Spherical harmonics to quantify cranial asymmetry in deformational plagiocephaly

Abstract

Cranial deformation and deformational plagiocephaly (DP) in particular affect an important percentage of infants. The assessment and diagnosis of the deformation are commonly carried by manual measurements that provide low interuser accuracy. Another approach is the use of three-dimensional (3D) models. Nevertheless, in most cases, deformation measurements are carried out manually on the 3D model. It is necessary to develop methodologies for the detection of DP that are automatic, accurate and take profit on the high quantity of information of the 3D models. Spherical harmonics are proposed as a new methodology to identify DP from head 3D models. The ideal fitted ellipsoid for each head is computed and the orthogonal distances between head and ellipsoid are obtained. Finally, the distances are modelled using spherical harmonics. Spherical harmonic coefficients of degree 2 and order − 2 are identified as the correct ones to represent the asymmetry characteristic of DP. The obtained coefficient is compared to other anthropometric deformation indexes, such as Asymmetry Index, Oblique Cranial Length Ratio, Posterior Asymmetry Index and Anterior Asymmetry Index. The coefficient of degree 2 and order − 2 with a maximum degree of 4 is found to provide better results than the commonly computed anthropometric indexes in the detection of DP.

Smartphone Photogrammetric Assessment for Head Measurements

“…Photogrammetric Medical Deformation Assessment Solutions (PhotoMeDAS, https: //PhotoMeDAS.eu, accessed on 9 November 2022, Universitat Politècnica de València, València, Spain) was developed as a cost-effective tool for measuring and evaluating cranial deformation in infants [17]. This innovative solution consists of a coded cap that is placed on the infant's head, a smartphone application used to record the head cap's position relative to its barycenter, and a cloud-based processing system that automatically generates the 3D model of the head along with anthropometric deformational indices.…”

Assessment of Cranial Deformation Indices by Automatic Smartphone-Based Photogrammetric Modelling

“…From the 21 anthropometric cranial parameters and indices determined automatically by PhotoMeDAS (Tables 3 and 4 Accuracies up to 2% in indices are sufficient for a proper diagnostic [13]. Therefore, the uncertainties obtained with PhotoMeDAS for the main anthropometric cranial indices, i.e., CI, OCLR, and MI, are acceptable, even assuming minor uncertainties of 0.5 mm in the coordinates; this is also true considering uncertainties up to 1.5 mm for TI, which is clearly a safe value for both the non-scale-corrected and the scale-corrected 3D models (Figures 7 and 8).…”

“…deformation in infants [11][12][13]. It is composed of a cod smartphone application used to record the overall hea a cloud-based processing system that yields the head' termination of deformational indices.…”

“…Assuming some typical uncertainties in the measurement of coordinates along each axis, σ x , σ y , and σ z , which can be determined after the comparison with the ground truth and be regarded as statistically different or statistically equal among them (at this stage, we will not necessarily restrict the derivation to the first case), we can compute the expressions for the uncertainty propagation of these coordinate measurement uncertainties, σ x , σ y , and σ z , throughout Equations ( 1)- (8). In doing so, we take into account that a tri-axial ellipsoid has been considered the ideal shape for a non-deformed cranium [13,25]. Let us denote by A, B, and C the semiaxes of the tri-axial ellipsoid along the x-, y-, and z-axes, respectively.…”

“…Photogrammetric Medical Deformation Assessment Solutions (PhotoMeDAS, https: //photomedas.eu, accessed on 9 November 2022, Universitat Politècnica de València, València, Spain), a low-cost tool, was developed for measuring and evaluating cranial deformation in infants [11][12][13]. It is composed of a coded cap fitted on the infant's head, a smartphone application used to record the overall head cap targeting its barycenter, and a cloud-based processing system that yields the head's 3D model with the automatic determination of deformational indices.…”