Rebecca J. Shipley

Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours

A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed on a micro-scale characterized by the inter-capillary distance, and the method of multiple scales is used to derive the continuum equations describing fluid and drug transport on the length scale of the tumour (under the assumption of a spatially periodic microstructure). The fluid equations comprise a double porous medium, with coupled Darcy flow through the interstitium and vasculature, whereas the drug equations comprise advection–reaction equations; in each case the dependence of the transport coefficients on the vascular geometry is determined by solving micro-scale cell problems.

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.

Medical Imaging and Physiological Modelling: Linking Physics and Biology

Medical image analysis is increasingly providing a sophisticated set of tools for processing measurement inputs into clinically relevant outputs, although this is, on the whole, completed without consideration of the underlying physiology. In contrast, physiological modelling provides a predictive tool based on a physical and biological understanding of the underlying processes. In this editorial, we discuss the possibility of integrating physiological modelling data with medical images and measurements with the goal of providing new types of physiologically meaningful information with increased clinical relevance.

Multiscale Modeling of Fluid Transport in Tumors

A model for fluid flow through the leaky neovasculature and porous interstitium of a solid tumor is developed. A network of isolated capillaries is analyzed in the limit of small capillary radius, and analytical expressions for the hydraulic conductivities and fractional leakage coefficients derived. This model is then homogenized to give a continuum description in terms of the vascular density. The resulting equations comprise a double porous medium with coupled Darcy flow through the interstitium and vasculature.

Design criteria for a printed tissue engineering construct: a mathematical homogenization approach

Cartilage tissue repair procedures currently under development aim to create a construct in which patient-derived cells are seeded and expanded ex vivo before implantation back into the body. The key challenge is producing physiologically realistic constructs that mimic real tissue structure and function. One option with vast potential is to print strands of material in a 3D structure called a scaffold that imitates the real tissue structure; the strands are composed of gel seeded with cells and so provide a template for cartilaginous tissue growth. The scaffold is placed in the construct and pumped with nutrient-rich culture medium to supply nutrients to the cells and remove waste products, thus promoting tissue growth. In this paper we use asymptotic homogenization to determine the effective flow and transport properties of such a printed scaffold system. These properties are used to predict the distribution of nutrient/waste products through the construct, and to specify design criteria for the scaffold that will optimize the growth of functional tissue.

A strategy to determine operating parameters in tissue engineering hollow fiber bioreactors

The development of tissue engineering hollow fiber bioreactors (HFB) requires the optimal design of the geometry and operation parameters of the system. This article provides a strategy for specifying operating conditions for the system based on mathematical models of oxygen delivery to the cell population. Analytical and numerical solutions of these models are developed based on Michaelis–Menten kinetics. Depending on the minimum oxygen concentration required to culture a functional cell population, together with the oxygen uptake kinetics, the strategy dictates the model needed to describe mass transport so that the operating conditions can be defined. If cmin ≫ Km we capture oxygen uptake using zero‐order kinetics and proceed analytically. This enables operating equations to be developed that allow the user to choose the medium flow rate, lumen length, and ECS depth to provide a prescribed value of cmin. When

High-speed camera characterization of voluntary eye blinking kinematics

c_{{\rm min}} {\not {\gg }}K_{m}

Fluid and mass transport modelling to drive the design of cell-packed hollow fibre bioreactors for tissue engineering applications

, we use numerical techniques to solve full Michaelis–Menten kinetics and present operating data for the bioreactor. The strategy presented utilizes both analytical and numerical approaches and can be applied to any cell type with known oxygen transport properties and uptake kinetics. Biotechnol. Bioeng. 2011; 108:1450–1461.

Definition and validation of operating equations for poly(vinyl alcohol)‐poly(lactide‐co‐glycolide) microfiltration membrane‐scaffold bioreactors

Blinking is vital to maintain the integrity of the ocular surface and its characteristics such as blink duration and speed can vary significantly, depending on the health of the eyes. The blink is so rapid that special techniques are required to characterize it. In this study, a high-speed camera was used to record and characterize voluntary blinking. The blinking motion of 25 healthy volunteers was recorded at 600 frames per second. Master curves for the palpebral aperture and blinking speed were constructed using palpebral aperture versus time data taken from the high-speed camera recordings, which show that one blink can be divided into four phases; closing, closed, early opening and late opening. Analysis of data from the high-speed camera images was used to calculate the palpebral aperture, peak blinking speed, average blinking speed and duration of voluntary blinking and compare it with data generated by other methods previously used to evaluate voluntary blinking. The advantages of the high-speed camera method over the others are discussed, thereby supporting the high potential usefulness of the method in clinical research.

Regulation of O2 consumption by the PI3K and mTOR pathways contributes to tumor hypoxia

A model for fluid and mass transport in a single module of a tissue engineering hollow fibre bioreactor (HFB) is developed. Cells are seeded in alginate throughout the extra-capillary space (ECS), and fluid is pumped through a central lumen to feed the cells and remove waste products. Fluid transport is described using Navier-Stokes or Darcy equations as appropriate; this is overlaid with models of mass transport in the form of advection-diffusion-reaction equations that describe the distribution and uptake/production of nutrients/waste products. The small aspect ratio of a module is exploited and the option of opening an ECS port is explored. By proceeding analytically, operating equations are determined that enable a tissue engineer to prescribe the geometry and operation of the HFB by ensuring the nutrient and waste product concentrations are consistent with a functional cell population. Finally, results for chondrocyte and cardiomyocyte cell populations are presented, typifying two extremes of oxygen uptake rates.