- Email: [email protected]
A mathematical model of countercurrent exchange of oxygen between paired arterioles and venules
1181
Mathematical and Computer Modelling Reports hfdd
Biosci.
Vol.
90. pp. 519-533,
GENETIC
1988
CONTROL
MODELS
WITH DIFFUSION
AND DELAYS
JOSEPHM. MAHAFFY Department of Mathematical Sciences, San Diego State University, San Diego, CA 92182, U.S.A. Abstract-A compartmental model of genetic control by repression is examined. The model includes spatial diffusion in the compartment representing the cytoplasm and time delays for transcription and translation. A stability analysis is discussed for a range of dilfusivities and cell radii. Numerical studies illustrate the analytical results and suggest a potential mechanism for the triggering of cell division based on the cell size.
hfarhl
Biosci.
Vol.
91, pp. 17-34,
1988
A MATHEMATICAL MODEL OF COUNTERCURRENT EXCHANGE OF OXYGEN BETWEEN PAIRED ARTERIOLES AND VENULES MAITHILISHARANand ALEK~ANDER S. POPEL Department of Biomedical Engineering, The Johns Hopkins University, School of Medicine, Baltimore, MD 21205, U.S.A. Abstract-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 Po, in the vessel. The closed form solution is compared with the corresponding numerical solution of the nonlinear problem. Under normal conditions, longitudinal gradients of venular PO2 are found to be small. Examples are presented where the model predicts significant gradients of venular Po, when the blood flow rate in the venule is several times smaller than that in the arteriole.
Lfarhl
Biosci.
Vol.
91. pp. 67-83.
1988
MUTATION-SELECTION BALANCE AND CONTINUUM-OF-ALLELES MODELS REINHARDBURGER Institut fiir Mathematik, Universitat Wien, Strudlhofgasse 4, A-1090 Wien, Austria Abstract-A discrete-time model for evolution of type densities in a haploid population that is governed by mutation and selection is analysed. Important special cases are the classical one-locus multiallele model, models like the stepwise-mutation model, and models with a continuum of possible allelic effects on a quantitative trait. Using methods from functional analysis, It is proved that for very general mutation and selection regimes a uniquely determined positive equilibrium density exists that is globally stable. Moreover, an upper bound for the equilibrium variance that can be maintained by a balance between mutation and Gaussian stabilizing selection is derived.
Mathematical and Computer Modelling Reports hfdd
Biosci.
Vol.
90. pp. 519-533,
GENETIC
1988
CONTROL
MODELS
WITH DIFFUSION
AND DELAYS
JOSEPHM. MAHAFFY Department of Mathematical Sciences, San Diego State University, San Diego, CA 92182, U.S.A. Abstract-A compartmental model of genetic control by repression is examined. The model includes spatial diffusion in the compartment representing the cytoplasm and time delays for transcription and translation. A stability analysis is discussed for a range of dilfusivities and cell radii. Numerical studies illustrate the analytical results and suggest a potential mechanism for the triggering of cell division based on the cell size.
hfarhl
Biosci.
Vol.
91, pp. 17-34,
1988
A MATHEMATICAL MODEL OF COUNTERCURRENT EXCHANGE OF OXYGEN BETWEEN PAIRED ARTERIOLES AND VENULES MAITHILISHARANand ALEK~ANDER S. POPEL Department of Biomedical Engineering, The Johns Hopkins University, School of Medicine, Baltimore, MD 21205, U.S.A. Abstract-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 Po, in the vessel. The closed form solution is compared with the corresponding numerical solution of the nonlinear problem. Under normal conditions, longitudinal gradients of venular PO2 are found to be small. Examples are presented where the model predicts significant gradients of venular Po, when the blood flow rate in the venule is several times smaller than that in the arteriole.
Lfarhl
Biosci.
Vol.
91. pp. 67-83.
1988
MUTATION-SELECTION BALANCE AND CONTINUUM-OF-ALLELES MODELS REINHARDBURGER Institut fiir Mathematik, Universitat Wien, Strudlhofgasse 4, A-1090 Wien, Austria Abstract-A discrete-time model for evolution of type densities in a haploid population that is governed by mutation and selection is analysed. Important special cases are the classical one-locus multiallele model, models like the stepwise-mutation model, and models with a continuum of possible allelic effects on a quantitative trait. Using methods from functional analysis, It is proved that for very general mutation and selection regimes a uniquely determined positive equilibrium density exists that is globally stable. Moreover, an upper bound for the equilibrium variance that can be maintained by a balance between mutation and Gaussian stabilizing selection is derived.