IJPAM: Volume 75, No. 1 (2012)

MODELING RED BLOOD CELL AND IRON DYNAMICS
IN PATIENTS WITH CHRONIC KIDNEY DISEASE

H.T. Banks$^1$, Karen M. Bliss$^2$, Hien Tran$^3$
$^{1,3}$Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC 27695, USA
$^2$United States Military Academy
West Point, NY 10996, USA


Abstract. Chronic kidney disease causes a slow loss of kidney function over time and can eventually lead to End Stage Renal Disease, where a patient must undergo dialysis to remove fluids and wastes from the body. These patients also suffer from a lack of the hormone erythropoietin (EPO), produced in the kidneys, that stimulates red blood cell (RBC) production. Without intervention, patients suffer from anemia. Patients are treated with both EPO and iron in order to stimulate RBC production.

We develop a partial differential equation model for RBC dynamics using two structure variables, one for age and one for cellular iron endowment. We couple this with a set of ordinary differential equations modeling iron dynamics. We take into account the effects of both inflammation and neocytolysis, which are known to affect patients undergoing treatment.

Received: February 11, 2012

AMS Subject Classification:

Key Words and Phrases: mathematical model, mathematical biology, erythropoiesis, erythrocyte, red blood cell, chronic kidney disease, dialysis, iron, neocytolysis, hepcidin, EPO, hemoglobin

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 1