Mathematical models of sleep regulation

Peter Achermann1, Alexander A Borbély

  • 1Institute of Pharmacology and Toxicology, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland. acherman@pharma.unizh.ch

Related Concept Videos

Sleep-Wake Cycles01:24

Sleep-Wake Cycles

Sleep is an essential physiological process vital to maintaining overall well-being. The reticular activating system (RAS), a network of neurons in the brainstem, regulates wakefulness and sleep. While it may seem passive, sleep consists of distinct cycles, each with its unique characteristics and functions. Two key sleep phases are non-rapid eye movement (NREM) and  rapid eye movement (REM).
NREM Sleep
NREM sleep comprises four progressive stages that seamlessly merge:
Management of Insomnia01:19

Management of Insomnia

The sleep cycle, an integral part of human health, consists of several stages with distinct characteristics and functions. It begins with a transition from wakefulness to sleep, known as the light sleep phase, followed by the restorative deep sleep phase, essential for physical recovery and growth. The cycle concludes with the Rapid Eye Movement (REM) phase, characterized by high brain activity and vivid dreaming. Insomnia, a prevalent sleep disorder, involves difficulty falling asleep, staying...
Pharmacokinetic Models: Overview01:20

Pharmacokinetic Models: Overview

Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...
Pharmacokinetic Models: Comparison and Selection Criterion01:26

Pharmacokinetic Models: Comparison and Selection Criterion

Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
Stages of Sleep01:22

Stages of Sleep

Sleep progresses through distinct stages, each characterized by specific brain wave patterns and physiological responses ranging from wakefulness to stages of non-rapid eye movement, known as non-REM, to rapid eye movement, referred to as REM. Understanding these stages helps in recognizing how sleep supports various bodily and cognitive functions.
Before sleep begins, in wakefulness, the brain exhibits primarily beta waves, which are high in frequency and low in amplitude, indicating alertness...
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...