Sean McElwain

A two-compartment mechanochemical model of the roles of transforming growth factor β

Publisher: Elsevier BV

Date: 03-2011

DOI: 10.1016/J.JTBI.2010.12.011

Abstract: The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor -β (TGFβ) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGFβ and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGFβ in dermal wounds will produce contractures due to the persistence of myofibroblasts in contrast, early elimination of TGFβ significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures.

Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth

Publisher: Elsevier BV

Date: 05-1978

DOI: 10.1016/0025-5564(78)90033-0

Wound healing angiogenesis: The clinical implications of a simple mathematical model

Publisher: Elsevier BV

Date: 05-2012

DOI: 10.1016/J.JTBI.2012.01.043

Abstract: Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

Cell migration in multicell spheroids: Swimming against the tide

Publisher: Springer Science and Business Media LLC

Date: 05-1993

DOI: 10.1007/BF02460655

Abstract: It is not clear whether concomitant therapy with corticosteroids and anti-tumor necrosis factor (TNF) agents is more effective at inducing remission in patients with Crohn's disease (CD) than anti-TNF monotherapy. We aimed to determine whether patients with active CD receiving corticosteroids during induction therapy with anti-TNF agents had higher rates of clinical improvement than patients not receiving corticosteroids during induction therapy. We systematically searched the MEDLINE, Embase, and CENTRAL databases, through January 20, 2016, for randomized trials of anti-TNF agents approved for treatment of CD and identified 14 trials (5 of adalimumab, 5 of certolizumab, and 4 of infliximab). We conducted a pooled meta-analysis of in idual patient and aggregated data from these trials. We compared data from participants who continued oral corticosteroids during induction with anti-TNF therapy to those treated with anti-TNF agents alone. The endpoints were clinical remission (CD activity index [CDAI] scores <150) and clinical response (a decrease in CDAI of 100 points) at the end of induction (weeks 4-14 of treatment). We included 4354 patients who received induction therapy with anti-TNF agents, including 1653 [38.0%] who were receiving corticosteroids. The combination of corticosteroids and an anti-TNF agent induced clinical remission in 32.0% of patients, whereas anti-TNF monotherapy induced clinical remission in 35.5% of patients (odds ratio [OR], 0.93 95% CI, 0.74-1.17). The combination of corticosteroids and an anti-TNF agent induced a clinical response in 42.7% of patients, whereas anti-TNF monotherapy induced a clinical response in 46.8% (OR 0.84 95% CI, 0.73-0.96). These findings did not change with adjustment for baseline CDAI scores and concurrent use of immunomodulators. Based on a meta-analysis of data from randomized trials of anti-TNF therapies in patients with active CD, patients receiving corticosteroids during induction therapy with anti-TNF agents did not have higher rates of clinical improvement compared with patients not receiving corticosteroids during induction therapy. Given these findings and the risks of corticosteroid use, clinicians should consider early weaning of corticosteroids during induction therapy with anti-TNF agents for patients with corticosteroid-refractory CD.

Plasticity field adjacent to faces of asperities on a rotating roll after initial indentation into a half-space

Publisher: Elsevier BV

Date: 2002

DOI: 10.1016/S0093-6413(02)00229-X

Bayesian modelling of an epidemic of severe acute respiratory syndrome

Publisher: Springer Science and Business Media LLC

Date: 08-04-2006

DOI: 10.1007/S11538-005-9005-4

Model of cold rolling of thin metal sheets between nonparallel rolls

Publisher: Elsevier BV

Date: 07-1994

DOI: 10.1016/0307-904X(94)90222-4

A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues II: Solutions to the Biphasic Equations for a Multicell Spheroid

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2006

DOI: 10.1137/040607125

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Publisher: Frontiers Media SA

Date: 30-09-2015

DOI: 10.3389/FPHYS.2015.00262

Approximate solution of an integro‐differential equation

Publisher: Informa UK Limited

Date: 1994

DOI: 10.1080/0020739940250101

Traveling Wave Model to Interpret a Wound-Healing Cell Migration Assay for Human Peritoneal Mesothelial Cells

Publisher: Mary Ann Liebert Inc

Date: 03-2004

DOI: 10.1089/107632704323061834

Abstract: The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over components of the extracellular matrix. Results were interpreted in terms of Fisher's equation, which includes terms for the modeling of random cell motility (diffusion) and proliferation. The model predicts that, after a short transient, the invading cell front will move as a traveling wave at constant speed. This is consistent with the experimental findings. Using the model, a relationship between the rate of cell proliferation and the diffusion coefficient was obtained. We used the model to deduce the cell diffusion coefficients under control conditions and in the presence of collagen IV and compared these with other published data. The model may be useful in analyzing the invasive capacity of cancer cells as well in predicting the efficacy of growth factors in tissue reconstruction, including the development of monolayer sheets of cells in skin engineering or the repair of injured corneas using grafts of cultured cells.

Interpreting scratch assays using pair density dynamics and approximate Bayesian computation

Publisher: The Royal Society

Date: 09-2014

DOI: 10.1098/RSOB.140097

Abstract: Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D , or the cell proliferation rate, λ . Estimating D and λ is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and λ have been proposed, these previous methods lead to point estimates of D and λ , and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and λ using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and λ from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and λ . We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and λ , as well as additional relevant parameters such as the strength of cell-to-cell adhesion or the strength of cell-to-substrate adhesion.

Type III secretion, contact-dependent model for the intracellular development of Chlamydia

Publisher: Springer Science and Business Media LLC

Date: 2006

DOI: 10.1007/S11538-005-9024-1

Abstract: The medically significant genus Chlamydia is a class of obligate intracellular bacterial pathogens that replicate within vacuoles in host eukaryotic cells termed inclusions. Chlamydia's developmental cycle involves two forms an infectious extracellular form, known as an elementary body (EB), and a non-infectious form, known as the reticulate body (RB), that replicates inside the vacuoles of the host cells. The RB surface is covered in projections that are in intimate contact with the inclusion membrane. Late in the developmental cycle, these reticulate bodies differentiate into the elementary body form. In this paper, we present a hypothesis for the modulation of these developmental events involving the contact-dependent type III secretion (TTS) system. TTS surface projections mediate intimate contact between the RB and the inclusion membrane. Below a certain number of projections, detachment of the RB provides a signal for late differentiation of RB into EB. We use data and develop a mathematical model investigating this hypothesis. If the hypothesis proves to be accurate, then we have shown that increasing the number of inclusions per host cell will increase the number of infectious progeny EB until some optimal number of inclusions. For more inclusions than this optimum, the infectious yield is reduced because of spatial restrictions. We also predict that a reduction in the number of projections on the surface of the RB (and as early as possible during development) will significantly reduce the burst size of infectious EB particles. Many of the results predicted by the model can be tested experimentally and may lead to the identification of potential targets for drug design.

Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Publisher: Elsevier BV

Date: 09-2014

DOI: 10.1016/J.JTBI.2014.04.026

Abstract: Cells respond to various biochemical and physical cues during wound-healing and tumour progression. in vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour-like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound-like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time-evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.

Elastohydrodynamics of the eyelid wiper

Publisher: Springer Science and Business Media LLC

Date: 08-12-2008

DOI: 10.1007/S11538-007-9252-7

Abstract: This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface. For the lubrication film to be effective, it is required that the orientation of the eyelid wiper changes between the opening and closing phases of a blink. In order to model this, the hydrodynamic model is coupled with an elastic mattress model for the soft tissue of the eyelid wiper and ocular surface. This leads to a one-dimensional non-linear partial differential equation governing the fluid pressure in the lubrication film. In order to solve the differential equation, a loading condition or constraint equation must be specified. The resulting system is then solved numerically. The model allows predictions of the tear film flux from under the upper eyelid, as well as normal and shear stresses acting on the ocular surface. These factors are important in relation to dry eye syndrome, deformation of the cornea and contact lens design. It is found that the pressure and shear stress under the eyelid act across a length of approximately 0.1 mm which is consistent with clinical observations. It order to achieve a flow of tears from under the upper eyelid during a blink, the model requires that the normal force the eyelid applies to the ocular surface during the closing phase of the blink is significantly higher than during the opening phase of the blink.

A Mathematical Model of Continuous HIV Mutations Eluding Immune Defence

Publisher: Hindawi Limited

Date: 2002

DOI: 10.1080/1027366031000088438

Abstract: We develop a description of HIV mutations based upon a continuum representation of the fitness of the virus, including the interaction of the virus with both specific Th1 lymphocytes as well as cross-reactive cells. This deterministic model allows a straightforward measure of the ersity of viral population and reproduces the observed increase in ersity as the disease progresses in an untreated patient. We use the ersity threshold theory, extending the modelling to track mutations on a continuum. When the ersity threshold is exceeded, the host immune system collapses.

Using Samples to Estimate the Sensitivity and Specificity of a Surveillance Process

Publisher: Cambridge University Press (CUP)

Date: 06-2008

DOI: 10.1086/588203

Abstract: Determining sensitivity and specificity of a postoperative infection surveillance process is a difficult undertaking. Because postoperative infections are rare, vast numbers of negative results exist, and it is often not reasonable to assess them all. This study gives a methodological framework for estimating sensitivity and specificity by taking only a small s le of the number of patients who test negative and comparing their findings to the reference or “gold standard” rather than comparing the findings of all patients to the gold standard. It provides a formula for deriving confidence intervals for these estimates and a guide to minimum requirements for s ling results.

Visual evoked potentials to small stimuli presented along a vertical meridian: Individual differences and dipole modelling

Publisher: Informa UK Limited

Date: 08-1994

DOI: 10.1080/00049539408259478

Dynamics of tear film deposition and draining

Publisher: Oxford University Press (OUP)

Date: 09-2005

DOI: 10.1093/IMAMMB/DQI012

Abstract: This paper investigates the deposition of the tear film on the cornea of the human eye. The tear film is laid down by the motion of the upper eyelid and then subsequently flows and thins. Of particular interest is the stability of the tear layer and the development of dry patches on the cornea. While there has been significant research on the behaviour of tear films between blinks, this paper focuses on understanding the mechanisms which control the shape and thickness of the deposited film and how this affects the subsequent film behaviour. Numerical and analytical methods are applied to a lubrication model which includes the effects of surface tension, viscosity, gravity and evaporation. The model reveals the importance of the eyelid velocity, motion of the surface lipid layer and the storage of tear film between blinks.

Standard melanoma-associated markers do not identify the MM127 metastatic melanoma cell line

Publisher: Springer Science and Business Media LLC

Date: 18-04-2016

DOI: 10.1038/SREP24569

Abstract: Reliable identification of different melanoma cell lines is important for many aspects of melanoma research. Common markers used to identify melanoma cell lines include: S100 HMB-45 and Melan-A. We explore the expression of these three markers in four different melanoma cell lines: WM35 WM793 SK-MEL-28 and MM127. The expression of these markers is examined at both the mRNA and protein level. Our results show that the metastatic cell line, MM127, cannot be detected using any of the commonly used melanoma-associated markers. This implies that it would be very difficult to identify this particular cell line in a heterogeneous s le and as a result this cell line should be used with care.

A mathematical model investigating the impact of an environmental reservoir on the prevalence and control of vancomycin-resistant enterococci [3]

Publisher: Oxford University Press (OUP)

Date: 15-05-2006

DOI: 10.1086/503439

Some Plastic Deformation Modes for Indentation of Half Space by a Rigid Body With Serrated Surface as a Model of Roughness Transfer in Metal Forming

Publisher: ASME International

Date: 26-03-2002

DOI: 10.1115/1.1446864

Abstract: This paper is concerned with the plastic deformation modes of the free surface of the half space between the teeth on the serrated surface of a rigid body. The rigid body indents the half space perpendicularly and the material of the half space is assumed to be elastic/rigid perfectly plastic. Plane-strain conditions are assumed. The emphasis in this paper is on the profile left on the surfaces of the material when the indentation proceeds to some depth and then the indenter is removed. Based on the observations from finite element results, slip line fields for the plastic deformation regions at various stages of indentation are proposed and the corresponding hodographs for the velocity field are presented. This has application in roughness transfer of final metal forming process.

Yield criterion of porous materials subjected to complex stress states

Publisher: Elsevier BV

Date: 05-2006

DOI: 10.1016/J.ACTAMAT.2005.12.028

Experimental and Modelling Investigation of Monolayer Development with Clustering

Publisher: Springer Science and Business Media LLC

Date: 13-04-2013

DOI: 10.1007/S11538-013-9839-0

Abstract: Standard differential equation-based models of collective cell behaviour, such as the logistic growth model, invoke a mean-field assumption which is equivalent to assuming that in iduals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, which aim to account for the dynamics of in iduals, pairs of in iduals, triplets of in iduals, and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean-field model to both data sets. Our results indicate that the mean-field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean-field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.

Conversion estimates for gas-solid reactions: Kinetics of arbitrary power-law type

Publisher: Elsevier BV

Date: 1993

DOI: 10.1016/0895-7177(93)90093-E

Dissociation and recombination of a diatomic molecules involving two states which only interact via the atomic species

Publisher: Elsevier BV

Date: 02-1977

DOI: 10.1016/0301-0104(77)85014-3

Characterizing an Outbreak of Vancomycin-Resistant Enterococci using Hidden Markov Models

Publisher: The Royal Society

Date: 13-03-2007

DOI: 10.1098/RSIF.2007.0224

Abstract: Background . Antibiotic-resistant nosocomial pathogens can arise in epidemic clusters or sporadically. Genotyping is commonly used to distinguish epidemic from sporadic vancomycin-resistant enterococci (VRE). We compare this to a statistical method to determine the transmission characteristics of VRE. Methods and findings . A structured continuous-time hidden Markov model (HMM) was developed. The hidden states were the number of VRE-colonized patients (both detected and undetected). The input for this study was weekly point-prevalence data 157 weeks of VRE prevalence. We estimated two parameters: one to quantify the cross-transmission of VRE and the other to quantify the level of VRE colonization from sporadic sources. We compared the results to those obtained by concomitant genotyping and phenotyping. We estimated that 89% of transmissions were due to ward cross-transmission while 11% were sporadic. Genotyping found that 90% had identical glycopeptide resistance genes and 84% were identical or nearly identical on pulsed-field gel electrophoresis (PFGE). There was some evidence, based on model selection criteria, that the cross-transmission parameter changed throughout the study period. The model that allowed for a change in transmission just prior to the outbreak and again at the peak of the outbreak was superior to other models. This model estimated that cross-transmission increased at week 120 and declined after week 135, coinciding with environmental decontamination. Significance . We found that HMMs can be applied to serial prevalence data to estimate the characteristics of acquisition of nosocomial pathogens and distinguish between epidemic and sporadic acquisition. This model was able to estimate transmission parameters despite imperfect detection of the organism. The results of this model were validated against PFGE and glycopeptide resistance genotype data and produced very similar results. Additionally, HMMs can provide information about unobserved events such as undetected colonization.

A re-examination of oxygen diffusion in a spherical cell with michaelis-menten oxygen uptake kinetics

Publisher: Elsevier BV

Date: 03-1978

DOI: 10.1016/0022-5193(78)90270-9

The Role of Mechanical Host-Tumour Interactions in the Collapse of Tumour Blood Vessels and Tumour Growth Dynamics

Publisher: Elsevier BV

Date: 02-2006

DOI: 10.1016/J.JTBI.2005.06.033

Abstract: A mathematical model of residual stress evolution in a growing vascular tumour is presented, in an attempt to elucidate the poorly understood phenomenon of vascular collapse. Whereas earlier studies in this area have neglected the effects of mechanical interactions between the tumour and the surrounding host tissue, the significance of these interactions for the long-term development of a tumour is now considered. The model predicts tumour stress distributions which reflect the distinctive patterns of vascular collapse reported in experimental studies. Moreover, while neglecting mechanical host/tumour interactions results in the eventual complete regression of the tumour to its avascular dormant size in the event of vascular collapse, this new model points to the possibility of oscillations in the tumour's size in the long term.

The use of hyperbaric oxygen therapy to treat chronic wounds: A review

Publisher: Wiley

Date: 05-2008

DOI: 10.1111/J.1524-475X.2008.00372.X

Two-dimensional plane strain rolling: An asymptotic approach to the estimation of inhomogeneous effects

Publisher: Elsevier BV

Date: 02-1995

DOI: 10.1016/0020-7403(94)00053-M

The effect of the lipid layer on tear film behaviour

Publisher: Springer Science and Business Media LLC

Date: 16-05-2006

DOI: 10.1007/S11538-006-9105-9

Abstract: This paper investigates the effect of surfactants during tear film deposition and subsequent thinning. The surfactants occur naturally on the surface of the tear film in the form of a lipid layer. A lubrication model is developed that describes lipid spreading and film height evolution. It is shown that lipids may play an important role in drawing the tear film up the cornea during the opening phase of the blink. Further, nonuniform distributions of lipids may lead to a rapid thinning of the tear film behind the advancing lipid front (shock). Experiments using a fluorescein dye technique and using a tearscope were undertaken in order to visualise the motion of the lipid layer and any associated shocks immediately after a blink. It is found that the lipid layer continues to spread upwards on the cornea after the opening phase of the blink, in agreement with the model. Using the experimental data, lipid particles were tracked in order to determine the surface velocity and these results are compared to the model predictions.

A mathematical model for the investigation of the Th1 immune response to Chlamydia trachomatis

Publisher: Elsevier BV

Date: 03-2003

DOI: 10.1016/S0025-5564(02)00180-3

Abstract: Chlamydia are bacterial pathogens of humans and animals causing the important human diseases trachoma, sexually transmitted chlamydial disease and pneumonia. Of the human chlamydial diseases, sexually transmitted disease caused by Chlamydia trachomatis is a major public health concern. Chlamydia trachomatis replicates intracellularly and is characterised by a complex developmental cycle. Chlamydia is susceptible to humoral and cell-mediated immunity. Here we investigate the Th1 cell-mediated immune response against Chlamydia-infected cells as the response changes over the chlamydial developmental cycle. We suggest a form for the immune response over one developmental cycle by modelling the change in the number of intracellular chlamydial particles and assume peptides are presented in proportion to the number of replicating forms of chlamydial particles. We predict, perhaps non-intuitively, that persistent Chlamydia should be induced and forced not to return to the lytic cycle. We also suggest that extending the length of the time of the lytic cycle will effectively decrease the required efficacy of the Th1 response to eliminate the pathogen. We produce plots of active disease progression, control and clearance for varying levels of Th1 effectiveness.

Comparison of two numerical approaches for bone remodelling

Publisher: Elsevier BV

Date: 2007

DOI: 10.1016/J.MEDENGPHY.2005.12.008

Abstract: This paper addresses the "checkerboard" phenomenon, which occurs in numerical simulation of bone remodelling. It attempts to answer the question: is an element-based approach suitable for bone remodelling? Two different numerical approaches, the element-based and the node-based finite element analyses, are implemented using ABAQUS. A comparison of the numerical results demonstrates that the checkerboard phenomenon occurs only in the element-based finite element analyses the node-based approach eradicates the checkerboard phenomenon but requires much more computational time. This study shows that it is essential to enforce the continuity of bone density across the element boundaries. As the node-based approach requires much more computational time, the first-order Adams-Bashforth integration method is introduced to reduce computational cost. The comparisons with Euler's forward method demonstrate that the first-order Adams-Bashforth method indeed enhances accuracy and reduces computational cost. This study concludes that the node-based approach with the first-order Adams-Bashforth integration scheme is to be recommended for computational bone remodelling studies.

A Fibrocontractive Mechanochemical Model of Dermal Wound Closure Incorporating Realistic Growth Factor Kinetics

Publisher: Springer Science and Business Media LLC

Date: 13-01-2012

DOI: 10.1007/S11538-011-9712-Y

Abstract: Fibroblasts and their activated phenotype, myofibroblasts, are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct processes: The cells are stimulated to change phenotype by the combined actions of transforming growth factor β (TGFβ) and mechanical tension. This observation indicates a need for a detailed exploration of the effect of the strong interactions between the mechanical changes and growth factors in dermal wound healing. We review the experimental findings in detail and develop a model of dermal wound healing that incorporates these phenomena. Our model includes the interactions between TGFβ and collagenase, providing a more biologically realistic form for the growth factor kinetics than those included in previous mechanochemical descriptions. A comparison is made between the model predictions and experimental data on human dermal wound healing and all the essential features are well matched.

Mathematical Model of Hyperbaric Oxygen Therapy Applied to Chronic Diabetic Wounds

Publisher: Springer Science and Business Media LLC

Date: 05-03-2010

DOI: 10.1007/S11538-010-9514-7

Abstract: The failure of certain wounds to heal (including diabetic foot ulcers) is a significant socioeconomic issue for countries worldwide. There is much debate about the best way to treat these wounds and one approach that is shrouded with controversy is hyperbaric oxygen therapy (HBOT), a technique that can reduce the risk of utation in diabetic patients.In this paper, we develop a six species mathematical model of wound healing angiogenesis and use it to investigate the effectiveness of HBOT, compare the response to different HBOT protocols and study the effect of HBOT on the healing of diabetic wounds that fail to heal for a variety of reasons. We vary the pressure level (1 atm-3 atm), percentage of oxygen inspired by the patient (21%-100%), session duration (0-180 minutes) and frequency (twice per day-once per week) and compare the simulated wound areas associated with different protocols after three weeks of treatment.We consider a variety of etiologies of wound chronicity and show that HBOT is only effective in treating certain causes of chronic wounds. For a wound that fails to heal due to excessive, oxygen-consuming bacteria, we show that intermittent HBOT can accelerate the healing of a chronic wound but that sessions should be continued until complete healing is observed. Importantly, we also demonstrate that normobaric oxygen is not a replacement for HBOT and supernormal healing is not an expected outcome. Our simulations illustrate that HBOT has little benefit for treating normal wounds, and that exposing a patient to fewer, longer sessions of oxygen is not an appropriate treatment option.

Diffusion theory can be applied to antibodies attaching to ligand sites

Publisher: Cambridge University Press (CUP)

Date: 04-2005

DOI: 10.1017/S1446181100009640

Abstract: Humoral immunity is that aspect of specific immunity that is mediated by B lymphocytes and involves the neutralising of disease-producing microorganisms, called pathogens, by means of antibodies attaching to the pathogen's binding sites. This inhibits the pathogen's entry into target cells. We present a master equation in both discrete and in continuous form for a ligand bound at n sites becoming a ligand bound at m sites in a given interaction time. To track the time-evolution of the antibody-ligand interaction, it is shown that the process is most easily treated classically and that in this case the master equation can be reduced to an equivalent one-dimensional diffusion equation. Thus well-known diffusion theory can be applied to antibody-ligand interactions. We consider three distinct cases depending on whether the probability of antibody binding compared to the probability of dissociation is relatively large, small or comparable, and numerical solutions are given.

A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2005

DOI: 10.1137/040607113

A comparison of methods to estimate the roll torque in thin strip rolling

Publisher: Elsevier BV

Date: 12-2001

DOI: 10.1016/S0020-7403(00)00049-7

A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: Predicting the impact of interventions

Publisher: Elsevier BV

Date: 04-2007

DOI: 10.1016/J.JTBI.2006.11.008

Abstract: To estimate the transmission rate of MRSA in an intensive care unit (ICU) in an 800 bed Australian teaching hospital and predict the impact of infection control interventions. A mathematical model was developed which consisted of four compartments: colonised and uncolonised patients and contaminated and uncontaminated health-care workers (HCWs). Patient movements, MRSA acquisition and daily prevalence data were collected from an ICU over 939 days. Hand hygiene compliance and the probability of MRSA transmission from patient to HCW per discordant contact were measured during the study. Attack rate and reproduction ratio were estimated using Bayesian methods. The impact of a number of interventions on attack rate was estimated using both stochastic and deterministic versions of the model. The mean number of secondary cases arising from the ICU admission of colonised patients, also called the ward reproduction ratio, R(w), was estimated to be 0.50 (95% CI 0.39-0.62). The attack rate was one MRSA transmission per 160 (95% CI 130-210) uncolonised-patient days. Results were not sensitive to uncertainty in measured model parameters (hand hygiene rate and transmission probability per contact). Hand hygiene was predicted to be the most effective intervention. Decolonisation was predicted to be relatively ineffective. Increasing HCW numbers was predicted to increase MRSA transmission, in the absence of patient cohorting. The predictions of the stochastic model differed from those of the deterministic model, with lower levels of colonisation predicted by the stochastic model. The number of secondary cases of MRSA colonisation within the ICU in this study was below unity. Transmission of MRSA was sustained through admission of colonised patients. Stochastic model simulations give more realistic predictions in hospital ward settings than deterministic models. Increasing staff does not necessarily lead to reduced transmission of nosocomial pathogens.

Do pioneer cells exist?

Publisher: Public Library of Science (PLoS)

Date: 21-01-2014

DOI: 10.1371/JOURNAL.PONE.0085488

A model of neutralization of Chlamydia trachomatis based on antibody and host cell aggregation on the elementary body surface

Publisher: Elsevier BV

Date: 02-2004

DOI: 10.1016/J.JTBI.2003.09.010

Abstract: Humoral immunity is that aspect of specific immunity that is mediated by B lymphocytes and involves the neutralizing of pathogens by means of antibodies attaching to the pathogen's binding sites. Antibodies bind to and block ligand sites on the pathogen which prevents these sites from attaching to target cell receptors and so cell entry is inhibited. Many studies investigate the role of humoral immunity for protection against chlamydial challenge and they have shown that neutralization of the chlamydial body requires a large number of attached antibodies. Steric hindrance greatly influences the number of available sites that may be bound, reducing relative occupancy well below 100%. We model steric effects of antibody Fab fragment attachment indicating that they must be taken into consideration to accurately model valency, the number of available binding sites. We derive a partial differential equation for the number of antibody Fabs and host cell receptors that are aggregated to extracellular chlamydial elementary bodies. We consider steric effects in describing the size distribution of aggregates. Our theory is in good agreement with Monte Carlo simulations of binding. We use our theoretical prediction for the valency in a model for the in-host population dynamics of a chlamydial infection and we fit our model to experimental data.

A mathematical model of tumour-induced capillary growth

Publisher: Elsevier BV

Date: 05-1985

DOI: 10.1016/S0022-5193(85)80255-1

Abstract: The corneal limbal vessels of an animal host respond to the presence of a source of Tumour Angiogenesis Factor (TAF) implanted in the cornea by the formation of new capillaries which grow towards the source. This neovasculature can be easily seen and studied and this paper describes a mathematical model of some of the important features of the growth. The model includes the diffusion of TAF, the formation of sprouts from pre-existing vessels and models the movement of these sprouts to form new capillaries as a chemotactic response to the presence of TAF. Numerical results are produced for various values of the parameters which characterize the model and it is suggested that the model might form the framework for further theoretical work on related phenomena such as wound healing or to develop strategies for the investigation of anti-angiogenesis.

How much information can be obtained from tracking the position of the leading edge in a scratch assay?

Publisher: The Royal Society

Date: 06-08-2014

DOI: 10.1098/RSIF.2014.0325

Abstract: Moving cell fronts are an essential feature of wound healing, development and disease. The rate at which a cell front moves is driven, in part, by the cell motility, quantified in terms of the cell diffusivity D , and the cell proliferation rate λ . Scratch assays are a commonly reported procedure used to investigate the motion of cell fronts where an initial cell monolayer is scratched, and the motion of the front is monitored over a short period of time, often less than 24 h. The simplest way of quantifying a scratch assay is to monitor the progression of the leading edge. Use of leading edge data is very convenient because, unlike other methods, it is non-destructive and does not require labelling, tracking or counting in idual cells among the population. In this work, we study short-time leading edge data in a scratch assay using a discrete mathematical model and automated image analysis with the aim of investigating whether such data allow us to reliably identify D and λ . Using a naive calibration approach where we simply scan the relevant region of the ( D , λ ) parameter space, we show that there are many choices of D and λ for which our model produces indistinguishable short-time leading edge data. Therefore, without due care, it is impossible to estimate D and λ from this kind of data. To address this, we present a modified approach accounting for the fact that cell motility occurs over a much shorter time scale than proliferation. Using this information, we ide the duration of the experiment into two periods, and we estimate D using data from the first period, whereas we estimate λ using data from the second period. We confirm the accuracy of our approach using in silico data and a new set of in vitro data, which shows that our method recovers estimates of D and λ that are consistent with previously reported values except that that our approach is fast, inexpensive, non-destructive and avoids the need for cell labelling and cell counting.

An Approximate Method of Estimating the Yield of a Strip Under Tension Cut by Serrated Surfaces on Opposite Faces

Publisher: ASME International

Date: 04-2003

DOI: 10.1115/1.1555656

Abstract: In view of the well-known disparity between predictions from temper rolling models and measured values from rolling mills, there is a need to obtain a better understanding of the effect of roll asperities on the yielding characteristics of the rolled strip. This paper models a roll with asperities as a rigid body with a regular serrated surface and the rolling process as an indentation, and uses the plane strain model and slip-line theory to determine the critical pressure that is required to yield the strip throughout the thickness beneath the tips of the asperities. The strip is also under lateral tension at both ends. The emphasis of the paper is the effect of the lateral tension and the thickness of the strip on the critical pressure. For the case when the indenting surface has sharp teeth, the critical pressure can be found in close form. For the case when the indenting surface has blunt teeth, a robust approximate scheme for estimation of the critical values that does not require extensive computation is given and this scheme can be used in an on-line control process. It is found that when the tooth angle is smaller than a critical angle, the sharper the tooth, the lower the average critical pressure needed to make the strip yield. When the tooth angle is larger than the critical angle, then the blunter the tooth, the lower the pressure that is needed. The effect of the asperities is to reduce the critical pressure and it is found that this effect is more pronounced for thin strips than for thick strips. The lateral tension reduces the critical pressure further. These findings give some implications for the rolling of metal sheets.

A two-phase model of solid tumour growth

Publisher: Elsevier BV

Date: 05-2003

DOI: 10.1016/S0893-9659(03)00038-7

A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

Publisher: Elsevier BV

Date: 2008

DOI: 10.1016/J.JTBI.2007.08.030

Abstract: This paper develops a simple mathematical model of the sitting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive attempt to address the question of how unchecked sprouting of the parent vessel is avoided at the initiation of angiogenesis, based on the idea that feedback regulation processes play the dominant role. No chemical interaction between the proangiogenic and antiangiogenic factors is assumed. The model is based on corneal pocket experiments, and provides a mathematical analysis of the initial spacing of angiogenic sprouts.

Yield Functions for Porous Materials with Cubic Symmetry Using Different Definitions of Yield

Publisher: Wiley

Date: 09-2006

DOI: 10.1002/ADEM.200600075

An approximate method for the solution of an influence function foil rolling model

Publisher: Elsevier BV

Date: 08-2004

DOI: 10.1016/J.IJMECSCI.2004.08.006

Analysis of Travelling Waves Associated with the Modelling of Aerosolised Skin Grafts

Publisher: Springer Science and Business Media LLC

Date: 25-06-2006

DOI: 10.1007/S11538-006-9138-0

Abstract: A previous model developed by the authors investigates the growth patterns of keratinocyte cell colonies after they have been applied to a burn site using a spray technique. In this paper, we investigate a simplified one-dimensional version of the model. This model yields travelling wave solutions and we analyse the behaviour of the travelling waves. Approximations for the rate of healing and maximum values for both the active healing and the healed cell densities are obtained.

Modelling external bone adaptation using evolutionary structural optimisation

Publisher: Springer Science and Business Media LLC

Date: 25-08-2007

DOI: 10.1007/S10237-006-0055-9

Abstract: External remodelling is significant in the bone healing process, and it is essential to predict the bone external shape in the design of artificial bone grafts. This paper demonstrates the effectiveness of the evolutionary structural optimisation (ESO) method for the simulation of bone morphology. A two-dimensional ESO strategy is developed which is capable of finding the modified bone topology beginning with any geometry under any loading conditions. The morphology of bone structure is described by the quantitative bone adaptation theory, which is integrated with the finite element method. The evolutionary topology optimisation process is introduced to find the bone shape. A rectangle, which occupies a larger space than the external shape of the bone structure, is specified as a design domain the evolutionary process iteratively eliminates and redistributes material throughout the domain to obtain an optimum arrangement of bone materials. The technique has been tested on a wide range of ex les. In this paper, the formation of trabecular bone architecture around an implant is studied as another ex le, the growth of the coronal section of a vertebral body is predicted. The ex les support the assertion that the external shape of bone structure can be successfully predicted by the proposed ESO procedure.

A mathematical model of wound healing and subsequent scarring

Publisher: The Royal Society

Date: 25-03-2009

DOI: 10.1098/RSIF.2008.0536

Abstract: Wound healing is a complex process involving the delicate interaction between elements that vary widely in nature and size scales, from the nanometre level, such as molecules, to cells measured in micrometres, and fibres with width and length measured on both scales. Hybrid approaches, where each species is represented by a model on an appropriate size scale, have received attention recently. In this study, we provide a review of earlier work on such hybrid models of wound healing. General models for each of the element types involved in dermal wound healing used in this research are described: cells, modelled as discrete in iduals chemicals, modelled as continua and fibres, modelled with a novel tensorial representation. Techniques for integrating such disparate models are outlined. A six-species model (fibrin, collagen, macrophages, fibroblasts, transforming growth factor-β (TGF-β) and tissue plasminogen activator) of dermal wound healing is presented. The role of the cytokine TGF-β in the healing cascade is investigated using the model, along with its role in the degree of scarring in the healed tissue.

Modelling novel coal based direct reduction process

Publisher: Informa UK Limited

Date: 2008

DOI: 10.1179/174328107X174654

Primary Alkaline Battery Cathodes A Three-Scale Model

Publisher: The Electrochemical Society

Date: 2000

DOI: 10.1149/1.1394015

New Insights into Vascular Collapse and Growth Dynamics in Solid Tumors

Publisher: Elsevier BV

Date: 06-2004

DOI: 10.1016/J.JTBI.2004.01.009

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Publisher: Wiley

Date: 07-02-2012

DOI: 10.1111/J.1524-475X.2012.00775.X

Optimization of coal pyrolysis modeling

Publisher: Elsevier BV

Date: 08-2000

DOI: 10.1016/S0010-2180(00)00115-2

Approximate modelling of coal pyrolysis

Publisher: Elsevier BV

Date: 05-1999

DOI: 10.1016/S0016-2361(98)00204-X

In vitro degradation of articular cartilage: Does trypsin treatment produce consistent results?

Publisher: Wiley

Date: 26-07-2006

DOI: 10.1111/J.1469-7580.2006.00605.X

Conversion estimates for gas-solid reactions: reversible kinetics independent of solid concentrations

Publisher: Elsevier BV

Date: 1994

DOI: 10.1016/0009-2509(94)87007-1

Approximations to the distributed activation energy model for the pyrolysis of coal

Publisher: Elsevier BV

Date: 04-2003

DOI: 10.1016/S0010-2180(02)00554-0

A linear-elastic model of anisotropic tumour growth

Publisher: Cambridge University Press (CUP)

Date: 06-2004

DOI: 10.1017/S0956792504005406

Abstract: This paper examines the effect of anisotropic growth on the evolution of mechanical stresses in a linear-elastic model of a growing, avascular tumour. This represents an important improvement on previous linear-elastic models of tissue growth since it has been shown recently that spatially-varying isotropic growth of linear-elastic tissues does not afford the necessary stress-relaxation for a steady-state stress distribution upon reaching a nutrient-regulated equilibrium size. Time-dependent numerical solutions are developed using a Lax-Wendroff scheme, which show the evolution of the tissue stress distributions over a period of growth until a steady-state is reached. These results are compared with the steady-state solutions predicted by the model equations, and key parameters influencing these steady-state distributions are identified. Recommendations for further extensions and applications of this model are proposed.

Use of a quantitative gene expression assay based on micro-array techniques and a mathematical model for the investigation of chlamydial generation time

Publisher: Springer Science and Business Media LLC

Date: 05-2004

DOI: 10.1016/J.BULM.2003.09.001

A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds

Publisher: Public Library of Science (PLoS)

Date: 31-07-2009

DOI: 10.1371/JOURNAL.PCBI.1000451

Assessing the role of spatial correlations during collective cell spreading

Publisher: Springer Science and Business Media LLC

Date: 16-07-2014

DOI: 10.1038/SREP05713

Abstract: Spreading cell fronts are essential features of development, repair and disease processes. Many mathematical models used to describe the motion of cell fronts, such as Fisher's equation, invoke a mean–field assumption which implies that there is no spatial structure, such as cell clustering, present. Here, we examine the presence of spatial structure using a combination of in vitro circular barrier assays, discrete random walk simulations and pair correlation functions. In particular, we analyse discrete simulation data using pair correlation functions to show that spatial structure can form in a spreading population of cells either through sufficiently strong cell–to–cell adhesion or sufficiently rapid cell proliferation. We analyse images from a circular barrier assay describing the spreading of a population of MM127 melanoma cells using the same pair correlation functions. Our results indicate that the spreading melanoma cell populations remain very close to spatially uniform, suggesting that the strength of cell–to–cell adhesion and the rate of cell proliferation are both sufficiently small so as not to induce any spatial patterning in the spreading populations.

Experimental study of coal based direct reduction in iron ore/coal composite pellets in a one layer bed under nonisothermal, asymmetric heating

Publisher: Informa UK Limited

Date: 02-2006

DOI: 10.1179/174328106X80064

Travelling waves in a wound healing assay

Publisher: Elsevier BV

Date: 05-2004

DOI: 10.1016/S0893-9659(04)90128-0

Foil rolling: a new interpretation of experimental results

Publisher: Elsevier BV

Date: 02-2002

DOI: 10.1016/S0924-0136(01)01158-X

A modified Hertzian foil rolling model: approximations based on perturbation methods

Publisher: Elsevier BV

Date: 08-2002

DOI: 10.1016/S0020-7403(02)00058-9

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Publisher: Springer Science and Business Media LLC

Date: 12-2013

DOI: 10.1186/1752-0509-7-137

Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

Publisher: The Royal Society

Date: 23-05-2012

DOI: 10.1098/RSPB.2012.0319

Abstract: The crosstalk between fibroblasts and keratinocytes is a vital component of the wound healing process, and involves the activity of a number of growth factors and cytokines. In this work, we develop a mathematical model of this crosstalk in order to elucidate the effects of these interactions on the regeneration of collagen in a wound that heals by second intention. We consider the role of four components that strongly affect this process: transforming growth factor- β , platelet-derived growth factor, interleukin-1 and keratinocyte growth factor. The impact of this network of interactions on the degradation of an initial fibrin clot, as well as its subsequent replacement by a matrix that is mainly composed of collagen, is described through an eight-component system of nonlinear partial differential equations. Numerical results, obtained in a two-dimensional domain, highlight key aspects of this multifarious process, such as re-epithelialization. The model is shown to reproduce many of the important features of normal wound healing. In addition, we use the model to simulate the treatment of two pathological cases: chronic hypoxia, which can lead to chronic wounds and prolonged inflammation, which has been shown to lead to hypertrophic scarring. We find that our model predictions are qualitatively in agreement with previously reported observations and provide an alternative pathway for gaining insight into this complex biological process.

A model of vascular compression in solid tumours

Publisher: Elsevier BV

Date: 06-1979

DOI: 10.1016/0022-5193(79)90339-4

An anisotropic model of vascular tumour growth

Publisher: Elsevier

Date: 2003

DOI: 10.1016/B978-008044046-0.50393-6

A model of wound-healing angiogenesis in soft tissue

Publisher: Elsevier BV

Date: 08-1996

DOI: 10.1016/0025-5564(96)00044-2

Abstract: Angiogenesis, or blood vessel growth, is a critical step in the wound-healing process, involving the chemotactic response of blood vessel endothelial cells to macrophage-derived factors produced in the wound space. In this article, we formulate a system of partial differential equations that model the evolution of the capillary-tip endothelial cells, macrophage-derived chemoattractants, and the new blood vessels during the tissue repair process. Chemotaxis is incorporated as a dominant feature of the model, driving the wave-like ingrowth of the wound-healing unit. The resulting model admits traveling wave solutions that exhibit many of the features characteristic of wound healing in soft tissue. The steady propagation of the healing unit through the wound space, the development of a dense band of fine, tipped capillaries near the leading edge of the wound-healing unit (the brush-border effect), and an elevated vessel density associated with newly healed wounds, prior to vascular remodeling, are all discernible from numerical simulations of the full model. Numerical simulations mimic not only the normal progression of wound healing but also the potential for some wounds to fail to heal. Through the development and analysis of a simplified model, insight is gained into how the balance between chemotaxis, tip proliferation, and tip death affects the structure and speed of propagation of the healing unit. Further, expressions defining the healed vessel density and the wavespeed in terms of known parameters lead naturally to the identification of a maximum wavespeed for the wound-healing process and to bounds on the healed vessel density. The implications of these results for wound-healing management are also discussed.

A comment on Lin's paper on nonlinear diffusion in biological systems

Publisher: Springer Science and Business Media LLC

Date: 1981

DOI: 10.1007/BF02460945

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

Publisher: Elsevier BV

Date: 06-2002

DOI: 10.1016/S0924-0136(02)00177-2

Computational Approaches to Solving Equations Arising from Wound Healing

Publisher: Springer Science and Business Media LLC

Date: 11-12-2008

DOI: 10.1007/S11538-008-9360-Z

Abstract: In the wound healing process, the cell movement associated with chemotaxis generally outweighs the movement associated with random motion, leading to advection-dominated mathematical models of wound healing. The equations in these models must be solved with care, but often inappropriate approaches are adopted. Two one-dimensional test problems arising from advection-dominated models of wound healing are solved using four algorithms--MATLAB's inbuilt routine pdepe.m, the Numerical Algorithms Group routine d03pcf.f, and two finite volume methods. The first finite volume method is based on a first-order upwinding treatment of chemotaxis terms and the second on a flux limiting approach. The first test problem admits an analytic solution which can be used to validate the numerical results by analyzing two measures of the error for each method: the average absolute difference and a mass balance error. These criteria as well as the visual comparison between the numerical methods and the exact solution lead us to conclude that flux limiting is the best approach to solving advection-dominated wound healing problems numerically in one dimension. The second test problem is a coupled nonlinear three species model of wound healing angiogenesis. Measurement of the mass balance error for this test problem further confirms our hypothesis that flux limiting is the most appropriate method for solving advection-dominated governing equations in wound healing models. We also consider two two-dimensional test problems arising from wound healing, one that admits an analytic solution and a more complicated problem of blood vessels growth into a devascularized wound bed. The results from the two-dimensional test problems also demonstrate that the flux limiting treatment of advective terms is ideal for an advection-dominated problem.

Quantifying the roles of cell motility and cell proliferation in a circular barrier assay

Publisher: The Royal Society

Date: 06-05-2013

DOI: 10.1098/RSIF.2013.0007

Abstract: Moving fronts of cells are essential features of embryonic development, wound repair and cancer metastasis. This paper describes a set of experiments to investigate the roles of random motility and proliferation in driving the spread of an initially confined cell population. The experiments include an analysis of cell spreading when proliferation was inhibited. Our data have been analysed using two mathematical models: a lattice-based discrete model and a related continuum partial differential equation model. We obtain independent estimates of the random motility parameter, D , and the intrinsic proliferation rate, λ , and we confirm that these estimates lead to accurate modelling predictions of the position of the leading edge of the moving front as well as the evolution of the cell density profiles. Previous work suggests that systems with a high λ / D ratio will be characterized by steep fronts, whereas systems with a low λ / D ratio will lead to shallow diffuse fronts and this is confirmed in the present study. Our results provide evidence that continuum models, based on the Fisher–Kolmogorov equation, are a reliable platform upon which we can interpret and predict such experimental observations.

The Nature of the Stresses Induced During Tissue Growth

Publisher: Elsevier BV

Date: 10-2005

DOI: 10.1016/J.AML.2004.09.019

The application of statistical process control charts to the detection and monitoring of hospital‐acquired infections

Publisher: Wiley

Date: 12-2001

DOI: 10.1046/J.1440-1762.2001.00423.X

Abstract: The monitoring of infection control indicators including hospital-acquired infections is an established part of quality maintenance programmes in many health-care facilities. However, surveillance data use can be frustrated by the infrequent nature of many infections. Traditional methods of analysis often provide delayed identification of increasing infection occurrence, placing patients at preventable risk. The application of Shewhart, Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) statistical process control charts to the monitoring of indicator infections allows continuous real-time assessment. The Shewhart chart will detect large changes, while CUSUM and EWMA methods are more suited to recognition of small to moderate sustained change. When used together, Shewhart and EWMA methods are ideal for monitoring bacteraemia and multiresistant organism rates. Shewhart and CUSUM charts are suitable for surgical infection surveillance.

Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

Publisher: Informa UK Limited

Date: 03-2003

DOI: 10.1088/1364-7830/7/1/307

Conversion estimates for gas-solid reactions: Improved estimates for irreversible systems

Publisher: Elsevier BV

Date: 06-1993

DOI: 10.1016/0895-7177(93)90028-W

The Migration of Cells in Multicell Tumor Spheroids

Publisher: Springer Science and Business Media LLC

Date: 03-2001

DOI: 10.1006/BULM.2000.0217

Abstract: A mathematical model is proposed to explain the observed internalization of microspheres and 3H-thymidine labelled cells in steady-state multicellular spheroids. The model uses the conventional ideas of nutrient diffusion and consumption by the cells. In addition, a very simple model of the progress of the cells through the cell cycle is considered. Cells are ided into two classes, those proliferating (being in G1, S, G2 or M phases) and those that are quiescent (being in G0). Furthermore, the two categories are presumed to have different chemotactic responses to the nutrient gradient. The model accounts for the spatial and temporal variations in the cell categories together with mitosis, conversion between categories and cell death. Numerical solutions demonstrate that the model predicts the behavior similar to existing models but has some novel effects. It allows for spheroids to approach a steady-state size in a non-monotonic manner, it predicts self-sorting of the cell classes to produce a thin layer of rapidly proliferating cells near the outer surface and significant numbers of cells within the spheroid stalled in a proliferating state. The model predicts that overall tumor growth is not only determined by proliferation rates but also by the ability of cells to convert readily between the classes. Moreover, the steady-state structure of the spheroid indicates that if the outer layers are removed then the tumor grows quickly by recruiting cells stalled in a proliferating state. Questions are raised about the chemotactic response of cells in differing phases and to the dependency of cell cycle rates to nutrient levels.

An analysis of a mathematical model of trophoblast invasion

Publisher: Elsevier BV

Date: 11-2001

DOI: 10.1016/S0893-9659(01)00079-9

Entropy Production in Chemically Reacting Systems

Publisher: Canadian Science Publishing

Date: 15-07-1974

DOI: 10.1139/V74-382

Abstract: Numerical integration of the gasdynamic equations describing the coupling between vibrational relaxation and dissociation for a hydrogen–helium mixture in a plane shock wave shows that the total entropy is a completely monotonic function of time this is found to be the case whether the system is considered to be isolated, or whether there is loss of energy or mass from the flow.

Modelling the reduction of an iron ore-coal composite pellet with conduction and convection in an axisymmetric temperature field

Publisher: Elsevier BV

Date: 07-2005

DOI: 10.1016/J.MCM.2005.05.014

An investigation of contact transmission of methicillin-resistant Staphylococcus aureus

Publisher: Elsevier BV

Date: 10-2004

DOI: 10.1016/J.JHIN.2004.06.010

Abstract: Hand hygiene is critical in the healthcare setting and it is believed that methicillin-resistant Staphylococcus aureus (MRSA), for ex le, is transmitted from patient to patient largely via the hands of health professionals. A study has been carried out at a large teaching hospital to estimate how often the gloves of a healthcare worker are contaminated with MRSA after contact with a colonized patient. The effectiveness of handwashing procedures to decontaminate the health professionals' hands was also investigated, together with how well different healthcare professional groups complied with handwashing procedures. The study showed that about 17% (9-25%) of contacts between a healthcare worker and a MRSA-colonized patient results in transmission of MRSA from a patient to the gloves of a healthcare worker. Different health professional groups have different rates of compliance with infection control procedures. Non-contact staff (cleaners, food services) had the shortest handwashing times. In this study, glove use compliance rates were 75% or above in all healthcare worker groups except doctors whose compliance was only 27%.

A model for the growth of a solid tumor with non-uniform oxygen consumption

Publisher: Elsevier BV

Date: 1977

DOI: 10.1016/0025-5564(77)90028-1

Migration of breast cancer cells: Understanding the roles of volume exclusion and cell-to-cell adhesion

Publisher: American Physical Society (APS)

Date: 10-2010

DOI: 10.1103/PHYSREVE.82.041901

A History of the Study of Solid Tumour Growth: The Contribution of Mathematical Modelling

Publisher: Springer Science and Business Media LLC

Date: 09-2004

DOI: 10.1016/J.BULM.2003.11.002

Mathematical modelling of aerosolised skin grafts incorporating keratinocyte clonal subtypes

Publisher: Springer Science and Business Media LLC

Date: 20-10-2007

DOI: 10.1007/S11538-006-9082-Z

Abstract: Severe burns can be very traumatic for the patient, and while burns caused by industrial or domestic accidents are common, there are also increasing numbers of burns associated with terrorism. A novel technique to assist in the healing process is to spray skin cells, keratinocytes, that are cultured from the patient's own tissue, directly onto the burn site. This process involves taking some undamaged skin from the patient, allowing the skin cells to proliferate rapidly in the laboratory over a period of 5-10 days, harvesting and separating the cells and then spraying them onto the burn. This paper deals with keratinocytes that have been cultured in vitro for a short period of time (early passage cultured cells). The spraying process has yet to be optimised with respect to the seeding density required for fastest re-epithelisation and thus there is a need for this process to be modelled. In this paper, we review some of the skin biology and develop a mathematical model of the growth patterns of cell colonies after they have been applied using a aerosolised technique. The model allows us to predict coverage over time and can be used as a decision support tool for clinicians.

Queensland University Of Technology

Location: Australia

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York University

Location: Canada

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Linkage Projects - Grant ID: LP0347112

Start Date: 02-2003

End Date: 12-2008

Amount: $793,510.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0773230

Start Date: 2007

End Date: 12-2011

Amount: $231,000.00

Funder: Australian Research Council

Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0453501

Start Date: 09-2004

End Date: 12-2005

Amount: $406,097.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0878011

Start Date: 2008

End Date: 06-2012

Amount: $240,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0453013

Start Date: 07-2005

End Date: 12-2006

Amount: $135,867.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354797

Start Date: 01-2004

End Date: 03-2005

Amount: $20,000.00

Funder: Australian Research Council

Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0668502

Start Date: 2006

End Date: 12-2007

Amount: $500,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP120100551

Start Date: 2012

End Date: 08-2017

Amount: $330,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0453210

Start Date: 07-2004

End Date: 12-2007

Amount: $275,000.00

Funder: Australian Research Council