A Design Method for Flexure-Based Compliant Mechanisms on the Basis of Stiffness and Stress Characteristics

Geometric nonlinearities of flexure hinges introduced by large deflections often complicate the analysis of compliant mechanisms containing such members, and therefore, Pseudo-Rigid-Body Models (PRBMs) have been well proposed and developed by Howell [1994] to analyze the characteristics of slender beams under large deflection. These models, however, fail to approximate the characteristics for the deep beams (short beams) or the other flexure hinges. Lobontiu's work [2001] contributed to the diverse flexure hinge analysis building on the assumptions of small deflection, which also limits the application range of these flexure hinges and cannot analyze the stiffness and stress characteristics of these flexure hinges for large deflection. Therefore, the objective of this thesis is to analyze flexure hinges considering both the effects of large-deflection and shear force, which guides the design of flexure-based compliant mechanisms. The main work conducted in the thesis is outlined as follows. 1. Three popular types of flexure hinges: (circular flexure hinges, elliptical flexure hinges and corner-filleted flexure hinges) are chosen for analysis at first. 2. Commercial software (Comsol) based Finite Element Analysis (FEA) method is then used for correcting the errors produced by the equations proposed by Lobontiu when the chosen flexure hinges suffer from large deformation. 3. Three sets of generic design equations for the three types of flexure hinges are further proposed on the basis of stiffness and stress characteristics from the FEA results. 4. A flexure-based four-bar compliant mechanism is finally studied and modeled using the proposed generic design equations. The load-displacement relationships are verified by a numerical example. The results show that a maximum error about the relationship between moment and rotation deformation is less than 3.4% for a flexure hinge, and it is lower than 5% for the four-bar compliant mechanism compared with the FEA results.

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.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Portal hypertension: a comparison between portal-venous pressure measurement and ARFI measurement of liver and spleen stiffness

PURPOSE. Portal pressure is measured invasively as Hepatic Venous Pressure Gradient (HVPG) in the angiography room. Liver stiffness measured by Fibroscan was shown to correlate with HVPG values below 12 mmHg. This is not surprising, since in cirrhosis the increase of portal pressure is not directly linked with liver fibrosis and consequently to liver stiffness. We hypothesized that, given the spleen’s privileged location upstream to the whole portal system, splenic stiffness could provide relevant information about portal pressure. Aim of the study was to assess the relationship between liver and spleen stiffness measured by Virtual Touch™ (ARFI) and HVPG in cirrhotic patients. METHODS. 40 consecutive patients (30 males, mean age 62y, mean BMI=26, mean Child-Pugh A6, mean platelet count=92.000/mmc, 19 HCV+, 7 with ascites) underwent to ARFI stiffness measurement (10 valid measurements in right liver lobe both surface and centre, left lobe and 20 in the spleen) and HPVG, blindly to each other. Median ARFI values of 10 samplings on every liver area and of 20 samplings on spleen were calculated. RESULTS. Stiffness could be easily measured in all patients with ARFI, resulting a mean of 2,61±0,76, 2,5±0,62 and 2,55±0,66 m/sec in the liver areas and 3.3±0,5 m/s in the spleen. Median HPVG was 14 mmHg (range 5-27); 28 patients showed values ≥10 mmHg. A positive significant correlation was found between spleen stiffness and HPVG values (r=0.744, p<0.001). No significant correlation was found between all liver stiffness and HVPG (p>0,05). AUROC was calculated to test spleen stiffness ability in discriminating patients with HVPG ≥10. AUROC = 0.911 was obtained, with sensitivity of 69% and specificity of 91% at a cut-off of 3.26 m/s. CONCLUSION. Spleen stiffness measurement with ARFI correlates with HVPG in patients with cirrhosis, with a potential of identifying patients with clinically significant portal hypertension.

Accuracy of liver stiffness measurement using fibroscan ® to predict the response to antiviral therapy in patients with chronic hepatitis c viral infection

Introduction: Antiviral therapy can prevent disease progression in patients with chronic hepatitis C . Transient Elastografy (TE; Fibroscan) is an accurate surrogate marker to liver fibrosis, by measuring liver stiffness (LS). LS decrease has been associated with sustained virologic response (SVR). Aim: to assess the changes of LS measurments in CHC patients during and one year after Interferon (IFN)-based antiviral therapy (IFN/ribavirin) or (telaprevir+IFN/ribavirin). Methods: consecutive 69 CHC patients (53.6% females, mean age 57.9 ± 11.4) who underwent antiviral therapy for at least 20 weeks were enrolled. LS was measured using FibroScan at baseline, after three months, at the end of treatment and one year after treatment discontinuation. Fibrosis was graded using METAVIR score. Results: twenty patients treated with triple therapy and 49 with IFN/ribavirin. Fifty patients had SVR and 19 were non-responders. SVR patients: F0-F1, F2 and F3 patients (39.1%, 7.2% and 17.4%; respectively) showed no significant LS decrease (P= 0.186, 0.068 and 0.075; respectively). Conversely, in F4 patients (36.2%) LS was significantly decreased (P=0.015) after one year of treatment completion. In all patients with no SVR, no significant decrease in LS was observed. Interestingly, all Patients with F4 fibrosis (even non-responders) showed an initial significant decrease in LS (P=0.024) at 3 months after the start of treatment. However, this decrease was not predictive of SVR; area under the ROC curve 0.369 (CI %: 0.145-0.592) P= 0.265. Conclusion: Our study showed that initial decrease in LSM, especially in patients with higher baseline fibrosis score is unlikely to predict an SVR. In addition no significant association was found between clinical or virological parameters and fibrosis improvement. Further studies are needed to delineate the most appropriate clinical scenarios for the LSM by Fibroscan in chronic hepatitis C and its role in monitoring the response to antiviral treatment.