Surgical instrumentation for the in vivo determination of lumbar spinal segment stiffness and viscoelasticity

The definition of spinal instability is still controversial. For this reason, it is essential to better understand the difference in biomechanical behaviour between healthy and degenerated human spinal segments in vivo. A novel computer-assisted instrument was developed with the objective to characterize the biomechanical parameters of the spinal segment. Investigation of the viscoelastic properties as well as the dynamic spinal stiffness was performed during a minimally invasive procedure (microdiscectomy) on five patients. Measurements were performed intraoperatively and the protocol consisted of a dynamic part, where spinal stiffness was computed, and a static part, where force relaxation of the segment under constant elongation was studied. The repeatability of the measurement procedure was demonstrated with five replicated tests. The spinal segment tissues were found to have viscoelastic properties. Preliminary tests confirmed a decrease in stiffness after decompression surgery. Patients with non-relaxed muscles showed higher stiffness and relaxation rate compared to patients with relaxed muscles, which can be explained by the contraction and relaxation reflex of muscles under fast and then static elongation. The results show the usefulness of the biomechanical characterization of the human lumbar spinal segment to improve the understanding of the contribution of individual anatomical structures to spinal stability.

Measuring localized viscoelasticity of the vitreous body using intraocular microprobes.

Vitrectomy is a standard ophthalmic procedure to remove the vitreous body from the eye. The biomechanics of the vitreous affects its duration (by changing the removal rate) and the mechanical forces transmitted via the vitreous on the surrounding tissues during the procedure. Biomechanical characterization of the vitreous is essential for optimizing the design and control of instruments that operate within the vitreous for improved precision, safety, and efficacy. The measurements are carried out using a magnetic microprobe inserted into the vitreous, a method known as magnetic microrheology. The location of the probe is tracked by a microscope/camera while magnetic forces are exerted wirelessly by applied magnetic fields. In this work, in vitro artificial vitreous, ex vivo human vitreous and ex vivo porcine vitreous were characterized. In addition, in vivo rabbit measurements were performed using a suturelessly injected probe. Measurements indicate that viscoelasticity parameters of the ex vivo human vitreous are an order of magnitude different from those of the ex vivo porcine vitreous. The in vivo intra-operative measurements show typical viscoelastic behavior of the vitreous with a lower compliance than the ex vivo measurements. The results of the magnetic microrheology measurements were validated with those obtained by a standard atomic force microscopy (AFM) method and in vitro artificial vitreous. This method allows minimally-invasive characterization of localized mechanical properties of the vitreous in vitro, ex vivo, and in vivo. A better understanding of the characteristics of the vitreous can lead to improvements in treatments concerning vitreal manipulation such as vitrectomy.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.