Scrapie is a chronic neurodegenerative disease affecting small ruminants and belongs to the transmissible spongiform encephalopathies. Scrapie is considered a serious animal disease and it has been notifiable in Norway since 1965. The clinical signs of scrapie might be vague and the farmers, if familiar with the signs of scrapie, are often in the best position for detecting scrapie suspects. In 2002, an anonymous questionnaire survey was conducted in order to assess Norwegian sheep farmers' vigilance of scrapie.Although the potential detection of a scrapie-positive animal would lead to the destruction of the sheep flock concerned, almost all the farmers (97 %) expressed their willingness to report scrapie suspects. This was most certainly dependent on the Government taking the economic responsibility for the control programme as nearly all the farmers responded that this was an important condition. Listeriosis is relatively common disease in Norwegian sheep and a differential diagnosis for scrapie. In a multinomial logistic regression the reporting behaviour for non-recovering listeriosis cases, used as a measurement of willingness to report scrapie, was examined. The reporting of non-recovering listeriosis cases increased as the knowledge of scrapie-associated signs increased, and the reporting behaviour was dependent on both economic and non-economic values.The results indicate that in 2002 almost all sheep farmers showed willingness to report any scrapie suspects. Nevertheless there is an underreporting of scrapie suspects and the farmers' awareness and hence their vigilance of scrapie could be improved. Furthermore, the results suggest that to ensure the farmers' compliance to control programmes for serious infectious diseases, the farmers' concerns of non-economic as well as economic values should be considered. Scrapie is a fatal neurodegenerative disease affecting sheep and goat. It belongs to the transmissible spongiform encephalopathies (TSE), and there are at least two types: classical and atypical scrapie . From thThe first case of scrapie in indigenous Norwegian sheep was detected in 1981 and an increasing number of cases was detected in the 1990s  leading From the first scrapie case in 1981, all small ruminants in scrapie-positive flocks were culled . The addScrapie has been notifiable in Norway since 1965  and the If the farmer is familiar with the signs of scrapie, he is in the best position to detect scrapie suspects. However, whether the farmer decides to report suspicious clinical cases and found-dead animals or to conceal them will depend on his motivation to report the disease . TherefoAcknowledging the importance of the farmers for the performance of the scrapie surveillance programmes, a questionnaire survey among Norwegian sheep farmers was conducted in 2002. The aims of the study were to analyse the sheep farmers' vigilance in reporting animals with a higher risk of having scrapie, measured as reporting animals showing typical scrapie-associated signs and non-recovering cases showing signs of listeriosis. In this study no differentiation was made between classical scrapie and atypical scrapie as the same control measures were applied to the two scrapie types in 2002.The questionnaires were returned from 2125 of 3000 farmers. Of these, 55 farmers who reported having less than ten breeding sheep were excluded from the study, giving a response rate of 70%. Farmers were considered as drop-outs when they had given no information on region, flock size, scrapie status, and reporting behaviour of non-recovering listeriosis cases or if they gave no answer to any of the questions concerning their knowledge or their willingness to report. In total 97 questionnaires were drop-outs, giving information from 1973 questionnaires (67%) that were available for analysis.Most farmers (97%) answered that they would be willing to report scrapie suspects. The remainder constituted those who would slaughter or kill the animal (2%) and those who did not know how they would act in the situation (1%). When there was a non-recovering listeriosis case, 21% of the farmers would report the animal as a scrapie suspect and 51% of the farmers would have the animal re-examined by a veterinary practitioner. The remaining farmers would cull the animal.Each of the scrapie-associated signs listed were correctly checked by 34% to 69% of the farmers. Itching and trembling were the most well-known signs, being recognised by 69% and 67% of the farmers, respectively. At least two associated and zero non-associated signs were checked by 71% of the farmers, and at least three associated and zero non-associated signs were checked by 47% of the farmers. Each of the signs considered as not being associated with scrapie was checked by 0.5% to 4% of the farmers. Approximately 2% of the farmers were not familiar with any scrapie-related symptoms, and approximately 6% did not answer the question.In the hypothetical situation where scrapie was detected in one of the farmer's sheep, the statement "Satisfied that the detection of scrapie would enable the eradication of the disease from the flock" was considered to be very important by 55% of the farmers and important or very important by 81% of them  at the same level as the year prior to the diagnosis . The ecoAlthough the farmers might express their true intention of reporting scrapie suspects, it is difficult to know what their behaviour would be when confronted with the actual situation. Results of surveys performed in the Netherlands and Great Britain have shown an underreporting of scrapie suspects -18. DuriThe fact that only 21% would notify non-recovering listeriosis cases while almost all would notify suspect scrapie cases supports that there is an underreporting in Norway. One explanation might be that listeriosis is a well known disease and that the farmers don't find it necessary to report it as scrapie suspects. However, the fact that "Notifying" non-recovering listeriosis cases was associated with better knowledge of scrapie-associated signs suggests that underreporting might partly be due to lack of knowledge of which signs should be reported as suspicious of scrapie. Whatever the reason, this does not necessarily represent a deliberate underreporting of scrapie to hide the disease.This might seem to be in contrast to the fact that 88% of the farmers recognised at least one of the scrapie-associated signs. Furthermore, the fact that each of the scrapie-associated signs were correctly identified by 34% to 69% of the Norwegian farmers, seems comparable with the results of studies from Ireland and the Netherlands where each of the scrapie-associated signs was correctly identified by 25% to 50% of the farmers ,22 HowevTo control serious infectious diseases it is important to ensure that the behaviour of the farmers does not undermine the disease control programmes. The results of the multivariate analysis indicate that farmers' attitudes and concerns of non-economic values might be important for their reporting behaviour. Therefore, both economic compensation as well as considering the farmers' non-economic values should be taken into account when designing a control programme. This might be valid for all diseases where extensive control measures are put in force. We are not aware that the importance of non-economic values for the reporting behaviour of serious diseases has been examined, and we would suggest that this is explored further in a sociological context.The disease produces neurological signs that most farmers are expected to be aware of, and the farmers have been given the information that animals that show neurological disorders should be regarded as scrapie suspects. Consequently we chose to use the reporting behaviour of non-recovering listeriosis cases as a measurement of the farmer's vigilance in reporting animals with signs suspicious of scrapie. However, as listeriosis as such is not a notifiable disease, the reporting behaviour of the farmers reflects both their knowledge of scrapie-associated signs and their willingness to report scrapie. The reporting of non-recovering listeriosis cases must therefore be considered an indirect measure for the farmers' vigilance. Nevertheless, we consider the fact that the factors farmers' knowledge, economy and non-economic values were important for the reporting behaviour to be reasonable for non-recovering listeriosis cases, as well as for scrapie suspects.In accordance with previous questionnaire surveys concerning scrapie -18,23 thThe response rate in this study, 70%, is high compared with the typical anonymous postal survey within health sciences  as well Information from 557 farmers was not included in the final model due to non-responses (missing) of one or more questions. There were from 10% to 20% non-responses for each of the questions concerning the farmers' anticipated reactions if scrapie was detected in their flock, which could indicate a non-response bias. We received no indications that these questions were controversial for the farmer, but the farmer might have considered these questions difficult due to their hypothetical form. The non-responses did not show any significantly different distribution for any of the response variables. Therefore, we do not expect that any substantial problem with non-response bias was created by this.The farmers' awareness of scrapie and their willingness to report scrapie should not be considered static. After this study was conducted, scrapie Nor98 – an atypical scrapie – has constituted most of the scrapie cases detected in Norway . The conThe farmers' vigilance is essential for the detection of classical scrapie as, despite the extensive surveillance programmes, most flocks with classical scrapie have been detected due to cases being notified or animals submitted to the laboratory for disease examination . The resThe study was designed as a cross-sectional study. Three thousand sheep farmers were randomly selected from the Register of Production Subsidies using a pseudo random number procedure . To exclThe data were collected by an anonymous questionnaire survey. The four-page questionnaire contained questions concerning location and flock characteristics, contact patterns and management, and the farmer's knowledge of scrapie and his attitude towards the Norwegian scrapie surveillance and control programme. The questionnaire (in Norwegian) is available from the corresponding author.® Access 2000 Version 9. Microsoft Corporation, WA, USA, 1992–2001).The questionnaire was accompanied by a covering letter and a free-post return envelope. It was mailed to all participants in March 2002 followed by a reminder card in April 2002. The data from the questionnaires were entered into an MS access database . The answers "Contact DVO for examination regarding scrapie" (in short "Notifying") and "Contact veterinary practitioner for further examination" (in short "Re-examine") were kept as separate categories, while the answers "Send to slaughter" or "Kill the animal" were grouped together in the category "Not report" giving three different categories in total. The answer "Don't know" was treated as missing.The farms were located in four geographical regions: South-Eastern, Western, Middle and Northern Norway, based on county. The farmers were asked to specify the flock size within one of four groups: 1–10, 10–49, 50–99 or ≥ 100 breeding sheep.Using check-boxes, the farmers were asked to mark the clinical signs they considered as associated with scrapie among ten different clinical signs, where emaciation, hair loss, lip smacking, pruritus and trembling were considered as scrapie-associated signs, and abortion, coughing, diarrhoea, fever, and frequent urinating were considered as not associated with scrapie. The question was considered answered when at least one of the check-boxes was marked. The information was collated into one variable by summing the number of correctly checked scrapie-associated signs. In the multivariate analysis, the variable was treated as a numerical variable.The information that the detection of a scrapie-positive animal would lead to the destruction of all the sheep in the flock was presented in the questionnaire. The farmers were then asked to give their anticipated reaction to seven concerns regarding the potential detection of scrapie in their flock Table . The reaThe farmers were asked about the importance of four factors which might affect whether they would report an animal with signs suggestive of scrapie. These were: "I need more knowledge of scrapie symptoms", "Having easy access to a DVO", "Being offered free examination of scrapie suspects", and "The Government compensates for the cost of the control measures when scrapie is detected". The answers were graded in four levels: not important, of minor importance, important, and very important. For the multivariate analysis, each variable was dichotomised to derive two evenly-sized groups Table .The farmers' reporting of non-recovering listeriosis was used as a measurement of the farmers' vigilance in reporting scrapie. The reporting behaviour of non-recovering listeriosis was analysed in a multinomial logistic regression with the farmer as the statistical unit and the response variable categorized in the three nominal categories: Notifying, Re-examine and Not report.The explanatory variables region, flock size, knowledge of scrapie-associated signs, each of the seven anticipated concerns of the farmer if scrapie were to be detected in their flock, and each of the four factors of potential importance for the reporting of scrapie suspects were considered as candidates for the multivariate analysis. All candidate variables were included in the initial model. Maximum likelihood estimation was used for model fitting, and the likelihood ratio test was used to assess the overall significance of the model. The best model fit was found by using backward stepwise deletion of insignificant terms. For each step the single least explanatory variable was removed until there were no significant difference between the full and all possible reduced models when using the likelihood ratio test with significance level of 0.05. Thereafter, all two-way interaction terms between the remaining explanatory variables were tested one by one for significance in the final multivariate model.The adjusted RRR  were used as measures of association between the response variable and the explanatory variable . For eac® for Windows . The descriptive analyses were conducted by using PROC FREQ and missing observations were included when calculating the population percentages. The multinomial logistic regression was conducted by using PROC CATMOD.All variable processing and statistical analyses were performed in SAS-PC SystemPH were main responsible for the design of the study, collecting the data, performing the statistical analysis and drafted the manuscript. SV participated in the design of the study and helped to draft the manuscript. JJ supervised in the design, the statistical analysis and the writing of the manuscript. All authors read and approved the final manuscript.


Recently, many researchers have used graph theory to study the aberrant brain structures in Alzheimer's disease (AD) and have made great progress. However, the characteristics of the cortical network in Mild Cognitive Impairment (MCI) are still largely unexplored. In this study, the gray matter volumes obtained from magnetic resonance imaging (MRI) for all brain regions except the cerebellum were parcellated into 90 areas using the automated anatomical labeling (AAL) template to construct cortical networks for 98 normal controls (NCs), 113 MCIs and 91 ADs. The measurements of the network properties were calculated for each of the three groups respectively. We found that all three cortical networks exhibited small-world properties and those strong interhemispheric correlations existed between bilaterally homologous regions. Among the three cortical networks, we found the greatest clustering coefficient and the longest absolute path length in AD, which might indicate that the organization of the cortical network was the least optimal in AD. The small-world measures of the MCI network exhibited intermediate values. This finding is logical given that MCI is considered to be the transitional stage between normal aging and AD. Out of all the between-group differences in the clustering coefficient and absolute path length, only the differences between the AD and normal control groups were statistically significant. Compared with the normal controls, the MCI and AD groups retained their hub regions in the frontal lobe but showed a loss of hub regions in the temporal lobe. In addition, altered interregional correlations were detected in the parahippocampus gyrus, medial temporal lobe, cingulum, fusiform, medial frontal lobe, and orbital frontal gyrus in groups with MCI and AD. Similar to previous studies of functional connectivity, we also revealed increased interregional correlations within the local brain lobes and disrupted long distance interregional correlations in groups with MCI and AD. Understanding the progression of Alzheimer's disease (AD) is essential. We investigated networks of cortical connectivity along a continuum from normal to AD. Mild Cognitive Impairment (MCI) has been implicated as transitional between normal aging and AD. By investigating the characteristics of cortical networks in these three stages , we found that all three networks exhibited small-world properties. These properties indicate efficient information transfer in the human brain. We also found that the small-world measures of the MCI network were intermediate to those of the normal controls and the patients with AD. This supports the opinion that MCI is a transitional stage between normal aging and AD. Additionally, we found altered interregional correlations in patients with MCI and AD, which may indicate that a compensatory system interacts with cerebral atrophy. The presence of compensatory mechanisms in patients with MCI and AD may enable them to use additional cognitive resources to function on a more nearly normal level. In future, we need to integrate the multi-level network features obtained with various functional and anatomical brain imaging technologies on different scales to understand the pathophysiological mechanism of MCI and AD. We propose brainnetome to represent such integration framework. Alzheimer's disease, the most common form of dementia, is associated with plaques and tangles in the brain which would lead to a loss of neurons and synapses Recently, studies of functional and structural brain networks in AD patients have indicated that cognitive function deficits could be due to abnormalities in the connectivity between different brain areas. These brain areas include the bilateral parietal regions, middle temporal gyrus, cingulum, medial frontal gyrus, precentral gyrus, fusiform, etc. The interregional correlation coefficients of the cortical networks were calculated to construct correlation matrices (90×90) for the NC, MCI and AD groups see . The imaSome recent studies demonstrated that small-world properties are exhibited in functional brain networks s  see . A precis  see . In FiguIn order to detect the specific between-group differences among the three cortical networks, a fixed sparsity threshold value (sp = 15%) was used. This sparsity value can ensure that the cortical networks are fully connected while minimizing the number of false-positive paths To ascertain the hub regions of the cortical networks, the normalized betweenness centrality  and connections. Future studies should be done to further investigate this issue and replicate our findings using diffusion-based imaging.In this paper, we only studied the global network manifestation of brain malfunction in MCI and AD based on gray matter volume correlations, an indirect anatomical connectivity. In order to understand the pathophysiological mechanism of MCI and AD, it is necessary to integrate the multi-level network features obtained with various functional and anatomical brain imaging technologies on different scales. On macroscale, such features can be obtained from networks based on illness special region of interest, networks related to special cognitive function, and whole brain networks. Here we would like to propose a concept of brainnetome to represent such integration framework. We define the essential components of brainnetome as network topological structure, performance, dynamics, manifestation of functions and malfunctions of brain on different scales. In fact, a big project (973 program) has been approved in China to conduct studies of brainnetome for four different diseases with focal lesion (stoke and glioma) and diffusion lesions (schizophrenia and AD). For AD, the goal is to find biomarkers on network level which can predict whom of MCIs will develop into AD. We envision that brainnetome will become an emerging co-frontier of brain science, information technology, neurology and psychiatry. Some long-standing issues in neuropsychiatry may be solved by combining brainnetome with genome.http://www.loni.ucla.edu/ADNI/). This project is the most comprehensive effort to date to identify neuroimaging and other biomarkers of the cognitive changes associated with MCI and AD. The primary goal of this project is to measure the progression of MCI and early AD, in order to develop improved methods for clinical trials in this area. This study included 98 NCs who ranged in age from 70.02 to 90.74  , 113 MCI subjects who ranged in age from 56.28 to 89.40  , and 91 AD subjects who ranged in age from 55.73 to 90.20  .All the subjects used in this study were selected from the Alzheimer's disease Neuroimaging Initiative (ADNI) database  implemented with Statistical Parametric Mapping software (SPM5) running under Matlab 7.0 on the Ubuntu operating system. VBM is a whole-brain, unbiased, semiautomatic, neuroimaging analysis technique that allows the investigation of regional differences in brain volume. In brief, the average gray matter volumes of each brain area were obtained for each subject using the following steps. First, all the structural images were corrected for non-uniformity artifacts. Then, the corrected images were registered to an asymmetric T1-weighted template using nonlinear normalization. Next, the corrected and normalized images were segmented into gray matter, white matter, cerebrospinal fluid and other background classes. Fourth, the resulting gray matter images were smoothed by a 4 mm isotropic Gaussian kernel to compensate for the inexact nature of the spatial normalization. Finally, from these smoothed gray matter images, we calculated the average gray matter volumes for each of n = 90 brain areas, which were comprised of 45 cortical regions in each hemisphere (excluding the cerebellum) in each participant.Before obtaining the structural cortical networks, the anatomical connection matrix was calculated. In this study, the structural connections of the cortical network are defined as statistical correlations between pairs of average gray matter volumes from the corresponding AAL areas. We considered that a structural connection existed if the correlation coefficient for a pair of brain areas was statistically significant. Subsequently, an interregional correlation matrix  was applied to threshold the interregional correlations matrices of the three cortical networks into binarized matrices. Sparsity is defined as the total number of edges, K, in a graph divided by the maximum possible number of edges. In our case, the maximum possible number of edges equals 90×89/2 = 4005. Since no definitive way for selecting a single threshold value exists, we thresholded each interregional correlations matrix repeatedly over a range of sparsities  and mean network shortest absolute path length (Lp). A shorter absolute path length and a higher global efficient may indicate a higher speed of information dissemination and more efficient information processing p is the average of the clustering coefficient over all the nodes in a network, where the clustering coefficient Ci of node i is defined as the number of existing connections among the immediately connected neighbors of the node divided by all their possible connections. Cp measures the extent of local cliquishness or local efficiency of information transfer of a network. Lp is the average of the mean shortest absolute path length over all nodes in the network, where the mean shortest absolute path length of node i is defined as the total shortest absolute path length between node i and all the others divided by i of a node i is the number of connections to the node) as the real network Small-worldness is a ubiquitous property of complex real-life networks that supports both modular and distributed dynamic processing as a principle of brain topology i would be normalized as We investigated the nodal characteristics of the cortical network among the NC, MCI and AD groups. To do this, we introduced the betweenness centrality of the nodes in the networks. Betweenness is a measure of the centrality of a node in a graph. The betweenness, B, of node i is defined as the the number of absolute shortest paths that are between any two other nodes and that run through node i. For further comparison, the betweenness BInterregional correlation differences. In order to test whether the interregional correlations of the cortical networks were significantly different among the NC, MCI and AD groups, Fisher's z transformation was applied to convert the correlation coefficients to z values which were approximately normally distributed p and Lp. In this permutation test, we obtained a reference distribution on which we calculated possible values of the test statistic after repeatedly rearranging the observed data from the NC, MCI and AD groups. First, we calculated the Cps and Lps of the real cortical networks at a given sparsity for each of the three groups separately. To test whether these measurements were significantly different between the three groups, we pooled the data from ADs with the data from the NCs. From this pooled group, we randomly choose some of the subjects to be considered as NCs and the rest to be considered as AD patients. The number of supposed AD patients was equal to the number of actual patients in the original group. We then calculated the differences between the new groups and repeated this process 1000 times. In each of the 1000 cases, we used the same sparsity threshold to generate corresponding binarized matrices and computed the Cp and Lp characteristics of the two cortical networks for each randomized groups, obtaining the between-group differences. We sorted the 1000 recorded differences and observed whether the between-group differences in the real cortical networks were contained within 95% (two-tailed) of the supposed between-group differences. If they were, we accepted the null hypothesis that the two groups had identical probability distributions at the 5% significance level; otherwise we rejected the null hypothesis. This permutation test procedure was repeated over the range of sparsity threshold values from Differences in network topology. We used a nonparametric permutation test to test the statistical significance of the between-group differences in the two characteristics of the cortical networks, C


Functionality, controllability and cosmetics are the key issues to be addressed in order to accomplish a successful functional substitution of the human hand by means of a prosthesis. Not only the prosthesis should duplicate the human hand in shape, functionality, sensorization, perception and sense of body-belonging, but it should also be controlled as the natural one, in the most intuitive and undemanding way. At present, prosthetic hands are controlled by means of non-invasive interfaces based on electromyography (EMG). Driving a multi degrees of freedom (DoF) hand for achieving hand dexterity implies to selectively modulate many different EMG signals in order to make each joint move independently, and this could require significant cognitive effort to the user.A Principal Components Analysis (PCA) based algorithm is used to drive a 16 DoFs underactuated prosthetic hand prototype  with a two dimensional control input, in order to perform the three prehensile forms mostly used in Activities of Daily Living (ADLs). Such Principal Components set has been derived directly from the artificial hand by collecting its sensory data while performing 50 different grasps, and subsequently used for control.Trials have shown that two independent input signals can be successfully used to control the posture of a real robotic hand and that correct grasps  may be achieved.This work demonstrates the effectiveness of a bio-inspired system successfully conjugating the advantages of an underactuated, anthropomorphic hand with a PCA-based control strategy, and opens up promising possibilities for the development of an intuitively controllable hand prosthesis. In the last thirty years several examples of robotic hands have been developed by research or industry, some designed to mimic the human hand in its manipulation dexterity and functionality, some aimed at achieving better anthropomorphism and cosmetic appearance . Great rAn advanced neuro-controlled prosthetic hand bi-directionally interfaced with a human being should address both functional and cosmetic issues; it should be dexterous enough to allow the execution of Activities of Daily Living (ADLs), and include proprioceptive and exteroceptive sensors for the delivery of consciously perceived sensory feedback . Market The communication interface between the user and the machine is the technological bottle-neck  which exAs a matter of fact, increasing the number of DoFs (i.e. dexterity) means either that the system should take care of carrying out the grasp with some level of automatism, as in the SAMS ,13,19, oAn innovative shared-control strategy could be achieved by observing and mimicking the natural biomechanical behaviour. As several studies in the neurophysiology literature report, low-dimensional modules formed by muscles activated in synchrony - also called "muscular synergies" - are used by the human nervous system to build complex motor output patterns during motor tasks ,25. In 1This concept has been exploited with the aim of controlling robotic grippers and dexterous hands by means of a lower-dimension input space, in a limited number of works. Brown and Asada explored the concept of biomechanical synergies and how they can be applied to a 17 DoFs robot anthropomorphic hand, by mechanically implementing Principal Components Analysis (PCA) and using common patterns of actuation called eigenpostures . CiocarlIn the present work a control method based on PCA (preliminary introduced in  and 41]41]) and ad-hoc built collecting data from the CyberHand sensors, in order to operate dimensionality reduction. The employment of this control strategy in driving the hand during the most typical grasps in ADLs is then presented. Different working conditions have been considered, in order to test the algorithm feasibility both simulating EMG user-generated control signals  and in the ideal case. The results obtained performing different grasping trials are finally described and discussed.The feasibility of exploiting such a control method for achieving real stable grasps is shown here on an anthropomorphic, underactuated prosthesis for the first time. This paper first of all describes the underactuated hand used, the proposed PCA-based control algorithm and particularly how the PCs matrix has been The human-sized robot hand used is a stand-alone version of the CyberHand prototype . It consThe fingers of the CyberHand comprise three phalanxes connected by hinge joints and on the hinge axes are assembled idle pulleys. A tendon is wrapped around each pulley from the base to the tip. The tendon is fixated at the fingertip and runs around the idle pulleys in the joints . When the tendon is pulled, by means of a linear slider actuated by a DC motor, the phalanxes flex starting from the base to the tip. When the motor releases the cable, torsion springs in the joints extend the finger. The CyberHand fingers thus exploit a differential mechanism that is based on elastic elements and mechanical stops. When the finger moves idling , the kinematics of such an underactuated finger depends on the length of the links/phalanxes, on the radii of the pulleys and on the stiffness of the joint torsion springs. These parameters have been chosen to obtain an anthropomorphic appearance  and a stable tip-to-tip pinch based on biological and neuroscience studies ,45. In cThe hand contains position (encoders integrated in the motors) and tendon tension sensors (able to measure the grasp force ), that cN × M) dataset matrix, where N is the dimension of the original amount of data and M is the dimension of each datum, its covariance matrix is a (M × M) matrix whose eigenvectors are the PCs, and their respective eigenvalues are the PCs weights (i.e. the amount of explained variance). The PCs can then be ordered in descending order according to their weights and used to constitute the columns of the PCs matrix (M × M). Therefore, by multiplying the original dataset by this matrix, a new (N × M) dataset is obtained, where rows/data are uncorrelated. Moreover, if the last PCs have a very low weight, they can be neglected (i.e. set to zero), obtaining a new dataset with reduced dimensionality, if compared to the original one.The PCA algorithm  allows tM-DoFs hand and a specific postures data set, we obtain M PCs constituting the M columns of the PCs matrix, once ordered according to their weight. If we suppose that only the two first PCs are significant, 2 inputs (In1 and In2), which represent the two principal hand DoFs in the new space, can be coupled to the first two PCs and remapped to the hand original M DoFs using the PCs matrix obtained from experimental data:Consequently, the PCA approach can be used for dimensionality reduction, just inverting its algorithm (explained above) and neglecting the less significant (low weight) PCs . For exaM-DoFs of the hand. The remaining components of the input vector, which are to be multiplied by the last PCs, are set to zero, in order to neglect the less significant PCs contribution.here the output vector consists of the desired This strategy could be exploited with a myoelectric hand prosthesis, where only few signals are available for control, but dexterity is desirable. By employing this "inverse PCA" algorithm, all DoFs of a dexterous robotic hand may be controlled in synergy by means of a simple two-signals control interface, e.g. two independent EMG channels tapped from the residual limb.x y real time coordinates of the mouse pointer over the monitor screen, properly calibrated into In1 and In2 range values , and fiM = 6 is the dimension of data).Wishing to employ the same control principle to drive a real robotic hand, like the CyberHand, all the described experimental procedure must be reproduced, entirely working with the artificial hand. To this aim, in order to control the six actuators of the CyberHand, a specific PCs matrix has been built just using the CyberHand prototype. The 29 objects listed in Table The obtained new matrix allows to calculate the 6 motor set-point positions (6 elements output vector in eq. (1)). Only the first two PCs have been considered significant (accounting for more than 90% of the data variance) and used subsequently to drive the hand (the remaining four PCs have been multiplied by a zero input).As a proof of concept, two independent signals like the mouse vertical and horizontal position signals have been used to modulate the two first PCs with the aim of demonstrating that they can be employed to achieve significant hand dexterity.In1 and In2 by acquiring (sampling frequency 100 Hz) the mouse cursor coordinates. It calculates the 6 set-point position values for the hand fingers by multiplying the two inputs for the CyberHand PCs matrix and sends them to the hand by means of the RS232 communication bus. Such program is also used to sample and acquire tendon tension and position sensors data.In order to experimentally test the potentiality of this control approach onto a real multi-DoF underactuated hand, a C written application for bi-directionally interfacing with the hand was implemented using LabWindows CVI . The software, running on a standard PC and graphically presented in Figure xy monitor screen plane; this is equivalent to the In1 and In2 plane, since the two spaces are proportionally bounded. Figure xy grid and how the hand behaves when varying In1 and In2, i.e. moving the mouse pointer over different areas of the screen using the computed PCs matrix. The map highlights that some areas (i.e. some PCs combinations) are more functional for certain grasp types rather than others. Generally, an excursion along the x axis (which is coupled with PC1) principally influences fingers flexion/extension, whereas variations along the y axis (coupled with PC2) mostly influence thumb abduction and slightly make the other fingers flex/extend.To allow a more immediate interpretation, results in this paper are presented with reference to the A neutral position area has been established in the left bottom corner of the map. With the mouse cursor in this area (a 15 × 15 pixels square area) the hand opens shaping in a relaxed posture. This option is fundamental for the application under investigation, as a grasp usually starts from the hand being opened. The farthest end area chosen is easily reached with a wide movement of the mouse  and does not require a precise positioning . Besides, the left bottom corner corresponds to an almost opened hand posture also when using the PCs matrix by itself.x, y pointer coordinates were noted down. Stable grasp points were characterized in terms of:The investigation on prehensile capabilities has been focused on the three forms indicated by Iberall & Arbib . Three c- number of fingers actually involved in holding the object;- tendon tension summation, i.e. grasping force ,46.grasp areas and for these grasp areas quantitatively represent the grasping force. Figure xy reference system, with color intensity based on the tendon tension summation.This procedure was manually executed and repeated (for each of the 3 objects/prehensile forms) in order to qualitatively localize The maps in Figure xy monitor screen plane, simulating user-generated input signals. Linear trajectories are desirable from an energy consumption point of view, as they represent the shortest path between two points. Three trajectories, one representative for each grasp, were generated using a Matlab  script, joining the open hand position - whose coordinates are  - to target positions  was generated with Matlab and added to the linear trajectories described above , joining the initial rest position with the identified stable points . Each time a target point was reached  in the PID algorithm, purposely set in the embedded controller in order to highlight such events.Generally speaking, as expected the recorded tension reaches a plateau every time the trajectory is kept constant in time (that is when a stable point has been reached), but with some delay with respect to the motor pattern generation, and shows a slight overshoot before settling. This last behaviour .The lateral grasp instead involves most of all thumb, which opposes to the volar aspect of the index: when the grasp force is sufficient, the object can be held between the thumb and index fingers. Thumb ab/adduction plays a role in influencing the thumb tension trend in time, causing tension oscillations; while the thumb is pressing against the object, an ab/adduction movement establishes a different thumb posture, with a consequent variation of its tendon tension.In tripod/precision grasps, only thumb index and middle fingers are involved and especially the first one exerts the most of grip force, opposing to the other two fingers.Figure The described behaviours are obtained when the hand is controlled by ideal linear trajectories in the monitor screen reference system.These same observations can be made when adding noise to the trajectories, with different noise gains (a displacement of 50 or 70 or 100 pixels at most). Obviously, the hand ability to firmly grasp the objects worsens while increasing noise amplitude. In all cases, a stable grasp is in the end achieved, even if with some delay and many more tension oscillations with respect to the ideal case ). When using the CyberHand map to perform the three considered grasps following the ideal linear trajectories, tension data show only very small fluctuations . Even if adding random noise varying into the range between 0 and 100 pixels  to the original In1, related to fingers flexion/extension) and the second input .These results show that not only the hand target point in the two inputs space influences grasp feasibility and stability, but also the trajectory followed in order to reach it and obviously the presence/absence of significant noise over the inputs. Linear diagonal trajectories are to be preferred to "right-angle" ones since they allow to operate a more balanced mixture between the contributions of the first input signal  and hold objects tightly if driven with this PCA-based algorithm. The feasibility of this approach has been demonstrated evaluating the hand performances also in a more real condition, that is in the presence of noisy input control signals. Trajectories in the inputs space , where abrupt changes in the predominance of one of the input signals over the other one do not occur, should preferably be followed. Otherwise, grasps are achieved with much more difficulty (sometimes grasps could even fail) and the hand performances significantly worsen.Results obtained driving the CyberHand with ideal linear Perspective work would firstly imply the acquisition of real efferent voluntary EMG signals picked up by surface sensors, then processed in order to extract significant intention-based features to be used as input signals. By this way, it would be possible to create an advanced, intuitive and biomimetic interface modulating PCs with EMG, thus setting up a complete 2-channel controller for a bio-inspired hand prosthesis, such as the CyberHand.CC hold shares in Prensilia Srl, the company that manufactures robotic hands as the one used in this work, under the license to Scuola Superiore Sant'Anna.GCM and CC have full access to the data in the study and take responsibility for the integrity of the data. Design of the CyberHand: CC and MCC. Design of the PCA based concept: ELS and GM. Study concept and design: CC, GCM and MCC. Software development, acquisition and interpretation of data: CC and GCM. Drafting of the manuscript: GCM and CC. Critical revision of the manuscript for important intellectual content: CC, MCC and GM. Study supervision: MCC and GM.All authors have read and approved the final manuscript.


Cartilage thickness and volume loss measurements using quantitative magnetic resonance imaging (qMRI) are suggested to detect significant cartilage changes over short time intervals. We aimed to compare these two different approaches looking at the global knee and subregions, using data from an osteoarthritis (OA) multicentre randomised clinical trial.Three hundred and fifty-five patients with symptomatic knee OA were recruited for a two-year, double-blind, randomised clinical trial evaluating the effect of 200 mg licofelone twice daily and 500 mg naproxen twice daily on cartilage loss, and 301 patients had baseline MRI. MRIs were performed at baseline, 6, 12 and 24 months. Cartilage volume and thickness in the global joint, medial and lateral compartments, and central weight-bearing subregions of the medial and lateral femoral condyles and tibial plateaus were analysed. Data were analysed for the mean value imputed for intent-to-treat (ITT-MVI) and statistical analyses were performed using two-sample Student's t-test.Cartilage mean thickness loss in the global joint, lateral and medial compartments, as well as in medial compartments stratified according to patients with or without meniscal extrusion, was significantly less in the licofelone compared with the naproxen group at 12 and 24 months. Interestingly, these data were similar to those found when using cartilage volume loss as an outcome. Although greater cartilage volume and mean thickness loss was seen in central weight-bearing subregions of the medial and lateral compartments compared with the whole compartment and also in patients with meniscal lesions/extrusion, suggesting good sensitivity to change, its high standard deviation precluded for the condyles a high statistical power and abrogated statistically significant differences between the treatment groups.These data demonstrate that both the measurement of cartilage thickness and that of cartilage volume provide the same level of sensitivity to estimate cartilage loss in a clinical trial. However, the potential of gaining statistical power with the use of thickness/volume change in knee subregions as an outcome seems negated by high inter-patient variability. Moreover, there is no superiority in statistical power by selecting patients with meniscal extrusion. Osteoarthritis (OA) is characterised by a number of structural changes that include the progressive loss over time of articular cartilage from the joint surfaces. Such loss has been evaluated mainly by arthroscopic and histological assessments in pre-clinical studies and with the use of X-rays in clinical studies. These methods have been recognised as having significant limitations, particularly in the assessment and quantification of cartilage loss in observational studies following the evolution of the disease, and in clinical trials with disease modifying OA drugs (DMOADs).A number of X-ray methods and techniques have been proposed and recommended for use in the assessment of drug effects in such trials -3. Some In recent years, the use of magnetic resonance imaging (MRI) for the assessment of musculoskeletal structural changes has expanded to include a number of new technologies that are capable of quantitatively and precisely evaluating cartilage volume/thickness over the joint surface, allowing for three-dimensional (3D) reconstruction mapping of the entire joint cartilage ,11. A fiThese methods to assess cartilage volume/thickness can be used in cross-sectional or longitudinal studies. In longitudinal studies, quantitative MRI (qMRI) has been found to be capable of precisely and reliably assessing changes in cartilage volume/thickness over time -21. MoreThe most important question, however, is the usefulness of these new investigative technologies in the context of multicentre clinical trials exploring the DMOAD effects of new drugs. A first DMOAD study has just been completed and the data of the 3D evaluation of cartilage volume loss in the major knee compartments over time in the different treatment groups have been reported . The preWe also explored whether the selective evaluation of subregions where the greatest loss of cartilage occurs, i.e. the weight-bearing areas of the condyles and plateaus, offers more sensitivity to assess changes between treatment groups than evaluation of the loss in the entire condyle, plateau or compartment. These questions of assessing the impact of DMOADs on knee structure are obviously of the utmost importance as they raise issues that cannot be answered solely by observational longitudinal studies, which have been the main focus of attention so far.The original study design and protocol have been previously described in detail . In thisBriefly, MRI acquisition allows a 3D image of knee surfaces to be produced. With the 3D surfaces of the femur and tibia, a bone-to-cartilage interface and a cartilage-to-soft tissue interface are generated. To enhance the accuracy of the numerical processing, a specific coordinate system is used to represent each surface, that is a 3D cylindrical coordinate system for the femur and 3D space coordinate system for the tibia . The samThe change in volume and mean thickness over time was obtained by subtracting the follow-up value (volume or mean thickness) from the initial (baseline) value. The percentage of cartilage loss was calculated by dividing the change (volume or mean thickness) by the baseline value, and the cartilage loss over time evaluated for the entire knee  and for each of the medial and lateral compartments. It was also calculated for: the subregions of the medial central condyle and tibia  as described previously ; the latThe extent of meniscal extrusion on the medial or lateral edges of the femorotibial joint space was evaluated for the anterior, middle and posterior horns of the menisci in which 0 = no extrusion, 1 = partial extrusion and 2 = complete extrusion with no contact with the joint space (severe). The percentage of cartilage loss in the medial compartment stratified by the absence (0) or presence (1 or 2) of meniscal extrusion was calculated as previously described .Between treatment groups, variable changes at all time points were assessed using a two-sample Student's t-test. All tests were two-sided, and a p ≤ 0.05 was considered statistically significant. All statistical analyses were performed using SAS software, version 9.1 .2). Three hundred and one patients, 147 in the licofelone group and 154 in the naproxen group, had a baseline MRI (ITT).Three hundred and fifty-five patients were enrolled in the study and randomly assigned to receive licofelone or naproxen . BaselinThe cartilage loss for the global, lateral and medial compartments is presented in terms of absolute value Table  and percTable The results of the absolute value of cartilage loss in the lateral central condyle and tibia  for both the volume and mean thickness measurements are described in Table The analyses stratified by the absence or presence of meniscal extrusion showed similar findings with the volume and mean thickness measurements in the medial compartment Table . In the 3) revealed that 92% of the findings were similar with the two methods.Comparisons of findings using changes in percentage between volume and mean thickness instead of the absolute value  knee and medial and lateral compartments provided exactly the same level of sensitivity to estimate between-treatment comparative changes in the therapeutic groups over the different time points of the study. The findings were similar when the data were analysed as absolute or relative (percentage) value of cartilage loss. Overall, these results showed that both methods of assessment, that is measuring changes in cartilage volume or mean thickness, offer the same level of sensitivity to evaluate cartilage loss at different times and to estimate the effects of treatment. These findings are in line with the calculation of the correlation coefficients between the changes over time of the two measurements, which are all greater than 0.90  regardless of the cartilage compartment , the time span  or treatment group chosen. This is inherent in the methodology because the cartilage volume and mean thickness computations assess the cartilage in a very similar way.The findings from the present study provide new information on comparative results of data generated differently, a finding that has not been reported before in the context of such studies. Previous observational longitudinal trials have employed both methods to assess cartilage loss. Although some suggestions have been made of the possible superiority of mean thickness over cartilage volume assessment in such trials, head-to-head data comparison has not been reported . The preAnother important issue to be addressed in the context of DMOAD trials is whether concentrating on the analysis of cartilage changes in the subregions, where the greatest loss of cartilage is found on the condyles and plateaus, would provide a better chance of finding significant differences between treatment groups and allow these differences to be observed earlier in the course of the trial. The results from longitudinal observational studies are certainly supportive of such an hypothesis ,12,21,26a priori hypothesis as to which area of the knee may show the greatest cartilage loss are difficult to answer. OA disease progression variability is such that any chosen knee subregion may not reflect, for a specific patient, the greatest cartilage loss over time. This is not a problem when a broader area of cartilage assessment is chosen, such as the global knee or the compartments.Research questions based on an Previous reports from longitudinal observational studies have stressed the fact that in patients with knee OA the presence of meniscal lesions or extrusion is among the most important risk factors of cartilage loss ,27. The More information gathered from future studies is needed before a final conclusion can be reached. Again, both methods of measurement, that is the percentage of cartilage volume loss and mean thickness loss, were found to provide the same level of accuracy to estimate the differences between the two treatment groups. It is noteworthy that elapsed time is important for the MRI changes because the most significant changes for both measurement techniques were seen after two years. In previous studies ,28, we dThe findings of this study demonstrate that, in the context of DMOAD trials in patients with knee OA, the measurement of cartilage loss estimated as either the change in volume or the change in mean thickness provides the same level of sensitivity to assess cartilage loss over time, as well as differences between treatment groups. Selection of patients with the greatest loss of cartilage based on certain risk factors such as meniscal extrusion, should be carefully considered, because it may not necessarily provide a better chance of identifying differences between treatment groups. The group with the more rapid progression of cartilage loss also presented higher variability between patients, as indicated by the greater standard deviation in this group. Moreover, the findings indicate that in the context of such DMOAD trials, strategies to select high-risk patients and/or to selectively analyse the subregions with greater cartilage loss, do not, in contrast to results from longitudinal observational studies, provide greater sensitivity to change and, therefore, do not provide any advantage over the use of a general patient cohort combined with the analysis of cartilage loss in the global knee or in the compartments.2D: two-dimensional; 3D: three-dimensional; DMOAD: disease modifying osteoarthritis drug; ITT: intent-to-treat; MRI: magnetic resonance imaging; MVI: mean value imputed; NSAID: non-steroidal anti-inflammatory drug; OA: osteoarthritis; qMRI: quantitative magnetic resonance imagingJPR is a consultant for ArthroVision Inc. JMP and JPP were consultants for Merckle GmbH and are consultants and shareholders in ArthroLab Inc. and ArthroVision Inc. FA is an employee of ArthroVision Inc. MD is a consultant for ArthroLab Inc. BH and DC received honoraria from ArthroLab Inc. PB and KHE are employees and SL a scientific advisor of Merckle GmbH. SL holds the patent for licofelone.All authors have read and approved the manuscript and contributed to the study design, data analysis, interpretation of data and drafting and revision of the manuscript. A data review committee  analysed the data, and JPR, MD and JMP were responsible for the accuracy of the data.


The analysis of expression quantitative trait loci (eQTL) is a potentially powerful way to detect transcriptional regulatory relationships at the genomic scale. However, eQTL data sets often go underexploited because legacy QTL methods are used to map the relationship between the expression trait and genotype. Often these methods are inappropriate for complex traits such as gene expression, particularly in the case of epistasis.Here we compare legacy QTL mapping methods with several modern multi-locus methods and evaluate their ability to produce eQTL that agree with independent external data in a systematic way. We found that the modern multi-locus methods  clearly outperformed the legacy QTL methods  in terms of biological relevance of the mapped eQTL. In particular, we found that our new approach, based on Random Forests, showed superior performance among the multi-locus methods.Benchmarks based on the recapitulation of experimental findings provide valuable insight when selecting the appropriate eQTL mapping method. Our battery of tests suggests that Random Forests map eQTL that are more likely to be validated by independent data, when compared to competing multi-locus and legacy eQTL mapping methods. For decades scientists have used a variety of analytical techniques to relate allelic inheritance patterns in the genome to variation in continuous physical traits of interest. The goal of such analyses is often to locate quantitative trait loci (QTL), or genomic locations that exert an influence on the manifested trait. Understanding the genomic location of these genetic control points may provide insight into the genetic and molecular framework responsible for enabling the trait.In the past decade, the advent of the DNA microarray and other high-throughput molecular technologies has updated the paradigm of the QTL. A QTL where mRNA expression is the complex trait of interest is generally referred to as an expression QTL or eQTL . By usinAlthough complex traits are by definition controlled by the coordination of multiple genes, the prevailing techniques for mapping them have been deeply rooted in univariate thinking - testing for genetic association to a trait one locus at a time, ignoring combinatorial effects and interactions. In contrast, Broman and Speed  defined cis-eQTL recovered by each method, 2) testing each method's high-scoring eQTL for enrichment of loci related to the target by KEGG pathway information, and 3) agreement of each method's high-scoring eQTL with systematic loss-of-function studies. In this framework we tested three variable importance measures from Random Forests (RF) [A systematic comparison of eQTL mapping approaches is necessary to inform the research community which methods work best and in which contexts. Toward that goal, the purpose of this work is twofold. First, we establish a framework for comparing available eQTL mapping methods based on the tendency of each method to map eQTL that are systematically supported by external biological data. This is important because methods papers proposing new (e)QTL mapping techniques often draw their conclusions either solely or largely on the basis of simulated data ,14,16-21sts (RF)  as well sts (RF) , the lassts (RF) , the elasts (RF) , Haley-Ksts (RF) , and comsts (RF) . We alsosts (RF) ,17,26,27In order to evaluate the performance of the eQTL mapping methods in a comprehensive way, we used both simulated data and a variety of published and previously unpublished experimental data from mouse and yeast. The mouse data sets include gene expression data from four tissues of recombinant inbred (RI) BXD mouse strains: regulatory T-cell , lung , hematopoietic stem cells , and hipWe note here that one of the goals of this comparison is to determine how susceptible each method is to the effects of linkage disequilibrium. In light of this goal we used all genotype data as-is, without prefiltering or fusing markers, or assigning surrogate eQTL post-hoc. This enables a straightforward comparison across all mapping methods.all causal loci in the 99th percentile of scores, over a range of increasing Gaussian noise in the trait. The results are given in Figure We first set out to examine the performance of each method when the underlying model generating the data was known completely. We used the actual BXD genotypes and generated traits based on four models: single causal locus, two epistatic causal loci, three additive causal loci, and three epistatic loci. These configurations were sufficient to clearly distinguish the performance of the methods. Further details of the construction of the simulated data are given in the methods section. The goal of this investigation was to determine how well each method performed at placing cis-eQTL found among all target transcripts in experimental data. Since promoter regions are often polymorphic, one would expect under optimal conditions to be able to recover an eQTL at the genomic location of many of the examined target transcripts. In this sense, the "external information" used in the benchmark is the knowledge of the genomic location of the gene -- which, when compared to QTL in general, is information unique to eQTL. The results of this assessment are shown in Figure cis-eQTL is also uncovered, with the larger studies  generally yielding higher proportions of cis-eQTL than smaller studies .A "back of the envelope" approach for gauging the practical performance of a mapping method is the proportion of We used the pathway information available in the KEGG database to establish relationships between target genes and potential regulators. KEGG was chosen because of its position as a standard in pathway information and because it is generally a better reflection of the molecular relationships between genes (compared to GO for instance). However, in principle other sources of pathway information could be used. One would not expect to recover an entire pathway in every eQTL map, but on a large scale there should be some overlap between the eQTL and the relationships contained in KEGG. We assert that methods that show higher agreement with the information in KEGG are more desirable for eQTL mapping. We formalize this by assessing the enrichment of high-scoring eQTL for loci near genes known to participate in the same pathways as the gene whose expression trait is being mapped. A graphical depiction of this idea is given in Figure P values to compare the eQTL mapping methods, with results for the yeast data shown in Figure P = 0.72 and P = 0.07, respectively, by the Kolmogorov-Smirnov test). In contrast, RFSF showed superior performance on the yeast data .We tested pathway enrichment in yeast and mouse eQTL separately. For yeast, we included an additional enrichment test, which connected target genes not to pathways in which they participate, but to pathways in which the target's known transcription factors participate. We used the distributional properties of the enrichment th percentile of scores contained a small number loci with scores of 0. We examined whether this effect put these sparse methods at a disadvantage for the enrichment tests. We found no systematic relationship between enrichment P value and the number of 0 scores in the 99th percentile.The mouse data showed more modest enrichment across all tissues and with all methods, suggesting perhaps that larger studies are needed to better recover the complex regulatory systems present in higher eukaryotes Figure . All metFinally, we combined data from two systematic loss of function studies ,32 to seth percentile are mutated. These values were aggregated over all target genes, forming a distribution for each eQTL mapping method. We compared these distributions to a null distribution (see methods for details) via the Kolmogorov-Smirnov test. We assert that the method that yields eQTL that are enriched for large changes in expression in the mutant study is the most desirable method.In this test, we collected the maximum absolute expression change observed for each target gene when genes co-localized with eQTL in the 99All methods produced score distributions that deviated significantly from the null distribution, suggesting that there is indeed consistency between the yeast eQTL data and independent mutant data. Although all methods showed significant deviation from the null, the magnitude of enrichment varied widely Figure . RFSF shAugmenting eQTL with independent information has been done previously to strengthen hypotheses suggested by the eQTL data -36. Althcis-eQTL proportions, and enrichment for KEGG pathway relationships. In preliminary analyses, we found related univariate mapping methods such as EM interval mapping [With few exceptions, the legacy methods -- HK and CIM -- stood out as the poor performers, particularly in the simulations,  mapping  and ANOV mapping -42, osteP value in the case of one-way ANOVA) that expresses the significance of the estimated correlation between a single marker and the trait, resulting in thousands of individual modeling attempts per expression trait. The multi-locus methods, in contrast, assign coefficients to multiple loci in a single final model. These coefficients are then used as locus scores. The disparity in performance between the two classes of methods is likely a result of scoring by contribution to the model (multi-locus approach), rather than scoring by significance (univariate approach).There is a fundamental difference in how the legacy linear methods  and the multi-locus linear methods  score loci. The univariate mapping methods rely on a LOD score   is a clacis-eQTL proportion test it was among the best, and in the KEGG and mutant enrichment tests it outperformed the competitors. This finding is somewhat surprising because RFSF is virtually ignored as a variable importance measure in most applications of RF, including QTL and GWAS [Although multi-locus methods in general outperformed the legacy methods HK and CIM, RFSF showed the most consistent performance overall. In the simulations and and GWAS ,17,26,27and GWAS . This iscis-eQTL proportion test and the KEGG enrichment test (see methods for details). We found that increasing the depth of the trees had a modest effect on the performance of RFPI and RFRSS, with an increase in percentage of cis-eQTL from 22.4% to 23.5% and 24.1% to 25.6%, respectively, and an increase in D statistic (for the KEGG enrichment test) from 0.186 to 0.225 and 0.241 to 0.318, respectively. Conversely, RFSF benefited more from the deeper forests, with an increase in percentage of cis-eQTL from 24.3% to 27.4% and an increase in D statistic (for the KEGG enrichment test) from 0.241 to 0.361  and grew several RFs with different characteristic tree depths. We then tested these forests with the 1 Figure . In addi1 Figure .th percentile 18.3% of the time, while RFPI scored the same loci in the 99th percentile only 10% of the time. These simulations also showed that RFPI is tightly coupled to a variable's proximity to the root node, while RFSF can give high scores even if the variable is not used close to the root node.To further explore this idea, we performed simulations where the expression trait was a function of eight loci, two with strong effects, and six with small effects. As expected, the loci with the stronger effects were used in splits closer to the root node. The causal loci with weaker effects were used to split closer to the leaves. In these simulations, RFSF scored the weak causal loci in the 99From these investigations we conclude that RFPI and RFRSS both essentially determine variable importance near the roots of the trees, and that biologically important splits further down the tree are not adequately reflected in the overall importance scores. RFSF on the other hand, recovers more biologically meaningful predictor variables (loci) when trees are grown deep, suggesting that even splits far down the tree can be reflected in this importance measure. Epistatic effects are an example of where this phenomenon is important -- often genetic interactions are weak and only present in a subset of the population. Such conditional effects are likely to manifest themselves deeper in the trees. RFSF is an attractive measure in these situations.http://cellnet.biotec.tu-dresden.de/RFSF.Because of its demonstrated performance advantages in finding biologically relevant loci, its ability to implicitly consider epistatic interactions, as well as its straightforward and readily available implementation, we recommend using Random Forests for eQTL mapping. We have prepared a short tutorial and example R code demonstrating mapping eQTL with the bias-corrected selection frequency at In this work we examined studies with genotype data in the range of thousands of markers. With the advent of next-generation sequencing and other ultra high-throughput methods, we expect to see more and more studies with hundreds of thousands, millions, or even tens of millions of SNPs. We wish to put the presented work in context by drawing a distinction between filtering methods, mapping methods, and explicit models Figure .The state of computer hardware at the time of this writing makes the multi-locus methods presented here impractical for exhaustive evaluations of data sets with millions of SNPs and tens of thousands of expression traits. The current solution to this problem is to filter the SNPs to a more tractable number using univariate tests or expert knowledge -46. ConsAs the number of markers considered falls into the tens of thousands, the problem transitions from filtering to mapping. Mapping is a combination of modeling and feature selection, and the methods we explored in this work address the mapping problem. Here the interplay between loci becomes important for accurately identifying the causal regions that should be included in an explicit model of the trait.Once causal loci have been identified reliably and the relationships between them have been characterized , one can construct a linear model, usually consisting of a handful of terms, that accurately describes the trait as a function of the genetic state of the organism. Such an explicit model, though desirable, is rarely attained.cis-eQTL is immediately extendible to physiological traits. Still, taken together, the evidence from this study indicates that QTL mapping - whatever the trait - should be performed using a multi-locus method. Using univariate methods such as HK will lead to severe underexploitation of the data.Most of the conclusions from our work have implications beyond eQTL mapping. Ideally, the concept of a knowledge-driven benchmark could be used for any physiological trait, but our approach depends on a fairly detailed knowledge of the molecular mechanisms underlying the mapped trait. Neither our notion of measuring the enrichment of regulator-target gene groups in common pathways, nor our counting of Some of the more specific conclusions from our work will need further validation in other organisms and populations. For example, the study populations used here all had roughly a 50/50 distribution of two possible alleles at each marker. Human populations are characterized by very uneven distributions of SNPs, where minor alleles can be extremely rare in a given population. Such a change in the characteristics of the data could influence the ranking of the individual methods. However, such fluctuations in the individual rankings are still unlikely to affect the general conclusion that multi-locus methods produce more informative results than univariate methods, even in GWAS and linkage studies in outbred populations -51.cis-eQTL and KEGG enrichment benchmarks. The results are depicted in Figure Finally, in this work we observed the expected relationship between study size and power to detect biologically interesting loci. We explored this phenomenon explicitly by taking subsets of decreasing sample size from the hippocampus study, and then comparing two representative methods - here RFSF and HK - using the We have compared modern machine learning and regression eQTL mapping methods with more classical mapping approaches from statistical genetics, and evaluated the methods based on their ability to lead users to loci that are more readily supported by external information. We found that the modern methods, which freely allow the consideration of all loci simultaneously, generally outperform their classical counterparts in this regard. In particular, we found that Random Forests consistently mapped the most promising eQTL. Random Forests bias-corrected selection frequency, a novel importance measure, performed better in these tasks than the established permutation importance and RSS importance.We used expression data from four eQTL studies in four different tissues in recombinant inbred BXD mouse strains: regulatory T-cell, lung, hematopoietic stem cells , and hipmtry parameter was set to the default  and the node size was also the default of 5, unless otherwise noted. We then extracted unscaled permutation importance measures (RFPI), residual sums of squares importance measures (RFRSS), and selection frequencies (RFSF) from the forests for use as the scores for each marker.We used the reference implementation of Random Forests  in R forWe estimated and accounted for bias in RFSF as follows. Using the actual genotype data as predictors, we fit 500 10-tree forests to independent draws from Gaussian noise. This resulted in 5,000 trees, equal in size to the forests used in this work. We collected the selection frequencies for each marker and subtracted the mean selection frequency to yield a vector of correction factors -- one value for each marker. Subtracting this vector of correction factors from the observed selection frequencies (from the observed data) gives bias-corrected selection frequencies Figure . In the spls R package to map eQTL, performing cross-validation on every target to determine the optimal parameters for each fit. eta, the thresholding value, was allowed to vary between 0.3 and 0.7, to prevent both overfitting and a model that was too sparse to score multiple loci. The number of hidden components was allowed to vary from 1 to 5. A final fit was performed with the optimal parameters, and the absolute value of the coefficients was used as the score for each marker.Chun and Keles  recentlyelasticnet package for R. The lasso is a special case of the elastic net with lambda equal to (or very near) 0. For each target gene examined, we took the absolute value of the lasso coefficients for a fit performed with the s parameter determined by 10-fold cross-validation, with an imposed minimum of 0.5. These coefficients were used as the score for each marker.The lasso , a regreThe use of the elastic net  was the qtl package for R. LOD scores were calculated at the marker locations.We used the implementation of Haley-Knott regression  availablqtl package for R, with the method argument set to "EM", and all other arguments set to their default. LOD scores were calculated at the marker locations.To perform composite interval mapping  we used To simulate eQTL with known underlying models, we used the full BXD genotype matrix, available from the GeneNetwork . This maall causal loci.Each model type  was simulated independently 50 times, and each mapping method was applied to the same data. For each simulation and for each mapping method, the maximum (i.e. worst) rank among the set of causal markers was recorded in each noise level. The median of these values (over the 50 simulations) was used to reflect the performance of a given mapping method over the increasing levels of noise. Lower values represent the ability of a method to assign high scores to cis-eQTL was assessed by counting the number of expression traits where a marker within 500 kb (for mouse) or 50 kb (for yeast) of the midpoint of the target gene's genomic location had a score in the 99th percentile of the scores for the respective target gene. These cutoffs, though arbitrary, reflect the difference in complexity between the yeast and mouse genomes - the conclusions drawn from the benchmark are not heavily influenced by this choice. This number was then divided by the number of total expression traits examined for the respective data set.Performance based on the proportion of recovered th percentile were selected for the enrichment test. The hypergeometric test was used to test this set for the enrichment of markers mapping to genes participating in the same KEGG pathway as the target gene. If multiple pathways existed for any expression trait, all were tested and the minimum P value was used as the representative P value.Each expression trait we tested mapped to at least one KEGG pathway, and each gene found in the KEGG pathway was mapped to the nearest marker. If no marker fell within 5 Mb of a gene, the gene was omitted. For each expression trait, the markers having scores in the 99In the case of the yeast eQTL data, we additionally assessed enrichment of pathways in which transcription factors binding to the target gene participate. As a basis for mapping transcription factors to their targets, we used . We did P values that deviate somewhat from the uniform distribution, we calculated an empirical null distribution of P values. To construct this distribution, we assigned scores to the markers, drawn randomly from a Gaussian distribution with mean 0 and standard deviation of 1. We then took the markers in the 99th percentile and performed the proposed enrichment test. This was performed for an equivalent number of expression traits contained in the actual data sets. The actual enrichment P values were corrected against this empirical null distribution of enrichment P values.Since in this test even randomly selected markers yield P values for each method. As a summary measure for each method's deviation from the uniform distribution, we used the D-statistic as given by the Kolmogorov-Smirnov test. The test was one-sided with the alternative hypothesis that the observed cumulative distribution function accumulated faster than the reference (i.e. uniform) distribution.We plotted the empirical cumulative distribution function (ECDF) of the corrected enrichment th percentile of scores for that target. For markers mapping to experimentally repressed regulator genes, we collected the maximum absolute log2 expression ratio (repressed expression divided by wild-type expression) for the appropriate target gene, aggregating them over the whole set of mapped expression traits. We then compared the distribution of the selected maximum absolute log2 ratios generated by each eQTL mapping method by the Kolmogorov-Smirnov (KS) test, collecting the associated P value and D statistic. As a reference distribution in the KS test, a null distribution was constructed by a similar aggregation of maximum absolute fold changes, only with the association between scores and markers randomized for each target gene. The test was one-sided with the alternative hypothesis that the observed cumulative distribution function accumulated slower than the reference distribution. Distributions with a tendency toward higher scores and deviating significantly from the reference distribution suggest an agreement between the eQTL and loss-of-function studies.Systematic loss of function data in yeast ,32 was unodesize argument to 5, 15, 29, 57, and 114.To assess the impact of tree depth on each RF importance measure, we used the yeast eQTL data and recomputed eQTL maps for all expression traits, varying the nodesize argument dictates whether or not a node may be split -- if the number of observations in the node under consideration is greater than nodesize, the node may be split. Otherwise the node is not split and is marked as a terminal node. The default value of nodesize is 5 -- this is the value used in the main body of the study. By selecting a nodesize of 114 (the number of samples in the yeast study), we ensure that splitting stops after the first split. The other values are intermediate steps, each about half the size of the last. We then assessed the improvement in the enrichment of KEGG pathway members and proportion of cis-eQTL identified when growing the trees deeper, using the forest with nodesize 114 as the baseline.The JM and AB conceived the benchmarks and analysis. JM performed the analysis and drafted the manuscript. RA assisted in the analysis. KS conceived and carried out the lung and T-cell studies. All authors reviewed the final manuscript.


Mathematical modeling is being applied to increasingly complex biological systems and datasets; however, the process of analyzing and calibrating against experimental data is often challenging and a rate limiting step in model development. To address this problem, we developed a systematic methodology for calibrating quantitative models of dynamic biological processes and illustrate its utility by validating a model of TRAIL (Tumor necrosis factor Related Apoptosis-Inducing Ligand)-induced cell death.We propose a serial framework integrating analysis and calibration modules and we compare various methods for global sensitivity analysis and global parameter estimation. First, adequacy of the network structure is checked by global sensitivity analysis to changes in concentrations of molecular species, validating that the model can reproduce qualitative features of the system behavior derived from experiments or literature surveys. Second, rate parameters are ranked by importance using gradient-based and variance-based sensitivity indices, and we systematically determine the optimal number of parameters to include in model calibration. Third, deterministic, stochastic and hybrid algorithms for global optimization are applied to estimate the values of the most important parameters by fitting to time series data. We compare the performance of these three optimization algorithms.in silico experiments and thereby provides a generalized workflow for the construction of predictive models of complex network systems.Our proposed framework covers the entire process from validating a proto-model to establishing a realistic model for  Comprehensive and predictive models of biological systems are expected to improve our ability to analyze complex systems, from molecular pathways to populations of organisms. Thus, there is much interest in sophisticated computational modeling techniques and high-throughput data generation . One of Model calibration or regression by data fitting is necessary for computational modeling in any field of science or engineering. Systems biology faces the same challenge to construct experimentally validated models. However, formal tools for quantitative biological models have not been established yet and manual analysis is common in practice. In fact, manual fitting has the advantage that researchers may apply their experimental intuition or prior knowledge to the model relatively easily with minimal aid of mathematical or computational skills. However, the structural complexity of signaling pathways makes it difficult to fit the model heuristically based on intuition or simple analyses only. There are three dominant differences between manual fitting and systematic calibration: (1) As in Yang's work , manual We have developed a systematic calibration procedure for testing and improving models as shown in Figure In the second step, we assess whether a subset of pathway reactions dominantly affects the model outputs, focusing on the outputs that are described by the experimental data to be used in the calibration step Figure .In the third step, we perform a quantitative fit, or calibration, of the model to experimental data, to determine parameter values that minimize the deviations between experimental results and model simulations Figure .Lastly, as the model evolves in light of newly available data, the overall procedure should be iterated. We believe that by implementing the intermediary steps where sensitivity analyses are used both to assess the qualitative behavior of the model and determine which parameters to optimize, our systematic method will significantly facilitate model calibration.Analysis of sensitivity with respect to initial species concentrations provides a criterion for the qualitative correctness of a cell signaling model. Sensitivity analysis assesses how changes in model inputs contribute to model output variability, and its ability to deduce model input-output relationships makes sensitivity analysis one of the critical parts of model development, verification, and evaluation. Changes in initial species concentrations can mimic the effects of mutations or changes in the expression level of the molecular players involved, and the sensitivity of the model output to changes in initial species concentrations should match the expected change in system behavior.The simplest and most generally used sensitivity analysis method is a gradient-based index as follows,yi and pj respectively. This method is often called local sensitivity because it reflects output variability accurately near a given nominal input value, p*. However, most kinetic parameters are quite uncertain and a range rather than a single parameter value is available, either from the literature or from biophysical constraints on the reactions. Thus, "model-independent", or more precisely, parameter-independent, global sensitivity analysis techniques have generated great interest[Sij(t)|dt, are then averaged to determine global sensitivity [where model outputs and inputs are represented as  interest. Averagisitivity . ImportaThe model on which we applied our methodology simulates the response of a single cell to TRAIL. TRAIL is a protein ligand which triggers the process of programmed cell death, or apoptosis. This model of TRAIL-induced cell death signaling network encompasses the activation of initiator (caspase-8 or C8) and effector (caspase-3 or C3) caspases, the onset of mitochondrial outer membrane permeabilization and the death of the cell, as marked by cleavage of the caspase-3 substrate, PARP. According to a recent study , extrinsm, agrees with its pro-apoptotic nature . We first evaluated sensitivities of the cleavage of PARP with respect to changes in initial species concentrations, sampling over a range of plausible parameter values (range described in Methods). In this case, instead of averaging the sensitivities over the sampled range of parameter values, we plotted their distributions in a box plot, to preserve the directionality of the effect in the sign of the sensitivities Figure . We intee Figure . By simiSecond, the absolute value of sensitivity provides a measure of how strongly the perturbation of a single species' concentration affects the model output. The sensitivity with respect to perturbation of XIAP was found to be relatively high on average, implying that the model output can be changed dramatically by small changes in XIAP Figure . This prIn a third type of assessment of the results our sensitivity analysis of PARP cleavage, we analyzed the influence of the uncertainty of rate constants on the sensitivity with respect to initial species concentrations. Sensitivities that are not affected by parameter values will have narrow distributions, and by consequence, their sensitivity value is very reliable. The sensitivities related to the perturbation of some species like XIAP and caspase-8 were found to be broadly distributed and thus to be relatively uncertain Figure . ParticuWhen global sensitivities are determined by averaging local sensitivities as we did above, no assumptions are made in the relationships between input parameters and output variables, so this method is applicable in most nonlinear and non-monotonic problems. For the model of TRAIL-induced apoptosis, the significance of each rate parameter to the total model output variation can be identified by global sensitivity analysis in a matrix of 70 parameters (inputs) by 58 variables  Figure . The heidelay) that measures how long it takes from the time of TRAIL addition to the time at which 50% of PARP is cleaved. Another is the switching time (tswitch), which measures the rapidity of PARP cleavage after caspase-3 (C3) activation. These features are variables that are discontinuous with respect to input parameter variation, and to determine the dominant parameters in controlling tdelay, we therefore explored other sensitivity analysis methods to replace gradient-based sensitivity analysis.Importantly, there are often biologically meaningful quantities of interest for which partial derivatives cannot be defined, and these may be the outputs for which the dominant parameters need to be identified. For example, for TRAIL-induced apoptosis we can define biologically meaningful features of the dynamic behavior of cell death. One example is the delay time  was explored. As the contour of the objective function showed, there exists a valley-shaped optimum in the lower part of parameter space. It is interesting that this characteristic contour of the objective function is relevant to the discussion of dominant parameters in sensitivity analyses. The parameter k8 was ranked as one of the eight most influential by only one type of sensitivity analysis , while k9 is ranked by all three sensitivities . Out of 6561 local estimations, 6550 cases successfully detected their adjacent optimum solutions, although 11 cases failed due to their poor initial guess values. In Figure For the model of TRAIL-induced cell death, we compared the performances of the deterministic multi-start method and SRES in a global optimization of the eight most dominant parameters identified by average of local sensitivities. For the multi-start method, local estimations started from the lower bound, middle value and upper bound in the range of each parameter so that the total number of cases was 6561 , a biologically relevant quantity that is not a state variable of the model. Undoubtedly, this type of sensitivity analysis will prove useful within our outlined framework for other models as well, for example in models of oscillatory systems where, in certain cases, the period of the oscillations is more meaningful than their amplitude. Finally, while comparing different model calibration algorithms, we showed that global sensitivity analysis could successfully identify the parameters to include in quantitative optimization, allowing great computational savings by constraining the search to the important model dimensions. In the future, we foresee that the predictive quality of models would be further improved by repeating this cycle of model validation, identification of dominant parameters and optimization with different model outputs that are controlled by other parameters, allowing the determination of more and more parameter values.In this report, we proposed a framework for efficiently calibrating computational models of biological systems, and applied it to a model of TRAIL-induced apoptosis while comparing several sensitivity analysis methods and model optimization algorithms. Importantly, we showed how sensitivity analysis can be used to rapidly test whether the model structure adequately allows qualitative matching to the behavior of the biological system. This step implements a minimal qualification, focusing the initial search on the qualitative performance of the proto-model. Within our framework, this validation step is required before proceeding to quantitative optimization of the model, ensuring that computationally costly optimization algorithms are used effectively. Furthermore, we showed how global sensitivity analysis methods can be used to identify the parameters that dominantly regulate the dynamics of the output of interest. With the application of Sobol's algorithms, we were also able to identify parameters that control the TRAIL-induced delay time to cell death (tdelay) varied from cell to cell due to inherent fluctuations in cell state [delay is the median in the population of more than 100 cells. The cleavage of effector caspase reporter protein (EC-RP) was quantified at 3-min intervals, and used for fitting the model output corresponding to cleavage of PARP, the effector caspase substrate. In addition, once the rapid cleavage of EC-RP is complete, then the output signal cannot be accurately measured by microscopy - it becomes extremely noisy as the cells detaches from the surface and moves out of the focal plane, and thus poorly reports cellular activity. Therefore we neglected the fluctuations in the experimental data after cleavage of PARP reaches a value of 1. Instead, we fit the model to a plateau with a value of one.The serial methodology was applied to fit a recently described mathematical model of TRAIL-induced cell death signaling . This moll state . Figure ll state  actuallyWe used the weighted least squares method for parameter estimation. The objective function to minimize isp is the set of parameters, Nexp is the number of experiments, wi is the weight associated with the measurement of the ith experiment, yi(p) is the corresponding value computed from the model. The weight may be given differently depending on reliability of specific experimental measurement. If there are uncertain or less confident data points, those should take less part in evaluating the objective function by using smaller weight than other data points. Since we took all the data with equal importance, the weights were all set equal to 1 in this case. The estimation calculation was stopped if the normalized difference of objective function values between two successive iterations was less than 1E-6.where 5, k–5, kc5), caspase-6 cleavage by caspage-3 , PARP cleavage by caspase-3 , Bid activation by cleaved caspase-8 , Bcl2 reacting with activated Bax in the mitochontrial compartment , Bax2 reacting with Bcl2 , Bax4 reacting with Bcl2 , Cytochrome c and Smac release from mitochondria  had a range set to between 10 and 1/10 times of their nominal value. The rate constants regarding ubiquitination of cleaved caspase-3 by XIAP  and XIAP reacting with the apoptosome and Smac  have an even narrower range between 2 and 1/2 times the nominal value. The nomimal values were either obtained from the literature or set by trial and error to allow the model to reproduced experimental data, as previously described [The plausible range for uncertain rate constant parameter values was set around a nominal value of the corresponding parameter. For most parameters, the upper and lower bounds were set as 100 and 1/100 times the nominal value, respectively. For several parameters whose nominal values are considered to be relatively certain by previous experiences we set narrower ranges to minimize the effect of uncertain parameter values in the global sensitivity analysis. For instance, forward, backward and catalytic rate constants relevant to caspase-3 cleavage by caspage-8  estimation solver and a weighted least square objective function. The High-Performance Computing facility at Harvard Medical School was utilized for intensive computations. The repetitive jobs of the multi-start estimation as well as Sobol's sensitivity analysis were parallelized and distributed to over 200 computing nodes . For comparisons between different algorithms, the CPU usage time of each node was summed as if a single computing machine was utilized.All computations were performed using JACOBIANKAK performed the simulations and SLS, SG, JGA and JMB contributed to analysis and interpretation of data. KAK wrote the draft and SLS, SG, and JGA revised the manuscript critically. PKS and DHK conceived of the study and participated in its design and coordination. All authors read and approved the final manuscript.The dominant parameters and the estimated results. This pdf file details the dominant parameters concerning their related reactions, parameter ranges and estimated values by different optimization methods.Click here for file