Finite Element Analysis of Liver Tissue Modeled Using Micro-CT

One important question for less invasive surgical techniques, such as laparoscopy, is the behavior of the tissue of interest. Non-destructive approaches to determine material properties are of particular benefit. This paper considers the material properties of lamb liver via spherical indentation and finite element analysis. The indentation is performed under a series of step loads with a non contacting laser displacement sensor monitoring indentation depth. The liver is also monitored using a high resolution imaging technique called micro computed tomography (micro-CT), which can create accurate 3D models and provide information about the shape of the indented surface. The 3D model from micro-CT is meshed using the NetGen software package. The loaddisplacement data is then compared to a finite element model in ANSYS based upon the meshed liver. Different approaches to building the model to reduce computational time are discussed. The optimal viscoelastic material properties of the liver tissue are obtained by comparing the experimental load-displacement data with that of the finite element model. INTRODUCTION The characterization of the material properties of biological tissues is highly useful to surgeons and tool makers. The surgeons need to know beforehand how the organs behave during surgery and the tool makers need the information to design appropriate tools for the surgeons. Most of the studies of biological materials are performed on animal organs due to the lack of availability of human tissues. However certain groups did perform experiments on human tissues. Carter et al. [1] and Kauer [2] performed in vivo experiments on human liver and human uteri respectively. Yeh et al. [3] performed ex vivo tests on human liver specimens and came up with the material properties. The ex vivo experiments are performed on tissues removed from the body while the in vivo experiments are performed within the body of the human or animal. The advantage of in vivo experiments is that the tissues are intact in the right orientation and provide accurate material properties. However, there are certain disadvantages to this method. The use of sophisticated tools and data collection systems is limited due to the space restrictions and most of the in vivo experiments are conducted using hand held probes inserted into the body through tiny insertions on the skin. Samur et al. [4] have reported that the data obtained from the tests performed on live animals contain heavy noise due to the breathing and other internal processes within the body. The data is hard to interpret unless the magnitude of load or deformation applied is considerably larger than the noise being generated. This problem has led researchers to euthanize the animals before performing in vivo tests. Brown et al. [5] reported that the elastic properties of a porcine liver do not show a considerable change within 3 hours of euthanizing the animal; however, the stress relaxation behavior varies as the dead tissues tend to stiffen over time. Most researchers perform experimentation on animal tissues and try to relate the results to human tissues. Ottensmeyer [6] and Valtorta [7] performed in vivo and ex vivo tests on porcine liver and came up with vastly varying material properties. In this paper, the tissue in study is the liver of a lamb. Image segmentation is used to develop accurate 3D models of the specimens [8]. Indentation tests are performed on the lamb liver tissue and the material properties are obtained using an inverse finite element solution using the ANSYS software. A 2D axisymmetric model is first used to obtain the viscoelastic material properties of the liver. Various researchers have used this technique to obtain the material properties[4,9,10]. Various combinations of elastic, Proceedings of the XIth International Congress and Exposition June 2-5, 2008 Orlando, Florida USA ©2008 Society for Experimental Mechanics Inc. viscoelastic and hyperelastic material models are studied and the best set of material properties are used to run the 3D simulation of the liver. The finite element results are compared with the image segmentation results to validate the accuracy of the model. EXPERIMENTAL SETUP Two types of experiments are performed on the lamb liver. The displacement control tests and the load control tests. For both the experiments the specimen is prepared in the same way. The liver sample is cut with a circular cutter made to the same diameter as the beaker in which the specimen is to be placed, so that there would be no movement along the edges of the sample. Figure 1 shows the liver sample and the circular cutter. Figure 1. Lamb liver cut to the beaker size using a circular cutter The displacement controlled tests are performed using a Dynamic Mechanical Analyzer (DMA). The DMA has precise displacement control and displacements can be applied at a required rate and the corresponding forces obtained are monitored. Indentation tests are performed using a 3/8ths inch indenter spherical diameter at different displacement histories. The load control tests are performed using a setup as described below. The glass beaker is placed in a cylindrical acrylic casing which has a clamp at the bottom. An aluminum indenter assembly is placed on the top of the casing. The assembly consists of a circular platform with an indenter passing through the center. The indenter can mover vertically through the center of the platform so that the tip of the indenter can be moved to the required position. The platform supports the loads applied during the tests. A lever is connected to the platform and a balancing weight is attached to the lever such that the weight of the assembly can be balanced by moving the balancing weight along the lever. A laser displacement sensor is placed above the assembly such that the laser beam is projected directly onto the tip of the indenter. The purpose of the sensor is to measure the displacement of the indenter during the test. The laser sensor is connected to a computer through a data acquisition card which transfers data during the test. The output of the sensor is voltage which relates to the distance moved by the indenter. The data acquisition software Labview is used to collect the data. The whole assembly is placed in the MicroCT machine. The assembly is shown in Figure 2 . Figure 2. Setup for load control tests The MicroCT machine is used to capture the shape of the specimen during the tests. The specimen (the whole assembly) is clamped to the rotating table of the MicroCT and X-Rays are projected onto the specimen as it rotates about its axis. The x-rays capture the images in segments from top to bottom of the specimen. The tests are performed by applying different loads on the top of the specimen. IMAGE SEMENTATION The images taken by the x-rays during the test are stacked up in order and a 3D model of the liver sample is obtained by a technique called image segmentation. A few of the x-ray images are shown in Figure 3. Figure 3. X-ray images of the specimen taken during the load control tests. The output of the image segmentation process is the data file containing the surface mesh points of the 3D liver sample in STL format (raw unstructured triangulated surface by the unit normal and vertices of the triangles using a three-dimensional Cartesian coordinate system). The imaging technique can also be used to enhance the quality or refine the 3D model of the sample. In this case, the irregularities of the sample which are really irrelevant to the analysis and can cause potential converging problems during analysis are removed during segmentation. Figure 4(a) shows a sample 3D model and Figure 4(b) shows the removal of irregularities on the outer surface of the sample. (a) (b) Figure 4. (a) 3D model generated by segmentation. (b) Smoothing the edges of the sample The STL output is loaded into a mesh generating software called NetGen which is then used to create different mesh densities. Different levels of mesh can be created based on the requirement of the analysis. The different mesh densities obtained from Net Gen are shown in Figure 5. (a) (b) (c) Figure 5. 3D models with (a) coarse (b) moderate and (c) fine meshes FINITE ELEMENT MODELING The finite element modeling of the liver is performed using ANSYS. A 2D axisymmetric model having approximately the same width and thickness of the actual sample is modeled using Plane 182 elements. Plane182 elements can be used with hyperelastic and viscoelastic models for large strain analysis. The spherical indenter is modeled as a rigid line with a pilot node at the center of the sphere. Contact elements are used to model the contact region between the indenter and the sample. The viscoelastic material properties are defined as a Prony series with four Prony terms while the hyperelastic properties are defined by the Neo-Hookean model. The initial elastic modulus and Poisson’s ratio are assumed (from values provided by various researchers) as 300KPa and 0.485 respectively. An inverse finite element analysis is done to match the experimental results to the simulation results by minimizing the error between the sets of results. The initial experimental data set used is that of a displacement controlled test shown in Figure 6. The displacement is ramped up to a value of 5 mm in 1 second and is held constant for 10 seconds. The force relaxes with time which shows that viscoelastic properties are required to model the specimen.