A distributed lumped parameter model of blood flow with fluid-structure interaction

Biomechanics and Modeling in Mechanobiology - A distributed lumped parameter (DLP) model of blood flow was recently developed that can be simulated in minutes while still incorporating complex...     

A global mathematical model of the cerebral circulation in man

A mathematical model of the cerebral circulation has been formulated. It was based on non-linear equations of pulsatile fluid flow in distensible conduits and applied to a network simulating the entire cerebral vasculature, from the carotid and vertebral arteries to the sinuses and the jugular veins. The quasilinear hyperbolic system of equations was numerically solved using the two-step Lax-Wendroff scheme. The model's results were in good agreement with pressure and flow data recorded in humans during rest. The model was also applied to the study of autoregulation during arterial hypotension. A close relationship between cerebral blood flow (CBF) and capillary pressure was obtained. At arterial pressure of 80 mmHg, the vasodilation of the pial arteries was unable to maintain CBF at its control value. At the lower limit of autoregulation (60 mm Hg), CBF was maintained with a 25% increase of zero transmural pressure diameter of nearly the whole arterial network.     

Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics

A formal sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy. We present results of both a differential analysis as well as a principle component based analysis and provide evidence that suggests the exact times at which specific parameters have the most influence over the solution. We offer insight into the pairwise mathematical relationships between the productively infected T-cell death rate δ, the viral plasma clearance rate c, and the time delay τ between infection and viral production as they relate to the viral dynamics. The results support the claim that the presence of a nonzero delay has a major impact on the model dynamics. Lastly, we comment upon the inadequacies of an alternative principle component based analysis.     

Purinergic receptors in the splanchnic circulation

There is considerable evidence that purines are vasoactive molecules involved in the regulation of blood flow. Adenosine is a well known vasodilator that also acts as a modulator of the response to other vasoactive substances. Adenosine exerts its effects by interacting with adenosine receptors. These are metabotropic G-protein coupled receptors and include four subtypes, A(1), A(2A), A(2B) and A(3). Adenosine triphosphate (ATP) is a co-transmitter in vascular neuroeffector junctions and is known to activate two distinct types of P2 receptors, P2X (ionotropic) and P2Y (metabotropic). ATP can exert either vasoconstrictive or vasorelaxant effects, depending on the P2 receptor subtype involved. Splanchnic vascular beds are of particular interest, as they receive a large fraction of the cardiac output. This review focus on purinergic receptors role in the splanchnic vasomotor control. Here, we give an overview on the distribution and diversity of effects of purinergic receptors in splanchnic vessels. Pre- and post-junctional receptormediated responses are summarized. Attention is also given to the interactions between purinergic receptors and other receptors in the splanchnic circulation.     

A mathematical model for the immunosenescence.

We propose a model for the dynamics of the immune system by considering the subpopulations of virgin and memory T lymphocytes on a time scale corresponding to the human life span. In the deterministic balance equation we introduce a fluctuating term in order to take into account the chronic antigenic stress. Starting from the hypothesis that the depletion of virgin cells with cytotoxic properties (CD8+) is a mortality marker, the model provides survival curves quite similar to the demographic curves.     

Three-dimensional response of a lumped parameter head-neck model due to impact and impulsive loading

A numerical procedure developed previously for predicting sagittal-plane motion of the human head-neck system due to impact and impulsive loading has been extended to three dimensions. In both situations, a lumped parameter approach is employed, but the current model lumps the mechanical response of each intervertebral joint into a single force-deformation relation evaluated from mechanical properties assembled by various investigators. Computations were performed to obtain the response of the model to a two-dimensional case of flexion whiplash, to one three-dimensional case of side impact to the skull and to another involving base acceleration normal to the sagittal plane. Agreement of the kinematic variables with the results of both the previous two-dimensional analysis and experimental data from a volunteer run is satisfactory, but somewhat poorer correspondence was found for the three-dimensional predictions upon comparison with data obtained from a physical model and from a volunteer when subjected to the prescribed loading. The differences in response are attributed to higher stiffness of facet separation of the model relative both to the structure and the volunteer, to insufficient damping, as well as to substantial differences in the mechanical deformation characteristic of the components of the prototypes and the numerical model.     

A mathematical model of the urethra

Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.     

Evolution of the dominance of rec-loci. A mathematical model

The possibility of evolutionary explanation of dominance relations for alleles in selective-neutral rec-loci was explored by means of numerical experiments. It was shown that selection for two-loci fitness system causing the secondary (induced) selection for the rec-system, results in changing the allele frequency of the second-level modificator gene controlling the dominance relations in the rec-locus. The dominance of rec-allele, providing the favourable for the given conditions level of crossing-over between selected fitness loci, is established, due to these changes. It was found that the neutral dominance modificator can influence the dynamics of the whole system.     

A mathematical model of the urethra

Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.     

A mathematical model for insulin kinetics. III. Sensitivity analysis of the model

A non-linear mathematical model involving four variables and several constants incorporating beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term had been applied in earlier papers to various forms of diabetes mellitus. In this paper, we examine the response of the system to variations in the parameters and to initial conditions using sensitivity analysis. It is found that such a method leads to results that are consistent with clinical findings. Further, it is suggested that such an analysis could help in making some predictions regarding future directions in the therapy of diabetes mellitus.     

A mathematical model for spreading cortical depression.

A mathematical model is derived from physiological considerations for slow potential waves (called spreading depression) in cortical neuronal structures. The variables taken into account are the intra- and extracellular concentrations of Na+, Cl-, K+, and Ca++, together with excitatory and inhibitor transmitter substances. The general model includes conductance changes for these various ions, which may occur at nonsynaptic and synaptic membrane together with active transport mechanisms (pumps). A detailed consideration of only the conductance changes due to transmitter release leads to a system of nonlinear diffusion equations coupled with a system or ordinary differential equations. We obtain numerical solutions of a set of simplified model equations involving only K+ and Ca++ concentrations. The solutions agree qualitatively with experimentally obtained time-courses of these two ionic concentrations during spreading depression. The numerical solutions exhibit the observed phenomena of solitary waves and annihilation of colliding waves.     

A problem in the mathematical biophysics of blood circulation: I

The standard approximation method used in mathematical biophysics is applied to the problem of flow of an incompressible viscous fluid in an elastic distensible tube. It is found that the wall of the tube may perform damped transversal harmonic oscillations due to that flow. The phenomenon is independent of the viscosity, the latter contributing only a damping factor. While, due to rather rough approximations, the practical applicability of the equation derived is rather limited, it is suggested that they may give a clue to the understanding of vibrations of the walls of blood vessels which long ago have been suggested as the possible source of some hemic murmurs.     

A mathematical model of the mechanism of vertebrate somitic segmentation.

A mathematical model for the mechanism of periodic pattern formation in the process of somitogenesis is proposed. It is assumed that the metameric arrangement first appears before somite formation at the stage of transition of mesodermal cells into a polarized state. The model is based on the assumption that besides the mechanism of contact cell polarization there exists a mechanism of polarization suppression due to excretion of some chemical substance by polarized cells. Periodicity appears as a result of interaction of a kinematic wave of somitogenic cell determination with the cell cycles of mesodermal cells.     

A lumped parameter model of mechanically mediated acute and long-term adaptations of contractility and geometry in lymphatics for characterization of lymphedema

A primary purpose of the lymphatic system is to transport fluid from peripheral tissues to the central venous system in order to maintain tissue–fluid balance. Failure to perform this task results in lymphedema marked by swelling of the affected limb as well as geometric remodeling and reduced contractility of the affected lymphatic vessels. The mechanical environment has been implicated in the regulation of lymphatic contractility, but it is unknown how changes in the mechanical environment are related to loss of contractile function and remodeling of the tissue. The purpose of this paper was to introduce a new theoretical framework for acute and long-term adaptations of lymphatic vessels to changes in mechanical loading. This theoretical framework combines a simplified version of a published lumped parameter model for lymphangion function and lymph transport, a published microstructurally motivated constitutive model for the active and passive mechanical behavior of isolated rat thoracic ducts, and novel models for acute mechanically mediated vasoreactive adaptations and long-term volumetric growth to simulate changes in muscle contractility and geometry of a single isolated rat thoracic duct in response to a sustained elevation in afterload. The illustrative examples highlight the potential role of the mechanical environment in the acute maintenance of contractility and long-term geometric remodeling, presumably aimed at meeting fluid flow demands while also maintaining mechanical homeostasis. Results demonstrate that contractility may adapt in response to shear stress to meet fluid flow demands and show that pressure-induced long-term geometric remodeling may attenuate these adaptations and reduce fluid flow. The modeling framework and illustrative simulations help suggest relevant experiments that are necessary to accurately quantify and predict the acute and long-term adaptations of lymphangions to altered mechanical loading.