Journal of the Royal Society Interface

Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng . 190 , 4379–4403) and Holzapfel et al . (Holzapfel et al . 2000 J. Elast . 61 , 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.

Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a ‘mixing network’. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections. Therefore, characteristics of mixing networks—and how these deviate from the random-mixing norm—have become important applied concerns that may enhance the understanding and prediction of epidemic patterns and intervention measures.

Here, we review the basis of epidemiological theory (based on random-mixing models) and network theory (based on work from the social sciences and graph theory). We then describe a variety of methods that allow the mixing network, or an approximation to the network, to be ascertained. It is often the case that time and resources limit our ability to accurately find all connections within a network, and hence a generic understanding of the relationship between network structure and disease dynamics is needed. Therefore, we review some of the variety of idealized network types and approximation techniques that have been utilized to elucidate this link. Finally, we look to the future to suggest how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control.

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

At present, strong requirements in orthopaedics are still to be met, both in bone and joint substitution and in the repair and regeneration of bone defects. In this framework, tremendous advances in the biomaterials field have been made in the last 50 years where materials intended for biomedical purposes have evolved through three different generations, namely first generation (bioinert materials), second generation (bioactive and biodegradable materials) and third generation (materials designed to stimulate specific responses at the molecular level). In this review, the evolution of different metals, ceramics and polymers most commonly used in orthopaedic applications is discussed, as well as the different approaches used to fulfil the challenges faced by this medical field.

Almost 30 years have passed since a term ‘tissue engineering’ was created to represent a new concept that focuses on regeneration of neotissues from cells with the support of biomaterials and growth factors. This interdisciplinary engineering has attracted much attention as a new therapeutic means that may overcome the drawbacks involved in the current artificial organs and organ transplantation that have been also aiming at replacing lost or severely damaged tissues or organs. However, the tissues regenerated by this tissue engineering and widely applied to patients are still very limited, including skin, bone, cartilage, capillary and periodontal tissues. What are the reasons for such slow advances in clinical applications of tissue engineering? This article gives the brief overview on the current tissue engineering, covering the fundamentals and applications. The fundamentals of tissue engineering involve the cell sources, scaffolds for cell expansion and differentiation and carriers for growth factors. Animal and human trials are the major part of the applications. Based on these results, some critical problems to be resolved for the advances of tissue engineering are addressed from the engineering point of view, emphasizing the close collaboration between medical doctors and biomaterials scientists.

Advanced therapies combating acute and chronic skin wounds are likely to be brought about using our knowledge of regenerative medicine coupled with appropriately tissue-engineered skin substitutes. At the present time, there are no models of an artificial skin that completely replicate normal uninjured skin. Natural biopolymers such as collagen and fibronectin have been investigated as potential sources of biomaterial to which cells can attach. The first generation of degradable polymers used in tissue engineering were adapted from other surgical uses and have drawbacks in terms of mechanical and degradation properties. This has led to the development of synthetic degradable gels primarily as a way to deliver cells and/or moleculesin situ, the so-called smart matrix technology. Tissue or organ repair is usually accompanied by fibrotic reactions that result in the production of a scar. Certain mammalian tissues, however, have a capacity for complete regeneration without scarring; good examples include embryonic or foetal skin and the ear of the MRL/MpJ mouse. Investigations of these model systems reveal that in order to achieve such complete regeneration, the inflammatory response is altered such that the extent of fibrosis and scarring is diminished. From studies on the limited examples of mammalian regeneration, it may also be possible to exploit such models to further clarify the regenerative process. The challenge is to identify the factors and cytokines expressed during regeneration and incorporate them to create a smart matrix for use in a skin equivalent. Recent advances in the use of DNA microarray and proteomic technology are likely to aid the identification of such molecules. This, coupled with recent advances in non-viral gene delivery and stem cell technologies, may also contribute to novel approaches that would generate a skin replacement whose materials technology was based not only upon intelligent design, but also upon the molecules involved in the process of regeneration.

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

Nature provides a wide range of materials with different functions and which may serve as a source of bio-inspiration for the materials scientist. The article takes the point of view that a successful translation of these ideas into the technical world requires more than the observation of nature. A thorough analysis of structure-function relations in natural tissues must precede the engineering of new bio-inspired materials. There are, indeed, many opportunities for lessons from the biological world: on growth and functional adaptation, about hierarchical structuring, on damage repair and self-healing. Biomimetic materials research is becoming a rapidly growing and enormously promising field. Serendipitous discovery from the observation of nature will be gradually replaced by a systematic approach involving the study of natural tissues in materials laboratories, the application of engineering principles to the further development of bio-inspired ideas and the generation of specific databases.

Falling poses a major threat to the steadily growing population of the elderly in modern-day society. A major challenge in the prevention of falls is the identification of individuals who are at risk of falling owing to an unstable gait. At present, several methods are available for estimating gait stability, each with its own advantages and disadvantages. In this paper, we review the currently available measures: the maximum Lyapunov exponent ( λ _S and λ _L ), the maximum Floquet multiplier, variability measures, long-range correlations, extrapolated centre of mass, stabilizing and destabilizing forces, foot placement estimator, gait sensitivity norm and maximum allowable perturbation. We explain what these measures represent and how they are calculated, and we assess their validity, divided up into construct validity, predictive validity in simple models, convergent validity in experimental studies, and predictive validity in observational studies. We conclude that (i) the validity of variability measures and λ _S is best supported across all levels, (ii) the maximum Floquet multiplier and λ _L have good construct validity, but negative predictive validity in models, negative convergent validity and (for λ _L ) negative predictive validity in observational studies, (iii) long-range correlations lack construct validity and predictive validity in models and have negative convergent validity, and (iv) measures derived from perturbation experiments have good construct validity, but data are lacking on convergent validity in experimental studies and predictive validity in observational studies. In closing, directions for future research on dynamic gait stability are discussed.

Co-culture techniques find myriad applications in biology for studying natural or synthetic interactions between cell populations. Such techniques are of great importance in synthetic biology, as multi-species cell consortia and other natural or synthetic ecology systems are widely seen to hold enormous potential for foundational research as well as novel industrial, medical and environmental applications with many proof-of-principle studies in recent years. What is needed for co-cultures to fulfil their potential? Cell–cell interactions in co-cultures are strongly influenced by the extracellular environment, which is determined by the experimental set-up, which therefore needs to be given careful consideration. An overview of existing experimental and theoretical co-culture set-ups in synthetic biology and adjacent fields is given here, and challenges and opportunities involved in such experiments are discussed. Greater focus on foundational technology developments for co-cultures is needed for many synthetic biology systems to realize their potential in both applications and answering biological questions.