Physicians use a variety of resources to remain current in their field of interest, including conferences, electronic media, periodicals, peer-reviewed journals, and textbooks.²² Historically, peer-reviewed journals have been used by physicians to maintain expertise in their particular fields, but this has become increasingly more difficult given the exponential expansion of scientific literature, which is currently doubling in size every 7 years.^20,27,28 Clinical researchers are faced with the increasing challenge of staying up-to-date on standards of practice and cutting-edge research. All neurosurgical subspecialties benefit from discoveries made in other disciplines, such as molecular biology, neurology, oncology, and radiology, and these discoveries may be more pertinent for one subspecialty than another. For this reason, it would be advantageous for researchers to know which scientific journals, including nonneurosurgical journals, contain the most useful information for general and subspecialty neurosurgeons.

In 1934, Samuel C. Bradford first described how information was scattered for a given subject based on the distribution of references.³ Bradford discovered that when equally dividing all references in a given subject into 3 groups, or zones, the citations for the first zone would come from a small “core” group of journals. The second zone would require more journals to achieve the same number of citations, and the third zone exponentially more than the second. In moving from Zone 1 to Zone 3 there is a “diminishing productivity” described by Bradford, which has become known as Bradford’s law of scattering, or Bradford’s distribution. Figure 1 depicts a graphical representation of Bradford’s law. Hjørland and Nicolaisen¹⁰ noted that Bradford’s law has influenced the methodology of building collections, selecting journals indexed in bibliographies, measuring the coverage of bibliographies, solving practical problems related to information seeking and retrieval, and arguing for updated organization of bibliographical work and scientific documentation. Bradford’s law of scattering, Lotka’s law of scientific productivity, and Zipf’s law of word occurrence are the 3 most commonly used principles in bibliometrics.

Graphical depiction of Bradford’s law. Each zone carries an equal number of citations, and zone size is equal to the number of journals in that zone.

Core journals have been identified in many fields by using Bradford’s law of scattering, including environmental and occupational health,²³ nursing,²⁴ physical and rehabilitation medicine,⁷ physical therapy,⁶ physics,²⁶ and science.⁴ In 2013, Madhugiri et al.¹⁹ were the first to apply Bradford’s law of scattering to identify core journals within the field of neurosurgery. They sampled all journal references from the 11 top neurosurgical journals based on impact factor (IF) over a 3-month period, excluding special and focused editions in which many articles about a single specific topic were published. They were able to fit Bradford’s law into 3 zones (p) for a total of 182 journals, with the 6 core journals within Zone 1 being Journal of Neurosurgery, Neurosurgery, Spine, Acta Neurochirurgica, Stroke, and Journal of Neurotrauma.¹⁹ Additionally, in 2014, we applied Bradford’s law to the field of pediatric neurosurgery.¹⁵ We examined all published articles in a 5-year period from the top 25 North American pediatric neurosurgeons based on h-index, as well as the top 25 European pediatric neurosurgeons. Using Bradford’s law of scattering, we were able to identify 9 core journals with a Bradford’s multiplier of 4. These journals are as follows: Journal of Neurosurgery, Neurosurgery, Epilepsia, Child’s Nervous System, Pediatric Neurosurgery, Neurology, Journal of Clinical Oncology, Cancer Research, and New England Journal of Medicine.¹⁵

We recently created productivity profiles for nearly all neurosurgical researchers in the US.¹⁴ Many of these bibliometric indices, particularly the h-index, have been widely applied in neurosurgery.^{1,8,11–14,17,25,29} Using this database, we examined 6 different neurosurgery subspecialties: neurosurgical oncology, peripheral nerve, skull base, spine, stereotactic and functional, and vascular. We identified the top 25 North American neurosurgeons in each of these subspecialties based on their h-index. By applying Bradford’s law to journal articles that were referenced by each of those neurosurgeons over a 5-year period (2009–2013), we identified the core journals for each of the neurosurgical subspecialties. These databases were then combined, including the pediatric neurosurgery database previously reported,³⁰ to create citation density zones and identify the core journals for neurosurgery overall.

Methods

Egghe’s Formulation of Bradford’s Law of Distribution

Bradford’s law uses 3 parameters to model the c:ck:ck² … ck^p−1 sequence using Egghe’s formulation. Parameter c defines the core number of journals. Parameter k defines the Bradford multiplier. These parameters are dependent on the choice of p, which represents the number of zones. They can be solved using the equations below:

[Eq. 1]

[Eq. 2]

The 2 constants in Equation 1, e and γ, represent Euler’s number and Euler’s constant, respectively, where e^γ = 1.781. Y_m and T describe qualities of the database; Y_m is the number of citations of the highest-ranked journal; and T is the cumulative number of journals in the database. Using these equations, a theoretical distribution of Bradford zones can be established for a citation database.

Egghe’s formulation has been the most widely used derivation of Bradford’s law for bibliometric analyses.⁵ Using Egghe’s formulation, one can create a graphical representation of Bradford’s distribution. The following equations are used for this:

[Eq. 3]

[Eq. 4]

[Eq. 5]

Each zone of journals should contain the same number of citations (A/p), where A is the total number of citations. Additionally, a separate analysis based on Bradford’s verbal formulation was performed; the total number of citations was separated into p zones, and the number of journals in each zone was matched to the appropriate citation density. From these counts of journals, c was given as the count of journals from the first zone, and k was a common multiplier between zones.

Results

Egghe’s Formulation of Bradford’s Law

The citation database was ranked in descending order of number of citations per journal (Table 3). The ranked citation density distribution can be seen in Fig. 2. The number of citations in the top journal, Journal of Neurosurgery, was used as Y_m (13,577) and the total number of journals cited was used as T (7458). Using these values in the previously described Egghe’s formulation, we solved for the theoretical citation distribution for 3 to 8 zones (p).

Citation counts for cumulative database of neurosurgery journals.

TABLE 3.

The top 100 journals ranked by the number of times article citations occur within papers by the top 150 academic neurosurgeons from 2009 through 2013

Rank	Journal	No. of Times Cited	Cumulative % of Total Citations	Bradford’s Theoretical % of Total Citations	Difference of Experimental vs Bradford Theoretical (%)
1	Journal of Neurosurgery	13577	7.40	14.32	48.30
2	Neurosurgery	11983	13.94	19.94	30.12
3	Spine	5006	16.66	23.51	29.11
4	Stroke	4995	19.39	26.12	25.79
5	Neurology	2963	21.00	28.19	25.50
6	American Journal of Neuroradiology	2731	22.49	29.90	24.78
7	Int Journal of Radiation Oncology Biology Physics	2510	23.86	31.36	23.91
8	New England Journal of Medicine	2378	25.16	32.63	22.90
9	Acta Neurochirurgica	2185	26.35	33.76	21.95
10	Surgical Neurology	2122	27.51	34.77	20.89
11	Epilepsia	2107	28.65	35.68	19.70
12	Journal of Neuroscience	1830	29.65	36.52	18.82
13	Cancer Research	1809	30.64	37.30	17.86
14	Journal of Neuro-Oncology	1753	31.59	38.02	16.89
15	Journal of Clinical Oncology	1747	32.55	38.69	15.87
16	Neurosurgical Focus	1732	33.49	39.31	14.81
17	Proc of the Natl Academy of Sciences of the USA	1707	34.42	39.90	13.74
18	Cancer	1631	35.31	40.46	12.73
19	Child’s Nervous System	1500	36.13	40.99	11.85
20	Nature	1421	36.90	41.49	11.05
21	Brain	1404	37.67	41.96	10.23
22	Journal of Neurology Neurosurgery and Psychiatry	1358	38.41	42.42	9.45
23	Science	1332	39.13	42.85	8.67
24	Lancet	1318	39.85	43.27	7.89
25	Annals of Neurology	1243	40.53	43.67	7.18
26	Radiology	1056	41.11	44.05	6.68
27	Journal of Neurotrauma	1041	41.67	44.42	6.18
28	Journal of Neurosurgery Spine	1009	42.22	44.78	5.70
29	Journal of the American Medical Association	1001	42.77	45.12	5.21
30	Clinical Cancer Research	882	43.25	45.45	4.84
31	Journal of Biological Chemistry	861	43.72	45.77	4.49
32	Brain Research	856	44.19	46.09	4.12
33	Journal of Cerebral Blood Flow and Metabolism	829	44.64	46.39	3.77
34	Pediatric Neurosurgery	826	45.09	46.68	3.41
35	Neuroimage	825	45.54	46.97	3.04
36	Neuroradiology	809	45.98	47.24	2.67
37	Journal of Neurophysiology	794	46.41	47.51	2.31
38	Neuro-Oncology	764	46.83	47.77	1.98
39	Movement Disorders	762	47.24	48.03	1.63
40	British Journal of Neurosurgery	699	47.63	48.28	1.35
41	Archives of Neurology	684	48.00	48.52	1.07
42	Laryngoscope	659	48.36	48.76	0.82
43	European Spine Journal	654	48.71	48.99	0.56
44	Journal of Clinical Endocrinology and Metabolism	649	49.07	49.21	0.30
45	Experimental Neurology	638	49.42	49.44	0.04
46	Cell	636	49.76	49.65	−0.22
47	Neurologia Medico Chirurgica	605	50.09	49.86	−0.46
48	Stereotactic and Functional Neurosurgery	603	50.42	50.07	−0.70
49	Acta Neurochirurgica Supplement	589	50.74	50.27	−0.93
50	Journal of Clinical Neuroscience	588	51.06	50.47	−1.17
51	Journal of Bone and Joint Surgery Series A	586	51.38	50.67	−1.41
52	Critical Care Medicine	573	51.70	50.86	−1.64
53	Acta Neuropathologica	560	52.00	51.05	−1.87
54	Circulation	557	52.30	51.23	−2.09
55	Oncogene	551	52.60	51.41	−2.32
56	Neurosurgery Clinics of North America	539	52.90	51.59	−2.54
57	Lancet Neurology	532	53.19	51.76	−2.75
58	Neuron	503	53.46	51.94	−2.94
59	Anesthesiology	482	53.73	52.10	−3.11
60	Neuroscience	479	53.99	52.27	−3.29
61	Journal of Neurosurgery Pediatrics	470	54.24	52.43	−3.45
62	Neurological Research	468	54.50	52.59	−3.62
63	Nature Medicine	463	54.75	52.75	−3.79
64	Neurosurgical Review	460	55.00	52.91	−3.96
65	Clinical Neurology and Neurosurgery	455	55.25	53.06	−4.13
66	Clinical Orthopaedics and Related Research	452	55.50	53.21	−4.30
67	Magnetic Resonance in Medicine	439	55.74	53.36	−4.46
68	Journal of Neuropathology and Experimental Neurology	434	55.97	53.50	−4.61
69	Minimally Invasive Neurosurgery	424	56.20	53.65	−4.76
70	Journal of Vascular Surgery	419	56.43	53.79	−4.91
71	American Journal of Roentgenology	418	56.66	53.93	−5.06
72	Neurocritical Care	413	56.88	54.07	−5.21
73	PLoS One	407	57.11	54.20	−5.36
74	Journal of Immunology	406	57.33	54.34	−5.50
75	Journal of Spinal Disorders and Techniques	403	57.55	54.47	−5.65
76	Cancer Cell	379	57.75	54.60	−5.78
77	Blood	359	57.95	54.73	−5.88
78	Clinical Neurosurgery	348	58.14	54.86	−5.98
79	Epilepsy Research	346	58.33	54.98	−6.08
80	Nature Genetics	345	58.52	55.11	−6.19
81	Journal of Trauma Injury Infection and Critical Care	341	58.70	55.23	−6.29
82	Journal of Comparative Neurology	336	58.89	55.35	−6.39
83	Journal of Neurochemistry	334	59.07	55.47	−6.48
84	Clinical Neurophysiology	331	59.25	55.59	−6.58
85	International Journal of Cancer	326	59.43	55.71	−6.68
86	Otolaryngology Head and Neck Surgery	325	59.60	55.82	−6.78
87	British Journal of Cancer	321	59.78	55.93	−6.87
88	Nature Neuroscience	316	59.95	56.05	−6.96
89	Annals of Surgery	308	60.12	56.16	−7.05
90	Journal of Spinal Disorders	303	60.28	56.27	−7.13
91	Journal of Neuroscience Research	299	60.45	56.38	−7.21
92	Journal of the National Cancer Institute	298	60.61	56.49	−7.30
93	Cerebral Cortex	296	60.77	56.59	−7.38
94	Journal of Magnetic Resonance Imaging	292	60.93	56.70	−7.46
95	Cerebrovascular Diseases	290	61.09	56.80	−7.54
96	Canadian Journal of Neurological Sciences	285	61.24	56.91	−7.62
97	Molecular Therapy	282	61.40	57.01	−7.70
98	American Journal of Pathology	279	61.55	57.11	−7.77
99	British Medical Journal	276	61.70	57.21	−7.84
100	Journal of Clinical Investigation	275	61.85	57.31	−7.92

As previously observed in our application of Bradford’s law, the citation distribution expected from Egghe’s formulation again did not fit the observed citation distribution identified by our citation database (Fig. 3), because Egghe’s formulation would predict that all zones carry an approximately equal distribution of citation density, but our distribution did not fit this expectation.³⁰ Therefore, Egghe’s formulation was again abandoned for the verbal formulation of Bradford’s law. A comparison of Bradford’s verbal law with Egghe’s formulation for combined neurosurgery and each subspecialty can be found in Table 4.

Graphical comparison of observed data versus Bradford’s graphical law for cumulative database of neurosurgery journals.

TABLE 4.

Comparison of 4-zone distribution of Bradford’s verbal formulation versus Egghe’s theoretical for all of neurosurgery and its subspecialties

Subspecialty	Zone	Bradford’s Verbal Formulation			Egghe’s Formulation
		Journals	Citations	% Difference from Theoretical*	Journals	Citations	% Difference from Theoretical*
Combined†	1	8	46143	0.63	4	35561	−22.45
	2	39	45738	−0.26	44	56923	24.14
	3	211	45892	0.08	550	63959	39.48
	4	7200	45648	−0.45	6860	26978	−41.17
Neurosurgical oncology	1	5	8016	−2.41	4	7256	−7.30
	2	27	7919	−1.17	29	8824	12.73
	3	141	7828	−0.01	242	9608	22.75
	4	2123	7546	3.59	2021	5621	−28.19
Pediatrics	1	9	6053	−1.73	5	4490	−24.54
	2	36	5928	0.37	37	7200	21.01
	3	160	5944	0.10	265	7557	27.01
	4	2026	5873	1.29	1924	4551	−23.51
Peripheral nerve	1	10	1836	2.22	9	1745	−7.07
	2	44	1884	−0.33	43	1927	2.62
	3	172	1877	0.04	219	2147	14.34
	4	1151	1914	−1.93	1106	1692	−9.89
Skull base	1	6	5996	−1.46	4	5269	−10.84
	2	32	5905	0.08	31	6348	7.42
	3	163	5912	−0.04	246	7257	22.80
	4	2042	5825	1.43	1963	4764	−19.38
Spine	1	3	6714	1.49	3	6714	−1.49
	2	43	6875	−0.87	31	7339	7.68
	3	215	6809	0.10	280	7937	16.45
	4	1995	6865	−0.72	2552	5273	−22.64
Stereotactic & functional	1	7	7108	2.09	6	6449	−11.17
	2	29	7240	0.27	42	9306	28.19
	3	125	7262	−0.03	303	8642	19.04
	4	2359	7429	−2.33	2169	4642	−36.06
Vascular	1	3	11489	12.23	3	11489	12.23
	2	22	10277	0.39	27	11119	8.62
	3	148	10234	−0.03	251	11594	13.26
	4	2084	8593	−16.06	2332	6746	−34.10

^*Percent difference compares each formulation’s value against the theoretical value.

^†In a 4−zone model (p = 4), the citation count per zone theoretically should be 45,855.

Verbal Formulation of Bradford’s Law

Using this method, we discovered that the distribution followed a pattern for certain values of p. Parameters c and k could be found for the first 3 zones that satisfy the verbal formulation, whereas all zones beyond 3 failed to reach the expected citation density for that Bradford multiplier. The closest fit across the first 3 zones was for p = 4 (Fig. 4). With this formula, the core journals of neurosurgery emerged as the top 8 ranked journals with a Bradford multiplier of 5. The core journals of neurosurgery ranked by citation are as follows: Journal of Neurosurgery, Neurosurgery, Spine, Stroke, Neurology, American Journal of Neuroradiology, International Journal of Radiation Oncology Biology Physics, and New England Journal of Medicine.

Zonal citation distribution of Bradford’s verbal formulation versus observed.

Discussion

Bradford’s law was used by Madhugiri et al. in 2013 to identify core journals for all of neurosurgery.¹⁹ The aim of our current study was to further establish the use of Bradford’s law in identifying core journals of neurosurgery by using a larger and more diverse sampling method while establishing the core journals for many neurosurgical subspecialties. Using the verbal formulation of Bradford’s law, we found 8 journals in the core with a Bradford multiplier of 5. The core journals of neurosurgery ranked by citation are as follows: Journal of Neurosurgery, Neurosurgery, Spine, Stroke, Neurology, American Journal of Neuroradiology, International Journal of Radiation Oncology Biology Physics, and New England Journal of Medicine.

Many mathematical approaches exist that apply Bradford’s law of scattering to data sets.^4,5,18,26 This study uses Egghe’s expansion of Leimkuhler’s method, which has been used in other studies.^5,18,19,26 This formulation relies on the use of exponential functions to predict zonal distribution and depends on the citation database parameters of total citations by the top journal and the total number of journals; however, no mathematical formulation has achieved consistent statistical significance.⁹ Additionally, how does this type of analysis compare with the more traditional journal ranking that uses the IF? Journal IF is defined as the average number of citations per paper from the prior 2 years of publication. This value is relevant for journals to compare their impact to that of other journals within equivalent fields of study. It is not useful for comparing journals across subjects due to the scope of readership differences. For example, Journal of Neurosurgery and New England Journal of Medicine were both found to be core journals for neurosurgery, but their IFs are quite different (3.227 vs 54.42, respectively [2013 IF]). The value of a Bradford’s law analysis is that it attempts to analyze utility to a given topic or field regardless of relative overall impact, and is inclusive of journals across traditional field barriers.

Practical application of Bradford’s law in neurosurgery may best be applied to neurosurgical subspecialties. Many neurosurgeons have completed fellowships resulting in specialized practices and research interests. An analysis targeted to the major subspecialties would yield more focused and practical results. Additionally, identifying these core journals in neurosurgical subspecialties may also guide medical students, residents, and fellows to the journals that will have the highest impact within their field of interest.

Our sampling method differs from that of Madhugiri et al.¹⁹ in that rather than sampling articles in neurosurgery-specific journals (22,850 citations over a 3-month period), we chose to sample all publications from the top 25 neurosurgeons as ranked by h-index for each chosen subspecialty (183,421 citations over a 5-year period from 150 neurosurgeons). These subspecialty databases were combined to evaluate neurosurgery as a whole. These parameters were chosen to construct a database large enough from which to draw meaningful conclusions, yet not broad enough to make data collection and analysis prohibitively labor intensive. Although seemingly arbitrary, any analysis of this type must adhere to specific parameters, because full and detailed sampling of all the neurosurgical literature is simply not possible. This type of sampling technique is not novel to Bradford’s law analyses.^9,26 We chose to sample the citations of highly cited neurosurgeons because it would capture those articles that neurosurgeons cite in journals that—although unconventional to neurosurgery— may be high-impact articles and relevant to their respective subspecialty.

Productivity, in the sense of citation or publication count, is not a guarantee of quality. The h-index does attempt to quantify and measure quality in terms of productivity. An author must continue to publish papers over time (productivity) and have his or her papers cited by peers over time (loosely correlated with quality or, more appropriately, relevance). A citation has been equated to a measure of trust between one author and another regarding the quality of the work.² Therefore, those neurosurgeons who are in the top 25 for each subspecialty as ranked by h-index are presumably currently publishing and citing relevant works in their subspecialty.^11,14

The citation distributions for neurosurgery and its subspecialties did not fit the expected distributions based on currently accepted formulations of Bradford’s law. This is an issue common to many other researchers and consistent with previous Bradford’s law studies in neurosurgery.^10,19,26,30 The observed distribution showed a greater number of citations in the central zones than expected, while the first and last zones contained fewer citations. This difference was consistent across subspecialties, although it was most exaggerated for pediatrics, in which the observed distribution was furthest from the model. Neurosurgery as a whole is a broad field encompassing most of the other subspecialties. Not surprisingly then, Egghe’s expected distribution as applied to neurosurgery as a whole most resembles the pediatrics distribution.

It has recently been suggested that highly interdisciplinary fields will produce a Bradford distribution with increased scatter, or similar to the distribution previously discussed. When a subject or field is highly interdisciplinary, the distribution of the information relevant to that field or subject will be scattered across a greater number of journals, diminishing the strength of the core journals while inflating the secondary zones. The highly interdisciplinary nature of neurosurgery may account for the distribution observed within neurosurgical literature.⁹ The concept of interdisciplinarity and its impact on the production of scientific literature has only recently been described by Hjørland.^9,10,21 Continued research on interdisciplinarity and its impact on the distribution of scientific literature is needed.

The differences in the distribution of the observed data and the expected model distribution may also be explained by the journals that make up each zone. The core zones for each subspecialty of neurosurgery are all different, but Journal of Neurosurgery and Neurosurgery are represented in the core of all neurosurgical specialties, ranking as the first and second journal, respectively, for all subspecialties except spine and vascular, for which they are second and third. These journals represent the most specific and inclusive journals of neurosurgery. The central zones contain some journals that, although less specific, traditionally have a higher impact with a much broader scope. These journals represent a smaller number of articles, but by virtue of the IF of these journals, they may be highly impactful. An analysis of the impact a specific research article has on a journal or zone was beyond the scope of this study.

How does this work affect the average neurosurgeon? The rapid expansion of scientific literature is likely to continue, making it even more difficult for general and subspecialty neurosurgeons to keep abreast of all pertinent research being published monthly or quarterly. We have shown that many journals with broader readership or that traditionally are nonneurosurgical, like New England Journal of Medicine, are publishing highly cited works that are having an impact within our field. Kondziolka responded to the article by Madhugiri et al. in which he calls into question the current structure of the flow of knowledge (i.e., article submission/peer review/publication/citation) as “fundamentally flawed.”¹⁶ There are many other avenues that clinician researchers can use to stay up to date on current research. These include conferences, advanced courses, journal clubs, teaching sessions for residents and fellows, electronic resources, and even our patients themselves. This paper serves to identify the core journals in the various neurosurgical subspecialties based on the academic productivity of the top-producing North American neurosurgeons. By identifying the core journals for each neurosurgical subspecialty, we believe readership can be directed to those journals most likely to have a consistently high impact while not overlooking those journals that may be traditionally nonneurosurgical but that may contain a smaller number of especially high-impact articles.

Conclusions

Bradford’s law of distribution has been underapplied to fields of academic medicine. We present the first core journal analysis for neurosurgical subspecialties and an expanded look at the core journals for all of neurosurgery. Although each subspecialty has its own unique core of journals, Journal of Neurosurgery and Neurosurgery are among the core journals for all subspecialties. We propose that the current core journals for neurosurgery ranked by citation are as follows: Journal of Neurosurgery, Neurosurgery, Spine, Stroke, Neurology, American Journal of Neuroradiology, International Journal of Radiation Oncology Biology Physics, and New England Journal of Medicine.

Acknowledgment

We thank Andrew J. Gienapp (Department of Medical Education, Methodist University Hospital, and Department of Neurosurgery, University of Tennessee Health Science Center, Memphis, TN) for technical and copy editing, preparation of the manuscript and figures for publishing, and publication assistance with this manuscript.

Author Contributions

Conception and design: Klimo, Venable, Shepherd. Acquisition of data: all authors. Analysis and interpretation of data: Klimo, Venable, Shepherd. Drafting the article: Klimo, Venable, Shepherd. Critically revising the article: all authors. Reviewed submitted version of manuscript: all authors. Approved the final version of the manuscript on behalf of all authors: Klimo. Statistical analysis: Venable, Shepherd. Study supervision: Klimo.