3:00 p.m., Friday (January 27, 2006)
San Diego State University
Mathematical Models for Red Blood Cell Production
Red blood cell production or erythropoiesis is the process by which stem cells
(primarily in the bone marrow) differentiate and proliferate to supply our bodies
with erythrocytes (red blood cells), the primary means of transporting oxygen to
all tissues of the body via the circulatory system. On average each day the body
must produce 3 billion new erythrocytes for each kilogram of body weight to supply
the body with oxygen, yet it responds rapidly to stress conditions such as
hemorrhaging or high elevation. The body uses a complex system of hormonal controls
to regulate this production process.
Our study examines an age-structured model for this regulatory process, including
an active degradation of mature cells (like a satiated predator population). With
a few simplifying assumptions the mathematical model can be reduced to a system of
delay differential equations with a state-dependent delay. Bifurcation analysis of
the complete age-structured model shows that a variable velocity of aging stabilizes
the model. Our model is compared to data for a rabbit with an induced auto-immune
hemolytic anemia and to data for normal human subjects following a loss of blood
typical of a blood donation.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).