Although the study has a strong limitation due to the absence of placebo (sham) control, it nevertheless shows that the method of stimulation in nonphantom limb hemisphere with 1

Hz stimulation ameliorates the phantom limb pain with longlasting antalgic effects. The effects of rTMS on pain are similar to effects obtained by Passard et al. [
11]. Passard in his work applied high frequency rTMS in the left motor cortex of patients with fibromyalgia for two weeks. He obtained the maximum result at the end of treatment, and this result lightly decreased in followup. Also, we obtained the maximum reduction of pain at the end of treatment but in weeks after the end of treatment the relief in pain reduced. In order to improve the results it would be probably necessary to have a longer period of stimulation or other parameters of stimulation like a higher intensity of stimulation, respecting the safety guideline [
16] and considering that stimulation is applied in the motor cortex area with high epileptic risk.
The low frequency rTMS has showed antidepressant effects [
17,
18], but in this case the relief in pain does not depend on mood change. In fact the mood of the patient remained stable, like the tests, Ham-D, Ham-A, and MRS show, remaining stable at ≤6.
Instead, the low frequency rTMS is known to reduce the excitability of the stimulated motor cortex. This can increase the excitability of the controlateral motor cortex via transcallosal pathways, and so it can have analgesic effects in a way similar to the epidural motor cortex stimulation and to the high frequency rTMS of motor cortex. In fact chronic motor cortex stimulation using implanted electrodes is an effective treatment of drug-resistant pain [
19], but its mechanism of action remains poorly understood. Some hypotheses resulted from electrophysiological and PET studies [
20,
21]. In these studies, cerebral blood flow was found to increase in thalamus ipsilateral to the stimulated motor cortex, in the orbitofrontal and anterior cingulated gyri, the anterior insula and upper brainstem near the periacqueductal gray matter. Cingulate/orbitofrontal activation should participate in a modulation of affective/emotional component of pain, while descending activation of the brainstem should inhibit the transmission of discriminative noxious information [
20,
21]. Besides, there are lines of evidence that chronic motor cortex stimulation using implanted electrodes might involve endogenous opioids system in the analgesic action. This hypothesis is supported by the demonstration that motor cortex stimulation via epidurally implanted electrodes induces changes in endogenous opioids systems in patients with neuropathic pain [
22]. Furthermore, it has recently been shown that naloxone reverses the antinociceptive effects of epidural motor cortex stimulation in the rat [
23]. Besides, a recent study shows the involvement of endogenous opioid systems in rTMS-induced analgesia [
24]. In fact, naloxone injection significantly decreased the analgesic effects of rTMS of motor cortex stimulation, but did not change the effects of rTMS of the dorsolateral prefrontal cortex or sham. The differential effects of naloxone on motor cortex and dorsolateral prefrontal cortex stimulation suggest that the analgesic effects induced by the stimulation of these two cortical sites are mediated by differential mechanisms [
24].
The physiopathology of the phantom limb pain is still an open field between various hypotheses. The two major research streams on the painful phantom limb are focused on the pivotal influence of the periphery and of the spinal cord, while the other is focused on the fundamental role of suprasegmental structures and of the cortex. These two research streams seem to be more complementary than in opposition [
25]. However, the results of our paper show that phantom limb pain could be generated by altered interhemispheric balance. This theory and the consequent strategy have shown effects in stroke recovery [
14] and in rehabilitation of visual spatial neglect [
13]. This hypothesis is consistent with the results of Röricht et al. [
26], which show higher excitability of the motor cortex contralateral to the intact arm in some patients with upper arm amputation, and higher excitability of the motor cortex controlateral to the amputated limb in other patients. Röricht says that variability in excitability in two hemispheres could depend on the site of amputation and on the time since amputation. The hypothesis of interhemisferic balance is in contrast with Schwenkreis et al. [
27] and colleagues that found a significant reduction of intracortical inhibition in forearm amputees and an enhancement of intracortical facilitation in upper arm amputees on the affected side, revealing a hyperexcitability of phantom limb hemisphere. Others studies, with EEG or with single-pulse and paired-pulse TMS investigations, are necessary to evaluate excitability of the nonphantom limb hemisphere and of phantom limb hemisphere and its modification with treatment, to understand the role of excitability in phantom limb pain.