State estimation in endocrine systems with pulsatile hormone secretion
Abstract:
Hormones are signaling molecules, acting as chemical messengers from one cell (or a group of cells) to another, and are produced by nearly every organ and tissue type in a multi-cellular organism. Hormonal (endocrine) regulation is a complex dynamic biological system where hormones, often represented as their serum concentrations, interact via numerous feedback and feedforward relationships.
Endocrine glands secrete their product (hormones) either in continuous (basal) or pulsatile (non-basal) manner. The pulsatile hormone secretion generally stems from the pulse dynamics of neurons. Hormone concentration pulses are modulated in amplitude and frequency with both characteristics imparting biological e?ect.
A recently proposed parsimonious mathematical model of non-basal hormone secretion is composed of a linear block describing the kinetics of the involved hormones in a closed loop with an amplitude and frequency pulse-modulated feedback. The output of the feedback construct is typically not available for measurement in endocrine systems. This poses an observation problem where the inaccessible for measurement hormone concentrations are reconstructed from the available in blood stream hormone measurements. In endocrinology, this is routinely done by means of deconvolution techniques.
A static gain observer for linear continuous plants with intrinsic pulse-modulated feedback is analyzed.
The purpose of the observer is to drive the state estimation error to zero and asymptotically synchronize the sequence of pulse modulation instants estimated by the observer with that of the plant. Conditions on the observer gain matrix locally stabilizing the observer error along an arbitrary periodic plant solution are derived and illustrated by simulation for the case of pulsatile testosterone regulation.