This article proposes a normalization multi-layer perception (NMLP) geometry classifier to autonomously determine the optimal four femtocell evolved Node Bs (FeNBs), which can use time difference of arrival (TDOA) to measure the location of the macrocell user equipment (MUE) with the lowest GDOP value. The iterative geometry training (IGT) algorithm is designed to obtain the training data for the NMLP geometry classifier. The architecture of the proposed NMLP geometry classifier is realized in the server of the cloud computing platform, to identify the optimal geometry disposition of four FeNBs for positioning the MUE located between two buildings. Six by six neurons are chosen for two hidden layers, in order to shorten the convergent time. The feasibility of the proposed method is demonstrated by means of numerical simulations. In addition, the simulation results also show that the proposed method is particularly suitable for the application of the MUE positioning with a huge number of FeNBs. Finally, three quadrilateral optimum geometry disposition decision criteria are analyzed for the validation of the simulation results. The latest Long Term Evolution-Advanced (LTE-A) standard anticipates the increasing use of small cells (known as femtocells) to provide the geo-location information required to meet the emerging communication and networking needs of future smart city applications ,2. An ovMUE localization is conventionally performed using a standalone GNSS/GPS system . HoweverExisting MUE positioning methods, including those based on time difference of arrival (TDOA), direction of arrival (DOA), or hybrid TDOA / DOA measurements, generally utilize a Gauss-Newton Interpolation (GNI) algorithm to estimate the location of the MUE in two-dimensional (2D) space ,10. MultTDOA positioning systems require at least four FeNBs to locate the moving MUE in three-dimensional (3D) space. However, the accuracy of the localization results depends on the geometry disposition of the selected FeNBs. The geometric dilution of precision (GDOP) contour map of four stations is simulated in . It showIn addition, three optimum geometry disposition decision criteria are analyzed for the square, lozenge, and other quadrilateral shape of the four FeNBs for positioning the moving MUE when two or more of the same quadrilateral shapes are determined. The derived analytical expressions are generally applicable to geometries where the MUE is surrounded by the selected FeNBs. A comparison of the analytical results with simulations using the typical geometries of outdoor positioning systems shows good agreement.The structure of the paper is described as follows. The scenarios under study include the combination of a macro cell with femtocells in outdoor environments, which are operated at the same frequency band. It is assumed that the interference coordination and smart digital beam forming techniques may be needed to solve the problems of co-channel interference and signal attenuations. The uplink transmissions from the MUE are conventionally handled using the Single Carrier-frequency division multiple access (SC-FDMA) scheme . Moreoven] in 3D space. The received signal at the reference FeNB (FeNB0) thus has the form:0; and the variable n is defined as the sampling instant. The received signals at three other arbitrarily-chosen FeNBs are given by:i. The discrete time delay between FeNBi and FeNB0 is estimated as:Assume that the moving MUE emits an SC-FDMA signal s[i, respectively, and is obtained from the measured time delay between FeNBi and FeNB0 as:M is the size of the FFT, i and FeNB0, and Four-FeNB TDOA localization schemes calculate the possible MUE location based on the TDOA measurements of three FeNB receiver pairs lying on separate hyperbola . In otheN is the number of measurements; nth estimated location of the MUE, respectively. To calculate the GDOP, it is necessary to know the positions of the FeNBs around the moving MUE. A symbol table is shown in The accuracy of range-based positioning location (PL) systems depends on the geometric relationship between the locations of the FeNBs and the location of the MUE, since errors arising from channel or hardware perturbations in the TDOA estimates are transformed into geographic position errors in the hyperbolic solution . The posP set of the four FeNBs are jth component of the ith input vector and P is the total number of four FeNBs in the coverage range of the target MUE. Note that each component in a vector of a quadrilateral is constituted by four FeNBs. The data normalization is obtained by:The architecture of the NMLP geometry classifier is shown in ith input component at the qth neuron of the input layer. The MLP network of the geometry classifier is composed of 12 (Q) inputs, which represent 12 features of the NMLP geometry classifier.The scaled input and output data are required for the MLP, in order to provide the correct value for an activation function. The linear scaling of data is the transformation from the original data variability within the interval  Formula :(9)ηiq=The sigmoid activation function  used is D = { obtained by (15)MSE=P is the total number of four FeNBs within the sphere.The performance of the NMLP geometry classifier will be evaluated in terms of the percentages for correct classification. It is defined on the difference between the desired output and the estimated output of the NMLP geometry classifier. The classification accuracy is defined as :(16)claR is the sphere radius; and T denotes the transpose of the matrix. In the second step, the selected set of FeNBs is updated as required, to ensure that all four FeNBs are located on the same plane. Note that the sufficient condition for such a case occurs when the parallelepiped volume constructed by the three vectors The flowchart of the IGT algorithm is shown in In the fourth step, a check is made to confirm that the four FeNBs are not located on a straight-line.If four FeNBs are located on a straight-line, this increases the radius, and if not, then the shape is an IQ. In general, two vectors are parallel if their outer product is equal to zero. Thus, the four FeNBs are not located on a straight-line if R of the MUE is initiated with 200 m and increased with the increment of 20 m.If the conditions associated with Steps 1, 2, and 3 are satisfied, the optimal four-FeNB disposition has a low GDOP. Otherwise, if the conditions associated with Steps 1, 2, and 4 are satisfied, the acceptable four-FeNB configuration is determined with a higher GDOP. A lower GDOP represents a better localization result. As soon as either case is satisfied, the coordinates of the moving MUE are estimated using the TDOA method. Finally, in the fifth step, a check is made to confirm that the four FeNBs and MUE are located within the designated sphere, i.e.:It was noted that the optimum quadrilateral shapes, consisting of four FeNBs, can be selected to measure the location of the moving MUE. The square is the best, the lozenge is next, and the IQ is the worst. When two or more of the same quadrilateral shapes are selected, the following three optimum geometry disposition decision criteria are considered, to determine the best accuracy of the TDOA positioning measures. The GDOP formulas of three optimum geometry disposition decision criteria are derived. Since the location of four FeNBs is fixed, the quadrilateral shape of the FeNBs does not change due to the movement of the MUE. Therefore, in order to simplify the proof of selecting the optimum shapes of four FeNBs, three different criteria are proved in the two dimensional space, and the results are still valid in the three dimensional space.Criterion 1: Square optimum geometry disposition decision criterion depends on the distance between the MUE and the square center. When the distance is shorter, the positioning accuracy is better.ith FeNB be given by [Let the distance from the MUE to the given by :(22)ri,i and FeNB0.The differential distance is obtained from subtracting two TDOA measurements between FeNBc is the light velocity and the measurement error is expressed as:The TDOA measurements for three pairs of FeNBs are given as:It is assumed that the errors in all actual measurements are random, independent, and have an identical root mean square (RMS) value The TDOA measurement errors for three pairs of FeNBs can be expressed as the matrix form.The error covariance matrix is:x, y) are given as:The partial derivatives of the noise free measurement Equations (23) with respect to the unknown MUE coordinates , the GDOP will be given by:nt noise .(33)G=10 , FeNB1 , FeNB2 , FeNB3 , and MUE  are substituted into Equation (29), to yield:For the simplification of proving the square optimum geometry disposition decision criterion, the coordinates of FeNBWhen the MUE moves from  to , the GDOPs for different average TDOA position measurement errors  are computed and these are shown in Criterion 2: Lozenge optimum geometry disposition decision criterion depends on the complementary angle difference (CAD), which is the difference between two complementary angles of a lozenge shape. When the CAD of the lozenge optimum geometry disposition is smaller, the positioning accuracy is better.0 , FeNB2 , FeNB1 , FeNB3, and MUE  into Equation (31), to yield:For simplification, the GDOP formula is derived by substituting the coordinates of FeNBSubstituting Equations (28) and (35) into Equation (33) yields:Then the GDOP of lozenge shape is expressed as:The CAD formula is derived as:N varies from 0 to 1 and N = 1, CAD = 0°. This is the square shape, which has a smaller GDOP value than the lozenge shape. When N = 0, CAD = 180°. This is the straight line, which has the largest GDOP value.Criterion 3: Irregular-quadrilateral optimum geometry disposition decision criterion depends on the distance between the diagonal intersection and the center of the IQ. When the distance is shorter, the positioning accuracy of the IQ optimum geometry disposition is better. 0 , FeNB1 , FeNB3 , and MUE  into Equation (31), to yield:For simplification, the GDOP formula is derived by substituting the coordinates of FeNBi and FeNB0 was successfully measured with a detection probability of Pd = 0.9, while the false alarm probability was equal to PFA = 10−4. Moreover, the signal-to-noise ratio (SNR) of the TDE receivers with a linear optimum filter was assumed to be −13 dB over the Rayleigh channels, with Pd = 0.9 and PFA = 10−4. The simulations considered the outdoor geo-location scenario shown in P = 1820. Moreover, the moving MUE was assumed to be located between two buildings and positioned at the boundary of a macrocell network. The coordinates of the MUE trajectory are , , , , , , , , , and . In simulations, the SC-FDMA signal was considered as it is used by LTE MUE as an uplink access scheme [In performing the simulations, it was assumed that the time delay between FeNB 0), 60, 0, 0,  to , the trajectory of the moving path is shown in This paper proposes a novel NMLP geometry classifier and IGT algorithm for autonomously reducing the positioning error of four-FeNB TDOA measurements. Three optimum geometry disposition decision criteria are analyzed for the square, lozenge, and other IQ shape of the four FeNBs, for positioning the moving MUE. The derived analytical expressions are generally applicable to geometries where the MUE is surrounded by the selected FeNBs. The simulation results have confirmed that the proposed NMLP geometry classifier and optimum geometry disposition decision criteria can provide accurate outdoor geo-location information on the MUE for indoor femtocells to support its quality of services in HetNet. A comparison of the analytical results with simulations using the typical geometries of outdoor positioning systems shows good agreement.The computational burden is mainly caused by the offline IGT algorithm simulations pertaining to the construction of the training data. Once the initial learning of the NMLP is finished using the collected training data to optimize network weights based on the NMLP network outputs of five neurons for five different shapes, the additional computation overhead in NMLP is light. Since the operations of the NMLP geometry classification are executed in the server, it is assumed that the computation ability of the server is powerful enough to determine the optimal geometry disposition for femtocell positioning networks. The information regarding the training data that governs the NMLP geometry classification operation of femtocell positioning networks is stored in a database. As soon as a new operation condition occurs, the new training data is generated from the simulation and included in the database to rerun the IGT training procedure of How to optimally determine four FeNBs to position the UE in indoor scenarios is another hot research topic in current telecommunication industries and academics. The proposed NMLP geometry classifier and IGT algorithm will be applied to the study of indoor femtocell positioning networks.


Cardiac dysfunction constitutes common cardiovascular health issues in the society, and has been an investigation topic of strong focus by researchers in the medical imaging community. Diagnostic modalities based on echocardiography, magnetic resonance imaging, chest radiography and computed tomography are common techniques that provide cardiovascular structural information to diagnose heart defects. However, functional information of cardiovascular flow, which can in fact be used to support the diagnosis of many cardiovascular diseases with a myriad of hemodynamics performance indicators, remains unexplored to its full potential. Some of these indicators constitute important cardiac functional parameters affecting the cardiovascular abnormalities. With the advancement of computer technology that facilitates high speed computational fluid dynamics, the realization of a support diagnostic platform of hemodynamics quantification and analysis can be achieved. This article reviews the state-of-the-art medical imaging and high fidelity multi-physics computational analyses that together enable reconstruction of cardiovascular structures and hemodynamic flow patterns within them, such as of the left ventricle (LV) and carotid bifurcations. The combined medical imaging and hemodynamic analysis enables us to study the mechanisms of cardiovascular disease-causing dysfunctions, such as how (1) cardiomyopathy causes left ventricular remodeling and loss of contractility leading to heart failure, and (2) modeling of LV construction and simulation of intra-LV hemodynamics can enable us to determine the optimum procedure of surgical ventriculation to restore its contractility and health This combined medical imaging and hemodynamics framework can potentially extend medical knowledge of cardiovascular defects and associated hemodynamic behavior and their surgical restoration, by means of an integrated medical image diagnostics and hemodynamic performance analysis framework. The modern medical imaging community in practice is associated with a landscape of non-invasive imaging, image processing and cardiovascular analyses components, which constitute the traditional means of assessing cardiovascular system performance. The present-day cardiologists diagnose patients with diseases via visual observations of the heart and arterial system, from well-established clinical imaging such as echocardiography, magnetic resonance imaging/angiography, chest radiography, and computed tomography, by which they provide their expert opinions on the appropriate medical treatment. In recent decades, high fidelity multi-physics computational platforms that yield cardiovascular hemodynamics patterns have been developed, are researched, and can be integrated as a support tool into the existing medical imaging systems to generate a more precision-based patient-specific diagnosis of cardiovascular conditions. This kind of integrated high-performance computational platform generates the relevant hemodynamics mechanics to support the medical imaging-based diagnosis by quantification of hemodynamic patterns and parametric values for decision making and generation of expert opinions for surgical treatment.Cardiac disease can introduce various cardiovascular defects in the human body, and can be examined using modern imaging diagnostics. Herein, we briefly assess the abnormality of some of these defects—such as septal defects, myocardial fibrillations, arrhythmias, heart valve failure and other heart diseases can be assessed for degrees of abnormality, and also evaluate the post-surgical treatment outcomes of some of these defects. Cardiac flow fields that are obtained from clinical ultrasound-based or phase-contrast MR image scan sequences can be analyzed, and interesting flow phenomena relating to the operation of cardiac structures such as heart valves can be discovered. Nevertheless, qualitative assessment of the cardiovascular defects does not give a proper evaluation of the underlying cause and effect, as well as comparison of the healthy and abnormal conditions. Appropriate hemodynamic analysis based parameters need to be used for quantitative studies. For instance, hemodynamic analysis of the heart structure has been investigated in the vascular network based on localized wall shear stress (WSS) regions, since it is known that the WSS has an implication on atherosclerosis . QuantifIn the context of atherosclerotic arteries, the superficial carotid bifurcation is an ideal target for non-invasive imaging via ultrasound (US), magnetic resonance imaging (MRI) or computed tomographic (CT) imaging, and is hence used as a case study for our review in this paper. The angiographic techniques such as magnetic resonance angiography, X-ray angiography, etc. are often commonly used in examining atherosclerosis. For example, cineangiograms are used by medical doctors to visually examine the degree of stenosis in carotid bifurcations or coronary arteries. However, they fail to explain the underlying cause of the problem from the blood flow perspective. It can be demonstrated that the plaque ulceration is related to the existence of high wall shear stress (WSS) at the upstream region of the plaque . In thisFrom the perspective of how cardiac diseases (such as cardiomyopathy) affect the heart and its consequential remodelling, surgical ventricular restoration (SVR) addresses the issue of restoring the performance and health of remodeled left ventricles with large akinetic walls and dilated ventricles . This tyIt may be of interest to experimentally determine the true flow fields which can be used as a more realistic version for analysis of the blood flow behavior in the heart. In addition, such information can also be used to validate the numerically computed flow fields. Functional medical imaging modalities are on the rise in terms of speed, accuracy and reliability in measurement of blood flow in the cardiovascular system. On the velocity-encoded (VENC) imaging technology front, phase contrast magnetic resonance imaging (PC-MRI) that is coupled with cardiac flow analysis , 17 giveTo developing an effective analytical computational simulation, the first step is to create the 3D computer model of the cardiovascular geometry. The detailed stages are presented in Fig. The usefulness of experimental measurements is on the validation of the numerically simulated results and as a form of support for fluid mechanists to review the accuracy of their simulation platform. In addition, experimental data can also be used to determine the boundary conditions when setting the numerical framework, as illustrated in Fig. The system integration of the components outlined in the previous sections gives rise to a systematic approach for assessing the cardiac health condition of cardiovascular patients. This forms a generic approach to constructing a system for analyzing cardiac defects via examination of the flow variations derived from medical imaging and post-processing techniques. Let us visit each stage of the flow chart in the subsequent sub-sections.This section reviews the medical imaging and visualization application, with unique quantification of some of the structural parameters, which can lead to a viable diagnostic system for evaluating cardiac related failures or health risk in patients. The ease and speed of these preparations are important considerations for medical doctors in order to quickly gain insights into the structures in the defective regions of the heart and to assist in strategizing surgical procedures, operations or artificial implantations.This imaging and geometrical reconstruction system are vital because of the technical feasibility of using measured information from medical imaging to determine blood flow information. The key success is the result of implementing high-performance computing as a post-processing tool for the reconstructed geometry, which is produced by medical image reconstruction of images from medical scanners. This renders the encoding of velocity information redundant, which reduces scanning and processing time. Medical image reconstruction and high-performance computing open up many new opportunities for flow analysis concurrent to the examination of cardiac chambers, septal defects, and heart valve behavior. It may also be of interest to cardiologists and physiologists to provide information on the structural shape and size of the cardiac chambers in relation to the behavior of the flow in the heart. Inevitably, errors and noise appear in measured data. Numerical simulation framework and other mechanism can be adjusted in the event of errors. To reduce the effect of noise, we usually solve with least squares. Reducing distance between the geometrical entities  is minimizing geometric errors.Typically, the first objective is to map the cardiovascular structure of the heart chamber or arteries. From medical imaging modalities such as the ultrasound, MRI or CT scans of cardiac chambers such as the left ventricle (LV) myocardium, the wall boundary can be extracted and reconstructed to derive the dynamic LV geometry. In the example illustrated in Fig. Next, we examine the elements of the medical imaging and anatomical reconstruction platform that comprises of a generic scanning modality, an image processing and a geometrical boundary definition and modeling framework. It is essential to establish a network of sub-components such that each of the components has a role in preparing the anatomical reconstruction. The system layout of this computational reconstruction serves to produce the computational mesh of the cardiovascular structures, such as the cardiac chamber or the artery, that are obtained from medical imaging modalities such as MRI, CT, or ultrasound. The core functionality of this system is the visualization of anatomical structures and identification of their defects. Observation of the structural details generated by the system can assist in identifying stenosis or regions of critical plaque growth in the case of the atherosclerotic arteries, and septal defects in the case of discontinuity in the myocardium of the heart which can occur in the atrium or ventricle. It is worthwhile noting that cine-images of the cardiac chamber such as the atrium can be constructed and played via a multimedia tool to observe irregularity in beating and assist in diagnosis of atrial fibrillation. In addition, the geometrical mesh of the left ventricle (LV) output by the system can be fed into a simulation modeler, and solved for the intra-cardiac flow by using computational fluid dynamics to obtain useful flow behavior such as vortices or other interesting flow patterns within the chamber. Useful hemodynamics indicators can also be derived for these cardiovascular structures to support medical diagnosis of the cardiac condition.From the computer architecture perspective, the procedures executed by the system of components are outlined as follows. After pre-processing, the medical images can be retrieved via a Receiver for post-processing at a later stage of the system. Practically, segmentation of the region of interest is semi-automatically determined with external peripherals. In the case of ultrasound or tagged MR imaging, tracking of moving signals encoded onto the medical images can be carried out by a motion estimation component to define the wall boundary. The geometrical structure is scaled and displayed via a suitable displaying element. Optionally, other measures such as the velocity of cardiac wall can be computed with a numerical simulation framework using computational fluid dynamics (CFD) and implemented for cardiac flow analysis. Note that the receiver, segmentation, boundary extraction, geometrical surface reconstruction elements forms the main processing system of this framework. The components within this processing system are utilized for post-processing medical images and outputting the geometry of the anatomical structure of interest. Outside of this system are the physical hardware that facilitates the medical scanning, user inputs and display, which we will not explore further. Let us examine each of the components with greater detail in the subsequent sections.Magnetic resonance imaging is a well-established medical imaging modality, and can be used effectively for imaging the heart and large arteries for cardiovascular study. Diagnostic system for detecting cardiac abnormalities and quantifying the degree of cardiovascular defects has proven to be clinically attractive –32. The Now let us examine a more practical example, in which magnetic resonance imaging (MRI) or computer tomography was performed to study myocardium problems. The images were then used to reconstruct diastolic to systolic LV anatomy Fig. . The parAfter extracting the cardiovascular structure by segmentation, the computational file can be saved as an IGES, STL, or STEP in order to be cross-compatible with a range of 3D modelling and meshing programs that can result in different types of mesh configurations. Typically, the meshing procedure begins by the application of a simple unstructured tetrahedral mesh all over, which produces a single contiguous mesh. However, for easier post-processing of local flow variables, the computational model may be split into smaller sub regions during the CAD surface and volume generation stage, prior to meshing. While the process of sub-dividing the computational model into smaller regions can be performed within some CFD packages, it is not always an easy task, and therefore it is recommended to be performed in CAD packages that have NURBS functionality.discrete values of the flow-field variables such as the velocity, pressure, and temperature.The generation of a quality mesh is of extreme importance for obtaining reliable computational solutions. A good quality mesh improves numerical stability, and increases the likelihood of attaining a reliable solution. A mesh can be viewed as a number of smaller mesh or grid cells that overlays an entire domain geometry. In general, the set of fundamental Navier–stokes equations representing the flow physics are applied onto each cell. These equations, which calculate the flow variables in each cell within the domain, are subsequently solved to yield the corresponding N number of cells is created. The original model is refined by cell adaptation techniques that include refining large volume cells, that display high velocity/pressure gradients and near wall refinements. This process is repeated twice, with each repeat producing a model with a higher cell count than the previous model. These models are used in simulation, and outputs such as velocity profiles are compared. Then, the model with the mesh that did not result in a significant difference in flow results presented by the mesh of higher density at its next step is selected for further runs. An example of a rectangular mesh for the left ventricular and corresponding computational geometry is demonstrated by Schenkel et al. [η. Computed information is then directly fed back to the physical domain via the one-to-one correspondence of grid points. Because of the need to solve the equations in the computational domain, they have to be expressed in terms of curvilinear coordinates rather than Cartesian coordinates, which means that they must be transformed from  to For the meshing of a cardiovascular structure, such as an atherosclerotic artery, surfaces are created and stitched up to create a computational mesh. An initial model with l et al. . The traScan images based on the velocity-encoded MRI modality, as shown in Fig. For a realistic simulation of cardiac structures, boundary conditions can be well-established and derived based on measurement of cardiac flow profiles obtained from velocity-encoded imaging modalities by the phase contrast MRI scans. The understanding and derivation of flow properties in such conditions are necessary. The accuracy of the hemodynamics of an isolated patient-specific cardiovascular structure highly depends on the application of the boundary conditions. As such, phase contrast MRI may be used to provide these boundary conditions for the computational model, which also serve the additional purpose of providing a basis for analysis of the flow nature in addition to the computational prediction after that.Q (ml/s), for the ICA, ECA and CCA [Specifically, let us examine the group mean blood flow waveform as shown by Fig.  and CCA , which wIn the context of intraventricular flow, the cardiac flow fields of a subject may also be fully measured and compared with the computational model as shown in Fig. Velocity vector plot and axial profiles arising from computational hemodynamics can be used to assess influence of arterial stenosis on the flow through a carotid bifurcation model. The flow patterns within the carotid artery due to the geometry of the bifurcation can be assessed by vector associated streamlines as well as flow profile plots .As seen in Fig. From the velocity vector plots and axial velocity profiles, we are able to examine regions of flow separations, accelerating and decelerating flows, as well as their transient magnitudes. From the simulation, we are only able to detect the flow and how it affects the vessel wall, specifically luminal diameter or stenosis, plaque volume and wall thickness. However, we are unable to assess the health conditions of atherosclerosis from the flow velocity information. As such, a more precise indicator should be deployed in order to assess the disease more appropriately. Together with medical imaging, we can then see a whole greater picture. By seeing all these, the doctor can identify the high risk plaques that are vulnerable to rupture and thrombosis better.For this purpose, let us discuss some parameters commonly used to assess blood flow. Certain hemodynamics parameters require a clear definition prior to performing simulation of the blood in the circulatory system comprising the arteries and heart.Resistance of blood to deformation under shear stress causes viscosity. Practically, we can describe its internal resistance to flow as a form of fluid ‘friction’. Binding of the molecules pertaining to the fluid is responsible for this viscosity. Mathematically, viscosity is defined as the ratio of the shear stress to the velocity gradient, which can be represented as the shear rate.Most fluids approximate Newtonian fluids, resulting in a constant viscosity. Nevertheless, blood, which consists of plasma, blood cells and other material carried throughout the bloodstream, tends to cause blood to become non-Newtonian due to the quantity of particles within the plasma. In fact, the blood viscosity changes with the shear rate of the flow. When the shear rate is sufficiently high, blood flow exhibits Newtonian flow behaviour. Realistically, under normal conditions it is not viable to ignore the non-Newtonian behaviour of the fluid.vz along the arterial radius:In fluid flow that is incompressible and under a steady flow field, the shear rate of strain of a material fluid element is defined as the rate of decrease of the angle formed by two mutually perpendicular lines on the element. As such, the shear strain rate τ and strain components with the viscosity μ as its gradient. Therefore, the equation for wall shear stress is given by:The rate of change in velocity along the radial section from the wall to the centre of the vessel, which was previously defined as the shear strain rate, is proportional to the wall shear stress. The mechanical characteristics of the flow can be described by the Poiseuille’s law model, which defines a linear relationship between the shear stress Blood flows along curved arteries with complex flow dynamics, such as variable axial velocities along the radial section . In the T is a cardiac cycle period and τw is the instantaneous wall shear stress. The atheroprotective effect of the endothelial cells is influenced by these hemodynamic indicators. Low TAWSS values (lower than 0.4 Pa) [2/N) [Three commonly adopted flow indicators to evaluate the total shear stress exerted on the wall throughout a cardiac cycle are the time-averaged wall shear stress (TAWSS), the oscillatory shear index (OSI), and the relative residence time (RRT), which are presented in the following equations: 0.4 Pa) , high OS 0.4 Pa) –43 and ha) [2/N) , 44 are a) [2/N) , 45.According to the thresholds of the local flow indicators, the outer-wall of the ICA at the bifurcation territory of the healthy carotid case study is where the low TAWSS, high oscillatory shear and long relative resident time exist. Therefore, it is a vulnerable site for atherosclerosis in the long term. The apex of the divider-wall of the bifurcation experiences the maximum TAWSS, as compared to the remaining portion of the healthy carotid bifurcation. Because this peak TAWSS value is much lower than the threshold, this site is still risk-free of getting direct endothelial injury from the blood flow.By referring to the values of TAWSS and OSI, the prediction of the degree of atheroprotectiveness or atherosusceptibility can be made. The fraction of luminal surface that is non-atheroprotective is more prone to atherogenesis. The studied diseased carotid bifurcation experiences a high TAWSS at the throat of the ICA stenosis, which gives a warning of stroke, and the blood transportation is also disturbed as the flow division value deviates from normal situation constantly. In such a case, a vascular intervention is required.From the physiological perspective, the carotid bulb is a common atheroprotective location for both the healthy case study and the diseased case study, because of the commonly formed disturbed flow at this region. Based on the arterial hemodynamics indicators, a strategy for cardiac management of the atherosclerotic patient can be devised based on the case study report of the diseased artery. Diagnosis via cardiovascular indicators is transferred electronically or in hard copy format to medical professionals for advice , 47.Computational medical imaging and fluid dynamics analysis can be applied in the context of evaluating the performance of heart pumping, such as its efficiency in contraction and dilation throughout the cardiac cycle. Let us study what happens to a cardiomyopathy left ventricle, which has reduced contractile capacity for pumping out adequate cardiac output (CO). A manifestation of cardiomyopathy and its decreased contractile capacity is the inability of the LV to retain its compact systolic curved shape. In other words, a cardiomyopathic left ventricle undergoes remodeling, its curvedness index decreases, and it becomes more spherically shaped—which further reduces its contractility index  of cardiomyopathy hearts. In other words, prior to carrying out SVR, we can simulate different measures of surgical truncation of the LV, determine the values of the truncated LV’s contractility index and analyse their intra-LV blood flow distributions. We can then arrive at what SVR measure provides the optimum value of the contractility index and optimum intra-LV blood flow for minimal truncation. This can facilitate preoperative modeling for patients to achieve optimized post-SVR flow performance . By knowWo, and the Reynolds Number, Re, as well as the exchange transfusion that is denoted by M, which represents the remaining fractional blood volume in the ventricle after an arbitrary number of cardiac cycles, n [The nature of intra-LV fluid flow can be characterized by means of the fluid dynamics parameters of the Womersley number, ycles, n .6\documeM, shows consistently higher value for a patient as compared to a healthy normal subject, which indicates that more of the blood volume remained in the left ventricle at the end of every cycle. The intraventricular condition of a patient is such that it has a much less efficient wash-out due to the greater residual volume in the left ventricle at the end of ejection. Furthermore, the Wo is demonstrated to be moderately lower for such a patient as compared to the healthy subject, and Re is in the order of one magnitude lower than in a healthy subject [As can be observed from the computed data, the exchange transfusion,  subject .ED SES)/SED × 100% for end diastole (ED) to end systole (ES) [It may be worthwhile mentioning here that traditional diagnosis of left ventricular (LV) dysfunction is based on cineangiograms, ultrasound monitoring or MRI scans of LV wall motion. Observation of the improvement in wall motion leading to a higher ejection-fraction after administration of myocardial vasodilators can determine if coronary bypass surgery can be beneficial. In this regard, flow related quantification parameters can be determined: (1) end-diastolic volume (EDV) and pressure (EDP), (2) stroke volume (SV) and stroke work (SW), (3) LV resistance-to-filling and contractility, (4) ejection fraction (EF = SW/EDV), (5) maximal rate of change of pressure-normalized stress, and (6) regional function in terms of change of the endocardial surface area (S) such that ΔS = (Sole (ES) .dσ*/dtmax, and its decrease in an infarcted LV progressing to heart failure [Furthermore, in the LVs, there is also reduced contractility; so we also need to provide an index for cardiac contractility, in terms of maximal rate-of-change of normalized systolic wall stress,  failure . This comax = 1.5 × dV/dtmax/Vm, given that dV/dt is the first derivative of the volume and Vm is the myocardium volume at end diastole [These above mentioned parameters can assess the heart performance , 52. Fordiastole , (4) thediastole , 54. As Let us elaborate on the use of some of these indices by providing the below (i) Table In general, cardiac medical imaging has been widely utilised for imaging patients with various cardiac conditions, such as diseases of the aorta , 26, 55,We can summarize the clinical applications of medical imaging in the cardiovascular system for which the following medical conditions are assessed : (1) peru) profile is analysed across an arc at each depth, as shown in Fig.  u is composed of basic non-vortical laminar flow (ub) and vortex flow (uv) components. If the Doppler velocity profile on the arc has both negative and positive fractions, it is considered to be a combination of non-vortical and vortical laminar flows. The vortex feature is assumed to be bilaterally symmetric so that the negative and positive components of uv perpendicular to the arc negate each other  analysis package (DAS-RS1) . In thisher Fig. . As illuIt is important to note that vessel or heart chamber imaging and visualization is not sufficient as a stand-alone information provider of the cardiac health assessment. The important hemodynamic parameters or indicators affecting cardiovascular health performance discussed in this paper can be coupled along with the information based on heart imaging to serve as a more potentially reliable diagnostic system for the assessment of heart disease and as a practical tool for physiological analysis. For example, in addition to the evaluation of atherosclerosis and heart pumping performance as discussed in this paper, hemodynamics performance indicators also have the potential applications for identifying risks after heart valve implant as well as determining the degree of atrial or ventricular septal defects. The simulation may also be used to examine the growth effect of cardiac tissue into the mesh of surgically implanted device from the fluid mechanical perspective, and hemodynamics indicators such as vorticity can be designed to assess its health performance .Quantification of cardiac health that uses an integrated image processing and high-performance computing approach can be used on a patient-specific basis without the need for additional diagnostics or in vivo procedures, and thereby making it attractive for future clinical practice. The healthcare industry comprising of hospitals, medical institutes and universities will benefit by using the simulated hemodynamics performance indicators for evaluation of cardiac health, and using the hemodynamic flow fields as an assessment for analysis of flow phenomena to assess the impact of cardiac pathology. Manufacturers of medical imaging machines can also beneficially incorporate such computer visualization techniques into their imaging systems. The imaging data can be transferred to dedicated computer laboratories with high-performance computing facilities, to generate the appropriate hemodynamics health indicators. This presents a viable integrated platform for the purpose of flow analysis and virtual intervention outcome prediction for vascular diseases. Medical organizations (from the cardiac discipline) can employ this platform to assess the health of human heart and arteries so that appropriate medical action can be taken.Being at the cutting edge of medical science, the recent developments in the fields of medical imaging modalities have given new dimensions to our understanding of the human cardiovascular system. However, the potential of using functional health indicators in terms of the hemodynamics within the heart still has some unexplored opportunities for cardiac health diagnostics. In this paper, we have shown that this concept can be integrated into the present medical image diagnostics by well-established computational modeling for the determination of appropriate hemodynamics indicators. Cardiac flow analysis contributes to the development of the framework behind the operation of future flow simulation or mapping systems using high-performance computing. This type of system will lead to a new perspective on cardiovascular performance, risk and health, which can be obtained by using insights from the combined field of medical imaging and computational hemodynamic modelling. Further patient-specific analyses involving the combined field of medical imaging and visualization and high-performance computing will significantly contribute towards providing more reliable and precise cardiovascular health performance indicators and associated benefits.Medical imaging-based diagnostics integrated with high-performance computing will ultimately have a big impact on more precise medical diagnostics. The computational flow indicators and visualization to couple with anatomical details will constitute a significant forefront in technological development of the next era. The introduction of new diagnostic procedures for the evaluation of heart defects, as well as the capability of the research to identify and quantify flow phenomena through it will potentially result in useful clinical information to provide cardiologists a leading edge in saving patients.


The ability to intercept or avoid a moving object, whether to catch a ball, snatch one’s prey, or avoid the path of a predator, is a skill that has been acquired throughout evolution by many species in the animal kingdom. This requires processing early visual cues in order to program anticipatory motor responses tuned to the forthcoming event. Here, we explore the nature of the early kinematics cues that could inform an observer about the future direction of a ball projected with an unconstrained overarm throw. Our goal was to pinpoint the body segments that, throughout the temporal course of the throwing action, could provide key cues for accurately predicting the side of the outgoing ball. We recorded whole-body kinematics from twenty non-expert participants performing unconstrained overarm throws at four different targets placed on a vertical plane at 6 m distance. In order to characterize the spatiotemporal structure of the information embedded in the kinematics of the throwing action about the outgoing ball direction, we introduced a novel combination of dimensionality reduction and machine learning techniques. The recorded kinematics clearly shows that throwing styles differed considerably across individuals, with corresponding inter-individual differences in the spatio-temporal structure of the thrower predictability. We found that for most participants it is possible to predict the region where the ball hit the target plane, with an accuracy above 80%, as early as 400–500 ms before ball release. Interestingly, the body parts that provided the most informative cues about the action outcome varied with the throwing style and during the time course of the throwing action. Not surprisingly, at the very end of the action, the throwing arm is the most informative body segment. However, cues allowing for predictions to be made earlier than 200 ms before release are typically associated to other body parts, such as the lower limbs and the contralateral arm. These findings are discussed in the context of the sport-science literature on throwing and catching interactive tasks, as well as from the wider perspective of the role of sensorimotor coupling in interpersonal social interactions. A smooth and successful interaction with the dynamic environment in which we live requires predictive abilities. This is true when interacting with inanimate moving objects , when moInterceptive sports that involve striking, hitting or catching fast moving balls serve as excellent examples of actions in which predictive strategies are a pre-requisite for successful performance . Within Precise predictions can be made based on the ball flight after ball release. These are used for compensating sensorimotor delays in interceptive tasks  as well Sport science literature has shown that expert players are able to pick up advanced information from an observed throwing action  and to eBeside the context of elite-sports performances, throwing and catching are fundamental skills in the human motor repertoire , and it In a recent proposal, Ansuini and colleagues suggested to approach the problem of intention-from-movement understanding taking “action execution” as a starting point . First, In this study, we take on the issue of characterizing the information embedded in the kinematics of unconstrained overarm throwing actions in relation to the outgoing ball direction. We asked twenty non-expert participants to throw a ball aiming at different targets on a vertical board placed at 6 m distance. By analyzing full body kinematics off-line, we looked for the cues about ball direction that are available from the thrower’s kinematics prior to ball release. Our long-term goal is to verify whether these visual cues are used by human catchers in interception tasks.We designed our analysis to perform a coarse spatial decoding of the region of space where the ball arrived (Right vs. Left). In doing so, we adopted a classification approach, using Linear Discriminant Analysis (LDA), to assess how well different subsets of kinematic predictors from the throwing action are able to discriminate whether the ball will fly toward the right or the left side. This choice is in line with the evidence that, during an interceptive task, advanced information from a throwing action is typically coupled to gross-movement responses functional for the catcher to reach the region of space in which the ball is predicted to arrive, so as to optimizing successful performances .how early useful information is available for a potential observer to make reliable predictions about the ball’s flight, and to determine how such early information is spatially structured in terms of specific visual cues from the whole-body kinematics, we applied LDA classification using different sets of predictors. These include the kinematics of individual markers placed on single joints across the whole participant’s body, and of sets of multiple joint-markers, across different temporal windows throughout the unfolding of the throwing action. In doing so, as an intermediate step, we adopted a spatiotemporal principal component analysis (stPCA) to obtain a compact description of the considered kinematics.In order to address the issue of The rationale for the choice of the described approach is rooted in the expectation that the obtained results would guide us in identifying, unbiasedly, the spatiotemporal structure of early information embedded in throwing actions, and in establishing how this structure depends on individual throwing styles. On the long-term this outcome would be useful for exploring to which extent humans are able to access and use the available visual cues, as well as for designing artificial agents that optimize their predictive abilities by exploiting previous knowledge about the spatiotemporal structure of the information available.Twenty right-handed participants , with normal or corrected-to-normal vision and no history of neurological conditions, participated in the experiment. Handedness was tested with the standard Edinburgh Handedness Questionnaire . Upon anThis study was carried out in accordance with Italian laws and European Union regulations on experiments involving human participants. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Ethical Review Board of the Santa Lucia Foundation.3. All positional data were reconstructed by a dedicated software . To minimize marker reconstruction artifacts, participants were required to wear a body fitted velcro suit and a beanie cap, upon which retroreflective markers (diameter 14 mm) were attached. Each participant was equipped with a standard biomechanical marker set consisting of 57 retroreflective markers. Eight of these markers, located on medial anatomical joints, were used only for calibration and were removed post calibration procedure  operating at 120 Hz was utilized to capture full body positional information of the participants throwing actions and the corresponding ball trajectories. Infrared cameras were strategically located to allow for a large and gap-free calibration volume of 10 × 6 × 3 mParticipants had to perform a series of overarm throws, starting from a fixed initial position. They were instructed to hit one of four circular targets arranged on a vertical target board placed at 6 m from the initial position (marked with a sign on the floor) and to start from a fixed posture . A second pure tone sound marked the end of the trial after 6 s. In addition, a USB video camera was located outside the capture volume  and recorded the target location, the participant throwing action and the ball trajectory, including its landing location on the target-board, for the full duration of the trial. The handling and communication of all of the above information was managed through a custom Matlab script that integrated Optitrack Natnet SDK1. The Natnet.NET client/server architecture allowed seamless communication between Motive and Matlab (v2014b), allowing for control via Matlab of Motive commands . The connection to the display computer was established using a UDP connection.The beginning of each trial was signaled with a computer-generated pure tone sound and by displaying the selected target on a computer monitor  perform multiple overarm shadow throws , (ii) perform overarm throws with the ball aiming to hit the rectangular board and, lastly, (iii) perform a minimum of 12 throws, 3 toward each circular target. Participants were then allowed to train further, until they felt at easy with the task. The training phase lasted about 5–7 min. The experimental recording session was initiated right next and had an average duration of 40 min.The experimental session consisted in a series of 120 throws, 30 for each of the four targets, presented in a pseudorandom order. No instruction was given regarding how to perform the throwing movement, nor feedback about performances during the experiment. To start from a fixed initial position, facing the targets-board and standing straight, with the arm along the body and the hands slightly separated from the thighs. Participants were therefore free to perform a step forward while throwing (with either of the two legs) or to throw standing at place. The session was divided into three blocks of 40 trials, although participants could ask at any moment to take a break if needed.The positional data of a subset of eighteen markers selected from the Motive biomechanical markerset and the positional data extracted from the ball trajectory after ball release were analyzed in this study. The subset of eighteen markers included left and right metatarsal (foot), lateral malleolus (ankle), femur epicondyle (knee), iliac crest (pelvis), acromion (shoulder), humerus epicondyle (elbow), ulna syloid process (wrist), second proximal phalanx (hand), seventh cervical vertebra (cv7) and anterior head .Altogether, data from 2400 throwing trials were recorded, 120 for each of the 20 participants.filtfilt function). Positional data were then differentiated (Matlab diff function) to obtain velocities and accelerations.For each trial the positional data from the eighteen joint-markers selected for the analysis of the throwing motion, as well as the ball center positional data, were first interpolated using a cubic spline method (to fill recording gaps), and subsequently filtered using a zero-lag Butterworth filter of order 5 and low pass frequency 15 Hz . Typically, recording data along the ball flight trajectory were missing when the ball flew close to the ceiling, at the boundary of the capture volume, or in the proximity of the target-board, as the latter introduces occlusions that limit the cameras field of view in its vicinity. Additionally, a few trials were excluded when the participants failed to follow the instruction and performed a step before starting the genuine throwing action .Table 1.All the data processing, including the automatized exclusion of bad-trials and the identification of key-events (see below) were performed with custom-made software coded in Matlab. Overall, 13.8% of the trials were excluded (331 over 2400). On average, 103.5 ± 14.5 good trials per participant were used for the analysis. Individual data is listed in For each trial, we identified three key events: throwing action onset, ball release and ball-impact on the target-board.throwing action onset was defined as the onset of the throwing hand initial rising movement. The procedure consisted of the following steps. First, the time at which the hand first rose 5 cm above the hip was identified based on the hand-hip distance profile. Next, the onset detection was based on the speed profile of the throwing hand in a 500 ms interval centered on this event. This was done to remove movements that occasionally participants performed before the actual throwing action, e.g., swinging arms. The throwing onset was then defined as the point at which the speed profile intercepts its tangent taken at the point where the speed reaches 20% of the maximum speed in this interval  hand speed profile reached its maximum value in the 500 ms interval centered on the time at which the hand-ball distances was above a given threshold. Such threshold was set according to the hand-ball distance calculated at the beginning of the trial, i.e., when the ball was held in the hand  on different sets of kinematic variables extracted from positional data with the aim to quantify the predictability of a throw’s outcome. Among a variety of possible classifiers, we adopted LDA for several reasons. First, in this study we were mainly interested in the spatiotemporal structure of the classification accuracy, rather than in the precision of the corresponding absolute values. Non-linear classifiers, with the drawback of increasing the level of complexity, could possibly result in an overall higher classification accuracy , but it The kinematic variables included are the joint-markers positions and velocities. Although it has been shown that accelerations play a critical role in the perception of biological motion , the visGN ≥ 2 groups  based on its measured parameters (features). LDA consists in finding discriminant functions that divide the features space into GN regions, so that each region spans the range of features values that most likely characterize a given class. This is done on the base of a set of previous observations for which the group assignment is known (training dataset), by maximizing the ratio of the between-groups to the within-group variabilities  of the ball’s landing position with respect to a separation region. The latter was defined as a vertical band centered at the lateral (x) coordinate corresponding to the mean x across all trials (therefore participant dependent) and having a width equal to 25% of the lateral separation between the targets, i.e, 22.5 cm . This choice allowed including in the analysis most of the performed throws, even for the poorly performing participants and, at the same time, to have an even repartition of the trials in the different classes.Because the focus of this study was to examine the nature of advanced visual cues that allow making reasonable predictions about the outgoing ball direction prior to ball release, classes were defined according to the region in which the outgoing ball landed on the targets-board. For the analysis presented in this paper, throws were grouped according to the Table 1), extending up to the time of ball release. The trials of equal duration were then aligned at the end of the time window, i.e., at ball release, and resampled on 100 time points.As the inter-individual variability observed in throwing styles was way larger than the intra-individual variability associated with throws to different targets, the analysis was conducted independently for each participant. For each participants, we considered the kinematics across a temporal window of fixed duration, equal to the individual’s average throwing duration , or during the whole duration of the action from action onset to the end of the corresponding decile . Our main analysis has been performed on the single joint-makers/time-decile datasets. The other datasets have been considered to address the question of whether integrating information across time and space allows making better predictions, or is instead detrimental because it cumulates non-informative variance that weaken classification performances.We adopted an exploratory approach. LDA was indeed performed on different sets of predictors. We considered kinematic variables (positions and velocities) from single joint-markers, and from subsets of joint-markers representing specific body parts, over different phases and durations of the throwing motion. When defining subsets of joint-markers we considered six different body districts: trunk (including right and left shoulder and hip), head (including anterior head and cv7 markers), right and left arms , and right and left legs . For both single joint-markers and body-parts, we performed the analysis on ten time intervals (deciles), and for each of them we considered two different subsets of data: Position and velocity were either monitored across the duration of the corresponding decile (time-through case (6 position-velocity coordinates × 4 joint-markers × 100 time samples). It was therefore necessary to adopt a dimensionality reduction technique to obtain a compact representation of the considered kinematics, in order to run LDA with the limited number of trials available. A similar two-step PCA/LDA approach has been previously adopted in the literature, e.g., for facial expression recognition  resulting from a leave-one-out cross validation procedure. The latter consists in performing the classification assignment of a single observation (the one left out) based on the training set defined by the rest of the observations, repeating the same procedure for all observation, and computing the percentage of misclassified observations.JN joint-markers across an arbitrary temporal interval of TN time samples, the features vector for a single observation  will be: q =  ∀ j ∈  ∧ ti ∈ .In order to obtain a compact representation of the individual throwing kinematics, we adopted spatiotemporal Principal Component Analysis (stPCA) . To perfF = 3 × 2 × Nj × NT. The whole set of NTrials observations can be then represented by stacking the features vectors representing single trials into a single NF × NTrial matrix, X = [x1 x2...xNTrials]. Standard principal component analysis (PCA) is then applied to this matrix X. The PCA returns a new set of NF features vectors, the principal components, defined as the linear combinations of the original features that maximize the variance observed in the datasets, ordered as function of decreasing variance accounted for (VAF). In this way it is possible to describe each observation as a linear combination of spatiotemporal principal components (stPCs) and, by neglecting a small part of the variance in the dataset, to use a limited number of stPCs for obtaining a parsimonious summarization of the observed datasets: xk ≃ l,k pl, with N < NF and k ∈ .The features space is then of dimension Ntime-through description of kinematics of the trunk body-part in the last decile of the throwing action, represented by 2400 scalars in the original feature space, can be described with less than 31 parameters in the stPCA space while accounting for 98% of the total variance (average across participants).The advantage of adopting a spatiotemporal description of the kinematics, instead of a classical time-dependent spatial description , is thatFigure 2 shows the distribution of ball landing positions on the targets-board, for the best and worst participants in terms of performance. In the cases of poorly performing participants, the distribution of the ball-board impact points was broad  and there was no segregation of the trials intended to hit different targets , but instead a substantial degree of overlap among them.Average performances in terms of success rate, i.e., the percentage throws in which the ball landed within the 20 cm disk of the instructed target, varied across participants from a minimum of 20% to a maximum of 66%. Although the success rate could vary with the targets location, there was no common trend across participants. Table 1 reports the summary statistics for these parameters at both the individual and the population levels.Data revealed a great variability in the duration of the throwing action, in the ball release speed and in the corresponding duration of the ball flight, particularly across participants. This variability reflects the fact that participants have been not assigned with specific constraints for the throwing task execution (see Section Protocol). Figure 3 shows the individual styles from the 20 participants recruited in the study. For each participant, the figure depicts the trajectories of the joint-markers included in the analysis averaged across all trials performed, independently on the target aimed for. The inter-individual differences in throwing styles are markedly evident.We next inspected the individual throwing style, namely the spatial features of the whole-body kinematics that characterizes an unconstrained overarm throwing action. elevation) and the other in which the hand is projected forward for executing the throw (forward-projection). During elevation, the throwing hand trajectory may have two main modes of execution. Some participants rise the throwing hand by moving the arm in front of the trunk  and in some cases slightly toward the body midline . Otherwise, the throwing hand is risen while moving backward and opening laterally towards the right side . Other important inter-individual differences can be appreciated in the stepping. Some participants adopt an “on-place” throwing strategy keeping the feet at place , while others undertake one prominent step, either with the left  or with the right  leg. Variability is there also in the degree of the trunk’s forward projection and in whether and how the left arm is involved in counterbalancing the throwing arm motion.Despite the large inter-individual variability in throwing styles, for all participants the throwing action can be clearly segmented into two phases: one in which the throwing hand is elevated at about the shoulder level . The map in the left panel represents the deviation from the corresponding initial values of the three positional coordinates  of each joint-marker through time. For this particular participant, the action starts with moving the right arm backward, while the hand and wrist start rising. This is compensated by left arm moving forward , and soon after is followed by a left step forward resulting in a trunk rotation, with right side moving backward and the left forward. All these kinematic features unfold during the elevation phase. The forward-projection phase starts only at the very end of throwing action, i.e., during the 9th decile, about 200 ms before ball release.A more detailed, though less intuitive, description of the throwing action kinematics is provided by the heat-map representations of elevation to the forward-projection phase is observed for all participants in our sample . Next, we assessed the impact of integrating advanced information across time (joint-marker/time-through) and/or across space (body-parts/time-decile or body-parts/time-through), by comparing prediction accuracies between the different predictor spaces considered, i.e., between different combinations of spatial and temporal information included in the LDA analysis.As a first exploratory step, we considered predictions associated with the kinematics of individual joint-markers at 10 non-overlapping time intervals of equal duration spanning the whole throwing action , on the basis of continuous variables , has on the intrinsic accuracy of the LDA results.Side classification (Right vs. Left). In principle, the same analysis can be applied to the classification of Elevation (Up vs. Down) and or Quadrant (Side × Elevation). In these cases, however, because the effect of gravity on the ball’s elevation at impact depends on the flight duration, the ball velocity at release acts as a confound in the relation between throwing kinematics and ball elevation at impact.Applying LDA classification on our dataset required separating the set of throws from a given participant into discrete groups (classes). In the analysis presented in this paper we have focused on the problem of Table 1.As described in Section “Materials and Methods,” throws were grouped based on the coordinates of the position in which the ball landed on the targets-board. This choice allowed including most of the performed throws in the LDA training, even for poorly performing participants. Only the throws in which the ball landed in the gray separation region were indeed excluded from the LDA analysis. The number of excluded trials depended on the participant’s performance and ranged from a maximum of 24 trials to a minimum of 3, with an average (±SD) of 17 (±6) trials removed per participant. The total number of trials used to perform LDA analysis for each participant is given in Side-classification using position and velocity of the ball at release as predictors. Once released, the ball moves according to the laws of motion along a defined parabolic trajectory. It follows that ball position and velocity at a single point in time, from release onward, univocally determine where the ball will land on the targets-board. The LDA classification based on these predictors should be then accurate at 100% level, so that deviations from perfect classification could provide a quantitative estimation of the effect of sub-optimally separated classes on the intrinsic LDA performances.The choice of grouping trials into discrete classes based on continuous variables can have implication for the intrinsic LDA accuracy. In fact, throws assigned to different classes may be closer to each other, if the corresponding ball’s arrival positions are close to the boundaries of the separation region, than throws assigned to the same class. To assess the effect of the dispersion of the ball’s arrival positions on classification performances, we performed LDA Table 1. The differences found between participants in the intrinsic accuracy of the LDA should be taken into account when comparing the predictability of the throwing kinematics across participants. To this end, we introduced an index that normalizes the ME based on body kinematics to the ME due to the dispersion of the ball’s arrival positions on the targets-board. In the following, when reporting results from the LDA applied to body-kinematics features we provide values for the Misclassification Index (MI), defined as:MEs of the ball landing side based on ball position and velocity at release range from 0 to 4.2 percent, less than 1 percent when averaged across participants. Individual MEs are listed in BodyKin and MEBall indicate the MEs obtained running LDA respectively on body kinematics and ball position plus velocity at release. If the classes are well separated and the ME based on ball data is zero, MIBK corresponds to the ME based on body kinematics. In contrast, if the ME based on body kinematics is equal to the ME based on the ball, indicating that the body kinematics is as informative as the ball kinematics at release, MIBK = 0.where METhe aim of the analysis presented in this section was to characterize whether the throwing kinematics allows disentangling the side in which the ball will land on the targets-board, both at a spatial  and at a temporal level.Figure 6 shows such a comparison for two representative participants, highlighting two main points. First, as expected (see Section Throwing Styles) the most dramatic differences between the kinematics leading to balls on different sides are associated with the forward-projection phase of the throwing arm. A second important point that emerges is related to the marked inter-individual differences. Trajectories corresponding to the ball landing on opposite sides tend in fact to diverge in the throwing arm at different stages for different participants . Furthermore, also depending on the participant, trajectories may diverge also for body parts other than the throwing arm .To a first approximation, one could address this issue by looking at the average differences in the joint-markers trajectories of throws to the left or to the right. PC spatiotemporal components that explain at least 98% of the total variance. The dimensionality of the predictors space, NPC, depends therefore on the specific participants and on the set of the kinematic variables included. The mean NPC values  used for LDA for different combinations of joint-marker sets and time intervals are summarized in Table 2. Mean NPC values range from 6 to 27, corresponding to original spaces with dimensionality between 60 (single joint-marker at one time-decile) to 1800 , demonstrating the efficacy of stPCA as a dimensionality reduction technique.Visualizing and inspecting differences in the individual average trajectories between left and right throws may give some hints about the kinematic cues that could provide useful predictions about the throwing outcome. However, the spatiotemporal stPCA + LDA approach described in Section “Analysis” was necessary to provide a quantitative characterization of the individual predictability of a thrower. LDA classification was run on the first Ntime-decile are shown in Figure 7. The color maps, one for each of the 20 participants recruited in the study, represent the MI, as defined in Section “Intrinsic LDA Accuracy” (MIBK), as a function of joint-marker and time decile throughout the throwing action course. The dataset reveals a considerable inter-individual variability in the predictability of the throwing action, both in its average level and in its spatiotemporal structure. Some participants are more predictable than others, reaching in fact different absolute minimum of the MIBK across joints and times . Individual MIBK minima range in fact from 0 to 22.6 , although on average participants display very low minima in MEs, i.e., 3.4 ± 5.2 (mean ± SD). Furthermore, the time intervals and joint-markers that provide information allowing for reliable predictions vary significantly across participants. This is clearly shown by the differences, found across individual maps, in the extent and shape of the bluish regions, which correspond to predictions accuracy higher than 80%.Results from stPCA + LDA analysis, for single joint-markers and the case of forward-projection phase. Although for some participants informative cues about the outcome are not available until the very end of the action , most of the participants display informative kinematic cues already during the 6–7th deciles, i.e., 400–500 ms before ball release, and in few cases even earlier . Second, when early information is available, it is not necessarily provided by the throwing arm, but instead by different body segments that vary across participants. Interestingly, the body segments that deliver early information seems to be associated to specific throwing styles. For example, participants for which early predictions are based on the left lower leg joint-markers  perform the throwing action with a prominent left step , and the same applies to participants delivering early information from the right lower leg . An insightful summary of the inter-individual variability in the spatio-temporal structure of throwing predictability in given in Figure 8.Despite the overall inter-individual differences, two important general results emerge. First, the throw’s outcome may become predictable with a reasonable accuracy (>80%) not only before ball release, but even before the Figure 8 displays the number of participants for which at least one joint-marker could predict the ball landing side, with at least 80% accuracy, as a function of time. In addition, for each temporal interval, the figure shows the distribution across participants of the body segments  containing the most informative joint-marker. Not surprisingly, the number of predictable participants increases throughout the action course. Interestingly, the spatial origins of the most informative joint-marker is modulated by the stage of the action at which predictions are made. The throwing arm results to be the most reliable source of information only at the very end of action, i.e., during the 9–10th deciles. Moving back in time, useful information is instead provided by other body segments, in particular the limbs contralateral (left) to the throwing arm. This could possibly reflect the relevance of early kinematic features tuning the forward-projection phase.single joint-markers and body-parts kinematics, both integrated either over time-decile or time-through temporal intervals .Results from Section “Spatiotemporal Predictability of Individual Throwers” provide insights on how early it is possible to predict the outcome of a throws and which are the body parts that, at different times throughout the action, provide the most reliable information. As a next step, we here look at the effect of integrating information both spatially (across different subsets of joint-markers) and temporally . We do this by comparing results from LDA applied on four different predictor spaces: Figure 9 shows LDA performances in terms of number of predictable participants, for the four different choices of spatial and temporal integration under consideration. Participants counts correspond to the number of participants for which Side predictions can be made with an accuracy higher than 80%, based on at least one of the spatial predictors (either a single joint-marker or a body part) for each temporal interval. Focusing on the comparison between single joint-markers and body-parts (red and blue bars respectively), it is evident that integrating information spatially to include multiple joints into body-parts results in a clear boost in predictability. This is particularly true for the early stages of the action. Looking for example at the time-decile results, it can be seen that integrating spatial information in such a fashion increases the number of “predictable” participants by more than 50% up to the 6th decile. On the other hand, looking at the effect of temporal integration it appears that integrating information across time , does not result in higher prediction accuracies with respect to taking into account only the information within the specific time-decile , and in some cases may even entail loss in accuracy.The focus of this study was to assess whether it is possible to predict the direction of a thrown ball based on advanced information from the whole-body kinematics of the thrower. In particular, we explored how early it is possible to make reliable estimates about the lateral direction (right versus left) in which the thrown ball will reach a vertical plane placed at 6 m from the thrower. In addition, we explored the spatial structure of the predictive information, namely what are the body parts from which it is possible to make the most accurate predictions, and how this spatial structure depends on time and on individual throwing strategies. The study represents an essential first step for establishing, in future studies, how human or robotic agents could take advantage of visual cues extracted from the observed biological motion in order to optimize interpersonal interaction strategies.Figure 3). This is not completely surprising, given that besides factors such age, gender and intrinsic inter-individual differences, the previous exposure to different sports and different skill levels are likely to play a crucial role in determining individual preferences for a specific throwing strategy. Similar considerations hold in the context of other ecological scenario, such as unconstrained ball catching . This implies that a hypothetical human or robot catcher could in principle improve interceptive performance of genuine throws, e.g., by reaching in advance the most likely region of ball arrival, before being able to acquire more refined information from the ball flight. Nonetheless, the extent to which this holds critically depends on the agent’s ability to read out the information available, something that needs to be tested with dedicated studies. Moreover, this conclusion would not extend to the case of deceptive throws, in which the kinematics of the throwing action is intentionally and skillfully decoupled from the ball’s trajectory  predictions can be made as early as 400–500 ms before ball release, and for a few participants even earlier . With respect to this latter result, it is interesting to mention that previous studies from the sport science literature have described the role of contralateral arm for increasing the accuracy of a throw . Thus, for a catcher to be able to take advantage of early information from the body kinematics, it would be probably necessary to have some a priori knowledge of the most informative body parts that characterize the specific thrower, so as to direct the attention toward these body parts early on.Third, we found a considerable inter-individual variability in the spatio-temporal structure of the information relevant for making reliable predictions. In fact, the spatial origin of early advanced information varies from participant to participant  and the individual throwing styles  suggests a possible link between the two. Participants who perform the throwing action with a prominent left (right) step tend to deliver early information mainly via the kinematics of the lower left (right) leg. A quantitative assessment of this potential correlation between throwing styles and spatiotemporal structure of predictability would require a formal, data-driven definition, of individual throwing styles. Although this is beyond the scope of the present study, it is important to notice that the observed link may have crucial implications. In fact, it suggests that, in a possible interactive scenario, a catcher that has knowledge of the throwing style of the opponent, would know in advance where to look for extracting more efficiently advanced information, and therefore for maximizing interception performances.Interestingly, a qualitative comparison between the spatiotemporal structure of predictability , we found that integrating information across multiple joint-markers is of clear advantage for boosting prediction accuracies. This result is in line with previous findings highlighting how anticipation skills are associated with a “global” perceptual processing of kinematic information rather than with localized information .Integrating information through the whole course of the action, instead, does not seem of clear advantage for increasing predictability accuracies. In some cases, temporal integration may even result in reduced predictions accuracies. This pattern of results may be explained by two different effects. A possibility is that taking into account information over extended time intervals may blur key relevant information, because of cumulating non-informative variance across time. A second possibility is that the observed loss in prediction accuracy is a result of the higher dimensionality of the predictors space, which introduces limitations in the intrinsic LDA accuracy .The present findings will guide future experimental studies in which we plan to explore sensorimotor strategies involved in interactive throwing and catching tasks. Indeed, the main aim of the current study was to provide a quantitative characterization of the information embedded in the throwing kinematics about the outgoing ball trajectory. The gathered knowledge about the spatiotemporal structure of the information available to a potential observer is in fact functional to the design of tailored experimental protocols that will assess whether and how human observers are able to read out the relevant information and, if this is case, whether and how the extracted information is used in interaction performances. While this principled approach has been previously introduced for the study of predictions from the kinematics of reach-to-grasp movements in the context of social neuroscience , 2015a, Previous studies provided robust evidence for the human ability to read out advanced information from throwing, hitting and kicking kinematics. In particular, these anticipatory skills have been shown to be higher for elite-sport players than for non-experts  and to bBeside the specificity of the throwing/catching scenario, the current study fits in the wider context of social neuroscience and human-robot interaction. It is indeed well established that humans, when observing an action, are extremely good at reading out subtle kinematic cues not only to infer actor’s attributes –such as emotional states , gender Importantly, the methodology that we have introduced for deciphering the spatiotemporal structure of the information embedded in the throwing kinematics about the outgoing ball trajectory, can be applied to other categories of whole-body actions involved in the interaction between two or multiples agents. As such, it provides a valuable tool to explore interpersonal communication strategies based on body kinematics in a large variety of interactive tasks. Furthermore, the insights gained from observed human behavior can provide a significant contribution in human-robot interaction research, both by guiding the design of better predictable robots, and by addressing potential strategies for artificially reading out relevant advanced information from human kinematics.Despite the novelty of the results and the potential future applications of the methodology, our study is subject to some limitations. From the methodological point of view, the combination of dimensionality reduction and classification techniques that we have used may become less reliable if the dimensionality of the predictor space grows too high with respect to the dimensionality of the dataset used to train the classifier. If, as we did, we fix a given degree of accuracy in the stPCA reconstruction (fixing a VAF threshold), the dimensionality of the predictor space depends on the kinematics taken into considerations. For example, when considering multiple joint-markers across the whole duration of the throwing action, the number of stPCs required to have a VAF above 98% could grow above 30. On the other hand, fixing the dimensionality of the stPCs space would correspond to different degrees of reconstruction accuracy for different subsets of kinematic variables considered. While the high dimensionality of the stPC representation may reflect an intrinsic and thus unavoidable feature of the data, it is also possible that there exists a more compact representation of the spatiotemporal variability of whole body kinematics. Rather than being only superimposed over a fixed time-interval, individual stPCs may also be shifted in time . The useAnother limitation of the study is linked to the choice of recruiting non-expert participants. While this choice was meant to provide a broad picture of the readability/predictability of individuals without a specific expertise in a complex whole-body action like an overarm throw, it is likely that such a population is characterized by a lower “signal-to-noise”  with respect to expert throwers. An additional drawback of having non-expert throwers as participants is related to their average poor performances  and the associated need to group throws into discrete groups (the side) on the base of continuous variables . It would be interesting in future studies to apply the same methods as to characterize the spatiotemporal structure of the predictability of expert throwers with respect to the outgoing ball trajectory.In this study we have provided a quantitative estimate of the accuracy that it possible to achieve when predicting whether a thrown ball will flight right or left, as a function of different visual cues from the whole-body throwing kinematics. We achieved this by introducing a novel method based on a combination of dimensionality reduction and machine learning techniques. The results provide novel insights into the spatiotemporal structures and inter-individual variability of the visual cues potentially available for predicting the outgoing ball trajectory. The results further provide preliminary evidence for a relationship between the spatiotemporal structure of the information available and the individual throwing styles.All authors conceived the study. AM, AD, and Ad’A designed the experiment. AM, AD, BC, and MR implemented the experimental setup. AM and AD conducted the experiments. AM analyzed the data. All authors discussed and interpreted the results. AM drafted the manuscript and all authors provided inputs to its final version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


As an optimal estimation method, the Kalman filter is the most frequently-used data fusion strategy in the field of dynamic navigation and positioning. Nevertheless, the abnormal model errors seriously degrade performance of the conventional Kalman filter. The adaptive Kalman filter was put forward to control the influences of model errors. However, the adaptive Kalman filter based on the predicted residuals (innovation vector) requires reliable observation information, and its performance is significantly affected by outliers in the measurements. In this paper, a novel adaptively-robust strategy based on the Mahalanobis distance is proposed to weaken the effects of abnormal model deviations and outliers in the measurements. In the proposed scheme, the judging index is defined based on the Mahalanobis distance, and the adaptively-robust filtering is performed when the observations are reliable, otherwise, the robust filtering is performed based on the robust estimation method. Various experiments with the actual data of GPS/INS integrated navigation systems are implemented to examine validity of the proposed scheme. Results show that both the influences of model deviations and outliers are weakened effectively by using the proposed adaptive robust filtering scheme. Moreover, the proposed scheme is easy to implement with a reasonable calculation burden. Since the properties of the Global Positioning System (GPS) and inertial navigation systems (INS) are complementary, the integration of these two systems has been extensively applied in the field of target tracking and navigation. As one of the most popular optimal estimators , the KalDifferent from the MMAE and IAE strategies, Chinese researchers have developed an adaptively-robust filter by introducing the adaptive factors and robust estimation method . Both adIn this paper, an improved adaptively-robust filter is proposed based on the adaptive Kalman filter, robust estimation method and Mahalanobis distance. In the proposed strategy, the Mahalanobis distance is adopted as error detection statistics, and it determines whether the adaptive strategy is performed or not. Two cases are considered in this paper, and contrastive experiments and analysis are performed with the data collected by the GPS/INS integrated navigation systems under real conditions. The obtained results show that an improved adaptively-robust strategy manifests better performance; meanwhile, it is easily implemented.The remainder of this paper is organized as follows: In The adaptive filter has been widely applied and investigated in the field of dynamic navigation and positioning. Different from the Sage-Husa filter , a new sFor the dynamic and measurement equations:Thus, solution of the adaptive Kalman filter is obtained by:The differences between conventional filters and adaptive filters originate from the adaptive factor. Consequently, to find a suitable adaptive factor becomes the key problem in the adaptive filter design. In recent years, four types of test statistic and adaptive factors have been proposed . The preSince the test statistic constructed by the predicted residual is applied in this paper, only this type of statistic is displayed. The test statistic based on the predicted residual is defined by:The test statistic and the adaptive factor constructed based on the predicted residual need no redundant measurements, and they are applicable when the number of measurements is less than that of the unknown parameters, accordingly, they are suitable for the GPS/INS integrated navigation systems. The adaptive factors are constructed by the test statistic. For instance, the two-segment adaptive factor is defined by :(15)αk={function ,23, the Although the influences of model deviations can be controlled with the adaptive filter, the adaptive factor cannot resist the influences of the outlying measurements. Consequently, the robust estimation method was adopted to develop the adaptively-robust filtering algorithm .ith diagonal element of the weight matrix, and For the adaptively-robust filtering algorithm, the extremum condition is defined by :(17)∑i=1function . The solThe adaptively-robust filtering algorithm can resist the effects of state perturbations and outlying measurements simultaneously. Moreover, it shows a noticeable flexibility because it can automatically select the most suitable algorithm from LS estimation, Kalman filter, robust filter, adaptive filter, and adaptively-robust filter .As mentioned above, estimates of the unknown parameters are closely related to the measurements, thus, the performance of the adaptive filter based on the predicted residual is determined by the quality of the measurements. With the outlying measurements, the predicted residual becomes unreliable and, consequently, the performance of the conventional Kalman filter may even be degraded by the adaptive factor. Namely, the adaptive factor may backfire with the unreliable residuals. Thus, the adaptive factor should be applied in a more suitable way, and an improved adaptively-robust strategy is proposed below.For the system defined by Equation (1), the measurements should be Gaussian distributed with the mean fined by :(20)ρλij=It is concluded that both the adaptive factor Three types of coupling have been developed for the GPS/INS integrated navigation systems, and the loosely-coupled system is designed in this paper. Considering the deviations of the position For the INS system, the nonlinear differential error model is defined by :(26){ΔR˙In general, dynamic models of the GPS/INS integrated navigation systems are nonlinear, thus, the Kalman filter cannot be applied directly. As such, the cubature Kalman filter is adopted to address the nonlinear problem in this paper.(a)Time update(b)Measurement updateThe iterative equations of the cubature Kalman filter are listed below :(a)Time Assume that The position and velocity differences between the GPS and INS are the measurement inputs in the loosely-coupled systems. Obviously, the measurement equation is linear in the loosely-coupled system, thus, the measurement equation should be rewritten by:In the context of multi-sensor fusion, the Kalman filter is the most commonly-used fusion method. As shown in Equation (42), estimation results are connected with the quality of the measurements, and imprecise measurements may result in large deviations of the estimates. Accordingly, the imprecise measurements should be addressed carefully. In the GNSS/INS integrated navigation systems, the adaptive factor and the robust estimation method constructed by the predicted residual can be adopted to improve the filtering performance .2 and (0.05 m/s)2. The sampling frequencies of GPS and INS were 1 Hz and 100 Hz, respectively. The results of a double difference carrier were used as references.Various contrastive experiments were designed and performed. Data in these experiments were collected in real environments by a vehicle equipped with the GPS/INS integrated navigation systems. The integrated systems were composed of two GPS receivers (a base station and a rover station) and a low-cost SPAN-CPT IMU . Scheme 1:the cubature Kalman Filter (CKF);Scheme 2:the adaptive filter performed at all epochs (AKF-ALL) (two-segment function was adopted in the adaptive filter and Scheme 3:the adaptive filter performed at the epochs without outliers (AKF-PARTIAL) (two-segment function was adopted in the adaptive filter and Scheme 4:the improved adaptively-robust filter (IARF)  Case 1x, y, and z directions of each scheme are displayed in In Case 1, four schemes were implemented based on the initial measurements. Errors of the position in In the initial measurements, the filter performance was mainly affected by abnormal deviations of the dynamic model and effects of the outlying measurements are negligible. When the vehicle was passing through the speed hump, the abnormal perturbations might occur and filter precision could be degraded. It is obvious that there exist abnormal perturbations in To compare the performance of each scheme in a clearer way, the root mean square error (RMSE) of the position errors in three directions for each scheme were calculated and they are listed in As displayed in (2) Case 2In order to test the robustness of the improved adaptively-robust strategy, the scattered outliers were added artificially to the initial measurements, thus, the data with outliers were constructed. Then, the aforementioned four schemes were performed with the data contained by the outlying measurements. The position errors of all schemes are displayed in Since outliers were added into the measurements, the filter performance was affected mainly by them. Obviously, The RMSE of the position errors in three directions for each scheme are listed in As can be seen in (1)Comparing the performance of different algorithms in this paper, it can be summarized that the adaptive filter is able to control the influences of dynamic model errors, but it cannot resist the influences of outlying measurements, thus, the performance of the Kalman filter may be degraded by the adaptive factor when outlying measurements exist.(2)Different from the conventional adaptively-robust filter, the adaptive factor of the new filtering strategy is performed according to the Mahalanobis distance. The proposed filtering strategy is verified in the loosely-coupled GPS/INS integrated navigation systems, and the robustness is demonstrated with both initial data and perturbative data.(3)Comparing two cases, precision improvements are more obvious with the outlying measurements, thus, it is concluded that the proposed filtering strategy is more applicable when system is contaminated with outlying measurements.In this paper, an improved adaptively-robust filter is proposed based on the adaptive filter, robust estimation method, and Mahalanobis distance, and a new filtering strategy is developed. The proposed strategy is tested with the data collected by the GPS/INS integrated navigation systems in real circumstances. The detailed conclusions are summarized as follows: