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Research Papers

Porohyperviscoelastic Model Simultaneously Predicts Parenchymal Fluid Pressure and Reaction Force in Perfused Liver

[+] Author and Article Information
Emma C. Moran

Department of Biomedical Engineering, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157;  Virginia-Tech Wake Forest University School of Biomedical Engineering and Sciences, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157emoran@wakehealth.edu

Smitha Raghunathan

Department of Biomedical Engineering, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157;  Virginia-Tech Wake Forest University School of Biomedical Engineering and Sciences, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157

Douglas W. Evans

Department of Biomedical Engineering, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157;  Virginia-Tech Wake Forest University School of Biomedical Engineering and Sciences, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157devans@wakehealth.edu

Nicholas A. Vavalle

Department of Biomedical Engineering, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157;  Virginia-Tech Wake Forest University School of Biomedical Engineering and Sciences, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157nvavalle@wakehealth.edu

Jessica L. Sparks

Department of Biomedical Engineering, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157;  Virginia-Tech Wake Forest University School of Biomedical Engineering and Sciences, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157jsparks@wakehealth.edu

Tanya LeRoith

 Department of Biomedical Sciences and Pathology, Virginia-Maryland Regional College of Veterinary Medicine, Duckpond Drive, Phase II, Virginia Tech (0442), Blacksburg, VA 24061tleroith@vt.edu

Thomas L. Smith

Department of Orthopaedics, Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157tsmith@wakehealth.edu

J Biomech Eng 134(9), 091002 (Aug 27, 2012) (9 pages) doi:10.1115/1.4007175 History: Received December 21, 2011; Revised July 12, 2012; Posted July 18, 2012; Published August 27, 2012; Online August 27, 2012

Porohyperviscoelastic (PHVE) modeling gives a simplified continuum approximation of pore fluid behavior within the parenchyma of liver tissue. This modeling approach is particularly applicable to tissue engineering of artificial livers, where the inherent complexity of the engineered scaffolds prevents the use of computational fluid dynamics. The objectives of this study were to simultaneously predict the experimental parenchymal fluid pressure (PFP) and compression response in a PHVE liver model. The model PFP matched the experimental measurements (318 Pa) to within 1.5%. Linear regression of both phases of compression, ramp, and hold, demonstrated a strong correlation between the model and the experimental reaction force (p<0.5). The ability of this PVE model to accurately predict both fluid and solid behavior is important due to the highly vascularized nature of liver tissue and the mechanosensitivity of liver cells to solid matrix and fluid flow properties.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Left: Cylindrical sample of bovine tissue used in experimental testing. Right: μCT image of perfused sample showing the portal vein with branching.

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Figure 2

Mechanical testing configuration for perfused bovine liver testing depicting (a) perfusion input tubing, (b) the specimen, (c) the saline boundary between the sample and platen, (d) the load cell, and (e) the wick-catheter parenchymal fluid pressure measurement system. The environmental chamber dimensions are 20 cm × 15 cm × 15 cm.

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Figure 3

Wick catheter system with syringe tip (a) withdrawn, shown inserted into a water column calibration device (b). Note the soluble dexon suture (d) extending past the catheter tip (c).

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Figure 4

Avascular model showing surface area over which the surface fluid load was applied. Middle: Portal model with simulated portal vein. The surface area of the fluid load is shaded and was directed into the tissue from the sides of the portal vein. Right: Red nodes indicate those included in the calculation for parenchymal fluid pressure.

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Figure 5

A representative H&E image of bovine liver. Void volume was determined from histological images using the methodology reported in Raghunathan The void ratio was calculated to be 0.2, according to the equation e=n/(1-n), where n = void volume/total volume.

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Figure 6

Equilibrium load versus strain results for perfused bovine liver samples (95% confidence intervals shown)

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Figure 7

The avascular models (top row) and portal models (bottom row) are cut in half, horizontally, displaying the middle of the tissue. Left: parenchymal fluid pressure (PFP); center: fluid velocity in the y-direction; right: fluid velocity in the x-direction.

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Figure 8

Reaction force of the ramp and hold of the average experimental data and PVE model prediction with error bars indicating standard deviation of the liver sample’s peak and relaxed reaction force

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Figure 9

Linear regression comparing experimental ramp phase data and hold phase data to their PVE model simulations

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Figure 10

Parenchymal fluid pressure (PFP) as a function of time for perfusion (A→B), compression (B→C), and hold (C→D). Measurements are shown as both the average of nodes from the entire model and the area of 77 nodes used to optimize PFP (refer to Fig. 4). Small oscillations in pressure during the hold phase can be attributed to instability in the PE finite element modeling in ABAQUS , as described by Stokes [51].

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Figure 11

Stress relaxation response of (1) the porohyperviscoelastic (PHVE) model that was optimized to the experimental pressure and reaction force, (2) the porohyperelastic (PHE) model in which the viscoelastic Prony series was removed, and (3) the viscohyperelastic (VHE) model in which all fluid components were removed. Note the small oscillations during the hold phase in the PHE model, which may be attributed to instability in the PE finite element modeling in ABAQUS , as described by Stokes [51]. The first two of these oscillations are shown, but the rest were removed for clarity.

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Figure 12

Compression response of the porohyperviscoelastic (PHVE) versus the (hyperelastic constants) poroviscoelastic (PVE) model (linear elastic constants). The relaxation response is the same in both models, therefore, just the compression portion of the curve is shown.

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