Table 1.

Material properties and element types used in the current model

Component	Element type	Material type	Material parameters	Cross-sectional area (mm2)	References
Cortical bone	Solid, C3D8Ra	Elastic	Ec = 12,000 MPa	–	Huang et al. [20]
			υd = 0.29
Cancellous bone	Solid, C3D8R	Elastic	E = 450 MPa	–	Huang et al. [20]
			υ = 0.29
Zygapophysial cartilage	Solid, C3D8R	Elastic	E = 10 MPa	–	Huang et al. [20]
			υ = 0.3
Annulus fibrosus	Solid, C3D8R	Elastic	E = 450 MPa	–	Huang et al. [20]
			υ = 0.4
Nucleus pulpous	Solid, C3D8R	Elastic	E = 1 MPa	–	Huang et al. [20]
			υ = 0.49
Endplate	Solid, C3D8R	Elastic	E = 1200 MPa	–	Huang et al. [20]
			υ = 0.29
Grey matter	Solid, C3D8R	Hyperelastic (Ogden)	μe = 4.1 kPa, αf = 14.7	–	Ichihara et al. [28]
White matter	Solid, C3D8R	Hyperelastic (Ogden)	μ = 4.0 kPa, α = 12.5	–	Ichihara et al. [28]
Pia matter	Solid, C3D8R	Elastic	E = 39.3 MPa	–	Jannesar et al. [25]
			υ = 0.3
Dura matter	Solid, C3D8R	Elastic	E = 80 MPa	–	Persson et al. [27]
			υ = 0.49
DLs	3D truss, T3D2b	Elasticplastic	Stress–strain curve	0.01	Polak et al. [23]
Nerve rootlet	3D truss, T3D2	Elasticplastic	Stress–strain curve	0.03	Singh et al. [24]
Nerve root	Solid, C3D8R	Elastic	E = 1.3 MPa	–	Nishida et al. [21]
			υ = 0.3
CSF	Solid	Mie–Grüneisen equations of state, Newtonian fluid	cog = 1,381,700 mm/s	–	Jannesar et al. [25] Panzer et al. [22]
			sh = 1.979
			Γ0i = 0.11
			μj = 0.0008 Pa s

DLs, denticulate ligaments; CSF, cerebrospinal fluid

^aAn 8-node linear brick, reduced integration, hourglass control

^bA 2-node linear 3D truss

^cElasticity modulus

^dPoisson's ratio

^eShear modulus

^fStrain hardening index

^gSound velocity

^hA constant define the linear relationship between the shock velocity and the particle velocity

ⁱMie–Grüneisen ratio (A material constant)

^jViscosity