Perturbational Complexity Index (PCI) is a quantitative measure used in

neuroscience Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...

to assess the level of

consciousness Consciousness, at its simplest, is awareness of a state or object, either internal to oneself or in one's external environment. However, its nature has led to millennia of analyses, explanations, and debate among philosophers, scientists, an ...

based on the

complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...

brain The brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for ...

responses to external perturbations, typically induced via

transcranial magnetic stimulation Transcranial magnetic stimulation (TMS) is a noninvasive neurostimulation technique in which a changing magnetic field is used to induce an electric current in a targeted area of the brain through electromagnetic induction. A device called a st ...

(TMS). It was introduced in 2013 by Italian M.D.–Ph.D. Marcello Massimini and colleagues as a practical application of principles from

Integrated Information Theory Integrated information theory (IIT) proposes a mathematical model for the consciousness of a system. It comprises a framework ultimately intended to explain why some physical systems (such as human brains) are conscious, and to be capable of pr ...

(IIT), which posits that conscious systems must exhibit both high integration and differentiation of information.

Concept

PCI quantifies the algorithmic complexity of the brain’s response to a controlled perturbation. In a typical protocol, a brief TMS pulse is delivered to the

cortex Cortex or cortical may refer to: Biology * Cortex (anatomy), the outermost layer of an organ ** Cerebral cortex, the outer layer of the vertebrate cerebrum, part of which is the ''forebrain'' *** Motor cortex, the regions of the cerebral cortex i ...

, and the resulting electrical activity is recorded with

electroencephalography Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The biosignal, bio signals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in ...

(EEG). The recorded spatiotemporal EEG response is then binarized and compressed using a

lossless Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statisti ...

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

to estimate its algorithmic complexity. The PCI value is normalized to control for signal length and

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...

. Formally, PCI is defined as the normalized

Lempel–Ziv complexity The Lempel–Ziv complexity is a measure that was first presented in the article ''On the Complexity of Finite Sequences'' (IEEE Trans. On IT-22,1 1976), by two Israeli computer scientists, Abraham Lempel and Jacob Ziv. This complexity measure is r ...

of the binarized EEG response: :

\text = \frac

, where,

S

is the spatiotemporal

matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ...

of EEG responses to TMS,

C(S)

denotes its Lempel–Ziv complexity, and

N

is a normalization constant (typically sequence length). This formalization captures both the integration (distributed activation) and differentiation (structured diversity) of cortical responses. Higher PCI values correspond to rich and differentiated responses, suggesting conscious states. Lower PCI values reflect stereotyped or globally synchronized responses, typically associated with unconscious states like

deep sleep ''Deep Sleep'' is a series of point-and-click adventure games created by Polish indie developer Mateusz Sokalszczuk (also known by his online name scriptwelder). The series consists of three free browser games in which the player attempts to na ...

general anesthesia General anaesthesia (UK) or general anesthesia (US) is medically induced loss of consciousness that renders a patient unarousable even by painful stimuli. It is achieved through medications, which can be injected or inhaled, often with an analgesi ...

, or

coma A coma is a deep state of prolonged unconsciousness in which a person cannot be awakened, fails to Nociception, respond normally to Pain, painful stimuli, light, or sound, lacks a normal Circadian rhythm, sleep-wake cycle and does not initiate ...

Clinical and scientific applications

PCI has been used to objectively differentiate among various states of consciousness, including: *

Wakefulness Wakefulness is a daily recurring brain state and state of consciousness in which an individual is conscious and engages in coherent cognition, cognitive and behavioral responses to the external world. Being awake is the opposite of being asleep, ...

REM sleep Rapid eye movement sleep (REM sleep or REMS) is a unique phase of sleep in mammals (including humans) and birds, characterized by random rapid movement of the eyes, accompanied by low muscle tone throughout the body, and the propensity of the s ...

* Non-REM sleep *

General anesthesia General anaesthesia (UK) or general anesthesia (US) is medically induced loss of consciousness that renders a patient unarousable even by painful stimuli. It is achieved through medications, which can be injected or inhaled, often with an analgesi ...

Vegetative state A vegetative state (VS) or post-coma unresponsiveness (PCU) is a disorder of consciousness in which patients with severe brain damage are in a state of partial arousal rather than true awareness. After four weeks in a vegetative state, the patie ...

/ Unresponsive Wakefulness Syndrome (VS/UWS) *

Minimally conscious state A minimally conscious state (MCS) is a disorder of consciousness distinct from persistent vegetative state (PVS) and locked-in syndrome. Unlike PVS, patients with MCS have partial preservation of conscious awareness. MCS is a relatively new cate ...

(MCS) *

Locked-in syndrome Locked-in syndrome (LIS), also known as pseudocoma, is a condition in which a patient is aware but cannot move or communicate verbally due to complete paralysis of nearly all voluntary muscles in their body except for vertical eye movements and ...

Its most notable clinical use is in the diagnosis and prognosis of

disorders of consciousness Disorders of consciousness are medical conditions that inhibit consciousness. Some define disorders of consciousness as any change from complete self-awareness to inhibited or absent self-awareness and arousal. This category generally includes m ...

(DoC), where behavioral assessments may be unreliable.

Relation to Integrated Information Theory

Although PCI was inspired by IIT, it is not a direct measure of IIT’s formal quantity ''Φ'' (phi). Rather, it is considered a proxy that empirically captures the principles of information integration and differentiation using experimentally accessible brain data.

Variants and developments

Several adaptations of PCI have been proposed, including: * PCI_st (State‑Transition) – A streamlined version based on state‑transition analysis rather than full Lempel–Ziv compression. PCI_st yields similar diagnostic and prognostic power in disorders of consciousness while being significantly faster to compute. * Regional PCI – A 2020 preprint by Caulfield et al. tested the reliability of PCI across three cortical targets (

premotor The premotor cortex is an area of the motor cortex lying within the frontal lobe of the brain just anterior to the primary motor cortex. It occupies part of Brodmann's area 6. It has been studied mainly in primates, including monkeys and humans ...

motor An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power gene ...

, parietal) using TMS‑EEG and found that motor and parietal stimulations offered the highest intra-subject reliability, recommending multiple-site acquisition with a regional focus.

Limitations

Some limitations of PCI include: * The need for TMS-EEG equipment and technical expertise * Sensitivity to preprocessing and binarization steps * Focus on the level, not the content, of consciousness

References