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.

adaptive capabilities of the pi3k/akt/mtor pathway in acute myeloid leukemia revealed by the use of selective inhibitors

Because of its aberrant activation, the PI3K/AKT/mTOR signaling pathway represents a pharmacological target in blast cells from patients with acute myelogenous leukemia (AML). Using Reverse Phase Protein Microarrays (RPMA), we have analyzed 20 phosphorylated epitopes of the PI3K/Akt/mTor signal pathway of peripheral blood and bone marrow specimens of 84 patients with newly diagnosed AML. Fresh blast cells were grown for 2 h, 4 h or 20 h untreated or treated with a panel of phase I or phase II Akt allosteric inhibitors, either alone or in combination with the mTOR kinase inhibitor Torin1 or the broad RTK inhibitor Sunitinib. By unsupervised hierarchical clustering a strong phosphorylation/activity of most of the sampled members of the PI3K/Akt/mTOR pathway was observed in 70% of samples from AML patients. Remarkably, however, we observed that inhibition of Akt phosphorylation, as well as of its substrates, was transient, and recovered or even increased far above basal level after 20 h in 60% samples. We demonstrated that inhibition of Akt induces FOXO-dependent insulin receptor expression and IRS-1 activation, attenuating the effect of drug treatment by reactivation of PI3K/Akt. Consistent with this model we found that combined inhibition of Akt and RTKs is much more effective than either alone, revealing the adaptive capabilities of signaling networks in blast cells and highliting the limations of these drugs if used as monotherapy.

Radar based improvements and diagnosis of the convective capabilities of the cosmo-2 model

In the last few years the resolution of numerical weather prediction (nwp) became higher and higher with the progresses of technology and knowledge. As a consequence, a great number of initial data became fundamental for a correct initialization of the models. The potential of radar observations has long been recognized for improving the initial conditions of high-resolution nwp models, while operational application becomes more frequent. The fact that many nwp centres have recently taken into operations convection-permitting forecast models, many of which assimilate radar data, emphasizes the need for an approach to providing quality information which is needed in order to avoid that radar errors degrade the model's initial conditions and, therefore, its forecasts. Environmental risks can can be related with various causes: meteorological, seismical, hydrological/hydraulic. Flash floods have horizontal dimension of 1-20 Km and can be inserted in mesoscale gamma subscale, this scale can be modeled only with nwp model with the highest resolution as the COSMO-2 model. One of the problems of modeling extreme convective events is related with the atmospheric initial conditions, in fact the scale dimension for the assimilation of atmospheric condition in an high resolution model is about 10 Km, a value too high for a correct representation of convection initial conditions. Assimilation of radar data with his resolution of about of Km every 5 or 10 minutes can be a solution for this problem. In this contribution a pragmatic and empirical approach to deriving a radar data quality description is proposed to be used in radar data assimilation and more specifically for the latent heat nudging (lhn) scheme. Later the the nvective capabilities of the cosmo-2 model are investigated through some case studies. Finally, this work shows some preliminary experiments of coupling of a high resolution meteorological model with an Hydrological one.

Dynamic analysis of the motorcycle chattering behaviour by means of symbolic multibody modelling

Aim of this research is the development and validation of a comprehensive multibody motorcycle model featuring rigid-ring tires, taking into account both slope and roughness of road surfaces. A novel parametrization for the general kinematics of the motorcycle is proposed, using a mixed reference-point and relative-coordinates approach. The resulting description, developed in terms of dependent coordinates, makes it possible to efficiently include rigid-ring kinematics as well as road elevation and slope. The equations of motion for the multibody system are derived symbolically and the constraint equations arising from the dependent-coordinate formulation are handled using a projection technique. Therefore the resulting system of equations can be integrated in time domain using a standard ODE algorithm. The model is validated with respect to maneuvers experimentally measured on the race track, showing consistent results and excellent computational efficiency. More in detail, it is also capable of reproducing the chatter vibration of racing motorcycles. The chatter phenomenon, appearing during high speed cornering maneuvers, consists of a self-excited vertical oscillation of both the front and rear unsprung masses in the range of frequency between 17 and 22 Hz. A critical maneuver is numerically simulated, and a self-excited vibration appears, consistent with the experimentally measured chatter vibration. Finally, the driving mechanism for the self-excitation is highlighted and a physical interpretation is proposed.

The assessment of change in rural landscape and the analysis of the driving forces. Proposal of a spatial model for the rural built environment

The presented study carried out an analysis on rural landscape changes. In particular the study focuses on the understanding of driving forces acting on the rural built environment using a statistical spatial model implemented through GIS techniques. It is well known that the study of landscape changes is essential for a conscious decision making in land planning. From a bibliography review results a general lack of studies dealing with the modeling of rural built environment and hence a theoretical modelling approach for such purpose is needed. The advancement in technology and modernity in building construction and agriculture have gradually changed the rural built environment. In addition, the phenomenon of urbanization of a determined the construction of new volumes that occurred beside abandoned or derelict rural buildings. Consequently there are two types of transformation dynamics affecting mainly the rural built environment that can be observed: the conversion of rural buildings and the increasing of building numbers. It is the specific aim of the presented study to propose a methodology for the development of a spatial model that allows the identification of driving forces that acted on the behaviours of the building allocation. In fact one of the most concerning dynamic nowadays is related to an irrational expansion of buildings sprawl across landscape. The proposed methodology is composed by some conceptual steps that cover different aspects related to the development of a spatial model: the selection of a response variable that better describe the phenomenon under study, the identification of possible driving forces, the sampling methodology concerning the collection of data, the most suitable algorithm to be adopted in relation to statistical theory and method used, the calibration process and evaluation of the model. A different combination of factors in various parts of the territory generated favourable or less favourable conditions for the building allocation and the existence of buildings represents the evidence of such optimum. Conversely the absence of buildings expresses a combination of agents which is not suitable for building allocation. Presence or absence of buildings can be adopted as indicators of such driving conditions, since they represent the expression of the action of driving forces in the land suitability sorting process. The existence of correlation between site selection and hypothetical driving forces, evaluated by means of modeling techniques, provides an evidence of which driving forces are involved in the allocation dynamic and an insight on their level of influence into the process. GIS software by means of spatial analysis tools allows to associate the concept of presence and absence with point futures generating a point process. Presence or absence of buildings at some site locations represent the expression of these driving factors interaction. In case of presences, points represent locations of real existing buildings, conversely absences represent locations were buildings are not existent and so they are generated by a stochastic mechanism. Possible driving forces are selected and the existence of a causal relationship with building allocations is assessed through a spatial model. The adoption of empirical statistical models provides a mechanism for the explanatory variable analysis and for the identification of key driving variables behind the site selection process for new building allocation. The model developed by following the methodology is applied to a case study to test the validity of the methodology. In particular the study area for the testing of the methodology is represented by the New District of Imola characterized by a prevailing agricultural production vocation and were transformation dynamic intensively occurred. The development of the model involved the identification of predictive variables (related to geomorphologic, socio-economic, structural and infrastructural systems of landscape) capable of representing the driving forces responsible for landscape changes.. The calibration of the model is carried out referring to spatial data regarding the periurban and rural area of the study area within the 1975-2005 time period by means of Generalised linear model. The resulting output from the model fit is continuous grid surface where cells assume values ranged from 0 to 1 of probability of building occurrences along the rural and periurban area of the study area. Hence the response variable assesses the changes in the rural built environment occurred in such time interval and is correlated to the selected explanatory variables by means of a generalized linear model using logistic regression. Comparing the probability map obtained from the model to the actual rural building distribution in 2005, the interpretation capability of the model can be evaluated. The proposed model can be also applied to the interpretation of trends which occurred in other study areas, and also referring to different time intervals, depending on the availability of data. The use of suitable data in terms of time, information, and spatial resolution and the costs related to data acquisition, pre-processing, and survey are among the most critical aspects of model implementation. Future in-depth studies can focus on using the proposed model to predict short/medium-range future scenarios for the rural built environment distribution in the study area. In order to predict future scenarios it is necessary to assume that the driving forces do not change and that their levels of influence within the model are not far from those assessed for the time interval used for the calibration.

Burnout and work engagement among teachers: an application of the job demands-resources model

The present dissertation focuses on burnout and work engagement among teachers, with especial focus on the Job-Demands Resources Model: Chapter 1 focuses on teacher burnout. It aims to investigate the role of efficacy beliefs using negatively worded inefficacy items instead of positive ones and to establish whether depersonalization and cynism can be considered two different dimensions of the teacher burnout syndrome. Chapter 2 investigates the factorial validity of the instruments used to measure work engagement (i.e. Utrecht Work Engagement Scale, UWES-17 and UWES-9). Moreover, because the current study is partly longitudinal in nature, also the stability across time of engagement can be investigated. Finally, based on cluster-analyses, two groups that differ in levels of engagement are compared as far as their job- and personal resources (i.e. possibilities for personal development, work-life balance, and self-efficacy), positive organizational attitudes and behaviours (i.e., job satisfaction and organizational citizenship behaviour) and perceived health are concerned. Chapter 3 tests the JD-R model in a longitudinal way, by integrating also the role of personal resources (i.e. self-efficacy). This chapter seeks answers to questions on what are the most important job demands, job and personal resources contributing to discriminate burned-out teachers from non-burned-out teachers, as well as engaged teachers from non-engaged teachers. Chapter 4 uses a diary study to extend knowledge about the dynamic nature of the JD-R model by considering between- and within-person variations with regard to both motivational and health impairment processes.

Thermochronologic and geodynamic evolution of the Pontides: Sakarya terrane (Karakaya Complex) and Istanbul terrane, Turkey.

An integrated array of analytical methods -including clay mineralogy, vitrinite reflectance, Raman spectroscopy on carbonaceous material, and apatite fission-track analysis- was employed to constrain the thermal and thermochronological evolution of selected portions of the Pontides of northern Turkey. (1) A multimethod investigation was applied for the first time to characterise the thermal history of the Karakaya Complex, a Permo-Triassic subduction-accretion complex cropping out throughout the Sakarya Zone. The results indicate two different thermal regimes: the Lower Karakaya Complex (Nilüfer Unit) -mostly made of metabasite and marble- suffered peak temperatures of 300-500°C (greenschist facies); the Upper Karakaya Complex (Hodul and the Orhanlar Units) –mostly made of greywacke and arkose- yielded heterogeneous peak temperatures (125-376°C), possibly the result of different degree of involvement of the units in the complex dynamic processes of the accretionary wedge. Contrary to common belief, the results of this study indicate that the entire Karakaya Complex suffered metamorphic conditions. Moreover, a good degree of correlation among the results of these methods demonstrate that Raman spectroscopy on carbonaceous material can be applied successfully to temperature ranges of 200-330°C, thus extending the application of this method from higher grade metamorphic contexts to lower grade metamorphic conditions. (2) Apatite fission-track analysis was applied to the Sakarya and the İstanbul Zones in order to constrain the exhumation history and timing of amalgamation of these two exotic terranes. AFT ages from the İstanbul and Sakarya terranes recorded three distinct episodes of exhumation related to the complex tectonic evolution of the Pontides. (i) Paleocene - early Eocene ages (62.3-50.3 Ma) reflect the closure of the İzmir-Ankara ocean and the ensuing collision between the Sakarya terrane and the Anatolide-Tauride Block. (ii) Late Eocene - earliest Oligocene (43.5-32.3 Ma) ages reflect renewed tectonic activity along the İzmir-Ankara. (iii) Late Oligocene- Early Miocene ages reflect the onset and development of the northern Aegean extension. The consistency of AFT ages, both north and south of the tectonic contact between the İstanbul and Sakarya terranes, suggest that such terranes were amalgamated in pre-Cenozoic times. (3) Fission-track analysis was also applied to rock samples from the Marmara region, in an attempt to constrain the inception and development of the North Anatolian Fault system in the region. The results agree with those from the central Pontides. The youngest AFT ages (Late Oligocene - early Miocene) were recorded in the western portion of the Marmara Sea region and reflect the onset and development of northern Aegean extension. Fission-track data from the eastern Marmara Sea region indicate rapid Early Eocene exhumation induced by the development of the İzmir-Ankara orogenic wedge. Thermochronological data along the trace of the Ganos Fault –a segment of the North Anatolian Fault system- indicate the presence of a tectonic discontinuity active by Late Oligocene time, i.e. well before the arrival of the North Anatolian Fault system in the area. The integration of thermochronologic data with preexisting structural data point to the existence of a system of major E-W-trending structural discontinuities active at least from the Late Oligocene. In the Early Pliocene, inception of the present-day North Anatolian Fault system in the Marmara region occurred by reactivation of these older tectonic structures. 


Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

From core rigidities to dynamic capabilities: the role of external knowledge. A multiple case study

This study focuses on the processes of change that firms undertake to overcome conditions of organizational rigidity and develop new dynamic capabilities, thanks to the contribution of external knowledge. When external contingencies highlight firms’ core rigidities, external actors can intervene in change projects, providing new competences to firms’ managers. Knowledge transfer and organizational learning processes can lead to the development of new dynamic capabilities. Existing literature does not completely explain how these processes develop and how external knowledge providers, as management consultants, influence them. Dynamic capabilities literature has become very rich in the last years; however, the models that explain how dynamic capabilities evolve are not particularly investigated. Adopting a qualitative approach, this research proposes four relevant case studies in which external actors introduce new knowledge within organizations, activating processes of change. Each case study consists of a management consulting project. Data are collected through in-depth interviews with consultants and managers. A large amount of documents supports evidences from interviews. A narrative approach is adopted to account for change processes and a synthetic approach is proposed to compare case studies along relevant dimensions. This study presents a model of capabilities evolution, supported by empirical evidence, to explain how external knowledge intervenes in capabilities evolution processes: first, external actors solve gaps between environmental demands and firms’ capabilities, changing organizational structures and routines; second, a knowledge transfer between consultants and managers leads to the creation of new ordinary capabilities; third, managers can develop new dynamic capabilities through a deliberate learning process that internalizes new tacit knowledge from consultants. After the end of the consulting project, two elements can influence the deliberate learning process: new external contingencies and changes in the perceptions about external actors.

Transposable elements: structure and dynamic of the autonomous retrotransposon R2 in Arthropoda with non-canonical reproduction

Eukaryotic ribosomal DNA constitutes a multi gene family organized in a cluster called nucleolar organizer region (NOR); this region is composed usually by hundreds to thousands of tandemly repeated units. Ribosomal genes, being repeated sequences, evolve following the typical pattern of concerted evolution. The autonomous retroelement R2 inserts in the ribosomal gene 28S, leading to defective 28S rDNA genes. R2 element, being a retrotransposon, performs its activity in the genome multiplying its copy number through a “copy and paste” mechanism called target primed reverse transcription. It consists in the retrotranscription of the element’s mRNA into DNA, then the DNA is integrated in the target site. Since the retrotranscription can be interrupted, but the integration will be carried out anyway, truncated copies of the element will also be present in the genome. The study of these truncated variants is a tool to examine the activity of the element. R2 phylogeny appears, in general, not consistent with that of its hosts, except some cases (e.g. Drosophila spp. and Reticulitermes spp.); moreover R2 is absent in some species (Fugu rubripes, human, mouse, etc.), while other species have more R2 lineages in their genome (the turtle Mauremys reevesii, the Japanese beetle Popilia japonica, etc). R2 elements here presented are isolated in 4 species of notostracan branchiopods and in two species of stick insects, whose reproductive strategies range from strict gonochorism to unisexuality. From sequencing data emerges that in Triops cancriformis (Spanish gonochoric population), in Lepidurus arcticus (two putatively unisexual populations from Iceland) and in Bacillus rossius (gonochoric population from Capalbio) the R2 elements are complete and encode functional proteins, reflecting the general features of this family of transposable elements. On the other hand, R2 from Italian and Austrian populations of T. cancriformis (respectively unisexual and hermaphroditic), Lepidurus lubbocki (two elements within the same Italian population, gonochoric but with unfunctional males) and Bacillus grandii grandii (gonochoric population from Ponte Manghisi) have sequences that encode incomplete or non-functional proteins in which it is possible to recognize only part of the characteristic domains. In Lepidurus couesii (Italian gonochoric populations) different elements were found as in L. lubbocki, and the sequencing is still in progress. Two hypothesis are given to explain the inconsistency of R2/host phylogeny: vertical inheritance of the element followed by extinction/diversification or horizontal transmission. My data support previous study that state the vertical transmission as the most likely explanation; nevertheless horizontal transfer events can’t be excluded. I also studied the element’s activity in Spanish populations of T. cancriformis, in L. lubbocki, in L. arcticus and in gonochoric and parthenogenetic populations of B. rossius. In gonochoric populations of T. cancriformis and B. rossius I found that each individual has its own private set of truncated variants. The situation is the opposite for the remaining hermaphroditic/parthenogenetic species and populations, all individuals sharing – in the so far analyzed samples - the majority of variants. This situation is very interesting, because it isn’t concordant with the Muller’s ratchet theory that hypothesizes the parthenogenetic populations being either devoided of transposable elements or TEs overloaded. My data suggest a possible epigenetic mechanism that can block the retrotransposon activity, and in this way deleterious mutations don’t accumulate.

Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

Modelling the dynamic response of rockfall protection barriers

Mountainous areas are prone to natural hazards like rockfalls. Among the many countermeasures, rockfall protection barriers represent an effective solution to mitigate the risk. They are metallic structures designed to intercept rocks falling from unstable slopes, thus dissipating the energy deriving from the impact. This study aims at providing a better understanding of the response of several rockfall barrier types, through the development of rather sophisticated three-dimensional numerical finite elements models which take into account for the highly dynamic and non-linear conditions of such events. The models are built considering the actual geometrical and mechanical properties of real systems. Particular attention is given to the connecting details between the structural components and to their interactions. The importance of the work lies in being able to support a wide experimental activity with appropriate numerical modelling. The data of several full-scale tests carried out on barrier prototypes, as well as on their structural components, are combined with results of numerical simulations. Though the models are designed with relatively simple solutions in order to obtain a low computational cost of the simulations, they are able to reproduce with great accuracy the test results, thus validating the reliability of the numerical strategy proposed for the design of these structures. The developed models have shown to be readily applied to predict the barrier performance under different possible scenarios, by varying the initial configuration of the structures and/or of the impact conditions. Furthermore, the numerical models enable to optimize the design of these structures and to evaluate the benefit of possible solutions. Finally it is shown they can be also used as a valuable supporting tool for the operators within a rockfall risk assessment procedure, to gain crucial understanding of the performance of existing barriers in working conditions.