Aminopeptidase N activity was identified in chondrocytes, but the activity was unchanged after stimulation with 14-3-3ε. Direct interaction between CD13 and 14-3-3ε was then demonstrated by surface plasmon resonance. Using labeled 14-3-3ε, we also found that 14-3-3ε binds to the surface of chondrocytes in a manner that is dependent on CD13. Taken together, these results suggest that 14-3-3ε might directly bind to CD13, which transmits its signal in chondrocytes to induce a catabolic phenotype similar to that observed in osteoarthritis. The 14-3-3ε-CD13 interaction could be a new therapeutic target in osteoarthritis.

Predicting Knee Osteoarthritis

Treatment options for osteoarthritis (OA) beyond pain relief or total knee replacement are very limited. Because of this, attention has shifted to identifying which factors increase the risk of OA in vulnerable populations in order to be able to give recommendations to delay disease onset or to slow disease progression. The gold standard is then to use principles of risk management, first to provide subject-specific estimates of risk and then to find ways of reducing that risk. Population studies of OA risk based on statistical associations do not provide such individually tailored information. Here we argue that mechanistic models of cartilage tissue maintenance and damage coupled to statistical models incorporating model uncertainty, united within the framework of structural reliability analysis, provide an avenue for bridging the disciplines of epidemiology, cell biology, genetics and biomechanics. Such models promise subject-specific OA risk assessment and personalized strategies for mitigating or even avoiding OA. We illustrate the proposed approach with a simple model of cartilage extracellular matrix synthesis and loss regulated by daily physical activity.

A computational analysis on the implications of age-related changes in the expression of cellular signals on the role of IGF-1 in intervertebral disc homeostasis

Insulin-like growth factor-1 (IGF-1) is a well-known anabolic agent in intervertebral discs (IVD), promoting both proteoglycan (PG) biosynthesis and cell proliferation. Accordingly, it is believed that IGF-1 plays a central role in IVD homeostasis. The IGF-mediated anabolic activity in IVD occurs when the growth factor, free from binding proteins (IGFBP), binds to IGF cell surface receptors (IGF-1R). Previous studies reported that, with aging, cellular expression of IGFBP increases, while that of IGF-1R decreases. Both changes in cellular signals are thought to be among the factors that are responsible for the age-related decline in IGF-mediated PG biosynthesis, which ultimately leads to disc degeneration. In this study, a computational model describing the role of IGF-1 in the homeostasis of IVD was deployed in a parametric analysis to investigate the effects of age-related changes in expression of IGF-1R and IGFBP on the IGF-mediated upregulation of PG biosynthesis and cellular proliferation. It was found that changes in the expression of IGF-1R and IGFBP mostly affected the nucleus pulposus, while in the most external disc regions (annulus fibrosus and cartilage endplates) the IVD homeostatic balance was unaltered. It was shown that a decrease of IGF-1R expression caused reduction of both PG levels and cell density in the tissue. In contrast, increase in IGFBP expression increased both PG and cell concentration, suggesting that such change in cellular signaling may be a plausible defense mechanism from age-related IVD degeneration.

Inducing chemotactic and haptotactic cues in microfluidic devices for three-dimensional in vitro assays

Microfluidic devices allow for the production of physiologically relevant cellular microenvironments by including biomimetic hydrogels and generating controlled chemical gradients. During transport, the biomolecules interact in distinct ways with the fibrillar networks: as purely diffusive factors in the soluble fluid or bound to the matrix proteins. These two main mechanisms may regulate distinct cell responses in order to guide their directional migration: caused by the substrate-bound chemoattractant gradient (haptotaxis) or by the gradient established within the soluble fluid (chemotaxis). In this work 3D diffusion experiments, in combination with ELISA assays, are performed using microfluidic platforms in order to quantify the distribution of PDGF-BB and TGF-β1 across collagen and fibrin gels. Furthermore, to gain a deeper understanding of the fundamental processes, the experiments are reproduced by computer simulations based on a reaction-diffusion transport model. This model yields an accurate prediction of the experimental results, confirming that diffusion and binding phenomena are established within the microdevice.

Computational systems biology approaches to anti-angiogenic cancer therapeutics

Angiogenesis is an exquisitely regulated process that is required for physiological processes and is also important in numerous diseases. Tumors utilize angiogenesis to generate the vascular network needed to supply the cancer cells with nutrients and oxygen, and many cancer drugs aim to inhibit tumor angiogenesis. Anti-angiogenic therapy involves inhibiting multiple cell types, molecular targets, and intracellular signaling pathways. Computational tools are useful in guiding treatment strategies, predicting the response to treatment, and identifying new targets of interest. Here, we describe progress that has been made in applying mathematical modeling and bioinformatics approaches to study anti-angiogenic therapeutics in cancer.

Modeling the role of IGF-1 on extracellular matrix biosynthesis and cellularity in intervertebral disc

The insulin-like growth factor-1 (IGF-1) is a well-known anabolic agent for intervertebral disc (IVD), promoting both proteoglycan (PG) biosynthesis and cell proliferation. Accordingly, it is believed that IGF-1 may play a central role in IVD homeostasis. Furthermore, the exogenous administration of IGF-1 has been proposed as a possible therapeutic strategy for disc degeneration. The objectives of this study were to develop a new computational framework for describing the mechanisms regulating IGF-mediated homeostasis in IVD, and to apply this numerical tool for investigating the effectiveness of exogenous administration of IGF-1 for curing disc degeneration. A diffusive-reactive model was developed for describing competitive binding of IGF-1 to its binding proteins and cell surface receptors, with the latter reaction initiating the intracellular signaling mechanism leading to PG production and cell proliferation. Because PG production increases cell metabolic rate, and cell proliferation increases nutritional demand, nutrients transport and metabolism were also included into the model, and co-regulated, together with IGF-1, IVD cellularity. The sustainability and the effectiveness of IGF-mediated anabolism were investigated for conditions of pathologically insufficient nutrient supply, and for the case of exogenous administration of IGF-1 to degenerated IVD. Results showed that pathological nutrients deprivation, by decreasing cellularity, caused a reduction of PG biosynthesis. Also, exogenous administration of IGF-1 was only beneficial in well-nourished regions of IVD, and exacerbated cell mortality in malnourished regions. These findings remark the central role of nutrition in IVD health, and suggest that adequate nutritional supply is paramount for achieving a successful IGF-based therapy for disc degeneration.

Osteoblast-chondrocyte interactions in osteoarthritis

There is now general agreement that osteoarthritis (OA) involves all structures in the affected joint, culminating in the degradation of the articular cartilage. It is appropriate to focus particularly on the subchondral bone because characteristic changes occur in this tissue with disease progression, either in parallel, or contributing to, the loss of cartilage volume and quality. Changes in both the articular cartilage and the subchondral bone are mediated by the cells in these two compartments, chondrocytes and cells of the osteoblast lineage, respectively, whose primary roles are to maintain the integrity and function of these tissues. In addition, altered rates of bone remodeling across the disease process are due to increased or decreased osteoclastic bone resorption. In the altered mechanical and biochemical environment of a progressively diseased joint, the cells function differently and show a different profile of gene expression, suggesting direct effects of these external influences. There is also ex vivo and in vitro evidence of chemical crosstalk between the cells in cartilage and subchondral bone, suggesting an interdependence of events in the two compartments and therefore indirect effects of, for example, altered loading of the joint. It is ultimately these cellular changes that explain the altered morphology of the cartilage and subchondral bone. With respect to crosstalk between the cells in cartilage and bone, there is evidence that small molecules can transit between these tissues. For larger molecules, such as inflammatory mediators, this is an intriguing possibility but remains to be demonstrated. The cellular changes during the progression of OA almost certainly need to be considered in a temporal and spatial manner, since it is important when and where observations are made in either human disease or animal models of OA. Until recently, comparisons have been made with the assumption, for example, that the subchondral bone is behaviorally uniform, but this is not the case in OA, where regional differences of the bone are evident using magnetic resonance imaging (MRI). Nevertheless, an appreciation of the altered cell function during the progression of OA will identify new disease modifying targets. If, indeed, the cartilage and subchondral bone behave as an interconnected functional unit, normalization of cell behavior in one compartment may have benefits in both tissues.

Computational simulation of the early stage of bone healing under different configurations of locking compression plates

Flexible fixation or the so-called 'biological fixation' has been shown to encourage the formation of fracture callus, leading to better healing outcomes. However, the nature of the relationship between the degree of mechanical stability provided by a flexible fixation and the optimal healing outcomes has not been fully understood. In this study, we have developed a validated quantitative model to predict how cells in fracture callus might respond to change in their mechanical microenvironment due to different configurations of locking compression plate (LCP) in clinical practice, particularly in the early stage of healing. The model predicts that increasing flexibility of the LCP by changing the bone-plate distance (BPD) or the plate working length (WL) could enhance interfragmentary strain in the presence of a relatively large gap size (> 3 mm). Furthermore, conventional LCP normally results in asymmetric tissue development during early stage of callus formation, and the increase of BPD or WL is insufficient to alleviate this problem.

Accumulation of exogenous activated TGF-β in the superficial zone of articular cartilage

It was recently demonstrated that mechanical shearing of synovial fluid (SF), induced during joint motion, rapidly activates latent transforming growth factor β (TGF-β). This discovery raised the possibility of a physiological process consisting of latent TGF-β supply to SF, activation via shearing, and transport of TGF-β into the cartilage matrix. Therefore, the two primary objectives of this investigation were to characterize the secretion rate of latent TGF-β into SF, and the transport of active TGF-β across the articular surface and into the cartilage layer. Experiments on tissue explants demonstrate that high levels of latent TGF-β1 are secreted from both the synovium and all three articular cartilage zones (superficial, middle, and deep), suggesting that these tissues are capable of continuously replenishing latent TGF-β to SF. Furthermore, upon exposure of cartilage to active TGF-β1, the peptide accumulates in the superficial zone (SZ) due to the presence of an overwhelming concentration of nonspecific TGF-β binding sites in the extracellular matrix. Although this response leads to high levels of active TGF-β in the SZ, the active peptide is unable to penetrate deeper into the middle and deep zones of cartilage. These results provide strong evidence for a sequential physiologic mechanism through which SZ chondrocytes gain access to active TGF-β: the synovium and articular cartilage secrete latent TGF-β into the SF and, upon activation, TGF-β transports back into the cartilage layer, binding exclusively to the SZ.

Modeling the Insulin-Like Growth Factor System in Articular Cartilage

IGF signaling is involved in cell proliferation, differentiation and apoptosis in a wide range of tissues, both normal and diseased, and so IGF-IR has been the focus of intense interest as a promising drug target. In this computational study on cartilage, we focus on two questions: (i) what are the key factors influencing IGF-IR complex formation, and (ii) how might cells regulate IGF-IR complex formation? We develop a reaction-diffusion computational model of the IGF system involving twenty three parameters. A series of parametric and sensitivity studies are used to identify the key factors influencing IGF signaling. From the model we predict the free IGF and IGF-IR complex concentrations throughout the tissue. We estimate the degradation half-lives of free IGF-I and IGFBPs in normal cartilage to be 20 and 100 mins respectively, and conclude that regulation of the IGF half-life, either directly or indirectly via extracellular matrix IGF-BP protease concentrations, are two critical factors governing the IGF-IR complex formation in the cartilage. Further we find that cellular regulation of IGF-II production, the IGF-IIR concentration and its clearance rate, all significantly influence IGF signaling. It is likely that negative feedback processes via regulation of these factors tune IGF signaling within a tissue, which may help explain the recent failures of single target drug therapies aimed at modifying IGF signaling.

A mathematical model for targeting chemicals to tissues by exploiting complex degradation

Background

In many biological and therapeutic contexts, it is highly desirable to target a chemical specifically to a particular tissue where it exerts its biological effect. In this paper, we present a simple, generic, mathematical model that elucidates a general method for targeting a chemical to particular tissues. The model consists of coupled reaction-diffusion equations to describe the evolution within the tissue of the concentrations of three chemical species: a (concentration of free chemical), b (binding protein) and their complex, c (chemical bound to binding protein). We assume that all species are free to diffuse, and that a and b undergo a reversible reaction to form c. In addition, the complex, c, can be broken down by a process (e.g. an enzyme in the tissue) that results in the release of the chemical, a, which is then free to exert its biological action.

Results

For simplicity, we consider a one-dimensional geometry. In the special case where the rate of complex formation is small (compared to the diffusion timescale of the species within the tissue) the system can be solved analytically. This analytic solution allows us to show how the concentration of free chemical, a, in the tissue can be increased over the concentration of free chemical at the tissue boundary. We show that, under certain conditions, the maximum concentration of a can occur at the centre of the tissue, and give an upper bound on this maximum level. Numerical simulations are then used to determine how the behaviour of the system changes when the assumption of negligible complex formation rate is relaxed.

Conclusions

We have shown, using our mathematical model, how complex degradation can potentially be exploited to target a chemical to a particular tissue, and how the level of the active chemical depends on factors such as the diffusion coefficients and degradation/production rates of each species. The biological significance of these results in terms of potential applications in cartilage tissue engineering and chemotherapy is discussed. In particular, we believe these results may be of use in determining the most promising prodrug candidates.