Table 3.

Calibrated parameters and prior distribution hyperparameters of stochastic Ogden-type models for mouse brain tissue, and the corresponding random linear shear modulus $\overline{\mu }$ of (2.14). The parameters are estimated by following the two-step strategy presented in §3.

stochastic model for mouse brain tissue	calibrated parameters (mean ± s.d.)	calibrated hyperparameters of prior probability distribution	random shear modulus (kPa) (mean ± s.d.)
one-term (two-parameter) Ogden (5.1)	c1=0.2454±0.0185	ρ1=175.6736	$\underset{\_}{\overline{\mu }}=0.2454\pm 0.0185$
	α1=−2.2111	ρ2=0.0014
three-term (three-parameter) Ogden (5.4)	c1=−1.1192±0.0255	ρ1=49.0153	$\underset{\_}{\overline{\mu }}=0.2265\pm 0.0324$
	c2=0.8167±0.0059	ρ2=0.0046
b=−3	c3=0.5291±0.0009	ξ1=7919
		ξ2=153 488
		ξ3=99 997
four-term (four-parameter) Ogden (5.4)	c1=−2.3043±0.3939	ρ1=57.7743	$\underset{\_}{\overline{\mu }}=0.2150\pm 0.0283$
	c2=1.7865±0.3491	ρ2=0.0037
b=−5	c3=1.1016±0.2035	ξ1=40
	c4=−0.3687±0.1305	ξ2=266
		ξ3=685
		ξ4=294
five-term (five-parameter) Ogden (5.4)	c1=−4.4681±0.0960	ρ1=51.4814	$\underset{\_}{\overline{\mu }}=0.2090\pm 0.0291$
	c2=2.5410±0.2452	ρ2=0.0041
b=−10	c3=3.4361±0.1178	ξ1=2771
	c4=−0.5959±0.0992	ξ2=2086
	c5=−0.7041±0.0969	ξ3=8388
		ξ4=6569
		ξ5=4502