TABLE 3.

Results of the hyper-viscoelastic properties of breast tissues, reported in the literature.

Experiment	Tissue types	Experimental protocol	Results/Conclusions	Authors
Ex vivo	Adipose Fibroglandular	Indentation tests Preload = 0.5 g 1.0mm and 0.1 Hz Preconditioning: 25 cycles + Test: 5 cycles + Inverse FEM Polynomial strain energy function (N = 2)	Hyperelastic parameters	Samani and Plewes (2004)
			(C 10, C 01, C 11, C 20, C 02) x 10−4 Nmm-2
			Adipose (3.1 ± 0.3, 3.0 ± 0.2, 22.5 ± 3, 38.0 ± 6, 47.2 ± 7)
			Fibroglandular (3.3 ± 0.4, 2.8 ± 0.3, 44.9 ± 8, 77.2 ± 11, 94.5 ± 13)
	Adipose (breast and abdominal)	Compression tests Preconditioning: 20 cycles: 10% at 1 Hz Test: 50% at 50%/s + hold for 15 min + Internal variable viscoelastic model elastic part (first-order Ogden - μ and α) + viscous part (superposition of exponentially decreasing functions - β 1, β 2, β 3, β 4, β 5)	Breast deep tissue	Calvo-Gallego et al. (2020)
			μ = 0.058, α = 8.875
			β 1 = 67.286, β 2 = 20.520, β 3 = 5.584, β 4 = 3.160, β 5 = 2.824
			Breast superficial tissue
			μ = 0.057, α = 7.949
			β 1 = 65.934, β 2 = 16.891, β 3 = 3.446, β 4 = 1.861, β 5 = 1.623
	Adipose Fibroglandular Mixed Tissues	Indentation tests 0.5–1.0mm and 0.1 Hz Preconditioning: 25 cycles + Test: 5 cycles + FEM models 3rd order Ogden, Veronda-Westman, 2nd order Polynomial and Yeoh models	No statistically significant differences among stress distributions	Dempsey et al. (2021)
	IDC	Ramp-relaxation tests 2, 4, 6% strain at 0.1s-1 + hold 180s + FEM model Maxwell model	Long-term shear moduli = 0.31–17.03 kPa	Mojra and Hooman (2021)
			Instantaneous shear moduli = 6.03–55.13 kPa
	Human DAT (breast and abdominal)	Indentation tests	Mean difference (9 points) of displacements between	Haddad et al. (2016)
		Preload = 0.1 g	“normal breast” and post-mastectomy(1)/post-lumpectomy(2)
		1.5 mm and 0.1 Hz	breast reconstructed using various DAT materials for a
		Preconditioning: 20 cycles + Test: 5 cycles	prone-to-supine(3)/prone-to-upright(4) body position change
		+
		FEM models	Yeoh: (1,3) 5.5 mm; (1,4) 5.4 mm; (2,3) −4.0 mm; (2,4) −0.6 mm
		Yeoh and Ogden models	Ogden: (1,3) 0.8 mm; (1,4) 0.8 mm; (2,3) −5.4 mm; (2,4) −0.7 mm
	Human DAT (breast)	Indentation tests	EDAT = 3.460 ± 1.210 kPa	Omidi et al. (2014)
		Preload = 0.1 g	First-order polynomial: (C01, C10) x 10−2
		0.5 mm and 0.1 Hz	3.917 ± 2.653, 9.997 ± 4.671
		Preconditioning: 20 cycles + Test: 5 cycles	Yeoh: (C10, C20, C30)
		+	0.1554 ± 3.728 × 10−2, (1.575 ± 0.440)x10−2, (8.820 ± 2.901)x10−8
		FEM models	Ogden: (μ, α)
		First-order polynomial, Yeoh, Ogden,	0.3306 ± 8.109 × 10−2, 3.780 ± 0.5431
		and Arruda–Boyce models	Arruda–Boyce: (μ, λ)
			0.1813 ± 0.1026, 1.028 ± 0.1655
In vivo	Cancer cases Fibroadenoma Mastopathy cases	MR Elastography	Shear modulus, kpa	Sinkus et al. (2005)
			Breast cancer = 2.9 ± 0.3; Fibroadenoma = 1.3 ± 0.7
			Mastopathy = 1.2 ± 0.4, Surrounding tissue = 0.87 ± 0.15
			Shear Viscosity, Pa.s
			Breast cancer = 2.4 ± 1.7, Fibroadenoma = 2.1 ± 1.4
			Mastopathy = 0.8 ± 0.3, Surrounding tissue = 0.55 ± 0.12