  A novel mathematical model for the hypothalamic pituitary adrenal (HPA) axis
is proposed to comprehend the oscillations observed in hormone concentration
and potential dysfunction within the HPA axis in stressful situation. This
model integrates impact of hippocampal receptors on the secretion of
corticotropin-releasing hormone (CRH), an additional signaling pathway
involving Arginine Vasopressin (AVP) for the production and secretion of
adrenocorticotropic hormone (ACTH), the inclusion of a daylight-related
function for modeling circadian rhythms, and a short negative feedback loop
from the pituitary to the hypothalamus in a minimal mechanistic model of the
HPA axis. This expansion allows us to estimate model parameters that led to a
significant reduction in the mean absolute percent error, thereby enhancing the
model's predictive accuracy with a demonstration of a strong fit to the
validation dataset. Through sensitivity and correlation analyses, our study
shows the parameters that exert the most significant influence on the dynamics
of cortisol within the system. This study reveals intricate interdependencies
within the model and among the various components of the HPA axis. Despite
current advancements in the model to comprehend the dynamics of the HPA Axis,
these models are still lacking in addressing major factors such as the impact
of genetic and epigenetics, the role of the amygdala in processing and
transmitting stress signals, and other minor impacting factors.
