We aimed to construct a novel device for cerebral PEMF stimulation and tested the hypothesis that the stimulation exerted an analgesic effect when applying a wave pattern known as CNP 
As hypothesized the weak field PEMF treatment for 30 minutes increased HPT compared to sham stimulation. The effect size as indicated by Cohen's d is 'medium' to 'large'. During sham exposure HPT increased by approximately 1°C. In addition, the PEMF effect added approximately 0.7°C to the HPT. Thus the HPT increasing effects of PEMF were similar in magnitude to the habituation effect that developed over the course of the experiment. Taking into consideration that the thermode temperature increased by 0.3°C/s, treated subjects allowed the already hot thermode to warm up for an additional 2 to 3 seconds on average.
Our PEMF effects on tQST results are in agreement with a previous study 
which used a very similar time varying magnetic pulse. Despite a significant number of methodological differences (within-subjects vs. between-subjects, nineteen radial electromagnets vs. three orthogonal Helmholz coils) they found a similar result to ours, being an increased HPT due to PEMF treatment and no treatment effect on WDT. They also observed that PEMF effects were more pronounced in women which is compatible with the fact that our effect was robust and that our population was mainly (90%) female. The increased HPT also confirms that the current arrangement of coils, using the international coordinate system derived from EEG, is effective for the induction of experimental analgesia. The trailing zeros in the CNP as described in the patent 
do not seem to be necessary for its analgesic effect because we omitted them in this study.
This study shows that the PEMF effect appeared to be quite specific for HPT. PEMF treatment had no effect on WDT, indicating that the ability to detect warmth, a non-noxious thermal stimulus, remained unaltered by the pulsating magnetic field. This is in agreement with the literature 
and it is a very advantageous property for an analgesic treatment: to only reduce pain without reducing a person's sensitivity. Finger tapping speed, handwriting, PANAS and POMS results were all unaffected by the PEMF treatment.
The digit to symbol substitution task showed a non-significant treatment effect with worse performance after PEMF than after sham. The fact that this did not reach significance was because we did not have a hypothesis about cognition so this is a result from an explorative analysis with a conservative multiple comparisons correction. However, there is some biological plausibility because it was recently shown that cognitive control and sensory processing can both be influenced simultaneously by one intervention or manipulation 
. These considerations combined with the need for analgesic treatments without cognitive side effects, motivate the future study of cognitive performance after PEMF treatment.
In order to gather information concerning the working mechanism of the induced analgesia, we also measured two emotional parameters and two motor parameters that are sensitive to dopaminergic tone. No treatment effects on the emotional state were found so we have no evidence that emotional changes were mediating the PEMF effects on HPT. We also found no treatment effects on the two behavioral indices of dopaminergic tone. Taken together these findings suggest that PEMF analgesia is not mediated by changes in emotion or in central dopaminergic tone.
The fact that pain tolerance was increased does not identify a single neuroanatomical structure as the mediating location because the level of pain tolerance is the end result of the total function of the anterolateral somatosensory system: nociceptors, thin fibers, dorsal horn, ventral commissure, spinothalamic tract, periaqueductal grey and reticular formation, ventromedial, mediodorsal and intrathalamic thalamus, insula and anterior cingulate cortex. The latter two are involved in the emotional aspects of pain such as tolerability and suffering. Therefore, these are plausible areas for mediation of increased pain tolerance and in fact a relatively recent study found support for the notion that brain activation in insula and anterior cingulate cortex as measured with fMRI was decreased by PEMF stimulation with the CNP
The mechanisms by which electromagnetic fields can influence biological systems are not yet fully understood. An abundance of mechanisms have been proposed and a large number of them have been confirmed experimentally (for review see e.g. 
). The most established mechanism is induction of an electrical potential due to changing magnetic flux density (Faraday's law). As a result ion motion (current) is altered, which in turn induces changes in synaptic potentials. Because synaptic potentials determine the likelihood of an action potential, this is a plausible mechanism for PEMF effects on neuronal activity: PEMF per se
may not induce action potentials like TMS does, but it can change the temporal probability of action potentials. A recent paper found evidence for magnetic sensitivity in the low mT range of cryptochrome, a protein that is expressed throughout the tree of life including humans 
. Human cryptochrome has indeed been shown to be sensitive to magnetic fields 
. Cryptochrome is thus a candidate mediator of the analgesic 
and antidepressant 
effects of PEMF on humans. Mediation of PEMF effects by cryptochrome, being a protein sensitive to both light and magnetic fields, could also explain why PEMF effects were reported to be highly dependent on lighting conditions 
We found no differences between the effects induced by the two field strengths: apparently the intensities were equipotent. Dose-dependency of PEMF effects is generally very steep and has been described for different systems to occur below 1 mT 
, below 500 nT 
and even below 50 nT 
. It appears that the two field strengths used in our study (0.4 and 1.1 mT) both induced the maximum effect.
Concerning the penetration depth of our stimulation, it is often heard that TMS penetrates 1–2 cm, although H-coils can reach up to 6 cm 
. Such statements are incomplete and inaccurate because what is implied is that TMS can induce action potentials at these depths. It is unknown whether magnetic fields have to induce action potentials in order to be effective at modulating biological functions. On the contrary, weak pulsed fields (PEMF) are effective in humans 
and it is highly unlikely that the direct induction of action potentials in the brain plays a role here. The magnetic permeability of biological tissues is very similar to that of air or vacuum meaning that the main factor determining the field strength of low frequency PEMF in the brain, apart from the current and the coil design, is the distance to the coil.
Thresholds for PEMF effects on living systems have been estimated at 500 nT 
and even 50 nT 
. Flux density was measured in our study at five distances from the coils with flux density values between 1 mT and 0.1 mT. These values fit very closely to an exponential dependence of flux density on distance. Extrapolating using this exponential dependence predicted flux densities of 500 and 50 nT to be reached at 2.2 and 2.9 cm from the coil respectively. This strengthens the notion that our stimulator induces biologically relevant magnetic fields in the brain 
In terms of safety, our newly designed magnetic stimulator conformed to the assessment criteria of the Dutch Work Group for the Classification of Instruments in University Hospitals (Wibaz) and is a class I, type B device according to the IEC 601-1988 norm. This indicates that the device is electrically safe to be used on humans. With regard to neurological safety, epileptic seizures are the main serious adverse event that can potentially be induced by magnetic stimulation. However, the risk of inducing seizures is controllable because it is a function of frequency and field strength
. Importantly, the stimulator described here falls well below the field strength described in the above paper: our field strength was not 100–220% 
of the motor evoked potential threshold, but in the order of 0.05%. Therefore it seems highly unlikely that induction of epileptic seizures is a risk with the current setup. None of the volunteers could detect the stimulation or had adverse effects or other complaints so that the PEMF procedure appears to be completely safe.
A strength of this study is that we provide data from an actual measurement of the magnetic field whereas this is frequently omitted in PEMF reports. Additionally, we confirmed our prediction that HPT would increase after PEMF treatment and we measured many additional parameters. This study was sham-controlled and volunteers detected no difference so it was truly double-blind for the whole duration of the experiment. Although the treatment groups (PEMF-sham and sham-PEMF) were not fully balanced with respect to age, gender and handedness, the use of a crossover design precluded confusing group effects for treatment effects. In the paired design every subject served as their own control thus reducing the obscuring effects of intersubject variability.
As a limitation, the generalizability of this trial is limited because it was performed in a relatively small group (n
20) consisting mostly of young women. Another limitation is that although the device permits considerable anatomical specificity of the PEMF stimulation, for this pilot we stimulated all locations simultaneously. Future studies should aim to elucidate the relative contribution of the individual electromagnets.
In summary, we built a magnetic stimulator capable of producing fluctuating magnetic fields with arbitrary temporal patterns within the 0–300 Hz frequency range. The use of an established coordinate system allows studies with anatomical specificity and integration with existing (EEG) literature. The use of nineteen small electromagnets makes it possible to stimulate specific neuroanatomical targets with the aim of modulating their function. This setup allows double-blind, sham-controlled experiments with arbitrary wave shape magnetic stimulation. These advantages, in addition to low cost and high safety, make this technology widely applicable for functional and clinical studies of the brain. As expected PEMF stimulation of the brain with this device caused increased pain tolerance in healthy subjects. At the same time, sensitivity to non-noxious thermal stimuli remained unchanged. We found no evidence for changes in emotional state and motor parameters that correlate with dopaminergic tone, thus it is unlikely that these would have mediated the changes in pain sensation.