The administration of inhaled anesthetics depends on diffusion from the lungs into the blood and the brain. Classical pharmacokinetic–pharmacodynamic (PK-PD) models treat this as deterministic, assuming uptake and washout produce consistent effects. In practice, however, both the movement of gas through the lungs and the timing of emergence vary widely, influenced by turbulence, gravity, and patient physiology. This leads to variable responses to gas anesthesia that are not fully predictable. Markov models, which use probabilistic state transitions where future states depend only on the current state, are a potential avenue for capturing the randomness within anesthesia gas diffusion patterns without the computational burden of full fluid dynamics. By representing airway segments or physiological states as nodes with transition probabilities, these models provide individualized, probabilistic views of anesthetic gas diffusion and patient response.
Upon administration, anesthetic gases must first transverse the branching lung. While computational fluid dynamics (CFD) can model airflow and deposition, it is computationally intensive and not scalable for clinical use. Sonnenberg et al. proposed a more efficient Markov chain model, where each airway segment is treated as a state with probabilities of retaining or transmitting inhaled particles. The model incorporated gravity, drag, and diffusion to predict whether particles move deeper into the lung or deposit on airway walls. Compared with CFD, it reproduced deposition patterns and identified optimal inhalation strategies that minimized upper-airway losses. While volatile anesthetic gases diffuse efficiently and largely reach the alveoli without depositing on airway walls, the Markov chain framework developed by Sonnenberg et al. for aerosol particles illustrates how probabilistic transitions can capture the complexity of gas transport through the airway tree 1.
Once in the bloodstream, gases are governed by diffusion gradients between alveoli, blood, and tissues. PK-PD models assume emergence occurs once effect-site concentration drops below a threshold. Stone et al. challenged this view, showing that gas kinetics alone cannot explain the variability in isoflurane emergence. They introduced a two-state Markov process model in which the brain can be responsive or unresponsive, with transitions occurring stochastically. Transition probabilities depend on anesthetic concentration but are triggered by random neuronal fluctuations. This explains why genetically identical mice with identical exposures showed significant differences in emergence time. Their research suggested that the brain might have natural barriers that make the gas wash out unevenly and that transitions from the asleep to the awake state can be influenced by random background neuronal “noise.” This approach explains why emergence is not a simple matter of crossing a threshold—diffusion provides the background conditions, but stochastic state switching determines the actual timing 2.
Markov models are not limited to modeling anesthesia gas transport or neuronal emergence. De Rocquigny et al. demonstrated the use of a Hidden Markov Model to classify anesthesia states—Awake, Loss of Consciousness, Anesthesia, Recovery, and Emergence—based on routine cardiopulmonary variables: mean blood pressure, heart rate, respiratory rate, and end-expiratory sevoflurane concentration. Although this work does not model diffusion directly, it highlights the same principle: anesthesia is best understood as a sequence of probabilistic transitions rather than deterministic thresholds 3.
No single study has yet combined anesthetic diffusion modeling with Markov models directly. Instead, different approaches address complementary pieces: lung transport modeled as Markov chains (Sonnenberg), neuronal emergence as a Markov process (Stone), and clinical monitoring with Hidden Markov Models (de Rocquigny). Classical models capture average trends, but emergence remains variable because consciousness does not follow a simple concentration threshold. Markov models aim to bridge this gap, providing a probabilistic framework that better reflects clinical reality: anesthetic gases diffuse predictably, but patients wake unpredictably.
References
- Sonnenberg AH, Herrmann J, Grinstaff MW, Suki B. A Markov chain model of particle deposition in the lung. Sci Rep. 2020;10:13573. doi:10.1038/s41598-020-70171-2
- Stone W, Voss LJ, Barnard JP, Sleigh JW. Gas kinetics cannot explain variability in isoflurane emergence: neuronal dynamics with stochastic state transitions provide a better account. Br J Anaesth. 2025;134(2):276-285. doi:10.1016/j.bja.2024.11.021.
- de Rocquigny G, Dubost C, Humbert P, Oudre L, Labourdette C, Vayatis N, Tourtier JP, Vidal PP. Assessment of the depth of anesthesia with hidden Markov model based on cardiopulmonary variables. Front Anesthesiol. 2024;3:1391877. doi:10.3389/fanes.2024.1391877