Mathematical Medicine and Biology-A Journal of the Ima最新文献

The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias, but their roles are poorly understood. This article describes both direct numerical simulations and an asymptotic theory of propagation and block of electrical excitation in a model of atrial tissue with myocyte-fibroblast coupling. In particular, three idealized fibroblast distributions are introduced: uniform distribution, fibroblast barrier and myocyte strait-all believed to be constituent blocks of realistic fibroblast distributions. Primary action potential biomarkers including conduction velocity, peak potential and triangulation index are estimated from direct simulations in all cases. Propagation block is found to occur at certain critical values of the parameters defining each idealized fibroblast distribution, and these critical values are accurately determined. An asymptotic theory proposed earlier is extended and applied to the case of a uniform fibroblast distribution. Biomarker values are obtained from hybrid analytical-numerical solutions of coupled fast-time and slow-time periodic boundary value problems and compare well to direct numerical simulations. The boundary of absolute refractoriness is determined solely by the fast-time problem and is found to depend on the values of the myocyte potential and on the slow inactivation variable of the sodium current ahead of the propagating pulse. In turn, these quantities are estimated from the slow-time problem using a regular perturbation expansion to find the steady state of the coupled myocyte-fibroblast kinetics. The asymptotic theory gives a simple analytical expression that captures with remarkable accuracy the block of propagation in the presence of fibroblasts.

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 circumferential, pure axial, isotropic and general anisotropic growth where the elements of the growth tensor are chosen to minimize the total energy. We suggest that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. Our framework is the theory of morphoelasticity on an axisymmetric arterial domain. For each case, we explore their specific effect on the Glagov curves. For the latter two cases, we also provide the changes in collagen fiber orientation and length in the intima, media and adventitia. In addition, we compare the total energy produced by growth in radial, circumferential and axial direction and deduce that using a radially dominant anisotropic growth leads to lower strain energy than isotropic growth.

The 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 number of differentiated cells. It is shown that the total cell number necessarily oscillates if the initial condition in the intracellular regulation is fixed. These oscillations can be suppressed if the initial condition is a random variable with a sufficiently large variation. Thus, the result of the work suggests a possible answer to the question about the role of stochasticity in the intracellular regulation.

Inflammation 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, and combination cancer therapies are explored. We then extend the model to consider simultaneous tumour implants at two distinct sites, which experimentally was shown to result in one large and one small tumour. We use this model to examine the role inflammation may play in the growth rate separation. Finally, we use this predictive two-tumour model to explore implications of inflammation on metastases, surgical removal of the primary and adjuvant anti-inflammatory treatments. This work suggests that improved tumour control can be obtained by targeting both the cancer and host, through anti-inflammatory treatments, including reduced metastatic burden post-surgical removal of primary tumours.

Acute 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 a proposed model of ALL during induction therapy would be a usable descriptor of the system. The model assumes the co-occurrence of the independent leukaemic and normal marrow populations. It is comprised of four delay-differential equations, capturing the fundamental characteristics of the blood and bone marrow myeloid leucocytes and B-lineage lymphoblasts. The effect of treatment was presumed to amplify cell loss within both populations. Clinical data was used to inform the construction, calibration and examination of the model. The model is promising-presenting a good foundation for the development of a clinical supportive tool. The predicted parameters and forecasts aligned with clinical expectations. The starting assumptions were also found to be sound. A comparative investigation highlighted the differing responses of similarly diagnosed patients during treatment and further testing on patient data emphasized patient specificity. Model examination recommended the explicit consideration of the suppressive effects of treatment on the normal population production. Additionally, patient-related factors that could have resulted in such different responses between patients need to be considered. The parameter estimates require refinement to incorporate the action of treatment. Furthermore, the myeloid populations require separate consideration. Despite the model providing explanation, incorporating these recommendations would enhance both model usability and predictive capacity.

Nearly 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 fungi but until now no predictive tools have been developed to qualify or quantify fungi-initiated siderophore-iron interactions. In this investigation, we construct the first mathematical models of siderophore function related to fungi. Initially, a set of partial differential equations are calibrated and integrated numerically to generate quantitative predictions on the spatio-temporal distributions of siderophores and related populations. This model is then reduced to a simpler set of equations that are solved algebraically giving rise to solutions that predict the distributions of siderophores and resultant compounds. These algebraic results require the calculation of zeros of cross products of Bessel functions and thus new algebraic expansions are derived for a variety of different cases that are in agreement with numerically computed values. The results of the modelling are consistent with experimental data while the analysis provides new quantitative predictions on the time scales involved between siderophore production and iron uptake along with how the total amount of iron acquired by the fungus depends on its environment. The implications to bio-technological applications are briefly discussed.

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 deformation during the uniaxial test, posing challenges for accurate measurement of tissue deformation. In this study, we measured the deformation locally at the middle of liver specimens and obtained the corresponding stress-stretch curves. Since the effect of the constrained boundary condition on the local deformation of specimen is minimized, the stress-stretch curves are thus more realistic. Subsequently, we fitted the experimental stress-stretch curves with several constitutive models and found that the first-order Ogden hyperelastic material model was most suitable for characterizing the mechanical properties of porcine liver tissues. To further verify the characterized material properties, we carried out indentation tests on porcine liver specimens and compared the experimental data with computational results by using finite element simulations. A good agreement was achieved. Finally, we constructed computational models of liver tissue with a tumor and investigated the effect of the tumor on the mechanical response of the tissue under indentation. The computational results revealed that the liver specimen with tumor shows a stiffer response if the distance between the tumor and the indenter is small.

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 responds to top predator cull. Defying crisp summary, the four analysed food web models show that this response may be either positive or negative or both, indicating that in terms of multispecies fishery management the harvest yield may not accrue as a consequence of predator removal. In addition, this multitude of behaviours points also to the fact that the response of fishery yield to top predator cull may be difficult to assess.