
Thomas WoolleyCardiff University | CU · School of Mathematics
Thomas Woolley
DPhil
About
135
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Publications (135)
A Viral Infection Risk Indoor Simulator (VIRIS) has been developed to quickly assess and compare mitigations for airborne disease spread. This agent-based simulator combines people movement in an indoor space, viral transmission modelling and detailed architectural design, and it is powered by topologicpy, an open-source Python library. VIRIS gener...
We investigate the formation of Turing patterns on regular polygonal domains, as the number of edges grow, leading to the limiting case of the circle. Using linear and weakly nonlinear analysis, and evidence by simulations, we demonstrate how the domain shape can fundamentally change the expected bifurcation structure. Specifically, on the square d...
In this paper, a method to study how the design of indoor spaces and people's movement within them affect disease spread is proposed by integrating computer-aided modeling, multi-agent movement simulation, and airborne viral transmission modeling. Topologicpy spatial design and analysis software is used to model indoor environments, connect spaces,...
A Viral Infection Risk Indoor Simulator (VIRIS) has been developed to quickly assess and compare mitigations for airborne disease spread. This agent-based simulator combines people movement in an indoor space, viral transmission modelling and detailed architectural design, and it is powered by topologicpy, an open-source Python library. VIRIS gener...
Periodic patterning requires coordinated cell–cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogeneous 2D field. Most activators and inhibitors studied in biological systems are proteins, and the roles of...
Bats play a pivotal role in pest control, pollination and seed dispersal. Despite their ecological significance, locating bat roosts remains a challenging task for ecologists. Traditional field surveys are time-consuming, expensive and may disturb sensitive bat populations. In this article, we combine data from static audio detectors with a bat mov...
We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our...
Background and Objective
Conventional (100 ms) pan-retinal photocoagulation (PRP) laser burns are larger than short-pulse (10 ms to 20 ms) PRP burns. This study investigates the effect of PRP burns of different sizes on retinal oxygenation.
Method
A mathematical model using COMSOL Multiphysics 6 was used to create a three-dimensional abstraction o...
Agenesis of the Corpus Callosum (ACC) can result in multiple neurological deficits including social and behavioural issues. However, the underlying aetiology, clinical co-morbidity and the contributing risk factors remain elusive, resulting in inaccurate prognosis and delayed therapy. The main objective of this study was to comprehensively describe...
Periodic patterning requires coordinated cell-cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogenous two-dimensional field. Most activators and inhibitors studied in biological systems are proteins, and...
Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ridges are epithelial structures that undergo a truncated hair follicle developmental program and fail...
Recent advances in high-resolution experimental methods have highlighted the significance of cell signal pathway crosstalk and localised signalling activity in the development and disease of numerous biological systems. The investigation of multiple signal pathways often introduces different methods of cell-cell communication, i.e. contact-based or...
Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary c...
Fine-grain patterns produced by juxtacrine signalling have previously been studied using static monolayers as cellular domains. However, analytic results are usually restricted to a few cells due to the algebraic complexity of non-linear dynamical systems. Motivated by concentric patterning of Notch expression observed in the mammary gland, we comb...
We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard-Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy-Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic poten...
We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, st...
We construct a spatially-compartmental, individual-based model of the spread of SARS-CoV-2 in indoor spaces. The model can be used to predict the infection rates in a variety of locations when various non-pharmaceutical interventions (NPIs) are introduced. Tasked by the Welsh Government, we apply the model to secondary schools and to Further and Hi...
Adult skeletal muscle has robust regenerative capabilities due to the presence of a resident stem cell population called satellite cells. Muscle injury leads to these normally quiescent cells becoming molecularly and metabolically activated and embarking on a program of proliferation, migration, differentiation, and fusion culminating in the repair...
We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard-Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy-Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic poten...
The formalism of a bone cell population model is generalised to be of the form of an S-System. This is a system of nonlinear coupled ordinary differential equations (ODEs), each with the same structure: the change in a variable is equal to a difference in the product of a power-law functions with a specific variable. The variables are the densities...
Purpose
A graphical user interface (GUI) was developed to aid in the assessment of changes in the radiation tolerance of spinal cord/similar central nervous system tissues with time between two individual treatment courses.
Methods
The GUI allows any combination of photons, protons (or ions) to be used as the initial, or retreatment, radiotherapy...
Mistakes in trunk neural crest (NC) cell migration may lead to birth defects of the sympathetic nervous system (SNS) and neuroblastoma (NB) cancer. Receptor tyrosine kinase B (TrkB) and its ligand BDNF critically regulate NC cell migration during normal SNS development and elevated expression of TrkB is correlated with high-risk NB patients. Howeve...
We propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can be split into two phases: dispersion and return. Dispersion is easily understood and can be modelled as simple...
Vitrification is the most common method of cryopreservation of gametes in fertility clinics due to its improved survival rates compared to slow freezing techniques. For the Open Cryotop® vitrification device, the number of oocytes, or embryos, mounted onto a single device can vary.
In this work, a mathematical model is developed for the cooling of...
Tissue regeneration is a process that recapitulates and restores organ structure and function. Although previous studies have demonstrated wound-induced hair neogenesis (WIHN) in laboratory mice (Mus), the regeneration is limited to the center of the wound unlike those observed in African spiny (Acomys) mice. Tissue mechanics have been implicated a...
Fine-grain patterns produced by juxtacrine signalling, have been studied using static monolayers as cellular domains. Unfortunately, analytical results are restricted to a few cells due to the algebraic complexity of nonlinear dynamical systems. Motivated by concentric patterning of Notch expression observed in the mammary gland, we combine concept...
Reaction-diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many prototypical "Turing systems" available, determining their parameters, functional forms, and general a...
We construct a compartmental individual-based model of Covid-19 infection spread. The model can be used to predict the infection trajectory in general environments with various interventions introduced. Tasked by the Welsh Government, we apply the model to secondary schools and Further and Higher Education environments. Specifically, we consider po...
We provide an open-source model to estimate the number of secondary Covid-19 infections caused by potentially infectious students returning from university to private homes with other occupants. Using a Monte-Carlo method and data derived from UK sources, we predict that an infectious student would, on average, infect 0.94 other household members....
A new graphical user interface (GUI) was developed to aid in the assessment of changes in the radiation tolerance of spinal cord/similar central nervous system tissues with time between two treatment courses. The GUI allows any combination of photons, protons (or ions) to be used as the initial, or retreatment, course. Allowances for clinical circu...
Reaction–diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal–mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction–diffusion systems and relate it to a range of existing models. We de...
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming \emph{E. coli} on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop a modelling framework for bi-layer reaction-diffusion systems and relate it to a range of existing mode...
In this paper, we present a framework for investigating coloured noise in reaction–diffusion systems. We start by considering a deterministic reaction–diffusion equation and show how external forcing can cause temporally correlated or coloured noise. Here, the main source of external noise is considered to be fluctuations in the parameter values re...
The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of 'stochastic elasticity' where the constitutive parameters are characterised by probability density functions. We consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stoc...
The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the constitutive parameters are characterised by probability density functions. We consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stoc...
Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities...
We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses acc...
Motivated by the need to quantify uncertainties in the mechanical behaviour of solid materials, we perform simple uniaxial tensile tests on a manufactured rubber-like material that provide critical information regarding the variability in the constitutive responses between different specimens. Based on the experimental data, we construct stochastic...
How spatial patterning arises in biological systems is still an unresolved mystery. Here, we consider the first model for spatial pattern formation, proposed by Alan Turing, which showed that structure could emerge from processes that, in themselves, are non-patterning. He therefore went against the reductionist approach, arguing that biological fu...
We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation can occur for some materials. In addition to the w...
Symmetry breaking and pattern formation from homogeneity is well-studied, but much less is known concerning pattern-forming instabilities in heterogeneous media. In general it is difficult to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. Here, we use a WKBJ asymptot...
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mecha...
When an elastic tube reinforced with helical fibres is inflated, its ends rotate. In large deformations , the amount and chirality of rotation is highly non-trivial, as it depends on the choice of strain-energy density and the arrangements of the fibres. For anisotropic hyperelastic tubes where the material parameters are single-valued constants, t...
In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stoch...
Cavitation in solids can be caused by tensile dead-load traction or impulse traction. The two different types of boundary conditions lead to different static and dynamic solutions. In addition, if the material is stochastic, i.e., the model parameters are represented by probability distributions, the expected behaviour is more complicated to descri...
Studying the progression of the proliferative and differentiative patterns of neural stem cells at the individual cell level is crucial to the understanding of cortex development and how the disruption of such patterns can lead to malformations and neurodevelopmental diseases. However, our understanding of the precise lineage progression programme...
The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters m...
Feathers are arranged in a precise pattern in avian skin. They first arise during development in a row along the dorsal midline, with rows of new feather buds added sequentially in a spreading wave. We show that the patterning of feathers relies on coupled fibroblast growth factor (FGF) and bone morphogenetic protein (BMP) signalling together with...
An expanding wave of EDA and a receding wave of CTNNB1 expression persist in the absence of feather patterning.
EDA and CTNNB1 expression in E8 and E9 FGF20sc/sc (i.e., scaleless mutant) embryos. The embryos (dorsal and lateral views) exhibit expansion of EDA expression despite the absence of feather primordium formation. CTNNB1 expression becomes...
Effects of ex vivo or in vivo application of EDAR-stimulating antibody on feather pattern.
(A) Comparison of the width of the patterned region, defined by FGF20 expression, in E6.5 skin explants cultured for 24 hours in the presence of 2 μg/ml mAb-EDAR3 (an activator of EDAR signalling). (B) Quantification of patterned region width between control...
Effects of FGF and BMP signal perturbation on feather primordium formation and relative timing of FGF20 expression with cell condensation.
(A) Time series of primordium development in CAG-GFP skin, beginning from E7.5, over 20 hours. Scale bar: 1 mm. (B) Effect of SU5402, an inhibitor of FGF receptor signalling, treatment on E6.5 skin explants afte...
Assessment of regulation of patterning genes.
(A) qRT-PCR detecting ETV5, BMP2, BMP4, and BMP7 expression in E6.5 skin explants cultured with 1 μg/ml FGF9 for 5 hours. ETV5 is a positive control, representing a general FGF target gene. Statistical significance from control was calculated using Student t test, (*p < 0.05). (B) qRT-PCR detecting AXIN...
Skin compression does not initiate the wave of feather primordium formation.
(A) Schematic of experimental approach. Skin explants were placed with the midline parallel to the edge of a gap in the underlying filter support. This creates a culture condition in which slightly more than one-half of the skin is attached to a filter substrate, and the r...
Induction of FGF20 expression in a wave by EDA and β-catenin signalling.
(A) Detection of FGF20 in E6.5 explants cultured for 24 hours. A stripe of faint expression is seen ahead of the most recently defined feather row on each side. (B) qRT-PCR detecting FGF20 expression in E6.5 skin explants cultured with either 30 μM CHIR99021 or 500 ng/ml Fc-ch...
Feather tract arrangements in different species.
Comparisons of feather distributions between E9.5 chicken, E10 duck, E18 ostrich, and E21 emu. Feather primordia are visualised by detection of the CTNNB1 transcript. Matching feather tracts in chicken, duck, and ostrich can be identified by the presence of the featherless (apteric) regions separatin...
Tinamou, a flighted ratite, has feather tracts and hexagonal arrangements of feather primordia.
(A) E12 chicken and E14 tinamou embryos were processed for haematoxylin staining to aid visualisation of feather arrangements in the developing embryos. Feather filaments were cut off and embryos dipped in haematoxylin to stain the remaining shaft. Compa...
Data pertaining to Fig 1D, 1E and 1H.
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Data pertaining to Fig 2D.
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Data pertaining to Fig 6D and 6F.
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Data pertaining to Fig 8E and 8F.
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Data pertaining to S2A and S2B Fig.
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Data pertaining to S17B Fig.
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Data pertaining to S19C Fig.
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Mathematical methods.
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Effects of in ovo inhibition of EDA signalling on feather primordium stability and growth.
(A) Continuous inhibition of EDA signalling from E5.5 to E11.5 or E13.5 results in the absence of feather formation and almost bare skin, as defined by CTNNB1 and SHH expression. Scale bar: 5 mm. (B) Transverse sections of embryos in (A) reveal loss of mesenc...
Tracking of individual cell movement in sparsely labelled Chameleon skin.
(A) Angle of movement relative to anterior-posterior axis over time calculated for each z-plane optical layer (1: most superficial epidermis; 6: deepest layer mesenchyme) from 2-dimensional single-cell tracking analysis. Cell movement in epithelial layers is more coordinated...
Feather pattern formation in ratite embryos.
Dorsal and lateral views of primordium pattern formation through in situ hybridisation to detect CTNNB1 transcripts in developing (A) ostrich and (B) emu embryos. Prior to the appearance of primordia, both species display a predefined CTNNB1-expressing dorsal tract; however, a medial-lateral patterning w...
Live cell imaging of epithelial cell movement in a TAT-Cre-induced Chameleon skin explant.
Representative confocal time-lapse video of labelled and cultured E6.5 Chameleon dorsal skin explant over a period of 9 hours. This z-plane is focussed on epithelial (epidermal) cells. Green and red colours indicate cells that have undergone random recombinat...
Live cell imaging of mesenchymal cell movement in a TAT-Cre-induced Chameleon skin explant.
Representative confocal time-lapse video of labelled and cultured E6.5 Chameleon dorsal skin explant over a period of 9 hours. This z-plane is focussed on dermal mesenchymal cells. Green and red colours indicate cells that have undergone random recombination...