Predictions of tumour morphological stability and evaluation against experimental observations

The hallmark of malignant tumours is their spread into neighbouring tissue and metastasis to distant organs, which can lead to life threatening consequences. One of the defining characteristics of aggressive tumours is an unstable morphology, including the formation of invasive fingers and protrusions observed both in vitro and in vivo. In spite of extensive biological, clinical and modelling study and research at physical scales ranging from the molecular to the tissue, the driving dynamics of tumour invasiveness are not completely understood, partly because it is challenging to observe and study cancer as a multi-scale system. Mathematical modelling has been applied to provide further insights into these complex invasive and metastatic behaviours. Modelling a solid tumour as an incompressible fluid, we consider three possible constitutive relations to describe tumour growth, namely Darcy''s law, Stokes'' law and the combined Darcy–Stokes law. We study the tumour morphological stability described by each model and evaluate the consistency between theoretical model predictions and experimental data from in vitro three-dimensional multicellular tumour spheroids. The analysis reveals that the Stokes model is the most consistent with the experimental observations, and that it predicts our experimental tumour growth is marginally stable. We further show that it is feasible to extract parameter values from a limited set of data and create a self-consistent modelling framework that can be extended to the multi-scale study of cancer.     

A review of back-calculation techniques and their potential to inform mitigation strategies with application to non-transmissible acute infectious diseases

Back-calculation is a process whereby generally unobservable features of an event leading to a disease outbreak can be inferred either in real-time or shortly after the end of the outbreak. These features might include the time when persons were exposed and the source of the outbreak. Such inferences are important as they can help to guide the targeting of mitigation strategies and to evaluate the potential effectiveness of such strategies. This article reviews the process of back-calculation with a particular emphasis on more recent applications concerning deliberate and naturally occurring aerosolized releases. The techniques can be broadly split into two themes: the simpler temporal models and the more sophisticated spatio-temporal models. The former require input data in the form of cases'' symptom onset times, whereas the latter require additional spatial information such as the cases'' home and work locations. A key aspect in the back-calculation process is the incubation period distribution, which forms the initial topic for consideration. Links between atmospheric dispersion modelling, within-host dynamics and back-calculation are outlined in detail. An example of how back-calculation can inform mitigation strategies completes the review by providing improved estimates of the duration of antibiotic prophylaxis that would be required in the response to an inhalational anthrax outbreak.     

Time and dose-dependent risk of pneumococcal pneumonia following influenza: a model for within-host interaction between influenza and Streptococcus pneumoniae

A significant fraction of seasonal and in particular pandemic influenza deaths are attributed to secondary bacterial infections. In animal models, influenza virus predisposes hosts to severe infection with both Streptococcus pneumoniae and Staphylococcus aureus. Despite its importance, the mechanistic nature of the interaction between influenza and pneumococci, its dependence on the timing and sequence of infections as well as the clinical and epidemiological consequences remain unclear. We explore an immune-mediated model of the viral–bacterial interaction that quantifies the timing and the intensity of the interaction. Taking advantage of the wealth of knowledge gained from animal models, and the quantitative understanding of the kinetics of pathogen-specific immunological dynamics, we formulate a mathematical model for immune-mediated interaction between influenza virus and S. pneumoniae in the lungs. We use the model to examine the pathogenic effect of inoculum size and timing of pneumococcal invasion relative to influenza infection, as well as the efficacy of antivirals in preventing severe pneumococcal disease. We find that our model is able to capture the key features of the interaction observed in animal experiments. The model predicts that introduction of pneumococcal bacteria during a 4–6 day window following influenza infection results in invasive pneumonia at significantly lower inoculum size than in hosts not infected with influenza. Furthermore, we find that antiviral treatment administered later than 4 days after influenza infection was not able to prevent invasive pneumococcal disease. This work provides a quantitative framework to study interactions between influenza and pneumococci and has the potential to accurately quantify the interactions. Such quantitative understanding can form a basis for effective clinical care, public health policies and pandemic preparedness.     

An ecophysiological model of plant–pest interactions: the role of nutrient and water availability

Empirical studies have shown that particular irrigation/fertilization regimes can reduce pest populations in agroecosystems. This appears to promise that the ecological concept of bottom-up control can be applied to pest management. However, a conceptual framework is necessary to develop a mechanistic basis for empirical evidence. Here, we couple a mechanistic plant growth model with a pest population model. We demonstrate its utility by applying it to the peach–green aphid system. Aphids are herbivores which feed on the plant phloem, deplete plants’ resources and (potentially) transmit viral diseases. The model reproduces system properties observed in field studies and shows under which conditions the diametrically opposed plant vigour and plant stress hypotheses find support. We show that the effect of fertilization/irrigation on the pest population cannot be simply reduced as positive or negative. In fact, the magnitude and direction of any effect depend on the precise level of fertilization/irrigation and on the date of observation. We show that a new synthesis of experimental data can emerge by embedding a mechanistic plant growth model, widely studied in agronomy, in a consumer–resource modelling framework, widely studied in ecology. The future challenge is to use this insight to inform practical decision making by farmers and growers.     

The radial growth phase of malignant melanoma: multi-phase modelling,numerical simulations and linear stability analysis

Cutaneous melanoma is disproportionately lethal despite its relatively low incidence and its potential for cure in the early stages. The aim of this study is to foster understanding of the role of microstructure on the occurrence of morphological changes in diseased skin during melanoma evolution. The authors propose a biomechanical analysis of its radial growth phase, investigating the role of intercellular/stromal connections on the initial stages of epidermis invasion. The radial growth phase of a primary melanoma is modelled within the multi-phase theory of mixtures, reproducing the mechanical behaviour of the skin layers and of the epidermal–dermal junction. The theoretical analysis takes into account those cellular processes that have been experimentally observed to disrupt homeostasis in normal epidermis. Numerical simulations demonstrate that the loss of adhesiveness of the melanoma cells both to the basal laminae, caused by deregulation mechanisms of adherent junctions, and to adjacent keratynocytes, consequent to a downregulation of E-cadherin, are the fundamental biomechanical features for promoting tumour initiation. Finally, the authors provide the mathematical proof of a long wavelength instability of the tumour front during the early stages of melanoma invasion. These results open the perspective to correlate the early morphology of a growing melanoma with the biomechanical characteristics of its micro-environment.     

Design and implementation of an adaptive fuzzy sliding mode controller for drug delivery in treatment of vascular cancer tumours and its optimisation using genetic algorithm tool

In this paper, the side effects of drug therapy in the process of cancer treatment are reduced by designing two optimal non‐linear controllers. The related gains of the designed controllers are optimised using genetic algorithm and simultaneously are adapted by employing the Fuzzy scheduling method. The cancer dynamic model is extracted with five differential equations, including normal cells, endothelial cells, cancer cells, and the amount of two chemotherapy and anti‐angiogenic drugs left in the body as the engaged state variables, while double drug injection is considered as the corresponding controlling signals of the mentioned state space. This treatment aims to reduce the tumour cells by providing a timely schedule for drug dosage. In chemotherapy, not only the cancer cells are killed but also other healthy cells will be destroyed, so the rate of drug injection is highly significant. It is shown that the simultaneous application of chemotherapy and anti‐angiogenic therapy is more efficient than single chemotherapy. Two different non‐linear controllers are employed and their performances are compared. Simulation results and comparison studies show that not only adding the anti‐angiogenic reduce the side effects of chemotherapy but also the proposed robust controller of sliding mode provides a faster and stronger treatment in the presence of patient parametric uncertainties in an optimal way. As a result of the proposed closed‐loop drug treatment, the tumour cells rapidly decrease to zero, while the normal cells remain healthy simultaneously. Also, the injection rate of the chemotherapy drug is very low after a short time and converges to zero.     

Experiments and theory of undulatory locomotion in a simple structured medium

Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode''s path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm''s locomotory dynamics.