Finite element analysis (FEA) is an ideal tool with which to investigate the role of the PDL, however inclusion of the PDL in FE models is complex and time consuming, therefore consideration must be given to how it is included. The aim of this study was to investigate the effects of including the PDL and its fibrous structure in mandibular finite element models. A high-resolution model of a human molar region was created from micro-computed tomography scans. This is the first time that the fibrous structure of the PDL has been included in a model with realistic tooth and bone geometry. The results show that omission of the PDL creates a more rigid model, reducing the strains observed in the mandibular corpus which are of interest when considering mandibular functional morphology. How the PDL is modelled also affects the strains. The inclusion of PDL fibres alters the strains in the mandibular bone, increasing the strains in the tooth socket compared to PDL modelled without fibres. As strains in the alveolar bone are thought to play a key role in bone remodelling during orthodontic tooth movement, future FE analyses aimed at improving our understanding and management of orthodontic treatment should include the fibrous structure of the PDL.Alveolar bone remodelling is vital for the success of dental implants and orthodontic treatments. However, the underlying biomechanical mechanisms, in particular the function of the periodontal ligament (PDL) in bone loading and remodelling, are not well understood. The PDL is a soft fibrous connective tissue that joins the tooth root to the alveolar bone and plays a critical role in the transmission of loads from the tooth to the surrounding bone. However, due to its complex structure, small size and location within the tooth socket it is difficult to study  One of the most widely used methods for theoretical analysis of biological structures is finite element analysis (FEA) . FEA is In any FE model of the mandible (i.e. the whole mandible or a section of the mandible), there are several different materials which need to be modelled. Depending on the size and level of complexity of the model, materials which are commonly considered include enamel, dentine, periodontal ligament (PDL), cortical bone and trabecular bone. Although there are many components involved, the PDL causes arguably the most difficulty in dental FE models . The PDLThe PDL contains both elastic components, mainly collagen fibres, and fluid components such as blood and lymph vessels and interstitial fluid . MicroCTWhen simulating masticatory loading of the mandible in a FE model, the way in which the PDL is modelled can have a considerable influence on the results produced. Whether to include the PDL and what material properties to assign if it is included, are the subject of much debate throughout the literature –20. Whene.g. from a new exercise regime, whereas bone resorption is often associated with a decrease in strain magnitudes, e.g. due to prolonged bed rest [Many experimental studies have shown that bone mass and structure is adapted to its mechanical environment and that strain magnitudes (among other factors such as strain frequency) play a key role in this adaptation. Bone formation has been linked to an increase in strain magnitude, bed rest –35. One bed rest . The crobed rest , typicalbed rest . Load trWhether orthodontic tooth movement is triggered by strains in the alveolar bone or in the PDL remains the subject of much debate within the literature . In the et al. [Different hypotheses have been suggested regarding the biomechanical nature of orthodontic tooth movement. According to the “pressure-tension hypothesis”  tooth moet al.  for a moet al. [Previous FE models have shown strains in the alveolar bone to be much lower than those predicted by Frost’s mechanostat, for example , 43–45. et al. , 48 showin vivo in humans) and consider how the bone might adapts to them. The results of our previous study [et al. [The aim of the current study was to investigate the effect of including the PDL in mandibular FE models under occlusal and orthodontic loads, and the effect of including the fibrous structure of the PDL in these models. The purpose is to increase our understanding of the stresses and strains in the bone under these loads . . The μCT data set was exported as a stack of 8-bit TIFF (tagged image file format) images with a voxel size of 0.040 mm in all three directions, and imported into AVIZO  for image segmentation.Since a detailed representation of the three-dimensional geometry of the trabeculae was to be included in the FE models, a Ray Casting Algorithm (RCA) method  was usedThe model contained just the molar region including the second premolar and first and second molars. Pre-mortem loss of the third molar meant it was not present in this specimen, and could, therefore, not be included in these models. Further manual segmentation was required to separate different materials within the model. A material was added to fill the space between each individual tooth and alveolar bone, to represent the PDL. This meant the PDL material completely surrounded the tooth root and joined the tooth root to the alveolar bone for all three teeth. Cortical and trabecular bone regions were also separated from each other, with alveolar bone being defined the same as cortical bone. A material was then added to fill the space between the trabeculae, creating a combined structure to represent the trabecular tissue as shown in Solid 10-noded high-order tetrahedral elements (SOLID187)  were useFor this study we use cortical bone to refer to the dense bone around the outer surface of the mandible; ‘trabecular bone’ refers to the material forming the individual trabeculae; ‘trabecular filling’ refers to the material in the pores surrounding the individual trabeculae; and ‘trabecular tissue’ refers to the trabecular bone and trabecular filling combined. These terms are illustrated in The boundary conditions applied to the model are shown in Three separate loads were applied to the models: an occlusal load and two different orthodontic loads. For the occlusal load, a total load of 500N was distributed over a small area around the centre of the occlusal surface of the crown of the first molar, directed in the corono-apical direction . A load Previous FEA studies of whole human mandibles using tetrahedral finite element meshes have included convergence tests, for example –63, and The six different models were created by varying the material properties assigned to different elements, with or without the addition of PDL fibres. All materials in the models were assigned homogeneous, isotropic and linear elastic material properties. The fibre-reinforced matrix structure of the PDL was represented in these models in a similar method to that used in an earlier model . AlthougThe first model to be developed was the most complex fibrous PDL and trabecular structure model. The material properties for the other models were then determined by optimisation so that the tooth displacement for each model matched the displacement in the fibrous PDL trabecular structure model. Therefore, the effective elastic modulus of the solid PDL was the same as the fibrous PDL, and the effective elastic modulus of the trabecular structure model was the same as the bulk trabecular material model. From this it follows that any differences observed in the strain values between models could then be attributed to structural differences , rather than to material property differences. The material properties assigned to each material in the models are shown in To provide a straightforward visual assessment of the results from the different models, pair-wise comparisons were made by subtracting the element strains in one model from those in a second model, and presenting the results as colour-coded difference plots. This was done for both maximum (tensile) and minimum (compressive) principal strains.i.e. in the bones surrounding the PDL, or whether it also affects bone further away from the PDL.To provide a more precise comparison of the results, maximum and minimum nodal principal strains were also plotted and compared for the different models. Strain magnitudes were extracted from nodes on the outer surface of the cortical bone along a plane in the buccolingual direction through the centre of where the 500N load was applied. Extracted strains were plotted from nodes on the buccal and lingual sides of the mandibular corpus, from the top down to the lowest node on the inferior surface. The fact that we obtained strains from the outer surface of the cortical bone for the occlusal loads allowed us to study if the ways in which the PDL and trabecular tissue are modelled only affects strains locally, i.e. adjacent to the PDL, around both the mesial and distal roots of the loaded molar. For the mesiodistal load, results were obtained from nodes on the mesial and distal sides of each tooth root. Similarly, for the buccolingual load, results were obtained from nodes on the buccal and lingual sides of each tooth root. In both cases, the nodes  were located on a plane approximately through the apex of the tooth roots. Again, maximum and minimum principal strains were extracted from each node and were plotted against those from other models.To compare the results from the two orthodontic loads, nodal strain values were selected from the inside surface of the alveolar bone, Difference contour plots comparing maximum principal strains and minimum principal strains for bulk trabecular material and trabecular structure models are shown in The difference plots for all three PDL types  show thae.g. no PDL vs solid PDL. In each case, strains in the second model have been subtracted from strains in the first model. As in The results in Comparing the solid PDL and fibrous PDL models, there are large differences in the alveolar process with the fibrous PDL model generally having the higher strains. However, for most of the mandibular body, especially on the lingual side, the strains are similar. In general, the plots show that strain magnitudes differ more between the no PDL model and either of the two models with a PDL (either solid or fibrous), than between the solid PDL and fibrous PDL models.με for the no PDL model, but strains of one to two magnitudes higher for the models including PDL (solid and fibrous). The fibrous PDL model shows the highest strain magnitudes of the three models. However, despite the large differences in strain magnitudes, there are some similarities in the spatial distribution of high versus low strain magnitudes between the fibrous and the solid PDL model Click here for additional data file.S2 Appendix(DOCX)Click here for additional data file.S3 Appendix(DOCX)Click here for additional data file.S4 Appendix(DOCX)Click here for additional data file.


Network oscillations are ubiquitous across many brain regions. In the basal ganglia, oscillations are also present at many levels and a wide range of characteristic frequencies have been reported to occur during both health and disease. The striatum, the main input nucleus of the basal ganglia, receives massive glutamatergic inputs from the cortex and is highly susceptible to external oscillations. However, there is limited knowledge about the exact nature of this routing process and therefore, it is of key importance to understand how time-dependent, external stimuli propagate through the striatal circuitry. Using a network model of the striatum and corticostriatal projections, we try to elucidate the importance of specific GABAergic neurons and their interactions in shaping striatal oscillatory activity. Here, we propose that fast-spiking interneurons can perform an important role in transferring cortical oscillations to the striatum especially to those medium spiny neurons that are not directly driven by the cortical oscillations. We show how the activity levels of different populations, the strengths of different inhibitory synapses, degree of outgoing projections of striatal cells, ongoing activity and synchronicity of inputs can influence network activity. These results suggest that the propagation of oscillatory inputs into the medium spiny neuron population is most efficient, if conveyed via the fast-spiking interneurons. Therefore, pharmaceuticals that target fast-spiking interneurons may provide a novel treatment for regaining the spectral characteristics of striatal activity that correspond to the healthy state. The basal ganglia (BG) comprise the largest subcortical system in the brain and play a crucial role in motor control and cognitive processes –8. DysfuRecently, oscillations (20–80 Hz) have been observed at the level of individual MSNs firing and local field potential in the striatum of both awake and anaesthetized animals , 37–39. Here, we use a spiking neuron network model of the striatum to isolate the mechanisms underlying the transmission of cortical oscillations to not only the MSNs that receive direct cortical inputs but also to the other unstimulated MSNs. We systematically studied the effect of FB and FF inhibitions, the density of outgoing projections and the overall activity of striatal cells on the oscillatory activity of the striatum. We show that FSIs, despite their asynchronous spiking, play a crucial role in efficient propagation of cortical oscillations to the MSNs, especially the ones that did not receive direct cortical oscillations. In the absence of FSI inputs, spread of oscillations to the unstimulated MSNs requires either unphysiologically high baseline firing rate of the MSNs or direct cortical stimulation of a very large fraction of MSNs. Our findings reveal a new role of FSIs in modulating the transfer of information from the cortex to striatum and by modulating the activity and properties of the FSIs, striatal oscillations can be controlled very efficiently.i was described by the following equation:CMSN and The neurons in the network were modeled as leaky integrate-and-fire neurons. We considered two types of striatal neurons: medium spiny neurons and fast-spiking neurons. Subthreshold dynamics of the membrane potential i was described similarly by the following equation:The subthreshold dynamics of the membrane potential The initial membrane potentials of both MSNs and FSIs were chosen from a uniform distribution from -86.3 to -55 mV and from -82 mV to -65 mV, respectively, in order to avoid any unwanted synchrony, caused by the initial conditions in the simulation runs.We have chosen to use the simple leaky integrate-and-fire neuron model that lacks oscillatory features and, therefore, all frequency responses are a direct outcome of network interactions . More coIt has been estimated that there are around 2800 MSNs located within the volume of the dendrites of one medium spiny cell. MSNs are the dominant neuron type in the striatum (up to 95% in rodents ), and thτexc and i was equal to:Excitatory synaptic input was modeled by transient conductance changes using the alpha-function such that:ectively . Inhibiti. The inner sum runs over the sequence of spikes (n’s), and the set m. The total inhibitory conductance i was given by:Here, DFF = 1 ms) compared to the delay used for FB inhibition (DFB = 2 ms)i. The excitatory conductance i was given by:MSNs mainly project onto the dendrites of other MSNs and FSIs tend to project onto the soma, therefore we used a shorter delay for FF inhibition  and number  of neurons, which depended on the particular studied setup, received the background activity and sinusoidal current, corresponding to an external stimulation from other brain areas, given for neuron  imposed . The sin imposed . The bacms using the fourth order Runge-Kutta method. This small time step was necessary because of the fast dynamics of the FSIs. Stimulation ran for 1 s and each explored scenario was repeated and averaged 10 times, yielding 10 trials.All network simulations were written in the Python interface to NEST . The dynIn this study, we wanted to better understand the sole striatal network response to oscillatory input and therefore we reduced our model in order to tackle this complex question. The 2800 MSNs located within the volume of the dendrites of one medium spiny cell constitute only a small volume of striatum and, hence, it is reasonable to assume a distance-independent random connectivity in the simulated subpart of the network. It is worth mentioning that our results remained qualitatively unchanged when we assumed distance-dependent connectivity (data not shown) or included GABAergic synapses between FSIs. In the striatum, FSIs are also interconnected by gap junctions, but it has been predicted that the synchronization effects due to gap junctions are quite low when they fire at moderate intensity . ModulatS(f) of the population activity, directly from the spike trains, using the Fast-Fourier-Transform with the sampling frequency set to 200 Hz. We defined the oscillations index as the relative power in the frequency band of interest as (±5 Hz around the driving frequency of interest Cf):Network activity in the population that consisted of MSNs was evaluated by counting the overall spiking activity in time bins of 5 ms, which was equal to the number of active cells per time bin. To estimate the strength of oscillations we used the fact that oscillations introduce peaks in the power spectral density of the population activity. Therefore, we estimated the spectrum Cf ± 5 band and, as a result, OI values were higher.When the network was oscillating strongly, most of the power was contained in the xi and yi denoted the two zero-mean vectors of two spike trains. For identical vectors xi and yi, the correlation C was equal to unity. Since we were interested in millisecond synchronization, the bin size was set to 1 ms.To measure the spike train synchronicity, we used Pearson’s correlation coefficient:The firing rate of individual neurons was estimated as the average spike count per second. The mean network firing rate was then obtained by averaging the firing rates of all neurons in the network. The values in different groups were compared using the Mann-Whitney U-test and a p < 0.01 was considered statistically significant.The striatum is a purely inhibitory recurrent network driven by excitatory inputs from the cortex and thalamus. An important feature of the striatum network is that the FF inhibition from FSIs to MSNs and FB inhibition from MSNs to other MSNs are clearly segregated. Individual striatal neurons do not act independently to affect rhythmic population activity, and here we use a spiking neuronal network model to study how they interact with each other and time-dependent external stimuli to induce oscillatory activity in the MSN population.When a fraction of MSNs was stimulated with sinusoidal inputs at 80 Hz in the addition to the background input, while the rest of MSNs received only the Poisson inputs , the aveNext we tested whether stimulation of FSIs alone was sufficient to transmit the cortical oscillations to MSNs over several frequencies . We founBecause connection between MSNs and FSIs are only unilateral and FSIs also receive incoherent oscillatory inputs, they exhibit asynchronous activity irrespective of the input amplitude . Raster max = 150 pA, the peak was not visible, while for Amax = 250 pA, it was already quite prominent) (max = 250). Increase of the inhibitory rise constant had a similar effect and augmented the peak of the oscillations in the MSN population.A detailed analysis of the FSIs activity showed that only a few FSIs spiked relative to the oscillation cycle  when oscominent) . When FSominent) . FinallyFFinh), and area of the IPSP. Indeed, increasing the strength of the FF inhibition (JFFinh) increased the OI  within a physiologic range, oscillations could be transferred to MSNs when as little as 16 FSIs  were driven by cortical inputs (max) was set to 350 pA  and was kept constant throughout all simulations. When only a fraction of FSIs were stimulated the irregular spiking activity of unstimulated FSIs could slightly impair the transmission of oscillations by adding noise to the oscillatory FSIs inputs to MSNs. In our model, cortical oscillations are first transferred to the FSI activity and then imprinted on to the activity of MSNs. That is, once oscillations are established in FSIs, e.g. by increasing the drive to FSIs, the transmission of the oscillations depends on the effective FSIs inputs to the MSNs. The effective FSIs input to MSNs in turns depends on the number of FSIs inputs to individual MSNs, strength of FF inhibition (Jd the OI . A simill inputs . The maxmax = 250pA) and Poisson-type synaptic background inputs while the rest of the MSN network received only Poisson-type synaptic background inputs and fired less than 1 Hz on average  increased the power of oscillations compared to the low firing rate (ongoing activity) . This surage see . For 6.2Oscillations are a ubiquitous feature of the population activity in the brain. Signatures of behavioral tasks and brain diseases (such as Parkinson's disease) can be observed in the dynamics of oscillatory activity of the BG . TherefoWe have shown that the selective activation of striatal FSIs via asynchronous oscillatory inputs could successfully entrain the MSN population to oscillate at the input driving frequency. Strong and divergent connectivity of FSIs implies that even weak oscillations in FSI population activity can be spread to the whole MSN population.Here we have used a reduced model of the striatum and simplified neuron models, yet the model is powerful enough to include the effects of neuro-modulators. In general, neuro-modulators such as acetylcholine (Ach) and dopamine affect the network activity by modulating the effective strength of cortical excitation, feedback and feedforward inhibitions . In our FSIs and feedforward inhibition are a common property of neuronal networks throughout the brain and play crucial role in neural computations. For instance, FF inhibition sets the window of temporal integration and spiking and thereby contributes to the control of firing rate and correlations. Moreover, FSIs provides a simple circuit mechanism to gate the propagation of spiking activity –64. Furt


Magnetic resonance-guided radiotherapy (MRgRT) is a new and evolving treatment modality that allows unprecedented visualization of the tumor and surrounding anatomy. MRgRT includes daily 3D magnetic resonance imaging (MRI) for setup and rapidly repeated near real-time MRI scans during treatment for target tracking. One of the more exciting potential benefits of MRgRT is the ability to analyze serial MRIs to monitor treatment response or predict outcomes. A typical radiation treatment (RT) over the span of 10-15 minutes on the MRIdian system  yields thousands of “cine” images, each acquired in 250 ms. This unique data allows for a glimpse in image intensity changes during RT delivery. In this report, we analyze cine images from a single fraction RT of a glioblastoma patient on the ViewRay platform in order to characterize the dynamic signal changes occurring during RT therapy. The individual frames in the cines were saved into DICOM format and read into an MIM image analysis platform  as a time series. The three possible states of the three Cobalt-60 radiation sources—OFF, READY, and ON—were also recorded. An in-house Java plugin for MIM was created in order to perform principal component analysis (PCA) on each of the datasets. The analysis resulted in first PC, related to monotonous signal increase over the course of the treatment fraction. We found several distortion patterns in the data that we postulate result from the perturbation of the magnetic field due to the moving metal parts in the platform while treatment was being administered. The largest variations were detected when all Cobalt-60 sources were OFF. During this phase of the treatment, the gantry and multi-leaf collimators (MLCs) are moving. Conversely, when all Cobalt-60 sources were in the ON position, the image signal fluctuations were minimal, relating to very little mechanical motion. At this phase, the gantry, the MLCs, and sources are fixed in their positions. These findings were confirmed in a study with the daily quality assurance (QA) phantom. While the identified variations were not related to physiological processes, our findings confirm the sensitivity of the developed approach to identify very small fluctuations. Relating these variations to the physical changes that occur during treatment shows the methodical ability of the technique to uncover their underlying sources. The use of magnetic resonance imaging (MRI) is rapidly gaining momentum in the management of cancer because of its improved diagnostic potential and wide availability. The non-invasive nature of MRI allows for frequent scanning and follow-up of patients. However, real-time imaging of patients during radiotherapy was not available until the recent release of the Tri-Cobalt-60 MRI-Guided RT (MRgRT) radiotherapy system MRIdian  -3.A typical treatment fraction on MRIdian yields thousands of images over the span of 10 to 15 minutes. Because of the short time of acquisition (250 ms per image) and the low-strength magnetic field (0.35T), these images are of low signal to noise ratio. However, this unique data allows for a glimpse in image intensity changes during RT delivery.The aim of this study is to identify and quantify the MR signal variations during MRIdian treatment of a patient with glioblastoma. We use principal component analysis (PCA) to take advantage of the collective power of multiple images which were acquired during a single fraction. The identified patterns were confirmed in another subsequent fraction on the same patient and in a phantom study.The MRIdian platform consists of a rotating circular gantry with three Cobalt-60 sources spaced in 120 degree intervals from each other. All treatments utilize a step-and-shoot intensity modulated radiation therapy (IMRT) delivery technique and the platform has a distinct procedure for delivering radiation. First, the gantry will rotate into the delivery position required, with all sources locked in the OFF position during rotation. When the gantry is secured, the multi-leaf collimators (MLC) will open to provide the correct aperture for RT delivery and the sources move into the READY position. Once all of the MLCs are in position, the sources then traverse to the ON position and radiation is delivered to the patient. Whenever an alteration is required to the shape of the beam at any of the sources, the source will return to the READY state until its MLC assumes the new aperture required, whereupon the source will return to ON. In the MRIdian software, these states are visualized on the cine as follows: green indicating OFF, yellow indicating READY, and orange indicating ON.The analysis was performed on a cine generated from the real-time tracking of RT treatment of a patient with glioblastoma. The patient was treated with 30 fractions at 60 Gy over six weeks and immobilized with a thermoplastic mask and surface coils surrounding the mask. A patient with a brain tumor was chosen for the study because of the essentially immobile head during RT and the reproducibility of the setup. Over 3000 MRIs are acquired over one treatment fraction (250 ms per image). The images are displayed in MRIdian’s console and the resulting movie captured in Ogg Vorbis (.ogv) format.A script was created in MATLAB  for converting the cine from .ogv file to pseudo-DICOM images. The individual frames of the video were extracted and rendered into greyscale. To speed the subsequent computation time, the cine were rescaled down from a 914 × 914 video resolution to 236 × 236 pixels. Synthetic DICOM headers were appended to the image arrays and saved as a dynamic series.The DICOM data were imported into the imaging analysis platform MIM  and read as a single time series. The patient brain was contoured , excluding the MRIdian tracking and boundary structures Figure . In addiWe applied the procedure to the 3rd and 20th treatment fractions performed on the patient . The results of the PCA analysis are shown in Figure To confirm these observations, we applied the plan for the third fraction to a daily quality assurance (QA) imaging phantom. The results of PCA analysis for this dataset are shown in Figure The use of MRI in the discovery and treatment of prostate cancer has been long known by the radiological community -8. HowevIn this case report, we characterized the changes of MR signal during a single fraction treatment on MRIdian. We found several distortion patterns in the data presumably resulting from the perturbation of the magnetic field due to the moving metal parts in the platform while treatment was being administered. Should these artifactual variations be isolated or otherwise compensated for, it could bring us closer to the ability to visualize the effects of treatment in real time and predict patient outcomes with a greater accuracy than what is currently standard .While the identified variations were not related to physiological processes, our findings confirm the sensitivity of the developed approach to identifying very small fluctuations. Relating these variations to the physical changes that occur during treatment shows the methodical ability of the technique to uncover their underlying sources.This report has several limitations. Besides the limited number of studies typical for case reports, the main drawback was that the area of the tumor (GTV) was excluded from the analysis. This was because the tracking and boundary are required for RT and appear on the cine. These contours produce movement and thereby the contours have to be excluded in the analysis. A potential remedy for this issue could be drawing the contours at the surface of the skull and thus excluding them from the Field of View of the analyzed area.The future application of this approach to LINAC-based MRIdian cines, where the instrumental-induced variations are significantly reduced, has the promise to identify patterns that will provide better insight into the underlying physiological changes.In this case report, we characterized the changes of MR signals during a single fraction treatment on MRIdian. We found several distortion patterns in the data likely resulting from the perturbation of the magnetic field due to the moving metal parts in the platform while treatment was being administered. While the identified variations were not related to physiological processes, our findings confirm the sensitivity of the developed approach to identify very small fluctuations.


In view of the multi-attribute decision-making problem that the attribute values are grey multi-source heterogeneous data, a decision-making method based on kernel and greyness degree is proposed. The definitions of kernel and greyness degree of an extended grey number in a grey multi-source heterogeneous data sequence are given. On this basis, we construct the kernel vector and greyness degree vector of the sequence to whiten the multi-source heterogeneous information, then a grey relational bi-directional projection ranking method is presented. Considering the multi-attribute multi-level decision structure and the causalities between attributes in decision-making problem, the HG-DEMATEL method is proposed to determine the hierarchical attribute weights. A green supplier selection example is provided to demonstrate the rationality and validity of the proposed method. Multi-attribute decision-making is a problem in which a decision-maker evaluates a finite set of alternatives associated with multiple attributes. It is widely used in various areas such as management ,2, the eNowadays, the current research about the multi-attribute decision-making method has resulted in many significant achievements, such as AHP , TODIM , ELECTREThe fusion of different data types of grey information from multiple sources is processed by kernel and greyness degree which are the common information characteristics of grey multi-source heterogeneous data.In order to measure the proximity of a selected alternative to the ideal solution and the negative ideal solution comprehensively and accurately, a grey relational bi-directional projection method is proposed based on kernel and greyness degree.The Hierarchical Group-Decision Making Trial and Evaluation Laboratory (HG-DEMATEL) method is proposed based on analyzing the causalities between attributes. It can effectively use group decision-making information and determine the hierarchical attribute weights.The validity of the proposed method is verified in the practical decision problem of green supplier selection.Additionally, in practical decision-making, the decision problem usually presents a multi-attribute multi-level decision-making structure, and the evaluation attributes are not entirely independent, but mostly causal. Most of the existing decision-making methods assume that the attributes are independent of each other, and the causalities between attributes are neglected. Decision Making Trial and Evaluation Laboratory (DEMATEL) is a method for analyzing complex system factors. It can recognize the causalities between complex social factors and identify the key elements based on graph theory . In the The remainder of this paper is organized as follows: in Green supplier selection is actually a kind of multiple attribute decision-making (MADM) problem. Recently, a variety of MADM methods for green supplier selection have been proposed. Govindan et al.  utilizedBesides that, the optimization models have also been widely adopted in the field of green supplier selection. Azadi et al.  proposedIn order to deal with the green supplier selection problem with the higher complexity, many scholars presented the integrated hybrid methods. Stanujkic et al.  studied According to the review and analysis on green supplier selection based on the above-mentioned references, we can see that most of the above decision-making methods assume that the attributes are independent of each other, and the causal relationships between attributes are neglected. Hence, it is necessary to study the decision problem with causalities between attributes. Meanwhile, the single uncertain decision-making information has been widely adopted in green supplier selection problems. However, little attention has been paid to the different types of uncertain mixed grey information from multiple sources to dispose multi-attribute green supplier selection. Therefore, it is advantageous to study the MADM method and its preference information under the grey multi-source heterogeneous information. This does not only improve the model ability of higher complexity and uncertainty, but also handle the green supplier selection problems with uncertain decision information.In real life, decision-making information is usually uncertain due to the difficulty of information acquisition and the limitation of decision maker’s own cognition. In most cases, a number is called a grey number Definition 1.Assume that the background or universe of an interval grey numberis, and letbe the measurement on the number field of interval grey number, thenis called the greyness degree of the interval grey number. In the absence of value distribution information of interval grey number,is referred to as the kernel of interval grey number .Assume tParticularly, when is, Yang  proposedDefinition 2.Ifis a union set of a set of interval sets, thenis called extended grey number, denoted as, where,,andare called the lower and upper bounds of .If⊗±iOn the basis of the relevant definitions of the kernel and greyness degree of an interval grey number , the defDefinition 3.Assume that the kernel of extended grey numberis, then(1) is unknown, then If the probability distribution of (2) is known, then, whereandare the probability and the kernel of interval grey numberrespectively, and the following conditions hold:, If the probability distribution of Definition 4.Assume that the background or universe of extended grey numberis,is the measurement on number field of interval grey number, then greyness degreeof extended grey numberis defined as follows:(1) is unknown, then If the probability distribution of (2) is known, then, whereis the probability of interval grey number, and conditions hold:, If the probability distribution of Definition 5.If the decision-making information obtained from information sources 1, 2,,is a data set which is a mixture of interval grey numbers, extended grey numbers and real numbers. , then the sequence composed of the mixed data from the data set is called grey multi-source heterogeneous data sequence.In a multi-attribute decision-making problem, To eliminate the dimensions of the different attributes and to increase comparability, the decision matrix For a real number, let For the benefit attribute For the cost attribute For interval grey number, let For the benefit attribute For the cost attribute For extended grey number, let For the benefit attribute For the cost attribute Although grey multi-source heterogeneous data have different data structures and grey information characteristics, it belongs to the category of “grey numbers”. Therefore, it can be aggregated by using the kernel and greyness degree which are the common information characteristics of grey multi-source heterogeneous data.In decision-making process, it is generally required that the optimal alternative should be as close as possible to the ideal solution and as far away as possible from the negative ideal solution. Based on this, in order to measure the proximity of a selected alternative to the ideal solution and the negative ideal solution comprehensively and accurately, the grey relational bi-directional projection method based on kernel and greyness degree is proposed to rank the alternatives. The proposed method integrates grey relational analysis theory with vector projection principle, and considers the effect of entire attribute space. The single direction deviation can be avoided especially when the sample size of attribute is spare and data is discretized.Definition 6.Assume that a vector constituted by a grey multi-source heterogeneous data sequence is, then the vectorcomposed of “the whole kernel” inis called kernel vector of, and the vectorcomposed of “the whole greyness degrees” inis called the greyness degree vector of, namelywhereis a real number,is an interval grey number, andis an extended grey number.Definition 7.Letandbe the positive and negative ideal kernel vector respectively, and letandbe the positive and negative ideal greyness degree vector respectively. Here the following notation is used.Definition 8.Assume that,,, then the kernel grey relational coefficientbetween the kernel vector of alternativeand the positive (negative) ideal kernel vector at attributeis expressed as follows:whereis a distinguished coefficient, its value is usually configured to 0.5.The kernel Definition 9.Assume that,,, then the greyness degree grey relational coefficientbetween the greyness degree vector of alternativeand the positive (negative) ideal greyness degree vector at attributeis expressed as follows:whereis a distinguished coefficient, its value is usually configured to 0.5.The greyness degree Obviously, the kernel grey relational coefficient between the positive (negative) ideal kernel vector and itself at each attribute is equal to 1. Similarly, the greyness degree grey relational coefficient between the positive (negative) ideal greyness degree vector and itself at each attribute is also equal to 1.Definition 10.Assume thatis an augmented matrix formed by positive (negative) ideal kernel vector and kernel vectors of all alternatives, then the weighted grey relational kernel matrixthat is about positive (negative) ideal kernel vector under the effect of weight vectorcan be constructed as follows:where the positive ideal kernel vector corresponds to the superscript, and the negative ideal kernel vector corresponds to the superscript Similarly, the weighted grey relational greyness degree matrix can be constructed and denoted as Definition 11.Assume thatis the kernel positive (negative) ideal alternative in, where, and let the (i + 1)-throw vectorbe called the alternative of alternativeon the kernel positive ideal alternativeis expressed as follows:Similarly, the projection value The larger the Definition 12.Assume thatis the greyness degree positive (negative) ideal alternative in, where, and let the (i + 1)-throw vectorbe called the alternative. Then the projection valueof alternativeon the greyness degree positive ideal alternativeis expressed as follows:Similarly, the projection value The larger the In making a decision on alternatives, the closer the alternative Let The larger the The larger the Definition 13.Assume thatandare kernel optimal membership degree and greyness degree optimal membership degree of alternativerespectively, then comprehensive optimal membership degreeof alternativeis expressed as follows:The larger theis, the better the alternativeis.In the decision-making problem where the decision information consists of grey multi-source heterogeneous data and the attribute system has a multi-hierarchical structure, there usually exist causalities between attributes. However, the determination of the traditional objective attribute weights mainly depends on attribute values distribution, and assumes that attributes are independent of each other. It can be seen that the causalities between attributes are ignored. The advantage of the DEMATEL method is that it can comprehensively use graph theory and matrix theory to analyze the causalities between complex system factors. It is especially more effective for the system with uncertain causalities between factors ,48.The initial direct relation matrix is the basis for causalities analysis of DEMATEL method, which has an important influence on final result of causalities analysis. It is usually determined by group multi-expert information aggregation. However, the current research mostly uses the mean method to aggregate the group information, which lacks scientific rationality. Therefore, in order to effectively aggregate experts’ evaluation information, the HG-DEMATEL method is proposed based on comprehensive consideration of differences and similarity degrees between initial direct relation matrixes given by experts. The proposed method is used to analyze the causalities between attributes and calculate the hierarchical attribute weights. The specific steps are as follows:Step 1: Determine the direct relationships between attributes which form the attributes set Step 2: Construct the overall initial direct relation matrix u-th expert based on an integer scale varying from (1)The difference value between aggregated matrix and original matrix is as small as possible.(2)The similarity degree value between aggregated matrix and original matrix is as big as possible.Assume that Therefore, an optimization model matrices . The symStep 3: Construct the normalized direct relation matrix Step 4: Calculate the total relation matrix The total relation matrix is the sum of direct relation matrix and indirect relation matrix, where the indirect relation matrix consists of a decreasing matrix sequence of Step 5: Calculate the structural correlation coefficients.j-th row and sum of the e-th column in The sum of the In order to get a causal diagram, the values of Step 6: Calculate the hierarchical attribute weights.In this step, we use the structural correlation coefficients to set the attribute weights that will be used in the decision process. The weight The weight f-th sub-attribute under the j-th attribute is defined as follows:j-th attribute in f-th sub-attribute in So the normalized attribute weight vector In summary, the main steps of the proposed decision-making method with grey multi-source heterogeneous data are given as follows:Step 1: Normalize the comprehensive decision matrix with Equations (1)–(6);Step 2: Construct the kernel vector and greyness degree vector of grey multi-source heterogeneous data sequence with Equations (7) and (8), then the positive and negative ideal kernel vector as well as the positive and negative ideal greyness degree vector are determined according to Definition 7;Step 3: Calculate the hierarchical attribute weights with Equations (20)–(26);Step 4: Calculate the projection values of each alternative on kernel positive and negative ideal alternative as well as greyness degree positive and negative ideal alternative with Equations (9)–15);Step 5: Calculate the comprehensive optimal membership degree of each alternative with Equations (16)–(19);Step 6: Rank alternatives. Sorting the values of the comprehensive optimal membership degree In this section, a case of green supplier selection about product material component is presented based on the proposed method.With the increasingly serious environmental problems, the green supply chain management (GSCM) has been accepted as a modern management mode. Because green supplier is the upstream of the entire supply chain, its function in cost savings and environmental protection can pass through the supply chain to all downstream links . It can Hence, a decision problem of a product material component manufacturer is taken as an example, which aims to select the best green supplier for production. The four potential green suppliers are denoted as In order to evaluate the potential green suppliers objectively and comprehensively, we investigate and obtain the decision information from multiple sources. Meanwhile, owing to the complexity and uncertainty of the actual decision environment, the obtained decision information is usually grey number, and then the fusion of different data types of grey information from multiple sources forms grey multi-source heterogeneous data sequence. The decision information about the four green suppliers are shown in To select the best green supplier for production, the proposed method with grey multi-source heterogeneous data is used to solve the green supplier selection problem. The main rationale is that the kernel and greyness degree which form the common information characteristics of grey multi-source heterogeneous data are utilized to handle the decision information. Considering the multi-attribute multi-level decision structure in green supplier selection, the HG-DEMATEL method is used to capture the causalities between hierarchical attributes and determine the importance of hierarchical attributes. On this basis, the grey relational bi-directional projection method is used to rank the green suppliers, which can measure the proximity and the changing direction between the green suppliers and the positive (negative) ideal solution more accurately.Step 1: Normalize the decision information in Step 2: Construct the kernel vector and greyness degree vector of each alternative with Equations (7) and (8), then kernel matrix Then, the positive and negative ideal kernel vector Step 3: Calculate hierarchical attribute weights.Firstly, the initial direct relation matrixes Secondly, the overall initial direct relation matrix Then, the total relation matrix Finally, the weights of attributes are calculated by Equations (22)–(25) and shown in Similarly, the normalized weights and overall weights of sub-attributes can be calculated by Equations (20)–(26), and the results are shown in Step 4: The projection values of each alternative Similarly, the projection values of each alternative Step 5: Calculate the comprehensive optimal membership degree The kernel optimal membership degree According to the kernel optimal membership degree Step 6: Rank alternatives.All alternatives are ranked based on the value The selection of green supplier is a key step in green supply chain management (GSCM). The proposed decision-making method integrating the HG-DEMATEL and the grey relational bi-directional projection method provides a useful, practical and valid selection tool, which can improve the quality of green supplier selection decisions. We adopt the different data types of grey information from multiple sources to describe the potential green supplier’s comprehensive performance objectively and comprehensively. It is obvious that the decision information from multiple sources can be useful in improving the accuracy of the green supplier selection decisions. Meanwhile, the kernel and greyness degree that are the common information characteristics of grey multi-source heterogeneous data are utilized to process the decision information and avoid the loss of information conversion in green supplier selection effectively.In making decisions about green supplier selection, the proposed grey relational bi-directional projection method is applied to evaluate the green suppliers. During the evaluation procedure, the distance proximity and the consistency of changing direction between each alternative and the ideal solution are simultaneously taken into consideration, which can more accurately measure the proximity and the similarity between them. By using the proposed method to evaluate and select the potential green suppliers, it can provide a reference value for how to choose the best green supplier to increase the competitiveness and economic level of the company. Moreover, the feasibility and effectiveness of the proposed method are further verified, which also provides some practical and theoretical guidance value for the enterprises that are implementing or will implement green supply chain management.In this section, the result analysis about the case in The causal diagram of attributes  and the As can be seen from (1)With respect to the green level (2)With respect to the product competitiveness (3)With respect to the enterprise competitiveness (4)With respect to the cooperation support For sub-attributes corresponding to each attribute, we can get the following analysis from In order to validate the robustness of the final recommendation based on the proposed method in green supplier selection, the following two aspects are considered in this section: the sensitivity analysis for variation of attribute weight; the sensitivity analysis for variation of attribute number.In order to investigate the influence of the change of attribute weights on the produced results, the sensitivity analysis of attribute weights is made in this part. A total of 13 sub-attributes weights constitutes the weight vector Hence, the new normalized weight vector From In order to further verify the validity of the final recommendation based on the proposed method for assessing green supplier, the sensitivity analysis for variation of attribute number is performed. In addition, in the green supplier selection process, the evaluation of alternatives may require the exclusion or addition of attributes. In this case, the proposed method should produce a robust and stable preference with the variation of attribute number.In the original case, the ranking result of four alternatives with thirteen attributes is Furthermore, the attribute green image ustomers ,44. ThirFrom the above analysis, it is shown that the final recommendation (1)If we use the method in reference  to deal (2)If we use the method in reference  to deal (3)If we use the classical GRA method to deal with the same problem in this paper, the value of grey relation degree of each alternative (4)If we use the classical TOPSIS method to deal with the same problem in this paper, the value of relative closeness of each alternative In order to verify the rationality and effectiveness of the proposed method, we compare the proposed method with several related methods. The comparison results can be seen in (1)A common method of solving hierarchical attribute weights, in which the causal relationships exist between attributes, is under consideration. The determination of the traditional objective attribute weights mainly depends on attribute values distribution, which assumes that attributes are independent. However, there usually exist causal relationships between attributes in the multi-hierarchical attribute system. The proposed HG-DEMATEL method may be a suitable way to solve this problem.(2)Different from the classical methods, such as TOPSIS, GRA, the proposed grey relational bi-directional projection method not only considers the measurement of distance proximity between alternatives and the ideal solution, but also takes the consistency of changing direction between them into account.(3)The decision-making information is usually the single homogeneous data in classical decision-making method, such as VIKOR, GRA, TOPSIS, while the proposed method can handle the composite decision-making information with two or more different types of grey information from multiple sources, which is more in line with the presentation of practical decision information.From This paper studies the multi-attribute decision-making problem that the attribute values are grey multi-source heterogeneous data. We define the grey multi-source heterogeneous data sequence, and then the grey relational bi-directional projection ranking method is proposed based on kernel vector and greyness degree vector of the sequence. Meanwhile, the HG-DEMATEL method is proposed to solve the problem of causalities between attributes and determine the hierarchical attribute weights. Finally, an illustrative example verifies the validity of the proposed method in green supplier selection. At the same time, the proposed method also provides a perspective to solve the uncertain decision-making problem whose decision-making information is grey multi-source heterogeneous data.In future research, we can further integrate DEMATEL and the Choquet integral to deal with the causalities between different sources attributes, and use fuzzy integral and fuzzy measure to fuse multi-source heterogeneous data. In addition, the proposed method can be further investigated to make it suitable for other similar supplier selection problem, such as low carbon supplier selection, strategic supplier selection and sustainable supplier selection.


Vibrothermography often employs a high-power actuator to generate heat on a specimen to reveal damage, however, the high-power actuator brings inconvenience to the application and possibly introduces additional damage to the inspected objects. This study uses a low-power piezoceramic transducer as the actuator of vibrothermography and explores its ability to detect multiple surface cracks in a metal part. Experiments were conducted on a thin aluminum beam with three cracks in different orientations. Detailed analyses of both thermograms and temperature data are presented to validate the proposed vibrothermography method. To further investigate the performance of the proposed vibrothermography method, we experimentally studied the effects of several critical factors, including the amplitude of excitation signal, specimen constraints, relative position between the transducer and cracks (the transducer is mounted on the same or the opposite side with the cracks). The results demonstrate that all cracks can be detected conveniently and simultaneously by using the proposed low-power vibrothermography. We also found that the magnitude of excitation signal and the specimen constraints have a great influence on detection results. Combined with effective data processing methods, such as Fourier transformation employed in this study, the proposed method provides a promising potential to detect multiple cracks on a metal surface in a safe and effective manner. Active infrared thermography (IRT) has received increasing attention in recent years due to its advantages of non-contact detection, high efficiency, and clear visualization. A few kinds of heating excitations are commonly used in active IRT to detect defects ,2,3,4,5.In recent years, the surface crack detection in metal parts using vibrothermography has become one of major research interests. The related works have been focused on the investigations of detection mechanisms, analysis of influential factors and defect characterization methods. In the current investigations, high power excitation devices are usually used to generate heat in the specimen with a single crack. To make the testing work more convenience and to avoid introducing new damage to the tested specimen, it is necessary to investigate vibrothermography with a low-power actuator to detect multiple cracks on metal parts. Recently, there has been increasing interest in using vibrothermography with low-power actuator to detect defects in composite materials, however, the related investigations on metal components are quite limited. In the previous work, we developed a coupled thermo-electro-mechanical analysis with implicit finite element method to simulate a low power piezoceramic ultrasonic actuator and the corresponding heat generation in metallic plates with multiple surface cracks , which oExperimental and numerical researches have been carried out to develop an improved understanding for the detection mechanisms of vibrothermography. Holand et al.  revealedIn addition to the detection mechanisms, the influential factor is another major research issue of vibrothermography. Holland et al.  stated tRecently, qualitative and quantitative methods to characterize the cracks detected by using vibrothermography have been developed. Holland et al.  performeThe power of excitation is one of the key factors for defect detection using vibrothermography. In the above-mentioned applications, high power (up to 2 kW) excitation devices, such as ultrasonic welding horns, are the usual choices of excitation sources. However, high power excitation is not necessary to guarantee enough heat generated around the cracks due to the nonlinear coupling between the horn and specimen . MoreoveMoreover, vibrothermography has been only verified efficient to detect single surface crack in metal parts. For multiple surface cracks in metal parts, to the authors’ knowledge, limited research of vibrothermography has been found. Different from detecting single cracks, detection of multiple surface cracks using vibrothermography is more complicated due to the interference among different cracks with same or different orientations. Since this interference might play significant roles on the mechanical wave propagation, which probably affects the detectability of vibrothermography. Hence, it is still necessary to investigate the detectability of vibrothermography with a low-power actuator for multiple surface cracks detection on metal parts.The experimental setup is shown in A thin aluminum beam with a dimension of 500 mm × 100 mm × 3 mm was used as the test specimen in this work. There are three cracks with different orientations on the surface of the specimen, as shown in In this section, we present the experimental results of multiple surface cracks detection using vibrothermography with the low-power actuator described in Measurements of electrical impedance of the piezoelectric transducer were performed prior to the vibrothermography test, as mentioned in . It was As shown in It is important to understand the thermal pattern of each crack. From Here we discuss the measured temperature data to reveal more information for characterization of the cracks. As shown in Therefore, the proposed low-power actuator based heating excitation can simultaneously generate obvious temperature risings in all cracks at different locations and in different orientations, which contributes to detect multiple surface cracks on such thin aluminum beam-like metal parts by using vibrothermography in a fast, effective, and simultaneous manner.In order to further investigate the effectiveness of vibrothermography with low-power actuator to detect multiple cracks on metal parts, here we analyze the influences of three significant factors on the detection results. These factors include the excitation signal amplitude, the constraint condition of the test object, and the relative position between the excitation and cracks (same or opposite side).A set of experiments were conducted to study the effect of the excitation signal amplitude on the cracks features detected in thermograms. As stated previously, the cracks cannot be visually detected from According to the fundamental of vibrothermography, heat energy generated around the cracks is closely related to the propagation of the mechanical wave. The constraint condition of the test object is a critical factor which affects the behavior of the mechanical wave propagation. Hence, it is necessary to investigate the possible effects of specimen’s constraint condition on crack detection. To the specimen used in this work, we considered three constraint conditions: rigidly fixed at both ends, partially fixed at both ends (the specimen was not very firmly fixed), and fixed at only one end (the other end is free). Finally, to further demonstrate the feasibility of the developed low-power vibrothermography, we experimentally investigated the influence of the PZT transducer position on the detection result. The results shown above  come froIn this work, the effectiveness of using vibrothermography with a low-power ultrasonic actuator to detect the multiple surface cracks on a metallic beam is experimentally studied. This low-power actuator involves two piezoceramic disks that are clamped with two metal blocks tightened by a bolt. An experimental apparatus was set up and series of experiments were conducted on a thin aluminum beam with three cracks in different orientations. The experimental results show that by applying an excitation signal with an amplitude of 80 V, all three cracks in the thin aluminum beam with different orientations can be simultaneously detected from the raw thermograms within the excitation time of 1–2 s. We also analyze the influences of several factors on crack detection using vibrothermography. The results indicate that the detectability of cracks is closely related to the amplitude of excitation signal. When the amplitude is set as no less than 80 V, effective detection for all cracks can be obtained. Moreover, it is demonstrated that using image processing methods to enhance the features of cracks in raw thermograms is a promising way to achieve effective detection using vibrothermography with lower power . It is also clearly revealed that vibrothermography is robust with respect to the factor of mounting the PZT transducer at the same location, but on the opposite side of the cracks. Finally, the experimental results suggest that the vibrothermography is sensitive to the constraint conditions of the specimen and the configuration of double fixed ends is found to be the best way for crack detection in the thin beam-like metal part presented in this research. However, this work presents only a preliminary attempt to investigate the effectiveness of vibrothermography with a low-power actuator to detect multiple cracks on metal parts. Combining with the numerical model presented in  and othe


We collected relevant observational and measured annual-resolution time series dealing with climate in northern Europe, focusing in Finland. We analysed these series for the reliability of their temperature signal at annual and seasonal resolutions. Importantly, we analysed all of the indicators within the same statistical framework, which allows for their meaningful comparison. In this framework, we employed a cross-validation procedure designed to reduce the adverse effects of estimation bias that may inflate the reliability of various temperature indicators, especially when several indicators are used in a multiple regression model. In our data sets, timing of phenological observations and ice break-up were connected with spring, tree ring characteristics  with summer and ice formation with autumn temperatures. Baltic Sea ice extent and the duration of ice cover in different watercourses were good indicators of winter temperatures. Using combinations of various temperature indicator series resulted in reliable temperature signals for each of the four seasons, as well as a reliable annual temperature signal. The results hence demonstrated that we can obtain reliable temperature information over different seasons, using a careful selection of indicators, combining the results with regression analysis, and by determining the reliability of the obtained indicator. The present global warming highlights the importance of detailed and reliable information on past climate to place the current change in a historical context, to predict the response of biological and physical phenomena to global warming , and to Fortunately, there are now multiple indicators of climate apart from surface temperature measurements e.g. , 3). Som. Som3]).Several natural phenomena and processes can be used as temperature indicators at high temporal resolution over varying time scales from biological archives spanning several millennia, to observational records spanning decades to several centuries. Such indicators include various tree ring properties, bud burst of leaves and flowering, and melting and freezing of seas, lakes and rivers. However, the characteristics and applicability of these various indicators differ.Tree ring-width measurements are one of the most widely applied indicators of past temperatures. Their popularity has been both due to their wide spatial coverage, the relative ease of measurements, and their unrivalled temporal resolution. The strength of the relationship between tree ring-widths and temperatures varies spatially, but it also seems to change through time , 6. TherMost plant species are dormant during winter at high latitudes. During the dormant period plant metabolism is rather inactive and the plants are not growing. The metabolism activates again in the spring, following increasing air temperatures and solar radiation. The initial growth of new cells occurs inside the buds, and thus bud development becomes visible only later as the buds burst, which is easy to observe. The timing of budburst reflects the temperatures before the event. Plant phenological events, especially those taking place in the spring (i.e. timing of flowering and leaf bud burst), are shown to be driven by ambient temperatures during a month or two preceding the event –20.Ice dynamics, i.e. ice formation, break-up and duration and extent of ice cover data series also have high potential as a climatic indicator , 22. In Some observational data on ice dynamics extend further back in time than instrumental temperature measurements, but there are also promising means to reconstruct ice conditions of lakes from the palaeolimnological records ,30,31. TDifferent indicator series used to estimate the past climates typically reflect the temperature history of only a fraction of the whole year. Tree-ring features usually reflect the conditions during the growing period, while spring phenological events are driven by the temperatures of late winter and early spring. Lake and river ice duration apparently depends on the temperatures throughout the winter, but also late autumn and early spring temperatures influence ice dynamics . TherefoWe have a versatile collection of these types of indicator time series available in Finland and the adjacent regions. In addition, we can make additional retrospective measurements, especially from tree rings and lake sediments. It is clear that some of these time series may reflect climatic features very closely, while some of them might be only loosely connected with temperature . AssessiIn this paper, we performed a detailed assessment of the reliability of temperature signal in various indicators, based on natural phenomena as climate indicators. Specifically, we (i) assembled all readily available and relevant biological and physical time series predominantly in Finland that are commonly considered potential climate indicators, along with relevant temperature measurements. We then (ii) identified the season of the climate that each series characterizes best, and (iii) determined numerically the reliability of temperature signal in each single indicator series, and in a combination of different series. With these analyses, we aimed to highlight the important aspect to obtain comparable results of reliability of various indicators and their combinations. We assessed all the time series within the same statistical framework to obtain comparable results.To compute the relationship between the temperature records and potential temperature indicators, we first explored the spatial variability in temperature measurements from four meteorological stations located along a transect from southern to northern Finland  in the cellulose of tree rings. For tree ring-width data, we assembled all ring-width series from the International Tree Ring Data Bank  Karst.) and 36 sites for Scots pine (Pinus sylvestris L.).We used three types of tree-ring data sensitive to variations in temperature: tree ring-widths, latewood densities and the ratios of stable carbon isotopes  chronology from southern Finland , we tesWe estimated the reliability of the identified temperature signal based on the fit on a data set not used in the training. This mimics the situation in which unseen data is used to assess the performance of the model. We proceeded with the stepwise cross-validation approach in determining the proportion of the variance of the measured temperatures explained by the different indicators. In the cross-validation process, the original data were first split randomly into five non-consecutive parts, four of which were combined and used together as a training set and the remaining part as a validation set. This cross-validation procedure was repeated 50 times to eliminate the variation between the data sets used in the estimation. We considered 50 divisions sufficiently large for time series of this length to eliminate the effect of a single division to the results, while keeping the computation time reasonable.The number of explanatory variables in the LARS models was selected using a second level of five-fold cross-validation within each training set of the first-level cross-validation described above, repeated 5 times. Each training set in the second level uses 80% of the corresponding first-level training set for training LARS models and the remaining 20% is used as a validation set for selecting the model complexity. We selected data that were not used for training when selecting model complexity, thus avoiding estimation bias, i.e., overfitting the model to the training data. For each training set in the first-level cross-validation, we selected the number of variables associated with the lowest sum of squared errors in the second-level validation sets.Finally for comparison, full regression models including all the indicators were used to predict the temperatures. We averaged the prediction time series obtained using the first-level validation data and used the averaged time series to calculate the proportions of explained variance for these regression model types. We estimated the variation of the prediction time series using 10 000 bootstrap replicates.The reliability of the indicator information was measured as one minus the ratio of the unexplained variance to the variance of temperature in the validation set. This approach is closely related to the coefficient of determination, i.e., the proportion of the variance explained, commonly used in regression analysis. The difference is that we only used the validation data set in the evaluation of reliability, avoiding estimation bias in the obtained reliabilities . NeglectThe reliability of temperature signal obtained from individual indicator time series varied within the year . AnalyzeThe reliability of the temperature signal in indicators based on the ring-widths was low for summer  temperatures (reliability < 0.08) . LatewooThe combination of carbon isotopes, latewood density and ring-width data in the same model produced a reliable summer temperature signal, resulting in a reliability of 0.55 , Table 2Based on the LARS models, the most informative combination of explanatory variables for spring  temperatures  were theIn this study, we analyzed the reliability of temperature signal in various commonly used temperature indicators. These indicators differ in their characteristics, including their sensitivity to climate, measurability and feasibility, and spatiotemporal scope (cf. ). Hence,Regardless of the application, an important aspect of these type of indicator data is their reliability. The use of a common statistical analysis framework in all our time series ensured comparability between the reliabilities of the different indicators. The use of separate validation data was a characteristic feature of the method we used for assessing the reliability of the temperature signal in the various indicators. This cross-validation procedure ensured that estimation bias did not increase artificially the reliabilities, and the obtained values contained useful, generalizable information on their reliability. In addition, the reliability allows not only comparing reliabilities of the temperature signal in single indicators but also reliabilities of multiple indicators without estimation bias. As a minor caveat, it should be noted that the serial correlation that was present in three of our indicator series  may have led to slightly overestimated reliabilities , 63.The temperature indicators analyzed carried information on the temperature conditions during and before their occurrence or formation. Different indicators capture the temperature signal from different parts of the year: ice melting moments and phenological events were related to spring temperatures, tree ring properties to summer temperatures, the freezing of lakes to autumn temperatures and the duration and extent of ice cover to winter temperatures.-1, and this energy is obtained from solar radiation and warm air. As an example, assume an ice covered lake with a 0.5 m thick ice cover, requiring over 16 000 kJ m-2 to melt. This energy is obtained during ~10 cloudless days if all energy comes from solar radiation. In reality, the snow cover and ice albedo are of importance to the energy balance. The cloudiness and temperature in spring varies greatly between years, and this results in variation in the availability of energy for melting and hence to variation in the dates of ice melting.For most of the indicators, especially those that are purely physical phenomena, the mechanisms connecting temperature and the indicator are well understood. As regards the ice dynamics, the energy pool explains the timing of melting and freezing moments –66. The Compared to the melting of ice, the freezing of water bodies is a simpler phenomenon since the solar radiation plays a minor role in the energy budget of the surface water in late autumn. The cooling of surface water and finally the freezing is caused by the heat flux from the lake into cold air. In addition, evaporative cooling, and stream outflow are significant processes . FreezinMany similar processes that govern freezing and melting dates govern the Baltic Sea ice extent and the ice duration in lakes. This is reflected in the correlations between these indicators and autumn and spring temperatures. However, these indicators respond to temperatures differently as the Baltic Sea ice extent was the most reliable indicator for winter temperatures (reliability = 0.72) and ice duration in lakes predicted most reliably the autumn temperatures.Although less straightforward compared to ice dynamics, the connection between timing of phenological events (flowering and bud burst) and temperatures is well understood. Our results were consistent with earlier studies that have reported temperature as the most important environmental factor controlling the timing of bud burst e.g., ,20). The. The20])Tree rings are perhaps the most widely used source of temperature indicators, especially in reconstructing past temperatures. Temperature affects all metabolic processes involved in the formation of tree rings, and thus several properties of tree rings reflect the temperature conditions during and preceding the formation of tree rings. The formation of a tree ring is a complex process as it includes several connected phenomena, such as synthesis of macromolecules, cell division and maturation of cells. Cell enlargement is also directly depending on tree water status , furtherOf various tree ring characteristics, ring-widths are the most commonly used indicators. In northern Europe, they have been used for past summer temperature reconstructions spanning centuries or millennia –71. HoweSimilar to previous studies e.g., ,76), lat, lat76])A third tree ring characteristic used as a temperature indicator was the carbon isotope composition. The temperature signal in the carbon isotopes of oak and Scots pine tree-rings from southern and central Finland (Bromarv and Ilomantsi) was weak (reliability = 0.05–0.08) compared to the maximum latewood density. The carbon isotope chronology from northern Finland was more sensitive to temperature variation than the southern chronologies (reliability = 0.22), but was still a poorer temperature indicator than latewood density. Similar to some other tree ring-based indicators , McCarroUsing a versatile collection of indicator series provided temperature information for various periods during the year, but their combination proved a reliable indicator of temperatures also at the annual level . DespiteHowever, it is noteworthy that low reliability of a given indicator does not mean that it is useless for climate change research. Even indicators with low strength of temperature signal may turn out useful, if the signal they contain is not present in other indicators, thus increasing the total reliability of obtained temperature signal. Proper application of these temperature indicators requires information on the season it indicates and on the reliability of the temperature signal in each indicator or in each indicator combination.The physical and biological phenomena behind the formation of each of these temperature indicators is not specific to the region where our data originates from, so the finding that a selected and tested combination of indicators perform well in predicting the temperature of different seasons is applicable to other regions. As an example, the usefulness of plant phenological time series that performed well as a temperature indicator here, has been used elsewhere in Europe to demonstrate that in Europe leaf unfolding has advanced six days since the early 1960s due to spring warming . HoweverEven if documentary records offer somewhat limited opportunities for past reconstruction of temperature, indicators from biological archives hold plenty of further potential . FindingA second promising source of future potential in biological archives is related to the ice phenology series that we found to be contain a temperature signal for autumn, winter, spring and annual temperatures. Longer ice phenology series would be a valuable addition to the commonly used biological indicators, which usually stress the active period during spring and summer. This is especially important because the winters are expected to exhibit the most prominent temperature increase . ExcludiWe studied the reliability of temperature signals in a collection of biological and physical indicators within the same statistical framework, using cross-validation methodology. This approach diminishes the adverse effect that estimation bias can have on the generalizability of our findings, as the cross-validation is not prone to overfitting and results in estimates of the true reliability of the indicators.Our analysis revealed the reliabilities of temperature signals in different indicators for each of the four seasons, as well as for the annual temperatures. Plant phenologies and ice break-up dates were reliable indicators of spring temperatures and tree ring properties carried a reliable summer temperature signal when several of these properties were combined. Lake freezing dates carried reliable autumn temperature signal and ice area of the Baltic Sea performed well as a winter temperature indicator. Using a combination of various indicators increased temperature signal reliability.We are facing the problem of missing temperature measurements before the construction of systematic network of temperature measurement stations. The temperature indicators are urgently needed to obtain climatic information before the systematic measurements since then we can properly assess the present warming, its strength and rate in the historical perspective. The weak knowledge of the climate in the past has undermined the efforts in placing the recent temperature changes into historical context. The unknown reliability of the temperature signal in the used indicators has been the dominant reason for the confusion in the discussion. The reliability should determine the weights of the indicators series in the argumentation.S1 TableAll data sets were obtained from the International Tree-Ring Data Bank (ITRDB). The search query covered all data sets that originated in Finland, and cover the time period 1850–1950. The series are listed from south to north.(DOCX)Click here for additional data file.S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.


Emerging microelectromechanical system (MEMS)-based sensors become much more applicable for on-body measurement purposes lately. Especially, the development of a finger tip-sized tri-axial force sensor gives the opportunity to measure interaction forces between the human hand and environmental objects. We have developed a new prototype device that allows simultaneous 3D force and movement measurements at the finger and thumb tips. The combination of interaction forces and movements makes it possible to identify the dynamical characteristics of the object being handled by the hand. With this device attached to the hand, a subject manipulated mass and spring objects under varying conditions. We were able to identify and estimate the weight of two physical mass objects (0.44 kg:  A prosperous recovery of arm and hand function after a neuromuscular accident requires adequate training of reach and grasp tasks. It is in many applications desired to evaluate task performances in a quantitative manner. However, the usual procedure is that patients visit the rehabilitation center on a regular basis where either the physical therapist (PT) or rehabilitation specialist (RS) assesses the patient’s performance using subjective measures. Hence, such an evaluation is just a snapshot of the patient’s capabilities under specific physical and environmental conditions. A continuous monitoring system that informs the PT with quantitative measures obtained in activities of daily living (ADL) would provide more detailed information about the patient’s recovery.A full evaluation of motor task performance during grasp movements requires, besides kinematic, also kinetic measures. Gathering both kinematic and kinetic measures allows for a full dynamic evaluation of tasks in terms of, e.g., movement trajectory, exerted forces, power exchange and the identification of load and body dynamics. In fact, such measures give much more detailed information of the subject’s performance compared to solely movement registration and, thus, allow for more specific clinical outcomes.Previously, we demonstrated the principle feasibility of estimating power exchange by handling passive spring and mass loads . SubsequMeasuring interaction forces, tactile information or having a haptic perception is of interest in many domains . Haptic Tactile sensing is important when visual or auditory information is not available or disrupted. Hence, for both humans and robots, tactile information is valuable for identifying and planning strategies during the manipulation of loads ,6.Measuring interaction kinematics and kinetics is essential in the field of neuromuscular modeling ,8 and esVarious groups exploited different force sensing modalities. An in-depth overview and comparison is given by Youssef et al. . They coRecently, Brookhuis et al. ,16,17,18Kinematic estimates can be obtained using widely-available MEMS-based inertial and magnetic sensors. By applying a suitable sensor fusion algorithm, they allow an accurate estimate of the sensors’ orientation with respect to a global coordinate frame ,20,21. SThe contribution of this paper is two-fold. First, an experimental system capable of measuring 3D hand and finger kinetics and kinematics is presented. The system combines a small, commercially available, inertial/magnetic sensor with a novel 6D force torque sensor, as described in the previous paragraph. The sensors are attached to the human hand and allow the measurement of interaction forces and movements simultaneously; Second, a method is presented to estimate the dynamic characteristic of a load being manipulated by the user’s hand. The method uses a recursive parametric approach, which is able to identify various properties of dynamic loads under time-varying conditions.The instrumentation setup comprises 3D accelerometers and gyroscopes embodied in a single chip (ST LSM330DLC), which are distributed along the dorsal side of the hand. Onto all digits of the index finger and thumb, a single chip was attached. In addition, custom-made cuffs  are attached to tips of the index finger and the thumb. Each cuff holds a 6D force/torque sensor on the palmar side of the tip; see The force/torque sensor was developed and built by Brookhuis et al. . Two silThe custom-made cuffs enforce a rigid connection between the dorsal  and palmar (force sensor) side of the tip. Hence, the relative orientation between the inertial and force sensor placed on the same tip is known at all times.The inertial sensors are used to estimate both the global orientation of the hand and the hand’s internal pose . These orientation estimates are used to express all measured signals in a common reference frame (coordinate transformation). In addition, the inertial sensor outputs are used to estimate (relative) translational movements of finger and thumb tips by applying forward kinematics.Kinetic outputs are used to measure the interaction forces between fingers and the object and to detect the contact between the finger and thumb with an arbitrary object.Eventually, both kinematic and kinetic estimates are used as an input of the identification algorithm to estimate the dynamic characteristics of the objects manipulated by the hand.In the next subsections, system identification methods  and the (a)The force generated by the human body and applied to an environmental object is minimally influenced by the joint movement of both bodies and can, therefore, be considered as an independent input.(b)The force generated by the human body and applied to an environmental object has a sufficiently high bandwidth, that is a larger bandwidth than the load.The human body is an active generator of force:The load is passive with a relatively low bandwidth.It should be noted that the relation between interaction force and movements at the interface of two bodies is, in general, determined by the dynamic characteristics of both bodies. Identification of such a system is a typical closed loop identification problem ,24. HoweThese conditions are often satisfied in our daily-life interactions with the environment. We will demonstrate that identification of the load characteristics is indeed possible under the above conditions.m is the mass and Consider a load with unknown internal dynamics being pinched by the index finger and thumb; see Inertial and gravitational perturbations act on the load, referred to as external dynamics; for instance, gravitational force (low bandwidth) or inertial displacements introduced by the arm. In addition, viscous and or elastic elements might be present. A non-zero net force would result in an acceleration of the whole object.Internal perturbations of the dynamics; for instance, grasping or pinching, referred to as internal dynamics. The difference in pinch forces is related to the load dynamics according to Newton’s third law. The object exerts equal, but opposite forces.In general, the load can be manipulated in two different ways:In order to demonstrate the principle of load identification, rather simple environmental loads will be used that can be manipulated by the index finger and thumb. These loads can be modeled as a mass, which is suspended by a spring-damper pair; see The total force exerted by springs and dampers is summed and modeled in a simple linear fashion:g implies that the vector is expressed in the global inertial reference frame.Now, for the first situation, i.e., when the (mass)load is accelerated, we assume that the relative acceleration of the mass with respect to the tips is negligible compared to the gravitational acceleration; see Equation    6) can bk:yk=Hkθ+e,quation  approach was deployed to estimate the optimal orientation between the sensor frame , thumb tip (t), index finger tip (i) and global frame (g). An i.i.d. Gaussian noise source is indicated with A are the directions of the horizontal force component:With the assumption that the horizontal components of the average net force in the global frame should be negligible, the following equation holds:Relative orientation obtained during movements: Under certain conditions, for instance picking up an object after it has been grasped, it is only the subject’s arm that is moving. That means that all digits are not or only relatively slowly moving with respect to each other. This makes it possible to use the relative accelerations and angular velocities as a measurement update. Both signals are measured in a different sensor frame, but should have the same magnitude. This allows us to update the relative orientation between segments during those pseudo static intervals.This can be modeled as:g et al. .A schematic overview of the implemented kinematic estimation algorithm is given in Two different experiments were conducted, each with a different load configuration being handled by the subject.A subject was seated at a desk with the PowerSensor hardware put on the left hand using Velcro straps; see The PowerSensor hardware deploys three triaxial gyroscope  mass loads  confirmed that no further ethical approval concerning the Medical Research Involving Human Subjects Act (WMO) was required, due to the nature of the study.An example reconstruction of the measured 3D forces during the first experiment, i.e., lifting a mass load (0.44 kg), is depicted in A time snapshot (at 11 s) of the same trial is used to reconstruct the measured forces in 3D; see The mass’s weight is estimated online using the RLS algorithm. A point estimate of the estimated weight value is determined at The estimation error is defined as the absolute difference between the estimated and true value of the mass weight parameter (first experiment) and spring stiffness parameter (second experiment). The experiments were repeated 10 times for both mass weights loads and the spring load. Absolute differences are given in box-plots see a and werLike the first experiment, an RLS algorithm was used to estimate the spring stiffness online. A point estimate of the parameter value was, arbitrarily, determined 0.5 s before the release of the spring object. The absolute error values of the estimated spring constant are We have demonstrated a novel device that allows the simultaneous measurement of thumb and finger movements and interaction forces with the environment. The system was tested during fairly simple hand motor tasks and was able to reconstruct the important dynamic characteristics of loads being manipulated by the index finger and thumb.Yet, the proposed device is a prototype and therefore in an experimental status that copes with various, mostly practical, issues. Those issues reflect the quality of the estimated parameters. It is our intention to show the feasibility of such a system. Further sensitivity analyses of different subsystems are required to improve the quality of the output data.First, attachment of the force sensors to the skin is a major concern. Human tissue deforms easily, especially when it is in contact with external objects. These deformations deteriorate kinematic estimates of motion capture (mocap) systems, often indicated as soft tissue artifacts (STA) ,30. STA Second, measuring interaction forces requires a proper coupling between the human tissue, force sensor and the environmental load. Force sensors are inherently stiff, which makes a good skin to sensor attachment rather difficult as the sensor easily tends to shift when forces are applied (STA). In our study, custom-made cuffs were designed and used to attach both force and movement sensors to the tips. The combination of cuff and stiff sensors results in the loss of touch and causes major difficulties in proper handling of the load. In this study, only two force sensors were used. Hence, grasping an object forces the subject to pinch between the index and thumb finger. If the center of mass (CoM) of the object is not positioned between the application points, an undesired moment is applied around the force sensor’s normal sensitive axis. Stability could be improved significantly when three or more fingers are used for grasping.Third, the electronic data acquisition circuitry requires improvements as it is currently sensitive for power supply fluctuations, which especially affect the daisy-chained force sensors. All force sensor data have been low pass filtered prior to further processing in order to minimize this effect as much as possible. Further improvements can be made in the sampling rate of the force sensor, which has been capped as the sensor used a 100-Hz clock to read each of the 12 force channels serially. The effective sample frequency is restricted to Fourth, as mentioned in the Methods section, it is necessary to express both force sensors in a common coordinate frame. The inertial sensors were used for this purpose. Prior to using the inertial sensors for kinematics estimates, a mapping  is required. Obtaining a proper calibration is a bit difficult because the subject is constrained in his/her movements due to the apparatus being attached to the subject’s hand. Another drawback of the inertial sensors is that the gyroscope and accelerometer pair provide only the relative orientation during sufficient common movement. In the static situation, only the relative inclination is provided. A traditional inertial and magnetic measurement unit (IMMU) provides heading information using a magnetometer. However, large disturbances due to the vicinity of magnetic materials make this approach challenging. In addition, the relative orientation between the rigid force and inertial sensor should be known. An improved version of the kinematic estimator is currently under development, which should avoid the usage of the magnetometers, but still provides robust heading estimates.Any of the mentioned errors could have been accumulated, which resulted in a fairly large mismatch between the true and estimated parameter values.Two different loads, indicated as a mass and a spring, were manipulated. They do not only differ in dynamic characteristics, but also in the way they are handled; the mass was primarily perturbed by an external gravitational force, whereas the spring was perturbed by internally-applied finger forces. Those two distinct load types are common in ADL tasks where grasping and releasing a load involves gripping forces and displacing a load involves one or more external force sources. The way forces act differently on both loads could also be an explanation for the relatively large errors of the spring’s constant estimate compared to the mass’ parameter estimates. The estimation quality of the spring relies heavily on the relative kinematics, whereas the mass estimate only requires a good estimate of the inclination during static, that is minimal movement, periods. The estimate of the relative orientation between the thumb an index finger tips could be improved when heading information is available during the complete movement and not only during the limited periods of the contact.In our study, the external dynamics were assumed to be rather simple, as only the gravitational acceleration was dominant. Higher order dynamics could be implemented fairly easily for various loads, like drag frictions and inertial accelerations. The latter would be practically easy, but requires either a fairly large mass or a large force sensor bandwidth, which are both troublesome for the current setup.Independent perturbations are required to identify parts of the closed loop system. Depending on the type (movement or force) and location where the perturbation enters the loop, different parts of the loop will be identified. Further research is required to analyze the estimation validity using measures of interaction forces and movement under such various conditions and excitations.A possible application in the rehabilitation field of the proposed device is the classification and quantification of various hand motor tasks. Especially in neurological diseases, it is often the case that the disease resulted in spasticity of the arm and hand muscles. Not only the grasps  could be assessed, but also the planning of the tasks and, hence, the strategy of different subjects aimed at performing a single task could be monitored using our device. Quantitative measures of not only the forces applied to an environmental object, but also measures from the corresponding arm and hand movements give much more information  about the efficiency by which the subject is performing the specific task.Further application areas can be found in machine learning, like the classification of various handled objects. Obviously, a physical interpretation of the quantitative outcomes might be impossible, but the requirements of the sensing hardware could be less strict.The current hardware has a large advantage, as it measures in multiple directions and, therefore, might enable the estimation of complex load dynamics, like a mug with a viscous or granular content.Body-worn unobtrusive sensing systems are of utmost importance for interaction measurements in ADL tasks.The development and preliminary validation of a hand-worn 3D force and movement setup has been presented. The setup allows for measurements of independent finger movements and forces using a custom-made hardware that includes 3D MEMS-based force and inertial sensors, which can be worn on small body surfaces, like finger tips.Two loads were manipulated by the hand, and their dynamic characteristics were estimated by simultaneously measuring kinematic and kinetic sensor data, applying orientation filters and subsequently applying a recursive system identification algorithm.The systems goes beyond pressure sensing and gesture recognition and, therefore, opens the ability to gather profound insights into interaction optimization between the human body and its environment.