Research Papers

A Small Deformation Thermoporomechanics Finite Element Model and Its Application to Arterial Tissue Fusion

[+] Author and Article Information
D. P. Fankell, E. A. Kramer, V. L. Ferguson

Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309

R. A. Regueiro

Department of Civil, Environmental,
and Architectural Engineering,
University of Colorado Boulder,
Boulder, CO 80309

M. E. Rentschler

Department of Mechanical Engineering,
University of Colorado Boulder,
1111 Engineering Drive UCB 427,
Boulder, CO 80309
e-mail: mark.rentschler@colorado.edu

1Corresponding author.

Manuscript received June 20, 2017; final manuscript received September 14, 2017; published online January 17, 2018. Assoc. Editor: Ram Devireddy.

J Biomech Eng 140(3), 031007 (Jan 17, 2018) (11 pages) Paper No: BIO-17-1271; doi: 10.1115/1.4037950 History: Received June 20, 2017; Revised September 14, 2017

Understanding the impact of thermally and mechanically loading biological tissue to supraphysiological levels is becoming of increasing importance as complex multiphysical tissue–device interactions increase. The ability to conduct accurate, patient specific computer simulations would provide surgeons with valuable insight into the physical processes occurring within the tissue as it is heated or cooled. Several studies have modeled tissue as porous media, yet fully coupled thermoporomechanics (TPM) models are limited. Therefore, this study introduces a small deformation theory of modeling the TPM occurring within biological tissue. Next, the model is used to simulate the mass, momentum, and energy balance occurring within an artery wall when heated by a tissue fusion device and compared to experimental values. Though limited by its small strain assumption, the model predicted final tissue temperature and water content within one standard deviation of experimental data for seven of seven simulations. Additionally, the model showed the ability to predict the final displacement of the tissue to within 15% of experimental results. These results promote potential design of novel medical devices and more accurate simulations allowing for scientists and surgeons to quickly, yet accurately, assess the effects of surgical procedures as well as provide a first step toward a fully coupled large deformation TPM finite element (FE) model.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Berjano, E. J. , 2006, “Theoretical Modeling for Radiofrequency Ablation: State-of-the-Art and Challenges for the Future,” Biomed. Eng. Online, 5(1), p. 24. [CrossRef] [PubMed]
Fankell, D. P. , Kramer, E. , Cezo, J. , Taylor, K. D. , Ferguson, V. L. , and Rentschler, M. E. , 2016, “A Novel Parameter for Predicting Arterial Fusion and Cutting in Finite Element Models,” Ann. Biomed. Eng., 44(11), pp. 3295–3306. https://www.ncbi.nlm.nih.gov/pubmed/26983840
Pearce, J. A. , 2010, “Models for Thermal Damage in Tissues: Processes and Applications,” Crit. Rev. Biomed. Eng., 38(1), pp. 1–20. [CrossRef] [PubMed]
Tungjitkusolmun, S. , Staelin, S. T. , Haemmerich, D. , Tsai, J.-Z. , Cao, H. , Webster, J. G. , Lee, F. T. , Mahvi, D. M. , and Vorperian, V. R. , 2002, “Three-Dimensional Finite-Element Analyses for Radio-Frequency Hepatic Tumor Ablation,” IEEE Trans. Biomed. Eng., 49(1), pp. 3–9. [CrossRef] [PubMed]
Datta, A. K. , and Rakesh, V. , 2010, An Introduction to Modeling of Transport Processes: Applications to Biomedical Systems, Cambridge University Press, Cambridge, UK.
Martin, C. , Sun, W. , and Elefteriades, J. , 2015, “Patient-Specific Finite Element Analysis of Ascending Aorta Aneurysms,” Am. J. Physiol.: Heart Circ. Physiol., 308(10), pp. H1306–H1316. [CrossRef] [PubMed]
Karajan, N. , 2012, “Multiphasic Intervertebral Disc Mechanics: Theory and Application,” Arch. Comput. Methods Eng., 19(2), pp. 261–339. [CrossRef]
Jin, Z. , 2014, Computational Modelling of Biomechanics and Biotribology in the Musculoskeletal System: Biomaterials and Tissues, Elsevier, Philadelphia, PA.
Regueiro, R. A. , Zhang, B. , and Wozniak, S. L. , 2014, “Large Deformation Dynamic Three-Dimensional Coupled Finite Element Analysis of Soft Biological Tissues Treated as Biphasic Porous Media,” Comput. Model. Eng. Sci., 98(1), pp. 1–39. http://www.techscience.com/doi/10.3970/cmes.2014.098.001.pdf
Jayaraman, G. , 1983, “Water Transport in the Arterial Wall—A Theoretical Study,” J. Biomech., 16(10), pp. 833–840. [CrossRef] [PubMed]
Chapelle, D. , Gerbeau, J.-F. , Sainte-Marie, J. , and Vignon-Clementel, I. E. , 2010, “A Poroelastic Model Valid in Large Strains With Applications to Perfusion in Cardiac Modeling,” Comput. Mech., 46(1), pp. 91–101. [CrossRef]
Diller, K. R. , and Hayes, L. J. , 1983, “A Finite Element Model of Burn Injury in Blood-Perfused Skin,” ASME J. Biomech. Eng., 105(3), pp. 300–307. [CrossRef]
Ehlers, W. , and Bluhm, J. , 2013, Porous Media: Theory, Experiments and Numerical Applications, Springer-Verlag, Berlin.
Bowen, R. M. , 1980, “Incompressible Porous Media Models by Use of the Theory of Mixtures,” Int. J. Eng. Sci., 18(9), pp. 1129–1148. [CrossRef]
De Boer, R. , 2005, Trends in Continuum Mechanics of Porous Media, Springer, Dordrecht, The Netherlands. [CrossRef]
Wang, W. , Regueiro, R. A. , and McCartney, J. S. , 2015, “Coupled Axisymmetric Thermo-Poro-Mechanical Finite Element Analysis of Energy Foundation Centrifuge Experiments in Partially Saturated Silt,” Geotech. Geol. Eng., 33(2), pp. 373–388. [CrossRef]
Holzapfel, G. A. , 2000, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Wiley, Medford, MA.
Lewis, R. W. , and Schrefler, B. A. , 1999, The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2nd ed., Wiley, Medford, MA.
Coussy, O. , 2004, Poromechanics, 2nd ed., Wiley, Chichester, UK.
Wang, W. , 2014, “Coupled Thermo-Poro-Mechanical Axisymmetric Finite Element Modeling of Soil-Structure Interaction in Partially Saturated Soils,” Ph.D. dissertation, University of Colorado Boulder, Boulder, CO. http://scholar.colorado.edu/cgi/viewcontent.cgi?article=1009&context=cven_gradetds
Coleman, B. D. , and Noll, W. , 1963, “The Thermodynamics of Elastic Materials With Heat Conduction and Viscosity,” Arch. Ration. Mech. Anal., 13(1), pp. 167–178. [CrossRef]
Pearce, J. , 2015, “Numerical Model Study of Radio Frequency Vessel Sealing Thermodynamics,” Proc. SPIE, 9326, p. 93260A.
Datta, A. K. , 2007, “Porous Media Approaches to Studying Simultaneous Heat and Mass Transfer in Food Processes—II: Property Data and Representative Results,” J. Food Eng., 80(1), pp. 96–110. [CrossRef]
Halder, A. , Dhall, A. , and Datta, A. K. , 2010, “Modeling Transport in Porous Media With Phase Change: Applications to Food Processing,” ASME J. Heat Transfer, 133(3), p. 031010. [CrossRef]
Halder, A. , Dhall, A. , and Datta, A. K. , 2007, “An Improved, Easily Implementable, Porous Media Based Model for Deep-Fat Frying—Part I: Model Development and Input Parameters,” Food Bioprod. Process., 85(3), pp. 209–219. [CrossRef]
Cezo, J. , 2013, “Thermal Tissue Fusion of Arteries: Methods, Mechanisms, & Mechanics,” Ph. D. dissertation, University of Colorado Boulder, Boulder, CO. http://scholar.colorado.edu/mcen_gradetds/74/
Cezo, J. D. , Passernig, A. C. , Ferguson, V. L. , Taylor, K. D. , and Rentschler, M. E. , 2014, “Evaluating Temperature and Duration in Arterial Tissue Fusion to Maximize Bond Strength,” J. Mech. Behav. Biomed. Mater., 30, pp. 41–49. [CrossRef] [PubMed]
Cengel, Y. , and Ghajar, A. , 2010, Heat and Mass Transfer: Fundamentals and Applications, 4th ed., McGraw-Hill, New York.
Johnson, M. , and Tarbell, J. M. , 2000, “A Biphasic Anisotropic Model of the Aortic Wall,” ASME J. Biomech. Eng., 123(1), pp. 52–57. [CrossRef]
Chen, S. S. , Wright, N. T. , and Humphrey, J. D. , 1997, “Heat-Induced Changes in the Mechanics of a Collagenous Tissue: Isothermal Free Shrinkage,” ASME J. Biomech. Eng., 119(4), pp. 372–378. [CrossRef]
Khalili, N. , Uchaipichat, A. , and Javadi, A. A. , 2010, “Skeletal Thermal Expansion Coefficient and Thermo-Hydro-Mechanical Constitutive Relations for Saturated Homogeneous Porous Media,” Mech. Mater., 42(6), pp. 593–598. [CrossRef]
Chen, R. K. , Chastagner, M. W. , Dodde, R. E. , and Shih, A. J. , 2013, “Electrosurgical Vessel Sealing Tissue Temperature: Experimental Measurement and Finite Element Modeling,” IEEE Trans. Biomed. Eng., 60(2), pp. 453–460. [CrossRef] [PubMed]
Karšaj, I. , and Humphrey, J. D. , 2012, “A Multilayered Wall Model of Arterial Growth and Remodeling,” Mech. Mater. Int. J., 44, pp. 110–119. [CrossRef]
Marbán, A. , Casals, A. , Fernández, J. , and Amat, J. , 2014, “Haptic Feedback in Surgical Robotics: Still a Challenge,” ROBOT2013: First Iberian Robotics Conference, Vol. 252, M. A. Armada , A. Sanfeliu , and M. Ferre , eds., Springer International Publishing, Cham, Switzerland, pp. 245–253. [CrossRef]


Grahic Jump Location
Fig. 1

A depiction of the deformation of each phase from its initial differential volume, dVα, in their respective reference configurations to the final smeared differential volume, dv, in the final current configuration

Grahic Jump Location
Fig. 2

Depiction of the problem setup for the balance equations where u, pℓ, and θ are the desired field variables. Fluxes and prescribed boundary conditions act on surfaces (Γ), while heat source (r) and phase transition (ρ̂v) act throughout the body (Ω).

Grahic Jump Location
Fig. 3

Depiction of the tissue clamped within the Conmed Altrus® jaws and the two-dimensional plane to be simulated

Grahic Jump Location
Fig. 4

Depiction of the quarter-symmetry section of tissue and applied boundary conditions. The device jaws apply temperature and pressure to the top. Symmetry boundary conditions are applied to the bottom and left edges. Heat and water are allowed to flow through the right edge.

Grahic Jump Location
Fig. 5

(a) The temperature (°C) within the tissue for an applied 170 °C and an Sr=0.3 at the end of 5 s. (b) and (c) The temperature at the center of the tissue as it is compared to published experimental results [5]. Only one data point can be compared as all other experimental points are located too far from the center plane of the tissue.

Grahic Jump Location
Fig. 6

(a) The water content at 5 s within the center plane of the tissue for a simulation applying 170 °C and an Sr=0.3. (b) Dots representing the average water content within the tissue for applied temperatures of 120–200 °C for an Sr of 0.25, 0.30, and 0.35 are plotted against measured experimental results. All simulated results of water content fell within one standard deviation of the average experimental results with an Sr of 0.30 producing results nearest the mean of the experimental results. Note: Experimental results include Cezo's published results and supplemental results obtained following the same procedure (T = 150C and T = 180C, n = 12).

Grahic Jump Location
Fig. 7

The average recorded stress–strain curves for eight porcine splenic arteries (standard deviation of 0.12 MPa) compared to the simulated stress–strain curves of a linear elastic (MSE = 0.33), bilinear elastic (MSE = 0.21), and exponential elastic (MSE = 0.18) solid material model before heating

Grahic Jump Location
Fig. 8

The average measured engineering strain (standard deviation of 0.033) for the eight fused porcine arteries during mechanical loading (0–2 s), while heated up to an applied temperature of 170 °C (2–3 s) and at a constant applied temperature of 170 deg (4–5 s)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In