Research Papers

Description and Validation of a Finite Element Model of Backflow During Infusion Into a Brain Tissue Phantom

[+] Author and Article Information
José J. García

Escuela de Ingeniería Civil y Geomática,
Universidad del Valle,
Cali, Colombia

Ana Belly Molano

Escuela de Ingeniería Mecánica,
Universidad del Valle,
Cali, Colombia

Joshua H. Smith

Department of Mechanical Engineering,
Lafayette College,
Easton, PA 18042
e-mail: smithjh@lafayette.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 15, 2011; final manuscript received May 17, 2012; published online August 31, 2012. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 8(1), 011017 (Aug 31, 2012) (8 pages) Paper No: CND-11-1113; doi: 10.1115/1.4007311 History: Received July 15, 2011; Revised May 17, 2012

An axisymmetric biphasic finite element model is proposed to simulate the backflow that develops around the external boundary of the catheter during flow-controlled infusions. The model includes both material and geometric nonlinearities and special treatments for the nonlinear boundary conditions used to represent the forward flow from the catheter tip and the axial backflow that occurs in the annular gap that develops as the porous medium detaches from the catheter. Specifically, a layer of elements with high hydraulic conductivity and low Young’s modulus was used to represent the nonlinear boundary condition for the forward flow, and another layer of elements with axial hydraulic conductivity consistent with Poiseuille flow was used to represent the backflow. Validation of the model was performed by modifying the elastic properties of the latter layer to fit published experimental values for the backflow length and maximum fluid pressure obtained during infusions into agarose gels undertaken with a 0.98-mm-radius catheter. Next, the finite element model predictions showed good agreement with independent experimental data obtained for 0.5-mm-radius and 0.33-mm-radius catheters. Compared to analytical models developed by others, this finite element model predicts a smaller backflow length, a larger fluid pressure, and a substantially larger percentage of forward flow. This latter difference can be explained by the important axial flow in the tissue that is not considered in the analytical models. These results may provide valuable guidelines to optimize protocols during future clinical studies. The model can be extended to describe infusions in brain tissue and in patient-specific geometries.

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Grahic Jump Location
Fig. 4

(a) Finite element mesh for the 0.98-mm-radius catheter. (b) Detail of the mesh near the catheter tip.

Grahic Jump Location
Fig. 3

A sketch of a portion of the inlet layer (horizontal) and backflow layer (vertical) of the finite element model in the initial configuration and in a representative deformed configuration. The solid lines illustrate the edges of the elements that are fixed on the outside of the catheter. The dashed lines illustrate the edges of the elements in the initial configuration, and the dash-dotted lines illustrate those same edges in the representative deformed configuration. The radial deformation h of the backflow layer indicated is a function of axial position.

Grahic Jump Location
Fig. 2

Representation of the radial displacement ur, radial fluid flux qr, fluid pressure p, and traction t, and nonlinear (NL1 and NL2) boundary conditions considered in the analysis

Grahic Jump Location
Fig. 1

(a) Sketch of the domain used in the finite element model of backflow around a 0.98-mm-radius catheter. (b) Sketch illustrating the size of the computational domain relative to that of a human brain, where the solid straight line represents the catheter.

Grahic Jump Location
Fig. 5

Comparison of the maximum fluid pressure as a function of the infusion flow rate among the finite element model (solid circles), the experimental results (open circles), and the analytical model (line) for a catheter of radius (a) 0.98 mm, (b) 0.50 mm, and (c) 0.33 mm

Grahic Jump Location
Fig. 6

Comparison of the backflow length as a function of the infusion flow rate among the finite element model (solid circles), the experimental results (open circles), and the analytical model (line) for a catheter of radius (a) 0.98 mm, (b) 0.50 mm, and (c) 0.33 mm

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Fig. 7

Contours of the maximum principal logarithmic strain for a 0.98-mm-radius catheter with a flow of 8 μl/min in a portion of the computational domain

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Fig. 8

Comparison of the (a) fluid pressure and (b) radial displacement distributions along a 0.98-mm-radius catheter obtained from the finite element model and the analytical model [14] for infusion of 1 and 8 μl/min. Distance is measured from the tip of the catheter.

Grahic Jump Location
Fig. 10

Comparison of the finite element fluid velocity (mm/s) distributions obtained for flow rates of (a) 1 μl/min and (b) 8 μl/min for a 0.98-mm radius catheter

Grahic Jump Location
Fig. 11

Comparison of the finite element radial displacement (mm) distributions obtained for flow rates of (a) 1 μl/min and (b) 8 μl/min for a 0.98-mm-radius catheter

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Fig. 9

Comparison of the finite element fluid pressure (Pa) distributions obtained for flow rates of (a) 1 μl/min and (b) 8 μl/min for a 0.98-mm-radius catheter

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Fig. 12

Direction and relative magnitude of the fluid velocity vectors in the neighborhood of the catheter tip showing important axial components toward the lower hemispherical domain for flow rates of (a) 1 μl/min and (b) 8 μl/min for a 0.98-mm-radius catheter

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Fig. 13

Relative distribution of flows for infusions rates of (a) 1 μl/min and (b) 8 μl/min for a 0.98-mm-radius catheter



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