Biomedical engineering principles: An introduction to fluid, heat, and mass transport processes (biomedical engineering and instrumentation, volume 2) : Marcel Dekker, Inc. New York, 1976, 448 pages, illus., $36.50

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23053/1/0000625.pd

Digital computer simulation of human systemic arterial pulse wave transmission: A nonlinear model

The transmission of pressure and flow pulse waves in human systemic arteries is modeled using one-dimensional, nonlinear transient analysis on a system of branching, nonuniform tubes. Nonlinearity results from the retention of the vessel cross-sectional area as a dependent variable and from an approximation to the convective acceleration terms.Coupling the momentum and continuity equations with a linear elastic membrane equation describing the vessel wall yields a system of quasi-linear, hyperbolic partial differential equations, solvable on a digital computer using the method fo characteristics and finite difference techniques. Appropriate boundary conditions enabling the application of the model to whole vascular beds are introduced.Using published data, a reference state for the human arterial system is defined in terms of vessel geometrical and physical parameters. Model behavior in this state is documented at 14 locations corresponding to vascular regions most frequently investigated clinically. Pressure and flow waveforms, and impedances from the model show reasonable agreement with clinical data reported in the literature.The model is found to reproduce the mechanical behavior of the real system with greater fidelity than previous models. Comparison of the nonlinear model with a linearized, lumped parameter model shows significant differences in performance. These differences are attributed mainly to the nonlinear interaction of vessel transverse and longitudinal impedance. It is concluded that the nonlinear effects of finite vessel wall displacements are of importance in determining arterial pulse propagation behavior, at least in the more distensible central vessels. Fluid friction and convective acceleration effects were found to be of lesser importance in determining overall pulse wave behavior.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34078/1/0000357.pd

The thermal entrance region in fully developed turbulent flow

The temperature profile and the local rate of heat transfer from the wall were measured at 0.453, 1.13, 4.12, and 9.97 tube diameters downstream from a step increase in wall temperature for air in fully developed turbulent flow at Reynolds numbers of 15,000 and 65,000 in a 1.52-in. tube. The velocity profile and the pressure were also measured at these lengths. Radial and longitudinal temperature gradients, radial heat fluxes, and eddy diffusivities for heat and momentum transfer were computed from the measurements. The longitudinal temperature gradients at all radii were found to differ significantly from the mixed mean temperature gradient. Although the radial heat flux was a maximum at the wall, the radial heat-flux density, in terms of which the eddy diffusivity for heat transfer is usually defined, was found to go through a maximum near the wall and then to decrease almost linearly across the thermal boundary layer. The eddy diffusivity for heat transfer was found to be independent of length in the thermal entrance region and hence a function only of the fluid motion, as previously hypothesized.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37310/1/690060220_ftp.pd

A model of the renal cortex and medulla

Mathematical models of the renal cortex and medulla are developed. The glomerular filtration rate is treated as an input parameter. The differential equations for transfer of water and solutes are developed under the assumption that the primary driving forces are the osmotic effect of the plasma proteins and the active transport of one solute across the walls of the nephric tubules. The system of simultaneous ordinary differential equations obtained for the stationary state for constant inputs in the medulla present a multiple-point boundary-value problem of some complexity.In the course of developing the model a number of problems were unearthed. First, it became apparent that the commonly accepted countercurrent exchange model for the medullary capillaries is not supported by anatomical studies and that a distributed capillary bed model might give a truer picture. Second, it became obvious that the information available on the sodium pump is as yet insufficient to let us decide unambiguously whether the pump is reversible or irreversible.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33390/1/0000789.pd

Immune-mediated competition in rodent malaria is most likely caused by induced changes in innate immune clearance of merozoites

Malarial infections are often genetically diverse, leading to competitive interactions between parasites. A quantitative understanding of the competition between strains is essential to understand a wide range of issues, including the evolution of virulence and drug resistance. In this study, we use dynamical-model based Bayesian inference to investigate the cause of competitive suppression of an avirulent clone of Plasmodium chabaudi (AS) by a virulent clone (AJ) in immuno-deficient and competent mice. We test whether competitive suppression is caused by clone-specific differences in one or more of the following processes: adaptive immune clearance of merozoites and parasitised red blood cells (RBCs), background loss of merozoites and parasitised RBCs, RBC age preference, RBC infection rate, burst size, and within-RBC interference. These processes were parameterised in dynamical mathematical models and fitted to experimental data. We found that just one parameter μ, the ratio of background loss rate of merozoites to invasion rate of mature RBCs, needed to be clone-specific to predict the data. Interestingly, μ was found to be the same for both clones in single-clone infections, but different between the clones in mixed infections. The size of this difference was largest in immuno-competent mice and smallest in immuno-deficient mice. This explains why competitive suppression was alleviated in immuno-deficient mice. We found that competitive suppression acts early in infection, even before the day of peak parasitaemia. These results lead us to argue that the innate immune response clearing merozoites is the most likely, but not necessarily the only, mediator of competitive interactions between virulent and avirulent clones. Moreover, in mixed infections we predict there to be an interaction between the clones and the innate immune response which induces changes in the strength of its clearance of merozoites. What this interaction is unknown, but future refinement of the model, challenged with other datasets, may lead to its discovery

Mathematical analysis and digital simulation of the control of erythropoiesis

A mathematical model is presented which represents the control system for erythropoiesis. In the model, it is postulated that the rate of erythropoiesis is controlled by a hormone, erythropoietin, which is released from the kidney in response to reduced renal oxygen supply. Equations are developed which relate erythropoietin release to arterial oxyhemoglobin concentration, and hemoglobin production to plasma erythropoietin concentration, with appropriate time delays. Effects of changes in plasma volume during hypoxia are included. The model is used with a digital computer to simulate the dynamic response of the erythropoietic system to a step decrease in the pO2 of inspired air. The response of the model compares favorably with experimental data obtained from mice subjected to different degrees of hypoxia.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33539/1/0000038.pd

The human side of hypoxia-inducible factor

When humans are exposed to hypoxia, systemic and intracellular changes operate together to minimise hypoxic injury and restore adequate oxygenation. Emerging evidence indicates that the hypoxia-inducible factor (HIF) family of transcription factors plays a central regulatory role in these homeostatic changes at both the systemic and cellular levels. HIF was discovered through its action as the transcriptional activator of erythropoietin, and has subsequently been found to control intracellular hypoxic responses throughout the body. HIF is primarily regulated by specific prolyl hydroxylase-domain enzymes (PHDs) that initiate its degradation via the von Hippel-Lindau tumour suppressor protein (VHL). The oxygen and iron dependency of PHD activity accounts for regulation of the pathway by both cellular oxygen and iron status. Recent studies conducted in patients with rare genetic diseases have begun to uncover the wider importance of the PHD-VHL-HIF axis in systems-level human biology. These studies indicate that, in addition to regulating erythropoiesis, the system plays an important role in cardiopulmonary regulation. This article reviews our current understanding of the importance of HIF in human systems-level physiology, and is modelled around the classic physiological response to high-altitude hypoxia

Predicting oral anticoagulant response using a pharmacodynamic model

We developed a pharmacokinetic and pharmacodynamic model of warfarin absorption, metabolism, and anticoagulant action appropriate for guiding anticoagulant therapy. The model requires only two independently adjustable parameters to describe warfarin's effect on individual patients. For any given individual, these parameters are rapidly and inexpensively identified using a computer program based on the model. Test data were generated by superimposing Gaussian noise on dose-response curves calculated with the model. Then the computer program was applied to the test data. Future prothrombin complex activities (PCA's) and maintenance doses were predicted accurately early in the course of drug administration. In addition, the program accurately predicted PCA response in two groups of normal volunteers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44006/1/10439_2006_Article_BF02363455.pd