title: Transcalvarial brain herniation volume after decompressive craniectomy is the difference between two spherical caps.
abstract: Decompressive craniectomy (DC) is a surgical procedure used to relieve severely increased intracranial pressure (ICP) by removing a portion of the skull. Following DC, the brain expands through the skull defect created by DC, resulting in transcalvarial herniation (TCH). Traditionally, people measure only changes in the ICP but not in the intracranial volume (ICV), which is equivalent to the volume of TCH (V(TCH)), in patients undergoing DC. We constructed a simple model of the cerebral hemispheres, assuming the shape of the upper half of a sphere with a radius of 8 cm. We hypothesized that the herniated brain following DC also conforms to the shape of a spherical cap. Considering that a circular piece of the skull with a radius of a was removed, V(TCH) is the volume difference between 2 spherical caps at the operated side and the corresponding non-operated side, which represents the pre-DC volume underneath the removed skull due to the bilateral symmetry of the skull and the brain. Subsequently, we hypothesized that the maximal extent of TCH depends on a because of the biomechanical limitations imposed by the inelastic scalp. The maximum value of V(TCH) is 365.0 mL when a is 7.05 cm and the height difference between the spherical caps (Δh) at its maximum is 2.83 cm. To facilitate rapid calculation of V(TCH), we proposed a simplified estimation formula, Vˆ(TCH)=1/2A(2)Δh, where A=2a. With the a value ranging between 0 and 7 cm, the ratio between Vˆ(TCH) and V(TCH) ranges between 0.77 and 1.27, with different Δh values. For elliptical skull defects with base diameters of A and C, the formula changes to Vˆ(TCH)=1/2ACΔh. If our hypothesis is correct, surgeons can accurately calculate V(TCH) after DC. Furthermore, this can facilitate volumetric comparisons between the effects of DCs in skulls of varying sizes, allowing quantitative comparisons between ICVs in addition to ICPs.
authors.affiliation: Institute of Biomedical Engineering, National Taiwan University, No.1, Sec.1, Ren'ai Rd., Taipei City 10051, Taiwan; Department of Neurosurgery, Taipei Hospital,Ministry of Health and Welfare, No.127, Siyuan Rd., New Taipei City 24213, Taiwan.
authors.forename: Chun-Chih
authors.initials: CC
authors.lastname: Liao
authors.affiliation: Institute of Biomedical Engineering, National Taiwan University, No.1, Sec.1, Ren'ai Rd., Taipei City 10051, Taiwan; Department of Surgery, Far Eastern Memorial Hospital, No.21, Sec.2, Nanya S. Rd., New Taipei City 22060, Taiwan.
authors.forename: Yi-Hsin
authors.initials: YH
authors.lastname: Tsai
authors.affiliation: Institute of Biomedical Engineering, National Yang-Ming University, No.155, Sec.2, Linong St., Taipei City 11221, Taiwan.
authors.forename: Yi-Long
authors.initials: YL
authors.lastname: Chen
authors.affiliation: Institute of Biomedical Engineering, National Taiwan University, No.1, Sec.1, Ren'ai Rd., Taipei City 10051, Taiwan.
authors.forename: Ke-Chun
authors.initials: KC
authors.lastname: Huang
authors.affiliation: Institute of Biomedical Engineering, National Taiwan University, No.1, Sec.1, Ren'ai Rd., Taipei City 10051, Taiwan; Graduate Institute of Medical Informatics, Taipei Medical University, No.250, Wuxing St., Taipei City 11031, Taiwan.
authors.forename: I-Jen
authors.initials: IJ
authors.lastname: Chiang
authors.affiliation: Institute of Biomedical Engineering, National Taiwan University, No.1, Sec.1, Ren'ai Rd., Taipei City 10051, Taiwan.
authors.forename: Jau-Min
authors.initials: JM
authors.lastname: Wong
authors.affiliation: Institute of Biomedical Engineering, National Taiwan University, No.1, Sec.1, Ren'ai Rd., Taipei City 10051, Taiwan; Clinical Center for Neuroscience, National Taiwan University Hospital, No.7, Zhongshan S. Rd., Taipei City 10002, Taiwan. Electronic address: xiao@ntuh.gov.tw.
authors.forename: Furen
authors.initials: F
authors.lastname: Xiao
mesh_terms: D001696:Biomechanical Phenomena; D019299:Decompression, Surgical / Q000009:adverse effects / Q000379:methods*; D004677:Encephalocele / Q000209:etiology / Q000503:physiopathology*; D006801:Humans; D019586:Intracranial Hypertension / Q000601:surgery*; D008959:Models, Neurological; D012886:Skull / Q000601:surgery*