Definitions

Three anatomical landmarks were used to define occipitofrontal circumference: anteriorly, the maximum frontal area (glabella), supraorbital, at forehead level, and posteriorly, the maximum occipital protuberance [5,11,34]. These points were manually identified once on the reference brain used for spatial normalization (see “Processing”, below). A third point was placed at the same level as the frontal and occipital points, to the left above the ear, allowing to create a horizontal plane, as recommended [35]. Regions of interest (ROIs) were generated around each point with a diameter of ±5 voxels (i.e., 1 cm) in each dimension, as illustrated in Fig 1.

Data preparation

Initially, each dataset was coregistered to the reference brain in order to optimize the starting conditions for subsequent data processing steps, using a rigid-body transformation [36] within the optimized approach by [37]. Following spatial normalization, images and segmentation results were visually inspected for quality control. To allow for comparison irrespective of spatial resolution of the input data, a voxel size of 1 × 1 × 1 mm was used.

Data processing

“Unified segmentation” [38] was employed to achieve spatial normalization, segmentation, and bias correction. We employed a recently-developed approach to a more robust affine spatial normalization (which integrates seamlessly into the unified segmentation approach [39]); otherwise, default settings were used for warping, bias correction, spatial sampling and tissue priors. The spatial normalization parameters resulting from unified segmentation were then inverted and used to denormalize the standard-space ROIs created above (see Fig 1), thus defining the reference points in the individual native space. Using Otsu's thresholding method available within Matlab, the T1-weighted image was separated from the background, ensuring that only the head (and not artefacts) was used for head circumference measurements. The gray matter partition resulting from segmentation was written out in native space, allowing for the determination of brain circumference.

To compensate for head positioning differences, 40 tilts of the head around the x-axis were simulated. To achieve this, the head was rotated forward in a “nodding” fashion by 18 ° and was then iteratively rotated back to −18 ° in 40 steps. For each tilt step, the head was scanned axially from bottom to top, and a slice was considered when at least 2 out of three ROIs (anterior forehead, occiput and/or above the left ear) were present. Slices meeting this criterion were saved as “valid slices”.

Thereafter, automated head/brain circumference measurement was achieved using a convex hull approach implemented in Matlab’s bwconvhull function [40]. This generates an “imaginary loop” on axial slices along the outer head/brain circumference, imitating the behavior of a measuring tape. While this may, for example, include the ears, this corresponds to the use of the measuring tape in practice. Further, the initial outer line generated using bwconvhull was smoothed using a Savitzky-Golay filter [41]. Here, each data point is smoothed taking into account its surrounding points using a local polynomial [42]. The filter width describes the number of points to each side of the point to be smoothed that are described by the polynomial. Here, a polynomial degree of 2 was used, resulting in a smoother outline (since the original coordinates can only be determined exactly to the nearest full voxel position). The best filter width was determined by using no filtering and filter widths in steps of 10 from 10 to 120 (i.e., 13 filtering steps).

After performing these steps on the head, they were likewise repeated on the gray matter partition to obtain brain circumference. To save time and to ensure correspondence, brain circumference was only determined on slices previously found valid for head circumference.

The following analyses were performed: in a first step, the question of which summary indicator to use in the presence of several measurements (mean, median, or maximum, i.e., 3 indicators) was addressed, by analyzing the validation dataset using all filtering steps and all indicators. The results matrix (13 filtering steps by three indicators) was then summarized using the mean difference (bias) and the median absolute deviation (MAD) from the ground truth, and results were then compared statistically to find the best approach. The performance of this best approach in the validation dataset and as compared to the ground truth (manual measurement) was then visualized by using Bland-Altman analyses [43]. As suggested there, percentiles were used instead of standard deviations if the difference to the mean was found to be non-normally distributed.

As reference values, the (sex-averaged) 3^rd and 97^th percentile from a recent and large developmental dataset were used [44].

To assess the reliability of the approach, the test-retest-dataset (3 subjects with 40 MRI datasets each) was analyzed using the above-determined settings, and the stability of results across multiple measurements was assessed, again using Bland-Altman analyses.

To finally explore the biological plausibility of the approach, the automatically-derived head and brain circumferences from the validation dataset were compared with each other and as a function of age.

Statistical analysis

All statistical analyses were carried out using MATLAB R2021a. An initial Kolmogorov-Smirnov-Lilliefors test was used to check for normal distribution. If the normal distribution was violated, a non-parametric Mann-Whitney U-test was used, otherwise a parametric T-test. All tests were two-sided. Significance was assumed at p ≤ 0.05. For multiple comparisons, Bonferroni correction was used to reduce the probability of type 1 errors.

To assess reliability in the test-retest dataset, Bland-Altman analyses were used again to illustrate agreement between measurements. As no gold standard was available here (head circumference was not known for the three subjects in the test-retest dataset), the mean of all measurements was instead used as the reference point per subject.

Validity

Validity provides information on whether a measurement method – in this case the algorithm – measures what it is supposed to measure, and therefore provides credible results [45]. This question was investigated using a validation dataset for which both MRI data and manually measured head circumference values were available, from a total of 153 subjects aged 0–226 months (0–18.8 years). Our automatically-obtained head circumference values were compared with those of the gold standard.

Comparison of different summarizing indicators: in the literature, different approaches are suggested if more than one manual head circumference measurement is available, such as using the mean [4,13,46–49] or the maximum value [15–17]. Other authors found no significant differences between using “only one measurement,” “maximum value from two measurements” and “mean value from two or three measurements” [50].

In our data, we found that the variant using the maximum of several values performed significantly better than the other approaches (Table 1), which is consistent with recommendations for the procedure of manual measurement (e.g., [16]). For this reason, the maximum value across measurements was used in this work.

Performance of the algorithm with regard to the gold standard: The maximum value approach showed an extremely low bias (0.04 cm) with the best Savitzky-Golay-filter setting of 50 (Table 2), indicating that no systematic deviation is to be expected. The median absolute deviation was 0.83 cm. This is within the range of observed errors of measurements in the clinical field: for example, while an inter-observer difference of > 0.5 cm was considered unacceptable, it was present in up to 26% of measurements seen by [51]. A median absolute deviation between manual measurements of up to 0.78 cm was also seen by [52] (see also reliability, below). These results demonstrate that the validity of the algorithm is very similar to that of the gold standard.

Both parameters are also depicted as a function of age in Fig 3. Interestingly, when additionally plotting anthropometric reference values from [44], several discrepancies seem present. For example, several subjects show extremely high manually-measured values (e.g., at age 2 months, manual value 47 cm; at age 116 months, manual value 60 cm; at age 134 months, manual value 60 cm), each of which corresponds to a head circumference percentile of > 99 each [53,54]. The corresponding algorithm outputs were 41.57, 55.36 and 56.24 cm, each safely within the normal range. Also, the automatically-determined values for the very young babies (middle panel) correspond better with the expected values from the reference dataset (gray lines), which may also suggest uncertainties with manual head circumference measurement or documentation. Of note, when summarizing over 20 subjects (lower panel in Fig 3), the curves are virtually indistinguishable, underlining the minimal systematic bias and suggesting that the algorithm will be particularly useful for group studies.

Reliability

These analyses were intended to test the reliability, i.e., the dependability or accuracy of measurement of the algorithm when used multiple times [55]. A dataset of three subjects with 40 MR examinations each was available for this purpose [31]. It is noteworthy that the algorithm was not repeatedly run on the same dataset, but run 40 times on 40 different datasets of the same subject, acquired over a period of several weeks. Hence, the variability due to different positioning in the scanner, differences in field homogeneity etc. is already inherent in our results.

The values obtained from these repeated analyses showed a very high degree of agreement. Bland-Altman analyses demonstrate that 95% of the measured values were within a corridor of 0.43 to 0.29 cm around the mean value; the corresponding standard deviation was 0.17 at most (cf. Table 3). In light of the known high inter-individual variance of manual measurements of head circumference, these are very low values. For example, an intra-examiner variability of at least 0.5 cm was seen in under 10% of cases and a corresponding interobserver variability in under 16% of cases [51]. Other authors observed a standard deviation of 0.6 cm in repeated measurements [47]. A similar standard deviation was also seen by others [52], despite the fact that the measurements were taken under optimal conditions and therefore likely underestimated real-world variability. Overall, therefore, these results demonstrate that the repeated application of the approach to repeated measures will yield very stable results.

Plausibility: Head and brain circumference

The new option to determine not only head circumference, but corresponding brain circumference (i.e., the gray matter hull perimeter) from MR images is intriguing as the latter may help to differentiate abnormal head from abnormal brain growth. Our results clearly demonstrate that the correspondence between the two measures is high, but their relation changes as a function of age (Fig 5). In infancy, they are closer, while later-on, brain circumference plateaus while head circumference continues to increase. The absolute difference between them changes significantly as a function of age, from 4.34 cm in children < 6 to 7.21 cm in children > 12. Our algorithm can therefore be used to supplement the existing percentile curves for head circumference with percentile curves for brain circumference, and publicly available datasets with brain MR data (total n > 45.000) could be used to this effect [56–58]. This would be of particular clinical benefit in the case of unusual discrepancy, for example in the entity of benign enlargement of subarachnoid space in infancy, BESS [25,59]. Here, children show a temporary and benign increase in head circumference, usually in the first year of life, due to extracerebral (usually frontal) accumulation of CSF. These two defining aspects (temporary and benign), however, can only be determined in hindsight. In such cases in particular, a normal brain circumference despite a large head circumference could help to confirm the diagnosis and thus avoid unnecessary diagnostic or therapeutic steps. In how far the brain circumference parameter may be of use in other specific physiological or pathological scenarios will have to be the subject of future studies.

Limitations

The approach presented here relies on landmark definitions defined in standard space and their transfer into native space by inverting the automated spatial normalization procedure. This approach allows for the investigation of larger groups (as necessary for the generation of robust reference data), but may fail in the case of severely abnormal head configuration, where manual identification of such landmarks may be more exact. To prevent that, we already used a more robust and less biased version to spatial normalization [39]. The ROI size was derived empirically while developing the algorithmic approach. The effect of this was not formally evaluated, but while a larger ROI size will automatically lead to more slices being considered as “potentially valid”, it will also reduce spatial specificity. The chosen ROI size was a compromise, designed to be inclusive enough to yield numerous intersecting slices but exclusive enough to still be spatially specific. Regarding reliability analyses, it must be acknowledged that repeated measures of only three subjects were available, potentially limiting generalizability. Further limitations include the nature of a retrospective study with regard to demographic data (manually measured head circumference). This type of study does not allow retrospective verification of clinical measurements and it cannot be ruled out that incorrect information is included in the analyses (as discussed above in the case of the probable outliers). The current manuscript was aimed to establish and evaluate the approach in the setting of healthy brain development, but its performance in specific pathological settings was not investigated here. While in general terms we would expect that lower data quality (low resolution clinical images, motion or implant artefacts etc.) has the potential to impact segmentation, the unified segmentation approach used here is rather robust. Further, higher-order cranial deformities may disrupt the assumption of convexity, which may impair the applicability of the convex hull approach used here. For most “unusual brains”, however, the approach should be sufficiently robust, and the visualizations included in the algorithm allow to assess data processing and analysis success. Finally, several settings (number of tilts, tilt steps, etc.) were decided on empirically, and the effect of changing either has not been investigated systematically. However, they have worked well in our extensive test runs and simulations and while specific scenarios may call for different settings, we hope that by transparently providing this information herein and in the toolbox, the user will be able to adapt these settings if need be.

Extensions

Based on the available data in the literature [44], the percentiles of head circumference can also be determined automatically if subject age and gender are provided. This functionality has now been implemented; an example can be found in the supplementary material 2. Additionally, other segmentation & normalization approaches such as implemented in CAT12 [60] can also be implemented.