In a first simulation, both observers were exposed to the same sensory information: noxious input for time steps S1−S5, and harmless input st S12−S18 for 40 learning trials. Results are shown in Figure 2. In the healthy observer (Figure 2A), the exposure to noxious stimuli between time steps 1 and 5 leads to an acute and highly precise inference to be in pain. In contrast, the presentation of harmless sensory information (time steps 12–18) decreases the probability of inferring to be in pain drastically. In the chronic pain model, however, the response to acute noxious sensations follows a different pattern (Figure 2B)—the baseline probability of inferring pain is at ceiling levels already. In contrast, harmless information barely has any significant effects on the probability of inferring pain, which remains high.

In another simulation, the two observers are exposed to only-noxious vs. only-harmless sensory observations for all 20 time steps and 40 learning trials. Results are shown in Figure 3. In individuals with chronic pain (3A,B), the type of sensory information the system is exposed to does not result in significant changes of p(pain). Especially compared to the healthy inference model (3C,D), exposure to harmless information does not lead to decreased probabilities of inferring pain. In healthy inference, prolonged exposure to noxious information leads to acute heightened probabilities of experiencing pain. In contrast, harmless stimulation results in very low probabilities of inferring pain. Of note, the inferred probabilities of pain at the first- and final time step differ from intermediate time steps. This is an artifact caused by the model architecture with a definite end node, and our batch-updates (learning) that are performed at the end of one time series (see figure caption for details).

Exposure therapy is an effective treatment for chronic pain, where patients with high levels of fear-avoidance are gradually exposed to stimuli or movements that elicit fear (49). Relating the idea of exposure therapy to our model, its goal would translate to changing the interpretation of harmless sensory information so that the inference becomes less biased towards pain. As an example, a person with chronic low back pain may avoid lifting a basket with groceries out of their car. In graded exposure therapy, the therapist would guide the patient through lifting baskets with increasing weight, all while closely monitoring the patient’s fearful assumptions and physical sensations. Over the course of the exposure treatment, we would expect a change in p(lift-basket∣pain) in this patient. Altered likelihoods may lead to less guarding behavior in patients, an increase in corrective sensory information and, ultimately, remission. In the specific case of fixed transition probabilities, however, this approach may not be sufficient. This picture would be in line with treatment-resistant chronic pain. The maintenance of p(pain) in these patients is mostly determined by the transition probabilities, while incoming sensory information is mostly disregarded. We simulated two observers who receive ten sessions of exposure therapy (presentation of harmless sensory information for one time step) over the course of fifty time steps. In both cases, the pre-set marginal probability of inferring pain is p(pain)=0.7, and the transition probabilities were sampled from the respective null space of a marginal p(pain)=0.7. Results are illustrated in Figure 5. In the case of the first patient, the likelihood functions, p(sensation∣pain) were ambiguous (p(noxious∣pain)=0.6, p(harmless∣pain)=0.4,p(noxious∣ pain¯)=0.6 p(harmless∣pain¯)=0.4, and imprecise (ν=20). In the simulation, the marginal probability of inferring pain dips slightly, before moving towards the initial, high p(pain)=0.7 again. In a second case, the likelihood functions were intact, that is, accurate (p(noxious | pain) = 0.8, p (harmless | pain) = 0.2, p(noxious pain¯)=0.1,p(harmless∣pain¯)=0.9) and precise (ν=100). Here, the inference moves away from the high prior faster and remains relatively pain-free for longer.

The experience of pain seems to be the result of an inferential process, where prior expectations are integrated with current sensory information over time (14, 16). This process is probabilistic and non-linear, with large inter-individual differences in the relationship between physical stimulation and pain experience. While statistical accounts of pain have gained momentum over the past decade, insights into computational underpinnings of the chronification of pain have been sparse (50, 18, 14).

We propose a Bayesian model for interoceptive perception and pain experience in chronic pain. Drawing on machine learning concepts such as belief-propagation and free-energy minimization, we demonstrate that the model captures well-studied phenomena such as decreased pain thresholds and allodynia (i.e. perceiving innocuous stimuli as painful) in individuals with chronic pain.

Our “chronic pain” observer is characterized by heightened prior expectations of pain, aberrant associations between sensory input and pain perception and heightened assumptions about the persistence of pain. In our model, this refers to overly precise priors for being in a state of pain, p(pain)), ambiguous top-down or likelihood functions p(sensation∣pain) and more rigid transition probabilities between hidden states p(paint∣paint−1), respectively.

It has been suggested that chronic pain is associated with a broad and heightened expectation of pain (51, 14, 24). Heightened expectations of pain may stem from early averse life events or injuries (52), or social factors such as an overprotective, fearful parental style (14). In the patient model, a heightened pain prediction led to inferring to be in pain more readily compared to the healthy model. Conflicting innocuous sensory stimulation hardly influenced the inferred state. In accordance with this, empirical studies suggest chronic pain patients may not attend to sensory information but rather rely on their prior expectations of pain (53, 54). Our observations fit into a larger discussion about expectations as core features of a multitude of mental disorders (51, 14). A further aspect of our model is that harmless sensory information is associated with pain over time. This phenomenon is commonly observed in patients and referred to as allodynia (55, 14). The Bayesian Brain hypothesis postulates that the perceiving individual perpetually tries to infer the real-world causes for incoming sensory information (22). We here present a perspective on pain as an abstract percept of the body’s state. Following this view, pain is an inference on a real-world “cause” (cmp. (56)), bodily damage, based on all available prior- and current sensory information. The chronic pain patient infers pain from a wide range of sensory stimuli that would not be perceived as painful by healthy controls. Further, the associations between sensory information and hidden state are noisy and unclear in the chronic pain observer. While a healthy observer maintains precise beliefs about the external causes of harmless sensory input, p(harmless∣pain), this probability is completely ambiguous in our patient model. Over time, the chronic pain patient is less and less likely to infer a pain-free state from any type of incoming sensation.

Contrarily, a flexible and highly dynamic pattern can be observed under healthy interoceptive inference. Here, noxious stimuli are associated with pain, and a pronounced and acute state of pain is inferred from incoming harmful stimuli. However, once the stream of harmful sensory input stops, the probability of pain normalizes very quickly. This dynamic pattern is in line with the function of pain as a warning signal—motivating quick and adaptive behavior change following a threat to the individual’s physical integrity (57).

Note that our results also hold under the active inference framework (23, 58). Canonical versions of active inference contain a generative model that is very similar to ours (Hidden Markov model, HMM), with the difference of an additional layer that models an agent’s actions, or choices (59). Actions then influence the transitions between states so that more likely, or expected states under the current observations, are reached. In other words, in active inference, an agent infers the hidden state from the combination of prior beliefs, sensory information and their own actions. As an example, consider the case of a child with chronic abdominal pain who involuntarily keeps picking at her abdomen (checking behavior, example from (14)), so that increased pain is experienced. Under active inference, this can be interpreted as causing observations (noxious sensations) that are expected under the most likely state (pain). Acting directly towards bringing about a certain observation changes the causal relationship between observation and hidden state (i.e., “do-operations”, (60)). However, it is impossible to act directly on one’s nociceptors, so that pain still needs to be inferred from sensations, even when the noxious stimulation is self-induced.

If the individual performs implicit Bayesian inference over hidden states, then we here demonstrate that this inference can be biased towards inferring pain. This has important implications for the treatment of chronic pain patients. Cognitive behavioral therapy (CBT) shows statistically significant, but small effects on certain aspects of chronic pain (pain, mood, disability, pain catastrophizing; (61)). Techniques usually include relaxation training, behavioral activation (i.e. engaging in behaviors that were previously avoided due to fear of pain), setting behavioral goals, problem-solving training and cognitive re-structuring (61, 62). Further, exposure therapy has shown promising results in the treatment of chronic pain (63, 64, 49). Exposure therapy seems to reduce disability more effectively than CBT in patients with chronic lower back pain (49). It is designed to specifically target emotional responses to pain- or expectations of pain, which lead to excessive guarding behaviors. Guarding behaviors, in turn, may limit the opportunity for receiving corrective, conflicting sensory information, leading to the solidification of fearful pain beliefs (65, 66). However, we show that inference can stabilize towards pain, even in light of conflicting sensory information. Specifically, when the transition probabilities between hidden states have a stable state with high marginal pain probability, a simulated patient model returns to the inference of being in pain while harmless sensory information is provided. In other words, the initial deviation from the high pain state, which might have been reached by therapeutic means, has vanished. This simulation could be a model for treatment-resistant chronic pain. We further show that these patients may be best served by targeting their beliefs about the associations between sensory stimuli and pain expectations (likelihoods). When likelihoods allow the precise and accurate association between sensory stimuli and pain, exposure to harmless sensory information leads to more promising results. However, when the patient does not have accurate likelihoods, exposure to certain sensory stimuli may not be a promising approach. It can hence be derived that patients may need to re-learn precise and accurate inferences about different types of sensory stimuli, ideally before being guided through exposure therapy.

One can speculate about the role of pharmacotherapy in the context of our model. Potentially, analgesics target the patient’s likelihood model by inhibiting the transmission of noxious information from pain receptors (67). This assumption requires empirical testing with appropriate data of medicated chronic pain patients. In this case, combining pharmacological and psycho-therapeutical strategies may be promising. More data is necessary to assess which treatments target what model parameter. For an overview of expected self-report scores and hypothesized underlying model parameters, see Figure 6.

In Figure 6, we illustrate two hypothetical patients, one developing chronic pain after an acute injury, whereas the other patient does not develop chronic pain beyond acute injury.

In the chronic pain patient, pain persists for prolonged periods post injury. Empirically, we expect to see pain and disability scores that are persistently heightened in the months following injury. In experiments (i.e. fear conditioning, pain ratings following noxious stimuli), our model predicts increased levels of prior expectations of pain (note the shift in probabilities over time), as well as decreased precision of sensory information, corresponding to an ambiguous and imprecise likelihood model. Finally, for pain to persist in a very rigid way, transitions towards a pain-free state become more unlikely until therapy can reverse this effect. We can speculate that likelihood models may be treated via medication-supported exposure therapy, whereas prior beliefs could be best targeted using CBT.

In the acute pain patient, the injury is followed by a quick recovery and remission into a pain-free state. The noxious stimulus leads to a transient state of experiencing pain, including an elevated prior expectation of pain, which is a consequence of learning about an acutely noxious stimulus. Disability and pain experience as assessed with self-report measures are elevated in times of acute injury. With the injury healing and the noxious information subsiding, the pain-free state is re-established within 4 months. Note that the likelihood and transition models are assumed to stay relatively intact in this patient.

Following our model, there are three factors that could be promising targets for patients with chronic pain. Firstly, therapy could target the heightened and generalized expectations of pain. This is in line with Rief et al. (51), Panitz et al. (71), who discuss the importance of psychological interventions that target expectations. Secondly, our model suggests a need for re-learning the associations between sensory information and the state of pain. This could be achieved via gradual, guided exposure to harmless stimuli in therapy. Lastly, a patient’s belief about the persistence of pain over time could be targeted specifically with cognitive interventions (e.g. retrospective evaluations, re-learning to differentiate pain intensities), which may be especially relevant in cases of treatment-resistant chronic pain.

The presented model makes several simplifying assumptions and can be extended in numerous ways. Currently, latent- and observable variables could only take one of two possible states for the sake of simplicity. Continuous random variables could allow for more complex conclusions. It is generally feasible to perform inference on graphical models with continuous random variable nodes (72, 73). However, this added complexity might detract from our main conclusions, which we expect to hold in the continuous case, too. In future work, we will extend our model to continuous sensory signals and internal states.

Further, future efforts to extend this framework should account for the vast heterogeneity that is found among chronic pain patients. Assuming a multitude of underlying etiological factors, they might need differential representation in quantitative terms as well.

With this model, we focus on computational and psychological aspects of pain inference. We have formalized a hypothesis about the generative process underlying chronic pain. While several salient features of acute and chronified pain perception are captured by our model, we do not have access to the true generative process and can hence not draw any definite conclusions about it.

Besides psychological factors (e.g. beliefs), a multitude of additional factors could be considered when extending this model. As Kiverstein and colleagues (2022) note, a model of chronic pain needs to take on a bio-psycho-social perspective, integrating a multitude of empirical findings under one approach. For example, pain experience seems to be alleviated by the presence of a close friend or partner, i.e. social support (74). In a recent review, Mohr and Fotopoulou (2018) argue that social support may serve as a security signal which renders prediction errors caused by threats to the physical integrity less precise. Future iterations of this model may be extended to incorporate these findings, e.g. by means of a context-layer. Here, however, we show that important characteristics of chronic pain experience can be simulated from a Bayesian perspective, by assuming that a) sensory information relates to pain experience through (biased) parameters of a generative model and b) the inferred states are marked by correlations, or stability, over time.

Rigid expectations that are not sufficiently constrained by incoming sensory information seem to lie at the heart of several mental disorders. Psychosis, for instance, can be regarded as resulting from an exaggerated and inflexible reliance on prior expectations (75, 76). Computational accounts of mental disorders can provide novel mechanistic insights into their etiology, exacerbation and maintenance over time (77).

The computational model of chronic pain presented here can be applied to empirical data. Below, we outline possible avenues towards testing the model presented here.

Firstly, data from learning experiments in chronic pain patients and controls could shed light on the real-world significance of the model’s parameters. In fear conditioning experiments, participants learn the association between a painful unconditioned stimulus (UCS, such as e.g. heat stimulation with a thermode or electric shocks) and unrelated, conditioned stimuli (CS, such as a visual cue). In a first step, significant group differences in model parameters would need to be investigated. Then, given their heightened pain prediction, our model would predict decreased pain thresholds in patients with chronic pain. Biased likelihood terms may lead to altered learning about the UCS-CS contingencies in chronic pain patients. Similarly, other assumptions that were used to furnish this model could be tested empirically (e.g. biased and imprecise likelihood models, heightened prior predictions of pain, or rigid and exaggerated beliefs about the persistence of pain in chronic pain patients).

A key challenge to empirical tests of our model in humans is the need to approximate observable sensations, i.e., nociceptor firing. Sensations can be approximated by measuring physical properties of experimental stimuli, such as the temperature of a heat thermode, the current used for electric stimuli, or the intensity of mechanical pressure. To empirically test our model, future studies could assess the relationship between physical sensations and the pain percept. For this, concurrent measurements of sensations (or proxies thereof, such as physical stimulus properties) and reports on the pain percept (e.g. pain scores) are necessary. Pain scores in response to stimuli with different intensities could be collected from healthy individuals and chronic pain patients. We would expect to find significant group differences with respect to prior, transition- and likelihood model parameters. Such data could further shed light on an important detail of patient experience: what model parameter is most relevant to the chronification of pain and the experience of patients? In all cases, the full Bayesian model would need to be compared to both simpler models, such as e.g. single-trial vs. sequential models, and more complex models, such as deeper predictive hierarchies, in a model comparison.

A novel Bayesian model is able to reproduce common features of healthy- and chronified pain perception. Machine learning approaches, such as a hidden Markov model and variational inference, allowed the exploration of parameters that may underlie the development of chronic pain. We have demonstrated that this model is able to capture many phenomena observed in individuals with chronic pain, and during acute, healthy pain perception. Additionally, the model was able to simulate rigid, treatment resistant chronic pain. Further research could significantly advance our mechanistic understanding of chronic pain, which may help to inform treatment selection.