Interphalangeal joint and tendon forces: normal model and biomechanical consequences of surgical reconstruction

Soft tissue reconstructive surgery for rheumatoid-related proximal interphalangeal joint deformities frequently fails to produce the long-term predicted results. Detailed information on the biomechanics of this joint, under both normal and pathological conditions, is required to assess the efficacy of such surgical intervention. A biomechanical model of the proximal interphalangeal joint has been developed to investigate tendon and joint loading during real life three-dimensional activities. Based on a rigid body mechanics approach, the model uses high resolution MRI scans to obtain anatomical tendon and bone geometries in conjunction with three-dimensional kinematic and loading data. The model incorporates an optimisation routine which minimises overall maximum tendon stress in the eight individual elements considered. Radial and ulnar joint force components are included at the proximal interphalangeal joint level. Two simulated pathological versions of the mathematical model are developed to accommodate the altered anatomic relationships after tendon reconstructive surgery. Joint forces of up to 450N and common usage of the extensor mechanism during normal pinching and grasping activities are predicted. The ulnar lateral bands of the extensor tendon are generally loaded to a greater extent than the radial bands. Extensor tendon and joint forces in the simulated pathological models are significantly higher than those in the normal model. Combined with the poor tendon quality of rheumatoid arthritis patients generally, these amplified internal forces may lead to further joint deformation.     

The confluence of machine learning and multiscale simulations

Multiscale modeling has a long history of use in structural biology, as computational biologists strive to overcome the time- and length-scale limits of atomistic molecular dynamics. Contemporary machine learning techniques, such as deep learning, have promoted advances in virtually every field of science and engineering and are revitalizing the traditional notions of multiscale modeling. Deep learning has found success in various approaches for distilling information from fine-scale models, such as building surrogate models and guiding the development of coarse-grained potentials. However, perhaps its most powerful use in multiscale modeling is in defining latent spaces that enable efficient exploration of conformational space. This confluence of machine learning and multiscale simulation with modern high-performance computing promises a new era of discovery and innovation in structural biology.     

Multiscale modeling of biomolecular systems: in serial and in parallel

Considerable progress has been recently achieved in the multiscale modeling of complex biological processes. Multiscale models have now investigated the structure and dynamics of lipid membranes, proteins, peptides and DNA over length and time scales ranging from the atomic to the macroscopic. Serial multiscale methods that parameterize low-resolution coarse-grained models with data from high-resolution models have studied long time or length scale phenomena that cannot be investigated with atomically detailed models. Parallel multiscale methods that directly couple high- and low-resolution models have efficiently explored slow structural transitions and the importance of long-wavelength fluctuations for biological molecules. The success of such models relies upon new theories and methods for constructing accurate multiscale bridges that transfer information between models with different resolutions.     

Contribution of biomechanics to management of ligament and tendon injuries

The contribution of biomechanics to the advancement of management of ligament and tendon injuries has been significant. Thanks to Professor Y.C. Fung's writing and guidance, our field of research has done fundamental work on anatomy and biology of ligaments and tendons, developed methods to accurately determine mechanical properties, identified various experimental factors which could change the outcome measurements as well as examined biological factors that change tissue properties in-vivo. Professor Fung also gave us his quasi-linear viscoelastic theory for soft tissues so that the time and history dependent properties of ligaments and tendons could be properly described. We have further adopted Professor Fung's eight steps on methods of approach for biomechanical investigation to understand as well as enhance the treatment of ligament and tendon injuries during work or sports related activities. Examples on how to better treat the tears of the medial collateral ligament of the knee, as well as how to improve reconstruction procedures for the anterior cruciate ligament are presented in detail. Currently the use of functional tissue engineering for ligament and tendon healing is a topic of great interest. Here the use of biological scaffolds, such as porcine small intestinal submucosa, has shown promise. For the last 35 to 40 years, the field of biomechanics has made great strides in the treatment of ligament and tendon injuries, and many patients have benefited. The future is even brighter because of what has been done properly in the past. Exciting advances can be made in the field of tissue engineering through novel in-vitro culture and bioscaffold fabrication techniques. Recent technology can also allow the collection of in-vivo data so that ligament and tendon injuries can be better understood. Yet, solving new and more complex problems must still follow the stepwise methods of approach as taught by Professor Fung.     

Biomechanics of tendon injury and repair

Many clinical and experimental studies have investigated how tendons repair in response to an injury. This body of work has led to a greater understanding of tendon healing mechanisms and subsequently to an improvement in their treatment. In this review paper, characterization of normal and healing tendons is first covered. In addition, the debate between intrinsic and extrinsic healing is examined, and the cellular and extracellular matrix response following a tendon injury is detailed. Next, clinical and experimental injury and repair methods utilizing animal models are discussed. Animal models have been utilized to study the effect of various activity levels, motions, injury methods, and injury locations on tendon injury and repair. Finally, current and future treatment modalities for improving tendon healing, such as tissue engineering, cell therapy, and gene therapy, are reviewed.     

Specific inhibition of type I and type II collagen fibrillogenesis by the small proteoglycan of tendon.

The small dermatan sulphate proteoglycan of bovine tendon demonstrated a unique ability to inhibit fibrillogenesis of both type I and type II collagen from bovine tendon and cartilage respectively in an assay performed in vitro. None of the other proteoglycan populations from cartilage, tendon or aorta, even those similar in size and chemical structure, had this effect. Alkali treatment of the small proteoglycan of tendon eliminated its ability to inhibit fibrillogenesis, whereas chondroitinase digestion did not. This indicates that its interaction with collagen depends on the core protein. Fibrillogenesis of pepsin-digested collagens was affected similarly, indicating that interaction with the collagen telopeptides is not involved. The results suggest that interactions between collagen and proteoglycans may be quite specific both for the type of proteoglycan and its tissue of origin.     

A multiscale, spatially distributed model of asthmatic airway hyper-responsiveness

We present a multiscale, spatially distributed model of lung and airway behaviour with the goal of furthering the understanding of airway hyper-responsiveness and asthma. The model provides an initial computational framework for linking events at the cellular and molecular levels, such as Ca²⁺ and crossbridge dynamics, to events at the level of the entire organ. At the organ level, parenchymal tissue is modelled using a continuum approach as a compressible, hyperelastic material in three dimensions, with expansion and recoil of lung tissue due to tidal breathing. The governing equations of finite elasticity deformation are solved using a finite element method. The airway tree is embedded in this tissue, where each airway is modelled with its own airway wall, smooth muscle and surrounding parenchyma. The tissue model is then linked to models of the crossbridge mechanics and their control by Ca²⁺ dynamics, thus providing a link to molecular and cellular mechanisms in airway smooth muscle cells. By incorporating and coupling the models at these scales, we obtain a detailed, computational multiscale model incorporating important physiological phenomena associated with asthma.     

An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool

A 3D anatomically based patient-specific finite element (FE) model of patello-femoral (PF) articulation is presented to analyse the main features of patella biomechanics, namely, patella tracking (kinematics), quadriceps extensor forces, surface contact and internal patella stresses. The generic geometries are a subset from the model database of the International Union of Physiological Sciences (IUPS) (http://www.physiome.org.nz) Physiome Project with soft tissue derived from the widely used visible human dataset, and the bones digitised from an anatomically accurate physical model with muscle attachment information. The models are customised to patient magnetic resonance images using a variant of free-form deformation, called 'host-mesh' fitting. The continuum was solved using the governing equation of finite elasticity, with the multibody problem coupled through contact mechanics. Additional constraints such as tissue incompressibility are also imposed. Passive material properties are taken from the literature and implemented for deformable tissue with a non-linear micro-structurally based constitutive law. Bone and cartilage are implemented using a 'St-Venant Kirchoff' model suitable for rigid body rotations. The surface fibre directions have been estimated from anatomy images of cadaver muscle dissections and active muscle contraction was based on a steady-state calcium-tension relation. The 3D continuum model of muscle, tendon and bone is compared with experimental results from the literature, and surgical simulations performed to illustrate its clinical assessment capabilities (a Maquet procedure for reducing patella stresses and a vastus lateralis release for a bipartite patella). Finally, the model limitations, issues and future improvements are discussed.     

Multiscale modeling of bone tissue with surface and permeability control

Natural biological materials usually present a hierarchical arrangement with various structural levels. The biomechanical behavior of the complex hierarchical structure of bone is investigated with models that address the various levels corresponding to different scales. Models that simulate the bone remodeling process concurrently at different scales are in development. We present a multiscale model for bone tissue adaptation that considers the two top levels, whole bone and trabecular architecture. The bone density distribution is calculated at the macroscale (whole bone) level, and the trabecular structure at the microscale level takes into account its mechanical properties as well as surface density and permeability. The bone remodeling process is thus formulated as a material distribution problem at both scales. At the local level, the biologically driven information of surface density and permeability characterizes the trabecular structure. The model is tested by a three-dimensional simulation of bone tissue adaptation for the human femur. The density distribution of the model shows good agreement with the actual bone density distribution. Permeability at the microstructural level assures interconnectivity of pores, which mimics the interconnectivity of trabecular bone essential for vascularization and transport of nutrients. The importance of this multiscale model relays on the flexibility to control the morphometric parameters that characterize the trabecular structure. Therefore, the presented model can be a valuable tool to define bone quality, to assist with diagnosis of osteoporosis, and to support the development of bone substitutes.     

Considerations for reporting finite element analysis studies in biomechanics

Simulation-based medicine and the development of complex computer models of biological structures is becoming ubiquitous for advancing biomedical engineering and clinical research. Finite element analysis (FEA) has been widely used in the last few decades to understand and predict biomechanical phenomena. Modeling and simulation approaches in biomechanics are highly interdisciplinary, involving novice and skilled developers in all areas of biomedical engineering and biology. While recent advances in model development and simulation platforms offer a wide range of tools to investigators, the decision making process during modeling and simulation has become more opaque. Hence, reliability of such models used for medical decision making and for driving multiscale analysis comes into question. Establishing guidelines for model development and dissemination is a daunting task, particularly with the complex and convoluted models used in FEA. Nonetheless, if better reporting can be established, researchers will have a better understanding of a model's value and the potential for reusability through sharing will be bolstered. Thus, the goal of this document is to identify resources and considerate reporting parameters for FEA studies in biomechanics. These entail various levels of reporting parameters for model identification, model structure, simulation structure, verification, validation, and availability. While we recognize that it may not be possible to provide and detail all of the reporting considerations presented, it is possible to establish a level of confidence with selective use of these parameters. More detailed reporting, however, can establish an explicit outline of the decision-making process in simulation-based analysis for enhanced reproducibility, reusability, and sharing.     

Using numerical approximation as an intermediate step in analytical derivations: some observations from biomechanics

We present four examples to illustrate the use of a type of numerical approximation as an intermediate step in analytical derivation of seemingly complicated biomechanical equations. The method involves examination of curve shapes to elucidate useful underlying trends, which may otherwise be overlooked through consideration of only the equations themselves. Two examples of the method's use are drawn from recently published results in the area of experimental methods in biomechanics of very soft tissues, and two others are taken from our current work on cartilage tissue mechanics. We think that such observations provide a useful means of circumventing complexity issues when deriving models for biomechanical analysis, and further that the method, while simple in concept, could be effective in a range of biomechanics applications.     

Tendon tissue engineering: progress, challenges, and translation to the clinic

The tissue engineering field has made great strides in understanding how different aspects of tissue engineered constructs (TECs) and the culture process affect final tendon repair. However, there remain significant challenges in developing strategies that will lead to a clinically effective and commercially successful product. In an effort to increase repair quality, a better understanding of normal development, and how it differs from adult tendon healing, may provide strategies to improve tissue engineering. As tendon tissue engineering continues to improve, the field needs to employ more clinically relevant models of tendon injury such as degenerative tendons. We need to translate successes to larger animal models to begin exploring the clinical implications of our treatments. By advancing the models used to validate our TECs, we can help convince our toughest customer, the surgeon, that our products will be clinically efficacious. As we address these challenges in musculoskeletal tissue engineering, the field still needs to address the commercialization of products developed in the laboratory. TEC commercialization faces numerous challenges because each injury and patient is unique. This review aims to provide tissue engineers with a summary of important issues related to engineering tendon repairs and potential strategies for producing clinically successful products.     

Structural changes in human type I collagen fibrils investigated by force spectroscopy

In the field of biomechanics, collagen fibrils are believed to be robust mechanical structures characterized by a low extensibility. Until very recently, information on the mechanical properties of collagen fibrils could only be derived from ensemble measurements performed on complete tissues such as bone, skin, and tendon. Here, we measure force-elongation/relaxation profiles of single collagen fibrils using atomic force microscopy (AFM)-based force spectroscopy (FS). The elongation profiles show that in vitro-assembled human type I collagen fibrils are characterized by a large extensibility. Numerous discontinuities and a plateau in the force profile indicate major reorganization occurring within the fibrils in the 1.5- to 4.5-nN range. Our study demonstrates that newly assembled collagen fibrils are robust structures with a significant reserve of elasticity that could play a determinant role in the extracellular matrix (ECM) remodeling associated with tissue growth and morphogenesis.     

Structural study of the calcifying collagen in turkey leg tendons

The calcified turkey leg tendon represents a simple bone-like tissue that is ideally suited to analysis by diffraction methods. In this paper we report some structural studies of the tendon collagen in the uncalcified, fully calcified and partially calcified states. The low-angle meridional X-ray pattern from the uncalcified tendon is very similar to that of the rat tail tendon, and the resulting one-dimensional structure of the collagen fibril exhibits no feature that could be related to its eventual calcification. The structure of the fully calcified tendon, as determined by a combination of X-ray and neutron diffraction analyses, shows that the mineral is associated with the collagen at the level of the hole or gap region. In the calcifying tendon, increases in the amplitudes of the first and second X-ray meridional reflections are correlated with an increase in the mineral content of the collagen. On the basis of simple models, it is shown that this change in the pattern can be explained by a nucleation mechanism of calcification. It is concluded that when collagen becomes calcified the mineral penetrates throughout the fibril and is crystalline in the hole region but amorphous between the collagen molecules. The mechanism of calcification and the mechanical implications of the fully calcified structure are also discussed.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.