An Overview of Modelling Craniosynostosis Using the Finite Element Method

Optimal untwisting of the orbital bandeau in unicoronal craniosynostosis correction: A finite element analysis

BACKGROUND

Surgical correction of unicoronal craniosynostosis (UCS) is highly complex due to its asymmetric appearance. Although fronto-orbital advancement (FOA) is a versatile technique for craniosynostosis correction, harmonization of the orbital bandeau in UCS is difficult to predict. This study evaluates the biomechanics of the orbital bandeau using different patterns and varying characteristics of inner cortical bone layer osteotomies in a finite element (FE) analysis.

METHOD

An FE model was created using the computed tomography (CT) scan of a 6.5-month-old male infant with a right-sided UCS. The unaffected side of the orbital bandeau was virtually mirrored, and anatomical correction of the orbital bandeau was simulated. Different combinations of osteotomy patterns, numbers, depths, and widths were examined (n = 48) and compared to an uncut model.

RESULTS

Reaction forces and maximum stress values differed significantly (p < 0.01) among osteotomy patterns and between each osteotomy characteristic. Regardless of the osteotomy pattern, higher numbers of osteotomies significantly (p < 0.05) correlated with reductions in reaction force and maximum stress. An X-shaped configuration with three osteotomies deep and wide to the bone was biomechanically the most favorable model.

CONCLUSION

Inner cortical bone layer osteotomy might be an effective modification to the conventional FOA approach in terms of predictable shaping of the orbital bandeau.

Geometric growth of the normal human craniocervical junction from 0 to 18 years old

The craniocervical junction (CCJ) forms the bridge between the skull and the spine, a highly mobile group of joints that allows the mobility of the head in every direction. The CCJ plays a major role in protecting the inferior brainstem (bulb) and spinal cord, therefore also requiring some stability. Children are subjected to multiple constitutive or acquired diseases involving the CCJ: primary bone diseases such as in FGFR-related craniosynostoses or acquired conditions such as congenital torticollis, cervical spine luxation, and neurological disorders. To design efficient treatment plans, it is crucial to understand the relationship between abnormalities of the craniofacial region and abnormalities of the CCJ. This can be approached by the study of control and abnormal growth patterns. Here we report a model of normal skull base growth by compiling a collection of geometric models in control children. Focused analyses highlighted specific developmental patterns for each CCJ bone, emphasizing rapid growth during infancy, followed by varying rates of growth and maturation during childhood and adolescence until reaching stability by 18 years of age. The focus was on the closure patterns of synchondroses and sutures in the occipital bone, revealing distinct closure trajectories for the anterior intra-occipital synchondroses and the occipitomastoid suture. The findings, although based on a limited dataset, showcased specific age-related changes in width and closure percentages, providing valuable insights into growth dynamics within the first 2 years of life. Integration analyses revealed intricate relationships between skull and neck structures, emphasizing coordinated growth at different stages. Specific bone covariation patterns, as found between the first and second cervical vertebrae (C1 and C2), indicated synchronized morphological changes. Our results provide initial data for designing inclusive CCJ geometric models to predict normal and abnormal growth dynamics.

Understanding the influence of surgical parameters on craniofacial surgery outcomes: a computational study

Sagittal craniosynostosis (SC) is a congenital condition whereby the newborn skull develops abnormally owing to the premature ossification of the sagittal suture. Spring-assisted cranioplasty (SAC) is a minimally invasive surgical technique to treat SC, where metallic distractors are used to reshape the newborn's head. Although safe and effective, SAC outcomes remain uncertain owing to the limited understanding of skull-distractor interaction and the limited information provided by the analysis of single surgical cases. In this work, an SC population-averaged skull model was created and used to simulate spring insertion by means of the finite-element analysis using a previously developed modelling framework. Surgical parameters were varied to assess the effect of osteotomy and spring positioning, as well as distractor combinations, on the final skull dimensions. Simulation trends were compared with retrospective measurements from clinical imaging (X-ray and three-dimensional photogrammetry scans). It was found that the on-table post-implantation head shape change is more sensitive to spring stiffness than to the other surgical parameters. However, the overall end-of-treatment head shape is more sensitive to spring positioning and osteotomy size parameters. The results of this work suggest that SAC surgical planning should be performed in view of long-term results, rather than immediate on-table reshaping outcomes.

Automated surgical planning in spring-assisted sagittal craniosynostosis correction using finite element analysis and machine learning

Sagittal synostosis is a condition caused by the fused sagittal suture and results in a narrowed skull in infants. Spring-assisted cranioplasty is a correction technique used to expand skulls with sagittal craniosynostosis by placing compressed springs on the skull before six months of age. Proposed methods for surgical planning in spring-assisted sagittal craniosynostosis correction provide information only about the skull anatomy or require iterative finite element simulations. Therefore, the selection of surgical parameters such as spring dimensions and osteotomy sizes may remain unclear and spring-assisted cranioplasty may yield sub-optimal surgical results. The aim of this study is to develop the architectural structure of an automated tool to predict post-operative surgical outcomes in sagittal craniosynostosis correction with spring-assisted cranioplasty using machine learning and finite element analyses. Six different machine learning algorithms were tested using a finite element model which simulated a combination of various mechanical and geometric properties of the calvarium, osteotomy sizes, spring characteristics, and spring implantation positions. Also, a statistical shape model representing an average sagittal craniosynostosis calvarium in 5-month-old patients was used to assess the machine learning algorithms. XGBoost algorithm predicted post-operative cephalic index in spring-assisted sagittal craniosynostosis correction with high accuracy. Finite element simulations confirmed the prediction of the XGBoost algorithm. The presented architectural structure can be used to develop a tool to predict the post-operative cephalic index in spring-assisted cranioplasty in patients with sagittal craniosynostosis can be used to automate surgical planning and improve post-operative surgical outcomes in spring-assisted cranioplasty.

Biomechanical Investigation of Hallux Valgus Deformity Treated with Different Osteotomy Methods and Kirschner Wire Fixation Strategies Using the Finite Element Method

The aim of this study was to propose a finite element method based numerical approach for evaluating various hallux valgus treatment strategies. We developed three-dimensional hallux valgus deformity models, with different metatarsal osteotomy methods and Kirschner wire fixation strategies, under two types of standing postures. Ten Kirschner wire fixations were analyzed and compared. The fixation stability, bone stress, implant stress, and contact pressure on the osteotomy surface were calculated as the biomechanical indexes. The results showed that the biomechanical indexes of the osteotomy and Kirschner wire fixations for hallux valgus deformity could be effectively analyzed and fairly evaluated. The distal metatarsal osteotomy method provided better biomechanical indexes compared to the proximal metatarsal osteotomy method. This study proposed a finite element method based numerical approach for evaluating various osteotomy and Kirschner wire fixations for hallux valgus deformity before surgery.

A preliminary analysis of replicating the biomechanics of helmet therapy for sagittal craniosynostosis

PURPOSE

The aim of this study was to investigate the biomechanics of endoscopically assisted strip craniectomy treatment for the management of sagittal craniosynostosis while undergoing three different durations of postoperative helmet therapy using a computational approach.

METHODS

A previously developed 3D model of a 4-month-old sagittal craniosynostosis patient was used. The strip craniectomy incisions were replicated across the segmented parietal bones. Areas across the calvarial were selected and constrained to represent the helmet placement after surgery. Skull growth was modelled and three variations of helmet therapy were investigated, where the timings of helmet removal alternated between 2, 5, and 8 months after surgery.

RESULTS

The predicted outcomes suggest that the prolonging of helmet placement has perhaps a beneficial impact on the postoperative long-term morphology of the skull. No considerable difference was found on the pattern of contact pressure at the interface of growing intracranial volume and the skull between the considered helmeting durations.

CONCLUSION

Although the validation of these simulations could not be performed, these simulations showed that the duration of helmet therapy after endoscopically assisted strip craniectomy influenced the cephalic index at 36 months. Further studies require to validate these preliminary findings yet this study can lay the foundations for further studies to advance our fundamental understanding of mechanics of helmet therapy.

A Computational Framework to Predict Calvarial Growth: Optimising Management of Sagittal Craniosynostosis

The neonate skull consists of several bony plates, connected by fibrous soft tissue called sutures. Premature fusion of sutures is a medical condition known as craniosynostosis. Sagittal synostosis, caused by premature fusion of the sagittal suture, is the most common form of this condition. The optimum management of this condition is an ongoing debate in the craniofacial community while aspects of the biomechanics and mechanobiology are not well understood. Here, we describe a computational framework that enables us to predict and compare the calvarial growth following different reconstruction techniques for the management of sagittal synostosis. Our results demonstrate how different reconstruction techniques interact with the increasing intracranial volume. The framework proposed here can be used to inform optimum management of different forms of craniosynostosis, minimising the risk of functional consequences and secondary surgery.

Predicting and comparing three corrective techniques for sagittal craniosynostosis

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.

Using Sensitivity Analysis to Develop a Validated Computational Model of Post-operative Calvarial Growth in Sagittal Craniosynostosis

Craniosynostosis is the premature fusion of one or more sutures across the calvaria, resulting in morphological and health complications that require invasive corrective surgery. Finite element (FE) method is a powerful tool that can aid with preoperative planning and post-operative predictions of craniosynostosis outcomes. However, input factors can influence the prediction of skull growth and the pressure on the growing brain using this approach. Therefore, the aim of this study was to carry out a series of sensitivity studies to understand the effect of various input parameters on predicting the skull morphology of a sagittal synostosis patient post-operatively. Preoperative CT images of a 4-month old patient were used to develop a 3D model of the skull, in which calvarial bones, sutures, cerebrospinal fluid (CSF), and brain were segmented. Calvarial reconstructive surgery was virtually modeled and two intracranial content scenarios labeled “CSF present” and “CSF absent,” were then developed. FE method was used to predict the calvarial morphology up to 76 months of age with intracranial volume-bone contact parameters being established across the models. Sensitivity tests with regards to the choice of material properties, methods of simulating bone formation and the rate of bone formation across the sutures were undertaken. Results were compared to the in vivo data from the same patient. Sensitivity tests to the choice of various material properties highlighted that the defined elastic modulus for the craniotomies appears to have the greatest influence on the predicted overall skull morphology. The bone formation modeling approach across the sutures/craniotomies had a considerable impact on the level of contact pressure across the brain with minimum impact on the overall predicated morphology of the skull. Including the effect of CSF (based on the approach adopted here) displayed only a slight reduction in brain pressure outcomes. The sensitivity tests performed in this study set the foundation for future comparative studies using FE method to compare outcomes of different reconstruction techniques for the management of craniosynostosis.

Computational modelling of patient specific spring assisted lambdoid craniosynostosis correction

Lambdoid craniosynostosis (LC) is a rare non-syndromic craniosynostosis characterised by fusion of the lambdoid sutures at the back of the head. Surgical correction including the spring assisted cranioplasty is the only option to correct the asymmetry at the skull in LC. However, the aesthetic outcome from spring assisted cranioplasty may remain suboptimal. The aim of this study is to develop a parametric finite element (FE) model of the LC skulls that could be used in the future to optimise spring surgery. The skull geometries from three different LC patients who underwent spring correction were reconstructed from the pre-operative computed tomography (CT) in Simpleware ScanIP. Initially, the skull growth between the pre-operative CT imaging and surgical intervention was simulated using MSC Marc. The osteotomies and spring implantation were performed to simulate the skull expansion due to the spring forces and skull growth between surgery and post-operative CT imaging in MSC Marc. Surface deviation between the FE models and post-operative skull models reconstructed from CT images changed between ± 5 mm over the skull geometries. Replicating spring assisted cranioplasty in LC patients allow to tune the parameters for surgical planning, which may help to improve outcomes in LC surgeries in the future.

The Science Behind the Springs: Using Biomechanics and Finite Element Modeling to Predict Outcomes in Spring-Assisted Sagittal Synostosis Surgery

Spring-assisted surgery for the correction of scaphocephaly has gained popularity over the past 2 decades. Our unit utilizes standardized torsional springs with a central helix for spring-assisted surgery. This design allows a high degree of accuracy and reproducibility of the force vectors and force distance curves. In this manuscript, we expand on the biomechanical testing and properties of these springs. Standardization of design has enabled us to study the springs on bench and in vivo and a comprehensive repository of calvarial remodeling and spring dynamics has been acquired and analyzed.Finite element modeling is a technique utilized to predict the outcomes of spring-assisted surgery. We have found this to be a useful tool, in planning our surgical strategy and improving outcomes. This technique has also contributed significantly to the process of informed consent preoperatively. In this article, we expand on our spring design and dynamics as well as the finite element modeling used to predict and improve outcomes.In our unit, this practice has led to a significant improvement in patient outcomes and parental satisfaction and we hope to make our techniques available to a wider audience.

Three-dimensional finite element analysis of the dural folds and the human skull under head acceleration

Bone and collagen fiber architecture adapt to external mechanical loads. In humans, due to the low insertion of the temporal muscle, mastication does not lead to a physiological loading of the calvaria. Forces applied to the skull by the dural folds can lead to compressive stresses in the calvaria. To investigate the relationship between mechanical loads and form in the skull and its membranes, in a finite element three-dimensional model of the human skull, loads due to head acceleration in daily activities are applied to the falx cerebri and the tentorium cerebelli. The dural folds are modeled as membranes. The stress paths in the dural folds correlate with anatomical fiber direction. Head accelerations of 9 g lead to compressive stress in the calvaria. Finite element analysis of the falx cerebri and the tentorium cerebelli can be used to study the influence of mechanical stresses on the ossification of the dural folds and their impact on calvarial growth. This study presents an example of functional loading of bone by fibrous membranes and describes a possible mechanism by which Wolff's law works on the bone of the calvaria creating evolutionarily beneficial lightweight constructions.

Modeling the effect of brain growth on cranial bones using finite-element analysis and geometric morphometrics

PURPOSE

Brain expansion during ontogeny has been identified as a key factor for explaining the growth pattern of neurocranial bones. However, the dynamics of this relation are only partially understood and a detailed characterization of integrated morphological changes of the brain and the neurocranium along ontogeny is still lacking. The aim of this study was to model the effect of brain growth on cranial bones by means of finite-element analysis (FEA) and geometric morphometric techniques.

METHODS

First, we described the postnatal changes in brain size and shape by digitizing coordinates of 3D semilandmarks on cranial endocasts, as a proxy of brain, segmented from CT-scans of an ontogenetic sample. Then, two scenarios of brain growth were simulated: one in which brain volume increases with the same magnitude in all directions, and other that includes the information on the relative expansion of brain regions obtained from morphometric analysis.

RESULTS

Results indicate that in the first model, in which a uniform pressure is applied, the largest displacements were localized in the sutures, especially in the anterior and posterior fontanels, as well as the metopic suture. When information of brain relative growth was introduced into the model, displacements were also concentrated in the lambda region although the values along both sides of the neurocranium (parietal and temporal bones) were larger than under the first scenario.

CONCLUSION

In sum, we propose a realistic approach to the use of FEA based on morphometric data that offered different results to more simplified models.

Predicting calvarial morphology in sagittal craniosynostosis

Early fusion of the sagittal suture is a clinical condition called, sagittal craniosynostosis. Calvarial reconstruction is the most common treatment option for this condition with a range of techniques being developed by different groups. Computer simulations have a huge potential to predict the calvarial growth and optimise the management of this condition. However, these models need to be validated. The aim of this study was to develop a validated patient-specific finite element model of a sagittal craniosynostosis. Here, the finite element method was used to predict the calvarial morphology of a patient based on its preoperative morphology and the planned surgical techniques. A series of sensitivity tests and hypothetical models were carried out and developed to understand the effect of various input parameters on the result. Sensitivity tests highlighted that the models are sensitive to the choice of input parameter. The hypothetical models highlighted the potential of the approach in testing different reconstruction techniques. The patient-specific model highlighted that a comparable pattern of calvarial morphology to the follow up CT data could be obtained. This study forms the foundation for further studies to use the approach described here to optimise the management of sagittal craniosynostosis.

A population-specific material model for sagittal craniosynostosis to predict surgical shape outcomes

Sagittal craniosynostosis consists of premature fusion (ossification) of the sagittal suture during infancy, resulting in head deformity and brain growth restriction. Spring-assisted cranioplasty (SAC) entails skull incisions to free the fused suture and insertion of two springs (metallic distractors) to promote cranial reshaping. Although safe and effective, SAC outcomes remain uncertain. We aimed hereby to obtain and validate a skull material model for SAC outcome prediction. Computed tomography data relative to 18 patients were processed to simulate surgical cuts and spring location. A rescaling model for age matching was created using retrospective data and validated. Design of experiments was used to assess the effect of different material property parameters on the model output. Subsequent material optimization-using retrospective clinical spring measurements-was performed for nine patients. A population-derived material model was obtained and applied to the whole population. Results showed that bone Young's modulus and relaxation modulus had the largest effect on the model predictions: the use of the population-derived material model had a negligible effect on improving the prediction of on-table opening while significantly improved the prediction of spring kinematics at follow-up. The model was validated using on-table 3D scans for nine patients: the predicted head shape approximated within 2 mm the 3D scan model in 80% of the surface points, in 8 out of 9 patients. The accuracy and reliability of the developed computational model of SAC were increased using population data: this tool is now ready for prospective clinical application.

Characterizing and Modeling Bone Formation during Mouse Calvarial Development

The newborn mammalian cranial vault consists of five flat bones that are joined together along their edges by soft fibrous tissues called sutures. Early fusion of these sutures leads to a medical condition known as craniosynostosis. The mechanobiology of normal and craniosynostotic skull growth is not well understood. In a series of previous studies, we characterized and modeled radial expansion of normal and craniosynostotic (Crouzon) mice. Here, we describe a new modeling algorithm to simulate bone formation at the sutures in normal and craniosynostotic mice. Our results demonstrate that our modeling approach is capable of predicting the observed ex vivo pattern of bone formation at the sutures in the aforementioned mice. The same approach can be used to model different calvarial reconstruction in children with craniosynostosis to assist in the management of this complex condition.