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Access Type

Open Access

Document Type


Degree Program

Mechanical Engineering

Degree Type

Master of Science (M.S.)

Year Degree Awarded

January 2008

Month Degree Awarded



Mathematical Model, PTH response, Calcium homeostasis, Reverses-sigmoid curve


A complex bio-mechanism, referred to as calcium homeostasis, regulates plasma ionized calcium (Ca++) concentration in the human body to within a narrow physiologic range which is crucial for maintaining normal physiology and metabolism. Various metabolic disorders and pathologic conditions originate from acute and/or chronic disturbances/disorders in calcium homeostatic system. This system relies on numerous sub-systems which operate in different time-scales ranging from minutes to weeks. In this thesis we focus on a particular sub-system that operates on the time-scale of minutes; the dynamics involves the response of the parathyroid glands to acute changes in plasma Ca++ concentration. We develop a two-pool, linear time-varying model describing the dynamics of the sub-system. We show that this model can predict dynamics observed in clinical tests of induced hypo- and hyper-calcemia in normal humans. In addition, we develop a new protocol for the construction of a Ca-PTH reverse sigmoid curve based on the mathematical model. This protocol removes deficiencies in current protocols in that the resulting curve is invariant with respect to the subject's axis dynamics and calcium clamp test dynamics.


First Advisor

Yossi Chait

Second Advisor

Christopher V. Hollot