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Mathematical Medicine and Biology: a Journal of the IMA

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 the impact on the within-host response not only of the exposure dose, but also of its duration and peak, for contrasted virulence levels...
May 21, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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 as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again...
May 15, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Larisse Bolton, Alain H J J Cloot, Schalk W Schoombie, Jacobus P Slabbert
No abstract text is available yet for this article.
April 12, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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 and have not accounted for bladder deformation. This study uses a finite element analysis approach with biphasic solute transport to investigate several parameters pertinent to intravesical delivery including solute concentration, solute transport properties and instillation volume...
April 5, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Ryan S Waters, Justin S A Perry, SunPil Han, Bibiana Bielekova, Tomas Gedeon
The immune system has many adaptive and dynamic components that are regulated to ensure appropriate, precise and rapid response to a foreign pathogen. A delayed or inadequate immune response can lead to prolonged disease, while an excessive or under-regulated response can lead to autoimmunity. The cytokine, interleukin-2 (IL-2) and its receptor IL-2R play an important role in maintaining this balance.The IL-2 receptor transduces pSTAT5 signal through both the intermediate and high affinity receptors, which differ from each other by the presence of CD25 chain in IL-2 receptor...
March 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Ezio Di Costanzo, Alessandro Giacomello, Elisa Messina, Roberto Natalini, Giuseppe Pontrelli, Fabrizio Rossi, Robert Smits, Monika Twarogowska
We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment...
March 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
N Eymard, V Volpert, P Kurbatova, V Volpert, N Bessonov, K Ogungbenro, L Aarons, P Janiaud, P Nony, A Bajard, S Chabaud, Y Bertrand, B Kassaï, C Cornu, P Nony
T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial...
March 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Eva Kaslik, Mihaela Neamtu
This article generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is undertaken for the system with general distributed delays. A thorough bifurcation analysis for the distributed delay model with several types of delay kernels is provided...
March 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Matthew R Myers, Prasanna Hariharan, Suvajyoti Guha, Jing Yan
Respiratory protective devices (RPDs) are critical for reducing the spread of infection via inhalable droplets. In determining the type of RPD to deploy, it is important to know the reduction in the infection rate that the RPD enables for the given pathogen and population. This paper extends a previously developed susceptible-infected-recovered (SIR) epidemic model to analyse the effect of a protection strategy. An approximate solution to the modified SIR equations, which compares well with a full numerical solution to the equations, was used to derive a simple threshold equation for predicting when growth of the infected population will occur for a given protection strategy...
March 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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 form of both direct physical interactions, as well as inputs from gradients of secreted signalling molecules. Furthermore, tumour cells can not only receive microenvironmental cues, but also produce them...
February 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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 thinning is divergent flow driven by a lower surface tension of the glob (via the Marangoni effect). We examine the glob-driven TBU hypothesis in a 1D streak model and axisymmetric spot model...
January 30, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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 early and late responding normal tissues do not exceed assigned tolerable levels. Linear constraints are set to limit the size of the daily doses...
January 15, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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 cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation...
January 15, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Iftah Nudel, Luis Dorfmann, Gal deBotton
Compartment syndrome (CS) occurs when the pressure in an enclosed compartment increases due to tissue swelling or internal bleeding. As the intra-compartmental pressure (ICP) builds up, the blood flow to the tissue or the organ is compromised, resulting in ischemia, necrosis and damage to the nerves and other tissues. At the present there are no established diagnostic procedures, and clinical observations such as pain, paralysis and even compartment pressure monitoring are an unreliable determinant of the presence of the syndrome...
December 11, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Giuseppe Pontrelli, Marco Lauricella, José A Ferreira, Gonçalo Pena
We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions...
December 11, 2017: Mathematical Medicine and Biology: a Journal of the IMA
N J Malunguza, S D Hove-Musekwa, S Dube, Z Mukandavire
Super-infection by multiple HIV-1 subtypes, previously thought restricted to high risk groups, has now been reported in the general heterosexual populations at relatively the same incidence rate as in high risk groups. We present a simple deterministic HIV model with super-infection by two HIV-1 subtypes. Mathematical characteristics including the basic reproductive number $(\mathcal{R}_0)$, invasion threshold $(\mathcal{R}_{21},\mathcal{R}_{12})$ and conditions for asymptotic stability are derived. In the absence of super-infection the model exhibits competitive exclusion, and all equilibria are globally attracting if they exist except for the disease free which is a saddle for $\mathcal{R}_0>1...
December 11, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Yichen Lu, Mei Yan Lee, Shu Zhu, Talid Sinno, Scott L Diamond
During clotting under flow, platelets bind and activate on collagen and release autocrinic factors such as ADP and thromboxane, while tissue factor (TF) on the damaged wall leads to localized thrombin generation. Towards patient-specific simulation of thrombosis, a multiscale approach was developed to account for: platelet signalling [neural network (NN) trained by pairwise agonist scanning (PAS), PAS-NN], platelet positions (lattice kinetic Monte Carlo, LKMC), wall-generated thrombin and platelet-released ADP/thromboxane convection-diffusion (partial differential equation, PDE) and flow over a growing clot (lattice Boltzmann)...
December 11, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Gürsan Çoban, M Serdar Çelebi
In this work, we constructed a novel collagen fibre remodelling algorithm that incorporates the complex nature of random evolution acting on single fibres causing macroscopic fibre dispersion. The proposed framework is different from the existing remodelling algorithms, in that the microscopic random force on cellular scales causing a rotational-type Brownian motion alone is considered as an aspect of vascular tissue remodelling. A continuum mechanical framework for the evolution of local dispersion and how it could be used for modeling the evolution of internal radius of biaxially strained artery structures under constant internal blood pressure are presented...
December 11, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Theresa Stocks, Thomas Hillen, Jiafen Gong, Martin Burger
The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction...
December 11, 2017: Mathematical Medicine and Biology: a Journal of the IMA
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 imperative to gain further insight into the dynamic behaviour of DSBs repair process. In this article, a continuous-time Markov chain (CTMC) model of the non-homologous end joining (NHEJ) mechanism is formulated according to the DSB complexity...
December 8, 2017: Mathematical Medicine and Biology: a Journal of the IMA
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