Bindi S. Brook

The EuroPhysiome, STEP and a roadmap for the virtual physiological human.

Biomedical science and its allied disciplines are entering a new era in which computational methods and technologies are poised to play a prevalent role in supporting collaborative investigation of the human body. Within Europe, this has its focus in the virtual physiological human (VPH), which is an evolving entity that has emerged from the EuroPhysiome initiative and the strategy for the EuroPhysiome (STEP) consortium. The VPH is intended to be a solution to common infrastructure needs for physiome projects across the globe, providing a unifying architecture that facilitates integration and prediction, ultimately creating a framework capable of describing Homo sapiens in silico. The routine reliance of the biomedical industry, biomedical research and clinical practice on information technology (IT) highlights the importance of a tailor-made and robust IT infrastructure, but numerous challenges need to be addressed if the VPH is to become a mature technological reality. Appropriate investment will reap considerable rewards, since it is anticipated that the VPH will influence all sectors of society, with implications predominantly for improved healthcare, improved competitiveness in industry and greater understanding of (patho)physiological processes. This paper considers issues pertinent to the development of the VPH, highlighted by the work of the STEP consortium.

Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes. The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method. Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

Airway smooth muscle in asthma: Linking contraction and mechanotransduction to disease pathogenesis and remodelling

Asthma is an obstructive airway disease, with a heterogeneous and multifactorial pathogenesis. Although generally considered to be a disease principally driven by chronic inflammation, it is becoming increasingly recognised that the immune component of the pathology poorly correlates with the clinical symptoms of asthma, thus highlighting a potentially central role for non-immune cells. In this context airway smooth muscle (ASM) may be a key player, as it comprises a significant proportion of the airway wall and is the ultimate effector of acute airway narrowing. Historically, the contribution of ASM to asthma pathogenesis has been contentious, yet emerging evidence suggests that ASM contractile activation imparts chronic effects that extend well beyond the temporary effects of bronchoconstriction. In this review article we describe the effects that ASM contraction, in combination with cellular mechanotransduction and novel contraction-inflammation synergies, contribute to asthma pathogenesis. Specific emphasis will be placed on the effects that ASM contraction exerts on the mechanical properties of the airway wall, as well as novel mechanisms by which ASM contraction may contribute to more established features of asthma such as airway wall remodelling.

A biomechanical model of agonist-initiated contraction in the asthmatic airway

This paper presents a modelling framework in which the local stress environment of airway smooth muscle (ASM) cells may be predicted and cellular responses to local stress may be investigated. We consider an elastic axisymmetric model of a layer of connective tissue and circumferential ASM fibres embedded in parenchymal tissue and model the active contractile force generated by ASM via a stress acting along the fibres. A constitutive law is proposed that accounts for active and passive material properties as well as the proportion of muscle to connective tissue. The model predicts significantly different contractile responses depending on the proportion of muscle to connective tissue in the remodelled airway. We find that radial and hoop-stress distributions in remodelled muscle layers are highly heterogenous with distinct regions of compression and tension. Such patterns of stress are likely to have important implications, from a mechano-transduction perspective, on contractility, short-term cytoskeletal adaptation and long-term airway remodelling in asthma.

A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties

Computations are reported for a one-dimensional model of time-dependent flow in collapsible tubes representing long mammalian veins. The tubes are taken to have uniform intrinsic properties and we concentrate on the effect of longitudinal gravity. The main application is to the jugular vein of the upright giraffe, with given inflow rate from the head, a given pressure, slightly above the external, atmospheric pressure, at the downstream (vena caval) end, and a variety of initial conditions. We show that: (i) previously calculated steady flows are the long time limits of unsteady computations, although only after a considerable time in which slowly-decaying waves and elastic jumps propagate up and down, (ii) steady flows are indeed not found when the steady-flow analysis shown them not to exist, although the consequent unsteadiness is of such small amplitude as to be practically unimportant, (iii) the time taken for the flow to become steady when the neck is raised from the horizontal or the head-down position can be several seconds longer than the neck-raising time itself (3-7s). We also find that roll-waves do not develop despite having been previously predicted for long collapsible tubes. Further application is made to the effect of postural changes on human neck and leg veins.

Radiological imaging as the basis for a simulation software of ventilation in the tracheo-bronchial tree

Abstract. The inhaled route is a promising new way for administering drugs to the human body. Flow and particle deposition in the human respiratory tract depends on the individuals anatomy as well as on the drug composition. A European Framework V Program supported project is currently developing a simulation tool for assessment of drug distribution and deposition. This tool relies heavily on the input of radiological data sets, which are obtained in humans. Both high temporal and spatial resolutions are required, and CT and MRI (including hyperpolarized helium-3 MRI) are applied. The radiological data are integrated into computation fluid dynamics software, which is capable of assessing air-flow profiles and compartmental behaviours. This is complemented by pharmacokinetic models, which should result in a simulation tool that will be of use for the theoretical design of new inhaled therapies. This article describes the special imaging requirements of each region of the respiratory tract and the feasibility of these sophisticated radiological techniques with a view of using these data in a simulation model of the lung.

Activation of Store-Operated Calcium Entry in Airway Smooth Muscle Cells: Insight from a Mathematical Model

Intracellular dynamics of airway smooth muscle cells (ASMC) mediate ASMC contraction and proliferation, and thus play a key role in airway hyper-responsiveness (AHR) and remodelling in asthma. We evaluate the importance of store-operated entry (SOCE) in these dynamics by constructing a mathematical model of ASMC signaling based on experimental data from lung slices. The model confirms that SOCE is elicited upon sufficient depletion of the sarcoplasmic reticulum (SR), while receptor-operated entry (ROCE) is inhibited in such conditions. It also shows that SOCE can sustain agonist-induced oscillations in the absence of other influx. SOCE up-regulation may thus contribute to AHR by increasing the oscillation frequency that in turn regulates ASMC contraction. The model also provides an explanation for the failure of the SERCA pump blocker CPA to clamp the cytosolic of ASMC in lung slices, by showing that CPA is unable to maintain the SR empty of . This prediction is confirmed by experimental data from mouse lung slices, and strongly suggests that CPA only partially inhibits SERCA in ASMC.

Mathematical modelling of cytokine-mediated inflammation in rheumatoid arthritis.

Rheumatoid arthritis (RA) is a chronic inflammatory disease preferentially affecting the joints and leading, if untreated, to progressive joint damage and disability. Cytokines, a group of small inducible proteins, which act as intercellular messengers, are key regulators of the inflammation that characterizes RA. They can be classified into pro-inflammatory and anti-inflammatory groups. Numerous cytokines have been implicated in the regulation of RA with complex up and down regulatory interactions. This paper considers a two-variable model for the interactions between pro-inflammatory and anti-inflammatory cytokines, and demonstrates that mathematical modelling may be used to investigate the involvement of cytokines in the disease process. The model displays a range of possible behaviours, such as bistability and oscillations, which are strongly reminiscent of the behaviour of RA e.g. genetic susceptibility and remitting-relapsing disease. We also show that the dose regimen as well as the dose level are important factors in RA treatments.

Nonlinear compliance modulates dynamic bronchoconstriction in a multiscale airway model

The role of breathing and deep inspirations (DI) in modulating airway hyperresponsiveness remains poorly understood. In particular, DIs are potent bronchodilators of constricted airways in nonasthmatic subjects but not in asthmatic subjects. Additionally, length fluctuations (mimicking DIs) have been shown to reduce mean contractile force when applied to airway smooth muscle (ASM) cells and tissue strips. However, these observations are not recapitulated on application of transmural pressure (PTM) oscillations (that mimic tidal breathing and DIs) in isolated intact airways. To shed light on this paradox, we have developed a biomechanical model of the intact airway, accounting for strain-stiffening due to collagen recruitment (a large component of the extracellular matrix (ECM)), and dynamic actomyosin-driven force generation by ASM cells. In agreement with intact airway studies, our model shows that PTM fluctuations at particular mean transmural pressures can lead to only limited bronchodilation. However, our model predicts that moving the airway to a more compliant point on the static pressure-radius relationship (which may involve reducing mean PTM), before applying pressure fluctuations, can generate greater bronchodilation. This difference arises from competition between passive strain-stiffening of ECM and force generation by ASM yielding a highly nonlinear relationship between effective airway stiffness and PTM, which is modified by the presence of contractile agonist. Effectively, the airway at its most compliant may allow for greater strain to be transmitted to subcellular contractile machinery. The model predictions lead us to hypothesize that the maximum possible bronchodilation of an airway depends on its static compliance at the PTM about which the fluctuations are applied. We suggest the design of additional experimental protocols to test this hypothesis.

The Role of Inflammation Resolution Speed in Airway Smooth Muscle Mass Accumulation in Asthma: Insight from a Theoretical Model

Despite a large amount of in vitro data, the dynamics of airway smooth muscle (ASM) mass increase in the airways of patients with asthma is not well understood. Here, we present a novel mathematical model that describes qualitatively the growth dynamics of ASM cells over short and long terms in the normal and inflammatory environments typically observed in asthma. The degree of ASM accumulation can be explained by an increase in the rate at which ASM cells switch between non-proliferative and proliferative states, driven by episodic inflammatory events. Our model explores the idea that remodelling due to ASM hyperplasia increases with the frequency and magnitude of these inflammatory events, relative to certain sensitivity thresholds. It highlights the importance of inflammation resolution speed by showing that when resolution is slow, even a series of small exacerbation events can result in significant remodelling, which persists after the inflammatory episodes. In addition, we demonstrate how the uncertainty in long-term outcome may be quantified and used to design an optimal low-risk individual anti-proliferative treatment strategy. The model shows that the rate of clearance of ASM proliferation and recruitment factors after an acute inflammatory event is a potentially important, and hitherto unrecognised, target for anti-remodelling therapy in asthma. It also suggests new ways of quantifying inflammation severity that could improve prediction of the extent of ASM accumulation. This ASM growth model should prove useful for designing new experiments or as a building block of more detailed multi-cellular tissue-level models.