Our results provide an interpretation of conflicting findings2,12 concerning the cortical representations in phantom pain by means of two variations of a computational model. The model simulations yielded that the nociceptive channels of the amputated finger showed a significantly stronger central nociceptive activity during the resting phase (no stimulation) on the PAIN condition than on the NOPAIN condition (Figure 4a, dark gray bars). We therefore identify the NOPAIN and PAIN conditions with scenarios where the subject experiences weak and strong phantom pain, respectively. On the basis of this identification, the model predicts that the degree of reorganization in the somatosensory map is stronger in patients with phantom pain than in patients without (or with less) phantom pain. This prediction would be in accordance with the maladaptive reorganization model. Furthermore, however, the model predicts that the representation of the phantom is preserved after amputation, regardless of there being phantom pain or not and that the activity of the phantom representation during executed phantom movements is stronger in patients with phantom pain than in patients without phantom pain. These latter two predictions would be in accordance with the persistent representation model. Summarizing, in view of our simulations the two explanatory models and their respective experimental findings can be reconciled.

Apart from explaining existing data, the model makes a prediction, which is, to our knowledge, not yet covered by experimental evidence and which could be easily tested by a questionnaire: Amputation patients suffering from phantom pain should feel fewer phantom sensations that are not painful than patients suffering, or suffering less, from phantom pain (Figure 4a, white bars).

We shall now discuss the individual model assumptions. According to assumption A1, the somatosensory cortex reorganizes itself in response to somatosensory input. This phenomenon has empirically been demonstrated for diverse types of stimulation, including nociception18,19,20,21,22,23,24. The Kohonen map14 used in our simulations is a rather abstract and idealized model of a biological self-organizing neural network. There are physiologically more elaborate and less idealized models for self-organizing maps encoding the location of receptors and other receptor properties, taking into account also temporal correlations in the receptor input25,26. Despite its known limitations, however, the Kohonen map is a numerically efficient and well-established tool to simulate the consequences of amputation and other sorts of sensory deprivation in the sensory cortex27,28,29. In the context of our study, the relevant function of the cortical map is its capability to organize itself according to the topology of the receptor space, which makes the Kohonen map a suitable choice here.

In model variation A, the integrated cortical map only contains where-information, that is, information about the location of the receptor on the skin and no other receptor properties. In particular, it does not contain what-information, that is, information about the modality of the stimulus, which is here either touch or nociception. Recent findings show that the topological representations of non-noxious tactile stimuli on the skin largely overlap with those of noxious tactile stimuli30, although the representations slightly differ on a smaller scale. Thus, it is not yet resolved, whether or not the modality is encoded in the location of the representation. In any case, the what-information is certainly processed in additional pathways; especially the encoding of painfulness is likely located in the insular-opercular region rather than S131,32. The different aspects about a stimulus are presumably at some stage bound together to yield a unified percept, though it is yet not fully understood and part of the notorious binding problem33, as to how this unification is actually accomplished in the brain. Here, we do not attempt to resolve this problem but rather computationally unify where and what-information (Figures 3–5).

In model variation B there are two modality-specific cortical maps. So, the two maps together encode what-information, in contrast to model variation A. In a biological system, these two modality-specific maps could either be spatially separate, or they could overlap to some extent. In either case, observable differences in cortical activity would strongly depend on the applied measurement method. If cortical reorganization is measured using tactile stimuli only, the model predicts that one observes more reorganization on the PAIN condition than on the NOPAIN condition, in accordance with the results of Flor et al2, supporting the maladaptive reorganization model (Figure 5b, white bars). If, on the other hand, cortical reorganization is measured using nociceptive stimuli only, the amount of reorganization is predicted to appear smaller on the PAIN condition than on the NOPAIN condition (Figure 5b, dark gray bars). This model prediction, which is to our knowledge not yet covered by experimental evidence, could be tested in a manner similar to the procedure used to establish the maladaptive reorganization model2, only with using nociceptive rather than non-nociceptive stimuli.

A third possible model variation, which we have not included in our simulations, is the case of a single unified cortical map that receives input from both tactile and nociceptive channels (as in model variation A), but which organizes itself not only according to the position of receptors (as in A and B), but also according to the modality of the stimulus. There are modeling approaches along this line, with a focus on the optic tectum and the primary visual cortex25,26. The resulting cortical structure contains modality-specific regions that are interspersed with each other, similar to the orientation-specific columnar structure of the primary visual cortex34,35. In the case of touch and nociception, such regions would, in effect, form two modality-specific sub-maps, a structure that resembles the situation described by our model variation B. While a classical Kohonen map, which has been implemented in our model, is indifferent with respect to temporal correlations between the afferent signals, the emerging structure of the biological somatosensory cortex will probably be influenced by the temporal coherence between nociceptive and tactile events. Therefore it is possible that the topological structure of the real somatotopic map also encodes modality to some degree. The existing experimental evidence is not decisive about this question and recently measured nociceptive and non-nociceptive representations of fingers in the primary somatosensory cortex turned out to be highly aligned at the resolved scale30.

Figure 2 shows a representative example from the set of simulated map formations. The exact structure of the simulated maps differed to some degree from simulation to simulation, due to the stochastic nature of the initial state of the map and due to the stochastic occurrence of spontaneous events during the training phase. At the end of each simulation, however, the fingers were mapped to a corresponding coherent region on the cortical map and the spatial relation between the fingers was always represented as well.

Assumption A2 postulates spontaneous neural activity in the sensory system that is increased in those parts affected by deafferentation and which is implemented in the computational model in the form of discreteneuronal noise (DNN) and spontaneouscoherent activity (SCA). The origin of the increase of spontaneous activity is still not completely understood, but there are several lines of explanation. Spontaneous activations of afferent fibers, also known as ectopic discharges, have been found after peripheral nerve lesion and neuropathic degeneration36,37,38,39,40,41,42,43,44,45. In certain cases the increase of spontaneous activity can be traced back to long-term alterations of the nervous system due to previous and recent nociceptive activity, a mechanism that is often referred to as pain memory46,47,48,49,50,51,52. As for the DNN, increased spontaneous activity of nociceptive fibers at the painful site has been measured in patients suffering from spontaneous pain in connection with CRPS53, diabetic neuropathy38 and phantom pain36 (measured in neuromata at the stump). Moreover, an increased spontaneous activity of nociceptive fibers in rats has been demonstrated to be a consequence of spinal cord injury43,45. It has been argued that an increased spontaneous activity of C- and Aδ-fibers is a possible cause for dysesthesia, that is, spontaneous pain40,54. As for the SCA, in the model this type of spontaneous activity is implemented to occur after the spinal gate in higher regions of the nociceptive pathway. The SCA is modeled in the form of coherent activity patterns resembling those patterns elicited by actual noxious stimulation. This type of activity may be a possible cause of more detailed painful experiences. About 40% of the patients describe their phantom pain as being close to actual pain experienced in the limb before or during its amputation and these sensations are often referred to as pain memories51,55,56,57,58,59. As for the possible site of the physiological mechanisms leading to pain memories, studies show that not only the cortex but also subcortical regions such as the cerebellum are involved in pain-related associative learning60,61. The central role of pain memories in the context of chronic pain and phantom pain has often been emphasized and is a matter of current debate1,13,56,62. One might conceptualize the SCA in our model as spontaneous occurrences of detailed pain memories, although it is not necessary to do so.

Assumption A3 postulates that phantom movements and attention to the phantom limb activate neural circuits that have stored sensory experiences of the missing limb. This assumption would be compatible with studies showing a modulation of phantom pain during the perception of the mirrored intact limb at the site of the phantom56. It would also be compatible with studies reporting phantom pain experiences elicited by concentration on the phantom limb58, by watching individuals whose corresponding intact limb is touched9 or by observing pain in others63,64. A crucial measurement in the study of Makin et al.12 in support of the persistent representation model, consisted in having the subject perform phantom movements while measuring the activity of the somatosensory cortex. To model an analogous scenario, our simulations involved, subsequent to a training phase where the model is trained with input from random somatosensory stimulations, a probing phase. Given that the subject executes a phantom movement, then according to assumption A3 the movement execution would activate neural circuits that increase the strength of spontaneous coherent activity (SCA) in the somatosensory channels corresponding to the moved (phantom) limb. In our simulations, during the probing phase the SCA strength of the affected somatosensory channels was multiplied by a factor of five and the resulting activity of the cortical map was calculated.

Assumption A4 postulates that a central gate is regulating the input to the somatosensory cortex. The central gate is probably the most speculative element in our model. A likely location for it might be the thalamus which is known to be a relay station for all afferent connections into the cortex65. There are two more gates in the model, the peripheral gate and the spinal gate, which are less speculative. The peripheral gates correspond to receptors in the periphery and the opening and closing of each gate would correspond to the lowering and raising of the gating threshold, leading to peripheral sensitization and desensitization, respectively. The gates are implemented as linear saturated functions (Figure 6). For stimuli of limited strength the linearity of the receptor response is a reasonable approximation66. The cut-off at the channels' maximum excitability has been implemented to take into account that any receptor will go to saturation for strong enough stimuli [ibid.]. Further, the spinal gates are simplified versions of neural mechanisms in the dorsal horn of the spinal cord, which have first been discovered and modeled by Melzack and Wall in the context of their seminal gate control theory15,16,17. Their closing and opening contributes to central sensitization and desensitization, respectively, which is induced and maintained in the body by activity in peripheral afferent fibers40,54, by neurogenic inflammation [ibid.] and also by descending supraspinal modulation67,68.

Figure 6 Input-output relation of the linear gates implemented in the model. External modulation affects threshold and gain, the output is cut off at unity. Full size image

There are certain limitations of the computational model. The model involves separate modality-specific channels from the periphery up to the central gate before the somatosensory cortex. This is an idealization in so far as there are wide dynamic range (WDR) neurons in the deep dorsal horn (laminae V–VI) that respond to stimuli in both the noxious and non-noxious domain, so that their firing rate encodes the strength of the stimulation but not the modality69,70. The functional role of WDR neurons is still controversial and some researchers hold that the WDR neurons, rather than the nociceptive specific (NS) neurons, are responsible for the subjective perception of the intensity of painful stimuli71,72,73. In any case, we do not expect the results of our numerical simulations to differ qualitatively if WDR neurons were included in the model. Our expectation is based on the fact that the self-organizing map used in the model encodes only where-information (see above), so the map would be reorganized regardless whether or not the altered input exclusively comes from nociceptive-specific channels.

The maladaptive reorganization model and the persistent representation model are each based on an empirically established relationship between a certain sort of physiological fact on one side and a subjective report of pain on the other side. These empirical findings are in so far unproblematic as a correlation is an objective statistical property of given data, while pain reports are an objective (though not necessarily reliable) measurement of a subjective experience. In order to relate our simulation results to the empirical findings, we have to assume a relationship between the simulated physiological state and a subjective experience of pain. We cannot “ask” the model to what extent it is in pain during the simulation. For this study, we have defined the central nociceptive activity as the remaining activity of nociceptive channels after having passed the central gate and we have taken this value as an estimate for the quantity of subjectively experienced pain. Generally, there will be further modulation by high-level processes, including cognition, visual perception, psychological influences and learning, which are not covered by the computational model.

The simulations suggest that phantom pain, maladaptive reorganization and persistent representation may all be caused by the same underlying mechanism. Accordingly, the reorganization of the somatosensory cortex would rather play the role of an epiphenomenon that is correlated with and therefore acting as a marker for, phantom pain. In our model, however, maladaptive reorganization in S1 would not cause the painful experience itself; instead, the causal driver of phantom pain, as far as our model suggests, is the abnormally enhanced spontaneous activity of deafferented nociceptive channels. As the model lacks a perceptual system, there is, however, room for potential causal influences on phantom pain other than spontaneous activity. A further limitation of the model is the lack of an underlying mechanism for the abnormal enhancement of spontaneous activity after deafferentation, which therefore remains unexplained.

To summarize, simulations of a computational model built upon physiologically plausible assumptions might help to reconcile two apparently contradictory empirical findings and their corresponding conceptual models. In agreement with one of these findings, the computational model predicts that an abnormally increased spontaneous neural activity following amputation induces cortical reorganization that is more pronounced in patients suffering from phantom pain as compared to patients without phantom pain. In agreement with the other one of these findings, the activity of the cortical representation of the missing limb during executed phantom movements is predicted to be stronger in patients suffering from phantom pain as compared to patients without phantom pain.