Thermophysical and mechanical properties of biological tissues as a function of temperature: a systematic literature review

Figures & data

Table 1. Key-words for query construction, divided by areas of interest.

Biological tissues	tissue OR ‘soft tissue’ OR liver OR muscle OR kidney OR lung OR pancreas OR skin OR dermis OR epidermis OR brain OR blood OR spleen OR heart OR myocardium OR breast OR uterus OR prostate OR ‘biliary ducts’ OR vein OR artery OR fat OR cartilage OR ligaments OR bones OR tumor OR carcinoma OR fibrotic OR sarcoma
Temperature dependence	temperature-dependent OR ‘temperature dependence’
Thermophysical properties	‘thermal properties’ OR ‘thermal conductivity’ OR ‘thermal diffusivity’ OR ‘heat capacity’ OR ‘convective heat transfer coefficient’ OR density
Mechanical properties	‘mechanical properties’ OR ‘Elastic modulus’ OR ‘Young’s modulus’ OR ‘shear modulus’
Blood perfusion and metabolic heat	‘Blood perfusion rate’ OR perfusion OR ‘blood perfusion’ OR ‘metabolic heat’

Figure 1. Flow chart of the present systematic literature search.

Figure 2. Techniques used for measuring thermal properties of biological tissues as temperature varies: setup and equipment. (a) Setup used to measure thermal properties with the dual-needle technique (top left); image of the galvanized container, employed to hold the tissue specimen and placed in the thermal bath, and of the utilized sensors, i.e., dual-needle sensor connected to the thermal properties analyzer and fiber optic sensors, housed in a needle, for temperature monitoring (top right) [62]. The heating needle of the instrument heats the tissue for t_h=30 s, and the monitoring needle measures the resulting tissue temperature for 90s. The initial temperature T_in is then subtracted to the readings to obtain the ΔT to be used in Equations (4)(8) $$\alpha ={\left[\frac{c}{P_{\mathit{transient}}/P_{\mathit{staedy}-\mathit{state}}\left(1+dk\right)}\right]}^2$$(8) and (5)(10) $$\sigma (t)={\sigma }_0\cdot \hspace{0.17em}\text{sin}\hspace{0.17em}(\omega t+\delta )$$(10) (bottom left). Thus, the thermal diffusivity, volumetric heat capacity, thermal conductivity, and the estimated error (i.e., S_yx) can be obtained for the specific tissue temperature (bottom right). (b) Illustration of the thermistor probe utilized for the measurement of thermal properties with the self-heated thermistor technique [121]. Below, the graph taken from Bhavaraju and Valvano (Reprinted by permission from Springer Nature Customer Service Center GmbH: Springer, International Journal of Thermophysics, [122], Copyright 2021) shows the trend of the applied thermistor power over the resulting temperature rise as a function of t^−1/2. The linear regression is employed to calculate the steady-state and transient terms. Two materials of known thermal properties are employed (e.g., agar-gelled water and glycerol) for the thermistor probe calibration. (c) Differential scanning calorimetry (DSC) systems: power compensation DSC (top left) and heat-flux DSC (top right), ‘R’ and ‘S’ represent the reference pan and the sample pan, respectively (figure modified from [123]). Below, example of DSC thermographs (heat flow versus temperature) attained with a differential scanning heat-flux calorimeter (bottom left) and resultant trend of specific heat capacity of biological tissues versus temperature (bottom right). Reprinted by permission from Springer Nature Customer Service Center GmbH: Springer Nature, Biophysics, [124], Copyright 2021. Through the measurement of the heat flux with the empty crucible pan, the crucible with reference material (with known mass and specific heat), and the crucible with the tissue sample under analysis, it is possible to calculate the specific heat capacity of the tissue sample, knowing the sample mass. The trends marked with 1 and 2 refer to the measurement on the wall of Baker’s cyst tissue and adipose tissue surrounding the cyst; 1’ and 2’ refer to the same samples undergoing reheating.

Table 2. Overview of the material thermal properties and relevant information which can be obtained through the dual-needle technique, self-heated thermistor technique, and differential scanning calorimetry.

		Thermal property and information obtainable with the measurement technique
		Thermal conductivity	Specific heat capacity	Volumetric heat capacity	Thermal diffusivity	Thermal transition temperatures of materials and thermal stability	Estimation of the enthalpy related to a specific process
Measurement technique	Dual-needle technique	X		X	X
	Self-heated thermistor technique	X			X
	Differential scanning calorimetry		X			X	X

Figure 3. Principal measurement techniques employed for characterizing the mechanical behavior of biological tissues: setup and instrumentation. (a) System (Endura TEC ELF 3220) used for dynamical mechanical analysis tests on liver tissue (left); close-up on the acrylic platens, the tissue specimen, the loading cell, and the mover of the system used for the measurement of the viscoelastic properties (right). Reprinted from [139], Copyright 2021, with permission from Elsevier. (b) Picture of the tissue specimen prepared for shear rheology tests, positioned between the upper and the lower plate of the parallel-plate system (a), sketch of the parallel-plate rheometer and the tissue (b): ‘H’ and ‘R’ represent the tissue specimen height and the plate radius, respectively. Reprinted from [140], Copyright 2021, with permission from IOS Press. (c) Setup employed to perform share wave elastography measurements on ex vivo porcine brain tissues. Reprinted from [141], Copyright 2021, with permission from Elsevier.

Table 3. Overview of the principal material parameters which can be obtained through classic stress-strain tests, dynamic oscillatory tests, and shear wave elastography.

Parameters that can be obtained through classic stress-strain tests (tension or compression)
Young’s modulus	$E$ (ratio between the uniaxial stress and the elastic deformation identified in the linear elastic region of the curve describing the stress-strain relationship)
Parameters that can be obtained through dynamic oscillatory tests
	Oscillatory tensile and compressive tests	Oscillatory shear tests
Storage modulus	$E\prime =\frac{{\sigma }_0}{{\epsilon }_0}\text{cos}\hspace{0.17em}\delta$	$G\prime =\frac{{\tau }_0}{{\gamma }_0}\text{cos}\hspace{0.17em}\delta$
Loss modulus	$E″=\frac{{\sigma }_0}{{\epsilon }_0}\text{sin}\hspace{0.17em}\delta$	$G″=\frac{{\tau }_0}{{\gamma }_0}\text{sin}\hspace{0.17em}\delta$
Complex modulus	$E^{*}=\frac{{\sigma }_0}{{\epsilon }_0}(\hspace{0.17em}\text{cos}\hspace{0.17em}\delta +i\hspace{0.17em}\text{sin}\hspace{0.17em}\delta )=E\prime +iE″$	$G^{*}=\frac{{\tau }_0}{{\gamma }_0}(\hspace{0.17em}\text{cos}\hspace{0.17em}\delta +i\hspace{0.17em}\text{sin}\hspace{0.17em}\delta )=G\prime +iG″$
Loss factor	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$	$\text{tan}\hspace{0.17em}\delta =G″/G\prime$
Parameters that can be obtained through shear wave elastography
Shear modulus	$G=\rho c_s{}^2$

Table 4. Thermophysical properties of biological tissues as a function of temperature.

Tissue	Conditions (in vivo, ex vivo, in vitro)	Temperature [°C]	Thermal conductivity [W/(m·K)]	Specific heat [J/(kg·K)]	Volumetric heat capacity [MJ/(m^3·K)]	Density [kg/m^3]	Thermal diffusivity [m^2/s]	Measurement approach	Reference
Human compact bone (axial direction)	ex vivo	21 36.7 50 65 80 95	12.26 12.90 12.67 12.25 11.87 11.54	1.254·10^3 0.825·10^3 0.922·10^3 1.190·10^3 1.564·10^3 1.941·10^3	–	–	5.82·10^−6 7.12·10^−6 6.73·10^−6 5.86·10^−6 4.90·10^−6 3.98·10^−6	Experimental setup including: two copper hollow cylinders, heating platforms, thermostat, distilled water, differential thermocouple	Zelenov, E. S.1986 [154]
Human compact bone (radial direction)		21 36.7 50 65 80 95	9.20 9.71 9.67 9.49 9.28 9.07	1.543·10^3 0.943·10^3 1.055·10^3 1.369·10^3 1.724·10^3 2.131·10^3	–	–	2.95·10^−6 6.04·10^−6 5.77·10^−6 4.91·10^−6 3.90·10^−6 2.92·10^−6
Human compact bone (tangential direction)		21 36.7 50 65 80 95	8.93 9.98 9.97 9.78 9.58 9.35	1.430·10^3 1.027·10^3 1.128·10^3 1.446·10^3 1.798·10^3 2.212·10^3	–	–	3.01·10^−6 5.05·10^−6 4.60·10^−6 3.66·10^−6 2.73·10^−6 1.75·10^−6
Bovine trabecular bone (defatted state)	ex vivo	37 47 57	0.43 0.43 0.44	–	–	–	–	Self-heated thermistor technique	Fajardo, J. E. Carlevaro, C. M. Vericat, F. Berjano, E. Irastorza, R. M. 2018 [155]
Bovine trabecular bone (non defatted state)		37 47 57	0.39 0.39 0.41	–	–	–	–
Bovine liver	ex vivo	21.0 31.5 41.5 58.4 64.4 72.5 84.8 90.4 92.4 93.5 94.4 99.1 101.1 101.9 102.9 104.1 105.5 107.2 108.5 110.1 111.5 112.6	0.50 0.48 0.51 0.52 0.58 0.53 0.56 0.57 0.76 0.81 1.19 2.25 0.66 0.55 0.46 0.38 0.31 0.27 0.25 0.22 0.21 0.19	–	3.49 3.36 3.50 3.52 3.32 3.41 3.14 3.36 3.84 3.99 4.17 7.31 2.41 2.14 1.94 1.78 1.54 1.38 1.30 1.03 0.96 0.89	–	0.14·10^−6 0.14·10^−60.14·10^−6 0.15·10^−60.18·10^−6 0.16·10^−6 0.18·10^−6 0.17·10^−60.20·10^−6 0.22·10^−6 0.29·10^−6 0.31·10^−6 0.27·10^−6 0.26·10^−6 0.24·10^−6 0.21·10^−6 0.21·10^−6 0.20·10^−6 0.20·10^−6 0.21·10^−6 0.22·10^−60.22·10^−6	Dual-needle technique	Lopresto, V.Argentieri, A.Pinto, R.Cavagnaro, M.;2019 [125]
Porcine liver	ex vivo	20 25 35 37 45 60 65 90 cooling 90 65 60 45 37 25	0.575 0.546 0.520 0.522 0.524 0.571 0.586 0.759 0.762 0.728 0.738 0.731 0.725 0.718	–	3.758 3.65 3.567 3.57 3.60 3.77 3.86 4.296 4.29 4.23 4.22 4.22 4.21 4.19		0.147·10^−6 0.144·10^−6 0.141·10^−6 0.141·10^−6 0.142·10^−6 0.148·10^−6 0.152·10^−6 0.192·10^−6 0.192·10^−6 0.197·10^−6 0.196·10^−6 0.196·10^−6 0.195·10^−6 0.193·10^−6	Dual-needle technique	Guntur, S. R.Lee, K. ILPaeng, D. G.Coleman, A. J.Choi, M. J.2013 [127]
Ovine liver	ex vivo	25.35 26.93 35.68 36.27 39.55 40.24 44.11 44.58 48.87 49.49 55.05 55.37 59.59 60.34 70.37 70.52 79.49 80.46 91.97 92.03 96.79 cooling 95.73 94.61 91.69 84.55 78.76 72.97 68.55 63.86 60.55 57.52 54.76 52.28 50.07 48.14 46.48 44.83 43.72 42.34 41.24 40.41 39.59 38.48 37.66	0.50 0.48 0.46 0.49 0.53 0.53 0.49 0.52 0.53 0.53 0.46 0.48 0.53 0.54 0.55 0.54 0.54 0.56 0.61 0.58 1.08 0.69 0.62 0.53 0.52 0.53 0.51 0.53 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51	–	3.39 3.32 3.23 3.25 3.52 3.52 3.42 3.50 3.52 3.55 3.33 3.38 3.42 3.53 3.50 3.53 3.42 3.37 3.41 3.55 5.05 3.85 3.66 3.57 3.60 3.60 3.54 3.54 3.54 3.54 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51	–	0.15·10^−6 0.15·10^−6 0.14·10^−6 0.15·10^−6 0.15·10^−6 0.15·10^−6 0.14·10^−6 0.15·10^−6 0.15·10^−6 0.15·10^−6 0.14·10^−6 0.14·10^−6 0.16·10^−6 0.15·10^−6 0.16·10^−6 0.15·10^−6 0.16·10^−6 0.17·10^−6 0.18·10^−6 0.16·10^−6 0.23·10^−60.18·10^−6 0.17·10^−6 0.15·10^−6 0.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−60.14·10^−6	Dual-needle technique	Silva, N. P.Bottiglieri, A.Conceição, R. C.O’Halloran, M.Farina, L.2020 [126]
	Room temperature 60 90 95	–	–	1128 1028 1031 1104	–
Porcine liver	ex vivo	25 37 50 80	0.49 0.50 0.52 0.55		–	–	–	Self-heated thermistor technique	Choi, J.Morrissey, M.Bischof, J. C.2013 [156]
		25 35 40 45 60 65 85 25 35 40 45 60 65 85		First heating 3.50·10^3 3.53·10^3 3.55·10^3 3.59·10^3 3.76·10^3 3.81·10^3 3.61·10^3 second heating 3.46·10^3 3.46·10^3 3.48·10^3 3.48·10^3 3.50·10^3 3.48·10^3 3.53·10^3	–	–	–	DSC
		25 35 40 45 60 65 85		Pre-heated samples: 3.00·10^3 2.99·10^3 3.01·10^3 3.04·10^3 3.08·10^3 3.09·10^3 3.16·10^3	–	–	–
Human liver	ex vivo	25 37 50 80	0.496 0.509 0.512 0.520		–	–	–	Self-heated thermistor technique
		25 35 40 45 60 65 85 25 35 40 45 60 65 85		First heating: 3.46·10^3 3.44·10^3 3.45·10^3 3.49·10^3 3.69·10^3 3.72·10^3 3.57·10^3 second heating: 3.45·10^3 3.39·10^3 3.39·10^3 3.39·10^3 3.44·10^3 3.44·10^3 3.54·10^3	–	–	–	DSC
		25 35 40 45 60 65 85		Pre-heated samples: 3.02·10^3 3.02·10^3 3.04·10^3 3.06·10^3 3.15·10^3 3.17·10^3 3.25·10^3	–	–	–
Porcine liver	ex vivo	25 37 45 60 65 90	0.350 0.502 0.534 0.672 0.718 0.948		–	–	–	Steady comparative method	Watanabe, H. Kobayashi, Y. Hashizume, M. Fujie, M. G. 2009 [157]
		25 37 45 60 65 90		3.38·10^3 3.41·10^3 3.43·10^3 3.60·10^3 3.75·10^3 3.66·10^3	–	–	–	DSC
		25 37 45 60 65 90		3.28·10^3 3.32·10^3 3.34·10^3 3.39·10^3 3.41·10^3 3.49·10^3	–	–	–	MDSC
Porcine liver	ex vivo	25 37 45 60 65 90 100	0.531 0.533 0.539 0.537 0.533 0.343 0.305	–	–	–	–	Unsteady hot- wire method	Watanabe, H.Yamazaki, N.Isobe, Y.Lu, X.Kobayashi, Y.Miyashita, T.Ohdaira, T.Hashizume, M.Fujie, M. G.2012 [158]
Ovine collagen	ex vivo	Cycle A* 25 35 47 55 cooling: 45 35 25	0.530 0.565 0.600 0.645 0.650 0.590 0.560	–	–	–	–	Unsteady hot-wire method	Bhattacharya, A.Mahajan, R. L.2003 [159]
		Cycle B**25 45 65 80 cooling: 70 63 45 25	0.560 0.635 0.670 0.800 0.830 0.745 0.675 0.625 (+12%)	–	–	–	–
Bovine liver	ex vivo	Run 1 25 40 65 80 25 (after cooling) Run 2 25 40 65 80 85 90 25 (after cooling)	0.53 0.6 0.656 0.72 0.541 0.512 0.59 0.648 0.71 0.725 0.73 0.64	–	–	–	–
Pig forelimb (across fibres)	in vivo		0.672	–	–	–	–	Invasive probe
Pig forelimb (along fibres)			0.350	–	–	–	–
Pig neck (fat)			0.528	–	–	–	–
Pig hind limb			0.640	–	–	–	–
Pig liver			2.175	–	–	–	–
Porcine myocardium	ex vivo	25 37 50 62 76	0.515 0.531 0.510 0.493 0.476	–	–	–	0.152·10^−6 0.161·10^−6 0.171·10^−6 0.171·10^−6 0.179·10^−6	Self-heated thermistor technique	Bhavaraju, N. C.Valvano, J. W.1999 [122]
Porcine nasal septum cartilage	ex vivo	27 37 50	0.478 0.518 0.576	–	–	–	0.128·10^−6 0.131·10^−6 0.140·10^−6	Self-heated thermistor technique	Youn, J. I. Telenkov, S. A. Kim, E. Bhavaraju, N. C. Wong, B. J.F. Valvano, J. W. Milner, T. E. 2000 [160]
Human brain (white matter)	in vitro	37 43 50 60	–	3.59·10^3 3.61·10^3 3.64·10^3 3.69·10^3	–	–	–	DSC	Sano, F.Washio, T.Matsumae, M.2019 [161]
Human brain (gray matter)		37 43 50 60	–	3.59·10^3 3.65·10^3 3.65·10^3 3.70·10^3	–	–	–
Glioblastoma		37 43 50 60	–	3.63·10^3 3.79·10^3 3.74·10^3 3.64·10^3	–	–	–
Diffuse astrocyotoma		37 43 50 60	–	3.75·10^3 4.03·10^3 4.02·10^3 3.97·10^3	–	–	–
Breast cancer		37 43 50 60	–	3.66·10^3 3.78·10^3 3.81·10^3 3.78·10^3	–	–	–
Lung adenocarcinoma		37 43 50 60	–	3.64·10^3 3.88·10^3 3.85·10^3 3.79·10^3	–	–	–
Human Baker’s cyst wall	ex vivo	40 55 68 85 95	–	3.47·10^3 3.64 ·10^3 4.46·10^3 3.85·10^3 3.86·10^3	–	–	–	DSC	Chernyadiev, S. A. Aretinsky, V. B. Sivkova, N. I. Zhilyakov, A. V. Korobova, N. Ju Gorbatov, V. I. Faizullin, M. Z. 2018 [124]
Human adipose tissue surrounding the Baker's cyst		40 55 68 85 95	–	2.31 ·10^3 2.39 ·10^3 2.49 ·10^3 2.58 ·10^3 2.60 ·10^3	–	–	–
Bovine liver	in vitro	25 50 60 75 83.5	–	3.411·10^33.452·10^33.592·10^3 3.877·10^3 4.187·10^3	–	–	–	Experimental apparatus including two plate electrodes, radiofrequency generator (375 kHz), thermocouples, Styrofoam (expanded polystyrene)	Haemmerich, D. dos Santos, I. Schutt, D. J. Webster, J. G. Mahvi, D. M. 2006 [162]
Porcine liver	ex vivo	22 28 36 46 55 65 73 82 92 94 97	0.515 0.504 0.537 0.550 0.559 0.571 0.607 0.603 0.858 1.099 1.635	–	3.48 3.66 3.70 3.50 3.55 3.50 3.48 3.51 3.63 3.98 4.99	–	0.148·10^−6 0.146·10^−6 0.144·10^−6 0.156·10^−6 0.160·10^−6 0.163·10^−6 0.166·10^−6 0.168·10^−6 0.206·10^−6 0.235·10^−6 0.297·10^−6	Dual-needle technique	Mohammadi, A. Bianchi, L., Asadi, S. Saccomandi, P. 2021 [71]
Calf brain	ex vivo	22 26 33 41 46 52 60 66 73 83 87 93 96 97	0.524 0.544 0.553 0.563 0.574 0.567 0.560 0.560 0.611 0.697 0.696 1.209 1.635 2.005	–	3.86 3.56 3.83 3.83 3.83 3.81 3.71 3.53 3.52 3.30 3.71 4.06 5.04 4.98	–	0.136·10^−6 0.143·10^−6 0.145·10^−60.147·10^−60.149·10^−6 0.149·10^−6 0.149·10^−6 0.158·10^−6 0.170·10^−6 0.205·10^−6 0.192·10^−6 0.305·10^−6 0.354·10^−6 0.373·10^−6
Porcine pancreas	ex vivo	22 25 26 28 31 33 38 45	0.510 0.520 0.520 0.521 0.531 0.532 0.529 0.524	–	3.63 3.72 3.70 3.68 3.76 3.66 3.73 3.70	–	0.142·10^−6 0.143·10^−6 0.143·10^−6 0.144·10^−6 0.145·10^−6 0.145·10^−6 0.145·10^−6 0.146·10^−6
Ovine kidney	ex vivo	20 32 46 63 80 90 93 94 95 cooling 95 93 85 78 71 62 58 55 52	0.52 0.52 0.53 0.51 0.53 0.60 0.67 0.70 0.74 0.70 0.64 0.55 0.52 0.50 0.48 0.47 0.47 0.46	–	3.54 3.54 3.59 3.45 3.02 3.00 3.05 3.23 3.44 3.66 3.47 3.41 3.29 3.19 3.14 3.11 3.10 3.07	–	0.146·10^−6 0.147·10^−6 0.148·10^−6 0.147·10^−6 0.174·10^−6 0.201·10^−6 0.208·10^−6 0.208·10^−6 0.209·10^−6 0.193·10^−6 0.182·10^−6 0.163·10^−6 0.160·10^−6 0.158·10^−6 0.154·10^−6 0.153·10^−6 0.152·10^−6 0.151·10^−6	Dual-needle technique	Silva, N. P. Bottiglieri, A. Porter, E. O’Halloran, M. Farina, L. 2021 [129]

*Cycle A is the result of the average of the cycles that reach a maximum temperature of 55 °C (in the article cycles 1,2,3 and 4) and in which no irreversible effects are observed.

**Cycle B is the result of the average of the cycles that reach a maximum temperature of 80 °C (cycles 5 and 6) and in which irreversible effects can be observed.

Figure 4. (a) Thermal conductivity of different tissues and biological media (i.e., trabecular bone, brain, lung, pancreas, spleen, collagen, liver, myocardium, septal cartilage, kidney) as a function of temperature. (b) Temperature dependence of thermal conductivity of liver investigated in different studies including measurements in human, bovine, ovine, porcine, and rabbit tissues.

Figure 5. (a) Specific heat relative to hepatic, adipose tissue, brain (white and gray matter), compact bone tissue in axial, radial, and tangential direction, as a function of temperature. (b) Temperature-dependent specific heat of tumorous tissues such as glioblastoma, diffuse astrocytoma, breast cancer, and lung adenocarcinoma. The results were attained from the study by Sano et al. [161].

Figure 6. Temperature dependence of volumetric heat capacity of different biological media, i.e., bovine liver, calf brain, ovine kidney, ovine liver, porcine liver, and porcine pancreatic tissue.

Figure 7. Thermal diffusivity of different biological materials (i.e., liver, brain, lung, pancreas, spleen, myocardium, and kidney tissue) versus temperature.

Table 5. Mechanical properties of biological tissues as a function of temperature.

Tissue	Conditions (in vivo, ex vivo, in vitro)	Temperature [°C]	Elastic modulus [kPa]	Shear modulus [kPa]	Loss factor tanδ	Storage modulus [kPa]	Loss modulus [kPa]	Complex modulus [kPa]	Stiffness [N/mm]	Measurement approach	Reference
Porcine brain	ex vivo	25 37 42 45 48	–	1.20 0.84 0.82 0.84 0.92	–	–	–	–	–	Shear wave elastography	Liu, Y. L.Li, G. Y.He, P.Mao, Z. Q.Cao, Y.2017 [141]
Bovine liver	ex vivo	25 37 45 60 65	–	3.4 2.78 3.53 15.03 33.42	–	–	–	–	–	Quantitative supersonic shear imaging technique	Sapin-De Brosses, E.Gennisson, J. L.Pernot, M.Fink, M.Tanter, M.2010 [113]
Bovine muscle		25 37 43 45 60 64	–	Transversal 33.00 25.08 22.40 20.79 13.86 19.80	–	–	–	–	–
		25 37 43 45 60 64	–	Longitudinal 78.00 53.82 46.02 41.34 21.06 31.20	–	–	–	–	–
Porcine septal cartilage	ex vivo	50 60 65 70 80	80 80 74 28 16	–	–	–	–	–	–	Step unconfined compression experiments	Protsenko, D.Zemek, A.Wong, B. J F2008 [164]
Rabbit septal cartilage	ex vivo	-before laser exposure -during first laser exposure -after first laser exposure -during second laser exposure -after second laser exposure -during third laser exposure -after third laser exposure -after 1 h in normal saline at 25 °C	6.08·10^3 5.41·10^3 4.94·10^3 5.05·10^3 4.17·10^3 4.17·10^3 3.71·10^3 ∼6.08·10^3	–	–	–	–	–	–	DMA	Chao, K. K. H.Ho, K. H. K.Wong, B. J F2003 [5]
Porcine septal cartilage	ex vivo	20 30 40 50 60 65 70	1.00·10^3 1.17·10^3 1.44·10^3 0.44·10^3 0.42·10^3 0.18·10^3 0.18·10^3	–	–	–	–	–	–	Method of elastography based on OCT	Liu, C. H.Skryabina, M. N.Li, J.Singh, M.Sobol, E. N.Larin, K. V.2014 [165]
		20 30 40 50 60 65	1.20·10^3 1.63·10^31.48·10^31.11·10^30.63·10^30.66·10^3	–	–	–	–	–	–	MMC
Bovine compact bone	ex vivo	0 25	28.2·10^6 26.2·10^6	–	–	–	–	–	–	Stress–strain tests (Tuckerman strain gauge employed for monitoring the strain)	Bonfield W., Li C.H., 1968 [166]
Collagen of bone		0 25	2.76·10^6 1.24·10^6	–	–	–	–	–	–
Porcine nasal septal cartilage	ex vivo	(f = 14 Hz) 45 48 57 60 66	–	–	–	E’ 21720 19300 14640 12030 6690	–	–	–	DMA	Chae Y., Aguilar G., Lavernia E.J., Wong B.J.F., 2003 [167]
		(f = 23 Hz) 48 57 60 63 66	–	–	–	E’ 19890 15310 14010 7460 4300	–	–	–
		(f = 37 Hz) 48 57 60 63 66	–	–	–	E’ 20110 15710 15730 12210 7210	–	–	–
		(f = 61 Hz) 45 48 57 60 63 66	–	–	–	E’ 22910 21320 17990 16400 10260 5550	–	–	–
Porcine liver	ex vivo	Strain sweep, γ = 0.001 −20 20 30 40 45 50 55 60 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =G″/G\prime$ 0.232 0.238 0.222 0.216 0.216 0.209 0.213 0.206 0.196 0.201	G’ 0.501 0.550 0.679 0.782 0.914 1.265 1.962 3.409 5.211 5.203	G’’ 0.116 0.131 0.151 0.169 0.197 0.265 0.418 0.702 1.020 1.047		–	Rotary shear rheology experiments with a parallel-plate system	Wex, C.Stoll, A.Fröhlich, M.Arndt, S.Lippert, H.2014 [114]
		Strain sweep, γ = 0.01 −20 20 30 40 45 50 55 60 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =G″/G\prime$ 0.245 0.243 0.235 0.230 0.228 0.218 0.218 0.213 0.209 0.207	G’ 0.466 0.542 0.633 0.738 0.875 1.282 1.776 3.409 4.785 4.990	G’’ 0.114 0.132 0.149 0.168 0.196 0.279 0.387 0.726 1.000 1.033		–
		Frequency sweep, f = 0.1 Hz −20 20 30 40 45 50 55 60 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =G″/G\prime$ 0.214 0.221 0.242 0.227 0.233 0.208 0.211 0.213 0.209 0.207			|G*| 0.352 0.375 0.525 0.601 0.740 0.948 1.620 2.025 3.859 3.995	–
		Frequency sweep, f = 1 Hz −20 20 30 40 45 50 55 60 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =G″/G\prime$ 0.219 0.233 0.237 0.227 0.226 0.213 0.211 0.206 0.207 0.207			|G*| 0.539 0.544 0.781 0.859 1.063 1.296 2.181 2.754 5.019 5.145	–
		Frequency sweep, f = 10 Hz −20 20 30 40 45 50 55 60 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =G″/G\prime$ 0.289 0.322 0.292 0.283 0.267 0.254 0.254 0.230 0.227 0.224			|G*| 0.770 0.781 1.117 1.233 1.526 1.861 2.967 3.636 6.758 6.928	–
Pig back skin	ex vivo	heating rate 2 °C/min 37 45 60 65 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.200 0.197 0.172 0.163 0.152 0.156	E’ 326 410 1630 2730 3600 4820	E’’ 65 81 280 445 547 752	–	–	DMA	Xu, F Seffen, K A Lu, T J 2008 [168]
		heating rate 5 °C/min 37 45 60 65 70 80 heating rate 10 °C/min 37 45 60 65 70 80	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.167 0.171 0.172 0.164 0.163 0.168	E’ 330 300 340 390 450 607	E’’ 55 51 58 64 73 102	–	–
		–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.176 0.170 0.141 0.146 0.154 0.160	E’ 260 250 240 270 320 452	E’’ 46 43 34 39 49 72		–	–
Thermal lesions in canine Liver tissues	ex vivo	f = 0.1 Hz 37 45 50 60 65 70 80 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.206 0.220 0.234 0.262 0.274 0.288 0.320 0.312	–	–	|E*| 5.04 7.23 9.44 13.80 15.88 18.09 13.43 29.62	–	DMA, thermal lesions prepared with RFA	Kiss, Miklos ZDaniels, Matthew J Varghese, Tomy 2009 [139]
		f = 1 Hz 37 45 50 60 65 70 80 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.257 0.268 0.279 0.300 0.310 0.321 0.363 0.366	–	–	|E*| 6.18 9.23 12.40 18.65 21.71 24.64 18.85 38.97	–
		f = 10 Hz 37 45 50 60 65 70 80 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.315 0.322 0.330 0.347 0.355 0.365 0.537 0.555	–	–	|E*| 8.47 12.90 17.31 26.10 30.50 35.15 29.87 59.76	–
Thermal lesions in canine Liver tissues	ex vivo	f = 0.1 Hz 37 45 50 60 65 70 75 80 90 f = 1 Hz 37 45 50 60 65 70 75 80 90	– –	– –	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.159 0.236 0.314 0.467 0.328 0.296 0.325 0.307 0.386 $\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.256 0.284 0.308 0.363 0.350 0.299 0.322 0.308 0.507	– –	– –	|E*| 2.53 3.79 3.81 4.96 12.91 20.27 15.81 22.08 33.90 |E*| 3.60 3.81 4.58 7.35 17.96 29.01 22.79 31.99 55.30	– –	DMA, thermal lesions prepared with DIB
			–			–	–		–
		f = 10 Hz 37 45 50 60 65 70 75 80 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.262 0.285 0.309 0.351 0.372 0.327 0.353 0.331 0.406	–	–	|E*| 4.24 5.27 6.56 9.05 25.04 40.78 33.95 46.25 87.92	–
Thermal lesions in porcine Liver tissues	ex vivo	f = 0.1 Hz 37 45 50 60 65 70 75 80 85 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.293 0.289 0.286 0.279 0.311 0.305 0.394 0.3990.439 0.362	–	–	|E*| 1.50 1.68 1.91 2.15 4.34 8.45 14.81 10.24 9.35 9.48	–	DMA, thermal lesions prepared with DIB
		f = 1 Hz 37 45 50 60 65 70 75 80 85 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.274 0.275 0.277 0.278 0.298 0.293 0.408 0.381 0.407 0.453	–	–	|E*| 2.04 2.30 2.55 3.08 6.04 11.81 21.17 16.35 16.13 15.68	–
		f = 10 Hz 37 45 50 60 65 70 75 80 85 90	–	–	$\text{tan}\hspace{0.17em}\delta =E″/E\prime$ 0.379 0.380 0.380 0.383 0.369 0.342 0.390 0.420 0.386 0.538	–	–	|E*| 2.93 3.10 3.40 4.09 8.78 17.15 31.21 26.45 26.13 28.82	–
Porcine liver	ex vivo	20 40 50 60 70 80 90	–	–	–	–	–	–	0.25 0.29 0.27 0.37 0.77 1.24 1.17	Indentation experiments	Wex, C.Arndt, S.Brandstädter, K.Herrmann, L.Bruns, C.2014 [98]
Porcine lumbar spine ligaments	ex vivo	4.4 12.8 21.1 29.4 37.8	–	–	–	–	–	–	434 361 299 221 216	Measurements performed with an environmentally-controlled uniaxial test fixture	Bass C.R., Planchak C.J., Salzar R.S., Lucas S.R., Rafaels K.A., Shender B.S., Paskoff G., 2007 [169]

Figure 8. Shear modulus of brain, liver, and muscle tissues as a function of temperature.

Figure 9. (a) Temperature dependence of storage modulus E' of porcine septal cartilage and back skin. (b) Trend of shear storage modulus G' of porcine liver specimens as a function of preparation temperature.

Figure 10. (a) Loss modulus E'' of porcine back skin versus temperature. (b) Trend of shear loss modulus G'' of porcine liver samples as a function of preparation temperature.

Figure 11. (a) Magnitude of complex modulus (|E*|) of canine and porcine liver samples prepared with radiofrequency ablation (RFA) or double immersion boiling (DIB) as a function of preparation temperature. (b) Magnitude of complex shear modulus (|G*|) of porcine liver versus preparation temperature.

Figure 12. (a) Loss factor (tanδ = E''/E') of porcine back skin versus temperature, and tanδ of porcine and canine liver samples prepared with radiofrequency ablation (RFA) or double immersion boiling (DIB) as a function of preparation temperature. (b) Loss factor (tanδ = G''/G') of porcine liver versus preparation temperature.

Figure 13. (a) Trend of blood flow versus heating time for different tissues, i.e., muscle, skin, and tumor at diverse hyperthermic temperatures: (A) 42 °C, (B) 43 °C, (C) 44 °C, (D) 45 °C. (b) Graphical representation combining the blood flow of muscle, skin, and tumor tissues as a function of heating time for all the above-mentioned temperatures, in the 42 °C–45 °C range.

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