Ramakrishnan, Rajasekhar Leonard, Edward F Dell, Ralph B
Published in
Mathematical biosciences

The occupancy principle and the mean-transit-time theorem are derived for the passage of a tracer through a system that can be described by a general pool model. It is proved, using matrix theory, that if (and only if) tracer entering the system labels equally all tracee fluxes into the system, then the integral of the tracer concentration is the s...

Ramakrishnan, Rajasekhar
Published in
Mathematical biosciences

Berman and Schoenfeld used matrix transformations to study unidentifiable pool models. It is possible to use the method to examine if two models are output-indistinguishable, that is, if given the nature of tracer injections and observations, the two models have the same responses. The method is applied to two three-pool models for whole-body chole...

Kaplan, D T Smith, J M Saxberg, B E Cohen, R J
Published in
Mathematical biosciences

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well ...

Sharan, Maithili Popel, Aleksander S
Published in
Mathematical biosciences

A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet PO2 in the vessel. The closed form solution is compared with the corresponding numerical solution of th...

Hesselmans, G H Johannesma, P I
Published in
Mathematical biosciences

Sensory receptors transform an external sensory stimulus into an internal neural activity pattern. This mapping is studied through its inverse. An earlier paper showed that within the context of a neuron model composed of a linear filter followed by an exponential pulse generator and a Gaussian stimulus ensemble a unique "most plausible" first-orde...

Fagarasan, J T Distefano, J J 3rd
Published in
Mathematical biosciences

Oscillations due to complex eigenvalues, known to exist but difficult to detect, are sometimes totally hidden in the output of compartmental models, i.e., none of their modes appear in the output. An example is constructed of a class of linear compartmental models with complex eigenvalues, which have oscillating modes appearing in the output for so...

Thieme, H R Heesterbeek, J A
Published in
Mathematical biosciences

Certain infectious plant diseases are controlled by inspection and subsequent hand removal of diseased parts. In this paper we give two sets of criteria from which one can conclude whether this control effort is adequate or not. These criteria do not require knowledge of the infection- or detection rate of the disease but only use the structure of ...

Hanson, F B Ryan, D
Published in
Mathematical biosciences

In linear, stochastic dynamics it is shown that the quasideterministic population size is equivalent to the mean population size. The quasideterministic dynamics are defined by the conditional infinitesimal mean of the process. The stochastic component of the dynamics includes both Gaussian and Poisson white noise, with amplitude coefficients propo...

Geiger, G
Published in
Mathematical biosciences

A structural stability approach to population-genetic systems and to dynamic evolutionary games is attempted in order to examine the theoretical significance of sociobiological selection models. A criterion of weak selection is derived that is not restricted to differential reproduction in polymorphic systems but describes possible directions of ev...

Liebovitch, L S
Published in
Mathematical biosciences

Ion channels in the cell membranes of the corneal endothelium, hippocampal neurons, and fibroblasts, and gramicidin channels in lipid bilayers have open and closed times that can be fit, in whole or part, by power law distributions. That is, the gating is self-similar when viewed at different time scales. Hence, kinetic processes at slow and fast t...