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ORIGINAL RESEARCH article

Front. Neurol., 21 August 2023

Sec. Headache and Neurogenic Pain

Volume 14 - 2023 | https://doi.org/10.3389/fneur.2023.1221209

Which headache disorders can be diagnosed concurrently? An analysis of ICHD3 criteria using prime encoding system

  • Department of Neurology, Rutgers Robert University Medical School, New Brunswick, NJ, United States

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Abstract

Introduction:

Real-life headache presentations may fit more than one ICHD3 diagnosis. This project seeks to exhaustively list all logically consistent “co-diagnoses” according to the ICHD3 criteria. We limited our project to cases of two concurrent diagnoses.

Methods:

We included the criteria for “Migraine” (1.1, 1.2, 1.3), “Tension-type headache” (2.1, 2.2, 2.3, 2.4), “Trigeminal autonomic cephalalgias” (3.1, 3.2, 3.3, 3.4, 3.5), and “Other primary headache disorders.” We also excluded “probable” diagnosis criteria. Each characteristic in the above criteria is assigned a unique prime number. We then encoded each ICHD3 criteria into integers through multiplication in a list format; we called these criteria representations. “Codiagnoses representations” were generated by multiplying all possible pairings of criteria representations. We then manually encoded a list of logically inconsistent characteristics through multiplication. All co-diagnoses representations divisible by any inconsistency representations were filtered out, generating a list of co-diagnoses representations that were logically consistent. This list was then translated back into ICHD3 diagnoses.

Results:

We used a total of 103 prime numbers to encode 578 ICHD3 criteria. Once illogical characteristics were excluded, we obtained 145 dual diagnoses. Of the dual diagnoses, two contained intersecting characteristics due to subset relationships, 14 contained intersecting characteristics without subset relationships, and 129 contained dual diagnoses as a result of non-intersecting characteristics.

Conclusion:

Analysis of dual diagnosis in headaches offers insight into “loopholes” in the ICHD3 as well as a potential explanation for the source of a number of controversies regarding headache disorders. The existence of dual diagnoses and their identification may carry implications for future developments and testing of machine-learning diagnostic algorithms for headaches.

Introduction

In clinical practice, patients’ headache profiles may satisfy more than one ICHD3 criteria. These “co-diagnoses” can be a source of diagnostic challenges and uncertainties. Consider the cases where headache differential diagnosis lies between cluster headache and paroxysmal hemicrania and when an indomethacin trial cannot be attempted. In these cases, management may be challenging (1, 2). A similar diagnostic dilemma exists between cluster headaches and migraines with aura: should we consider cluster headache cases with aura symptoms a special subtype of cluster headache or a subtype of migraine with aura? Or do these cases necessarily imply the co-existence of two separate headache disorders? (see de Coo et al., Rozen vs. Peng et al.) (3–6). Finally, in the cases of intractable headaches with an identifiable date of onset and lack of photo-phobia, phono-phobia, or nausea: should we consider these new daily persistent headaches or chronic tension-type headaches? (Lobo et al. vs. Nierenberg et al.) (7, 8). The reader may have ready answers for each of the scenarios above; however, one has to agree that those opinions are not likely shared among our colleagues. It is not the goal of this article to weigh in on each of these issues, but rather to identify the conditions of possibilities that give rise to their existence.

We can reformulate these dilemmas as the following: In the ICHD3 criteria, what are the headache disorders that can be diagnosed without logical contradictions? Or equivalently: Which headache presentations require more than one ICHD3 diagnosis to fully account for the clinical description? We call these sorts of questions “co-diagnosis” problems. (When co-diagnosis is restricted to two diagnoses, we use the term “dual diagnosis.”) The answer to the co-diagnosis problem is fundamental to headache classification as a scientific endeavor—it forces us to examine the limitation of our classification project and asks when the current paradigm is unable to assign unique diseases with a unique diagnosis.

We propose that the solution to the co-diagnosis problem can be obtained by a novel technique of automated diagnosis through prime number representation—this technique converts ICHD3 criteria into numerical values and as a result, allows the classification to be manipulated mathematically. This method was first presented at the American Headache Society’s 2022 Denver Scientific Meeting and is described in greater detail in phase 1 of the Methods section (9). We will demonstrate that by encoding ICHD3 as numerical data it is possible to enumerate all possible dual diagnoses for primary headache disorders in ICHD3.

Methods

There are two phases to this study. Since our technique is novel, the first phase will provide an intuitive description and rationale of our methods. Phase 2 then presents an implementation for calculating ICHD3 dual diagnoses of primary headache disorders. Finally, we analyzed the result based on a paradigm of “intersecting characteristics” outlined below.

Phase 1: automated diagnosis method’s theoretical construction

We will first demonstrate that any ICHD3 criteria can be readily translated into numerical data through prime number representations. Let us consider as a motivating example the migraine criteria taken from ICHD3 below. [The demonstration here is an adaptation of a more formal mathematical treatment that is available in Supplementary material (10)].

ICHD3 Criteria for Migraine without aura:

  • At least five attacks fulfilling criteria B–D.

  • Headache attacks lasting 4–72 h (when untreated or unsuccessfully treated).

  • Headache has at least two of the following four characteristics:

    • unilateral location

    • pulsating quality

    • moderate or severe pain intensity

    • aggravation by or causing avoidance of routine physical activity (e.g., walking or climbing stairs)

  • During headache at least one of the following:

    • nausea and/or vomiting

    • photo-phobia and phono-phobia

  • Not better accounted for by another ICHD-3d diagnosis.

Notice that each of the above statements is either true or false based on specific conditions. For example, if a patient’s headache attacks last 4 to 72 h, then statement B is true. The conglomerate of all the components of the criteria—i.e. statements A to E—allows the user of ICHD3 to determine if a diagnosis is true or false. For this article, we call each of the conditions in a statement a “characteristic.” For example, in the statement D2: “photo-phobia” and “phono-phobia” are characteristics. According to D2, both characteristics need to be true in order for statement D2 to be true.

Viewed this way, ICHD3 criteria are propositional statements in disguise. A propositional statement, or simply a proposition, is a declarative sentence that is either true or false, but not both (11). When combining multiple propositional statements, two basic “operators” allow for calculation/derivation of the resultant statement’s veracity: the AND operator—also called conjunction and conventionally denoted by —and the OR operator—also called disjunction and denoted by When an AND operator is applied to two statements, the result is true only if both statements are true; when an OR operator is applied to two statements, the result is true as long as one of the two statements is true. (For a more thorough introduction to propositional logic, we refer the readers to A Logical Introduction to Proof by Daniel Cunningham.)

Since all criteria are logical statements in disguise, one can translate the example of migraine without aura above into the following propositional logic statement: (We use the alphanumeric designation of the criteria as short-hand for each characteristic.)Now any logical statement can be translated into its disjunctive normal form (the disjunctive normal is simply a series of logic AND statements which are connected by OR) (12). Therefore one can translate the above into the following equivalent logical statement:

Given any criteria in disjunctive normal form, we propose the following algorithm:

  • Step 1: Each characteristic in the ICHD3 is assigned a unique prime number (Table 1). Negations crucial to diagnostic criteria are also assigned a prime number.

  • Step 2: If AND is used between two characteristics, then the corresponding prime numbers for those two characteristics are multiplied together. These are called encodings.

  • Step 3: All encodings that are separated by OR in the disjunctive normal form are then combined in a list.

  • Step 4: We do not encode the ubiquitous criteria “Not better accounted for by another ICHD-3 diagnosis,” given that it is recursively referring to the totality of ICHD3 encodings, creating a logical impasse.

Table 1

2 1 min to 24 h with severe intensity
3 1 to 14 days per month
5 1 to 600 s
7 15 min up to 4 h after waking
11 15 to 180 min
13 1–6 cm in diameter
17 2 to 30 min
19 30 min to 7 days in duration
23 4 to 72 h
29 Abrupt explosive intensity just before or with orgasm
31 Aggravated by physical activity
37 At least one aura symptom is positive
41 At least one aura symptom is unilateral
43 At least one aura symptom spreads gradually over 5 min
47 Between 1 s to 2 h
53 Bilateral location
59 Brainstem aura
61 Brought on by cold stimuli
67 Brought on by exercise
71 Brought on by sex
73 Brought on within 1 h of compression
79 Brought on within 1 h of traction
83 Clearly remembered onset
89 Conjunctival injection
97 Constant
101 Developing only during sleep and causing wakening
103 Each individual aura symptom lasts 5–60 min
107 Every other day to 8 per day
109 Eyelid edema
113 Fixed in size and shape
127 Forehead and facial sweating
131 Fully reversible
137 Greater than 1 per day
139 Greater than 15 days per month
149 Greater than 2 episodes
151 Greater than 20 episodes
157 Greater than 5 episodes
163 Greater than 5 min
167 Greater than 5 per day
173 Greater than 8 days per month
179 Hours to days
181 Increasing in intensity with increasing sexual excitement
191 Indomethacin responsive
193 Irregular frequency
197 Lacrimation
199 Less than 12 days per year
211 Less than 48 h
223 Max within 1 min
227 Maximal at site of compression
229 Maximal at site of traction
233 Mild to moderate pain
239 Miosis
241 Moderate to severe
251 More than 1 episode per day
257 More than 10 episodes
263 More than 3 months
269 More than 10 days per month
271 Motor aura
277 Nasal congestion
281 Nausea/vomiting
283 No conjunctival injection
293 No eyelid edema
307 No forehead and facial sweating
311 No lacrimation
313 No miosis
317 No nasal congestion
331 No nausea/vomiting
337 No orbital or supraorbital or temporal pain
347 No phonophobia
349 No photophobia
353 No ptosis
359 No restless
367 No rhinorrhea
373 Nonpulsating
379 Not aggrevated by activity
383 Orbital or supraorbital or temporal pain
389 Phonophobia
397 Photophobia
401 Provoke by cough
409 Provoke by valsalva
419 Ptosis
421 Pulsating
431 Relieve by triptan or ergot
433 Resolve within 1 h after removal of compression
439 Resolve within 1 h after removal of traction
443 Resolve within 30 min after removal of cold
449 Restless
457 Retinal aura
461 Rhinorrhea
463 Round or elliptical
467 Sensory aura
479 Severe
487 Sharply contoured
491 Single or series of stabs
499 Speech and/or language aura
503 Sudden
509 The aura is accompanied or followed within 60 min by headache
521 Two or more aura symptoms occur in succession
523 Unilateral
541 Unremitting within 24 h
547 Up to 72 h with mild intensity
557 Up to few seconds
563 Visual aura

Prime number assignments for headache characteristics.

For example, in migraine without aura the first conjunction in the distinctive normative form, when excluding criteria E, is . This is therefore encoding as:

Repeating this procedure for the totality of migraine without aura criteria yields:

[7580756461,13242732241,16451185183,102951563551,127894697713,223417708453,319149 8470081,3964735629103,4166259653173,6925948962043,7277988854713,9041302068919,538 43667737173,56580493999543,70288832213209,122786715194029,1669153699852363,17539 95313985833,2178953798609479,3806388171014899,29591598361760989,9173395492145906 59].

In other words, this algorithm ensures that each numerical identification—encoding—uniquely describes a class of disease presentation sharing similar characteristics. For example, the encoding 223417708453 describes situations that are true for characteristics 157, 23, 523, 421, and 281. Notice that in a circumstance where an arbitrary additional characteristic, let us call it x, is true in addition to 157, 23, 523, 421, 281, then the new number x*157*23*523*421*281 will divide our encoding of 223417708453 without remainder. We will see how this property can be exploited to automate the diagnosis below.

Now a patient’s headache profile, thought of as a collection of headache characteristics, can be expressed using only logical conjunction. Therefore, a patient profile can be expressed as an integer. For example, a patient who has the phenotype of the following characteristic: five headaches, each lasting 4 to 72 h, unilateral, pulsating, with nausea, and photophobia can be represented as 157*23*523*421*281*397 = 8869683025841.

We now observe that a patient profile, represented/encoded as a number, must divide without remainder at least one number in its corresponding diagnosis’ encoding, assuming that a diagnosis exists. This observation forms the basis for automated diagnosis. For example, the encoding of a migraine without aura patient’s profile (such as 88696830255841 above) must be divided by at least one number in the migraine without aura encodings (in this case, 223417708453) without remainder.

How this method works can be understood intuitively: Consider a patient profile satisfying a migraine diagnosis. Then this patient’s profile, when translated into a propositional statement, must satisfy one of the many conjunctions in the migraine criteria’s disjunctive normal forms (Since that is the implication of the OR operator). Encoding both the patient’s profile and the conjunction that it satisfies using our algorithm implies that both must share at minimum a collection of prime numbers. Since both sets of prime numbers are “bundled” together by multiplication in the algorithm, one of the two encodings must divide the other without remainder. The bigger of the two encodings must be the patient profile since it has more “variables” to encode than those in the criteria. Therefore, the patient profile’s encoding must be divisible by the encoding of one of the conjunctions in the disjunctive normal form. Notice we use prime numbers as building blocks for encoding since they have the property of not being able to be divided by each other.

A caveat: although theoretically possible, in practice logical conflicts cannot exist within a patient’s clinical profile unless there exists more than one headache diagnosis—for example, it makes no sense to be both photophobic and not photophobic at the same time in either the criteria or user encoding. We will apply this observation directly below for a dual-diagnosis problem below.

Armed with the prime number automated diagnosis above, we can now tackle the uniqueness problem as follows: To obtain all possible combinations of dual diagnoses, we multiplied all the encodings of each ICHD3 diagnosis by those from another. This list, let us call it M, represents patient profiles that satisfy two ICHD3 diagnoses concurrently. Not every pairing of two ICHD3 encodings is possible as some of these pairings would contain characteristics that are contradictory. This contradiction is manifested by the co-occurrence of two logically contradictory characteristics in the same patient profile—if A and B are logically contradictory characteristics, then its encoding is simply the prime representation of A multiplied by the prime representation of B. Therefore, to obtain a logically consistent list of dual diagnoses, we simply eliminate from the list M those that are divisible by A*B.

Phase 2: implementation of automated diagnosis for the purpose of extracting dual diagnoses

Due to the limitations in computational power, we only included ICHD3 primary diagnosis up to two layers deep in terms of ICHD3 classification. ICHD3 criteria for “Migraine” (1.1, 1.2, 1.3), “Tension-type headache” (2.1, 2.2, 2.3, 2.4), “Trigeminal autonomic cephalalgias” (3.1, 3.2, 3.3, 3.4, 3.5), and “Other primary headache disorders” are included in this study. We excluded “Complications of migraine”(1.5) and “Episodic syndrome that may be associated with migraine” (1.6) since these diagnoses require diagnoses of migraine as the first assumption. We also excluded “probable” diagnosis criteria.

We then encoded all included criteria into their numerical encodings (Table 2). All possible take-two combinations encodings in Table 2 are multiplied together. We called this list M’ which represents the list M that was described in the last section.

Table 2

Migraine without aura:
7580756461,13242732241,16451185183,102951563551,127894697713,223417708453,3191498470081,3964735629103,4166259653173,6925948962043,7277988854713,9041302068919,53843667737173,56580493999543,70288832213209,122786715194029,1669153699852363,1753995313985833,2178953798609479,3806388171014899,29591598361760989,917339549214590659.
New daily persistent headache:
1145520433.
Primary exercise headache:
2106413.
Primary thunderclap headache:
17411171.
Cold-stimulus headache:
4026427.
External compression headache:
1069111207.
External traction headache:
1183350401.
Cluster headache:
1577982193416431,1932584933510011,2251727399594233,3492836989921763,4237502744118281,4911247950296083,7428927404960501,7960831515100871,8173593159157019.
Paroxysmal Hemicrania:
699200435231955421,856324128542507201,997735452522003803,1547668379108935033,1877628135061093771,2176163152351142153,3291741374856059791,3527426914821887461,3621701130808218529.
Short lasting unilateral neuralgiform headaches:
444401003390335,544266397410635,634145252028905,983674131099955,1193391458542585,1383135707181155,2092180004725285,2301897332167915.
Hemicrania continua:
54659995058027,66943140014887,77997970476061,120988977825071,146783582234477,170121557652511,257331886846217,275756604281507,283126491255623.
Migraine with aura:
75121389451,179941932871,188719588133,209121705769,345049093919,581872457273,594604896163,635348700611,716836309507,826512945899,866830650577,889227610013,910191718697,932604566599,954591314731,960542072261,1033426681907,1057790375783,1393787513933,1424286146623,1461777148759,1493763519629,1521881771231,1596119906413,1619807110787,1655251467697,1717073020447,1768673409809,1800832679981,1995517294033,2233913264179,2286579195751,2475417400847,2533776946643,2596169469181,2657375822089,4084418344297,4180711114693,4283658263531,4384648242239,4746756454183,4858664268427,6887746063999,7038462608069,7050129075331,7204398858161,7223733676877,7381802247487,7394037810713,7520755549093,7555832948803,7698062163217,7887621673439,8004677858161,8073577390691,8179834922891,8193393249709,8372679754079,8485341431141,8685388773329,8740337530027,8899260525343,8946396568063,9109066274467,9861342744299,10093830196031,10260855840551,10502762068619,11299697190653,11370137553043,11638195805767,11924778409289,12205912674341,12521286076129,13132080518867,17303362063217,17681991430027,17711299872173,18098855668063,18893605403819,19173995799781,19339034214911,19593558071111,19626034993489,20055488713259,20109312668063,20549341391653,20583402554147,20936157339367,21033805235857,21316833351403,21429740616523,21819391308607,21957433307141,22475093817329,23621355875879,24178244423051,24773617138117,25357670980273,31455913801007,51901998960457,57513025875101,60318539332423,87524773154719,89439976068389,95568625392133,96986910793067,99109162670377,101717979612241,103943755971371,105900368677769,107825924039621,111066240320587,119482780692553,125311209019019,144483943052083,243650044187461,248981555001191,266042389605127,300164058812999.
Chronic migraine:
47943440512446421,83751819318423001,104043233975143063,651102853410965911,808852238322886393,1412974242049523533,20184188455739943241,20663622860864407451,25074419388009478183,26348930066400847453,36097034126240313431,43802201503535229523,44842633843286660153,46028628871181563393,57180458193890635759,74589881356425382327,178668785574693357667,187384336090532058041,207642102154373361613,280625329820126307641,340526792333935171453,342607760128665739163,348615314717164035383,357835469611443767023,444531949184762684449,577755521692989825821,590397874465265314351,608991898323344642723,630853403336546877647,711764461079110004239,776547512891224440469,820665099843083049623,860697543737867588629,882936037451639990801,903751818295293585869,926006088059037063523,947837272846283516887,953745926844664084697,1026114854335689719039,1050306167208043897091,1383926017078557024641,1414208862091216915771,1451434603277511025843,1483194660242007984833,1511113966131728567387,1584826842528398253601,1608346452280485190799,1643540028916819658869,1704924174212751870619,1756159474153089956693,1788091207101178791137,1981398364625630552341,2218107606280949245183,2270400909375981447427,2457903023176187001419,2515849656335547009311,2577800731623805879537,2638574029815329790253,4055519765243973517069,4151131233186856979161,4253349997694899054487,4353625439683776831803,4713171619067320573891,4824287649379320273079,6839013035854228403323,6988663211693489418713,7000247134931341843087,7153425409218679738997,7172623427847117593729,7329573612263903536699,7341722604927992664701,7467543774379124667961,7502372990156176311631,7643595886938161005909,7831814202397618554203,7948042176803562738997,8016454222886363981807,8121959948724866081207,8135422346001289168993,8313440340443330507483,8425304899750395166457,8623936842377123539733,8678496818873036776279,8699385224423915536871,8836295382665048589211,8883097922657862790651,9044616688346739322159,9791570559169378166423,10022413087086927356987,10188256971222665177027,10428451634591372411063,10556330562351990315043,10807074756232085096873,11092899557954756777713,11219748183226937444081,11289690157300791142111,11356388858618765252243,11555851811303953212259,11840406750339854124653,12119551899660243612857,12432693932764984735333,13039166807534008380959,13780490424727643217919,17180935187633793305909,17556885629376327076279,17585986704827517313121,17970800418281073490651,18759927042952435141463,18878748848023683924413,19038333586296906095737,19202204301332453258747,19454927319038632706147,19487174456700762428053,19838339043479253822383,19913589652689838192343,19967032785628462490651,20403948163869785521081,20437768332637384985519,20788027263812157859459,20884984269894220543189,21166009870104651271831,21278118279854880638071,21665012067435212794939,21802077374242019218457,22316075269116094327733,23454227153359208166083,24007175534184965529527,24072972899627957654539,24598335794986486613209,24644777481566864012129,25178257267559841896821,31233353050604717749739,32148238864619339782937,51534775553466102497389,57106102640327302767377,59891766183757902902371,77006246582692837154477,80762648855019317015671,86905507114147634100763,88807159348592877735353,89493746028534918855203,94892446498817657366041,96300697072433864814359,98407933332224540193229,100998292051576980171157,103208320324040371422167,105151089363554701405613,107063020799267216627417,110280410795923223425399,118637401426215023830381,124424591739688927431863,143461672486675906952191,146767047495926058896243,147663944615454933579253,154227087402532263586913,187147950606785090153029,191593270098632716997519,241926141425870440875097,247219930078515308290307,249012629849678614928851,254461483894529350485281,264160053766978884018979,271897816838051704265857,298040301143906035476323,306770482725096411827009,334691978056117733842139,353706658032368794387513,370960641351020930699099,380545432141656836035231,389517033685271535509539,399108623953444974378413,408517864596748195778297,411064494470050220504407,442255502218682268905809,452681958066666919646221,596472113360858077620271,609524019561314490697301,625568314012607252138333,639256898564305441463023,651290119402775012543797,683060369129739647302031,693197320932889117234369,708365752463149272972539,734822319085696056236789,756904733359981771334683,770667310260608058980047,853982695153646768058971,956004378307089124673873,978542791941048003841037,1059356202988936597611589,1084331201880620761013041,1111032115329860334080447,1137225406850407139599043,1747929018820152585856739,1789137561503535358018391,1833193849006501492483897,1876412564503707814507093,2031376967818015167347021,2079267976882487037697049,2947614618453172441832213,3012113844239893939465303,3017106515155408334370497,3083126351373250967507707,3091400697402107682897199,3159046226885742424317269,3164282442723964838486131,3218511366757402731891191,3233522758757311990312961,3294389827270347393546779,3375511921233373596861493,3425606178202335540507707,3455091770064022876158817,3500564737900417281000217,3506367031126555631835983,3583092786731075448725173,3631306411792420316742967,3716916779064540245624923,3740432128934278850576249,3808443309928635941949941,3828615204665538862770581,3898229792677444647850529,4220166911002001989728313,4319660040534465690861397,4391138754596968691298637,4494662654508881509168153,4549778472373707825783533,4781039709478500171194303,4835711466970810038398911,4865856457796640982249841,4980572130672003834483629,5103215309396477127725443,5223526868753564997141367,5358491085021708420928523,5619880894047157612193329,5801586468810337794743899,5939391373057614226923089,7404983065870164914846779,7567017706261196969876249,7579560269780659961955151,7745414980279142674470581,8085528555512499545970553,8205521775693966527262647,8276150053874287354519957,8385073674505650696349357,8398972190838028606490843,8582757140309320260899833,8605791130605867333470581,8794101658627877559585911,8808678151366712928758689,8959639750703040037426829,9001428220324409054114459,9122550254015104698159161,9170868978617453555008601,9337620201064576714618709,9396695348298310283154967,9618228440989036655252923,10108771903097818719581773,10347092655233720143226137,10375451319739649749106309,10601882727639175730293079,10851828882318291857529851,13461575164810633350137509,22211488263543890176374659,24612730237981067492739487,25813351225199656150921901,37456273566197630297428853,38275885679243530303937143,40898644440990410324763671,41505600438218995734988729,42413819266188776823281699,43530263874229678453768667,44482786059661400082953977,45320119515692076305819203,46144161964484170366416727,47530857053042909296346969,51132720014698675270894211,53626999039805927723132953,61831980841757315896394321,80660766711524373855955499,104270166954550160017166807,106551789863840097873122317,113852983173567899012179949,128455369793023501290295213,2500483768057255589534620469.
Primary headache associated with sexual activity:
613582,3829598,167814677,1047395053.
Primary stabbing:
14937586453,15465416363,16204378237,16415510201,16521076183,16732208147,18632395823,19371357697.
Nummular:
331231589.
Hypnic headache:
14155130507,14655311797,15355565603,15555638119,15655674377,15855746893,17656399537,18356653343, 17956508311.
Primary cough:
1412526109,1440706181.
Infrequent tension type headache:
1378253359942681,1386197183342927,2206388426002661,2219105362175587,2241879928833803,2254801426982701,9699783080351321,9755689611073807,9855811762608983,9912617594093761,15777758744434123,15868696835180141,514088503258620013,517051549386911771,522358023418276099,525368732486969333,836221213455008519,841040932264547473,3676217787453150659,3697406362596972853,194839542735016984927,195962537217639561209.
Frequent tension type headache:
21262771073163,21385323067821,34038685022703,34234873409001,34586224191969,34785568423623,149641766231883,150504254798061,152048872391109,152925234768003,243408709879329,244811641924743,7931013610289799,7976725504297233,8058590236728777,8105037442704159,12900661623604437,12975017022011379,56714229401883657,57041112568465119,3005854158299833821,3023178966128651307.
Chronic tension type headache:
5029577936481697,5058566858305799,8051641932650957,8098049090764219,8181158961058211,8228312615012437,9281386088971379,9334881109657093,14858184597366199,14943822548936033,15097190247725977,15184205753476559,35396840949201377,35600857323548359,35966227130689871,36173525269771657,57576835707070051,57908690667917717,65319943607289139,65696427432115013,66370666560757597,66753206425661099,106250037026448857,106862429170693519,1876032570307672981,1886845438148063027,1906210037926563163,1917196839297897821,3051572292474712703,3069160605399639001,3461957011186324367,3481910653902095689,3517645327720152641,3537919940560038247,5631251962401789421,5663708746046756507,13415402719747321883,13492724925624828061,24756258627162583681,24898945996771589927,711016344146608059799,715114421058115887233,1312081707239616935093,1319644137828894266131.

Prime number encodings for selected primary headache disorders.

We further generated, by hand, a list of mutually logically exclusive characteristics (Table 3). This list in Table 3 is then encoded as a list of composite numbers. We called this list L’.

Table 3

1 min to 24 h with severe intensity Constant
1 min to 24 h with severe intensity Unremitting within 24 h
1 min to 24 h with severe intensity Up to 72 h with mild intensity
1 min to 24 h with severe intensity Up to few seconds
1 to 14 days per month Constant
1 to 14 days per month Every other day to 8 per day
1 to 14 days per month Greater than 1 per day
1 to 14 days per month Greater than 15 days per month
1 to 14 days per month Greater than 5 per day
1 to 14 days per month Less than 12 days per year
1 to 14 days per month More than 1 episode per day
1 to 14 days per month Unremitting within 24 h
1 to 600 s 15 min up to 4 h after waking
1 to 600 s 15 to 180 min
1 to 600 s 30 min to 7 days in duration
1 to 600 s 4 to 72 h
1 to 600 s Greater than 5 min
1 to 600 s Constant
1 to 600 s Hours to days
1 to 600 s Unremitting within 24 h
15 min up to 4 h after waking 4 to 72 h
15 min up to 4 h after waking Constant
15 min up to 4 h after waking Unremitting within 24 h
15 min up to 4 h after waking Up to few seconds
15 to 180 min 4 to 72 h
15 to 180 min Constant
15 to 180 min Unremitting within 24 h
15 to 180 min Up to few seconds
2 to 30 min 4 to 72 h
2 to 30 min Constant
2 to 30 min Hours to days
2 to 30 min Unremitting within 24 h
2 to 30 min Up to few seconds
30 min to 7 days in duration Constant
30 min to 7 days in duration Unremitting within 24 h
30 min to 7 days in duration Up to few seconds
4 to 72 h Between 1 s to 2 h
4 to 72 h Constant
4 to 72 h Unremitting within 24 h
4 to 72 h Up to few seconds
Abrupt explosive intensity just before or with orgasm Increasing in intensity with increasing sexual excitement
Aggravated by physical activity Restless
Aggravated by physical activity Not aggrevated by activity
Between 1 s to 2 h Constant
Between 1 s to 2 h Unremitting within 24 h
Bilateral location Unilateral
Brought on by Primary exercise headache Restless
Conjunctival injection No conjunctival injection
Constant Developing only during sleep and causing wakening
Constant Each individual aura symptom lasts 5–60 min
Constant Every other day to 8 per day
Constant Fully reversible
Constant Hours to days
Constant Irregular frequency
Constant Less than 12 days per year
Constant Less than 48 h
Constant Resolve within 1 h after removal of compression
Constant Resolve within 1 h after removal of traction
Constant Resolve within 30 min after removal of cold
Constant Up to 72 h with mild intensity
Constant Up to few seconds
Every other day to 8 per day Unremitting within 24 h
Every other day to 8 per day constant
Eyelid edema NO eyelid edema
Forehead and facial sweating No forehead and facial sweating
Fully reversible Unremitting within 24 h
Greater than 15 days per month Less than 12 days per year
Greater than 8 days per month Less than 12 days per year
Hours to days Resolve within 1 h after removal of compression
Hours to days Resolve within 1 h after removal of traction
Hours to days Resolve within 30 min after removal of cold
Hours to days Unremitting within 24 h
Hours to days Up to few seconds
Hours to days Constant
Irregular frequency Unremitting within 24 h
Irregular frequency Constant
Lacrimation No lacrimation
Less than 12 days per year More than 10 days per month
Less than 12 days per year Unremitting within 24 h
Less than 12 days per year Constant
Less than 48 h Unremitting within 24 h
Less than 48 h Constant
Mild to moderate pain Severe
Miosis No miosis
Moderate to severe Up to 72 h with mild intensity
More than 1 episode per day Unremitting within 24 h
More than 1 episode per day Constant
Nasal congestion No nasal congestion
Nausea/vomiting No nausea/vomiting
No orbital or supraorbital or temporal pain Orbital or supraorbital or temporal pain
No phonophobia Phonophobia
No photophobia Photophobia
No ptosis Ptosis
No restless Restless
No rhinorrhea Rhinorrhea
Nonpulsating Pulsating
Severe Up to 72 h with mild intensity
Unremitting within 24 h Up to 72 h with mild intensity
Unremitting within 24 h Up to few seconds

A list of logically contradicting characteristics.

Any number in list M’ that was divisible by any number in list L’ was then excluded. The resulting list was therefore the totality of all possible patient clinical profiles with dual diagnosis that contains non-contradictory criteria. We then diagnosed these clinical profiles using the automated diagnosis technique discussed in Phase 1. Since multiple duplicates in dual diagnoses are possible – for example, there are multiple ways in which a patient profile may be able to satisfy concurrent diagnoses of cluster and migraine with aura—eliminating the duplicates generates the results presented in Table 4.

Table 4

Intersecting characteristics
1. Dual diagnoses with intersecting characteristics with subset relationships:
Migraine without aura Chronic migraine
Migraine with aura Chronic migraine
2. Dual diagnoses with intersecting characteristics without subset relationships:
Migraine without aura Migraine with aura
Cluster headache Chronic tension type headache
Cluster headache Infrequent tension type headache
Hemicrania continua Chronic tension type headache
Hemicrania continua Nummular headache
New daily persistent headache Chronic tension type headache
Paroxysmal hemicrania Infrequent tension type headache
Paroxysmal hemicrania Short lasting unilateral neuralgiform headaches
Short lasting unilateral neuralgiform headaches Primary headache associated with sexual activity
Short lasting unilateral neuralgiform headaches Primary stabbing headache
New daily persistent headache Hemicrania continua
New daily persistent headache Nummular headache
New daily persistent headache Primary thunderclap headache
Chronic tension type headaches Chronic Migraine
Non-intersecting characteristics
Migraine without aura Cold stimulus headache
Migraine without aura External compression headache
Migraine without aura Primary exercise headache
Migraine without aura Nummular headache
Migraine without aura Primary headache associated with sexual activity
Migraine without aura Primary thunderclap headache
Migraine without aura External traction headache
Cluster headache Chronic Migraine
Cluster headache Primary Cough Headaches
Cluster headache Hypnic headache
Cluster headache Migraine with aura
Cluster headache Migraine with aura
Cluster headache Nummular headache
Cluster headache paroxysmal hemicrania
Cluster headache Primary headache associated with sexual activity
Cold stimulus headache Cluster headache
Cold stimulus headache External compression headache
Cold stimulus headache frequent tension type headache
Cold stimulus headache Hypnic headache
Cold stimulus headache infrequent tension type headache
Cold stimulus headache Migraine with aura
Cold stimulus headache Nummular headache
Cold stimulus headache paroxysmal hemicrania
Cold stimulus headache Primary headache associated with sexual activity
Cold stimulus headache Primary stabbing headache
Cold stimulus headache Short lasting unilateral neuralgiform headaches
Cold stimulus headache External traction headache
External compression headache Cluster headache
External compression headache Frequent tension type headache
External compression headache Hypnic headache
External compression headache Infrequent tension type headache
External compression headache Migraine with aura
External compression headache Nummular headache
External compression headache Paroxysmal hemicrania
External compression headache Primary headache associated with sexual activity
External compression headache Primary stabbing headache
External compression headache Short lasting unilateral neuralgiform headaches
External compression headache External traction headache
Primary exercise headache Chronic tension type headache
Primary exercise headache Cluster headache
Primary exercise headache Cold stimulus headache
Primary exercise headache External compression headache
Primary exercise headache Frequent tension type headache
Primary exercise headache Hypnic headache
Primary exercise headache Infrequent tension type headache
Primary exercise headache Migraine with aura
Primary exercise headache Nummular headache
Primary exercise headache Paroxysmal hemicrania
Primary exercise headache Primary headache associated with sexual activity
Primary exercise headache Primary stabbing headache
Primary exercise headache Short lasting unilateral neuralgiform headaches
Primary exercise headache Primary thunderclap headache
Primary exercise headache External traction headache
Hypnic headache Chronic tension type headache
Hypnic headache Frequent tension type headache
Migraine with aura Chronic tension type headache
Migraine with aura Frequent tension type headache
Migraine with aura Hypnic headache
Migraine with aura Infrequent tension type headache
Migraine with aura Nummular headache
Migraine with aura Primary headache associated with sexual activity
Migraine with aura Primary stabbing headache
Nummular headache Chronic tension type headache
Nummular headache Frequent tension type headache
Nummular headache Hypnic headache
Nummular headache Infrequent tension type headache
paroxysmal hemicrania Hypnic headache
paroxysmal hemicrania Migraine with aura
Paroxysmal hemicrania Nummular headache
Paroxysmal hemicrania Primary headache associated with sexual activity
Primary headache associated with sexual activity Chronic tension type headache
Primary headache associated with sexual activity Frequent tension type headache
Primary headache associated with sexual activity Hypnic headache
Primary headache associated with sexual activity Infrequent tension type headache
Primary headache associated with sexual activity Nummular headache
Primary headache associated with sexual activity Primary stabbing headache
Primary stabbing headache Nummular headache
Short lasting unilateral neuralgiform headaches Migraine with aura
Short lasting unilateral neuralgiform headaches Nummular headache
Primary thunderclap headache chronic tension type headache
Primary thunderclap headache Cluster headache
Primary thunderclap headache Cold stimulus headache
Primary thunderclap headache External compression headache
Primary thunderclap headache frequent tension type headache
Primary thunderclap headache Hemicrania continua
Primary thunderclap headache Hypnic headache
Primary thunderclap headache infrequent tension type headache
Primary thunderclap headache Migraine with aura
Primary thunderclap headache Nummular headache
Primary thunderclap headache paroxysmal hemicrania
Primary thunderclap headache Primary headache associated with sexual activity
Primary thunderclap headache Primary stabbing headache
Primary thunderclap headache External traction headache
External traction headache Cluster headache
External traction headache Frequent tension type headache
External traction headache Hypnic headache
External traction headache infrequent tension type headache
External traction headache Migraine with aura
External traction headache Nummular headache
External traction headache Paroxysmal hemicrania
External traction headache Primary headache associated with sexual activity
External traction headache Primary stabbing headache
External traction headache Short lasting unilateral neuralgiform headaches
Chronic migraine Cold stimulus headache
Chronic migraine External compression headache
Chronic migraine Primary cough headache
Chronic migraine Primary exercise headache
Chronic migraine Hypnic headache
Chronic migraine Nummular headache
Chronic migraine paroxysmal hemicranias
Chronic migraine Primary headache associated with sexual activity
Chronic migraine Primary stabbing headache
Chronic migraine Short lasting unilateral neuralgiform headaches
Chronic migraine Primary thunderclap headache
Chronic migraine External traction headache
Cold stimulus headache Primary cough headache
Primary cough headache External compression headache
Primary cough headache Primary exercise headache
Primary cough headache Frequent tension type headache
Primary cough headache Hypnic headache
Primary cough headache Infrequent tension type headache
Primary cough headache Migraine with aura
Primary cough headache Nummular headache
Primary cough headache Paroxysmal hemicranias
Primary cough headache Primary headache associated with sexual activity
Primary cough headache Primary stabbing headache
Primary cough headache Short lasting unilateral neuralgiform headaches
Primary cough headache Primary thunderclap headache
Primary cough headache External traction headache

Logically possible dual-diagnoses, classified.

Analysis of results as “intersecting” vs. “non-intersecting” characteristics

We will now introduce a paradigm to interpret the results through the concept of “intersecting characteristics”: We defined a dual diagnosis pair as having “intersecting characteristics” if there exists at least one characteristic shared between the two diagnoses. If this does not exist then we described the pair as having “non-intersecting characteristics” [Non-intersecting characteristics are “less interesting” in the sense that it is always possible to obtain dual diagnosis whose characteristics are non-intersecting. We previously put forth this notion in a preprint (13)]. For example, primary stabbing headaches and SUNCT are a dual diagnosis pair with intersecting characteristics given that each contains duration measured in seconds. On the contrary, cold-induced headache and nummular headache are a dual diagnosis pair with non-intersecting characteristics as the characteristics in their criteria do not overlap.

We then classified our results through the following. First, we separated those with intersecting characteristics from those with non-intersecting characteristics. We further differentiated those with intersecting characteristics due to a subset relationship vs. those with intersecting characteristics without a subset relationship. For example, chronic migraine is a subset of migraine without aura since chronic migraine is defined as the existence of migraine without aura or migraine with aura greater than 15 days per month. This would be an example of an intersecting characteristic that contains a subset relationship.

Software instrumentation

The above methods were implemented through custom code written by the author in Haskell Programming Language (Haskell 2010) via the Glasgow Haskell Compiler. The code is available for review upon inquiry to the author.

Results

A total of 103 prime numbers were used to encode characteristics from the included ICHD3 diagnosis criteria (Table 1). A total of 578 encodings were generated (Table 2). A total of 99 pairs of illogical characteristics were found (Table 3). Once illogical characteristics were excluded, a total of 253,842 composite numbers representing unique dual-diagnosis clinical profiles were obtained. A number of profiles, although unique, yielded duplicate dual diagnoses; once these duplicates were removed, we obtained 145 possible logical dual diagnoses (Table 4).

Using our classification schema above, we obtained the following: 2 dual diagnoses with intersecting characteristics due to subset relationships and 14 dual diagnoses with intersecting characteristics without subset relationships. The remaining 129 dual diagnoses were the result of non-intersecting characteristics. This breakdown of results is shown in Table 4. The intersecting diagnosis that are subsets of each other contains only two pairs of dual diagnosis: migraine with or without aura and chronic migraine. This is to be expected given that we defined chronic migraine through the existence of migraine with aura or migraine without aura.

Discussion

In clinical practice, patients with two concurrent ICHD3 diagnoses are common. Indeed, when managing secondary headaches with etiology which cannot be removed, it is recommended that one treat the phenotype of the disease; some would even suggest that secondary headaches may be triggers of underlying primary headaches and therefore should be treated according to the primary headache it provokes (14). Indeed, this is the preferred treatment method for post-traumatic headaches (15). Furthermore, medication overuse headache is by definition a co-diagnosis according to the ICHD3 (16).

Therefore, secondary headaches with a primary headache phenotype are a non-controversial manifestation of the dual diagnosis problem. In this way, the prevalence of co-diagnosis as a result of secondary headache is essentially the prevalence of secondary headaches in general – approximately 12.9% of headache patients seen at a tertiary headache center in one estimate to 18% of all patients with headaches by World Health Organization estimate in 2011 (17).

Dual diagnosis in primary headaches, however, can be a source of controversy as discussed in our introduction. This stems from the fact that primary headache disorders are phenotypically defined; controversies arise not necessarily from a disagreement in regards to pathophysiology, but rather toward an a priori definition. In other words, the problem is a Kantian one: What are the conditions of possibilities of being diagnosed with a specific kind of primary headache disorder? What are the redundancies in the contemporary classifications of headache disorders? And finally, how do our contemporary definitions of primary headaches inadvertently enable diagnostic uncertainties through the possibility of co-diagnosis? The results presented here may provide some answers. Our discussion will be organized around a few canonical diseases.

The migraine/TTH dilemma

While the split between migraine without aura and tension-type headaches is an old one, that migraine with aura and tension-type headache can be co-diagnosed is not surprising; migraine with aura patients can often have a headache that is not phenotypically like migraine without aura—the exemplary case being migraine with aura without headaches. However, this study demonstrates that it is possible to have a migraine with aura diagnosed concurrently with a chronic tension-type headache and chronic migraine. This is due to the “loophole” that allows for the co-existence of migraine with aura and chronic tension-type headache. In this case, if aura occurs greater than 15 days per month, one can obtain diagnoses that are a combination of chronic migraine, migraine with aura, and chronic tension-type headache.

Cluster headaches, TAC, and SUNCT/SUNA

Our results highlight some of the peculiarities of our contemporary classification of TAC. We show that cluster headache can be diagnosed together with hypnic headache and that cluster headache has a non-intersecting phenotypical relationship with migraine with aura. This is, of course, a source of contemporary debate mentioned previously. Indeed, one can make the same argument for any TAC being co-diagnosed with migraine with aura following the same logic. If we use de Coo et al.’s estimate, an aura is prevalent in 7.0% of cluster headaches diagnoses; we can therefore estimate that migraine with aura can be co-diagnosed in approximately 7% of cluster headache patients (4). Our study demonstrates that since cluster headache can be diagnosed together with migraine with aura, it is theoretically possible to have a chronic migraine form of cluster headache with migraine with aura. If a patient contains a co-diagnosis of migraine with aura with 15 days of aura and cluster headache, that person satisfies a chronic migraine diagnosis.

Our data also support the dilemma between paroxysmal hemicranias and cluster headaches in clinical diagnosis. Fortunately, an indomethacin trial can often be used to differentiate the two (16). Nevertheless, a co-diagnosis between cluster headache and paroxysmal hemicranias is possible as cluster headache is not defined as unresponsive to an indomethacin trial.

Short-lasting unilateral neuralgia form headaches can be co-diagnosed with sex headaches and primary stabbing headaches. This is due to the fact that all of these headache types are short lasting in nature and raises the theoretical possibility of subtypes of short-lasting unilateral neuralgia form headaches to be further classified by their provoking characteristics.

New daily persistent headaches and status migrainosus

New daily persistent headaches (NDPH) can be logically diagnosed with chronic tension-type headaches; empirically, multiple researchers of new daily persistent headaches separate migraine vs. tension-type headaches characteristics in NDPH (8). Specifically, Lobo et al. studied NDPH’s primary headache phenotypes; if we interpret this to mean co-diagnoses of a primary headache disorder with NPDH then the prevalence of co-diagnosis of TTH in NDPH was 8.8% whereas the prevalence of co-diagnosis with chronic migraine was 89.7% according to Lobo et al.’s study (7). Even though it may be intuitively obvious what kind of clinical phenomenology a migraine-like NDPH represents, according to the ICHD3 definition, it is actually impossible to diagnose a new daily persistent headache concurrently with either migraine with or without aura. This is due to (1) a limitation of the current study of not including status migrainosus and (2) from an artifact of the classification guideline which suggests that a migraine, both migraine without aura as well as migraine with aura, must not be constant. Indeed, migraine without aura is limited to a 72-h duration according to the classification, and migraine with aura also is limited by the fact that the migraine aura must be reversible. It is only the concept of status migrainosus which allows one to bridge this gap and therefore allows for the possibility of migrainous NDPH.

The concurrent diagnosis of new daily persistent headaches with hemicranias continua, nummular headaches, or thunderclap headaches coincidentally describes the sub-classification of new daily persistent headaches that was presented by Rosen in a prior review article (18). For instance, the lock-sided headache nature of some new daily persistent headaches may be attributed to a cervicogenic cause, of which nummular headache, being lock sided in nature, can be another manifestation. That new daily persistent headache can be concurrently diagnosed with thunderclap headache coincides with Rosen’s proposal of a persistent RCVS subtype of NDPH (18, 19).

Non-intersecting characteristics

Non-intersecting characteristics represent the majority of dual diagnoses. This leads to the question of headache triggers in primary headache disorders. For example, it is possible to co-diagnose migraine without aura with cold-induced headaches, compression headaches, or exercise headaches. These potential co-diagnoses invite the question of whether stimulus-related headaches and migraine can be interpreted as the same entity.

Secondary headaches: post-traumatic headaches and medication overuse headaches

While this project is limited to primary headache disorders, some of the implications of our methodology and results can be translated to secondary headaches. We can examine two such cases: post-traumatic headaches (PTH) and medication overuse headaches (MOH).

Post-traumatic headaches represent approximately 4% of symptomatic headache disorders (20). According to ICHD3, PTH is characterized by combinations of the following: a temporal relationship with the insult, regain of consciousness following the trauma, discontinuation of medication which can hinder the ability to report the existence of headache, and whether there is a resolution of headache within 3 months (see ICHD3 criteria 5.1 and 5.2). Notice that none of these are among the list of characteristics of primary headaches (see Table 1). In the language of this article then, PTH forms a “non-intersecting characteristic” with each of the primary headache disorders. Therefore, PTH can be concurrently diagnosed, at least theoretically, with any of the primary headache disorders. Even though this statement is a theoretical one, we do have some empirical evidence: It is well established that PTH often exhibits migraine or tension-type headache phenotypes (15). Furthermore, we have also observed cases of post-traumatic trigeminal autonomic cephalalgias (21–24). Of note, sub-classifications of acute or posttraumatic headaches do involve nausea or vomiting in 5.1.2 and 5.2.2. Yet, given the fact that these criteria are listed under a logical OR statement, PTH can easily satisfy tension-type headache criteria or migraine criteria as a concurrent diagnosis.

Medication overuse headache has a prevalence of approximately 30 to 50% of patients seen in headache centers (25). Medication overuse headache is unique in that it must be part of a dual diagnosis. This is due to its definitional requirements: (1) An existence already of another headache disorder, (2) occurrence of more than 15 days/month, and (3) regular overuse for more than 3 months of the inciting medication (see 8.2 of ICHD3). “Regular overuse for more than 3 months of medication” is not a characteristic that is within the criteria for any of the primary headache disorders. However, “the occurrence of more than 15 days/month” is a characteristic that is found in primary headache disorders; specifically, this criterion is logically contradictory to two characteristics according to Table 3: “1 to 14 days per month” and “less than 12 days per year.” Therefore, primary headache disorders containing any of these two characteristics cannot be concurrently diagnosed with MOH. Since “1 to 14 days/month” and “no more than 12 days per year” arise from criteria of frequent and infrequent episodic tension-type headaches, respectively, we can therefore deduce that these headaches cannot be concurrently diagnosed with MOH. For the same reason, episodic migraine (i.e., those with less than 15 days per month) cannot carry a concurrent diagnosis with MOH; in other words, MOH diagnosis in migraine implies a concurrent diagnosis with chronic migraine.

Diagnostic uncertainty and co-diagnoses

Our approach in this article can be described as meta-scientific in nature (26). Highlighting a priori co-diagnoses in the ICHD3 leads to a fundamental question: Are co-diagnoses an inevitable by-product of headache taxonomy or should we eliminate them in future classifications? In other words, are co-diagnoses simply the loci of diagnostic uncertainties or are they inevitable by-products of shared pathophysiology between different disorders? For example, when a patient receives a dual diagnosis of both cluster headache and migraine with aura, should that reflect a diagnostic uncertainty between cluster headaches vs. migraine with aura or alternatively an appropriate description of that particular patient’s underlying pathophysiology?

If it is the former, then future revisions and constructions of ICHD may benefit from our meta-scientific project. For example, clarifying, amending, or even adding new characteristics to our current criteria of cluster headaches and/or migraine with aura, may prevent a co-diagnosis of migraine with aura and cluster headache, and as a result, significantly decrease clinical diagnostic uncertainty. If so, our project offers a comprehensive list of co-diagnoses for this kind of future work.

Limitations

First, although phase one of this study constructs an algorithm of automated diagnosis, it is not intended to be a substitute for detailed clinical history taking. Indeed, it is only through careful communication with our patients that accurate input data can be obtained in the first place.

Second, despite our attempt to rule out obvious logical contradictions, this is not a foolproof method. For example, concurrent diagnosis of cold-induced headache with hypnic headache is on paper logically consistent but in practice impossible—it would be unlikely for one to be woken up at night from a hypnic headache while triggering that same headache through a cold stimulus. However, these sorts of occurrences in the data appear to be rare. The only other two instances that follow a similar argument are the compression headache and hypnic headache pairing as well as the primary cough headache and hypnic headache pairing.

This study is also limited by having included only four headache categories—migraine, tension-type headache, trigeminal autonomic cephalalgia, and other primary headaches. Other primary headaches, such as those described in the addendum section of the ICHD3, have been excluded. The future direction for our project will involve the inclusion of other primary headaches as well as secondary headaches.

Status migrainosus is considered a “complication of migraine” in the ICHD3 and therefore excluded based on our inclusion criteria. This proves to be an important omission as it limits the duration of migraine attacks. The complicated relationship of status migrainosus to intractable headaches is not lost for those conducting research on status migrainosus (27). As such, although our omission causes the study to be incomplete, it does show us the importance of rethinking duration in migraine definitions.

Finally, even though the clinical utility of our result may be limited in clinical practice, our project may carry implications for machine learning algorithms in headaches as well as clinical trial design. In most machine learning diagnostic classification algorithms, the goal of classification is binary or, alternatively, organized in sequential layers of binary classification (28, 29). Our study on concurrent diagnosis challenges this principium tertii exclusi approach. This project’s identification of the specific cases in which this assumption is violated will likely improve the data science endeavor to construct automated diagnostic algorithms in the future. Indeed, this same concern can be carried over into clinical trial design: the inclusion of co-diagnosed patients in clinical trials—such as those co-diagnosed with migraine with aura/cluster in a cluster trial—may not be methodologically sound. Our article, therefore, stresses that inclusion/exclusion criteria in clinical trials must take into account the possibility of co-diagnoses in trial design.

Conclusion

Prime number encoding of ICHD3 allows for an exhaustive study of the structure of contemporary headache diagnoses. In our pilot study of this approach, these important results are obtained: (1) Status migrainosus is required for modeling migraine intractability in our classification and (2) the possibility of a dual diagnosis of chronic migraine and migraine with aura allows for loopholes in diagnoses which enable the construction of large concurrent diagnoses in headache diagnoses such as co-diagnoses of chronic migraine, chronic tension-type headaches, and migraine with aura. This may be undesirable in our classification.

Funding

Article processing fee is supported by Rutgers Neurology Department.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Statements

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

PZ was responsible for the entirety of the manuscript, including conceptualization, data analysis, as well as drafting of manuscript.

Conflict of interest

PZ has received an honorarium from Lundbeck Biopharmaceuticals, Board Vitals, and Fieve Clinical Research, collaborates with Headache Science Incorporated without receiving financial support, and has ownership interest in Cymbeline LLC.

Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fneur.2023.1221209/full#supplementary-material

    Abbreviations

  • ICHD3

    International classification of headache disorders, 3rd edition

  • NDPH

    New daily persistent headache

References

  • 1.

    Shah ND Prakash S . Coexistence of cluster headache and paroxysmal hemicrania: does it exist? A case report and literature review. J Headache Pain. (2009) 10:21923. doi: 10.1007/s10194-009-0104-8

  • 2.

    Prakash S Patell R . Paroxysmal Hemicrania: An Update. Curr Pain Headache Rep. (2014) 18:407. doi: 10.1007/s11916-014-0407-6

  • 3.

    Rozen TD . Cluster headache with aura. Curr Pain Headache Rep. (2011) 15:98100. doi: 10.1007/s11916-010-0168-9

  • 4.

    de Coo IF Wilbrink IF Ie LA Haan GD Ferrari MD . Aura in Cluster Headache: A Cross-Sectional Study. Headache. (2018) 58:120310. doi: 10.1111/head.13344

  • 5.

    Applebee AM Shapiro RE . Cluster-migraine: does it exist?Curr Pain Headache Rep. (2007) 11:1547. doi: 10.1007/s11916-007-0014-x

  • 6.

    Peng KP Schellong M May A . Aura in trigeminal autonomic cephalalgia is probably mediated by comorbid migraine with aura. Cephalalgia. (2022) 42:316. doi: 10.1177/03331024211030499

  • 7.

    Lobo R Wang M Lobo S Bahra A . Time to retire 'New daily persistent headache': Mode of onset of chronic migraine and tension-type headache. Cephalalgia. (2022) 42:38595. doi: 10.1177/03331024211044440

  • 8.

    Nierenburg H Newman LC . Update on New Daily Persistent Headache. Curr Treat Options Neurol. (2016) 18:25. doi: 10.1007/s11940-016-0408-3

  • 9.

    Zhang P . No machine learning required: A number theory diagnostic methods for primary headache disorders. American Headache Society 64th Annual Scientific Meeting June 9-12, 2022 Denver, Colorado. Headache. (2022) 62:91129. doi: 10.1111/head.14317

  • 10.

    Zhang P . Disease Diagnosis and Classification as Prime Number Representations. hal-03723482. (2022). Lyon, France. Available at: https://hal.science/hal-03723482/

  • 11.

    Cunningham D . A Logical Introduction to Proof. New York:Springer (2013).

  • 12.

    Weisstein E. W . “Disjunctive Normal Form.” Math World. Mathworld. (2005). Available at: Wolfram.com (Accessed 13 August 2022).

  • 13.

    Zhang P. A Mathematical Interpretation of International Classification of Headache Disorders 3rd Edition. (2021). Available at: https://osf.io/fqr64

  • 14.

    Schankin CJ Straube A . Secondary headaches: secondary or still primary?J Headache Pain. (2012) 13:26370. doi: 10.1007/s10194-012-0443-8

  • 15.

    Ashina H Eigenbrodt AK Seifert T Sinclair T Scher AI Schytz HW et al . Post-traumatic headache attributed to traumatic brain injury: classification, clinical characteristics, and treatment. Lancet Neurol. (2021) 20:4609. doi: 10.1016/S1474-4422(21)00094-6

  • 16.

    International Headache Society . International Classification of Headache Disorders. Cephalalgia. (2018) 38:1211. doi: 10.1177/0333102417738202

  • 17.

    Do TP Remmers A Schytz HW Schankin C Nelson SE Obermann M et al . Red and orange flags for secondary headaches in clinical practice: SNNOOP10 list. Neurology. (2019) 92:13444. doi: 10.1212/WNL.0000000000006697

  • 18.

    Rozen TD . The Three T's of NDPH (How Clinical Observations Have Led to Improved Treatment Outcomes). Headache. (2019) 59:14016. doi: 10.1111/head.13624

  • 19.

    Jamali SA Rozen TD . An RCVS Spectrum Disorder? New Daily Persistent Headache Starting as a Single Thunderclap Headache (3 New Cases). Headache. (2019) 59:78994. doi: 10.1111/head.13495

  • 20.

    Ashina H Porreca F Anderson T Amin FM Ashina M Schytz HW et al . Post-traumatic headache: epidemiology and pathophysiological insights. Nat Rev Neurol. (2019) 15:60717. doi: 10.1038/s41582-019-0243-8

  • 21.

    Putzki N Nirkko A Diener HC . Trigeminal Autonomic Cephalalgias: A Case Of Post-Traumatic SUNCT Syndrome? 2. Cephalalgia. (2005) 25:3869. doi: 10.1111/j.1468-2982.2004.00860.x

  • 22.

    Grangeon L O'Connor E Chan CK Akijian L Pham Ngoc TM Matharu MS . New insights in post-traumatic headache with cluster headache phenotype: a cohort study. J Neurol Neurosurg Psychiatry. (2020) 91:5729. doi: 10.1136/jnnp-2019-322725

  • 23.

    Heir GM DiPede L Kuchukulla M Kalladka M Aziz S . Diagnosis and management of traumatically induced hemicrania continua and neuropathic pain secondary to facial gun shot wound. J Oral Rehabil. (2022) 49:8317. doi: 10.1111/joor.13324

  • 24.

    Matharu MJ Goadsby PJ . Post-traumatic chronic paroxysmal hemicrania (CPH) with aura. Neurology. (2001) 56:2735. doi: 10.1212/wnl.56.2.273

  • 25.

    Vandenbussche N Laterza D Lisicki M Lloyd J Lupi C Tischler H et al . Medication-overuse headache: a widely recognized entity amidst ongoing debate. J Heaache Pain. (2018) 19:50. doi: 10.1186/s10194-018-0875-x

  • 26.

    Ioannidis JPA Fanelli D Dunne DD Goodman S . Meta-research: Evaluation and Improvement of Research Methods and Practices. PLoS Biol. (2015) 13:e1002264. doi: 10.1371/journal.pbio.1002264

  • 27.

    Iljazi A Chua A Rich-Fiondella R Veronesi M Melo-Carrillo A Ashina S et al . Unrecognized challenges of treating status migrainosus: An observational study. Cephalalgia. (2020) 40:81827. doi: 10.1177/0333102420911461

  • 28.

    Kwon J Lee H Cho S Chung C-S Lee MJ Park H . Machine learning-based automated classification of headache disorders using patient-reported questionnaires. Sci Rep. (2020) 10:14062. doi: 10.1038/s41598-020-70992-1

  • 29.

    Cowan RP Rapoport AM Blythe J Rothrock J Knievel K Peretz AM et al . Diagnostic accuracy of an artificial intelligence online engine in migraine: A multi-center study. Headache. (2022) 62:87082. doi: 10.1111/head.14324

Summary

Keywords

headaches classification, International Classification of Headache Disorders, 3rd edition, headache diagnosis, number theory in medicine, automated diagnosis

Citation

Zhang P (2023) Which headache disorders can be diagnosed concurrently? An analysis of ICHD3 criteria using prime encoding system. Front. Neurol. 14:1221209. doi: 10.3389/fneur.2023.1221209

Received

12 May 2023

Accepted

31 July 2023

Published

21 August 2023

Volume

14 - 2023

Edited by

Sait Ashina, Beth Israel Deaconess Medical Center and Harvard Medical School, United States

Reviewed by

Mansoureh Togha, Tehran University of Medical Sciences, Iran; Roberta Messina, Vita-Salute San Raffaele University, Italy; Renato Arruda, University of São Paulo, Ribeirão Preto, Brazil

Updates

Copyright

*Correspondence: Pengfei Zhang,

Disclaimer

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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