Table 3.

Human IVD motion segment stiffness and apparent modulus values

Parameter	Values	Facet joints removed	Ligaments removed	Reference
Axial stiffness	1.73 ± 0.45 kN/mm, 2 kN/mm	Yes	Yes	Beckstein et al. [62] and Marini et al. [67]
	1.17 ± 0.68 kN/mm	Yes	No	Shea et al. [61] and O'Connell et al. [68]b
	1.4 ± 0.48 kN/mm	No	No	Landham et al. [69], Frei et al. [70], Okawa et al. [71], and McGlashen et al. [72]b
0.44–2.42 kN/mm	n.s.	n.s.	Nachemson et al. [60], Gardner-Morse and Stokes [63], Kiehl et al. [73],b and Stokes and Gardner-Morse [74]
Dynamic stiffness	5.0–30 Hz: 0.25–3.66 kN/mm	Yes	Yes	Izambert et al. [75]
	0.001–1.0 Hz: 3.51–5.14 kN/mm	Yes	No	Costi et al. [76]
	0.01–10.0 Hz: 3.24–4.15 kN/mm	No	No	Smeathers and Joanes [77]
0.42±0.20 kN/mm	No	No	Alkalay et al. [78]
Apparent modulusa	2.16–10.48 MPa	No	No	Keller et al. [79]
Torsional stiffness	3.18 ± 0.89 N m/deg	Yes	Yes	Showalter et al. [65]
	2.1–2.9 N m/deg	Yes	No	Costi et al. [76] and Amin et al. [80]
	7.78–3.63 N m	No	No	Zirbel et al. [81]
	8.40 ± 1.09 N m/deg	No	No	Schmidt et al. [82]
	10–13 N m/deg	n.s.	n.s.	Stokes and Gardner-Morse [74]
3.51±1.77 N m/deg	n.s.	n.s.	Thompson et al. [66] and Haughton et al. [83]
Flexion stiffness	2.30–3.30 N m/deg	Yes	No	Costi et al. [76] and Amin et al. [80]
	4.89–6.64 N m/deg	Yes	No	Garges et al. [84]
	0.02 kN/mm	No	No	Brown et al. [85]
	1.80–5.50 N m/deg	No	No	Schmidt et al. [82] and Miller et al. [86]
0.07–0.36 kN/mm	n.s.	n.s.	Thompson et al. [66]
Extension stiffness	1.6–3.5 N m/deg	Yes	No	Costi et al. [76] and Amin et al. [80]
	7.21–9.09 N m/deg	Yes	No	Garges et al. [84]
	2.60–7.60 N m/deg	No	No	Schmidt et al. [82] and Miller et al. [86]
0.19−1.02 kN/mm	n.s.	n.s.	Thompson et al. [66]
Left-right lateral bending stiffness	3.4–4.6 N m/deg	Yes	No	Costi et al. [76]
	1.11 ± 0.67 N m	No	No	Zirbel et al. [81]
	2.30–4.40 N m/deg	No	No	Schmidt et al. [82] and Miller et al. [86]
	2.90–4.30 N m/deg	n.s.	n.s.	Gardner-Morse and Stokes [74]
4.21–10.04 N m/deg	n.s.	n.s.	Gardner-Morse and Stokes [63]
Anterior–posterior shear stiffness	0.11–0.21 kN/mm	Yes	No	Costi et al. [76] and Amin et al. [80]
	0.44–0.61 kN/mm	No	Yes	Lu et al. [64]
	0.10–0.27 kN/mm	No	No	Miller et al. [86] and Bisschop et al. [87,88]
0.26–0.45 kN/mm	n.s.	n.s.	Stokes and Gardner-Morse [74]

^aCalculated from three-parameter-solid model; and n.s. indicates motion segment preparation details not specified.

^bCalculated from reported force and displacement values.