A new approach for the dynamic modelling of the human knee

Mathematical models of the knee joint are important tools which have both theoretical and practical applications. They are used by researchers to fully understand the stabilizing role of the components of the joint, by engineers as an aid for prosthetic design, by surgeons during the planning of an operation or during the operation itself, and by orthopedists for diagnosis and rehabilitation purposes. The principal aims of knee models are to reproduce the restraining function of each structure of the joint and to replicate the relative motion of the bones which constitute the joint itself. It is clear that the first point is functional to the second one. However, the standard procedures for the dynamic modelling of the knee tend to be more focused on the second aspect: the motion of the joint is correctly replicated, but the stabilizing role of the articular components is somehow lost. A first contribution of this dissertation is the definition of a novel approach — called sequential approach — for the dynamic modelling of the knee. The procedure makes it possible to develop more and more sophisticated models of the joint by a succession of steps, starting from a first simple model of its passive motion. The fundamental characteristic of the proposed procedure is that the results obtained at each step do not worsen those already obtained at previous steps, thus preserving the restraining function of the knee structures. The models which stem from the first two steps of the sequential approach are then presented. The result of the first step is a model of the passive motion of the knee, comprehensive of the patello-femoral joint. Kinematical and anatomical considerations lead to define a one degree of freedom rigid link mechanism, whose members represent determinate components of the joint. The result of the second step is a stiffness model of the knee. This model is obtained from the first one, by following the rules of the proposed procedure. Both models have been identified from experimental data by means of an optimization procedure. The simulated motions of the models then have been compared to the experimental ones. Both models accurately reproduce the motion of the joint under the corresponding loading conditions. Moreover, the sequential approach makes sure the results obtained at the first step are not worsened at the second step: the stiffness model can also reproduce the passive motion of the knee with the same accuracy than the previous simpler model. The procedure proved to be successful and thus promising for the definition of more complex models which could also involve the effect of muscular forces.

Changes in tumor stiffness for early prediction of tumor response to sorafenib: a proof-of-concept study with elastosonography in an animal model of Hepatocellular Carcinoma (HCC)

Background and aims: Sorafenib is the reference therapy for advanced Hepatocellular Carcinoma (HCC). No method exists to predict in the very early period subsequent individual response. Starting from the clinical experience in humans that subcutaneous metastases may rapidly change consistency under sorafenib and that elastosonography a new ultrasound based technique allows assessment of tissue stiffness, we investigated the role of elastonography in the very early prediction of tumor response to sorafenib in a HCC animal model. Methods: HCC (Huh7 cells) subcutaneous xenografting in mice was utilized. Mice were randomized to vehicle or treatment with sorafenib when tumor size was 5-10 mm. Elastosonography (Mylab 70XVG, Esaote, Genova, Italy) of the whole tumor mass on a sagittal plane with a 10 MHz linear transducer was performed at different time points from treatment start (day 0, +2, +4, +7 and +14) until mice were sacrified (day +14), with the operator blind to treatment. In order to overcome variability in absolute elasticity measurement when assessing changes over time, values were expressed in arbitrary units as relative stiffness of the tumor tissue in comparison to the stiffness of a standard reference stand-off pad lying on the skin over the tumor. Results: Sor-treated mice showed a smaller tumor size increase at day +14 in comparison to vehicle-treated (tumor volume increase +192.76% vs +747.56%, p=0.06). Among Sor-treated tumors, 6 mice showed a better response to treatment than the other 4 (increase in volume +177% vs +553%, p=0.011). At day +2, median tumor elasticity increased in Sor-treated group (+6.69%, range –30.17-+58.51%), while decreased in the vehicle group (-3.19%, range –53.32-+37.94%) leading to a significant difference in absolute values (p=0.034). From this time point onward, elasticity decreased in both groups, with similar speed over time, not being statistically different anymore. In Sor-treated mice all 6 best responders at day 14 showed an increase in elasticity at day +2 (ranging from +3.30% to +58.51%) in comparison to baseline, whereas 3 of the 4 poorer responders showed a decrease. Interestingly, these 3 tumours showed elasticity values higher than responder tumours at day 0. Conclusions: Elastosonography appears a promising non-invasive new technique for the early prediction of HCC tumor response to sorafenib. Indeed, we proved that responder tumours are characterized by an early increase in elasticity. The possibility to distinguish a priori between responders and non responders based on the higher elasticity of the latter needs to be validated in ad-hoc experiments as well as a confirmation of our results in humans is warranted.

The potential of the 3-UPU translational parallel manipulator and a procedure to select the best architecture

The 3-UPU three degrees of freedom fully parallel manipulator, where U and P are for universal and prismatic pair respectively, is a very well known manipulator that can provide the platform with three degrees of freedom of pure translation, pure rotation or mixed translation and rotation with respect to the base, according to the relative directions of the revolute pair axes (each universal pair comprises two revolute pairs with intersecting and perpendicular axes). In particular, pure translational parallel 3-UPU manipulators (3-UPU TPMs) received great attention. Many studies have been reported in the literature on singularities, workspace, and joint clearance influence on the platform accuracy of this manipulator. However, much work has still to be done to reveal all the features this topology can offer to the designer when different architecture, i.e. different geometry are considered. Therefore, this dissertation will focus on this type of the 3-UPU manipulators. The first part of the dissertation presents six new architectures of the 3-UPU TPMs which offer interesting features to the designer. In the second part, a procedure is presented which is based on some indexes, in order to allows the designer to select the best architecture of the 3-UPU TPMs for a given task. Four indexes are proposed as stiffness, clearance, singularity and size of the manipulator in order to apply the procedure.