The sphenoidal emissary foramina prevalence: a meta-analysis of 6,369 subjects

Purpose To estimate the prevalence of the sphenoidal emissary foramina (SEF), and the effect of possible moderators on it. Methods A systematic online literature search was conducted. The pooled prevalence with 95% confidence intervals was estimated. Outlier and influential analyses were performed. The presence of small-study effect and publication bias were evaluated. Moderator analyses were executed to investigate the effect of the specimens’ continent of origin, type of study (dried skull or imaging), probing for the evaluation of SEF patency (conduction and instruments used), side dominance (bilateral or unilateral), morphometric data [SEF diameter, distances SEF–Foramen ovale (FO) and SEF–Foramen spinosum (FS)], and the methodology used for the morphometric measurements (caliper, DICOM Viewer, and image analysis software) on the estimated prevalence. Results In total, 6,460 subjects from 26 studies were included in the meta-analysis. The overall SEF prevalence was estimated as 38.1%. The heterogeneity was high and statistically significant. No indications of publication bias and small-study effect were identified. The conducted subgroup analyses did not yield statistically significant differences in the SEF prevalence between groups, except of the type of side dominance. Both results of the univariable and multivariable regression analyses showed the association of the unilateral dominance with a decrease in the reported SEF prevalence. Conclusion The identification of more unilateral than bilateral foramina in a given cohort is associated with a decrease in the reported crude SEF prevalence. Laterality-specific estimates should be established for a precisive estimation of the emissary foramina prevalence.


Introduction
The constant foramina (foramina ovale and spinosum, FO and FS) are located in the posterior part of the greater wings of the sphenoid bone. FO transmits the mandibular nerve and occasionally the accessory meningeal artery and the lesser superficial petrosal nerve. FS is perforated by the middle meningeal artery and the meningeal branch of the trigeminal nerve [12]. Occasionally, anteromedially or anteriorly to the FO [19,31], a small sized foramen-the so-called sphenoidal emissary foramen (SEF) or foramen of Vesalius (FV) can be unilaterally or bilaterally identified. SEF has not been identified in any other primates than human [40]. As per its content, SEF transmits a sphenoidal emissary vein (SEV) connecting the pterygoid venous plexus to the cavernous sinus [24]. Therefore, it is important in neurosurgical procedures, such as in FO cannulation for trigeminal nerve rhizotomy, as well as pathway of spreading  [22,25,35]. The SEF occurrence varies widely among different studies' samples [13].
The current meta-analysis provides a more precise estimation of the SEF prevalence and pinpoints the variables associated with the SEF presence.

Search strategy
A systematic literature search was conducted by two independent assessors in August 2022 using Publish or Perish software [15]. Through this application, all available databases except for the Web of Science (Crossref, GoogleScholar, OpenAlex, PubMed, Scopus, and Semantic Scholar) were scanned using combinations of the following keywords: ["foramen Vesalius", "sphenoidal emissary foramen", "presence", "occurrence", "prevalence", "incidence")]. Notably, in Semantic Scholar and OpenAlex, only single keywords were used since both databases' application programming interfaces did not support the use of Boolean operators. After duplicates' removal, each publication's reference list was manually scanned for potentially non-identified studies. The systematic literature search flowchart (Fig. 1) is based on the PRISMA 2020 Statement [29].

Criteria for study selection and data inclusion and extraction
All original studies reporting data regarding SEF prevalence were included with no restriction on language or publication date. Case reports, review articles, letters to the editor, conference abstracts, doctoral thesis, studies with no fulltext or detailed abstracts available, and articles that could not be cross-verified by multiple secondary sources were excluded. Out of each publication, the extracted data included the authors, year of publication, continent of origin (Europe, Asia, and America), type of data (dried skulls and imaging), probing for evaluating SEF patency (yes or no), instrument used for probing (bristle, wire, and other), total sample, reported SEF frequency (total, bilateral, and unilateral), type of dominance (bilateral: when the bilateral to unilateral foramina ratio was greater than 1, otherwise, unilateral), morphometric data (SEF diameter, SEF-FO, and SEF-FS distances), and the  publications not mentioning the continent of origin, the country where the study originated from, was eventually recorded and in case of an article written in a non-Latin language (e.g., Russian), the full paper was downloaded and translated using the Google Translate website (https:// trans late. google. com). Additionally, in manuscripts where only the bilateral or unilateral percentages were reported, the respective frequencies (bilateral and unilateral frequency) were calculated by converting each percentage to integers with no decimal approximation.

Quality assessment
The quality assessment was performed according to the Anatomical Quality Assessment (AQUA) tool [16], a tool consisting of 25 questions and dividing into 5 areas:  [21,37]. Heterogeneity presence across studies was estimated by constructing a forest plot and tested using the Cochran's Q statistic and its respective p value. The Higgins I 2 statistic and its respective 95% CI were used for quantifying the magnitude of true heterogeneity in effect sizes. An I 2 value of 25%, 50%, and 75% indicated low, moderate, and high heterogeneity. To detect studies that overly contributed to the heterogeneity, a Baujat plot [2] was created. To determine if the potential outlying studies, as evaluated in this plot, were also influential, screening for externally studentized residuals with z-values larger than two in absolute value and leaveone-out diagnostics were performed [38]. With the outlying and influential studies removed, the pooled prevalence, its' respective 95% CI, and the substantial heterogeneity were re-evaluated through moderator analyses. In the conducted subgroup analyses, the following covariates were evaluated: continent of origin, type of data, probing, sample size, dominance, study quality, and measurements. As per the sample size, all manuscripts were divided into two categories (small and large studies) based on the median sample size (n = 239 subjects). In the performed univariable regression analyses, except of the aforementioned covariates, the SEF diameter, as well as the SEF-FO and SEF-FS distances were assessed as per their relationship with the respective effect sizes. Moreover, the presence of interrelated moderators was checked to avoid potential multicollinearity issues prior the conduction of the multivariate regression analysis. Due to the limited availability of data about the SEF diameter, and the SEF-FO, and SEF-FS distances in the given dataset, they were not used in this analysis. To detect the presence of publication bias, a Doi plot and a funnel plot were created. The asymmetry of each plot was estimated by calculating the LFK index [9] and Egger's tests' p value, respectively. Additionally, to detect the presence of the small-study effect, the phenomenon that smaller studies may show different, often larger effects than large ones [33], a funnel plot of the prevalence against the sample size was constructed and regression-based Egger's test was estimated. The arithmetic difference between percentages was expressed in percentage point units [39]. Unless otherwise stipulated, the statistical significance was established at p = 0.05 (two-tailed).

Fig. 5
Forest plot displaying the re-calculated pooled effects, with one study omitted each time, using the leave-one-out method. The further a box deviates from the reference line, the more pronounced the impact of the corresponding missing study will be on the original summary proportion 1 3

Prevalence of the sphenoidal emissary foramen (SEF)
A random-effects model analysis yielded an initial overall SEF prevalence of 39.8% (95% CI 34.0−45.7) (Fig. 2). The estimated heterogeneity was statistically significant (p < 0.001), and of high magnitude (I 2 = 95.8%; 95% CI 92.9-97.7). The Baujat plot and the influence diagnostics are presented in Figs. 3 and 4. According to them, even though several studies were initially identified as outliers, the diagnostics indicated that only the Ginbserg et al. [10] study had an influential effect. The forest plot illustrating the results of the leave-one-out analyses is presented in Fig. 5

Publication bias and small-study effect
Both the produced Doi and funnel plots (Fig. 6) for the assessment of presence of publication bias were assessed as asymmetric implying that bias might be present. However, the estimated LFK index (LFK index = 0.78) and the Egger's test p value for the quantification of each plots' asymmetry, respectively, were not deemed consistent with publication bias. As per the small-study effect, according to the data presented in Table 2 as well as on the interpretation of the produced funnel plot (Fig. 6) and the respective Egger's test p value, the SEF prevalence was not moderated by the sample size. Therefore, no small-study effect was present.

Moderator analysis
The results of the subgroup analyses are summarized in Table 2. The SEF prevalence varied significantly only by the type of dominance (p = 0.016). The results of the performed regression analyses display the existence of a statistically significant, and a marginally non-significant association of the reported SEF prevalence with dominance (p = 0.005), and type of data (p = 0.060), respectively (Table 3). Specifically, according to the multivariable regression results, the unilateral dominance was associated with a 13.0 percentage points decrease in the reported SEF prevalence. In other words, when a sample of dried skulls is examined, the reported SEF prevalence will be 13.0% smaller if the frequency of the identified unilateral foramina exceeds the one of the bilateral. This finding highlights the necessity of the simultaneous recording and reporting of the unilateral and bilateral SEF prevalence (laterality-specific prevalence). The performed moderator analyses explained 32.3% of the residual heterogeneity (R 2 = 32.3%).

Study's limitations
First, it should be noted that the unidentified heterogeneity remains on moderate levels. This indicates that the reported summary estimates must be interpreted with caution. Moreover, the small number of imaging studies and articles from various geographic locations (e.g., Europe), as well as the lack of a "gold standard" for measuring foramina dimensions and relative distances should be considered. Therefore, more effort should be made toward this direction.

Conclusion
The SEF prevalence is estimated at 38.1%. The unilateral dominance is associated with a decrease in the SEF prevalence. Therefore, laterality-specific estimates should be established and followed for the estimation of the emissary foramina prevalence. Funding Open access funding provided by HEAL-Link Greece. Open access funding was provided by the Hellenic Academic Libraries Link (HEAL-Link). The authors did not receive support from any organization for the submitted work.
Data availability Literature and Rstudio data are available if requested.

Competing interests
The authors declare no competing interests.

Conflict of interest
The authors have no relevant financial or nonfinancial interests to disclose.

Ethical approval This declaration is not applicable.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.