Abstract
Robotic surgery is an attractive, minimally invasive and high precision alternative to conventional surgical procedures. However, it lacks the natural touch and force feedback that allows the surgeon to control safe tissue manipulation. This is an important problem in standard surgical procedures such as clamping, which might induce severe tissue damage. In complex, heterogeneous, large deformation scenarios, the limits of the safe loading regime beyond which tissue damage occurs are unknown. Here, we show that a continuum damage model for arteries, implemented in a finite element setting, can help to predict arterial stiffness degradation and to identify critical loading regimes. The model consists of the main mechanical constituents of arterial tissue: extracellular matrix, collagen fibres and smooth muscle cells. All constituents are allowed to degrade independently in response to mechanical overload. To demonstrate the modularity and portability of the proposed model, we implement it in a commercial finite element programme, which allows to keep track of damage progression via internal variables. The loading history during arterial clamping is simulated through four successive steps, incorporating residual strains. The results of our first prototype simulation demonstrate significant regional variations in smooth muscle cell damage. In three additional steps, this damage is evaluated by simulating an isometric contraction experiment. The entire finite element simulation is finally compared with actual in vivo experiments. In the short term, our computational simulation tool can be useful to optimise surgical tools with the goal to minimise tissue damage. In the long term, it can potentially be used to inform computer-assisted surgery and identify safe loading regimes, in real time, to minimise tissue damage during robotic tissue manipulation.
Similar content being viewed by others
References
Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J Mech Phys Solids 41(2): 389–412
Balzani D, Schröder J, Gross D (2006) Simulation of discontinuous damage incorporating residual stresses in circumferentially overstretched atherosclerotic arteries. Acta Biomat 2(6): 609–618
Balzani D, Schröder J, Gross D (2007) Numerical simulation of residual stresses in arterial walls. Comput Mater Sci 39: 117–123
Balzani D, Böse D, Brads D, Erbel R, Klawonn A, Reinbach O, Schröder J (2011) Parallel simulation of patient-specific atherosclerotic arteries for the enhancement of intravascular ultrasound diagnosis. Eng Comp (submitted)
Barone GW, Conerly JM, Farley PC, Flanagan TL, Kron IL (1989) Assessing clamp-related vascular injuries by measurement of associated vascular dysfunction. Surgery 105(4): 465–471
Böl M, Abilez OJ, Assar AN, Zarins CK, Kuhl E (2012) In vitro/in silico characterization of active and passive stresses in cardiac muscle. Int J Multiscale Comput Eng (in press)
Callera GE, Varanda WA, Bendhack LM (2000) Impaired relaxation to acetylcholine in 2k-1c hypertensive rat aortas involves changes in membrane hyperpolarization instead of an abnormal contribution of endothelial factors. Gen Pharmacol 34(6): 379–389
Calvo B, Pena M, Martinez M, Doblaré M (2007) An uncoupled directional damage model for fibred biological soft tissues. Formulation and computational aspects. Int J Numer Methods Eng 69: 2036–2057
Dargazany R, Itskov M (2009) A network evolution model for the anisotropic mullins effect in carbon black filled rubbers. Int J Solids Struct 46(16): 2967–2977
De S, Rosen J, Dagan A, Hannaford B, Swanson P, Sinanan M (2007) Assessment of tissue damage due to mechanical stresses. Int J Robot Res 26: 1159–1171
Ehret A, Itskov M (2009) Modeling of anisotropic softening phenomena: application to soft biological tissues. Int J Plast 25: 901–919
Famaey N, Vander Sloten J (2008) Soft tissue modelling for applications in virtual surgery and surgical robotics. Comput Methods Biomech Biomed Eng 11(4): 351–366
Famaey N, Verbeken E, Vinckier S, Willaert B, Herijgers P, Vander Sloten J (2010) In vivo soft tissue damage assessment for applications in surgery. Med Eng Phys 32: 437–443
Famaey N, Sommer G, Vander Sloten J, Holzapfel GA (2012) Arterial clamping: finite element simulation and in vivo validation. J Mech Behav Biomed Mater (accepted)
Fung YC (1970) Mathematical representation of the mechanical properties of the heart muscle. J Biomech 3(4): 381–404
Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3(6): 15–35
Gestrelius S, Borgström P (1986) A dynamic model of smooth muscle contraction. Biophys J 50(1): 157–169
Gleason RL, Gray SP, Wilson E, Humphrey JD (2004) A multiaxial computer-controlled organ culture and biomechanical device for mouse carotid arteries. J Biomech Eng 126(6): 787–795
Göktepe S, Kuhl E (2010) Electromechanics of the heart—a unified approach to the strongly coupled excitation-contraction problem. Comput Mech 45: 227–243
Göktepe S, Acharya SNS, Wong J, Kuhl E (2011) Computational modeling of passive myocardium. Int J Numer Methods Biomed Eng 27: 1–12
Gupta V, Reddy NP, Batur P (1997) Forces in laparoscopic surgical tools. Presence 6: 218–228
Hai CM, Murphy RA (1988) Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J Physiol 254(1 Pt 1): C99–106
Hill A (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B 126: 136–195
Hokanson J, Yazdani S (1997) A constitutive model of the artery with damage. Mech Res Commun 24(2): 151–159
Holzapfel GA, Ogden RW (2010a) Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta. J R Soc Interface 7: 787–799
Holzapfel GA, Ogden RW (2010b) Constitutive modeling of arteries. Proc R Soc Lond A 466: 1551–1597
Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61: 1–48
Hsi C, Cuenoud H, Soller BR, Kim H, Favreau J, Salm TJV, Moran JM (2002) Experimental coronary artery occlusion: relevance to off-pump cardiac surgery. Asian Cardiovasc Thorac Ann 10(4): 293–297
Itoh A, Krishnamurthy G, Swanson J, Ennis D, Bothe W, Kuhl E, Karlsson M, Davis L, Miller DC, Ingels NB (2009) Active stiffening of mitral valve leaflets in the beating heart. Am J Physiol Heart Circ Physiol 296: 1766–1773
Kroon M (2010) A constitutive model for smooth muscle including active tone and passive viscoelastic behaviour. Math Med Biol 27(2): 129–155
Kuhl E, Ramm E (1999) Simulation of strain localization with gradient enhanced damage models. Comput Mater Sci 16: 176–185
Kuhl E, Maas R, Himpel G, Menzel A (2007) Computational modeling of arterial wall growth: Attempts towards patient specific simulations based on computer tomography. Biomech Model Mechanobiol 6: 321–331
Kwoh YS, Hou J, Jonckheere EA, Hayall S (1988) A robot with improved absolute positioning accuracy for ct guided stereotactic brain surgery. IEEE Trans Biomed Eng 35: 153–161
Mahnken R, Kuhl E (1999) Parameter identification of gradient enhanced damage models with the finite element method. Eur J Mech/A Solids 18: 819–835
Manchio JV, Gu J, Romar L, Brown J, Gammie J, Pierson RN, Griffith B, Poston RS (2005) Disruption of graft endothelium correlates with early failure after off-pump coronary artery bypass surgery. Ann Thorac Surg 79(6): 1991–1998
Matsumoto T, Hayashi K (1994) Mechanical and dimensional adaptation of rat aorta to hypertension. J Biomech Eng 116(3): 278–283
Miehe C (1995) Discontinuous and continuous damage evolution in ogden-type large-strain elastic materials. Eur J Mech A/Solids 14: 697–720
Mohr FW, Falk V, Diegeler A, Walther T, Gummert JF, Bucerius J, Jacobs S, Autschbach R (2001) Computer-enhanced robotic cardiac surgery: experience in 148 patients. J Thorac Cardiovasc Surg 121: 842–853
Murtada S-I, Kroon M, Holzapfel GA (2010) A calcium-driven mechanochemical model for prediction of force generation in smooth muscle. Biomech Model Mechanobiol 9(6): 749–762
O’Connell MK, Murthy S, Phan S, Xu C, Buchanan J, Spilker R, Dalman RL, Zarins CK, Denk W, Taylor CA (2008) The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3d confocal and electron microscopy imaging. Matrix Biol 27(3): 171–181
Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the mullins effect in filled rubber. Proc R Soc A 455: 2861–2877
Pena E, Alastrué V, Laborda A, Matrínez M, Doblaré M (2010) A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour. J Biomech 43: 984–989
Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E (2011) Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech Model Mechanobiol 10: 799–811
Rhodin JAG (1979) Architecture of the vessel wall. In: Berne RM (ed) Handbook of physiology, section 2, volume 2. Am. Physiol. Soc., Bethesda
Rodríguez JF, Cacho F, Bea JA, Doblaré M (2006) A stochastic-structurally based three dimensional finite-strain damage model for fibrous soft tissue. J Mech Phys Solids 54(4): 864–886
Sacks MS, Sun W (2003) Multiaxial mechanical behavior of biological materials. Annu Rev Biomed Eng 5: 251–284
Schmitz A, Böl M (2011) On a phenomenological model for active smooth muscle contraction. J Biomech 44: 2090–2095
Simo J, Ju J (1987) Strain- and stress-based continuum damage models. Int J Solids Stuct 23: 821–840
Stålhand J (2009) Determination of human arterial wall parameters from clinical data. Biomech Model Mechanobiol 8(2): 141–148
Stålhand J, Klarbring A, Holzapfel GA (2008) Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains. Prog Biophys Mol Biol 96: 465–481
Stålhand J, Klarbring A, Holzapfel GA (2011) A mechanochemical 3d continuum model for smooth muscle contraction under finite strains. J Theor Biol 268(1): 120–130
Tsamis A, Bothe W, Kvitting JP, Swanson JC, Miller DC, Kuhl E (2011) Active contraction of cardiac muscle: in vivo characterization of mechanical activation sequences in the beating heart. J Mech Behav Biomed Mater 4: 1167–1176
Vito RP, Dixon SA (2003) Blood vessel constitutive models-1995–2002. Annu Rev Biomed Eng 5: 413–439
Volokh KY (2008) Prediction of arterial failure based on a microstructural bi-layer fiber matrix model with softening. J Biomech 41(2): 447–453
Volokh KY (2011) Modeling failure of soft anisotropic materials with application to arteries. J Mech Behav Biomed Mater 4(8): 1582–1594
Yang J, Clark JW Jr, Bryan RM, Robertson C (2003) The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model. Med Eng Phys 25(8): 691–709
Zulliger MA, Rachev A, Stergiopulos N (2004) A constitutive formulation of arterial mechanics including vascular smooth muscle tone. Am J Physiol Heart Circ Physiol 287(3): H1335–H1343
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Famaey, N., Vander Sloten, J. & Kuhl, E. A three-constituent damage model for arterial clamping in computer-assisted surgery. Biomech Model Mechanobiol 12, 123–136 (2013). https://doi.org/10.1007/s10237-012-0386-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-012-0386-7