Journal of mathematical biology
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Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. ⋯ In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size.
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Comparative Study
Mathematical model of nitric oxide convection and diffusion in a renal medullary vas rectum.
In this study, the generation, convection, diffusion, and consumption of nitric oxide (NO) in and around a single renal medullary descending or ascending vas rectum in rat were modeled using CFD. The vascular lumen (with a core RBC-rich layer and a parietal layer), the endothelium, the pericytes and the interstitium were represented as concentric cylinders. We accounted for the generation of NO by vascular endothelial cells, and that by the epithelial cells of medullary thick ascending limbs (mTALs) and inner medullary collecting ducts (IMCDs), the latter via interstitial boundary conditions. ⋯ Our results suggest that convection (i.e., blood flow per se) does not significantly affect NO concentrations along the cortico-medullary axis, because the latter are mostly determined by the rate of NO production and that of NO consumption by hemoglobin. However, the shear stress-mediated effects of blood flow on NO generation rates, and therefore NO concentrations, were predicted to be important. Finally, we found that unless epithelial NO generation rates (per unit tubular surface area) are at least 10 times lower than endothelium NO generation rates, NO production by mTALs and IMCDs affects vascular NO concentrations, with possible consequences for medullary blood flow distribution.
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Most attempts to study intracranial pressure using lumped-parameter models have adopted the classical "Kellie-Monro Doctrine," which considers the intracranial space to be a closed system that is confined within the nearly-rigid skull, conserves mass, and has equal inflow and outflow. The present work revokes this Doctrine and develops a mathematical model for the dynamics of intracranial pressures, volumes, and flows that embeds the intracranial system in extensive whole-body physiology. The new model consistently introduces compartments representing the tissues and vasculature of the extradural portions of the body, including both the thoracic region and the lower extremities. ⋯ To validate the model in situations involving normal physiology, the model's response to a realistic pulsatile cardiac output is examined. A well-known experimentally-derived intracranial pressure-volume relationship is recovered by using the model to simulate CSF infusion tests, and the effect on cerebral blood flow of a change in body position is also examined. Cardiac arrest and hemorrhagic shock are simulated to demonstrate the predictive capabilities of the model in pathological conditions.
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Considerable research has been aimed at improving the efficacy of chemotherapeutic agents for cancer therapy. A promising two-step approach that is designed to minimize systemic drug toxicity while maximizing activity in tumors employs monoclonal antibody-enzyme conjugates for the activation of anti-cancer prodrugs. A mathematical model based on the biology of human 3677 melanoma xenografts in nude mice is presented, analyzed, and numerically simulated to study the biodistribution, pharmacokinetics, and intratumoral localization properties of L49-beta-lactamase fusion proteins in solid tumor masses. ⋯ The model was used to examine various dosing strategies in an attempt to determine which regimen would provide the best biodistribution results. The results of administering a uniform dose of conjugate via bolus injection, multiple injections, and continuous infusion were compared. The model predicts that when saturation of binding sites does not occur, dosing strategy has little effect on the amount of conjugate that localizes in the tumor.
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"Mayer waves" are long-period (6 to 12 seconds) oscillations in arterial blood pressure, which have been observed and studied for more than 100 years in the cardiovascular system of humans and other mammals. A mathematical model of the human cardiovascular system is presented, incorporating parameters relevant to the onset of Mayer waves. ⋯ The results agree with clinical observations of Mayer waves in human subjects, both in the period of the oscillations and in the observed age-dependence of Mayer waves. This leads to a proposed explanation of their occurrence, namely that Mayer waves are a gain-induced oscillation.