CT sample & images

High-resolution full-head CT scans were acquired of 92 embalmed decedents representing body donors to the UQ anatomy program and comprising 53 males and 39 females. Participants ranged in age from 51 to 100 years. Note here that this sample represents the same set as that employed by Humphrey et al. [31] for eye assessment. CTs were acquired using a 16-slice Biograph helical CT (Siemens Global, Germany) using a slice thickness = 0.75 mm, pitch = 0.5 and a reconstruction increment = 0.5 mm. Other CT settings included: 130 kV, 220 mAs, CT dose volume = 60.48 mGy, dose length product = 1620.26 mGy*cm.

Per [31], decedents were specifically chosen for this study, rather than living subjects, since at the thin slice thickness settings used to acquire high-clarity images at the preset field-of-view size (whole head), produced ionizing radiation doses that exceeded permissible levels for clinical scans of living subjects [31]. Relevant here is also that the lens of the eye is an especially radiosensitive organ as relates to head CTs [61]. A second major advantage of using decedents was that all participants were precisely stationary during scan acquisition (no movement due to breathing, heartbeat, blood pulse, blinking, muscle tone), such that the anatomical clarity of the CT scans was very high [31]. Once acquired, the CT images were reviewed in OsiriX MD 14.0.1 (Pixmeo, Switzerland) where .stl files of the surface meshes of the face and skull were saved (resolution = 0.1, iteration = 5) and these files transferred to Blender 4.4.3 for analysis. The skull was segmented at Hounsfield units of 300–400, while the soft tissue surface of the face was acquired at values between −200 and −350. In Blender, the heads were reorientated precisely to Frankfurt Horizontal, ready for measurement.

In contrast to the advantages listed above, the downside of using cadavers for this nose investigation was that the nose is an extremely pliable structure, such that the noses needed to be carefully screened for any exhibiting deviation or compression, even light compressive forces, since elastic recoil of the living state had been lost. Subsequently, the sample sizes used to test each of the methods differ due to careful screening and the application of exclusion criteria applicable to particular targeted measurements characterising each method.

In this study we employ the standardized nomenclature of [62] whereby soft tissue analogues of hard tissue anatomical landmarks are differentiated by a prime symbol (′). That is, the hard tissue alare is denoted by the abbreviation al, while the point on the widest margin of the alar wings of the soft nose in frontal view (also alare [62, 63]) is designated al′ (see e.g., Fig. 1).

Fig. 1

Measurements taken to support estimation and assessment using Method 1 in Blender: (a) maximum nasal aperture width measured from left to right alare (al–al); (b) maximum nose width measured across the alae (al′–al′), as seen in frontal view of the 3D mesh; and (c) inferior oblique view of (b) to show the 3D geometry of the alae, with wing attachment into the face, from a slightly different vantage point

Method 1: nose width estimator after [58]

Alare landmarks were placed in orthogonal view on the .stl models of each skull and the intervening distance measured. For this measurement, the al landmarks were placed on the most lateral point of the nasal aperture boundary, meaning that left and right alare did not necessarily sit at the same horizontal level. On the .stl model of the face mesh (skin surface only), the al′ were positioned following 3D rotation of the head and nose to precisely determine the anatomically widest points of the nasal wings, anterior to their insertion into the face (Fig. 1).

The al–al measurement was entered into the nose width estimation formulae following [58] per Eq. 1 below, to estimate the soft tissue width of the nose (al′–al′). The estimated dimension of the nose width (NWest) was compared to the ground-truth nose width (NWGT) for error. All three of the: mean error, mean absolute error and the standard error of the estimate were calculated (the latter using Eq. 2). Note here that the three decimal places provided by default in Blender for measurements were used for inputs to equations, but that all outputs were rounded to only one decimal place for reporting as more reasonably justified by the precision of the data (see 2.6 Intra-observer Error section below).

Where:

NWest = estimated nose width (mm).

X = al–al distance (mm).

$$SEE=\sqrt-x_)}^2}}$$

(2)

Where:

xi_est= estimated measurement for individual “i”.

xi_GT= ground truth dimension of individual “i”.

n = the sample size.

As mentioned above, since the soft nose is readily deformable, individuals in the subject pool (total of 92 individuals) were screened for any trace of any soft tissue compression or deformation to the alae that would risk making the method 1 measurements non-representative, and these individuals excluded. This yielded a study sample of 63 individuals (39 males and 24 females) for this part of the study.

Method 2: nasal tip shape estimator after [60]

On the orthogonal view of the skull mesh (and with the face surface mesh invisible), a black locator (sphere) was placed at rhinion (rhi) in Blender. The skull mesh was then turned off, the face mesh turned on, and a red locator (sphere) positioned on pronasale (prn′). Both meshes were then made visible and the head was dorsally rotated after [60], until the prn′ (red) landmark directly overlaid the rhi (black) per [52] (see Fig. 2). Meshes were then exported from Blender to MATLAB for quantitative analysis of the curves.

Fig. 2

Curve extraction and measurement for Method 2 using Blender & MATLAB. (a) Example placement of rhinion (rhi) and pronasale (prn′) landmarks on the CT scan (profile view) with both skull and face rendered at their original positions. (b) Dorsal rotation of the head to superimpose the rhi and prn′ after [52, 60], such that the correct alignment level (for curve extraction) occurs when the two landmarks superimpose. (c) A view of scans with the rhi and prn′ landmarks reduced to analysis size (so that they do not obstruct visual inspection and manual landmarking of curve outlines). (d) Curves outlined on the example CT for demonstration purposes only. Soft tissue nasal-tip curve = green dash; and hard tissue curve of superior nasal aperture = blue dash. NB. This is a demonstration CT of the second author (CNS), not one of the subjects in the sample. The nose tip curve should not be mistaken for the for the nasal bridge curve since both occupy similar regions. (e) A sagittal multiplanar reconstruction to show axis aligning rhi and prn′ and at rhi (yellow line), and projection of a 2nd multiplanar plane at rhi (blue line) orthogonal to the yellow reference line in order to set uniform start and end points to the nasal curves—see (f) to (h); (f) on the multiplanar slice, parasagittal planes (red lines) are projected from the most lateral extent of the nasal aperture near the site where the anterior cortical edge of the maxillae starts to turn horizontal across the maxillary sinuses. (g) The parasagittal planes define the start/stop points for curve extraction where they cross the respective tissue contours: i.e., hard tissue start point = blue H1 landmark; hard tissue end point = blue H31 landmark; soft tissue start point = green S1 landmark; soft tissue stop point = green S31 landmark. (h) Resulting soft and hard tissue curves each including a total of 31 landmarks. Soft tissue curve is in green. Hard tissue curve is in blue. Note that landmark #16 falls centrally at the apex of each curve and that landmarks #2–15 and #17–30 are equidistantly spaced relative to the segments #1–16 and #16–31, respectively. (a–d) Compiled in Blender. (e–h) Undertaken in MATLAB using meshes only, but illustrated here using Osirix’s view of the CT, so that other anatomical features can clearly be seen in the illustration to facilitate orientations/understanding

The length of the curves (i.e., their start and finish points) were determined by projecting planes at the edges of the widest point of the nasal aperture in the same region as visible on an oblique reconstructed slice positioned at rhi and orthogonal to the axis that superimposed rhi and prn′ (Fig. 2). The intersection of the planes, with the hard and soft tissue curves defined after [52, 60], set the start (point #1) and end points (point #31) to be quantitatively analyzed within MATLAB (Fig. 2). One median landmark (point 16) was positioned at the central apex of each curve, and 14 equidistantly spaced semi-landmarks placed between point 1 & 16 and point 16 & 31, so that each curve was described by a total of 31 landmarks (Fig. 2). This enabled the soft and hard tissue curves to be compared quantitatively using standard geometric morphometric techniques [64].

For shape analysis, the two curves from each subject were registered using the “procrustes()” function in MATLAB, to remove the effects of translation, rotation, and scaling [65, 66]. Geometric dissimilarity between the curves was calculated via the default Procrustes distance (d) statistic, which represents the sum of squared deviations. This metric is sometimes also termed m2. The d statistic is standardized by the scale of the target data and provides a value between 0 (identical shape) and 1 (high dissimilarity). In addition to d, mean point-to-point distances and total Euclidean distances (Ed) between point pairs were calculated, thereby providing error statistics additionally in millimeter units, rather than just d.

Since Method 2 concerned specific dorsum and nose tip shapes, we screened the 92 subject pool for any hint of nose tip deviation or compression (even minor ones), such that only the highest fidelity data were included for analysis. For Method 2, this yielded an analytical sample of 31 subjects (20 males and 11 females). Since Method 2 did not concern the alae specifically, individuals excluded for Method 1 were not necessarily the same as those excluded for Method 2.

Method 3: pronasale position estimator after Gerasimov’s revised two-tangent method [3, 53, 54]

The two tangents to estimate the pronasale position from the hard structural framework of the nose were placed in Blender, with only the hard tissue layer of the skull visible (soft tissue layer hidden to eliminate viewing bias). Rather than positioning each tangent manually, by eyeballing the bone contour shape as has universally been undertaken previously [3, 43, 44, 51, 56, 58], we used Blender’s edit mode tool to select triangular faces from the tessellation mesh, calculate the mean of the normal values for each face, and reapply the mean value back to each tessellation triangles, such that a tangent could be attached to the mean result in the region of interest (Fig. 3). Thereby, the tangent was set in a precisely quantitative manner from the tessellation triangles in the regions of interest.

Fig. 3

Estimation of pronasale using two-tangents following Gerasimov’s revised methods in Blender and using Blender’s edit tool. (a) The first tangent is set using the very distal tip (measured last 2 mm) of the nasal bones in the median plane superior to rhinion. White dashed box highlights the relevant region on a profile view of the hard nasal bridge and the same region enlarged in (b) and (c). (b) The relevant faces of tessellation mesh bordering the median plane are selected (orange highlight). (c) The mean of the normals for the selected triangular faces is calculated and the normals for the faces remapped to the mean value (note stretching of the tessellation mesh at the sides of the region of interest (white arrow) to accommodate for this command. The remeshed region displays the mean orientation. A tangent (orange cylinder) is then attached to the surface describing the mean value. (d) the region of interest in the anterior floor of the nasal aperture (left side), behind the anterior rim and adjacent to the vomer bone (orange highlight) for projection of the second tangent (note small undulations in the ‘flat’ region of interest). (e) the normals for the selected faces are averaged and the mean remapped back to all faces in the region of interest, yielding a precisely flat surface and with all normals exact to the mean. A tangent (represented by the orange cylinder) is attached to the plane and projected from that surface. (f) Zoomed out view of the nasal floor showing the flat remeshed region of interest (see area within the black dashed box) and the attached tangent

Triangular faces in the last measured 2 mm of the nasal bone proximal to rhinion (rhi) were selected and used for projecting the upper tangent, T1 (Fig. 3) per [53, 54]. Once the faces were selected, the mean of their normals was calculated and all selected triangular faces remapped to the mean value (Fig. 3). The tangent was then attached to the remapped area, such that the tangent followed the direction set by the mean direction of the bone surface, in the selected area of interest (Fig. 3).

Similar was undertaken for the lower tangent, T2, but with respect to the floor of the nasal aperture close to, but just behind, the anterior most lip of the nasal aperture [53, 54]. That is, the superior surface of the palatine process of the maxillary bone was selected in its central region at the floor of the nasal aperture and before it transitioned upwards at its medial extent toward the vomer bone and/or laterally at the lateral nasal aperture wall. This follows directions by Ullrich and Stephan [53, 54]. For the selected area, the mean of the normals for the selected tessellation mesh was calculated and the normals of the selected faces remapped to this mean (Fig. 3). A tangent was then attached to the remapped faces, such that the tangent represented the mean surface direction, similar in principle to that undertaken for T1 (Fig. 3). The procedure was undertaken on both left and right sides of the nasal aperture for T2 to assess if there was any difference by side. Since as it turns out that there was next-to-no or negligible difference between the sides, only the data for the left side will be presented in this paper. The intersection of two tangents (T1 & T2), as seen best from a lateral or profile view, estimated the position of the pronasale (prn′est) (Fig. 4).

Fig. 4

Estimation of the pronasale by the two tangent method (prn′est) and comparison to the ground truth pronasale position (prn′). (a) Tangent 1 (T1) is projected from the distal tip of the nasal bones, while tangent 2 (T2) is projected from the floor of the nasal aperture (see Fig. 3). The crossing of the tangents provides the pronasale point estimation (prn′est). The ground truth soft tissue profile is shown in the background, note zeroing of the prn′ to (0,0) after [49, 56]. (b) Zoomed view of (a) to show error measurement on x and y coordinate axes (Δx and Δy respectively) and Euclidean distance (Ed)

After tangents were finalized, the soft tissue layer was made visible, so that the ground truth position of pronasale (prn′) could be established and the distance between prn′est and prn′ measured to establish the estimation error in millimeters. To calculate this error, the ground truth position of pronasale (prn′) was zeroed on the x, y cartesian grid after protocols by [49, 56], such that it held a value of (0,0). The distance of the prn′est from the 0,0 position was calculated in three manners: (1) x-coordinate error only (Δx); (2) y-coordinate error only (Δy); and (3) the Euclidean distance (Ed) representing the shortest distance ‘as the crow flies’ between prn′est and prn′ (Fig. 4). Each of the three aforementioned distances were mathematically calculated in the following manner:

$$\triangle x\;=\;prn'_\left(x,\right)\;-\;prn'\left(x,\right)$$

(3)

$$\triangle y\;=\;prn'_\left(,y\right)\;-\;prn'\left(,y\right)$$

(4)

For Method 3, we carefully reviewed and screened full-face 3D renders of all 92 subjects so that any subject with any hint of soft tissue compression/deformation visible along the median plane was removed. Per these criteria, the total sample size used to assess the two-tangent method was 43 individuals (27 males and 16 females) after 49 individuals were removed.

Error measurements

In this study we calculated the mean error, the mean absolute error (MAE) and the SEE wherever possible since each statistic gives slightly different information. For example, a major limitation to using means on raw error values alone is that raw values with opposite signs (+ and −) average towards zero. Thus, mean errors can be misleading, since small values close to zero do not necessarily mean that most individuals possess nil error. In these cases, the mean absolute error (MAE) or alternatively the standard error of the estimate (SEE) offers improvements and more useful information. Signed errors are, however, useful for indicating if there tends to be an under- or over-estimation across the entire sample. In addition, the standard error of the estimate belongs to the class of deviation statistics, such that one standard error of the estimate is the magnitude that spans 65% of error observations when applied as a ± range. This is helpful. For pronasale position, all three error values (mean, MAE and SEE) were calculated for the: x-coordinate, the y-coordinate and the Euclidean distance (Ed).

Intra-observer error

Intra-observer error was calculated by remeasuring 10 subjects with > 8 months (254 days) intervening between the 1st and 2nd set (repeat) measurements to avoid any recall biases. The technical error of measurement (TEM) and relative TEM (rTEM) [67,68,69] served as the basis for the test-retest analysis using the following equations:

$$TEM=\sqrt^_-_\right)}^}}$$

(6)

$$rTEM\:=\frac\times\:100\%$$

(7)

Where:

x1i = the first measurement of an individual “i”.

x2i = the second repeat measurement of an individual “i”.

n = the sample size.