Mathematical model of testosterone regulation by pulse-modulated feedback

Abstract

A mathematical model of the pulse-modulated regulation of non-basal testosterone secretion in the male is introduced. The suggested model is of third order, reflecting the three most significant hormones in the regulation loop, but yet is shown to be capable of sustaining periodic solutions with one or two pulses of gonadotropin-releasing hormone (GnRH) in each period. Lack of stable periodic solutions is otherwise a main shortcoming of existing low-order hormone regulation models. The periodic mode with two GnRH pulses in the least period has not yet been described in medical literature but is supported by experimental data.

Nonlinear Model Predictive Control Using Robust Fixed Point Transformation-Based Phenomena for Controlling Tumor Growth

“…It is worth mentioning that the underlying system model describes a positive dynamical system, which entails that the control signal must remain positive for all times. Previous simulations showed that when the input signal is zero, the model attains a steady state of x 1 = x 2 = 1.734 × 10 4 (mm 3 ). This steady state yields a worst case scenario, so that the controller is designed according to this initial value in order to deal with minor initial tumor volumes as well.…”

“…In the past decades, physiological systems gained attention among control engineers. This particular interest covers a significant variety of topics including automated anesthesia [1], diabetes control [2] and hormonal regulation [3]. Tumor growth control is no exception as cancerous diseases are responsible for 1,359,500 deaths in the European Union annually, based on [4].…”

Impulsive model of endocrine regulation with a local continuous feedback

“…The rest of the paper is organized as follows. In Section 2, the impulsive Goodwin' oscillator proposed in [35,[43][44][45] is recapitulated and an extension to it is introduced, which is the main contribution of this work. The mathematical properties of this model are discussed in Section 3.…”

“…In this section, the model of impulsive (or hybrid) Goodwin's oscillator, proposed in [35,[43][44][45][46] to portray the pulsatile feedback mechanism of the testosterone regulation in the male, is extended to include a local continuous feedback. This extension is supported by biological facts and is also shown to impact the assumptions that are critical for the use of the readily available model analysis.…”