Sarah L. Waters

An integrative computational model for intestinal tissue renewal.

Objectives:  The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

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.

Theoretical models for coronary vascular biomechanics: Progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Steady flows in pipes with finite curvature

Motivated by blood flow in a curved artery, we consider fluid flow through a uniformly curved pipe, driven by a steady pressure gradient. Previous studies have typically considered pipes with asymptotically small curvature in which only the centrifugal effect is retained in the governing equations. Here we consider flows in pipes of finite curvature, and determine the effects of both the centrifugal and Coriolis forces on the flow. The flow behavior is governed by two dimensionless parameters: the curvature, δ, and the Dean number, D. Asymptotic solutions are developed for D⪡1 (using regular perturbation expansions) and D⪢1 (using matched asymptotic expansions and the Pohlhausen method). For intermediate values of D we use a pseudospectral code to obtain solutions. For values of D greater than a critical value, Dc, multiple steady solutions to the governing equations exist; we determine how Dc and the form of the solutions depends on δ. The results indicate that while many of the qualitative features of s...

The propagation of a liquid bolus along a liquid-lined flexible tube

We use lubrication theory and matched asymptotic expansions to model the quasi-steady propagation of a liquid plug or bolus through an elastic tube. In the limit of small capillary number, asymptotic expressions are found for the pressure drop across the bolus and the thickness of the liquid film left behind, as functions of the capillary number, the thickness of the liquid lining ahead of the bolus and the elastic characteristics of the tube wall. These results generalize the well-known theory for the low capillary number motion of a bubble through a rigid tube (Bretherton 1961). As in that theory, both the pressure drop across the bolus and the thickness of the film it leaves behind vary like the two-thirds power of the capillary number. In our generalized theory, the coefficients in the power laws depend on the elastic properties of the tube. For a given thickness of the liquid lining ahead of the bolus, we identify a critical imposed pressure drop above which the bolus will eventually rupture, and hence the tube will reopen. We find that generically a tube with smaller hoop tension or smaller longitudinal tension is easier to reopen. This flow regime is fundamental to reopening of pulmonary airways, which may become plugged through disease or by instilled/aspirated fluids.

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcys law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

Unsteady flows in pipes with finite curvature

Motivated by the study of blood flow in a curved artery, we consider fluid flow through a curved pipe of uniform curvature, δ, driven by a prescribed oscillatory axial pressure gradient. The curved pipe has finite (as opposed to asymptotically small) curvature, and we determine the effects of both the centrifugal and Coriolis forces on the flow. In addition to δ, the flow is parameterized by the Dean number, D , the Womersley number, α, and a secondary streaming Reynolds number, R s . Asymptotic solutions are developed for the case when δ≪1, α≪1 and the magnitude of the axial pressure gradient is small, using regular perturbation techniques. For intermediate values of the governing parameters, a pseudospectral code is used to obtain numerical solutions. For flows driven by a sinusoidal pressure gradient ( D =0), we identify three distinct classes of stable solutions: 2π-periodic symmetric, 2π-periodic asymmetric, and asymmetric solutions that are either quasi-periodic, or periodic with period 2π k for k ∈ . The transition between solutions is dependent on the value of δ; thus pipes with finite curvature may exhibit qualitatively different transitions between the solution classes as the governing parameters are varied from those of curved pipes with asymptotically small curvature. When α≫1, matched asymptotic expansions are used to simplify the system, and the resulting equations are solved analytically for R s ≪1, δ≪1 and numerically for larger parameter values. We then determine the effect of a non-zero steady component of the pressure gradient ( D ≠0), and show that, for certain parameter values, when D is above a critical value the periodic asymmetric solutions regain spatial symmetry. Finally, we show that the effects of finite curvature can lead to substantial quantitative differences in the wall shear stress distribution and discuss briefly the physiological implications of the results for blood flow in arteries.

The propagation of a surfactant laden liquid plug in a capillary tube

This paper considers the propagation of a liquid plug, forced by a driving pressure ΔP, within a rigid tube. The tube is already lined with a liquid precursor film of thickness h2. Both the plug and the precursor film, as well as the interface, contain small amounts of surfactant whose concentrations are assumed to be near equilibrium. Since the motions are slow, we seek asymptotic solutions for small capillary number, Ca≪1, and also assume that sorption kinetics control the surfactant flux to the interface compared to bulk diffusion. An additional asymptotic assumption is that the Stanton number, St, is sufficiently large such that β∝Ca1/3/St≪1, which relates the importance of sorption kinetics to convection. The surfactant strength is measured by the surface elasticity, E=M/β where M is the Marangoni number. The results of the analysis are that, for a given plug Ca, ΔP increases with increasing E but decreases with increasing h2. The trailing film thickness, h1, increases with ΔP, but at a slower rat...

A multiphase model for tissue construct growth in a perfusion bioreactor

The growth of a cell population within a rigid porous scaffold in a perfusion bioreactor is studied, using a three-phase continuum model of the type presented by Lemon et al. (2006, Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol., 52, 571-594) to represent the cell population (and attendant extracellular matrix), culture medium and porous scaffold. The bioreactor system is modelled as a 2D channel containing the cell-seeded rigid porous scaffold (tissue construct) which is perfused with culture medium. The study concentrates on (i) the cell-cell and cell-scaffold interactions and (ii) the impact of mechanotransduction mechanisms on construct composition. A numerical and analytical analysis of the model equations is presented and, depending upon the relative importance of cell aggregation and repulsion, markedly different cell movement is revealed. Additionally, mechanotransduction effects due to cell density, pressure and shear stress-mediated tissue growth are shown to generate qualitative differences in the composition of the resulting construct. The results of our simulations indicate that this model formulation (in conjunction with appropriate experimental data) has the potential to provide a means of identifying the dominant regulatory stimuli in a cell population.