A Nomogram to Predict Posterior Cranial Fossa Volume Based on Age and Gender

Abstract

Background

The posterior cranial fossa (PCF) is a critical region housing vital structures like the medulla, pons, midbrain, cerebellum, and lower cranial nerves. Several diseases are linked to the posterior fossa, including Arnold–Chiari malformation and posterior fossa tumors. Linear measurement–based formulae are commonly used, as they align well with manual planimetric segmentation, although the latter is labor intensive. Nomograms enhance patient prognosis in various medical fields, including cancer and surgery. However, there is currently no nomogram for predicting the PCF volume (PCFV) based on age and gender in Northern India's population. Our study aims to develop a nomogram using MRI-based volumetric analysis from a Northern Indian tertiary care center.

Materials and Methods

Patients of all age groups, who underwent MRI of the brain at the imaging center in our diagnostic and interventional radiology department and did not have any pathological finding related to posterior fossa, were included in the study. We analyzed 1,132 MR images without any radiologically detectable pathologies.

Results

The mean PCFV was 229.95 (±10.16) mL in males and 207.67 (±9.86) mL in females. We developed a nomogram for estimating the PCFV based on age and gender for clinical application.

Conclusion

The PCFV varies depending on age and gender. Our findings reveal that the PCFV rises exponentially during the first 2 years of life, followed by a linear increase. The nomogram is a simple technique that may be used in everyday practice to estimate the posterior cerebral fossa volume for a given age and gender. It can be used to study the disease processes affecting the PCF such as including but not limited to Chiari I malformation, Dandy–Walker malformations, cerebellar vermian hypoplasia, and olivopontocerebellar atrophy.

Keywords

magnetic resonance imaging - nomogram - posterior cranial fossa - posterior cranial fossa volume

Introduction

The posterior cranial fossa (PCF) is a critical region housing critical structures like the medulla, pons, midbrain, cerebellum, and lower cranial nerves. Alterations in PCF size in pediatric population are associated with various central nervous system illnesses.[1] Several diseases are linked to the posterior fossa volume, including Chiari malformation, posterior fossa tumors, craniovertebral junction disorders, myelomeningocele, Dandy–Walker syndrome, and platybasia.[1] PCF volume (PCFV) plays a crucial role in conditions like Chiari malformation type I (CMI). CMI involves cerebellar tonsil descent into the cervical canal, often due to a small PCFV caused by occipital bone dysplasia.[2] [3] Research suggests embryological flaws in paraxial mesoderm lead to these PCFV geometry issues.[4] The primary treatment for CMI has been posterior fossa decompression, addressing issues like foramen magnum narrowing due to posterior cranial vault anatomy distortion.[5] In myelomeningocele patients, a link exists between myelomeningocele level and Chiari II malformation severity, potentially tied to PCFV constraints.[6] PCF crowding has also been associated with primary cough headaches.[7] As the PCFV plays a significant role in several pathologies, understanding the average PCF geometry is crucial.

The PCF is bounded by the tentorium cerebelli, clivus, and a line between basion and opisthion. Advancements in magnetic resonance imaging (MRI) enable better quantification of brain structures, including PCF. Various studies have been done to define the values of PCFV based on different automated and manual methods. Among them, linear measurement–based formulae are commonly used. Although manual planimetric segmentation method is considered the gold standard for PCFV measurement, it is labor intensive.[8] The PCFV varies widely across studies, which may be attributed to the differences in the imaging modalities used to measure the PCFV, segmentation protocols, and landmarks used in the measurement protocol. Normative data are necessary for the quantitative assessment of morphological alterations in the posterior fossa. However, there are currently no nomogram for predicting the PCFV.[8] Nomograms are valuable tools for clinical decision-making, offering continuous probability scores. Our study aims to fill this gap using MRI-based volumetric analysis from a high-volume tertiary care center.

Materials and Methods

We included patients who underwent MRI in the Department of Diagnostic and Intervention Radiology at our institute between April 2021 and June 2022. Patients of all age groups, who do not have any pathological finding related to the posterior fossa at the time of imaging, were included. Patients who had radiologically detectable posterior fossa pathologies/lesions at the time of imaging were excluded from the study. All patients had undergone T1- and T2-weighted (T2W) axial, sagittal, and coronal images in a 1.5-T MRI machine (Discovery MR 750W 3T, Wipro GE Healthcare Pvt. Ltd., Milwaukee, WI, United States).

The medical records including MR images of patients who satisfy the inclusion criteria were retrieved for the study. RadiAnt DICOM Viewer (Medixant, RadiAnt DICOM Viewer, version 2021.1. Jun 27, 2021. URL: https://www.radiantviewer.com) was utilized to view the MR images and to measure various parameters of the PCF. The diameters measured on RadiAnt DICOM Viewer were entered into Microsoft Excel sheets 2021 (Microsoft Corporation, Redmond, WA, United States).

The PCFV was defined as the space enclosed by the tentorium cerebelli superiorly, the foramen magnum inferiorly, the clivus up to the dorsum sella anteriorly, and occipital bone between the tentorial attachment and foramen the magnum posteriorly. In this study, the PCF was considered a spheroid and its volume was calculated based on three linear measurements including anteroposterior diameter, height, and transverse diameter of the PCF. The anteroposterior diameter and height of the PCF were measured from the dorsum sella to the torcula and a line joining the junction of the vein of Galen and straight sinus to the midpoint of the basion–opisthion line from a the midsagittal T2W sequence. The transverse diameter of the PCF was calculated by the maximum width of the cerebellar hemisphere in axial T2W sequence. The protocol for T2W sagittal sequence included in the following: repetition time (TR)/echo time (TE): 7,450/102; field of view (FOV): 26; 5-mm slice thickness without gap; and matrix of 384 × 288.

The formula for the volume of a spheroid is applied to calculate the PCFV.

Spheroid volume = 4/3 × π × r ³.

PCFV = 4/3 × π × a/2 × b/2 × c/2,

where a, b, and c are the anteroposterior diameter, height, and transverse diameter of the PCF, respectively.

Statistical Analysis

The quantitative variables were presented as the mean and standard deviation (SD) and the qualitative variables were presented as frequency and percentage. The normality of distribution for a variable was assessed using a histogram and confirmed using the Shapiro–Wilk test. Continuous variables were compared using the Mann–Whitney U test and categorical variables were compared by the chi-squared test. Spearman's correlation coefficient was used to find the strength and direction of the relationship between the PCFV, age, and gender. A p-value of less than 0.05 was considered statistically significant. All statistical analyses were carried out using IBM SPSS version 25 (SPSS Inc., Chicago, IL, United States). Nomogram was developed on R Studio Desktop (RStudio Team, 2020. RStudio: Integrated Development for R. RStudio, PBC, Boston, MA, United States).

Results

A total of 1,754 patients were screened. After excluding patients failing to meet the eligibility criteria, the number of patients finally enrolled in the study was 1,132. There were 609 males (53.8%) and 523 females (46.2%). The mean age (SD) was 37.78 (±23.59) years, with age ranging from 5 days to 89 years.

[Fig. 1] shows the mean PCFV among different age groups in the male population. The PCFV followed a sigmoid curve with respect to age. The PCFV showed an initial exponential growth from birth to 2 years of age, followed by a slow linear growth for the remainder of the life. The mean PCFV for patients in the age group of 0 to 1 years was 91.35 mL and that for those in the age group of 1 to 2 years was 193.28 mL, with +112.08% increase in the volume in 1 year. However, the percentage change for the rest of the life followed a linear curve. For ages 1 to 2 and 3 to 10 years it was from 193.28 to 210.8 (+8.8%) mL. [Fig. 1] also shows the mean anteroposterior diameter, height, and transverse diameter of the PCF in different age groups among the male population. It can be appreciated that all three parameters showed a rapid increase during the first 2 years of life, followed by a slow and steady increase till 80 years of age.

Fig. 1 Line chart of various parameters in the male population. The line charts depict variation in (A) mean volume, (B) anteroposterior diameter, (C) height, and (D) transverse diameter of posterior cranial fossa (PCF) with respect to different age groups. PCFV, posterior cranial fossa volume.

[Fig. 2] shows the mean PCFV among different age groups in the female population. Similar to males, the PCFV showed an exponential growth from birth to 2 years of age, then a linear growth for the remainder of life in females as well. The mean PCFV for the age group of 0 to 1 year was 81.77 mL and that for the age group of 1 to 2 years it was 163.45 mL, with +99.88% increase in 1 year. However, the percentage change for the rest of the life followed a linear curve. From ages 1 to 2 to 3 to 10 years, it was +20.85%, increasing from 163.45 to 197.12 mL. All three measurements of the PCF in females also followed the same trend as that of males with increasing age.

Fig. 2 Line chart of various parameters in the female population. The line charts depict variation in (A) mean volume, (B) anteroposterior diameter, (C) height, and (D) transverse diameter of posterior cranial fossa (PCF) with respect to different age groups. PCFV, posterior cranial fossa volume.

The PCFV was significantly higher in males compared to females. The mean PCFV in males was 142.31 (±72.07) mL compared to 131.52 (±68.51) mL in females (≤2 years of age). Similarly, the mean PCFV was 229.95 (±10.16) mL in males older than 2 years and 207.67 (±9.86) mL in females (p < 0.001). Spearman's correlation analysis showed a positive and statistically significant correlation between age and PCFV ([Fig. 3]; r = 0.375, p < 0.001). Similarly, the anteroposterior diameter (r = 0.64, p < 0.001), height (r = 0.67, p < 0.001), and transverse diameter (r = 0.35, p < 0.001) of the PCF also showed a positive correlation with age. On linear regression analysis, age (coeff = 0.39, p < 0.001) and gender (coeff = –0.18, p < 0.001) predicted the PCFV. [Table 1] shows the analysis of variance (ANOVA) table for the linear regression analysis. The PCFV varies as a function of age and gender (PCFV ∼ 215.179 + 0.598(Age) – 12.879(Sex); [Fig. 4]). The scatter plot depicts the relationship of PCFV with respect to age and gender ([Fig. 3]).

Fig. 3 Scatter plot. (A) Linear association between age and PCFV. (B) Positive linear correlation between age, gender, and PCFV. PCFV, posterior cranial fossa volume.

Table 1 Analysis of variance (ANOVA) table

	Unstandardized B	Coefficients Standard error	Standardized coefficients Beta	t	Sig.
Constant	215.179	3.420		62.917	0.0001
Age	0.598	0.41	0.391	14.605	0.0001
Gender	–12.879	1.936	–0.178	–6.652	0.0001
	Sum of squares	df	Mean square	F	Sig.
Regression	280,140.734	2	140,070.367	133.036	0.0001
Residual	1,188,694.288	1,129	1,052.874
Total	1,468,835.022	1,131

Note: Both age and gender are predictors of posterior cranial fossa volume (PCFV).

Dependent variable: PCFV.

Predictors: (constant): sex, age.

Fig. 4 Nomogram for posterior cranial fossa volume (PCFV) based on age and gender.

[Fig. 4] depicts the nomogram for the PCFV as a function of age and gender. From the nomogram, we can calculate the total points for a particular age and gender (we have arbitrarily assigned values for each gender as male = 1 and female = 2, for calculation purpose). From the “total points” axis, we can extrapolate onto the axis “linear predictor” to obtain the PCFV. [Fig. 5] shows an example of how to calculate the PCFV. To calculate the PCFV for a 40-year-old man, we can add 40 points for the age (40 years) and 20 points for gender (male = 1 = 20 points), which gives total of 60 points. From the “total points” axis, we can extrapolate 60 points to the “linear predictor” axis that gives a value of 225 mL.

Fig. 5 Nomogram for PCFV. It depicts calculation of PCFV for a 40-year-old man. PCFV, posterior cranial fossa volume.

Discussion

The PCF is an anatomically complex and surgically challenging area to access. The PCFV has been implicated in many pathologies. There are several methods for calculating the posterior fossa volume using dry skull, MRI, and CT imaging. The manual planimetric image segmentation technique provides a relatively more accurate measure of the PCFV and is the gold standard technique against which other methods are compared.[8] But this technique is labor intensive and time-consuming. The other technique is based on the linear measurements. The PCF is considered an inverted cone, spheroid, or ellipsoid. Two or more linear measurements are taken, and the volume is calculated from these measurements. Based on the linear measurements taken in three orthogonal planes, the spheroid formula has the best concordance with the manual segmentation technique. The PCFV can also be estimated by considering the PCF to be an inverted cone. However, this technique often underestimates the volume. The tentorium, which forms the natural superior boundary of the PCF, has an upward slope. However, the base of the inverted cone is approximated to a horizontal line joining the dorsum sella to the inion, which ignores a significant proportion of the volume contributed by the tentorial slope. Although the PCFV can be easily measured with linear measurements, one should be aware that such estimates may not be accurate.

Given the difficulties and disadvantageous with each technique, we need a technique that is easy to use and reliable for calculating the PCFV. After analyzing 1,132 MR images of the brain without any detectable abnormalities, we were able to create a nomogram for estimating the PCFV. To date, this is the largest sample included in any such study. A nomogram, by definition, is a graphical representation of complex mathematical function/formula. In this case, we can calculate the PCFV based on age and gender. Hence, it can be used in clinical practice for studying the relationship between PCFV and various posterior fossa pathologies. The nomogram is a widely accessible tool and is easy to apply.[9] [10] [11] The results from our study have shown that age has a statistically significant positive correlation with the PCFV. From birth to 2 years, the PCFV increases exponentially. Beyond 2 years of age, it increases in a linear fashion slowly. The mean anteroposterior diameter, height, and transverse diameter of the PCF also show a positive correlation with age and follow the same trend as the PCFV with increasing age. The PCFV was found to be higher in males than in females. Lirng et al[7] also reported that the PCFV was related to age and sex and these two variables account for 57.5% of variance in the volume.

Prassopoulos et al[1] reviewed 181 brain CT images in children with no abnormal findings to determine normative data for the PCFV. The PCFV was calculated by summing the consecutive CT cross-sectional areas. They found that the PCFV increased rapidly during first 3 years of life, followed by a linear and smaller increase in the volume. Our results are concurrent with this study. Kanodia et al examined the PCFV calculated from the CT images in 100 patients. They did not find a significant difference in the PCFV between different age groups.[12]

The PCFV plays a significant role in the pathogenesis of CMI. Several authors evaluated the PCFV in patients with Chiari malformation.[4] [13] [14] [15] [16] While few authors reported no difference in the PCFV compared to the control groups, the majority have reported a significantly smaller PCF in patients with CMI. Similarly, a small PCFV has also been reported in children with rickets and myelomeningocele. Several other diseases like Dandy–Walker malformations, autism, olivopontocerebellar atrophy, cerebellar vermian hypoplasia, and Down's syndrome have also been shown to be associated with alterations in the posterior fossa volume. To evaluate the impact of the PCFV on disease process, the normal range in variation of the PCFV over the complete natural age range should be known and can be easily calculated from the nomogram developed from large data. In other words, the nomogram could be used to study the above-mentioned disease processes.

Study Limitations

The major advantage of our study is that we included a large number of patients to develop the nomogram. There are certain limitations to this study. This was a retrospective study based on patient records. The PCFV depends on multiple other factors including race, ethnicity, height, body mass index (BMI), demographic factors, and nutritional deficiency. We could not study all the factors that could affect the skull growth, hence PCFV. The findings of this study can, however, serve as a starting point for further investigation into the diseases of the PCF and how changes in the PCFV affect their pathophysiology and clinical course.

Conclusion

The PCFV shows age- and gender-dependent variations. Age and gender are significant predictors of the PCFV. Our results show an exponential increase in the PCFV during the first 2 years of life, which is then followed by a linear increase. The PCFV is larger in males compared to females. The nomogram is a simple tool that is easily accessible and can be used in day-to-day practice for estimating the PCFV for a particular age and gender.

Conflict of Interest

None declared.

Ethical Approval Statement

The Institutional Ethics Board approved the study.

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Publication History

Article published online:
21 May 2025