Using Multi-Physics Finite Element Analysis to Simulate Biological Tissue and Medical Device Performance
The ability to accurately model and simulate biological tissue and its interactions with foreign medical tools is becoming of utmost importance as surgical procedures and medical devices become more complex and numerous. Traditionally, medical device designers and surgeons have solely relied on extensive, costly experimental testing, and empirical evidence to develop new medical devices and surgical techniques. Accurately simulating, through computational modeling, the internal physics occurring within biological tissue when interacting with medical devices allows for faster, more accurate, and safer device design by allowing a more comprehensive design process.
When attempting to simulate biological tissue, especially soft biological tissue, several challenges present themselves. Firstly, the mechanical structure of biological tissue is inherently complex. It is heterogeneous and often multi-phasic, meaning it is composed of several different materials and often has fluid flowing through and interacting with the solid tissue. Additionally, nearly all biological tissue acts non-linearly and undergoes large deformations. Thus, computational modeling efforts have been limited in scope and accuracy; however, great advancements in this arena are currently being made. Structural Integrity (SI), through utilizing its non-linear computational modeling capabilities and building on work conducted at the Advanced Medical Technologies Laboratory at the University of Colorado, has the ability to provide high fidelity simulations to evaluate the safety and performance of medical devices and procedures.
Mechanical Structure and Modeling Soft Biological Tissue
Most soft biological tissues (i.e. blood vessels, cartilage, muscle, liver, etc.) consist of a fibrous (typically collagenous) extra-cellular matrix (ECM) which provides the primary structural strength. This ECM is a porous structure with hydrophilic molecules attached to it. This means water or other fluids flow through the structure and also become bound to the structure when the tissue is acted upon by outside mechanical or thermal loads. Thus, stiffness and strength of the tissue are non-linearly dependent not only on the stress within the tissue but on the tissue water content and porosity as well. To model this phenomenon several approaches can be taken. They vary from simply using a non-linear hyperelastic material model with factors accounting for the water content in the tissue to modeling the tissue as a porous medium where both the stress in the tissue and water transport through the tissue are simulated. Additionally, surgeons often employ tools that use heat and/or energy to impart physical change within the tissue during procedures such as Lasik surgery, electrocautery, tumor removal, and fusion of bowel, skin, and arterial tissue. This adds yet another factor to account for during the simulation of surgeries. The sections following provide examples of two cutting-edge methods now available at Structural Integrity to simulate the multi-physics occurring in biological tissue during surgery.
Predictive Thermo-Mechanical Damage Modeling of Arterial Tissue Fusion and Cutting
Currently, surgeons employ electro-surgical devices to cut and fuse closed arteries during surgery to eliminate the introduction of foreign objects such as sutures and mechanical clips into the body. To design these devices engineers must use solely empirical evidence to evaluate design performance. This means they must construct and conduct numerous costly experimental studies during each design iteration. The study presented in this section provides an example of how non-linear thermo-mechanical finite element (FE) modeling can be used to elucidate material properties from mechanical testing via inverse finite element methods and to predict a medical devices ability to cut an artery using temperature and pressure.
The first necessary step to employing a predictive model was to determine the conditions at which an artery is cut. Previous studies had been conducted in which sections of arteries had been cut into strips. For each strip a temperature and pressure was applied via a surgical device and the surgical outcome (whether the artery was cut or not) was recorded. As the primary metrics determining tissue strength, tissue strain energy and tissue temperature, for each test could not be easily calculated by hand, an inverse FE method was used to determine the strain energy and the temperature occurring within the tissue during each test. Each simulation was conducted using the FE software Abaqus. In Abaqus, a non-linear anisotropic, hyperelastic thermo-mechanical user subroutine, that accounts for the change in water content and material properties of the tissue representing the artery wall, was implemented to represent the internal mechanics occurring in the artery tissue. Using these simulations, a damage equation, representing when artery tissue is cut as a function of tissue strain energy and temperature was developed. This equation was then used in simulations in Abaqus to evaluate device performance. Figure 2 shows a full surgical simulation setup in Abaqus. Figure 3 shows the ability of the Abaqus model to predict a surgical outcome. This ability to accurately predict surgical device performance allows for device designers to generate and evaluate numerous prototypes without going through costly experimental studies. Structural Integrity’s experience in advanced non-linear FE modeling can provide valuable support to medical device companies saving them both time and resources.
Large Deformation Thermo-Poromechanics Modeling
While examining the strength and deformation of biological tissue is important, to completely evaluate medical device performance and accurately capture the physics occurring within biological tissue a multi-physics modeling approach must be taken. As noted earlier, biological tissue is typically biphasic (or triphasic if heated to boiling temperatures as seen during fusion and ablation), thus a poromechanics or thermo-poromechanics (TPM) FE model must be used. Poromechanics and thermo-poromechanics FE modeling efforts have been used extensively in geomechanics for years. However, their use in biomechanics has been limited due the fact that biological tissue undergoes very large strains (10’s to 1000’s of percent) and rotations regularly. Only recently have both computational power and porous media FE theory been able to capture the intense coupled non-linearities that occur in multi-physics modeling of biological tissue. Recently, at the University of Colorado, a large deformation, fully coupled, thermo-poromechanics FE code has been developed. It has shown the ability to accurately capture the highly non-linear, large deformation mechanics occurring within tissue during arterial fusion. Structural Integrity is working to commercialize and extend these capabilities to be able to simulate a wide range of surgical and medical procedures.
The newly developed large deformation, coupled TPM code has been shown to accurately predict not only tissue deformation, but also the heat and water transport – including water phase change – occurring during a thermal tissue fusion surgical procedure. Figure 6 shows the predicted artery wall temperature, water content, and deformation occurring during a thermal tissue fusion simulation.
Presented here are just two of countless ways the FE modeling capabilities and expertise at Structural Integrity can be utilized to analyze medical devices and procedures. With complex non-linear FE modeling experience along with the development of large deformation, TPM FE code, SI can provide valuable services to medical companies looking to gain a fuller understanding of their procedures, get products to market less expensively, quicker and develop safer more effective products.
 Fankell, D.P., Kramer, E.A., Cezo, J., Ferguson V.L., Taylor, K.D, Rentschler, M.E. “ A novel parameter predicting arterial fusion and cutting in finite element models”, Annals of Biomedical Engineering, 2016
 Fankell, D.P., “A thermo - poromechanics finite element model for predicting arterial tissue fusion”, Doctoral Dissertation, presented at the University of Colorado, July 2017