Abstract
Blood pressure in humans presents a circadian variation profile with a morning increase, a small postprandial valley, and a deeper descent during night-time rest. Under certain conditions, the nocturnal decline in blood pressure can be reduced or even reversed (non-dipper), which is related to a significantly worse prognosis than a normal fall pattern (dipper). Despite several advances in recent years, our understanding of blood pressure's temporal structure, its sources and mechanisms is far from complete. In this work, we developed an ordinary differential equation-based mathematical model capable of capturing the circadian rhythm of blood pressure in dipper and non-dipper patients with arterial hypertension. The model was calibrated by means of global optimization, using 24-h data of systolic and diastolic blood pressure, physical activity, heart rate, blood glucose and norepinephrine, obtained from the literature. After fitting the model, the mean of the normalized error for each data point was <0.2%, and confidence intervals indicate that all parameters were identifiable. Sensitivity analysis allowed identifying the most relevant parameters and therefore inferring the most important blood pressure regulatory mechanisms involved in the non-dipper status, namely, increase in sympathetic over parasympathetic nervous tone, lower influence of physical activity on heart rate and greater influence of physical activity and glucose on the systemic vascular resistance. In summary, this model allows explaining the circadian rhythm of blood pressure and deepening the understanding of the underlying mechanisms and interactions integrating the results of previous works.
Highlights
Homeostatic regulatory mechanisms allow keeping physiological variables in the human body within acceptable ranges
The chosen input variables included in the model are norepinephrine (NE), physical activity (A), and glycemia, and the dependent variables are systemic vascular resistance (SVR), systolic blood pressure (SBP), diastolic blood pressure (DBP), and heart rate (HR)
By including this variable, we include its direct effect and, indirectly, other relevant regulatory mechanisms. The variations of this catecholamine have been related to the circadian variation profile of blood pressure and a positive correlation has been observed between urine norepinephrine and the fall in blood pressure at night rest (Arita et al, 1996; Därr et al, 2016)
Summary
Homeostatic regulatory mechanisms allow keeping physiological variables in the human body within acceptable ranges. Blood pressure is regulated mainly by the neurohumoral system that includes the renin-angiotensin-aldosterone system, natriuretic peptides of the endothelium, the sympathetic nervous system and the immune system These regulatory mechanisms allow the human body to respond to changes in factors such as physical activity and diet (Peixoto and White, 2007). This work’s objective was to develop a mathematical model using ordinary differential equations (ODEs) based on the mechanisms of physiological control of blood pressure to explain the circadian variation profile of dipper and nondipper patients with essential hypertension. The development of this model allowed explaining dipper and non-dipper patterns integrating the results of previous works that attempted to explain differences between these subjects, evaluating different physiological variables
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