Development of a finite element model of decompressive craniectomy

Poroelastic modelling of brain tissue swelling and decompressive craniectomy treatment in ischaemic stroke

Brain oedema or tissue swelling that develops after ischaemic stroke can cause detrimental effects, including brain herniation and increased intracranial pressure (ICP). These effects can be reduced by performing a decompressive craniectomy (DC) operation, in which a portion of the skull is removed to allow swollen brain tissue to expand outside the skull. In this study, a poroelastic model is used to investigate the effect of brain ischaemic infarct size and location on the severity of brain tissue swelling. Furthermore, the model will also be used to evaluate the effectiveness of DC surgery as a treatment for brain tissue swelling after ischaemia. The poroelastic model consists of two equations: one describing the elasticity of the brain tissue and the other describing the changes in the interstitial tissue pressure. The model is applied on an idealized brain geometry, and it is found that infarcts with radius larger than approximately 14 mm and located near the lateral ventricle produce worse brain midline shift, measured through lateral ventricle compression. Furthermore, the model is also able to show the positive effect of DC treatment in reducing the brain midline shift by allowing part of the brain tissue to expand through the skull opening. However, the model does not show a decrease in the interstitial pressure during DC treatment. Further improvement and validation could enhance the capability of the proposed poroelastic model in predicting the occurrence of brain tissue swelling and DC treatment post ischaemia.

Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model

This paper investigates the complex time-dependent behavior of cortex tissue, under adiabatic condition, using a two-phase flow poroelastic model. Motivated by experiments and Biot's consolidation theory, we tackle time-dependent uniaxial loading, confined and unconfined, with various geometries and loading rates from 1μm/s to 100μm/s. The cortex tissue is modeled as the porous solid saturated by two immiscible fluids, with dynamic viscosities separated by four orders, resulting in two different characteristic times. These are respectively associated to interstitial fluid and glial cells. The partial differential equations system is discretized in space by the finite element method and in time by Euler-implicit scheme. The solution is computed using a monolithic scheme within the open-source computational framework FEniCS. The parameters calibration is based on Sobol sensitivity analysis, which divides them into two groups: the tissue specific group, whose parameters represent general properties, and sample specific group, whose parameters have greater variations. Our results show that the experimental curves can be reproduced without the need to resort to viscous solid effects, by adding an additional fluid phase. Through this process, we aim to present multiphase poromechanics as a promising way to a unified brain tissue modeling framework in a variety of settings.

Transcranial direct current stimulation in patients after decompressive craniectomy: a finite element model to investigate factors affecting the cortical electric field

Objective

To simulate the process of transcranial direct current stimulation (tDCS) on patients after decompressive craniectomy (DC), and to model cortical electric field distributions under different electrode montages, we constructed a finite element model that represented the human head at high resolution.

Methods

Using computed tomography images, we constructed a human head model with high geometrical similarity. The removed bone flap was simplified to be circular with a diameter of 12 cm. We then constructed finite element models according to bioelectrical parameters. Finally, we simulated tDCS on the finite element models under different electrode montages.

Results

Inward current had a linear relationship with peak electric field value, but almost no effect on electric field distribution. If the anode was not over the skull hole (configuration 2), there was almost no difference in electric field magnitude and focality between the circular and square electrodes. However, if the anode was right over the hole (configuration 1), the circular electrodes led to higher peak electric field values and worse focality. In addition, configuration 1 significantly decreased focality compared with configuration 2.

Conclusion

Our results might serve as guidelines for selecting current and electrode montage settings when performing tDCS on patients after DC.

Simulating Expansion of the Intracranial Space to Accommodate Brain Swelling after Decompressive Craniectomy: Volumetric Quantification in a 3D CAD Skull Model with Contour Elevation

Background: Decompressive craniectomy (DC) can be used to augment intracranial space and halt brainstem compromise. However, a widely adopted recommendation for optimal surgical extent of the DC procedure is lacking. In the current study, we utilized three-dimensional (3D) computer-assisted design (CAD) skull models with defect contour elevation for quantitative assessment. Methods: DC was performed for 15 consecutive patients, and 3D CAD models of defective skulls with contour elevations (0-50 mm) were reconstructed using commercial software. Quantitative assessments were conducted in these CAD subjects to analyze the effects of volumetric augmentation when elevating the length of the contour and the skull defect size. The final positive results were mathematically verified using a computerized system for numerical integration with the rectangle method. Results: Defect areas of the skull CAD models ranged from 55.7-168.8 cm², with a mean of 132.3 ± 29.7 cm². As the contour was elevated outward for 6 mm or above, statistical significance was detected in the volume and the volume-increasing rate, when compared to the results obtained from the regular CAD model. The volume and the volume-increasing rate increased by 3.665 cm³, 0.285% (p < 0.001) per 1 mm of contour elevation), and 0.034% (p < 0.001) per 1 cm² of increase of defect area, respectively. Moreover, a 1 mm elevation of the contour in Groups 2 (defect area 125-150 cm²) and 3 (defect area >150 cm², as a proxy for an extremely large skull defect) was shown to augment the volume and the volume-increasing rate by 1.553 cm³, 0.101% (p < 0.001) and 1.126 cm³, 0.072% (p < 0.001), respectively, when compared to those in Group 1 (defect area <125 cm²). The volumetric augmentation achieved by contour elevation for an extremely large skull defect was smaller than that achieved for a large skull defect. Conclusions: The 3D CAD skull model contour elevation method can be effectively used to simulate the extent of a space-occupying swollen brain and to quantitatively assess the extent of brainstem protection in terms of volume augmentation and volume-increasing rate following DC. As the tangential diameter (representing the degree of DC) exceeded the plateau value, volumetric augmentation was attenuated. However, an increasing volumetric augmentation was detected before the plateau value was reached.

Bulging brains

Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 to 56 ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.

Stress Singularities in Swelling Soft Solids

When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening. At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. We also consider the possibility of damage triggered by zones of either high shear stresses or high fiber stretches.

Modelling of Brain Deformation After Decompressive Craniectomy

Hyperelastic finite element models, with either an idealized cylindrical geometry or with realistic craniectomy geometries, were used to explore clinical issues relating to decompressive craniectomy. The potential damage in the brain tissue was estimated by calculating the volume of material exceeding a critical shear strain. Results from the idealized model showed how the potentially damaged volume of brain tissue increased with an increasing volume of brain tissue herniating from the skull cavity and with a reduction in craniectomy area. For a given herniated volume, there was a critical craniectomy diameter where the volume exceeding a critical shear strain fell to zero. The effects of details at the craniectomy edge, specifically a fillet radius and a chamfer on the bone margin, were found to be relatively slight, assuming that the dura is retained to provide effective protection. The location in the brain associated with volume expansion and details of the material modeling were found to have a relatively modest effect on the predicted damage volume. The volume of highly sheared material in the realistic models of the craniectomy varied roughly in line with differences in the craniectomy area.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.