Predicting and comparing three corrective techniques for sagittal craniosynostosis

Abstract

Sagittal synostosis is the most occurring form of craniosynostosis, resulting in calvarial deformation and possible long-term neurocognitive deficits. Several surgical techniques have been developed to correct these issues. Debates as to the most optimal approach are still ongoing. Finite element method is a computational tool that’s shown to assist with the management of craniosynostosis. The aim of this study was to compare and predict the outcomes of three reconstruction methods for sagittal craniosynostosis. Here, a generic finite element model was developed based on a patient at 4 months of age and was virtually reconstructed under all three different techniques. Calvarial growth was simulated to predict the skull morphology and the impact of different reconstruction
techniques on the brain growth up to 60 months of age. Predicted morphology was then compared with in vivo and literature data. Our results show a promising resemblance to morphological outcomes at follow up. Morphological characteristics between considered techniques were also captured in our predictions. Pressure outcomes across the brain highlight the potential impact that different techniques have on growth. This study lays the foundation for further investigation into additional reconstructive techniques for sagittal synostosis with the long-term vision of optimizing the management of craniosynostosis.

Full text

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Predicting and comparing three
corrective techniques for sagittal
craniosynostosis
Connor Cross1, Roman H. Khonsari2, Dawid Larysz3, David Johnson4, Lars Kölby5 &
Mehran Moazen1*
Sagittal synostosis is the most occurring form of craniosynostosis, resulting in calvarial deformation
and possible long-term neurocognitive decits. Several surgical techniques have been developed
to correct these issues. Debates as to the most optimal approach are still ongoing. Finite element
method is a computational tool that’s shown to assist with the management of craniosynostosis.
The aim of this study was to compare and predict the outcomes of three reconstruction methods for
sagittal craniosynostosis. Here, a generic nite element model was developed based on a patient
at 4 months of age and was virtually reconstructed under all three dierent techniques. Calvarial
growth was simulated to predict the skull morphology and the impact of dierent reconstruction
techniques on the brain growth up to 60 months of age. Predicted morphology was then compared
with in vivo and literature data. Our results show a promising resemblance to morphological outcomes
at follow up. Morphological characteristics between considered techniques were also captured in
our predictions. Pressure outcomes across the brain highlight the potential impact that dierent
techniques have on growth. This study lays the foundation for further investigation into additional
reconstructive techniques for sagittal synostosis with the long-term vision of optimizing the
management of craniosynostosis.
Sagittal craniosynostosis is the result of the premature fusion of the sagittal suture, with an occurrence rate of
1 in every 10,000 live births1–4. It is the most common form of craniosynostosis, with several studies reporting
a signicant increase in its presents over the last 30 years5,6. Raised intracranial pressure, potentially leading
to cognitive impairment has been related to the calvarial deformation3,7,8. e rst corrective techniques were
developed in the late nineteenth century to restore the normative skull shape9,10. In recent times, craniofacial
centres have adopted a number of techniques. ese range from strip craniotomy (removal of the fused suture)
and total calvarial remodelling (reshaping of bone) to spring assisted cranioplasty (bone widening using springs)
and helmet therapy (postoperative skull shaping)11–15. As a result, the most optimum method of treatment and
their respective outcomes are still debated among craniofacial surgeons16–20.
Finite element (FE) method is a powerful computational tool used to analyse a wide range of engineering
solutions21. Recently, FE studies have investigated the management of craniosynostosis22–26. Advanced methods
have accurately simulated calvarial growth and bone formation in developed models27–32. Such methods have the
potential to investigate the biomechanics of craniosynostosis and predict various sagittal synostosis outcomes
under a range of reconstructions. However, validating our approach with pre-existing data is critical for building
condence in our FE predictive results33.
e aim of this study was to investigate the potential biomechanical dierences between three corrective
techniques used for the management of sagittal craniosynostosis i.e. two variations of spring-assisted cranioplasty
(SAC) vs. modied strip craniotomy (MSC) using a generic FE approach. e primary intention for this research
was to directly compare the spring vs. the strip techniques since from a biomechanical point of view the main
dierence between these techniques are the width of craniotomy and the presence or absence of the springs.
OPEN
1Department of Mechanical Engineering, University College London, London, UK. 2Department of Maxillofacial
Surgery and Plastic Surgery, School of Medicine, Necker – Enfants Malades University Hospital, Assistance
Publique – Hôpitaux de Paris, University of Paris, Paris, France. 3Department of Head and Neck Surgery for
Children and Adolescents, University of Warmia and Mazury in Olsztyn. Ul, Zolnierska 18a, 10-561 Olsztyn,
Poland. 4Oxford Craniofacial Unit, Oxford University Hospital, NHS Foundation Trust, Oxford, UK. 5Department
of Plastic Surgery, Sahlgrenska University Hospital, The Sahlgrenska Academy, University of Gothenburg,
Gothenburg, Sweden. *email: m.moazen@ucl.ac.uk
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Materials and methods
A preoperative generic 3D model of a sagittal craniosynostosis patient at 4months of age was developed based
on computed tomography (CT) data. is generic model was then virtually reconstructed based on two varia-
tions of spring-assisted cranioplasty (SAC) and the modied strip craniotomy (MSC). Post-operative calvarial
growth was modelled using the FE method. Given the importance of validation of the computational models,
results obtained from the SAC methods were compared versus a series of invivo CT data while results obtained
from the MSC technique were compared vs. published data in the literature. e overall morphology of the skull,
spring displacement, the pattern of bone formation across the calvarial, and the level of contact pressure that each
technique imposes on the growing brain (here, the intracranial volume) was investigated post-operatively. Note
the generic preoperative model used in this study was described and validated in detail elsewhere34.
Surgical techniques. Spring-assisted cranioplasty (SAC): e SAC procedure and parameters replicated in
this study were based on the standard Gothenburg procedure, as detailed by Lauritzen etal.,10 and more recently
by Satanin etal.,35. A 1mm wide craniotomy, extending from the anterior fontanelle to lambdoid suture was
performed. Two holes were burred approximately 15mm apart, across the craniotomy for spring placement
(Fig.1A). ese were performed 40mm (anterior spring), 55mm (middle spring – for 3 SAC) and 75mm (pos-
terior spring) from the coronal suture. e quantity of springs used can vary between two (i.e. 2 SAC) and three
(i.e. 3 SAC). Insitu spring displacement of approximately 5mm occurs naturally (denoted as: ‘release’), allowing
for mediolateral widening upon insertion of the springs (Fig.1B). ese were then removed in a secondary pro-
cedure 5months post-insertion (Fig.1C). Aer which, calvarial growth continued unaided (Fig.1D).
Modied strip craniotomy (MSC): For our comparative technique, we reconstructed the procedure described
by omas etal.,13. In brief, A 50mm wide vertex craniotomy was created across the anteroposterior, extending
from coronal to lambdoid.
Image processing. A previously described model was used for this study34. In short, CT data of a pre-
operative sagittal synostosis patient at 4months of age was obtained from the Hôpital Necker – Enfants Malades
Craniofacial Surgery Unit (Centre de Référence Maladies Rares Craniosténoses et Malformations Craniofaciales
CRANIOST, Paris, France). Full ethical protocol for undertaking this study was approved by the institutional
review board and committee from the Necker – Enfants Malades University Hospital. Informed consent was
granted from the patient’s guardian. All patient information was anonymized prior to the retrieval of CT data
in accordance with the HIPAA (1996). Image resolution was measured at 0.625 × 0.625mm. Full consent was
granted by the child’s guardians for the purposes of this study. e image processing package, Avizo (V9.2.0;
ermo Fisher Scientic, Mass, USA) was used for 3D model development. e calvarial bone, sutures, and
intracranial volume (ICV i.e. all internal calvarial components) were all segmented in preparation for FE simu-
lations. Calvarial bone was automatically highlighted using the Hounseld scale method. Sutures and ICV were
Preoperative
3 months -insertion Release
Postoperative
9 months -removal 36 months
(A) (B) (D)
(C)
MPa
30 230 530830 2030 3230 6830Bone Craniotomy
(0.3MPa)
Follow up
15 mm
Figure1. Simulation workow. All techniques were replicated at 4months of age, when spring insertion (A)
and ‘release’ (B) were replicated for SAC. Skull growth, calvarial healing and bone formation at sutures were
replicated up to 9months of age, when springs were removed (C). Skull growth then continued up to 36months
of age [D].
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highlighted manually. e detailed 2 SAC, 3 SAC and MSC craniotomies, based on the techniques described
above, were then replicated on the pre-operative model prior to calvarial growth.
Finite element analysis. A quadratic tetrahedral mesh consisting of 4 million elements in total was
selected aer a mesh convergence study. Where 3,100,000 elements were used to mesh the bone, sutures, and
craniotomy based on the von Mises strain and 900,000 elements were used to mesh the ICV based on the con-
tact pressure. Mesh convergences was seen to have been achieved once both the strain and pressure values had
plateaued by ± 5%. Alterations to individual element geometries were performed to reduce the initial penetration
between elements and decrease the aspect ratio. e fully meshed model was then imported into the FE package,
ANSYS (V19.0; Canonsburg, PA, USA), to simulate calvarial growth, bone formation and contact between the
ICV-inner calvarial interface. All materials were dened as linear isotropic. Bone, ICV, suture and craniotomy
properties were assigned an elastic modulus of 421MPa, 10MPa, 30MPa and 0.3MPa, respectively32,34,36,37.
Sensitivity tests were carried out which varied these stinesses initially (see: Supplementary TableS1 & S2) to
achieve the target craniotomy widening (i.e. approx. 5mm) seen aer spring ‘release’. Both the ICV and crani-
otomy Poisson’s ratio was selected as 0.1. A Poisson ratio of 0.3 was selected for the bone and sutures.
Boundary conditions: A Hertzian frictional contact method was used to predict pressure changes across the
ICV-inner calvarial interfaces, as previously implemented by Malde etal.,32. To summarise, a penalty-based
surface to surface contact was established with a normal contact stiness of 50N/mm, a penetration tolerance
of 0.5mm and a normal/tangential friction coecient of 0.1 to reduce the level of penetration. ese surfaces
were initially in contact, which then allowed the freedom of movement in the normal/tangential direction dur-
ing skull growth. All bone-suture, bone-craniotomy and craniotomy-suture interfaces were assumed to be in
bonded contact, with no relative motion or separation authorised. Nodal constraints were placed around the
foramen magnum and across the nasal ridge in all degrees of freedom to avoid rigid body motion. ermal
expansion analogy was used to model the ICV growth as previously described by Libby etal.,31. Here, the ICV
was increased from the initial pre-operative volume (measuring 659ml) to the target invivo follow-up volume
in ve load-steps for both SAC (i.e.1240ml) and six for MSC (i.e. 1376ml). e predicted target volumes were
correlated with values seen in the literature to estimate the age of the model at each load-step38.
Bone formation: A previously described algorithm detailed by Marghoub etal.,28 was implemented to simulate
the bone formation at the sutures and craniotomies during calvarial growth. In brief, elements were selected at a
specied radius along the bone-suture/bone-craniotomy linings. e elastic modulus of these newly and previ-
ously selected elements was increased by 100MPa for each month of growth. e elastic modulus of bone was also
increased by 125MPa for each month of growth. ese changes in the elastic modulus of the bone/newly formed
bone were estimated based on extrapolation of the bone properties that were measured during the development
of normal mouse37 to human (considering ICV growth). A radius of 0.2mm for every month of calvarial growth
was selected for the coronal, lambdoid and squamosal suture formation based on observations in literature39,40
and prior sensitivity studies34 to predict the timing of closure. e metopic suture and anterior fontanelle were
set to completely form by 24months of age to represent the invivo scenario41,42. A sensitivity study was carried
out to investigate the morphological eect of dierent rates for bone formation at the craniotomies (see: Sup-
plementary TableS3 & FigureS1). Following these sensitivity tests, a rate of 10.8mm per month of growth was
specied for the rate of calvarial healing. Aer each load-step, the geometry of the skull, displacement across the
springs length and forces were updated to the newly deformed shape and values, respectively, which was then
used to estimate the morphology of the skull at the next step/age. No adaptive remeshing algorithm was used
here, as the geometry was updated at each interval. is approach avoided element distortions that would have
otherwise occurred due to the large deformations occurring.
Spring mechanics: To replicate the characteristics of the SAC, linear spring elements (i.e., COMBIN14) were
positioned approximately 15mm across the craniotomy at insertion (i.e. 5mm from the craniotomy into the
parietal bone on either side plus the 5mm gap between equalling to a total of 15mm – see Fig.1A). ese ele-
ments behave under Hookean law, where the outward force was directly proportional to the level of tension/
compression26,43. Here, a series of invitro measurements were carried out to identify the force–length relationship
of the springs (See Appendix S6). In short, an average force of 8N was produced when crimping a wire initially
measuring 100mm to 15mm (based on leg-to-leg measurements – See: Fig.1A). ese values were used to
calculate the spring stiness (K) at ‘release’ using Eq.1:
where
f
represents the bilateral force and
dx
represents the change in spring displacement (here initially, 100mm
minus 15mm). A sensitivity test was carried out to investigate the eect of altering the initial spring force val-
ues by updating the spring stiness on the predicted morphology (see: Supplementary TableS4 & S5). During
‘release’ and calvarial growth, spring forces and spring leg distances values were automatically calculated and
updated using Eq.2:
Upon removal, the modelled springs were given a xed force of 0N. e growth then continued unaided to
the target follow up age. Note that the spring stiness remained unchanged throughout all simulations.
Simulation and measurements: Both SAC and MSC techniques underwent calvarial growth up to the follow-
up ages of 36 and 60months, respectively. Both predicted SAC calvarial morphologies were compared against
a series of patient CT data sets undergoing the standard Gothenburg SAC procedure and retrieved from the
Department of Plastic Surgery at the Sahlgrenska University Hospital (Gothenburg, Sweden). Full ethical proto-
cols for undertaking this study were reviewed and approved by the institutional review board and committee at
(1)
K
=
f/dx
(2)
f
=
K
∗
dx
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the Department of Plastic Surgery at the Sahlgrenska University Hospital. Informed consent was granted from
all patient’s guardians. All patient CT information provided was anonymized in accordance with the Health
Insurance Portability and Accountability Act of 1996 (HIPAA). CT data was grouped in accordance with the
number of springs used for the treatment and classied as 2 SAC (n = 10) and 3 SAC (n = 8), respectively. e
pre-operative CT for both groups were taken at a mean age of 4.9 ± 1.3 and 4.1 ± 0.7months, respectively. Post-
operative CT was taken at 10 ± 1.3months of age, where the springs were removed. Follow-up CT was taken at
36 ± 2.0months of age. Predicted MSC morphology was compared against reported CI outcomes of the same
technique detailed by omas etal.,13 as CT data for this technique was unavailable for direct morphological
comparisons. Measurements of the length (from glabella to opisthocranion), width (between the le and right
euryons) and circumference were undertaken. e cephalic index (CI) was calculated by multiplying the width
against the length and dividing by one hundred. 3D distance mapping was also used to observe predicted under-
or over-estimation vs. the CT data provided. Our predicted morphology was compared against a single CT skull
that matched closest to the overall mean length/width measurements within both SAC groups. e predicted
spring opening was measured during skull growth and compared against CT data at 9months of age by manu-
ally measuring the leg-to-leg distance against each CT patient data using the aforementioned image processing
soware. Predictive bone formation was recorded throughout our simulations to observe dierences in suture
and craniotomy closure times between techniques. Contact pressure across the ICV surface was recorded to
observe the eects each considered technique had on the brain (here ICV) growth.
Results
Morphological comparisons. Table1 provides a summary of the invivo CT and predicted measurements
corresponding to each technique at dierent ages. At pre-operative, the 4months of age model used for the FE
simulations measured a skull length, width, circumference, ICV and cephalic index of 137.2mm, 108.1mm,
430.6mm, 659.9ml and 78.7, respectively. e average age of patients who were treated with 2 SAC, 3 SAC (from
our CT data) and MSC (from the literature13) were 4.9 ± 1.3, 4.1 ± 0.7 and 6months (range: 3.1–9.5), respectively
with corresponding CI of 76.9 ± 2.7, 74.3 ± 3 and 65.7 ± 4.7.
Table 1. Overview of predicted vs. invivo measurements across all technique. Dashes indicate unavailable
data. e pre-operative FE model used for this study was at the age of 4months with skull length, width,
circumference, ICV and cephalic index of 137.2mm, 108.1mm, 430.6mm, 659.9ml, 78.7 respectively. NA at
the pre-operative stage for prediction data corresponds to the initial FE model that was the same model across
all techniques that was then reconstructed to replicate each technique i.e. predicted the shape at dierent ages.
2 SAC 3 SAC MSC [omas etal., 2015]
Clinical data Prediction data Clinical data Prediction data Clinical data Prediction data
n: 10 1 8 1 34 1
(%) Male: 80 1 50 1 N/A 1
Preoperative
Age (months): 4.9 ± 1.3 N/A 4.1 ± 0.7 N/A 6.0 ± 3.1–9.5 N/A
Mean length (mm): 148.5 ± 6.1 N/A 150.5 ± 9.9 N/A - N/A
Mean width (mm): 114.3 ± 5.7 N/A 111.5 ± 5.6 N/A - N/A
Mean circumference
(mm): 455.3 ± 68.0 N/A 457.2 ± 27 N/A - N/A
Mean intracranial
volume (ml): 800.9 ± 102.1 N/A 800.8 ± 88.6 N/A - N/A
Mean cephalic index: 76.9 ± 2.7 N/A 74 ± 3.4 N/A 65.7 ± 4.7 N/A
Postoperative:
Age (months): 10.9 ± 1.3 9.0 10.6 ± 0.3 9.0 12 9.0 12.0
Mean length (mm): 162.5 ± 8.0 143.3 165.2 ± 6.1 142.4 - 143.2 143.4
Mean width (mm): 129.8 ± 5.0 112.5 129.1 ± 6.6 113.6 - 112.9 116.2
Mean circumference
(mm): 486.5 ± 59.4 397.3 429.0 ± 107.0 397.2 - 395.5 416.8
Mean intracranial
volume (ml): 1089.2 ± 144.9 829.5 1131.2 ± 130.5 829.5 - 817.4 1007.0
Mean cephalic index: 79.9 ± 2.9 78.5 78.2 ± 4.5 79.7 73.3 ± 5.2 78.8 81.1
Follow up
Age (months): 37.15 ± 2.0 36.0 37.6 ± 1.3 36.0 60 36 60
Mean length (mm): 176.9 ± 9.3 163.8 178.8 ± 8.8 163.4 - 155.8 155.1
Mean width (mm): 135.1 ± 5.4 122.3 132.7 ± 6.4 121.2 - 122.3 124.7
Mean circumference
(mm): 512.4 ± 35.4 454.4 523.2 ± 37.0 453.3 - 429.4 437.0
Mean intracranial
volume (ml): 1245.0 ± 166.8 1261.0 1239.0 ± 133.8 1261.0 - 1240.4 1376.9
Mean cephalic index: 76.4 ± 2.5 74.6 74.3 ± 3.8 74.1 71.5 ± 4.3 78.4 80.3
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At the post-operative stage, the FE model predicted CI’s of 78.5, 79.7 and 78.8 at 9months of age and 74.6,
74.1 and 80.3 at 36months of age for the 2 SAC, 3 SAC and MSC technique, respectively. At 12months of age,
CI of 81.1 was predicted for MSC. e invivo CT and literature13 CI measurements were 79.9 ± 2.9, 78.2 ± 4.5
and 73.3 ± 5.2, at 9–12months of age, and 76.4 ± 2.5, 74.3 ± 3.8 and 71.5 ± 4.3 at 36months of age for the 2 SAC,
3 SAC and at 60months of age for the MSC, respectively. Hence, while the FE model captured the post-operative
relapse in the SAC techniques, it failed to capture the relapse in the MSC technique (Fig.2).
Spring opening. Increased spring opening from insertion (15.2mm) to ‘release’ (19.5mm) was predicted
in both SAC techniques, which in turn lead to a 5mm widening of the craniotomy (Fig.3). By 9months of age,
FE models under-predicted the spring opening data observed invivo in the anterior (29.2mm; 31.1mm vs.
Figure2. Predicted vs. invivo cephalic index data with SD. Showing 2 SAC (A), 3 SAC (B) & MSC outcomes
(C).
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45.5 ± 10.5mm; 39.0 ± 8.5mm), central (31.9mm vs. 43.1 ± 5.0mm) and posterior springs (29.2mm; 31.3mm
vs. 51.4 ± 8.9mm; 42.3 ± 3.7mm).
Figure3. Predicted vs. invivo spring opening data with SD. Showing anterior (A), central (B) & posterior (C)
springs in both SAC techniques. Diagrams show regions where measurements were performed.
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3D displacement mapping results highlight the under- and over-prediction at several ages for both 2 SAC and
3 SAC techniques (Fig.4 & 5, respectively). Note that pre-operative CT data is compared against the predictive
release morphology. An under-prediction of the anterior and posterior regions was evident from release to post-
operative (i.e. 9months) across both techniques. By follow up (i.e. 36months), a good morphological match was
observed, with minimal under-prediction across the mediolateral.
Bone formation. Predicted bone formations and overall calvarial morphologies are shown in Fig.6. At
9months of age, both SAC techniques predicted complete closure of the craniotomy, while MSC showed large
areas of patency. All sutures showed little formation by this age. By 36months of age, bone was formed across all
the sutures in all considered techniques, with some patency observed at the lambdoid suture in the SAC method.
By this time, new bone was formed at the MSC craniotomy, with all sutures showing complete closure and nar-
rowing compared to the SAC outcomes. Comparing the overall predicted morphology of the skull at 36months
of age between both SAC and MSC techniques highlighted the larger anteroposterior growth of the skull in the
SAC technique in contrast to the larger dorsoventral growth of the skull in the MSC technique.
Contact pressure. Brain growth and contact pressure across the ICV at dierent ages are shown in Fig.7.
When simulating spring release, pressure changes were negligible. At 9months of age, greater pressure was
observed across the ICV in both SAC vs. MSC. At 36months of age, an even distribution of the pressure was
observed in the SAC vs. MSC. Greater concentration of high pressure was observed at the anterior, mediolateral
and across the anterior fontanelle in MSC while both SAC techniques highlighted minor elevated levels of pres-
sure at the mediolateral sides of the skull in the temporal regions.
Discussion
Many variations of sagittal craniosynostosis correction exist, ranging from invasive to non-invasive procedures14.
Large debates over the optimal outcome between techniques are still ongoing. Since the mid-twentieth century,
computational models using nite element (FE) method have been widely used to investigate the biomechanics
of a range of clinical conditions and their managements44–46. FE shows promise in assisting with the manage-
ment of various forms of craniosynostosis33. In this study, we attempted to illustrate the use of FE method in
which the biomechanics of three corrective techniques were compared. Morphological outcomes were compared
against our own CT data used for this study and literature data at various postoperative and follow up time
points. Our results highlight the potential impact of the surgical techniques on the overall morphology of the
skull, the pattern of bone formation across the craniotomies and other sutures as well as the pressures that they
Figure4. 2 SAC 3D distance plot at respective ages against mean invivo CT skull.
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may apply across the whole intracranial volume. e work here shows promising perspectives in optimizing the
management of craniosynostosis.
Morphological comparisons. Our results under-predicted changes in skull length and width in predictive
vs. invivo data. is could have been attributed to predicted ICV measurements, particularly at postoperative
time points. e simulations were run by increasing the ICV to an ‘average’ value at a specic age based on the
literature and our previous studies34,38. However, when comparing the FE results vs. the average ICV of the
patients considered in this study at 9–12months of age, there was a 20% dierence between the two (based
Figure5. 3 SAC 3D distance plot at respective ages against mean invivo CT skull.
Figure6. Bone formation predictions across sutures/craniotomy across all techniques.
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on the SAC technique). is could explain the large under-predictions in morphological outcomes at this age
range. A closer match was achieved at 36months, as this variation (between the in silico and invivo ICVs) was
seen to reduce to 1% (based on the SAC technique). is closer match in volume by 36months may be attrib-
uted to the reduction in growth seen aer the rst year of life vs. our predicted linear growth in this study. One
could argue that the preoperative CT data from our SAC cohort could have been used to develop a FE model
for a true validation of the FE results. However, we considered (1) using a generic model to compare dierent
surgical techniques (2) to keep a level of consistency regarding the preoperative morphology between our com-
pared techniques shown here and thus, chose to utilize our previously validated FE model34. e CI was seen
to vary slightly from the preoperative period to the time of spring removal in predictive and CT data (Fig.2).
By 36months, there was a reasonable match between the in silico and invivo data. Although a more signicant
relapse was seen in predictive outcomes, it is interesting to see this postoperative pattern being accurately pre-
dicted. Further, the antero-posterior growth vector of the skull observed post-operatively in the SAC technique
invivo was also captured by the in silico FE results (Table1).
Reported data for MSC by omas etal.,13 was limited for the present study. Nevertheless, a comparison
of CI was undertaken to highlight the potentials as well as the limitations of our modelling approach. Greater
changes were seen in reported invivo data vs. our predicted data. Further, our predicted CI at 60months of age
overpredicted what was clinically observed in the study13 (see Fig.2C). e dierences between the invivo and in
silico results here could be due to a number of factors e.g. (1) the initial CI of the patient that we used to develop
the FE models was considerably higher than the average pre-operative CI of the patients considered in the study
of omas etal.,13 (i.e. 78.7 vs. 65.7). e pre-operative CI has indeed been shown to be clinically a major factor
in determining the postoperative outcomes13; (2) there could have been minor surgical technical details that
have not been captured in the simulations performed here; (3) It is also possible that the ICV of the patients in
the study of omas etal.,13 were lower than the ‘average’ values that were used in the FE simulations to model
skull growth in the present study. Nevertheless, we believe that the virtual comparative nature of the assessments
made between the dierent techniques considered here is interesting and valuable. Allowing our predictions
to determine the growth under two extreme conditions (i.e. 5mm vs. 50mm craniotomy). Our predictions,
considering their limitations, highlights that SAC technique can perhaps lead to a more antero-posterior growth
of the skull whereas MSC technique used here can perhaps lead to a more dorsal–ventral growth of the skull.
All techniques demonstrated an improvement in the CI before relapsing, although this was seen to be greater in
the MSC predictions. is dierence was attributed to the greater increase in length seen in SAC vs. MSC and a
reduction in width. It could be argued that if further growth was undertaken beyond 60months for MSC, this
relapse would continue beyond the value seen in the SAC. Considering morphological measurements shown,
our current analysis highlights improved outcomes in the MSC vs. SAC predictions. On the other hand, it must
be noted that the MSC technique is no longer performed at the Oxford Craniofacial Unit given that the study of
omas etal.,13,47 highlighted that the total calvarial remodelling technique performed in this unit resulted in
higher CI and better clinical outcomes for these patients.
Spring opening. Considering both SAC techniques, although our comparison of spring opening distance
was restricted to a single time point, predictive results appeared to match in the low range of invivo data at
9months (Fig.3). However, reports from Windh etal.,48 and Lauritzen etal.49, agree well with the distance meas-
ured upon release. Our spring predictions only gain an additional 11mm in length from release to 9months.
Other centres have documented these changes in greater detail. Yang etal.,43 studied the spring opening and
bi-temporal displacement of SAC patients during the entire 3months of treatment. Spring opening was seen to
Figure7. ICV pressure predictions across ICV-bone surface for all techniques.
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increase rapidly from 7–10mm to 23mm in the rst 2h aer insertion. is rate of opening was seen to decrease
to 4mm aer only 8h following insertion, aer which the length was seen to plateau. Although these larger dis-
placements were not seen in our predictions, it should be noted that a larger spring forces were used upon inser-
tion (14N vs. 8N). Further, such levels of insitu craniotomy and spring widening observed in this work do not
fully reect the larger levels seen in other craniofacial centres under dierent operative parameters26. However,
as our intention was to focus on a single centres SAC conditions (i.e. Gothenburg, Sweden), such considerations
were examined in a sensitivity analysis (See: Supplementary TableS4). Both 2 SAC and 3 SAC techniques show
little change in opening spring length by 9months, with all springs displacing by approximately 10mm from
‘release’ to removal. Interestingly, incorporation of a middle spring for 3 SAC showed little eect on morphologi-
cal outcomes, particularly that of biparietal widening. Nonetheless, these predictions, cross-referenced with our
morphological measurements, may prove informative for surgeons in reducing the risk of damaging the sagittal
sinus and/or lower risk of spring dislodgement as fewer distractors may be necessary to achieve the same mor-
phological goals with regards to this study50,51.
Bone formation. A previously developed approach to model bone formation detailed by Marghoub etal.,28
was adopted in this study. Given that the formation rate at the cranial sutures and craniotomies in humans
could be dierent from what was used in our previous study, various sensitivity tests were carried out to justify
the choice of this parameter (see Supplement FigureS1 & TableS3). Overall, we observed that the patterns of
bone formation at dierent sutures and craniotomies appeared to match that of the invivo observations from
the literature39–42 and the CT cohort used at 9 and 36months of age. For example, our results showed a greater
posterior/occipital narrowing at 36months of age in both SAC models. Such a phenomenon was caused by
the fusion of the craniotomy and the patency of the lambdoid sutures, allowing for angular changes across the
parietal bone plates, a phenomenon also reported in the clinical study of Satanin etal.,35. Further, considering
the pattern of bone formation across the MSC technique, our model predicted initial bone formation across the
craniotomy by 36months of age. is is in line with observational studies of the same technique performed at
a similar age52,53. A minor vertex bulging was evident by 36months across the anterior-fontanel region. Such
characteristics have been linked to ossication delays reported by Marucci etal.,54, who investigated the causes
of ‘copper beaten’ appearances in previously treated MSC patients. Although our predictions display bone for-
mation at the craniotomy by 36months of age, large patency was seen at 9months, which has resulted in a
characteristic vertex bulging.
Contact pressure. Further to predicting morphological and ossication outcomes, this work highlights the
changes in pressure across the, here, ICV. Our results highlight that the MSC technique perhaps constrains the
growth of the ICV (as a whole) to a larger extent compared to the SAC techniques. is observation was most
apparent by 36months, where pressure was higher in isolated regions (Fig.7). is prediction suggests that
improved morphological outcomes, as seen in this work, may not correlate to unrestricted growth and thus,
lower overall pressure. Whether this higher pressure has any neurofunctional impact on brain growth or not can
not be commented based on our data at present and requires a much more detailed clinical investigation. None-
theless, this study highlights the huge potentials of nite element methods in understanding the biomechanics
of dierent management techniques have on brain growth.
Limitations. Despite promising resemblances between the in silico and invivo results reported in this
study, our study has several limitations. (1) Our simulations establish a bone-craniotomy & bone-suture lining
method of formation. In reality, it is known that the dura mater possesses osteogenic properties which pro-
mote spontaneous ‘islands’ of bone across large calvarial defects55. Such advanced complexities and factors of
ossication were not modelled in this study while these can be considered in future studies. Further, the values
determined for replicating bone stiness changes (i.e. 100 and 125MPa for each month) and constituting the
stage of ‘closed’ for both sutures and craniotomy stated here is highly generic and may not represent the true
changes in ossication postoperatively. (2) Our approach in predicting ICV pressure postoperatively aimed to
compare the potential benets between techniques and assess brain growth56. It has been suggested that dierent
surgical techniques can result in dierent neuropsychological outcomes, but such relations are disputed56,57. If at
all, surgical outcome relates to neuropsychological outcome, our presented method predicts relevant skull size
measures such as length, width and ICV and also predicts a more dynamic parameter, pressure, in the form of
contact pressure mapping. erefore, the presented method provides not only predictions of the morphological
outcome but introduces a parameter with potential direct physiological signicance. If in the future, we manage
to determine the impact of the dierent outcome parameters on neuropsychological outcomes, FE models will
add considerable value to surgical planning.
Conclusion
e current study is, to the best of our knowledge, the rst comparative analysis in predicting various treatment
outcomes for sagittal craniosynostosis using a FE approach. e discussed results show promising perspectives in
accurately predicting post-operative morphology and characteristics seen invivo and various reported scenarios.
Further work aims to broaden the current number of techniques in this study and evaluated the biomechanical
impact of these techniques accordingly.
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Received: 16 April 2021; Accepted: 8 October 2021
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Acknowledgements
is work was supported by the Rosetrees Trust through the PhD research project [A1899] and PhD Plus project
[PhD2021\100017].
Author contributions
C.C., L.K., M.M. contributed to writing the main manuscript text. R.H.K., DL, L.K., D.J. contributed to providing
clinical data detailed in the main manuscript text and guidance/support throughout the study. All authors have
reviewed the submitted manuscript.
Competing interests
e authors declare no competing interests.
Additional information
Supplementary Information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 021- 00642-7.
Correspondence and requests for materials should be addressed to M.M.
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