PainVector: A Multidimensional Computational Framework for the Digital Representation of Pain

1. Introduction

Pain is one of the most complex phenomena encountered in clinical medicine and neuroscience. Contemporary definitions emphasize that pain is a personal experience influenced by biological, psychological, and social factors, and that pain should not be equated with nociceptive activity alone [1].

This complexity creates a fundamental measurement problem. Traditional clinical instruments such as the NRS and VAS provide useful and clinically established estimates of perceived pain intensity. However, they compress a multidimensional phenomenon into a single scalar value. For example, two individuals may both report $\mathrm{NRS}=7$ while differing substantially in age, cultural background, behavioral expression, physiological response, pain duration, or response to intervention. Therefore, although a scalar intensity score is clinically useful, it may not fully describe the structure or dynamics of an individual’s pain state.

Physiological signals provide a potentially complementary source of information. HRV, EDA, and peripheral temperature can capture aspects of autonomic and physiological regulation [2,3]. However, these signals are not pain-specific and may also respond to stress, emotion, physical activity, environmental conditions, medication, and other physiological processes [4,5]. Consequently, the problem is not simply to replace subjective pain assessment with physiological measurement; instead, a computational framework is needed that can represent multiple heterogeneous sources of pain-related information within a common mathematical structure.

This paper introduces PainVector, a multidimensional computational representation framework designed for this purpose. The central proposition is: pain can be represented computationally as a structured multidimensional state without claiming that the representation directly captures subjective consciousness or the complete biological mechanism of pain. PainVector therefore focuses on representation, rather than claiming direct measurement of subjective experience.

2. Related Work

Physiological approaches to pain assessment have been reviewed extensively in recent years. Deep-learning-based pain assessment from video, facial expression, and biosignals has been surveyed systematically [6], and scoping reviews of physiological markers across pain types report growing interest in objective, signal-based assessment as a complement to self-report [7]. HRV-based approaches have been reviewed specifically in relation to nociception and clinical pain states [4], and EDA has been reviewed for its clinical applicability to pain monitoring [5]. Multimodal physiological sensing pipelines combining several signal types for acute pain assessment have also been proposed and evaluated in clinical and experimental settings [8], and machine-learning approaches that jointly model physiological and psychosocial factors have shown that demographic and contextual variables materially affect pain-related signal interpretation [9]. Broader surveys of artificial intelligence methods for automatic pain assessment discuss both the promise and the methodological heterogeneity of this literature, including limited external validation and inconsistent signal preprocessing across studies [10].

The great majority of this literature targets pain classification or intensity estimation directly from raw or lightly processed signals (e.g., deep networks mapping biosignals or video to a pain score or category). PainVector differs in aim: rather than proposing another end-to-end estimator, it proposes an explicit, individually-normalized, multidimensional representation layer that separates self-report from physiological inference, exposes contextual and functional weighting as interpretable parameters, and adds temporal, predictive, controllability, localization, and confidence dimensions on top of a single fused intensity value. This positions PainVector as a candidate intermediate representation onto which existing or future estimators (including the deep-learning methods reviewed above) could be mapped, rather than as a competing classifier. This distinction, and its empirical implications, are discussed further in Section 12.

3. Problem Definition

The principal challenges addressed by PainVector are:

1.

Pain is not directly observable.

2.

Pain reports are individual-dependent and context-dependent.

3.

A single scalar such as NRS cannot represent all relevant dimensions of a pain state.

4.

Physiological signals are heterogeneous and noisy.

5.

Physiological signals are not uniquely specific to pain.

6.

Individuals may differ in their expression and reporting of pain.

7.

Pain is dynamic rather than static.

8.

Prediction and response to intervention require temporal information.

9.

Multimodal pain data require a common computational representation.

The objective of PainVector is therefore: to construct a structured, machine-readable, multidimensional representation of pain-related state information that can be analyzed, compared, tracked over time, and potentially used for prediction and intervention evaluation.

The framework is not intended to: directly measure subjective consciousness; establish the presence of pain solely from physiological signals; replace clinical assessment; establish a universal biological equation for pain; or claim that cultural or behavioral coefficients can be assumed without empirical calibration. These distinctions are essential because pain and nociception are not equivalent phenomena [1].

4. Scope and Conceptual Architecture

PainVector is designed as a representation layer between heterogeneous pain-related observations and downstream computational applications. The architecture consists of five conceptual layers.

Layer 1 — Input Layer. The framework receives self-reported pain, physiological signals, contextual variables, temporal information, and optional clinical information. The initial physiological implementation includes HRV, EDA, and peripheral temperature. Future extensions may include EEG, EMG, facial expression, movement, respiratory variables, neuroimaging, and wearable-derived measurements.

Layer 2 — Normalization Layer. Raw physiological measurements are transformed relative to an individual’s baseline.

Layer 3 — Contextual and Functional Modulation Layer. Individual and contextual variables modify the interpretation and weighting of the available measurements.

Layer 4 — Multimodal Fusion Layer. Perceived and physiologically inferred components are combined into a unified pain-state representation.

Layer 5 — State Representation and Analysis Layer. The resulting PainVector can be used for longitudinal monitoring, comparison, prediction, intervention-response evaluation, state-transition analysis, localization, semantic interpretation, confidence estimation, and future human–machine interaction.

5. Mathematical Representation of PainVector

PainVector is defined as

$${\mathbf{PV}}_t={\left\{I_{\mathrm{perceived}},I_{\mathrm{inferred}},I_{\mathrm{final}},D,P,Ctl,L,M,Conf\right\}}_t$$

(1)

where $I_{\mathrm{perceived}}$ is the context-adjusted perceived pain intensity, $I_{\mathrm{inferred}}$ is the physiologically inferred pain-related intensity, $I_{\mathrm{final}}$ is the fused pain representation, D is duration, P is predictability, $Ctl$ is controllability, L is localization, M is semantic meaning/interpretation, and $Conf$ is the confidence or uncertainty associated with the representation. The vector is therefore not intended to represent pain as a single number; instead, it represents pain as a multidimensional state.

6. Methods

6.1. Signal Normalization

For each physiological feature $x_i$, an individual baseline is estimated:

$${\mu }_i=E[x_i\mid \mathrm{baseline}],{\sigma }_i=\mathrm{SD}[x_i\mid \mathrm{baseline}]$$

(2)

The standardized deviation is

$$z_i={\displaystyle \frac{x_i-{\mu }_i}{{\lambda }_i{\sigma }_i+ϵ}}$$

(3)

where $x_i$ is the observed feature, ${\mu }_i$ is the individual’s baseline mean, ${\sigma }_i$ is the baseline standard deviation, ${\lambda }_i$ is a feature-specific scaling parameter, and $ϵ$ prevents numerical instability.

The standardized value is transformed into a bounded representation:

$$s_i=\mathrm{clip}\left(f_i\left(z_i\right),0,1\right)$$

(4)

where $f_i$ is a feature-specific transformation. This distinction is important because the direction of physiological change is not necessarily identical across signals: for example, a decrease in a particular HRV measure may be interpreted differently from an increase in EDA. The framework therefore does not assume a common monotonic relationship across raw physiological variables; instead $s_i=f_i(x_i,{\mu }_i,{\sigma }_i)$ is calibrated empirically for each feature. The normalized physiological representation becomes

$$\mathbf{s}=[s_{HRV},s_{EDA},s_{Temp},\dots ,s_n]$$

(5)

6.2. Perceived Pain Representation

The basic self-reported pain value is normalized as

$$s_{\mathrm{self}}={\displaystyle \frac{\mathrm{NRS}}{10}},0\le s_{\mathrm{self}}\le 1$$

(6)

Because self-report may be influenced by contextual and behavioral factors, PainVector permits contextual modulation. Let C denote a context/cultural calibration factor and E an individual pain-expression calibration factor. Then

$$I_{\mathrm{perceived}}=\mathrm{clip}\left({\displaystyle \frac{s_{\mathrm{self}}}{C·E}},0,1\right)$$

(7)

The parameters C and E are not assumed to be universal constants; they represent calibration parameters that would require empirical estimation from appropriate populations. In a clinically validated implementation, these parameters should be estimated from data rather than manually assigned.

6.3. Physiological Inference

The physiologically inferred component is defined as

$$I_{\mathrm{inferred}}={\displaystyle \sum _{i=1}^n}{w}_i{s}_i,w_i\ge 0,{\displaystyle \sum _{i=1}^n}{w}_i=1$$

(8)

For the initial implementation,

$$I_{\mathrm{inferred}}=w_{HRV}{s}_{HRV}+w_{EDA}{s}_{EDA}+w_{Temp}{s}_{Temp}$$

(9)

An illustrative configuration may use $w_{HRV}=0.30$, $w_{EDA}=0.40$, $w_{Temp}=0.30$. These values are illustrative model parameters rather than clinically validated weights; they should ultimately be estimated or optimized using empirical data.

6.4. Contextual and Functional Weighting

PainVector allows physiological components to receive different functional weights according to individual and contextual conditions:

$${\tilde{w}}_i={\displaystyle \frac{w_{i0}·A_i·g_i(C,E)·h_i\left(B_i\right)}{{\sum }_{j=1}^n{w}_{j0}·A_j·g_j(C,E)·h_j\left(B_j\right)}}$$

(10)

where $w_{i0}$ is the initial weight, $A_i$ represents age-dependent modulation, $g_i(C,E)$ represents contextual modulation, $h_i\left(B_i\right)$ represents baseline-deviation modulation, and $B_i$ represents the magnitude of deviation from the expected baseline state.

Age-dependent modulation is represented generally as $A_i=A_i\left(\mathrm{age}\right)$ rather than assuming a universal linear relationship. For a simple illustrative model,

$$A_i\left(\mathrm{age}\right)=1+{\alpha }_i{\displaystyle \frac{\mathrm{age}-{\mathrm{age}}_0}{100}}$$

(11)

where ${\alpha }_i$ controls the magnitude of age-dependent modulation and ${\mathrm{age}}_0$ is a reference age. This formulation preserves the age-dependent weighting concept while avoiding a common multiplier that would cancel during normalization.

6.5. Baseline Deviation

The deviation of each component from its expected state is

$$B_i=|s_i-{\mu }_i^{*}|$$

(12)

where ${\mu }_i^{*}$ represents the expected normalized baseline value. The functional modulation is then

$$h_i\left(B_i\right)=1+{\kappa }_i{B}_i,{\kappa }_i\ge 0$$

(13)

where ${\kappa }_i$ controls the sensitivity of the model to deviations from baseline. This allows the framework to distinguish an individual’s absolute physiological value from the individual’s deviation from their own expected state, which is central to the personalized nature of PainVector.

6.6. Final Pain Representation

The perceived and inferred components are combined through a fusion coefficient:

$$I_{\mathrm{final}}=\eta I_{\mathrm{perceived}}+(1-\eta )I_{\mathrm{inferred}},0\le \eta \le 1$$

(14)

The parameter $\eta$ controls the relative contribution of self-report and physiological information; $\eta =0.5$ produces equal weighting. $\eta$ should ultimately be calibrated empirically rather than assumed to be universally optimal. $I_{\mathrm{final}}$ is a computationally fused representation and should not be interpreted as a direct measurement of subjective pain.

6.7. Temporal Dimension: Pain Duration

If M pain episodes are observed and the duration of episode m is ${\tau }_m$, the mean episode duration is

$$D={\displaystyle \frac{1}{M}}{\displaystyle \sum _{m=1}^M}{\tau }_m$$

(15)

Alternatively, the framework can preserve the complete temporal sequence, $D_t={\tau }_t$, allowing PainVector to represent dynamic pain trajectories rather than only an average duration.

6.8. Predictability

Given an observed future pain state $I_{t+1}$ and a prediction ${\widehat{I}}_{t+1|t}$, the prediction error is

$$\mathrm{MSE}={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}{\left(I_{t+1}-{\widehat{I}}_{t+1|t}\right)}^2$$

(16)

A normalized predictability score is defined as

$$P=1-{\displaystyle \frac{\mathrm{MSE}}{\mathrm{Var}\left(I_{t+1}\right)+ϵ}}$$

(17)

where $ϵ$ prevents division by zero. This formulation is analogous to a variance-normalized prediction score. Because the resulting value can become negative when predictions perform worse than a simple variance-based reference, the model should not automatically assume $0\le P\le 1$ unless an additional bounding transformation is applied; if a bounded representation is required, $P_{\mathrm{bounded}}=\mathrm{clip}(P,0,1)$ can be used.

6.9. Controllability

Pain can also be represented as a dynamic system influenced by interventions. A simplified state-transition model is

$$I_t={\beta }_0+{\beta }_1{I}_{t-1}+{\beta }_2{a}_{t-1}+{ϵ}_t$$

(18)

where $I_{t-1}$ is the previous state, $a_{t-1}$ represents an intervention or action, ${\beta }_0,{\beta }_1,{\beta }_2$ are model parameters, and ${ϵ}_t$ represents unexplained variation. A conceptual controllability index is

$$Ctl={\displaystyle \frac{\mathrm{Var}(I_t\mid \mathrm{observed})-\mathrm{Var}(I_t\mid \mathrm{optimal}\mathrm{action})}{\mathrm{Var}(I_t\mid \mathrm{observed})+ϵ}}$$

(19)

Controllability reflects the potential reduction in state variability achievable through an intervention policy. This component should be interpreted as a model-based property, not as a direct physiological measurement; its clinical validity requires longitudinal intervention data.

6.10. Localization

Pain location can be represented probabilistically:

$$L=arg\underset{l}{max}P(\mathrm{location}=l\mid \mathbf{F})$$

(20)

where l represents a candidate anatomical region and $\mathbf{F}$ represents available features. A future implementation may represent localization as a full distribution $L=[P\left(l_1\right),P\left(l_2\right),\dots ,P\left(l_k\right)]$ rather than retaining only the maximum-probability location.

6.11. Semantic Meaning

Pain can also be associated with contextual or semantic interpretations:

$$M=arg\underset{m}{max}P(\mathrm{meaning}=m\mid \mathbf{F})$$

(21)

where m represents a semantic category (e.g., acute, chronic, nociceptive, neuropathic, musculoskeletal, procedure-related, stress-associated). This component should not be interpreted as a definitive clinical diagnosis; it represents a future computational semantic layer that requires supervised clinical validation.

6.12. Confidence and Uncertainty

PainVector includes an explicit confidence dimension:

$$Conf=\lambda Con{f}_{\mathrm{var}}+(1-\lambda )Con{f}_{\mathrm{entropy}}$$

(22)

where $Con{f}_{\mathrm{var}}$ represents confidence derived from model variance, $Con{f}_{\mathrm{entropy}}$ represents confidence derived from predictive uncertainty or entropy, and $\lambda$ controls their relative contribution. Alternatively, uncertainty may be represented directly as $U=1-Conf$. This allows the system to distinguish a high pain estimate with high confidence from a high pain estimate with substantial uncertainty, a distinction that is important for clinical decision-support systems.

7. Complete PainVector Definition

The complete representation is therefore

$$\begin{array}{|c|}\hline {\mathbf{PV}}_t={\left[I_{\mathrm{perceived}},I_{\mathrm{inferred}},I_{\mathrm{final}},D,P,Ctl,L,M,Conf\right]}_t\\ \hline\end{array}$$

(23)

which can be interpreted as the pipeline

$$\mathrm{Pain}\to \mathrm{Multimodal}\mathrm{Observations}\to \mathrm{Normalized}\mathrm{State}\to \mathrm{Contextual}\mathrm{Integration}\to \mathrm{Fusion}\to \mathrm{Multidimensional}\mathrm{Representation}$$

8. Computational Pipeline

The complete computational pipeline proceeds as follows: (1) baseline estimation (${\mu }_i,{\sigma }_i$); (2) signal normalization ($x_i\to s_i$); (3) perceived pain representation ($\mathrm{NRS}\to I_{\mathrm{perceived}}$); (4) physiological inference ($\mathbf{s}\to I_{\mathrm{inferred}}$); (5) contextual weighting ($w_i\to {\tilde{w}}_i$); (6) multimodal fusion ($I_{\mathrm{perceived}},I_{\mathrm{inferred}}\to I_{\mathrm{final}}$); (7) dynamic representation ($D,P,Ctl$); (8) extended representation ($L,M,Conf$); producing the final output ${\mathbf{PV}}_t$.

9. Synthetic Proof-of-Concept Dataset

To demonstrate the internal computational structure, a synthetic dataset of ten simulated individuals is generated using the open-source script accompanying this paper (painvector_demo.py; fixed random seed for reproducibility). The data are synthetically generated and are not clinical patient data. An example run is shown in Table 1.

These data are intended only to demonstrate how heterogeneous inputs can be transformed into a common computational representation. They do not demonstrate clinical accuracy, diagnostic performance, or physiological validity.

10. Migraine Demonstration Scenario

To illustrate the multidimensional nature of the framework, consider two hypothetical individuals with migraine, both reporting $\mathrm{NRS}=7$, so $s_{\mathrm{self}}=0.7$ for both. The individuals differ in contextual and physiological parameters (Table 2).

Thus, despite identical NRS values, the computational representations differ substantially ($I_{\mathrm{final},A}=0.811$ vs. $I_{\mathrm{final},B}=0.535$). This example demonstrates the mechanism of the framework, not evidence that the resulting difference accurately reflects actual clinical pain; the difference arises purely from the combination of contextual calibration and physiological inputs as defined in Section 6.2, Section 6.3, and Section 6.6.

11. Validation Framework

The present work establishes a computational framework rather than a clinically validated diagnostic system. Future empirical validation should occur in multiple stages: (1) construct validation of individual dimensions (e.g., perceived pain versus established clinical scales, physiological components versus experimentally induced pain, duration versus longitudinal records, localization versus documented anatomical location); (2) convergent validation against established instruments (NRS, VAS, multidimensional pain questionnaires, clinical outcomes); (3) predictive validation of subsequent pain intensity, trajectory, treatment response, exacerbation, and recovery using prospective longitudinal datasets; (4) sensitivity analysis over $\eta$, $w_i$, ${\lambda }_i$, ${\kappa }_i$, and contextual parameters; and (5) external validation across age groups, sexes, cultural populations, pain conditions, clinical environments, wearable devices, and measurement protocols.

12. Discussion

PainVector proposes a shift from scalar pain scoring toward multidimensional computational representation. Traditional instruments answer a relatively narrow question — how intense is the pain according to the patient’s report — whereas PainVector attempts to represent a broader state: the current computationally observable configuration of pain-related information for a given individual. This distinction is central to the framework.

The model does not assume that physiological signals constitute pain itself; physiological measurements are treated as complementary observations that may contribute information about the state of the individual. This distinction is particularly important because physiological responses can be influenced by many factors unrelated to pain. As reviewed in Section 2, contemporary machine-learning approaches to pain assessment continue to investigate physiological and multimodal markers while highlighting methodological heterogeneity and the need for stronger external and clinical validation [6,10]. PainVector therefore positions multimodal physiological information as part of a representation architecture rather than as an objective replacement for subjective reporting, and, unlike the direct classifiers surveyed above, is explicitly designed as an intermediate, interpretable state onto which such estimators could in principle be mapped.

Another important property of the framework is individual baseline normalization: rather than assuming that the same physiological value has the same meaning for every person, PainVector compares measurements against an individual’s own baseline, creating a pathway toward personalized computational pain representation. The framework also introduces temporal dimensions, modeling $\mathrm{Pain}\left(t_1\right),\mathrm{Pain}\left(t_2\right),\mathrm{Pain}\left(t_3\right),\dots$ rather than an isolated measurement, enabling trajectory → prediction → response → control analysis and thus the possibility of moving from static assessment toward dynamic pain-state modeling.

13. Relationship to AI and Human–Machine Systems

PainVector can function as an intermediate representation layer for future AI systems. Rather than feeding raw heterogeneous signals directly into a black-box model, a computational system could receive ${\mathbf{PV}}_t$ as a structured state representation, yielding the conceptual pipeline

$$\mathrm{Raw}\mathrm{Data}\to \mathrm{PainVector}\to \mathrm{AI}\mathrm{Model}\to \mathrm{Prediction}/\mathrm{Decision}$$

Potential applications include clinical decision support, longitudinal monitoring, personalized pain management, digital therapeutics, wearable systems, rehabilitation, and human–machine interaction. However, such future applications should be distinguished from claims about machine consciousness or artificial subjective experience: PainVector itself makes no claim that a machine possessing a PainVector necessarily experiences pain.

14. Limitations

Several limitations must be acknowledged. (1) Synthetic demonstration data: the present proof-of-concept dataset is synthetic and therefore cannot establish clinical validity. (2) Physiological non-specificity: HRV, EDA, and temperature are influenced by many physiological and psychological processes and are not specific biomarkers of pain. (3) Parameter calibration: parameters such as $C,E,\eta ,w_i,{\lambda }_i,{\kappa }_i$ currently represent framework parameters and require empirical estimation. (4) Cultural modeling: cultural effects on pain expression are complex and should not be reduced to simplistic universal coefficients. (5) Individual expression: pain expression varies across individuals, making calibration essential. (6) Simplified dynamic model: the current controllability and prediction equations are intentionally simplified representations of potentially much more complex nonlinear systems. (7) Localization and meaning: these dimensions require appropriate supervised datasets and clinical annotation. (8) No claim regarding consciousness: PainVector does not model subjective consciousness, suffering, phenomenology, or artificial sentience. (9) Clinical validation: remains necessary before the framework can be considered for clinical decision-making.

15. Future Work

Future development of PainVector may include clinical data collection; longitudinal datasets; adaptive individual baseline estimation; machine-learning-based parameter estimation; EEG, EMG, and respiratory-signal integration; facial-expression analysis; wearable-device integration; personalized calibration; nonlinear dynamical modeling; reinforcement-learning-based intervention optimization; multicenter and cross-cultural validation; and integration with personalized medicine platforms. A particularly important future direction is an adaptive PainVector,

$$P{V}_{t+1}=F(P{V}_t,X_t,A_t)$$

(24)

where $P{V}_t$ represents the current pain state, $X_t$ represents new multimodal observations, and $A_t$ represents an intervention or action — transforming PainVector from a static representation into a dynamic state-space model.

16. Conclusion

PainVector introduces a multidimensional computational framework for representing pain-related state information. Instead of reducing pain to a single scalar value, the framework integrates self-report, physiological signals, context, and temporal dynamics into the structured representation ${\mathbf{PV}}_t$ defined above. The framework separates perceived pain from physiologically inferred information and provides an explicit multimodal fusion mechanism, further introducing temporal, predictive, controllability, localization, semantic, and uncertainty dimensions. The current work should be considered a theoretical and computational framework with synthetic proof-of-concept demonstration, rather than a clinically validated pain measurement system. Its principal contribution is therefore not the claim that pain has been solved computationally, but the proposal of a structured mathematical representation through which heterogeneous pain-related observations can be integrated, analyzed, compared, and potentially modeled dynamically. Future empirical validation will determine whether the proposed representation provides clinically meaningful advantages over existing pain assessment approaches.