Zubin Trivedi, a doctoral researcher at the Institute for Modelling and Simulation of Biomechanical Systems and SFB 1313 member (research project C03), will defend his dissertation:
Title: "Simulating Vertebroplasty using a Multiphase Continuum-Mechanical Approach: Rheological Characterization, Numerical Simulations, and Experimental Validation"
Date: 18 April 2024
Time: 10 am CET
Venue: Pfaffenwaldring 7, 70569 Stuttgart, room: 2.157
Abstract
Percutaneous vertebroplasty, is a minimally invasive surgical procedure used to treat vertebral fractures. In this procedure, a material called bone cement is injected through the skin directly into the vertebra, which then cures and solidifies inside the vertebra. The augmentation of the vertebra due to the injected and solidified bone cement restores the load-carrying capacity. According to studies, most patients experience instant pain relief after the procedure, and can resume their normal daily life. However, there are also cases in which the bone cement leakage occurs during the injection process. The cement could leak outside the vertebra, and potentially constrict the nerves or the spinal canal to cause paralysis, or leak into the circulatory system through the blood vessels and cause embolism. Leakage could be prevented by controlled and stable injection and intermittent imaging during the procedure. However, the inside of the vertebra is a complex biological environment made of porous trabecular cancellous bone filled with marrow, the specifics of which are often unknown. The bone cement and the marrow inside the vertebra are materials that exhibit complex non-linear behaviours. The behaviour of the bone cement is particularly important, since it goes through a range of conditions while it is injected. Due to many such dependencies, the outcome of vertebroplasty is difficult to predict and control. Nonetheless, the practitioners must rely solely on their skill, dexterity, and intuition to carry out the procedure successfully.
The work presented in this thesis was aimed towards developing a computational model for reliably simulating vertebroplasty, which can be used by practitioners to predict the outcome of the procedure before actually doing it, based on the inputs specific to each patient, and use the predictions to determine the best operating conditions during vertebroplasty. The simulations provided by such a tool could help the practitioners identify potential pitfalls beforehand, and thereby, reduce the chances of leakage and resulting complications.
The simulation of vertebroplasty requires proper modelling of the flow of the bone cement during the injection. Broadly categorized, there are two kinds of cement flow occurring during vertebroplasty: the free flow in the injection syringe and cannula; and the porous media flow, i.e. the flow within the porous trabecular structure inside the vertebra. Modelling the flow behaviour of the bone cement requires first understanding the rheological behaviour of the bone cement. Hence, one of the objectives of the thesis was to characterize the behaviour of the bone cement in its curing stages by conducting rheological and injection tests in conditions relevant to vertebroplasty. The results showed that the bone cement has a complex viscoelastic behaviour. The rheology of the bone cement evolves over a two-phase curing process, during which the behaviour could be altered by deformations and temperature. The dependence of cement viscosity on the rate of deformation was measured using oscillatory and rotational tests on the rheometer, and compared to measurements using a custom-made injector setup that was developed to replicate a vertebroplasty setting. The flow curves obtained from rotational tests were found to be affected by wall slip and "ridge"-like formations in the test sample, as was confirmed visually by optical microscopy. These formations caused underestimation of the viscosity of the bone cement, even at low shear rates if the testing time was sufficiently long. The Cox-Merz rule used to obtain shear-thinning characteristics from oscillatory frequency sweep, which is often assumed to be true rather than being explicitly investigated, was found to be conditionally valid. Thus, drawbacks of conventionally-used testing methods used for measurements on the bone cement were identified in this work. The injection experiments could be used to reliably obtain the rheological parameters of the bone cement. These were then used for analytical calculations to understand the flow of bone cement in the injection cannula and the influence of the geometry of the injection apparatus on the flow.
The main objective of the thesis was to develop a computationally feasible and experimentally validated model for simulating vertebroplasty. A multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media was developed for this purpose. A combined finite element–finite volume approach, using the so-called Box discretization, was used for stable numerical treatment of the solid deformation and the fluid flow parts of the problem. The upscaling of viscosity to the macro-scale is not trivial in the case of non-Newtonian fluids. Therefore, three different rheological upscaling methods were compared to determine the most suitable approach for this application. To validate the computational model, a simple benchmark problem was devised that could be set up experimentally as well as simulated using the computational model. Furthermore, simulations were run to investigate the influence of bone marrow and parameters like permeability, porosity, etc. The results from the simulation of the benchmark problem by the presented model were close to the experiment when used with the correct rheological upscaling models. Out of the three rheological upscaling methods used, the semi-analytical averaging of the viscosity gave the best results. It was found that a higher cement viscosity compared to the marrow gave important benefits like stable injection, better interdigitation, and less dependence on pore uniformity, which could reduce the risk of cement leakage. In this regard, the marrow viscosity is identified as the threshold for categorization of bone cements as 'high- 'or 'low-' viscosity in the context of vertebroplasty.