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Mathematical modelling of fungi-initiated siderophore-iron interactions. Math. Med. Biol. (IF 1.392) Pub Date : 2020-07-14 M Jabed A Choudhury,Philip M J Trevelyan,Graeme P Boswell
AbstractNearly all life forms require iron to survive and function. Microorganisms utilize a number of mechanisms to acquire iron including the production of siderophores, which are organic compounds that combine with ferric iron into forms that are easily absorbed by the microorganism. There has been significant experimental investigation into the role, distribution and function of siderophores in
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Mathematically modelling inflammation as a promoter of tumour growth. Math. Med. Biol. (IF 1.392) Pub Date : 2020-05-20 Kathleen P Wilkie,Farjana Aktar
AbstractInflammation is now known to play a significant role in tumour growth and progression. It is also difficult to adequately quantify systemic inflammation and the resulting localized effects in cancer. Here, we use experimental data to infer the possible contributions of inflammation in a mouse model of cancer. The model is validated by predicting tumour growth under anti-inflammatory treatments
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Describing the evolution of myeloid-derived leucocytes in treated B-lineage paediatric acute lymphoblastic leukaemia with a data-driven granulocyte-monocyte-blast model. Math. Med. Biol. (IF 1.392) Pub Date : 2020 Larisse Bolton,Thomas M Acho,David K Stones,Cang Hui
AbstractAcute lymphoblastic leukaemia (ALL) is associated with a compromised myeloid system. Understanding the state of granulopoiesis in a patient during treatment, places the clinician in an advantageous position. Mathematical models are aids able to present the clinician with insight into the behaviour of myeloid-derived leucocytes. The main objective of this investigation was to determine whether
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The influence of a lipid reservoir on the tear film formation. Math. Med. Biol. (IF 1.392) Pub Date : 2020 Kara L Maki,Richard J Braun,Gregory A Barron
AbstractWe present a mathematical model to study the influence of a lipid reservoir, seen experimentally, at the lid margin on the formation and relaxation of the tear film during a partial blink. Applying the lubrication limit, we derive two coupled non-linear partial differential equations characterizing the evolution of the aqueous tear fluid and the covering insoluble lipid concentration. Departing
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Informed and uninformed empirical therapy policies Math. Med. Biol. (IF 1.392) Pub Date : 2019 Houy N, Flaig J.
AbstractWe argue that a proper distinction must be made between informed and uninformed decision making when setting empirical therapy policies, as this allows one to estimate the value of gathering more information about the pathogens and their transmission and thus to set research priorities. We rely on the stochastic version of a compartmental model to describe the spread of an infecting organism
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Simple model of atherosclerosis in cylindrical arteries: impact of anisotropic growth on Glagov remodeling. Math. Med. Biol. (IF 1.392) Pub Date : 2020-08-19 Navid Mohammad Mirzaei,Pak-Wing Fok
In 1987, Seymour Glagov observed that arteries went through a two-stage remodeling process as a result of plaque growth: first, a compensatory phase where the lumen area remains approximately constant and second, an encroachment phase where the lumen area decreases over time. In this paper, we investigate the effect of growth anisotropy on Glagov remodeling in five different cases: pure radial, pure
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Corrigendum: A proposed fractional order Gompertz model, and its application to tumour growth data. Math. Med. Biol. (IF 1.392) Pub Date : 2020-08-10 Larisse Bolton,Alain H J J Cloot,Schalk W Schoombie,Jacobus P Slabbert
AbstractTissue level cardiac electrophysiology is usually modelled by the bidomain equations, or the monodomain simplification of the bidomain equations. One assumption made when deriving the bidomain equations is that both the intracellular and extracellular spaces are in electrical equilibrium. This assumption neglects the disturbance of this equilibrium in thin regions close to the cell membrane
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Stochastic intracellular regulation can remove oscillations in a model of tissue growth. Math. Med. Biol. (IF 1.392) Pub Date : 2020-07-31 M Banerjee,V Volpert
AbstractThe work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of ordinary differential equations with bistable dynamics. Intracellular regulation and cell fate are controlled by the extracellular regulation through the
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Bifurcation analysis of a phage-bacteria interaction model with prophage induction. Math. Med. Biol. (IF 1.392) Pub Date : 2020-07-28 H M Ndongmo Teytsa,B Tsanou,S Bowong,J M-S Lubuma
A predator-prey model is used to investigate the interactions between phages and bacteria by considering the lytic and lysogenic life cycles of phages and the prophage induction. We provide answers to the following conflictual research questions: (1) what are conditions under which the presence of phages can purify a bacterial infected environment? (2) Can the presence of phages triggers virulent bacterial
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The optimal age of vaccination against dengue in Brazil based on serotype-specific forces of infection derived from serological data. Math. Med. Biol. (IF 1.392) Pub Date : 2020-07-16 Sandra B Maier,Eduardo Massad,Marcos Amaku,Marcelo N Burattini,David Greenhalgh
In this paper, we study a single serotype transmission model of dengue to determine the optimal vaccination age for Dengvaxia. The transmission dynamics are modelled with an age-dependent force of infection. The force of infection for each serotype is derived from the serological profile of dengue in Brazil without serotype distinction and from serotype-specific reported cases. The risk due to an infection
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Mechanical characterization of porcine liver properties for computational simulation of indentation on cancerous tissue. Math. Med. Biol. (IF 1.392) Pub Date : 2020-05-05 Yingqiao Yang,Kewei Li,Gerhard Sommer,Kai-Leung Yung,Gerhard A Holzapfel
An accurate characterization of soft biological tissue properties is essential for a realistic simulation of surgical procedures. Unconfined uniaxial compression tests with specimens affixed to the fixtures are often performed to characterize the stress-stretch curves of soft biological tissues, with which the material parameters can be obtained. However, the constrained boundary condition causes non-uniform
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Modelling the inclusion of swelling pressure in a tissue level poroviscoelastic model of cartilage deformation. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-18 Jonathan P Whiteley,Eamonn A Gaffney
Swelling pressure in the interstitial fluid within the pores of cartilage tissue is known to have a significant effect on the rheology of cartilage tissue. The swelling pressure varies rapidly within thin regions inside pores known as Debye layers, caused by the presence of fixed charge, as observed in cartilage. Tissue level calculation of cartilage deformation therefore requires resolution of three
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The interplay between fishery yield and top predator culling in a multispecies fishery context. Math. Med. Biol. (IF 1.392) Pub Date : 2020-01-11 Michel Iskin da S Costa,Lucas Dos Anjos
In food webs, fishery can play the role of top predator, competing thus with other top predators for valuable food resources. In this view, it has been claimed in fisheries management that culling of top predators can be a means to improve fishery yield. To investigate this hypothesis, we use theoretical population models to assess in a multispecies context how fishery yield from target species harvest
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Allostery in oligomeric receptor models. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-10 Gregory Douglas Conradi Smith
We show how equilibrium binding curves of receptor homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric
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A mathematical model of viral oncology as an immuno-oncology instigator. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-28 Tyler Cassidy,Antony R Humphries
We develop and analyse a mathematical model of tumour-immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. We derive a necessary and sufficient condition for local stability of the cancer-free equilibrium in which the amount of tumour-immune interaction completely characterizes disease progression. Consistent
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A model of strongly biased chemotaxis reveals the trade-offs of different bacterial migration strategies. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-28 R N Bearon,W M Durham
Many bacteria actively bias their motility towards more favourable nutrient environments. In liquid, cells rotate their corkscrew-shaped flagella to swim, but in surface attached biofilms cells instead use grappling hook-like appendages called pili to pull themselves along. In both forms of motility, cells selectively alternate between relatively straight 'runs' and sharp reorientations to generate
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Existence of solutions and numerical approximation of a non-local tumor growth model. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-28 Lucia Maddalena,Stefania Ragni
In order to model the evolution of a heterogeneous population of cancer stem cells and tumor cells, we analyse a nonlinear system of integro-differential equations. We provide an existence and uniqueness result by exploiting a suitable iterative scheme of functions which converge to the solution of the system. Then, we discretize the model and perform some numerical simulations. Numerical approximations
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A hybrid discrete-continuum approach for modelling microcirculatory blood flow. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-28 Rebecca J Shipley,Amy F Smith,Paul W Sweeney,Axel R Pries,Timothy W Secomb
In recent years, biological imaging techniques have advanced significantly and it is now possible to digitally reconstruct microvascular network structures in detail, identifying the smallest capillaries at sub-micron resolution and generating large 3D structural data sets of size >106 vessel segments. However, this relies on ex vivo imaging; corresponding in vivo measures of microvascular structure
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A Markov decision process approach to optimizing cancer therapy using multiple modalities. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-28 Kelsey Maass,Minsun Kim
There are several different modalities, e.g. surgery, chemotherapy and radiotherapy, that are currently used to treat cancer. It is common practice to use a combination of these modalities to maximize clinical outcomes, which are often measured by a balance between maximizing tumor damage and minimizing normal tissue side effects due to treatment. However, multi-modality treatment policies are mostly
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Optimal control with MANF treatment of photoreceptor degeneration. Math. Med. Biol. (IF 1.392) Pub Date : 2020-02-28 Erika T Camacho,Suzanne Lenhart,Luis A Melara,M Cristina Villalobos,Stephen Wirkus
People afflicted with diseases such as retinitis pigmentosa and age-related macular degeneration experience a decline in vision due to photoreceptor degeneration, which is currently unstoppable and irreversible. Currently there is no cure for diseases linked to photoreceptor degeneration. Recent experimental work showed that mesencephalic astrocyte-derived neurotrophic factor (MANF) can reduce neuron
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Analytic solutions for calcium ion fertilisation waves on the surface of eggs. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-04 Bronwyn H Bradshaw-Hajek,Philip Broadbridge
The evolution of calcium fertilisation waves on the cortex of amphibian eggs can be described by a nonlinear reaction-diffusion process on the surface of a sphere. Here, we use the nonclassical symmetry technique to find an exact analytic solution that describes the evolution of the calcium concentration. The solutions presented compare well with published experimental results. The analytic solution
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An implicit discontinuous Galerkin method for modeling acute edema and resuscitation in the small intestine. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-04 Travis B Thompson,Beatrice M Riviere,Matthew G Knepley
Edema, also termed oedema, is a generalized medical condition associated with an abnormal aggregation of fluid in a tissue matrix. In the intestine, excessive edema can lead to serious health complications associated with reduced motility. A $7.5\%$ solution of hypertonic saline (HS) has been hypothesized as an effective means to reduce the effects of edema following surgery or injury. However, detailed
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Stability and Hopf bifurcation analysis of lac Operon model with distributed delay and nonlinear degradation rate. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-04 Zenab Alrikaby
We propose a simple model of lac operon that describes the expression of B-galactosidase from lac Z gene in Escherichia coli, through the interaction among several identical mRNA. Our goal is to explore the complex dynamics (i.e. the oscillation phenomenon) of this architecture mediated by this interaction. This model was theoretically and numerically investigated using distributed time delay. We considered
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A mathematical model of white blood cell dynamics during maintenance therapy of childhood acute lymphoblastic leukemia. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-04 Thuy T T Le,Felix Jost,Thomas Raupach,Jakob Zierk,Manfred Rauh,Meinolf Suttorp,Martin Stanulla,Markus Metzler,Sebastian Sager
Acute lymphoblastic leukemia is the most common malignancy in childhood and requires prolonged oral maintenance chemotherapy to prevent disease relapse after remission induction with intensive intravenous chemotherapy. In maintenance therapy, drug doses of 6-mercaptopurine (6-MP) and methotrexate (MTX) are adjusted to achieve sustained antileukemic activity without excessive myelosuppression. However
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Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-04 Lucia Carichino,Sarah D Olson
Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signalling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending
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A simple mathematical model to describe antibody-dependent enhancement in heterologous secondary infection in dengue. Math. Med. Biol. (IF 1.392) Pub Date : 2019-12-04 Miller Cerón Gómez,Hyun Mo Yang
We develop a mathematical model to describe the role of antibody-dependent enhancement (ADE) in heterologous secondary infections, assuming that antibodies specific to primary dengue virus (DENV) infection are being produced by immunological memory. The model has a virus-free equilibrium (VFE) and a unique virus-presence equilibrium (VPE). VFE is asymptotically stable when VPE is unstable; and unstable
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An evaluation of some assumptions underpinning the bidomain equations of electrophysiology. Math. Med. Biol. (IF 1.392) Pub Date : 2019-11-01 Jonathan P Whiteley
Tissue level cardiac electrophysiology is usually modelled by the bidomain equations, or the monodomain simplification of the bidomain equations. One assumption made when deriving the bidomain equations is that both the intracellular and extracellular spaces are in electrical equilibrium. This assumption neglects the disturbance of this equilibrium in thin regions close to the cell membrane known as
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Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer. Math. Med. Biol. (IF 1.392) Pub Date : 2019-09-02 Angela M Jarrett,Meghan J Bloom,Wesley Godfrey,Anum K Syed,David A Ekrut,Lauren I Ehrlich,Thomas E Yankeelov,Anna G Sorace
The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural
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Optimal modality selection in external beam radiotherapy. Math. Med. Biol. (IF 1.392) Pub Date : 2019-09-02 Sevnaz Nourollahi,Archis Ghate,Minsun Kim
The goal in external beam radiotherapy (EBRT) for cancer is to maximize damage to the tumour while limiting toxic effects on the organs-at-risk. EBRT can be delivered via different modalities such as photons, protons and neutrons. The choice of an optimal modality depends on the anatomy of the irradiated area and the relative physical and biological properties of the modalities under consideration
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Lattice and continuum modelling of a bioactive porous tissue scaffold. Math. Med. Biol. (IF 1.392) Pub Date : 2019-09-02 Andrew L Krause,Dmitry Beliaev,Robert A Van Gorder,Sarah L Waters
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport
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Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period. Math. Med. Biol. (IF 1.392) Pub Date : 2019-09-02 Bruno Buonomo,Rossella Della Marca,Alberto d'Onofrio
Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susce
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Models of cytokine dynamics in the inflammatory response of viral zoonotic infectious diseases. Math. Med. Biol. (IF 1.392) Pub Date : 2019-09-02 Wenjing Zhang,Sophia Jang,Colleen B Jonsson,Linda J S Allen
Inflammatory responses to an infection from a zoonotic pathogen, such as avian influenza viruses, hantaviruses and some coronaviruses, are distinctly different in their natural reservoir versus human host. While not as well studied in the natural reservoirs, the pro-inflammatory response and viral replication appear controlled and show no obvious pathology. In contrast, infection in humans results
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Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry. Math. Med. Biol. (IF 1.392) Pub Date : 2019-06-13 Sean G Smith,Boyce E Griffith,David A Zaharoff
Ailments of the bladder are often treated via intravesical delivery-direct application of therapeutic into the bladder through a catheter. This technique is employed hundreds of thousands of times every year, but protocol development has largely been limited to empirical determination. Furthermore, the numerical analyses of intravesical delivery performed to date have been restricted to static geometries
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Modeling dynamics for oncogenesis encompassing mutations and genetic instability. Math. Med. Biol. (IF 1.392) Pub Date : 2019-06-13 Artur C Fassoni,Hyun M Yang
Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three
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A unidimensional diffusion model applied to uremic toxin kinetics in haemodiafiltration treatments. Math. Med. Biol. (IF 1.392) Pub Date : 2019-06-13 Miquel Gomez,Francisco Maduell
Kinetic modelling in haemodialysis is usually based upon the resolution of volume-defined compartment models. The interaction among these compartments is described by purely diffusive processes. In this paper we present an alternative kinetic model for uremic toxins in post-dilutional haemodiafiltration treatments by means of a unidimensional diffusion equation. A wide range of solutes such as urea
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Functional optimality of the sulcus pattern of the human brain. Math. Med. Biol. (IF 1.392) Pub Date : 2019-06-13 S Heyden,M Ortiz
We develop a mathematical model of information transmission across the biological neural network of the human brain. The overall function of the brain consists of the emergent processes resulting from the spread of information through the neural network. The capacity of the brain is therefore related to the rate at which it can transmit information through the neural network. The particular transmission
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Why, when and how should exposure be considered at the within-host scale? A modelling contribution to PRRSv infection. Math. Med. Biol. (IF 1.392) Pub Date : 2019-06-13 Natacha Go,Catherine Belloc,Caroline Bidot,Suzanne Touzeau
Understanding the impact of pathogen exposure on the within-host dynamics and its outcome in terms of infectiousness is a key issue to better understand and control the infection spread. Most experimental and modelling studies tackling this issue looked at the impact of the exposure dose on the infection probability and pathogen load, very few on the within-host immune response. Our aim was to explore
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The ups and downs of S. aureus nasal carriage. Math. Med. Biol. (IF 1.392) Pub Date : 2019-06-13 Angela M Jarrett,Nicholas G Cogan
Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified
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Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity. Math. Med. Biol. (IF 1.392) Pub Date : 2019-03-15 Pavol Bokes,John R King
Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former is affiliated with the myeloid and the latter with the erythroid lineage within the haematopoietic system. On a molecular level, PU.1 and GATA-1 positively
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Simulated ablation for detection of cells impacting paracrine signalling in histology analysis. Math. Med. Biol. (IF 1.392) Pub Date : 2019-03-14 Jake P Taylor-King,Etienne Baratchart,Andrew Dhawan,Elizabeth A Coker,Inga Hansine Rye,Hege Russnes,S Jon Chapman,David Basanta,Andriy Marusyk
Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources, which is extremely difficult, as phenotypes of tumour cells integrate hardwired (epi)mutational differences with the dynamic responses to microenvironmental cues. The later comes in
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Corrigendum to: A proposed fractional-order Gompertz model and its application to tumour growth data. Math. Med. Biol. (IF 1.392) Pub Date : 2018-04-17 Larisse Bolton,Alain H J J Cloot,Schalk W Schoombie,Jacobus P Slabbert
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Mathematical modelling of glob-driven tear film breakup. Math. Med. Biol. (IF 1.392) Pub Date : 2018-02-02 L Zhong,C F Ketelaar,R J Braun,C G Begley,P E King-Smith
Evaporation is a recognized contributor to tear film thinning and tear breakup (TBU). Recently, a different type of TBU is observed, where TBU happens under or around a thick area of lipid within a second after a blink. The thick lipid corresponds to a glob. Evaporation alone is too slow to offer a complete explanation of this breakup. It has been argued that the major reason of this rapid tear film
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Optimal number and sizes of the doses in fractionated radiotherapy according to the LQ model. Math. Med. Biol. (IF 1.392) Pub Date : 2018-01-19 C Bruni,F Conte,F Papa,C Sinisgalli
We address a non-linear programming problem to find the optimal scheme of dose fractionation in cancer radiotherapy. Using the LQ model to represent the response to radiation of tumour and normal tissues, we formulate a constrained non-linear optimization problem in terms of the variables number and sizes of the dose fractions. Quadratic constraints are imposed to guarantee that the damages to the
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Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion. Math. Med. Biol. (IF 1.392) Pub Date : 2018-01-19 Vasiliki Bitsouni,Dumitru Trucu,Mark A J Chaplain,Raluca Eftimie
Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled
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The effect of stochasticity on repair of DNA double strand breaks throughout non-homologous end joining pathway. Math. Med. Biol. (IF 1.392) Pub Date : 2017-12-14 Fazeleh S Mohseni-Salehi,Fatemeh Zare-Mirakabad,Soudeh Ghafouri-Fard,Mehdi Sadeghi
DNA double strand breaks (DSBs) are the most lethal lesions of DNA induced by ionizing radiation, industrial chemicals and a wide variety of drugs used in chemotherapy. In the context of DNA damage response system modelling, uncertainty may arise in several ways such as number of induced DSBs, kinetic rates and measurement error in observable quantities. Therefore, using the stochastic approaches is
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Fluid dynamics in heart development: effects of hematocrit and trabeculation. Math. Med. Biol. (IF 1.392) Pub Date : 2017-11-22 Nicholas A Battista,Andrea N Lane,Jiandong Liu,Laura A Miller
Recent in vivo experiments have illustrated the importance of understanding the haemodynamics of heart morphogenesis. In particular, ventricular trabeculation is governed by a delicate interaction between haemodynamic forces, myocardial activity, and morphogen gradients, all of which are coupled to genetic regulatory networks. The underlying haemodynamics at the stage of development in which the trabeculae
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Pathogen transfer through environment-host contact: an agent-based queueing theoretic framework. Math. Med. Biol. (IF 1.392) Pub Date : 2017-11-07 Shi Chen,Suzanne Lenhart,Judy D Day,Chihoon Lee,Michael Dulin,Cristina Lanzas
Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes
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Numerical optimal control for HIV prevention with dynamic budget allocation. Math. Med. Biol. (IF 1.392) Pub Date : 2017-11-07 Dmitry Gromov,Ingo Bulla,Oana Silvia Serea,Ethan O Romero-Severson
This article is about numerical control of HIV propagation. The contribution of the article is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relevant
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Modelling recurrence and second cancer risks induced by proton therapy. Math. Med. Biol. (IF 1.392) Pub Date : 2017-11-07 V S K Manem,A Dhawan
In the past few years, proton therapy has taken the centre stage in treating various tumour types. The primary contribution of this study is to investigate the tumour control probability (TCP), relapse time and the corresponding secondary cancer risks induced by proton beam radiation therapy. We incorporate tumour relapse kinetics into the TCP framework and calculate the associated second cancer risks
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Aqueous humour flow in the posterior chamber of the eye and its modifications due to pupillary block and iridotomy. Math. Med. Biol. (IF 1.392) Pub Date : 2017-11-03 M Dvoriashyna,R Repetto,M R Romano,J H Tweedy
The anterior chamber (AC) and posterior chamber (PC) of the eye are connected through the pupil and are filled with aqueous humour. The aqueous flows from the posterior to the AC at an approximately constant rate, and the intraocular pressure is governed by this rate and the resistance to aqueous outflow. In some patients the iris and lens come into contact, leading to pressure build-up in the PC,
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Global well-posedness of infectious disease models without life-time immunity: the cases of cholera and avian influenza. Math. Med. Biol. (IF 1.392) Pub Date : 2017-11-01 Kazuo Yamazaki
We study the systems of partial differential equations with diffusion that model the dynamics of infectious diseases without life-time immunity, in particular the cases of cholera from Wang & Wang (2015, J. Biol. Dyn., 9, 233-261) and avian influenza from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829-2848). In both works, similarly to all others in the literature on various models
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Mathematical model of calcium exchange during haemodialysis using a citrate containing dialysate. Math. Med. Biol. (IF 1.392) Pub Date : 2017-10-24 Julien Aniort,Laurent Chupin,Nicolae Cîndea
Calcium has two important roles in haemodialysis. It participates in the activation of blood coagulation and calcium intakes have a major impact on patient mineral and bone metabolism. The aim of this article is to propose a mathematical model for calcium ions concentration in a dialyzer during haemodialysis using a citrate dialysate. The model is composed of two elements. The first describes the flows
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Extended models for nosocomial infection: parameter estimation and model selection. Math. Med. Biol. (IF 1.392) Pub Date : 2017-10-19 Alun Thomas,Karim Khader,Andrew Redd,Molly Leecaster,Yue Zhang,Makoto Jones,Tom Greene,Matthew Samore
We consider extensions to previous models for patient level nosocomial infection in several ways, provide a specification of the likelihoods for these new models, specify new update steps required for stochastic integration, and provide programs that implement these methods to obtain parameter estimates and model choice statistics. Previous susceptible-infected models are extended to allow for a latent
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Computed flow and fluorescence over the ocular surface. Math. Med. Biol. (IF 1.392) Pub Date : 2017-10-17 Longfei Li,R J Braun,W D Henshaw,P E King-Smith
Fluorescein is perhaps the most commonly used substance to visualize tear film thickness and dynamics; better understanding of this process aids understanding of dry eye syndrome which afflicts millions of people. We study a mathematical model for tear film flow, evaporation, solutal transport and fluorescence over the exposed ocular surface during the interblink. Transport of the fluorescein ion by
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Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model. Math. Med. Biol. (IF 1.392) Pub Date : 2017-10-11 Alexander Nestor-Bergmann,Georgina Goddard,Sarah Woolner,Oliver E Jensen
Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we
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Analysing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling. Math. Med. Biol. (IF 1.392) Pub Date : 2017-10-11 Atanaska Dobreva,Ralf Paus,N G Cogan
Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages-growth (anagen), regression (catagen) and relative quiescence (telogen)-only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially.
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Flow in the anterior chamber of the eye with an implanted iris-fixated artificial lens. Math. Med. Biol. (IF 1.392) Pub Date : 2017-10-11 Jennifer H Tweedy,Jan O Pralits,Rodolfo Repetto,Paolo Soleri
Flow in the aqueous humour that fills the anterior chamber of the eye occurs in response to the production and drainage of the aqueous humour, and also due to buoyancy effects produced by thermal gradients. Phakic intraocular lenses are manufactured lenses that are surgically inserted in the eyes of patients to correct refractive errors. Their presence has a dramatic effect on the circulation of the
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Pattern formation in multiphase models of chemotactic cell aggregation. Math. Med. Biol. (IF 1.392) Pub Date : 2017-05-19 J E F Green,J P Whiteley,J M Oliver,H M Byrne,S L Waters
We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture
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Modelling and mathematical analysis of the M$_{2}$ receptor-dependent joint signalling and secondary messenger network in CHO cells. Math. Med. Biol. (IF 1.392) Pub Date : 2017-05-16 Benjamin Engelhardt,Janine Holze,Christina Elliott,George S Baillie,Maik Kschischo,Holger Fröhlich
The muscarinic M$_{2}$ receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M$_{2}$ receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M$_{2}$ receptor-dependent signalling pathway combined
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Finite-time parametric identification for the model representing the metabolic and genetic regulatory effects of sequential aerobic respiration and anaerobic fermentation processes in Escherichia coli. Math. Med. Biol. (IF 1.392) Pub Date : 2017-03-25 Alfonso Sepúlveda-Gálvez,Jesús Agustín Badillo-Corona,Isaac Chairez
Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a
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