Locally Affine Diffeomorphic Surface Registration and Its Application to Surgical Planning of Fronto-Orbital Advancement

Abstract

Metopic craniosynostosis is a condition caused by the premature fusion of the metopic cranial suture. If untreated, it can result into brain growth restriction, increased intra-cranial pressure, visual impairment, and cognitive delay. Fronto-orbital advancement is the widely accepted surgical approach to correct cranial shape abnormalities in patients with metopic craniosynostosis, but the outcome of the surgery remains very dependent on the expertise of the surgeon because of the lack of objective and personalized cranial shape metrics to target during the intervention. We propose in this paper a locally affine diffeomorphic surface registration framework to create an optimal interventional plan personalized to each patient. Our method calculates the optimal surgical plan by minimizing cranial shape abnormalities, which are quantified using objective metrics based on a normative model of cranial shapes built from 198 healthy cases. It is guided by clinical osteotomy templates for fronto-orbital advancement, and it automatically calculates how much and in which direction each bone piece needs to be translated, rotated, and/or bent. Our locally affine framework models separately the transformation of each bone piece while ensuring the consistency of the global transformation. We used our method to calculate the optimal surgical plan for 23 patients, obtaining a significant reduction of malformations (p < 0.001) between 40.38% and 50.85% in the simulated outcome of the surgery using different osteotomy templates. In addition, malformation values were within healthy ranges (p > 0.01).

Figures

Fig. 1

Cranial bones: (a) frontal, (b) lateral and (c) posterior views of the cranium of a healthy control subject (age 1 month). The main cranial bones are labeled in black as F (frontal), P (parietal), T (temporal), and O (occipital) and are separated by open sutures. The main sutures are labeled in blue as MS (metopic), CS (coronal), SqS (squamous), SS (sagittal), and LS (lambdoid).

Fig. 2

Pipeline of the proposed framework. We segment the cranial bones from the CT image of a patient, and we evaluate different subdivisions of the cranial bones following a set of predefined osteotomy templates. For each osteotomy template evaluated, we calculate the optimal surgical plan using the registration framework proposed, which minimizes the difference between the patient’s cranial shape and its closest normal from a normative statistical shape multi-atlas. Finally, we evaluate the surgical outcome from the optimal plan calculated with each osteotomy template based on different criteria: minimization of malformations, minimization of curvature discrepancies, or minimum bone stress.

Fig. 3

Dynamic weighting scheme proposed. (a) illustrates the problem of the weighting scheme proposed in [18] with an example of which the source surface includes two affine areas (labeled as 1 and 2). The affine regions were predefined before registration so, if a part of the surface was transformed to another region during registration, it would lose its affine properties (as represented with stripes); (b) shows how the proposed scheme updates the regions at each temporal integration step, thus preserving the local properties in the source mesh (e.g. affine). Note how the moving surface becomes more similar to the target surface during registration in terms of distance and curvature.

Fig. 4

Frontal view of the digital osteotomy templates used to calculate the optimal surgical plan, together with the cranium of the reference control case used for segmentation. Each osteotomy template considered the subdivision of the frontal bones and supra-orbital bar in (a) 6, (b) 5, (c) 4, (d) 3, and (e) 2 bone pieces. Each color represents a bone piece remodeled and repositioned during surgery using a local affine transformation.

Fig. 5

Simulated correction of cranial shape abnormalities using our automatic osteotomy plan for a patient with metopic craniosynostosis. Superior (first row) and frontal (second row) views of the malformations and curvature discrepancies on the cranial shape on (b) the pre-operative mesh, and the simulated outcome of the surgical planning calculated for osteotomy plans with (c) 2, (d) 3, (e) 4, (f) 5, and (g) 6 bone pieces. For an improved visualization, Figures (c)–(g) only show the malformations and curvature discrepancies in the transformed bone pieces. As it can be observed, Figures (c)–(g) are more similar to (a) than (b).

Fig. 6

Bar diagram showing on how many patients we should use each osteotomy template to obtain the optimal surgical plan according to the three criteria considered: (1) minimization of malformations, (2) minimization of curvature discrepancies, and (3) minimization of bone stress.