Mechanical characterization of biological tissues: Experimental methods based on mathematical modelling

다국어 초록 (Multilingual Abstract)

Purpose To illustrate a systematic procedure for mechanicalcharacterization or mechanical behavior of biological tissueswith a semi-empirical method based on mathematical models.
Methods The method is composed of a series of procedures:construction of cell elements on the specimen, imageprocessing, continuum mechanics, hyperelasticity and so on.
An element used in the method, which is similar to finiteelement methods, is defined by placing markers on thespecimen. The change of the locations of the element duringa motion is monitored to calculate the displacement for stressestimation owing to external impacts or forces.
Results The validity of the method for mechanicalcharacterization or mechanical behavior of biological tissuesis shown through material test simulations with mathematicalmodels, resulting in good agreement overall.
Conclusions A general review of mathematical modeling ofbiological tissues is served and a semi-empirical method,which makes good use of both finite element methods andmathematical models based on the phenomenologicalmodeling technique, is introduced to assess the stress-strainresponses of biological tissues subjected mechanical loadings.

참고문헌 (Reference)

1 반용, "뇌 조직의 기계적 물성에 관한 젤라틴을 이용한 수치해석 및 실험적 연구" 대한기계학회 39 (39): 169-176, 2015

2 Chen EJ, "Young’s modulus measurements of soft tissues with application to elasticity imaging" 43 (43): 191-194, 1996

3 Sever A, "Unstable abdominal aortic aneurysms:a review of mdct imaging features" 23 (23): 187-196, 2016

4 Zhil GP, "United constitutive modeling of rubber-like materials under diverse loading conditions" 62 (62): 90-105, 2013

5 Miller K, "Total lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation" 23 (23): 121-134, 2007

6 Chuong CJ, "Three-dimensional stress distribution in arteries" 105 (105): 268-274, 1983

7 Wagner DR, "Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrous" 22 (22): 901-909, 2004

8 Baillargeon B, "The living heart project: a robust and integrative simulator for human heart function" 48 (48): 38-47, 2014

9 Rodriguez JP, "The effect of material model formulation in the stress analysis of abdominal aortic aneurysms" 37 (37): 2218-2221, 2009

10 Liu Y, "Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment" 293 (293): H3290-H3300, 2007

11 Tong J, "Structure, mechanics, and histology of intraluminal thrombi in abdominal aortic aneurysms" 43 (43): 1488-1501, 2015

12 Haines DW, "Strain-energy density function for rubberlike materials" 27 (27): 345-360, 1979

13 Weizsacker HW, "Strain energy density function for arteries from different topographical sites" 40 (40): 139-141, 1995

14 Grujicic M, "Seat-cushion and soft-tissue material modeling and a finite element investigation of the seating comfort for passengervehicle occupants" 30 (30): 4273-4285, 2009

15 Portnoy S, "Real-time patient-specific nite element analysis of internal stresses in the soft tissues of a residual limb: a new tool for prosthetic fitting" 35 (35): 120-135, 2007

16 Niroomandi S, "Real-time deformable models of non-linear tissues by model reduction techniques" 91 (91): 223-231, 2008

17 Fung YC, "Pseudoelasticity of arteries and the choice of its mathematical expression" 237 (237): H620-H631, 1979

18 Nah C, "Problems in determining the elastic strain energy function for rubber" 45 (45): 232-235, 2010

19 Margulies SS, "Physical model simulations of brain injury in the primate" 23 (23): 823-836, 1990

20 Xenos M, "Patient-based abdominal aortic aneurysm rupture risk prediction with fluid structure interaction modeling" 38 (38): 3323-3337, 2010

21 Rossi S, "Orthotropic active strain models for the numerical simulation of cardiac biomechanics" 28 (28): 761-788, 2012

22 Kaliske M, "On the nite element implementation of rubber-like materials at finite strains" 14 (14): 216-232, 1997

23 Nolan DR, "On the compressibility of arterial tissue" 44 (44): 993-1007, 2016

24 Germain S, "On inverse form finding for anisotropic materials" 10 (10): 159-160, 2010

25 Sun W, "Numerical approximation of tangent moduli for finite element implementations of nonlinear hyperelastic material models" 130 (130): 061003-, 2008

26 Holzapfel GA, "Nonlinear solid mechanics: a continuum approach for engineering" John Wiley & Sons 2000

27 Bonet J, "Nonlinear continuum mechanics for finite element analysis" Cambridge University Press 1997

28 Puglisi G, "Multi-scale modelling of rubber-like materials and soft tissues: an appraisal" 472 (472): 20160060-, 2016

29 Maas A, "Moderate and severe traumatic brain injury in adults" 7 (7): 728-741, 2008

30 Misra S, "Modelling of non-linear elastic tissues for surgical simulation" 13 (13): 811-818, 2010

31 Volokh KY, "Modeling failure of soft anisotropic materials with application to arteries" 4 (4): 1582-1594, 2011

32 Ommaya AK, "Mechanisms of impact head injury" 15 (15): 535-560, 1994

33 Goriely A, "Mechanics of the brain: perspectives, challenges, and opportunities" 14 (14): 931-965, 2015

34 Holbourn AHS, "Mechanics of head injuries" 242 (242): 438-441, 1943

35 Miller K, "Mechanical properties of brain tissue in-vivo: experiment and computer simulation" 33 (33): 1369-1376, 2000

36 Miller K, "Mechanical properties of brain tissue in tension" 35 (35): 483-490, 2002

37 Rashid B, "Mechanical characterization of brain tissue in tension at dynamic strain rates" 33 (33): 43-54, 2014

38 Erkamp RQ, "Measuring the elastic modulus of small tissue samples" 20 (20): 17-28, 1998

39 Samani A, "Measuring the elastic modulus of ex vivo small tissue samples" 48 (48): 2183-2198, 2003

40 Feng Y, "Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter" 23 (23): 117-132, 2013

41 Hickling R, "Mathematical model of a head subjected to an axisymmetric impact" 6 (6): 115-132, 1973

42 Bycroft GN, "Mathematical model of a head subjected to an angular acceleration" 6 (6): 487-495, 1973

43 Krishnamurthy G, "Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis" 295 (295): H1141-H1149, 2008

44 Davis FM, "Local mechanical properties of human ascending thoracic aneurysms" 61 (61): 235-249, 2016

45 Hardy WN, "Literature review of head injury biomechanics" 15 (15): 561-586, 1994

46 Holzapfel GA, "Large strain analysis of soft biological membranes: formulation and finite element analysis" 132 (132): 45-61, 1996

47 Swanson SR, "Large deformation finite element calculations for slightly compressible hyperelastic materials" 21 (21): 81-88, 1985

48 Lu J, "Inverse elastostatic stress analysis in pre-deformed biological structures: demonstration using abdominal aortic aneurysms" 40 (40): 693-696, 2007

49 Maier A, "Impact of calcification on patient-specific wall stress analysis of abdominal aortic aneurysms" 9 (9): 511-521, 2010

50 Taylor CA, "Image-based modeling of blood flow and vessel wall dynamics: applications, methods and future directions" 38 (38): 1188-1203, 2010

51 Steinmann P, "Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for treloars data" 82 (82): 1183-1217, 2012

52 Gasser TC, "Hyperelastic modelling of arterial layers with distributed collagen fibre orientations" 3 (3): 15-35, 2006

53 Molony DS, "Fluid-structure interaction of a patientspecific abdominal aortic aneurysm treated with an endovascular stent-graft" 8 (8): 24-, 2009

54 Scotti CM, "Fluid-structure interaction in abdominal aortic aneurysms: effects of asymmetry and wall thickness" 4 (4): 64-, 2005

55 Simon BR, "Finite element models for arterial wall mechanics" 115 (115): 489-496, 1993

56 Pan Y, "Finite element modeling of cns white matter kinematics: use of a 3d rve to determine material properties" 1 (1): 19-, 2013

57 Weiss JA, "Finite element implementation of incompressible, transversely isotropic hyperelasticity" 135 (135): 107-128, 1996

58 Post A, "Finite element analysis of the effect of loading curve shape on brain injury predictors" 45 (45): 679-683, 2012

59 Libertiaux V, "Experimental vitrification of brain tissue incompressibility using digital image correlation" 4 (4): 1177-1185, 2011

60 Morales DM, "Experimental models of traumatic brain injury: do we really need to build a better mousetrap?" 136 (136): 971-989, 2005

61 Hayashi K, "Experimental approaches on measuring the mechanical properties and constitutive laws of arterial walls" 115 (115): 481-488, 1993

62 Raghavan ML, "Ex vivo biomechanical behavior of abdominal aortic aneurysm: assessment using a new mathematical model" 24 (24): 573-582, 1996

63 Maquet PG, "Evolution of the maximum stress in osteo-arthritis of the knee" 10 (10): 107-117, 1977

64 Dorfmann A, "Evaluating patient-specific abdominal aortic aneurysm wall stress based on flow-induced loading" 9 (9): 127-139, 2010

65 Kroon M, "Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis" 464 (464): 807-825, 2008

66 Chenevert TL, "Elasticity reconstructive imaging by means of stimulated echo mri" 39 (39): 482-490, 1998

67 Krouskop TA, "Elastic moduli of breast and prostate tissues under compression" 20 (20): 260-274, 1998

68 Lally C, "Elastic behavior of porcine coronary artery tissue under uniaxial and equibiaxial tension" 32 (32): 1355-1364, 2004

69 Di Martino ES, "Effect of variation in intraluminal thrombus constitutive properties on abdominal aortic aneurysm wall stress" 31 (31): 804-809, 2003

70 Pervin F, "Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression" 42 (42): 731-735, 2009

71 Fallenstein GT, "Dynamic mechanical properties of human brain tissue" 2 (2): 217-226, 1969

72 Soza G, "Determination of the elasticity parameters of brain tissue with combined simulation and registration" 1 (1): 87-95, 2005

73 Brands DW, "Design and numerical implementation of a 3-d non-linear viscoelastic constitutive model for brain tissue during impact" 37 (37): 127-134, 2004

74 Bader H, "Dependence of wall stress in the human thoracic aorta on age and pressure" 20 (20): 354-361, 1967

75 Sabet AA, "Deformation of the human brain induced by mild angular head acceleration" 41 (41): 307-315, 2008

76 Hagemann A, "Coupling of fluid and elastic models for biomechanical simulations of brain deformations using FEM" 6 (6): 375-388, 2002

77 Horgan CO, "Constitutive models for compressible nonlinearly elastic materials with limiting chain extensibility" 77 (77): 123-138, 2004

78 Miller K, "Constitutive modelling of brain tissue:experiment and theory" 30 (30): 1115-1121, 1997

79 Merckel Y, "Constitutive modeling of the anisotropic behavior of mullins softened filled rubbers" 57 (57): 30-41, 2013

80 Odegard GM, "Constitutive modeling of skeletal muscle tissue with an explicit strain-energy function" 130 (130): 061017-, 2008

81 Miller K, "Constitutive model of brain tissue suitable for finite element analysis of surgical procedures" 32 (32): 531-537, 1999

82 Balzani D, "Constitutive framework for the modeling of damage in collagenous soft tissues with application to arterial walls" 213-216 : 139-151, 2012

83 Govindjee S, "Computational methods for inverse deformations in quasi-incompressible finite elasticity" 43 (43): 821-838, 1998

84 Chatelin S, "Computation of axonal elongation in head trauma finite element simulation" 4 (4): 1905-1919, 2011

85 Carew TE, "Compressibility of the arterial wall" 23 (23): 61-68, 1968

86 Chuong CJ, "Compressibility and constitutive equation of arterial wall in radial compression experiments" 17 (17): 35-40, 1984

87 Currie PK, "Comparison of incompressible elastic strain energy functions over the attainable region of invariant space" 10 (10): 559-574, 2005

88 Roth S, "Child head injury criteria investigation through numerical simulation of real world trauma" 93 (93): 32-45, 2009

89 Shafieian M, "Changes to the viscoelastic properties of brain tissue after traumatic axonal injury" 42 (42): 2136-2142, 2009

90 Fung YC, "Biomechanics: mechanical properties of living tissues" Springer 1993

91 Sayed TE, "Biomechanics of traumatic brain injury" 197 : 4692-4701, 2008

92 Prevost TP, "Biomechanics of brain tissue" 7 (7): 83-95, 2011

93 Holzapfel GA, "Biomechanical behavior of the arterial wall and its numerical characterization" 28 (28): 377-392, 1998

94 Samani A, "Biomechanical 3-d finite element modeling of the human breast using mri data" 20 (20): 271-279, 2001

95 Miehe C, "Aspects of the formulation and finite element implementation of large strain isotropic elasticity" 37 (37): 1981-2004, 1994

96 Gefen A, "Are in vivo and in situ brain tissues mechanically simliar?" 37 (37): 1339-1352, 2004

97 Guo Z, "Application of a new constitutive model for the description of rubber-like materials under monotonic loading" 43 (43): 2799-2819, 2006

98 OGara PT, "Aortic aneurysm" 107 (107): e43-e45, 2003

99 Case ME, "Abusive head injuries in infants and young children" 9 (9): 83-87, 2007

100 Misra JC, "A study on rotational brain injury" 17 (17): 459-466, 1984

101 Helderman F, "A numerical model to predict abdominal aortic aneurysm expansion based on local wall stress and stiffness" 46 (46): 1121-1127, 2008

102 Firoozbakhsh KK, "A model of brain shear under impulsive torsional loads" 8 (8): 65-73, 1975

103 Ljung C, "A model for brain deformation due to rotation of the skull" 8 (8): 263-274, 1975

104 Dal H, "A fully implicit finite element method for bidomain models of cardiac electromechanics" 253 (253): 323-336, 2013

105 Shum J, "A framework for the automatic generation of surface topologies for abdominal aortic aneurysm models" 39 (39): 249-259, 2011

106 Sussman T, "A finite element formulation for nonlinear incompressible elastic and inelastic analysis" 26 (26): 357-409, 1987

107 Horgan C, "A description of arterial wall mechanics using limiting chain extensibility constitutive models" 1 (1): 251-266, 2003

108 Metz H, "A comparison of the elasticity of live, dead, and fixed brain tissue" 3 (3): 453-458, 1970

109 Doyle BJ, "A comparison of modelling techniques for computing wall stress in abdominal aortic aneurysms" 6 (6): 38-, 2007

110 Mihai LA, "A comparison of hyperelastic constitutive models applicable to brain and fat tissues" 12 (12): 20150486-, 2015