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.

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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

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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).

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Fig. 3

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

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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.

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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.

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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).

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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

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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)



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