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.

Theoretical investigation of the interaction of a polymer film with a nanoparticle

The fundamental aim in our investigation of the interaction of a polymer film with a nanoparticle is the extraction of information on the dynamics of the liquid using a single tracking particle. In this work two theoretical methods were used: one passive, where the motion of the particle measures the dynamics of the liquid, one active, where perturbations in the system are introduced through the particle. In the first part of this investigation a thin polymeric film on a substrate is studied using molecular dynamics simulations. The polymer is modeled via a 'bead spring' model. The particle is spheric and non structured and is able to interact with the monomers via a Lennard Jones potential. The system is micro-canonical and simulations were performed for average temperatures between the glass transition temperature of the film and its dewetting temperature. It is shown that the stability of the nanoparticle on the polymer film in the absence of gravity depends strongly on the form of the chosen interaction potential between nanoparticle and polymer. The relative position of the tracking particle to the liquid vapor interface of the polymer film shows the glass transition of the latter. The velocity correlation function and the mean square displacement of the particle has shown that it is caged when the temperature is close to the glass transition temperature. The analysis of the dynamics at long times shows the coupling of the nanoparticle to the center of mass of the polymer chains. The use of the Stokes-Einstein formula, which relates the diffusion coefficient to the viscosity, permits to use the nanoparticle as a probe for the determination of the bulk viscosity of the melt, the so called 'microrheology'. It is shown that for low frequencies the result obtained using microrheology coincides with the results of the Rouse model applied to the polymer dynamics. In the second part of this investigation the equations of Linear Hydrodynamics are solved for a nanoparticle oscillating above the film. It is shown that compressible liquids have mechanical response to external perturbations induced with the nanoparticle. These solutions show strong velocity and pressure profiles of the liquid near the interface, as well as a mechanical response of the liquid-vapor interface. The results obtained with this calculations can be employed for the interpretation of experimental results of non contact AFM microscopy

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

In vivo evaluation of the translations of the gleno-humeral joint using Magnetic resonance imaging

Gleno-humeral joint (GHJ) is the most mobile joint of the human body. This is related to theincongr uence between the large humeral head articulating with the much smaller glenoid (ratio 3:1). The GHJ laxity is the ability of the humeral head to be passively translated on the glenoid fossa and, when physiological, it guarantees the normal range of motion of the joint. Three-dimensional GHJ linear displacements have been measured, both in vivo and in vitro by means of different instrumental techniques. In vivo gleno-humeral displacements have been assessed by means of stereophotogrammetry, electromagnetic tracking sensors, and bio-imaging techniques. Both stereophotogrammetric systems and electromagnetic tracking devices, due to the deformation of the soft tissues surrounding the bones, are not capable to accurately assess small displacements, such as gleno-humeral joint translations. The bio-imaging techniques can ensure for an accurate joint kinematic (linear and angular displacement) description, but, due to the radiation exposure, most of these techniques, such as computer tomography or fluoroscopy, are invasive for patients. Among the bioimaging techniques, an alternative which could provide an acceptable level of accuracy and that is innocuous for patients is represented by magnetic resonance imaging (MRI). Unfortunately, only few studies have been conducted for three-dimensional analysis and very limited data is available in situations where preset loads are being applied. The general aim of this doctoral thesis is to develop a non-invasive methodology based on open-MRI for in-vivo evaluation of the gleno-humeral translation components in healthy subjects under the application of external loads.

Conformational transitions of glycine induced by vibrational excitation of the O-H stretch

Vibrational energy flow and conformational transitions following excitation of the OH stretching mode of the most stable conformer of glycine are studied by classical trajectories. "On the fly" simulations with the PM3 semiempirical electronic structure method for the potential surface are used. Initial conditions are selected to correspond to the v = 1 excitation of the OH stretch. The main findings are: (1) An an equilibrium-like ratio is established between the populations of the 3 lowest-lying conformers after about 10 picoseconds. (2) There is a high probability throughout the 150 ps of the simulations for finding the molecule in geometries far from the equilibrium structures of the lowest-energy conformers. (3) Energy from the initial excited OH (v = 1) stretch flows preferentially to 5 other vibrational modes, including the bending motion of the H atom. (4) RRK theory yields conformational transition rates that deviate substantially from the classical trajectory results. Possible implication of these results for vibrational energy flow and conformational transitions in small biological molecules are discussed.

Real-Time Joint Coupling of the Spine for Inverse Kinematics

In this paper we propose a simple model for the coupling behavior of the human spine for an inverse kinematics framework. Our spine model exhibits anatomically correct motions of the vertebrae of virtual mannequins by coupling standard swing and revolute joint models. The adjustement of the joints is made with several simple (in)equality constraints, resulting in a reduction of the solution space dimensionality for the inverse kinematics solver. By reducing the solution space dimensionality to feasible spine shapes, we prevent the inverse kinematics algorithm from providing infeasible postures for the spine.In this paper, we exploit how to apply these simple constraints to the human spine by a strict decoupling of the swing and torsion motion of the vertebrae. We demonstrate the validity of our approach on various experiments.

Surgical Treatment of Traumatic Myositis Ossificans of the Extensor Carpi Radialis Muscle in a Dog

OBJECTIVES To report clinical signs, diagnostic imaging findings, and outcome in a dog with traumatic myositis ossificans of the origin of the extensor carpi radialis muscle. STUDY DESIGN Clinical report. ANIMALS An 8-month-old intact female Irish Setter Dog. METHODS After radiographic and computed tomographic evaluation of an osseous proliferation arising from the cranial cortex of the right distal humeral diaphysis, the protruding bone was surgically removed and evaluated by histopathology. RESULTS Traumatic myositis ossificans was successfully treated with surgical removal of the osseous proliferation resulting in improved postoperative range of motion of the right elbow joint. There was no evidence of lameness or abnormal bone regrowth associated with the surgical site radiographically at follow up. CONCLUSION Surgical removal of a traumatic myositis ossificans lesion resulted in full return to function in a young, competitive show dog.

Mechanical actuator for biomimetic propulsion and the effect of the caudal fin elasticity on the swimming performance

This paper presents a mechanical actuator for the biomimetic propulsion of swimming devices and the experimental study of the effect of the caudal fin elasticity on the overall performance. The design of the proposed drive allows the DC motor to operate at constant speed, so all the power of the motor is spent only for the motion of the caudal fin. A prototype of the actuator, in which the caudal fin serves as a driving element, is manufactured and tested in both laboratory and natural conditions. The swimming speed, the thrust efficiency and the maneuverability are evaluated for caudal fins with different stiffness. The caudal fin whose rigidity varies relative to both vertical and horizontal cross-section, exhibits the best performance. The achieved results also confirm that the proposed actuator could be of great interest to applications in the field of underwater operation, ocean investigation and environmental protection.

Surveillance and diagnostics of the beam mode vibrations of the ringhals pwrs

Surveillance of core barrel vibrations has been performed in the Swedish Ringhals PWRs for several years. This surveillance is focused mainly on the pendular motion of the core barrel, which is known as the beam mode. The monitoring of the beam mode has suggested that its amplitude increases along the cycle and decreases after refuelling. In the last 5 years several measurements have been taken in order to understand this behaviour. Besides, a non-linear fitting procedure has been implemented in order to better distinguish the different components of vibration. By using this fitting procedure, two modes of vibration have been identified in the frequency range of the beam mode. Several results coming from the trend analysis performed during these years indicate that one of the modes is due to the core barrel motion itself and the other is due to the individual flow induced vibrations of the fuel elements. In this work, the latest results of this monitoring are presented.

Surveillance and diagnostics of the beam mode vibrations of the ringhlas PWRs

Surveillance of core barrel vibrations has been performed in the Swedish Ringhals PWRs for several years. This surveillance is focused mainly on the pendular motion of the core barrel, which is known as the beam mode. The monitoring of the beam mode has suggested that its amplitude increases along the cycle and decreases after refuelling. In the last 5 years several measurements have been taken in order to understand this behaviour. Besides, a non-linear fitting procedure has been implemented in order to better distinguish the different components of vibration. By using this fitting procedure, two modes of vibration have been identified in the frequency range of the beam mode. Several results coming from the trend analysis performed during these years indicate that one of the modes is due to the core barrel motion itself and the other is due to the individual flow induced vibrations of the fuel elements. In this work, the latest results of this monitoring are presented.

Comparative study of the effect of several trains on the ballast rotation

The ballast pick-up (or ballast train-induced-wind erosion (BTE)) phenomenon is a limiting factor for the maximum allowed operational train speed. The determination of the conditions for the initiation of the motion of the ballast stones due to the wind gust created by high-speed trains is critical to predict the start of ballast pick-up because, once the motion is initiated, a saltation-like chain reaction can take place. The aim of this paper is to present a model to evaluate the effect of a random aerodynamic impulse on stone motion initiation, and an experimental study performed to check the capability of the proposed model to classify trains by their effect on the ballast due to the flow generated by the trains. A measurement study has been performed at kp 69 + 500 on the Madrid – Barcelona High Speed Line. The obtained results show the feasibility of the proposed method, and contribute to a technique for BTE characterization, which can be relevant for the development of train interoperability standards

Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning.

The tectorial membrane has long been postulated as playing a role in the exquisite sensitivity of the cochlea. In particular, it has been proposed that the tectorial membrane provides a second resonant system, in addition to that of the basilar membrane, which contributes to the amplification of the motion of the cochlear partition. Until now, technical difficulties had prevented vibration measurements of the tectorial membrane and, therefore, precluded direct evidence of a mechanical resonance. In the study reported here, the vibration of the tectorial membrane was measured in two orthogonal directions by using a novel method of combining laser interferometry with a photodiode technique. It is shown experimentally that the motion of the tectorial membrane is resonant at a frequency of 0.5 octave (oct) below the resonant frequency of the basilar membrane and polarized parallel to the reticular lamina. It is concluded that the resonant motion of the tectorial membrane is due to a parallel resonance between the mass of the tectorial membrane and the compliance of the stereocilia of the outer hair cells. Moreover, in combination with the contractile force of outer hair cells, it is proposed that inertial motion of the tectorial membrane provides the necessary conditions to allow positive feedback of mechanical energy into the cochlear partition, thereby amplifying and tuning the cochlear response.

The neck region of the myosin motor domain acts as a lever arm to generate movement.

The myosin head consists of a globular catalytic domain that binds actin and hydrolyzes ATP and a neck domain that consists of essential and regulatory light chains bound to a long alpha-helical portion of the heavy chain. The swinging neck-level model assumes that a swinging motion of the neck relative to the catalytic domain is the origin of movement. This model predicts that the step size, and consequently the sliding velocity, are linearly related to the length of the neck. We have tested this point by characterizing a series of mutant Dictyostelium myosins that have different neck lengths. The 2xELCBS mutant has an extra binding site for essential light chain. The delta RLCBS mutant myosin has an internal deletion that removes the regulatory light chain binding site. The delta BLCBS mutant lacks both light chain binding sites. Wild-type myosin and these mutant myosins were subjected to the sliding filament in vitro motility assay. As expected, mutants with shorter necks move slower than wild-type myosin in vitro. Most significantly, a mutant with a longer neck moves faster than the wild type, and the sliding velocities of these myosins are linearly related to the neck length, as predicted by the swinging neck-lever model. A simple extrapolation to zero speed predicts that the fulcrum point is in the vicinity of the SH1-SH2 region in the catalytic domain.

Vertical crustal motion along the Mediterranean and Black Sea coast derived from ocean altimetry and tide gauge data

Tide gauge (TG) data along the northern Mediterranean and Black Sea coasts are compared to the sea-surface height (SSH) anomaly obtained from ocean altimetry (TOPEX/Poseidon and ERS-1/2) for a period of nine years (1993–2001). The TG measures the SSH relative to the ground whereas the altimetry does so with respect to the geocentric reference frame; therefore their difference would be in principle a vertical ground motion of the TG sites, though there are different error sources for this estimate as is discussed in the paper. In this study we estimate such vertical ground motion, for each TG site, from the slope of the SSH time series of the (non-seasonal) difference between the TG record and the altimetry measurement at a point closest to the TG. Where possible, these estimates are further compared with those derived from nearby continuous Global Positioning System (GPS) data series. These results on vertical ground motion along the Mediterranean and Black Sea coasts provide useful source data for studying, contrasting, and constraining tectonic models of the region. For example, in the eastern coast of the Adriatic Sea and in the western coast of Greece, a general subsidence is observed which may be related to the Adriatic lithosphere subducting beneath the Eurasian plate along the Dinarides fault.

Simulation of the secondary electrons energy deposition produced by proton beams in PMMA: influence of the target electronic excitation description

We have studied the radial dependence of the energy deposition of the secondary electron generated by swift proton beams incident with energies T = 50 keV–5 MeV on poly(methylmethacrylate) (PMMA). Two different approaches have been used to model the electronic excitation spectrum of PMMA through its energy loss function (ELF), namely the extended-Drude ELF and the Mermin ELF. The singly differential cross section and the total cross section for ionization, as well as the average energy of the generated secondary electrons, show sizeable differences at T ⩽ 0.1 MeV when evaluated with these two ELF models. In order to know the radial distribution around the proton track of the energy deposited by the cascade of secondary electrons, a simulation has been performed that follows the motion of the electrons through the target taking into account both the inelastic interactions (via electronic ionizations and excitations as well as electron-phonon and electron trapping by polaron creation) and the elastic interactions. The radial distribution of the energy deposited by the secondary electrons around the proton track shows notable differences between the simulations performed with the extended-Drude ELF or the Mermin ELF, being the former more spread out (and, therefore, less peaked) than the latter. The highest intensity and sharpness of the deposited energy distributions takes place for proton beams incident with T ~ 0.1–1 MeV. We have also studied the influence in the radial distribution of deposited energy of using a full energy distribution of secondary electrons generated by proton impact or using a single value (namely, the average value of the distribution); our results show that differences between both simulations become important for proton energies larger than ~0.1 MeV. The results presented in this work have potential applications in materials science, as well as hadron therapy (due to the use of PMMA as a tissue phantom) in order to properly consider the generation of electrons by proton beams and their subsequent transport and energy deposition through the target in nanometric scales.