Cartwright, Husain, 1986
This model can be solved and can reproduce one oscillation (which is true to the published results,) but is unable to produce further oscillations.
ValidateCellML verifies this model as valid CellML, although unit inconsistencies are detected.
Blood testosterone levels in human males fluctuate over 2-3 hour periods. Testosterone secretion from the testes is stimulated by luteinizing hormone (LH) and the production of LH is, in turn, stimulated by the hypothalamic hormone luteinizing hormone releasing hormone (LHRH). Interestingly, the observed fluctuations in the blood levels of testosterone can be traced back to the pulsatile release of LHRH. Several mathematical models have been proposed to describe the pulsatile release of these three hormones. These models can be divided into two different classes:
Those which assume the existence of a neural clock; a pulse-generator which forces the hypothalamic secretion of LHRH.
And those which assume there is no external pulse input, but explain the hormone pulsatility through interactions between the components of the system which produce feedback oscillations.
In the paper described here, Cartwright and Husain propose mathematical model incorporating time delays and negative feedback loops to describe the kinetics of the hormone cascade in the secretion of testosterone. Their model falls into the second category of models described above. The model has three components; the hypothalamus, pituitary and testes, and the rate of LH release from the pituitary depends on the the LHRH concentration, and the rate of testosterone synthesis in the testes depends on the LH concentration (as summarised in the figure below).
|Schematic diagram of the mathematical model representing the luteinizing hormone releasing hormone (LHRH), luteinizing hormone (LH), and testosterone system. The model has three main components: the hypothalamus which secretes LHRH, the pituitary which responds to LHRH by secreting LH, and the testes which, in responds to LH, secrete testosterone. Finally, LH and testosterone feedback on the hypothalamus to regulate LHRH secretion.|
The complete original paper reference is cited below:
A model for the control of testosterone secretion, Mark Cartwright and Masud Husain, 1986, Journal of Theoretical Biology 123, 239-250. PubMed ID: 3306160
It should be noted that in its current form, the CellML description of the this model is unable to perfectly capture the simulation results of the published model, this is due to the time delays which are difficult to describe in the CellML code.