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

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

Evaluation of a computer‐assisted method for individualized anticoagulation: Retrospective and prospective studies with a pharmacodynamic model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109889/1/cptclpt1982136.pd