Methods
Verisimilitude (or “truthlikeness”) of a theory
a can be expressed ad modum Popper [
14] as:
where Vs(
a) is the verisimilitude of
a, CT
v(
a) is a measure of the truth content of
a, and CT
f(
a) is a measure of the falsity of
a [
14].
When calculating Vs(
a) in Table
1, both CT
v(
a) and CT
f(
a) were given arbitrary values of 0, 0.25, 0.5, 0.75, or 1.0 for simplicity. The results for verisimilitude, Vs(
a), can thus be −1.0 (very unlikely), −0.75 (most unlikely), −0.5 (unlikely), −0.25 (probably unlikely), 0 (undecided), +0.25 (probably likely), +0.5 (likely), +0.75 (most likely), or +1.0 (very likely).
Table 1
Verisimilitude calculations for proposed migraine and cluster headache mechanisms (for details, see text)
Vasodilation of large cranial arteries is involved in migraine pain |
Vasodilation of large arteries during migraine is undecided (0) | Increased temporal pulsations during migraine and the effect of ergotamine [ 15]. Decreased blood velocity in MCA during migraine measured with TCD [ 17‐ 19] (1.0) | No change in MCA velocity measured with TCD [ 20, 21] No vasodilatation measured directly with MCA in MMA and MCA during NTG-induced migraine [ 22] (1.0) |
Calcitonin gene-related peptide (CGRP) is increased in the external jugular vein (EJV) during migraine |
CGRP increase in EJV during migraine remains undecided (0) | CGRP was increased in EJV in two studies [ 23, 24]. In one study, sumatriptan treatment normalized CGRP levels [ 24] (1.0) | CGRP was unchanged in two studies on spontaneous migraine [ 26, 27] and one study in nitroglycerin-induced migraine [ 27] (1.0) |
Migraine is a dysfunction of the sensory modulatory network with the dominant disturbance affecting abnormal processing of essentially normal neuronal traffic [ 7] |
Whether a migraine attack is a pure neuronal process without vascular components being involved is unresolved (0). See text | A migraine attack must start in the brain to cause the prodromes and aura. Persistent activation in the brain stem is observed by PET during migraine attack [ 4, 33]. Few cases of symptomatic migraine are caused by brain stem lesions [ 35, 36]. Other migraine symptoms, photo- and phonophobia, have no peripheral cause [ 7]. The β-blockers used in migraine prophylaxis probably exert their effect in the CNS [ 37]. Valproate and topiramate also most likely work in the CNS [ 29] (1.0) | C-fos expression and “evoked potential” are observed in TNC after superior sagittal sinus stimulation in the cat model of migraine. [ 42]. There may be a peripheral source for activity. No other part of the body experiences pain without nociceptive input, except thalamic pain and other neuronal lesions with sensory sign [ 129]. A pure neuronal disorder does not explain the co-morbidities of migraine with aura and stroke and ischemic heart disease [ 48, 49, 129]; a vascular or systemic factor must be involved . A central theory would not explain possible CGRP increases in EJV [ 23, 24]. Systemic endothelial dysfunction present in migraine [ 127] (1.0) |
Does aura trigger headache in migraine attacks? |
Aura is likely to trigger a migraine attack (+0.25) | Clinically, the headache in migraine is contralateral to aura in 92% [ 58] Experimentally, CSD activates trigeminal afferents and evokes a series of cortical meningeal and brain stem events consistent with headache development in rats [ 44]. CSD activates matrix metalloproteinase, which opens the blood–brain barrier [ 62] (0.75) | Clinically, there are well-documented cases of headache ipsilateral to aura [ 57]. Patients with aura but no headache challenge the notion that aura causes headache. [ 57]. Aura does not necessarily precede headache [ 57]. Experimentally, no correlation between CSD and neurogenic inflammation and nociception in rats. [ 66] (0.5) |
Brain stem activation occurs during spontaneous and provoked migraine attacks |
Brain stem most likely activated during migraine, but lateralization doubtful; pathophysiological implications somewhat unclear. (+0.75) | Two PET studies in spontaneous [ 33, 34] and one in NTG-induced migraine [ 4], showed brain stem activation which persisted after sumatriptan treatment [ 4, 33, 34] (1.0) | Lateralization of activation and pain is inconsistent. In one study, PET activation was ipsilateral [ 4], in two others contralateral [ 33, 34] or bilateral [ 34] to pain (0.25) |
Regional cerebral blood flow (rCBF) is normal in migraine without aura |
No firm conclusions (0) | rCBF measurements were normal in one SPECT study [ 68]. Brain stem activated in migraine but no occipital hypoperfusion observed by PET [ 4, 34]. Normal rCBF measured with PWI [ 69] (1.0) | Occipital hypoperfusion was observed with PET ( n = 6) [ 73]. Spreading oligemia observed with PET in one case [ 74]. A SPECT study showed focal hypoperfusion in 74% of patients [ 70]. Patchy hypoperfusion was observed [ 71]. Small general reduction of CBF [ 72] (1.0) |
NO is involved in migraine pathophysiology. iNOS inhibitors will be effective migraine prophylactics |
NO is likely involved in migraine (+0.5) | Nitroglycerin induces genuine migraine attacks [ 22, 75‐ 83]. L-NMMA is effective in migraine [ 84] (1.0) | INOS inhibitors (GW273629, GW274150) were ineffective in treating migraine attacks [ 85, 86]. GW274150 was ineffective as a prophylactic agent [ 86, 87] (0.25) |
Dural neurogenic inflammation (NI) is involved in migraine, predicting effectiveness of NI inhibitors in migraine |
NI unlikely to have a pivotal role in migraine pain (–0.5) | Endothelin and NK-1 receptor antagonists effectively inhibit NI in animal studies [ 94, 95]. In addition, triptans and ergot alkaloids inhibits NI [ 90, 91] (0.5) | Randomized clinical trials show no effect of substance P, neurokinin-1 antagonists [ 96‐ 98], neurosteroid ganaxolone [ 99], endothelin antagonist [ 100], or specific NI blockers [ 101, 102] (1.0) |
Aura is common in cluster headache patients [Schürks-et al-2006]a |
Aura must be rare in cluster headache (−0.5) | Aura occurred in 4% [ 106],14% [ 103], 23% [ 104], and 28% [ 105] of cluster headache patients (0.5) | None of 554 cluster headache patients experienced aura [ 111] (1.0) |
Hypothalamic activation is specific for cluster headache and other trigeminal autonomic cephalalgia (TAC) [ 133] |
Hypothalamic activation is not cluster headache specific; the Popper falsification rule [ 8] was used | Activation in the posterior hypothalamus during nitroglycerin-induced cluster headache attacks was observed by PET [ 112, 113]. In migraine without aura, no hypothalamic activation was found in two PET studies [ 4, 33]. In two SUNCT patients, functional MRI identified hypothalamic activation [ 116, 117] | Activation was observed in both the hypothalamus and brain stem ( n = 7) with PET [ 34] |
To exemplify, we chose both easy problems and problems requiring extensive comments and where the result of the analyses remains open for discussion. Our judgment of the evidence, indicated as CT
v(
a) and CT
f(
a), is given in Table
1 together with the calculated Vs(
a).
Discussion
Current migraine-mechanism theories vary from the notion that the migraine attack “consists of an abnormal perception of otherwise normal circumstances, such as pain without evidence of primary nociceptive activation” [
7] to “migraine may be a local manifestation of a systematic vascular abnormality rather than a primary cerebral phenomenon” [
120] or to “migraine is a neurovascular disorder” [
121].
Popper’s verisimilitude calculation does not resolve problems always. Potentially, both the CTv(a) and CTf(a) can be 1.0 with a resulting verisimilitude of 0. Sometimes, one must fall back to the Popper falsification method, where negative facts that can falsify the hypothesis are the main stay. Migraine data are often not validated well enough to allow clear-cut conclusions. Particularly, confirmatory studies using the same methodology are often lacking.
In areas like migraine research, which is often descriptive, many cases of contradictory data exist because of both biological variability per se and different methods of measuring the biological signal.
No grand unifying theory exists in migraine research that can be falsified by itself or by its predictions [
8], leaving only isolated relevant problems of basic and clinical migraine research for testing.
When evaluating the problems, we often used a mixture of facts from both kinds of research. Verisimilitude determinations can supplement the usual pros and cons by forcing judgement of the evidence for hypothesis
a when assigning values to CT
v(
a) and CT
f(
a) [
14]. According to Popper, Vs(
a) calculation is an objective method for judging a scientific theory or the predictions derived from a theory [
14].
Verisimilitude measures the best correspondence with facts and should not be confused with probability [
14]. One can apply the simple verisimilitude formula to any field one knows well. Notably, verisimilitude calculations should not be applied to quantitative migraine treatment trials when a systematic review or meta-analysis is more appropriate [
10‐
13].
Despite efforts at objectivity, some subjectivity remains in assigning values to Ct(a) and Ctf(a). Some may disagree with my calculations, but anyone can easily assign alternative Ct(a) and Cf(a) values and calculate verisimilitude for themselves.
Among the 10 cases judged by verisimilitude calculations, there were two −0.5 (unlikely), four 0 (undecided), one +0.25 (probably likely), one +0.5 (likely), and one +0.75 (most likely) (Table
1). For one item, the falsification ad modum Popper [
8] was found to be more suitable. There was no −1.0 (very unlikely), probably because there is always some historical or recent evidence for the hypothesis tested [
89‐
91,
104,
105]. The −0.5 depend on the formulation of the question. In four cases, we could not decide whether the theory was true or false because the evidence for and against it was of equal weight.
The verisimilitude approach is not problem-free. To illustrate, I discuss two problems in detail: migraine as a pure CNS disorder, possible aura in cluster headache, and cortical spreading depression (CSD).
The theory that
migraine is a dysfunction of the sensory modulatory network [
7] can be re-formulated as
migraine is a pure human brain disease. Many good arguments exist for both sides and the CT
v(
a) and CT
f(
a) will still be 1.0 with the facts used in my analysis (Table
1), and verisimilitude will be 0. However, when using my prerogative as author and using our “natural instincts” (see vignette) combined with Popper’s falsification theory [
8], I believe that the verisimilitude should be negative.
Thus, the theory that migraine is a brain disease would predict that there is no non-brain disorder associated with it. The main falsifying argument of this prediction is the cardiovascular comorbidity associated with migraine [
56]. For example, there is an association between cervical arterial dissection and migraine, mainly migraine with aura [
52,
53]. Additionally, migraine, particularly migraine with aura, is a risk factor for ischemic stroke [
47,
56]. The arteries of the systemic circulation were also investigated [
56,
120,
122]. Migraineurs with recent onset (<6 years) had decreased brachial arterial diameters and compliances [
56]. Decreased flow-mediated dilatation of the brachial artery was also found in two other studies in migraineurs [
120,
122].
Furthermore, some genetic arteriopathies are associated with migraine [
123,
124] and in CADASIL, where the
notch-
3 gene appears to be expressed exclusively in vascular smooth muscles within adult brain [
125]. rCBF changes during migraine were similar in one case to migraine with aura [
6,
126].
Circulating endothelial progenitor cell numbers and functions (i.e. endothelial repair markers) [
127], are reduced, especially in migraine with aura patients [
128]. In two studies [
48,
129], the von Willebrand factor, a plasma marker of endothelial dysfunction, was increased in migraine. Thus, there is good evidence that migraine is associated with endothelial dysfunction, and could be the underlying link between migraine and cardiovascular risk [
49,
128].
I believe that the arguments against the predictions of the neuronal theory of migraine falsify this theory [
7]. Migraine is unlikely to be a brain-only disease. Another argument against the neuronal theory is that no other part of the human body experiences pain without nociceptive input except thalamic pain and other neuronal lesions with sensory signs [
130]. In migraine, there can be allodynia, but no sensory signs [
130]. I believe that, in addition to a clear CNS component, there is also a peripheral component in the headache phase. Regarding the source of pain, Goadsby recently stated “The pain process is likely to be a combination of direct factors, i.e. activation of the nociceptors of pain-producing intracranial structures, in concert with a reduction in the normal functioning of the endogenous pain control pathways that normally gate that pain” [
7]. I agree that there is both a peripheral and central aspect of migraine headache. Because of the pulsating pain in migraine, I believe vascular nociception most likely [
131] even though the verisimilitude of large arterial vasodilation during migraine was zero.
The question of aura in cluster headache
Four recent papers report prevalences of 4 to 28% for aura in cluster headache [
103‐
106]. One may wonder how such a frequent and characteristic phenomenon went unrecognized by Baylor Horton, who described histaminic cephalalgia in 1938 (
n = 181) [
131]. Horton later in 1956 reported seeing 1,176 patients (1,023 men and 153 women) with histaminic cephalalgia [
133]. Aura is not mentioned by Kudrow whose book from 1980 included 495 patients [
132]. However, the cluster headache expert John R. Graham wrote “Now to our surprise we were able to establish that in 20 cluster headache patients brief episodes of scintillating scotoma rarely, but occasionally, did precede the cluster headache attacks” [
107]. However, there are inconsistencies in the prevalences reported. The highest reported prevalence is 28% (
n = 76) [
105] and the lowest is 4% (
n = 101) [
107], a difference of 24% (95% CI 13–34%,
P < 0.0001, Fisher’s exact test). The difference between the 23 [
104] and 4% [
106] prevalence is 19% (95% CI 13–26%,
P < 0.0001). Also, prevalence was significantly different between the two largest studies: 23 (
n = 246) [
104] versus 13% (
n = 230) [
103], a difference of 10% (95% CI 2–16%,
P = 0.01). These differences demonstrate that the method of registering “so-called aura” must have varied considerably.
In contrast, no reports of aura in cluster headache were reported in a large series of 554 cluster headache patients from one Swedish center [
111]. Karl Ekbom, who has a special interest in aura [
110], personally interviewed 427 patients, and observed and questioned about 100 of them during spontaneous or provoked cluster headache attacks [
111].
Confronted with these incomparable data, it is a matter of belief or trust. Both sets of contradictory data cannot be an approximation of the truth and I calculated the verisimilitude to be −0.5. In my opinion, aura must be rare among cluster headache patients.
In conclusion, I believe verisimilitude calculations are suitable for many migraine and cluster headache mechanism problems. Contradictory data concerning a specific problem are common and a verisimilitude calculation enforces a qualitative judgement of the data. Sometimes, the resulting verisimilitude is zero, but both, CT
v(
a) and CT
f(
a), cannot be an approximation of the truth. In some cases, further investigation is needed or a clearer hypothesis should be formulated, and appropriate investigations aimed at falsifying the thesis [
8] should be performed. Finally, positive evidence is never conclusive; but neither is negative evidence, nor would it be a good idea to pretend that it was [
1].