The meeting 'From sensory perception to motor output: genetic bases of behavior in the zebrafish embryo' was held at Minerve (South of France) on March 16–18, 2007. The meeting site was beautifully situated in the heart of the Minervois wine country, and its remoteness promoted conversations and interaction over the course of the program. The meeting covered neurogenesis and eye development on day 1, ear and lateral line development on day 2, and brain connectivity and behavior on day 3. Underlying all sessions, however, ran the growing importance of live imaging, an approach that takes full advantage of the transparency of fish embryos and early larvae, as illustrated by several movies and links in this report. The meeting 'From sensory perception to motor output: genetic bases of behavior in the zebrafish embryo'  was heldThe sessions were roughly organized in terms of neurogenesis and eye development on day 1, ear and lateral line development on day 2, and brain connectivity and behavior on day 3. Underlying all sessions, however, ran the growing importance of live imaging, an approach that takes full advantage of the transparency of fish embryos and early larvae. The imaging methods are expanding at a fast rate, with a rapidly increasing panoply of green fluorescent protein (GFP)-expressing reporter lines, fluorescent protein spectral variants, and photoactivatable compounds. Many fascinating movies were presented at the meeting exploring crucial steps in cell migration  similar to that of the eyed fish, but gets rid of the newly formed cohorts of retinal cells by continuous apoptosis. This observation makes the 'energy-saving' explanation somewhat unlikely, although not impossible. He added that it could be more energy efficient to kill newly born cells than to evolve new mechanisms to uncouple stem cell division in the retina and central nervous system. Because blind fish have an expanded mouth and increased number of taste buds, an alternative explanation for eye loss is indirect selection based on an advantageous increase in mouth development.sonic hedgehog (shh), an expansion that also leads to the observed changes in head and mouth morphology. He proposed that there is a trade-off between vision and food detection and that this sensory trade-off played a major role in driving eye degeneration. Other factors are probably at work, though, since only a subset of the ten or so genetic factors (quantitative trait loci (QTL)) implicated in the differences between eyed and surface forms affect both the eyes and the taste buds. Because the surface and cave forms are fully interfertile, QTL analysis can be applied at many levels, for example, development, morphology, and behavior. Astyanax may well turn out to be an excellent system to study evolution caught in the act.Jeffery found that eye loss is due to an expanded domain of expression of the gene shh expression in eye development .rx3 in the formation of the eye fields in medaka and in zebrafish. This gene is expressed very early in the presumptive fields, and mutations in both species result in an eyeless phenotype.Felix Loosli expanded on eye field specification and subsequent morphogenesis. The eye fields are defined at neural plate stages as parts of the diencephalon that will evaginate to form the optic cups. Loosli examined the roles of the transcription factor encoded by rx3:gfp transgenic line allowed the examination of cell movements during the transition from neural plate to optic cup. Surprisingly, the formation of the optic cup is not a simple evagination process. Eye precursor cells behave differently from other central nervous system neurons as soon as the convergence of the neural plate, remaining stationary as they are passed by their neighbors and predetermining the site of evagination. At a later stage eye precursors actively migrate away from their region of origin to form the optic cup. Evagination can thus be viewed as tissue morphogenesis driven by the active behavior of individual cells, rather than as a supracellular process globally determined by external constraints.The generation of an Kristen Kwan took over the session to discuss the transition between the early evagination process and the fully formed optic cup. Using fluorescent membrane and chromatin markers, she described eye morphogenesis in live embryos: soon after the appearance of the wing-like evagination of the lateral forebrain, the optic stalk constricts, generating a 'flipper'-like structure. The lateral part of the optic vesicle will become neural retina, while the medial aspect will form pigmented epithelium. Next, the lens is induced by the neural retina, initiating a complicated torsional movement whereby the retina enwraps the freshly induced lens . PhotoacHer description of early eye morphogenesis suggests that this process involves a very complex sequence of morphogenetic events not unlike the transformation of insect imaginal discs into adult parts such as thorax and wing. To date, such wide-scale changes in tissue shape are not understood in any system, and even the relatively simple process of germ band elongation in fly embryos is still poorly understood. Sophisticated imaging tools may make eye morphogenesis amenable to genetic dissection, and Kwan demonstrated how time-lapse analyses using different fluorescent reporters will facilitate this analysis.Sensory cells develop a transducing system that allows them to transform physical stimuli  into electrical input. This places special constraints on their differentiation program: they must organize synapses that are capable of sustained activity, they have to control the size of their transducing apparatus to provide a reliable estimate of stimulus intensity, and they must have the capability to optimally occupy body space to provide complete but non-redundant information.Monte Westerfield concentrated on a particular set of genes that cause degenerative deafness as well as blindness, the Usher genes. In humans, mutations in these genes produce deafness, as well as photoreceptor degeneration. Westerfield showed that inactivating the fish homolog of any of the known human Usher genes also leads to functional blindness, making the fish an appropriate model to better understand the basis for the human disease. This result led him to develop the idea that degenerative diseases may reveal developmental mechanisms that have gone awry.The Usher proteins all contain PDZ domains and/or PDZ binding domains, suggesting that they probably interact to form a large protein complex involved both in hearing and in vision. One possible role of the Usher proteins may be to assemble the ribbon synapses that are exclusively assembled in photoreceptors (and bipolar cells) in the retina and in hair cells in the inner ear. Ribbon synapses are a specialized type of glutamate synapse that are suitable to handle graded signaling over long times. Impairment in the assembly or maintenance of these specialized synapses may ultimately lead to cell damage and loss, thus explaining the defects associated with the Usher syndrome.Drosophila and mutated in human retinal disease. Ongoing characterization of these genes is revealing new regulators of this important process.Jarema Malicki focused on another common feature of photoreceptors and hair cells: the presence of apical cilia. One of the most striking aspects of ciliated receptors is their complex polarized organization. Malicki has discovered a class of mutations that produce a loss of surface area in either the ciliary or non-ciliary compartment of the apical surface. Molecular analysis of these mutations has identified members of the Crumbs complex, implicated in defining apical domains in Another crucial aspect of ciliated sensory cells is the architecture of the cilium. Some sensory neurons feature a structurally simple cilium while others, such as vertebrate photoreceptors, for example, differentiate complex membrane folds on their surface. Cilium differentiation relies on a specialized transport system that transfers material to and from the ciliary compartment . Transported molecules move as membrane-linked densities, and transport itself depends on a set of so-called intraflagellar transport (IFT) proteins.Numerous mutations in zebrafish, including some in IFT genes, have been shown to disrupt cilium maintenance. Their analysis reveals that genetic mechanisms of ciliogenesis are rather diverse and that even structurally simple cilia are not all equal when it comes to the genetic regulation of their formation. In recent years, the list of cilia functions has been rapidly expanding. In keeping with this trend, the analysis of zebrafish mutants suggests that photoreceptor cilia, in addition to their well-established role in sensing light, may also be involved in the regulation of photoreceptor gene transcription – perhaps to adjust the amount of protein synthesis to environmental conditions.Alvaro Sagasti re-examined the basic problem of 'tiling': how are two-dimensional fields compartmentalized into subsets of abutting sub-fields? He used as a model system the innervation of the head skin by trigeminal neurons. Trigeminal neurons extend neurites, usually called axons even though they are not presynaptic, which extend and ramify until the head epidermis is entirely innervated. He showed that repulsive interactions between left and right neurons mediate the almost perfect ipsilateral confinement of expanding axons , and areTaking advantage of the accessibility of the trigeminal neuritic trees, he then examined what happens after neurite severing. The availability of fluorescent reporter lines makes it possible to follow the process of reinnervation in real time. If the ablation is made at a time when the tiling is still being set up, both the amputated neuron and its neighbors extend into the emptied region and contribute to its innervation, resulting in an expanded field for the neighbors and a shrunken field for the amputated neuron. The real surprise came, however, from later ablations. If a branch is cut after tiling has been fully established, all surrounding neurites react to the change but somehow they are unable to invade the emptied region Figure . Movies A recurrent theme of the meeting was the role and mechanism of cell migration, a process that plays a crucial role in the development of the cerebellum (R Köster), of the hindbrain (H Okamoto and M Rossel), of the eye (K Kwan and F Loosli) and of the lateral line . The buzz expression 'chain migration' was often used to emphasize the difference between these collective processes and individual cell migration, although intense discussions demonstrated that an operational definition of 'chain migration' has yet to be given.Tatjana Piotrowski set the stage for the following talks by providing an excellent and lavishly illustrated introduction to the lateral line system, its function and its development. She concentrated on the most intriguing part of this development, the long-range migration that gives rise to the posterior lateral-line system (PLL). In this process, a primordium arises adjacent to the otic vesicle, moves to the tip of the tail and deposits in its wake five to six small groups of cells, each of which will form a neuromast.Piotrowski provided evidence that Wnt signaling is active in the migrating PLL primordium, and that a mutation affecting Apc, a key regulator of Wnt signaling, results in the deposition of a disorganized stream of cells instead of the precise pattern of neuromasts. The human homolog of the affected gene has been implicated in colorectal cancer, adding one more to the ever-expanding catalog of cancer-associated genes that are also involved in primordium migration.per se. Even though Apc plays roles in other processes besides Wnt signaling, work in the Piotrowski lab has demonstrated that the lateral line phenotype in apc mutant embryos is exclusively caused by Apc's function in regulating Wnt signaling.The Apc mutant shows no obvious defect in cell differentiation nor in the pattern of expression of other genes already known to play important roles in primordium migration, suggesting that Apc may be more directly involved in the organization of the primordium than in migration Darren Gilmour introduced his talk with breathtaking movies that illustrate how local interaction can mediate large-scale coherent movements: he showed how a school of thousands of fish fans out from an intruding diver or how a large flock of birds reacts instantly to the arrival of a prey bird as if the entire school and flock were a single organism, even though as Gilmour noted very few of the fish and birds actually saw the arriving danger.Gilmour focused on the PLL primordium as a typical example of collective cell migration. Using a GFP reporter line specific for lateral line cells  is of concern. Allende demonstrated dose-dependent effects on neuromasts after copper exposure, with hair cells lost at lower doses and additional loss of support cells at higher doses.Sox2, a gene encoding a transcription factor expressed early in neural tissue and involved in stem cell maintenance, is expressed in support cells within the neuromast . Contrary to surface neuromasts, which are sensitive to water velocity, canal neuromasts are most sensitive to acceleration. This dual perception of velocity and acceleration may allow the lateral line system to discriminate between different types of stimuli.Canal neuromasts are present on the head but not on the trunk and tail of adult zebrafish . Head canal neuromasts expand greatly during juvenile growth and become very elongate, as is usually the case for canal neuromasts in other fish species. Zebrafish canal neuromasts are unique, however, in that their long axis is orthogonal to the canal axis , while in the species examined to date the long axis of the neuromasts parallels the axis of the canal. The reason underlying this difference is anyone's guess, but the finding illustrates how adaptive interpretations based on a limited sampling of species may be misleading.The continuous growth of the fish requires that bones and canals, which are embedded in those bones, are remodeled throughout life. Webb examines this process by focusing on the two main players: osteoblasts that form new dermal bone, and osteoclasts that allow bone resorption. She finds that osteoclasts are present on the inner surface of the head canals, opening the way to a genetic analysis of how this remodeling is controlled.Tanya Whitfield presented work from her group on development and evolution of the inner ear. Contrary to the mammalian inner ear, the zebrafish otic vesicle does not form by invagination of an epithelial placode but by cavitation, whereby a mesenchymal mass of cells becomes organized as an epithelium surrounding a central lumen. Whitfield showed that correct patterning of the A/P axis of the otic vesicle depends on Hh signaling, as the ear shows a duplication of anterior elements in embryos in which Hh signaling is down-regulated, and a duplication of posterior structures when Hh signaling is elevated in the embryo.otx1 expression in the ear: the two sensory patches are juxtaposed in zebrafish embryos in which Otx1 function has been knocked down by morpholino injection.These duplicated phenotypes are reminiscent of the relatively symmetrical inner ear found in the lamprey. The similarity is only superficial, however; analysis of molecular markers and hair cell polarity patterns in the lamprey demonstrates that the otic vesicle in this species actually has significant asymmetries about the A/P axis, and closely resembles the developing zebrafish ear. The two separate sensory patches present in the zebrafish otic vesicle would, therefore, result from the splitting of a single sensory patch present in the common ancestor of lampreys and teleosts, rather than from the development of a new patch. Splitting of an ancestral patch appears to have been dependent on the acquisition of a new domain of How Hh signaling acts to polarize the otic vesicle is not clear, since A/P polarity can be detected as soon as cavitation begins, at a stage when the long axis of the vesicle is parallel to the major sources of Hh signaling, the notochord and floorplate. Furthermore, an excess of Hh signaling is detrimental to the establishment of the other two axes (D/V and M/L) as well. It seems likely, therefore, that other factors act in addition to Hh proteins to establish the axes of the inner ear.robo2 mutants. The shift does not result from a general remodeling of the hindbrain in robo2 mutants because other axonal trajectories such as reticulospinal projections growing in close vicinity to the dopaminergic fibers retain their normal positions.After dealing with the development of sensory capabilities, the talks focused on the integrative capabilities of the brain. Jörn Schweitzer introduced the change in focus with a nice movie exploring the ordered complexity of the dopaminergic system and its connectivity Figure . He demoorthopedia gene, otpa, is a key transcriptional regulator of ventral diencephalic dopaminergic neurons in fish. The lack of otpa activity leads to a strong reduction of dopaminergic diencephalic neurons and their respective projections into the spinal cord. Behavioral analysis of otpa mutant larvae indicates defects in the motor system, such as a delay in the initiation of movementsThe connectivity of dopaminergic neurons relates directly to behavior as demonstrated by the analysis of zebrafish mutants affecting the specification of dopaminergic neurons. Schweitzer showed that the gad2, a marker of inhibitory neurons. The analysis of gad2:gfp neurons reveals that they project to the contralateral side of the hindbrain, presumably allowing for an instantaneous comparison between left and right inputs. This comparison may be important to help fish swim against water flow (and explain why river fish are not washed out in the oceans).The sensory neurons of the PLL extend a peripheral axon to the migrating primordium  projection to higher brain centers in adult fish. Inactivation of atoh1a removes this component of the projection without affecting the contralateral projection of the gad2+ neurons.A second component is revealed by the expression of the Alain Ghysen also examined the second-order PLL projection with the slightly different aim of understanding how sensory inputs are handled by the brain and integrated in a coherent behavior. He relied on DiI labeling of the synaptic field formed by the afferent neurons that innervate the posterior lateral line. He confirmed the data of Okamoto about the early presence of a projection to the torus semicircularis in 4 dpf larvae . An interesting question (S Wilson) was whether the proportion is the same in blind and eyed forms – because the blind form is less social than the eyed form, a difference in proportion might point to an effect of socialization in setting the balance between left-finned and right-finned fishA similar left-right bias was also noticed by Anukampa Barth (poster session) when she examined the balance between fear and curiosity of fish presented with an unexpected stimulus on either the right or the left eye. It will be interesting to find out whether these 'psychological' differences between right and left brain are associated with lateralization of the habenular system discussed by Wilson and Okamoto.The question of brain laterality was taken to a more developmental level by Wilson and Okamoto. Steve Wilson discussed the origin and selective advantages of laterality. As he explained, very little is presently understood about the population biology and evolution of laterality. The most basic questions, such as whether bilateral symmetry is a default state or whether it is a feature superimposed on a fundamentally asymmetric structure, still remain quite open. Even more importantly, while it is clear that asymmetries pervade the organization and function of brain and body alike, what exactly is their adaptive value (if any) is still a matter of speculation – an ingredient that fortunately was abundant throughout the meeting.Wilson concentrated on the special case of a forebrain structure, the habenula, which provides input to a midbrain structure, the interpeduncular nucleus (IPN). The axons from the left and right habenulae innervate two non-overlapping regions of the IPN . This asfgf8. A second step is the choice of whether the parapineal will be localized left or right. This step requires nodal function. In the absence of nodal, however, the migrating cells decide to migrate either right or left, instead of forming two small parapineal nuclei on either side of the midline. Thus, there must be at least one additional step forcing the cells to migrate to only one side of the brain even in the absence of nodal, setting up this fundamental asymmetry of the brain.Genetic analysis suggests that the lateralization of the habenula comprises several components. A first step would be the lateral migration of pineal neurons to form the parapineal nucleus, a step that appears to depend on the bilateral expression of Hitoshi Okamoto showed that the difference in connectivity between left and right habenula depends on a large size difference between two subnuclei, a medial one that is prominent in the right habenula and projects to the ventral IPN, and a lateral one that is prominent in the left habenula and projects to the dorsal IPN. He then examined the pattern of neurogenesis of the habenula precursor cells by using both bromodeoxyuridine (BrdU)-pulse labeling and cell-lineage tracing using photoconversion of differentiated neurons in a HuC-Kaede transgenic line. He showed that neurogenesis follows different time courses in the prospective left and right habenular regions, suggesting that lateralization is set up very early in brain development.In order to determine whether this temporal difference in neurogenesis is responsible for the differences in neuronal identity between medial and lateral subnuclei, Okamoto used heat-shock activation of Notch to block neurogenesis at different times. He observed that a marker for the early neurons forming the lateral subnucleus  is markedly depleted when Notch activation is forced early on, while a marker for the late neurons that form the medial subnucleus is ectopically expressed on both sides of the midline, instead of being largely restricted to the right side. The link between the asymmetric localization of the parapineal discussed by Wilson, and the asymmetric neurogenesis reported by Okamoto, remains to be discovered.Okamoto also examined the tectobulbar tract that connects the optic tectum to the reticulospinal neurons in the hindbrain using another transgenic line, Tg [brn3a:GFP]. Because reticulospinal neurons in turn control spinal motoneurons, this pathway is an essential component of the visual control of motion. The neural circuits controlling visuo-motor transformation might be lateralized as suggested by the observation that when fish approach a new object they do so very carefully and use their right eye . On the contrary, they display no ocular dominance when they encounter a well-known object. No morphological asymmetry could be detected in this pathway, however, leaving open the possibility that, in this case, lateralization is at the level of function. The possibility of labeling single tectal efferent neurons  present in the skin of all ostariophysians fish.Jesuthasan described electroporation techniques developed in his lab to label and follow cells within the nervous system. These electroporation methods are likely to be useful to a number of labs interested in dissecting circuit function. More generally, this talk made it clear that new techniques for the analysis of brain circuits will be critical to understanding complex individual and social behaviors.Michael Granato took on the same theme in embryos – where the manifestation of fear is called 'startle response'. The startle response is induced by a sudden, intense sensory stimulation and comprises a very stereotyped set of muscle contractions called 'C-turn' Figure , the resGranato's question was, can this innate strong response be modulated? It is known in humans (and very convincingly demonstrated by Granato through movies exploring the startled behavior of unsuspecting graduate students) that sensory information can be 'gated', that is, that previous experience can modify our response to a frightening stimulus. This 'pre-pulse inhibition' is reduced in human schizophrenia, Tourette and a mild version of autism, Asperger's syndrome.The conclusion of the work is that a non-frightening pre-pulse can inhibit startle response by as much as 70% as long as it is provided less than 100 ms before the startling stimulus. Similar to the situation in humans, this pre-pulse inhibition is enhanced by agents such as nicotine and haloperidol, which are known in humans to reduce fright. Granato described his ongoing search for mutations that alter the startle response and may yield useful cues about the human response and its modulation.Florian Engert explored another aspect of cross-modality: how exactly does visual information impinge upon orientation to  prey? He showed that visual control of movement is already very sophisticated in the early larva. For example, a spot corresponding to a visual angle of 1 (about the apparent size of a paramecium) elicits a tracking behavior, a spot of 5 elicits an escape behavior, while a spot of 20 elicits an optomotor response. These differences appear innate, implying a high level of genetic control of visual processing circuits.Detailed analysis of prey-tracking also revealed interesting subtleties. For example, tracking of the prey by rotating an eye is achieved by smooth continuous movement of the eye, while tracking by rotating the body axis is achieved in jerks. Some aspects of this tracking are rather puzzling: for example, why is it that the movement of an eye tracking a moving paramecium is accompanied by the antagonistic (apparently meaningless) movement of the other eye? Clearly we need to understand more of the underlying connectivity to make sense of such nonsense. In order to better analyze prey-tracking responses like these, which likely involve the coordinated action of a number of neurons, Engert is developing a system of live imaging of neuronal activity. Contrary to the usual systems based on magnetic resonance or positron emission, however, the system he is developing can allow single-cell reconstruction of neuronal activity.This last talk reinforced the take-home lesson of the entire meeting; that methods to visualize neural development and function in real time and at the level of the single cell will probably be crucial in our attempts to understand the brain. The advent of such imaging methods in the zebrafish embryo may well represent a unique opportunity to break the genetic code of behavior.The author(s) declare that they have no competing interests.Migration of the posterior lateral line primordium as visualized in a claudin-GFP line. Movie provided by D GilmourClick here for filecxcr7 morphant embryo. Movie provided by D GilmourMigration of the posterior lateral line primordium in a Click here for filecxcr4b mutant embryo. Movie provided by D GilmourMigration of the posterior lateral line primordium in a Click here for fileTime-lapse observation of a growing lateral line axon in a 28 hph embryo injected with the HuC-Kaede plasmid. Time-lapse observation of a growing lateral line axon in a 28hph embryo injected with the HuC-Kaede plasmid, as described in . In thisClick here for fileTime-lapse observation of the same lateral line axon displayed in three dimensions. Movie by Hideomi Tanaka, Tomomi Sato and Hitoshi OkamotoClick here for fileSecond-order projection from the lateral line to the torus semicircularis. A series of 22 frontal planes, from posterior to anterior, taken from a 300 micron thick frontal vibratome section. The fibers enter as bundles (first frames) and arborize as they reach their targets. The LT branch arborizes along the torus semicircularis; as this branch reaches its most anterior extent (last frames) a few fibers escape and climb dorsally into the overlying tectum (yellow arrows). Also present in this figure is the PM branch that arborizes just anterior to the oculomotor nucleus. Movie provided by A Ghysen.Click here for fileThree-dimensional stack documenting the second-order projection illustrated Figure 8, from the most ventral to the most dorsal plane . The dorsal planes reveal a few fibers climbing dorsally from the anterior tip of the LT branch into the deep layer of the optic tectum (yellow arrows). Movie provided by A Ghysen.Click here for fileA blind Mexican cave fish leisurely swimming in an annular arena with Lego landmarks to which the fish is accustomed. This clip shows part of the last training trial (control) after the fish had been repeatedly presented with the experimental arena. Movie provided by T Burt de Perera.Click here for fileThe same cavefish in the same arena, after two of the landmarks had been switched , changing their order. Note how much faster the fish is swimming in the test trial than in the control, indicating that it had recognized a change in its environment. Movie provided by T Burt de Perera.Click here for fileIndividual efferent neuron in the optic tectum, stochastically labeled with the Cre-loxP/Gal4-UAS system. Individual efferent neuron in the optic tectum, stochastically labeled with the Cre-loxP/Gal4-UAS system described in . Movie bClick here for fileThe fish startle response. The time of mechanical stimulation is shown on the lower line. Movie provided by Michael Granato.Click here for file


Stereotactic radiotherapy, which delivers an ablative high radiation dose to a target volume for maximum local tumor control, requires a rapid dose fall-off outside the target volume to prevent extensive damage to nearby normal tissue. Currently, there is no tool to comprehensively evaluate the dose gradient near the target volume. We propose the dose gradient curve (DGC) as a new tool to evaluate the quality of a treatment plan with respect to the dose fall-off characteristics.differential and cumulative, were generated. The performance of the DGC was evaluated using stereotactic radiosurgery plans for virtual targets.The average distance between two isodose surfaces was represented by the dose gradient index (DGI) estimated by a simple equation using the volume and surface area of isodose levels. The surface area was calculated by mesh generation and surface triangulation. The DGC was defined as a plot of the DGI of each dose interval as a function of the dose. Two types of DGCs, Over the range of dose distributions, the dose gradient of each dose interval was well-characterized by the DGC in an easily understandable graph format. Significant changes in the DGC were observed reflecting the differences in planning situations and various prescription doses.The DGC is a rational method for visualizing the dose gradient as the average distance between two isodose surfaces; the shorter the distance, the steeper the dose gradient. By combining the DGC with the dose-volume histogram (DVH) in a single plot, the DGC can be utilized to evaluate not only the dose gradient but also the target coverage in routine clinical practice. Stereotactic radiotherapy, often referred to as stereotactic radiosurgery (SRS) or stereotactic ablative radiotherapy (SABR), is a highly focused radiotherapy technique that delivers an intense radiation dose concentrated on a tumor, while limiting the dose to the surrounding normal tissues. SRS or SABR plans should be evaluated based on the quality of target coverage to maximize the dose to the target, and on the steepness of the dose gradient outside the target volume to minimize the dose to organ-at-risks (OARs). A dose-volume histogram (DVH) is most commonly used as a plan evaluation tool to achieve these two objectives . To dete50%, has been widely adopted as a benchmark for assessing the dose gradient beyond the PTV extending into normal tissue structures [50% have allowed quantitative analysis of the dose gradient and comparison of competing plans on the basis of these scores, the complexity of the dose profile over the range of dose distribution cannot be taken into account. Furthermore, the current volume-based indices are highly dependent on target volume and shape, and would provide misleading results especially when examining small target volumes or complex target shapes [Dose fall-off characteristics near the target volume can be evaluated by visual inspection of two-dimensional isodose distributions, section by section. It is possible to visualize cross sectional dose profile using dosimetry software, but objective measurement of the dose gradient is nearly impossible. The gradient index (GI), defined as the ratio of the volume of half the prescription isodose to that of the prescription isodose, has been proposed as a simple dose gradient measurement tool . The ratructures , 13. Altt shapes .differential and cumulative, are available. The performance of DGC was systemically investigated with virtual structures.We propose the dose gradient curve (DGC) as a distance-based dose gradient evaluation tool which is independent of target volume and shape to complement the DVH and/or the conformity index. The dose gradient is represented as a form of a dose gradient index (DGI), the average distance between two isodose surfaces; the shorter the distance, the steeper the dose gradient. The DGC is defined as a plot of DGI as a function of the dose over the range of dose distributions. Two types of DGCs, V and S represent the volume and surface area of an isodose level, and the subscripts L and H represent the lower and higher doses (The DGI measures the average distance between two isodose surfaces. The isodose surface is defined as the uniform dose contour receiving a certain dose. The volume and surface area of each isodose level are used to estimate the average distance between two isodose surfaces . The isoer doses .d to produce a double-layer structure with uniform spacing (d (DGIsphere = DGIcube = d).The accuracy of the DGI in estimating the average distance between two isodose surfaces was verified mathematically using simple geometric objects: a sphere and a cube. Each of these structures was expanded uniformly by a distance  spacing . The DGI3 in volume with a concave and convex surface was created using the Eclipse treatment planning system . This structure was uniformly expanded to generate a multi-layer structure at regular intervals of 1 mm  provides high-quality mesh generation and surface triangulation. Using three-dimensional data points representing the isodose surface, the volume of the isodose contour and its surface area were calculated  was defined as the DGI of each dose interval, and the dDGI for dose i (Gy or %) was calculated as:V and S represent the volume and surface area of an isodose level, and d is the calculation interval. The differential DGC (dDGC) is a plot of the dDGI as a function of the dose (The the dose . From thcumulative DGC (cDGC) is a plot of the cumulative DGI (cDGI) and is generated by summing the dDGI values from the reference dose to the desired dose , and then every point plotted in the cDGC indicates the average distance from the reference isodose to each isodose surface. By default, the prescription dose (100% isodose) is used as the reference dose. The minimum dose covering 100% of the target volume (D100%) is also used as the reference dose, and then the cDGC originates from the point representing 100% target coverage. The plotting range of the cDGC is from the reference dose to the dose where the isodose surface intersects the body surface (cropped 3 mm from the skin surface).The red dose . The cDGThe performances of the DGCs were evaluated with a virtual structure in various planning situations. A solitary intracranial spherical target of 3 cm diameter was generated in contouring software. The SRS plan for the virtual target was produced using Dynamic Arc (DA), and the prescription dose was 15 Gy in a single fraction.The dosimetric influence of the number of arcs with respect to the dose gradient was studied using two virtual targets of 1 cm diameter; one was on the peripheral part of the brain, and the other was near the brainstem. For each of these targets, single fraction SRS plans (24 Gy) were generated using 1, 2, 3, 4, 5, and 7 arcs.Structure delineation and generation of SRS plans were performed with the Eclipse treatment planning system using a calculation grid size of 1 mm, and each isodose level was converted to a structure volume. All plans were designed to be delivered on Novalis Tx linear accelerator consisting of high-definition multileaf collimators (HD-MLCs: 2.5 mm leaf width at isocenter). Three-dimensional coordinate data of all isodose structures were exported to the R environment using the Mirada RTx .sphere) as:r is the radius of the sphere, and d is the distance between the spheres. In the same way, the DGI of a cube (DGIcube) can be expressed as:a is the edge length of the cube. The relative error (er) of the DGI for simple geometric structures can be described as:r = a = 10 mm, we find that the relative error for d = 1 mm is 0.0055 (0.0055 mm), and the relative error for d = 0.3 mm is 0.0006 (0.0002 mm).Mathematical verification of the DGI was performed using simple geometric objects. For a sphere, as shown in The accuracy of the DGI was investigated by using the multi-layer structure at 1-mm regular intervals with an irregular surface and shape, as shown in differential DGC (dDGC) at a millimeter scale (cumulative DGC (cDGC) was generated. The cDGC demonstrated a characteristic rotated sigmoid shape when plotted with the cDGI on the y-axis versus the isodose level on the x-axis. The cDGC started from the prescription isodose level (cDGI100% = 0) and moved downward from there. All plot options for the DGC are listed in The data from er scale . From thThe dDGCs for varying calculation intervals (step sizes) were plotted . The dDG100% = 100%). The combined plot demonstrated the influence of varying the number of arcs on the cDGC and the DVH  with varying tumor locations, and all plans were normalized to deliver the prescription dose (24 Gy) to cover 100% of the target volume  in such a way that the cDGC could be plotted in a more easily comparable format . As step size refers to the interval between isodose levels used in calculating the dDGC, the average distance increases with increasing step size . The dDGThe dose-volume histogram (DVH) has been accepted as an essential tool for plan evaluation and can be generated by the treatment planning system. The incorporation of the DGC into the treatment planning system could enable immediate calculation and visualization of the DGC just as for the DVH, which uses the same coordinate system as the DGC. By virtue of the combined plot of the DGC and the DVH, the dose gradient as well as the target coverage can be evaluated in a single plot with double y-axis.Increasing the number of arcs provides additional flexibility when tailoring the dose distribution. A key question is what number of arcs should be used to generate the maximum dose gradient for an SRS/SABR plan. In this study, the dosimetric influence of the number of arcs with regard to dose fall-off characteristics was studied by the use of the cDGC. Without any consideration of OAR sparing near the target volume, the cDGC showed that the maximum steepness of the dose gradient was obtained using 3 dynamic arcs . The dosThe SRS/SABR dose should be prescribed to the target volume between the 60% and the 90% isodose levels of the total dose (not the prescription dose), and a 50% higher dose prescribed to the isocenter is acceptable , 16. The50% have been used for evaluating the dose fall-off outside the target volume [30% and R60%. For example, when the cDGI of 50% (cDGI50%) was the same, the actual dose gradient outside the prescription isodose volume could vary, as shown in Various indices such as the Gradient Index (GI), the Conformity Gradient Index (CGI), and Rt volume , 11. HowThere are several limitations associated with this study. The DGC did not provide any directional information but provided the average distance between two isodose surfaces. However, the DGC can be modified to represent the dose gradient only in a particular direction by means of the Volume-of-Interest (VOI). We can define the VOI enclosed by two radial planes to form a cylindrical sector-like volume with its axis passing through the isocenter. This allows to narrow down the range of calculation in a specified direction, as shown in In this study, we proposed and assessed the DGC as a new tool to evaluate the quality of a treatment plan. The DGC rendered it possible to evaluate the dose gradient comprehensively over the range of dose distributions and to compare rival plans objectively. Despite certain limitations, our results demonstrate that the DGC, as a complementary tool, provides useful information that cannot be obtained by any other indices or display tools. Moreover, in combination with the DVH in a single plot at the same dose scale, the DGC can be utilized to evaluate not only the dose gradient but also the target coverage in routine clinical practice.S1 Code(PDF)Click here for additional data file.


In the past decades, the inappropriate subsidy policies in many nations have caused problems such as serious oversupply, fierce competition and subpar social welfare in the photovoltaic (PV) industry in many nations. There is a clear shortage in the PV industry literature regarding how dual supply chains compete and the key decision issues regarding the competition between dual PV supply chains. It is critical to develop effective subsidy policies for the competing PV supply chains to achieve social welfare maximization. This study has explored the dual PV supply chain competition under the Bertrand competition assumption by three game-theoretical modeling scenarios (or supply chain strategies) considering either the public subsidy or no subsidy from a social welfare maximization perspective. A numerical analysis complemented by two sensitivity analyses provides a better understanding of the pricing and quantity decision dynamics in the dual supply chains under three different supply chain strategies and the corresponding outcomes regarding the total supply chain profits, the social welfare and the required total subsidies. The key findings disclose that if there are public subsidies, the dual PV supply chains have the strongest intention to pursue the decentralized strategy to achieve their maximal returns rather than the centralized strategy that would achieve the maximal social welfare; however, the government would need to pay for the maximal subsidy budget. Thus, the best option for the government would be to encourage the dual PV supply chains to adopt a centralized strategy since this will not only maximize the social welfare but also, at the same time, minimize the public subsidy. With a smart subsidy policy, the PV industry can make the best use of the subsidy budget and grow in a sustainable way to support the highly demanded solar power generation in many countries trying very hard to increase the proportion of their clean energy to combat the global warming effect. Several subsidy policies such as shared solar energy arrangements and performance-based incentive (PBI) are proposed to integrate the market users and the PV supply chains. This study serves as a pioneering study into the dual PV supply chain research which is very limited in the PV management and policy study literature. The findings and several untended issues provide a foundation for the future PV supply chain studies. Given the abundance of sunshine across the globe, solar power has the potential to supply a significant amount of electricity that is both economically and environmentally attractive. Solar power generates electricity with no global warming pollution, no fuel costs, and no risks of fuel price spikes, and has the potential to help move the world toward cleaner, reliable, and affordable sources of electricity ,2. The iThe solar photovoltaic energy, a major source of solar power, has been encouraged and developed by many countries to counter the impact due to the global warming effect. Photovoltaics (PV) industry policies are made and implemented by many governments. Large-scale photovoltaic energy development programs can be seen in many developed and developing nations. Furthermore, costs for large-scale PV projects have dropped significantly since 2010 owning to the reductions in technology prices, innovative financing, and growing networks of solar installers and financial partners. By 2050, it is estimated the PV global cumulative installed capacity could reach 16% of the global electricity production  measures the degree of product substitutability, with γ = 0 and 1 representing the cases of completely independent and homogenous products, respectively. Besides, a is the maximum demand (when its own retail price and its competitor’s retail price are both zero), b is the reaction extent of the PV system demand w.r.t. the change of its own retail price, d is the reaction extent of the PV system demand w.r.t. the change of its competitor’s retail price, b > d. The decision variables are the wholesale price Both PV supply chains may adopt a pure decentralized strategy, i.e., the members in a PV supply chain compete in a Stackelberg way ,24,25,26iSC and jSC, the profit functions of the PV system assembler iPA and jPA, and the profit functions of the module supplier iMS and jMS are represented as follows:The profit functions of the PV supply chain CS for the dual competing PV supply chains can be defined as follows [Following Singh and Vives (1984), the representative consumer surplus  follows :(7)CSSW and a PV system assembler (PA) make optimal decisions in a Stackelberg way [i chooses his optimal wholesale price i chooses his optimal retail price s to achieve the social welfare maximization, module supplier i now cooperates with PV assembler i to make joint decisions; they will bargain over the wholesale price decentralized scenario: both competing supply chains adopt a decentralized strategy; (2) a centralized scenario: both competing supply chains adopt a centralized strategy; and (3) a hybrid scenario: one supply chain adopts a centralized strategy while the other supply chain adopts a decentralized strategy.In a decentralized PV supply chain, the government decides the optimal subsidy factor berg way ,24,25,26The game-theoretical decision models regarding the module suppliers (MSs) and the PV system assemblers (PAs) in the dual competing PV supply chains are developed in this section. The optimal conditions for three modeling scenarios are derived through the theoretical modeling analyses resulting in the equilibrium  wholesale price and retail price for each scenario. Thus, the profits of the dual PV supply chains, MSs, PAs and the social welfare can be calculated for the numerical analysis study in the next section and also compared.For the convenience of notation, let iPA and the module supplier iMS play the Stackelberg game, so do jMS and jPA. iMS acts as a Stackelberg leader and iPA acts as a Stackelberg follower, so do jMS and jPA. iMS first decides the wholesale price of a module, iPA then decides the retail price of a PV system to maximize his profit, so do jMS and jPA. Finally, the retail price competition occurs in the PV market. The Stackelberg game model for the dual competing PV supply chains can be formulated as:In the decentralized modeling scenario, the government announces the subsidy factor first, then, the PV system assembler Solving this two-stage Stackelberg game, we can obtain the equilibrium government subsidy factor iPA, iMS, iSC, jPA, jMS, jSC, the equilibrium SW, CS and TS as follows:We can get also the equilibrium profits of iMS and the PV system assembler iPA cooperate with each other via Nash bargaining mechanism, so do jMS and jPA. iMS and iPA bargain over the wholesale price of a module to achieve cooperation within the PV supply chain i. The PV supply chain i then sets the retail price of a PV system to maximize its profit, so do jMS and jPA. At last, the retail price competition occurs in the PV market. The Stackelberg game-Nash bargaining model for the dual competing PV supply chains can be formulated as:In the centralized modeling scenario, the government announces the subsidy factor first, then, the module supplier Solving this two-stage Stackelberg game-Nash bargaining problem, we can obtain the equilibrium government subsidy factor iPA, iMS, iSC, jPA, jMS, jSC, the equilibrium SW, CS and TS as follows:We can also get the optimal (or bargaining) profits of iPA and the module supplier iMS play a Stackelberg game, iMS acts as a Stackelberg leader and iPA acts as a Stackelberg follower; jPA and jMS cooperate with each other via a Nash bargaining mechanism. iMS first decides the wholesale price of a module, iPA then decides the retail price of a PV system to maximize his profit; jMS and jPA bargain over the wholesale price of a module to achieve cooperation within the PV supply chain j. The PV supply chain j then decides the retail price of a PV system to maximize its profit. At last, the retail price competition occurs in the PV market. The Stackelberg game-Nash bargaining model for the dual competing PV supply chains can be formulated as:In the hybrid modeling scenario, the government announces the subsidy factor first, then, the PV system assembler Solving this two-stage Stackelberg game-Nash bargaining problem, we can obtain the equilibrium government subsidy factor Hereinto,iPA, iMS, iSC, jPA, jMS, jSC, the equilibrium SW, CS and TS as follows:We can also get the optimal (or bargaining) profits of To validate the impact and the necessity of the public subsidy, the equilibrium and cooperation of the dual PV supply chains without the government’s subsidy, i.e., iPA and the module supplier iMS play the Stackelberg game, so do jMS and jPA. iMS acts as a Stackelberg leader and iPA acts as a Stackelberg follower. iMS first decides the wholesale price of a module, iPA then decides the retail price of a PV system to maximize his profit, so do jMS and jPA. Finally, the retail price competition occurs in the PV market. The Stackelberg game model for the dual competing PV supply chains can be formulated as:In the decentralized modeling scenario, the PV system assembler Solving this two-stage Stackelberg game, we can obtain the equilibrium wholesale price iPA, iMS, iSC, jPA, jMS, jSC, SW and CS as follows:We can also get the equilibrium profits of iMS and the PV system assembler iPA cooperate with each other via Nash bargaining mechanism, so do jMS and jPA. iMS and iPA bargain over the wholesale price of a module to achieve cooperation within the PV supply chain i. The PV supply chain i then decides the retail price of a PV system to maximize its profit, so do jMS and jPA. At last, the retail price competition occurs in the PV market. The Stackelberg game-Nash bargaining model for the dual competing PV supply chains can be formulated as:In the centralized modeling scenario, the module supplier Solving this two-stage Stackelberg game-Nash bargaining problem, we can obtain the bargaining wholesale price iPA, iMS, iSC, jPA, jMS, jSC, SW and CS as follows:We can also get the optimal (or bargaining) profits of iPA and the module supplier iMS play the Stackelberg game, iMS acts as a Stackelberg leader and iPA acts as a Stackelberg follower; jPA and jMS cooperate with each other via Nash bargaining mechanism. iMS first decides the wholesale price of a module, iPA then decides the retail price of a PV system to maximize his profit; jMS and jPA bargain over the wholesale price of a module to achieve cooperation within the PV supply chain j. The PV supply chain j then decides the retail price of a PV system to maximize its profit. Finally, the retail price competition occurs in the PV market. The Stackelberg game-Nash bargaining model for the dual competing PV supply chains can be formulated as:In the hybrid modeling scenario, the PV system assembler Solving this two-stage Stackelberg game-Nash bargaining problem, we can obtain the equilibrium (or bargaining) wholesale price iPA, iMS, iSC, jPA, jMS, jSC, SW and CS as follows:We can also get the optimal (or bargaining) profits of a = 5000, b = 3, d = 1. The bargaining power of a MS is set as: τ = 0.4 lower than that of a PA. In MS1, MS2 and PA1, PA2 in the dual PV supply chains are set according to the average costs of the PV industry. The two supply chains have a similar cost structure where the supply chain i has a one dollar advantage over the supply chain j for both module unit costs and BoS unit costs and the same seller-buyer relationship and market size to begin with. The sensitivity analysis is conducted by adding a dollar to the unit costs twice on the supply chain j as shown in Sensitivity One and Sensitivity Two.Due to the high conversion efficiency and its popular application, a PV system with modules of 6 × 12 (72) solar cells (max output-power: 335 Watt) for general solutions is used for the numerical analysis of the PV supply chain models developed in (1)i and j, the wholesale price of a module for the centralized scenario is less than that of the hybrid scenario; and the wholesale price of a module for the hybrid scenario is less than that of the decentralized decision i, the retail price of its PV system under the centralized scenario is less than that under the decentralized scenario, and the retail price of a PV system under the decentralized scenario is less than that under the hybrid scenario; for the higher cost PV supply chain j, the retail price of a PV system under the centralized scenario is more than that under the decentralized scenario, and the retail price of a PV system under the decentralized scenario is more than that under the hybrid scenario i, the ordering quantity of a PV system under the centralized scenario is larger than that under the decentralized scenario, and the ordering quantity of a PV system under the decentralized scenario is larger than that under the hybrid scenario; for the higher cost PV supply chain j, the ordering quantity of a PV system under the centralized scenario is less than that under the decentralized scenario, and the ordering quantity of a PV system under the decentralized scenario is less than that under the hybrid scenario i and j, the equilibrium  profits of the PV supply chains and their members under the centralized scenario are less than those under the hybrid scenario, and the equilibrium  profits of the PV supply chains and their members under the hybrid scenario are less than those under the decentralized scenario Among the three modeling scenarios, the equilibrium social welfare under the centralized scenario is more than that under the hybrid scenario, and the equilibrium social welfare under the hybrid scenario is more than that under the decentralized scenario see .(6)Among the three modeling scenarios, the customer’s surplus under the centralized scenario is more than that under the hybrid scenario, and the customer’s surplus under the hybrid scenario is more than that under the decentralized scenario see .(7)Among the three modeling scenarios, the government’s subsidy under the centralized scenario is less than that under the hybrid scenario, and the government’s subsidy under the hybrid scenario is less than that under the decentralized scenario see .(8)i are fixed, when the unit module cost and the unit assembly cost of PV supply chain j increases by a dollar, the equilibrium  profits of PV supply chain i and j and their members will decrease, the trend also holds for the equilibrium social welfare, the customer’s surplus and the government’s subsidy (see When the unit module cost and the unit assembly cost of PV supply chain sidy see . Neverth(9)i and j and their members under the government’s subsidy are more than those without the subsidy. The trend holds also for the equilibrium social welfare and the customer’s surplus  profits of PV supply chain plus see .(10)Between the subsidy and no subsidy, the dual PV supply chains have the largest incentive to seek subsidies and pursue the decentralized strategy to achieve their maximum returns; however, the government would need to pay the maximal subsidy budget. The best option for the government would be to encourage the dual PV supply chains to adopt a centralized strategy since this will not only maximize the social welfare but also, at the same time, minimize the public subsidy. If there is no public subsidy, the optimal strategy for the dual supply chains would be to pursue the centralized strategy to gain the most returns for the supply chain members and the supply chains comparing to the decentralized or the hybrid strategies. The centralized strategy also creates the maximal social welfare when there is no subsidy.The numerical and sensitive analysis results of the dual competing PV supply chain equilibrium and cooperation under the social welfare maximization and the results with and without the government’s subsidy are shown and compared in i and j can create the highest total PV system demands, total supply chain profits and social welfare in the dual supply chain system when there is no government subsidy  as the suppliers. If both module suppliers have the market power powers within their own supply chains, they would have higher motivations to take the decentralized strategy to charge much higher wholesale prices and maximize their own profits rather than to be a “nice guy” to sacrifice for the goodness of the supply chains and the society. If one supplier has the market power and the other does not, the hybrid strategy would become the best supply chain strategy for the dual supply chains but the total supply chain profits and the social welfare would be in the middle of those created by the other two supply chain strategies.It is obvious that taking the centralized strategy for both supply chain sidy see . Under tsidy see . HoweverSince the competition now is between two supply chains, the supply chain members in each supply chain should take the cooperative approach to create the highest demands in the market and maximize the total supply chain profits. Thus, under the case without the public subsidy, it is the best from the social welfare maximization and the total supply chain perspective for the dual supply chains to adopt a centralized strategy.Therefore, an innovative mechanism should be developed in the dual supply chains to provide more incentives to the module suppliers, such as offering higher wholesale prices, revenue-sharing by the PV assemblers, to ensure the supply chains would move towards a centralized supply chain system. In other words, new methodologies or innovations should be developed to deal with the problem that the Nash bargaining under the Bertrand competition could not resolve in this study. This provides a new direction for the future study of the dual supply chain competition.When the public subsidy is available, the centralized and the decentralized strategies create the same amount of the social welfare value which is better than that of the hybrid strategy. However, the decentralized strategy consumes three times more subsidy money than that of the centralized strategy, in the mean times, also takes away three times more supply chain profits than that of the centralized strategy.Since the dual supply chains, with the subsidy money, can sell PV systems to the market with prices much lower than their costs, much more demand can be created. This serves well the purpose of promoting the solar energy industry. However, the decentralized dual supply chains reap too much subsidy money due to the market power of the module suppliers. Thus, from the public policy perspective, gearing the dual supply chains to take a centralized strategy would serve the public interest best since this not only creates the largest social welfare effect but also uses the least amount of subsidy money (comparing to the other two supply chain strategies).To avoid over-subsidizing to the PV industry, it would be wise for a government to set a threshold or ceiling to the subsidy based on the centralized modeling results and develop policies that can encourage the members in PV supply chains to cooperate and form centralized supply chains.An effective subsidy mechanism must integrate the market users and the PV supply chains. There are several directions to design an effective subsidy mechanism . Shared Whenever possible, incentives should be awarded to the high-performing PV system assemblers and their supply chains. Direct incentives can be adjusted to encourage the PV system installations that maximize peak energy production. A performance-based incentive (PBI) is based on the actual energy production of a PV system. PBIs inherently incentivize optimal system design and encourage active, ongoing maintenance ,36. PBIsThis study has explored the dual PV supply chain competition under the Bertrand competition assumption by three game-theoretical modeling scenarios (or supply chain strategies) considering either the public subsidy or no subsidy from a social welfare maximization perspective. A numerical analysis complemented by two sensitivity analyses provides a better understanding of the pricing and quantity decision dynamics in the dual supply chains under three different supply chain strategies and the corresponding outcomes regarding the total supply chain profits, the social welfare and the required total subsidies.The key findings reveal that if there is no public subsidy, the optimal strategy for the dual supply chains would be to pursue the centralized strategy to gain the most returns for the supply chain members and the supply chains comparing to the decentralized or the hybrid strategies. The centralized strategy also creates the maximal social welfare when there is no subsidy. Furthermore, if there are public subsidies, the dual PV supply chains have the strongest intention to pursue the decentralized strategy to achieve their maximal returns rather than the centralized strategy that would achieve the maximal social welfare; however, the government would need to pay for the maximal subsidy budget. Thus, the best option for the government would be to encourage the dual PV supply chains to adopt a centralized strategy since this will not only maximize the social welfare but also, at the same time, minimize the public subsidy.To prevent over-subsidizing to the PV industry, this study recommends a government could set a threshold or ceiling to the subsidy based on the centralized modeling results and develop policies that can encourage the members in the PV supply chains to cooperate and form centralized supply chains. Several subsidy policies such as shared solar energy arrangements and performance-based incentives (PBIs) are proposed to integrate the market users and the PV supply chains. With a smart subsidy policy, the PV industry can make the best use of the subsidy budget and grow in a sustainable way to support the highly demanded solar power generation in many countries trying very hard to increase the proportion of their clean energy to combat the global warming effect.In conclusion, this study serves as a pioneering study into the dual PV supply chain research which is very limited in the PV management and policy study literature. The findings and several untended issues, such as how to set and allocate the subsidy threshold, provide a foundation for the future PV supply chain studies. With the methodology developed in this study looking at the dual PV supply chains, it is possible to extend the PV supply chain study to look at more than two competing supply chains which present an even more realistic picture in the PV industry and also a more challenging research problem for the future.


Spin-orbit-related effects offer a highly promising route for reading and writing information in magnetic units of future devices. These phenomena rely not only on the static magnetization orientation but also on its dynamics to achieve fast switchings that can reach the THz range. In this work, we consider Co/Pt and Fe/W bilayers to show that accounting for the phase difference between different processes is crucial to the correct description of the dynamical currents. By tuning each system towards its ferromagnetic resonance, we reveal that dynamical spin Hall angles can non-trivially change sign and be boosted by over 500%, reaching giant values. We demonstrate that charge and spin pumping mechanisms can greatly magnify or dwindle the currents flowing through the system, influencing all kinds of magnetoresistive and Hall effects, thus impacting also dc and second harmonic experimental measurements. The electric resistance of magnetically ordered systems, for example, depends on the direction of their magnetization, a phenomenon given the general name of magnetoresistance. Systems exhibiting relatively large magnetoresistance are used in sensing devices for reading information stored in magnetic media. Understanding how the spin of the electron can affect its propagation in materials with strong spin-orbit interaction is the main focus of various recent developments. A plethora of novel magnetoresistive effects have been discovered in the last years: spin Hall4, unidirectional spin Hall5 and, independently, linear spin Hall6, as well as Hanle7, and Rashba-Edelstein effects8. A common characteristic shared by all of them is the appearance of non-equilibrium spin polarizations accumulated at the interfaces/edges of those systems due to the flow of an electric current.The interrelation between magnetic properties and electric currents has been studied for more than a century13. These torques can be effective even at room temperatures and may be used for magnetization switching purposes19. In certain metallic systems, the induced spin-orbit torques and magnetoresistive effects can reach fairly high intensities21. Although the connection between the magnetoresistance and static torques is well-established, a dynamical connection between these two effects is missing. Unraveling how the induced dynamics influences the magnetoresistance and the Hall currents are essential questions, especially for prospective spintronics applications within the THz frequency range.This spin accumulation can also be used to excite spin waves in adjoining magnetic units, by means of the so-called spin-orbit torques, when time-dependent (ac) currents are applied22 or doubled-frequency (second-harmonic) voltages24. These measurements depend both on the transverse magnetization components, and on the magnetoresistance . The latter is assumed to be independent of both the frequency of the oscillatory electric field and intensity of the bias magnetic field that may be swept through the ferromagnetic resonance. The measurements are usually described by simple functional forms25, and the characteristics of the magnetization dynamics are studied within a semi-classical approach. In addition, even though the effect of the magnetization precession on second order signals is commonly accessed, measurements of its feedback in the first order signal are scarce27, specially for the in-plane geometry29, where the pumped currents may give rise to important contributions yet to be explored.The effective magnetic fields that drive the magnetization into precession in those systems are obtained experimentally through second order signals, either dc (rectified)dynamical magnetoresistance originating from spin and charge pumping. This can be one order of magnitude larger than the dc values. The magnetization dynamics also induces currents along the transverse directions that substantially influence Hall effects. We show that charge to spin conversion in the dynamical regime hinges crucially on signal dephasing, implying that the spin Hall angle is a complex quantity. It is characterized by an amplitude and a phase difference, contrary to what is assumed in common phenomenological approaches. This complex nature allows striking variations — up to 500% — on the generated transverse spin currents. Our approach is based on realistic descriptions of the electronic structure of the system. The theory describes collective spin excitations in the presence of spin-orbit interaction, and naturally takes into account all the intrinsic spin-orbit-related mechanisms, with no need for any adjustable parameters.In this work, we investigate the intrinsic feedback of the current-induced magnetization dynamics to the electric current that drives it. By applying a time-dependent electric field to ferromagnetic/heavy metal bilayer systems such as Co/Pt(001) and Fe/W(110), we demonstrate the emergence of an enhanced In the systems we have considered, we further show that magnetic excitations are the main source — but not the only one — of the dynamic contributions. They can be manipulated by varying the frequency and intensity of the applied fields, which can also affect second order signals measured in experiments. Moreover, since the spin-pumping contribution is switched on or off by changing the magnetization direction, it leads to an angular dependence of the currents that deviates starkly from the static counterpart. This change in current signals provides an efficient way of manipulating magnetic states and establish a powerful ingredient for the development of spintronic devices.G and conductivity d is the length of the sample along the direction of the applied electric field, and S is the cross-sectional area.We consider metallic bilayer heterostructures consisting of a ferromagnetic metal deposited on a heavy metal substrate. The systems are subjected to a time-dependent uniform electric field given by 32. Here, the spin Hall magnetoresistance (SMR)4 is also included in A schematic setup and our choice of axes are illustrated in Fig. The dynamical contribution, To reveal the spin-orbit origin of these effects, they are usually given in terms of the spin Hall angle 33. The motion of the magnetization is described by introducing the even and odd spin-orbit torques11  and Fe/W(110), manifesting different aspects of the phenomena due to the character of their charge to spin conversion. There are two main differences between these systems. First, Co/Pt(001) presents an uniaxial perpendicular anisotropy, while Fe/W(110) has a biaxial in-plane anisotropy with the long axis being the lowest-energy direction. The second difference is the band filling of the substrate, which, according to Hund’s rule, leads to parallel  orbital and spin moments in Pt (W) due to the spin-orbit coupling40. For a monolayer of Co deposited on Pt(001), we have found values of 17.Pt and W are known to have strong spin-orbit coupling and relatively high spin Hall angles. We have calculated x axis in each case. In Fig. We start by exploring the behavior of the longitudinal and transverse currents, calculated as functions of the applied electric field frequency, for different thicknesses of the heavy metal substrate. The time-dependent electric field is applied along the [110] and [1 entclass1pt{minimaentclass1pt{minimaentclass1pt{minimamaximum, whereas the corresponding ones for Fe/W(110) display a minimum. This means that the dynamical contribution to Surprisingly, from the results of Figs. entclass1pt{minimasee Fig.  — an enh29.An advantage of our approach is that all dephasing effects are naturally taken into account, and based on the underlying electronic structure. Since these factors are also layer-dependent and include the oscillatory induced magnetic moments, they may give different contributions to the total currents. For instance, our results show that increasing the thickness of the Pt(001) substrate leads to an increase of the current flowing through the Co layer, while the current on the Fe layer is quite insensitive on the thickness of W(110). The importance of how the current is distributed between the ferromagnetic and heavy metal layers has been raised in refs The excitation of the spin waves depends on the relative angle between the magnetization and the induced spin accumulation at the interface of the bilayer. Hence, the angular dependence of the currents with respect to the magnetization direction — which defines the magnetoresistance ratios and the Hall currents — can be drastically modified. To investigate this effect, we focus on bilayers consisting of a ferromagnetic monolayer deposited on four layers of heavy metal substrate. As in experimental setups, we consider a magnetic field larger than the anisotropy, to orient the magnetization along any chosen direction. Since increasing the static effective magnetic field diminishes the ability of the ac electric field to drive the magnetization precession, the dynamical charge currents are even stronger for smaller and more realistic external fields  and Fe/W(110) that unveil the complex nature of spin-charge excitations in these systems. They show that relevant physical mechanisms are being neglected by current phenomenological approaches, which consequently fail to properly describe the amplitude and angular dependence of the ac currents induced in such setups. Our material-dependent first-principles approach avoid these pitfalls by taking into account the lattice structure and all the dephasing factors between different physical quantities, which are intrinsically determined by the electronic structure. Although our main focus is metallic multilayers, the underlying processes discussed here also apply to other systems such as magnetic insulators in contact with heavy metals (e.g. YIG/Pt), and magnetic semiconductors with relatively large SOC, where the spin pumping contribution to the magnetoresistance can be also relevant45. Our work indicates a huge potential for magnifying even further these angles in the ac regime.We propose that the dynamical contributions, that are present not only in the charge but also in the spin currents, can be used to manipulate the spin Hall angle of the system. This means that the flow of spin currents can be controlled by changing either the frequency of the electric field or the intensity of the magnetic field. Recently, giant spin Hall angles were measured for a few systems in the dc limitThe dynamical processes we describe manifest prominently in the ac currents flowing with the same frequency as the external perturbation . Nevertheless, the frequency and field dependence of the current response may also affect dc and second harmonic signals, especially for frequencies close to the ferromagnetic resonance of the system  and the two spin components included per atom. The hopping matrices are obtained from density functional calculations based on the real-space linear-muffin tin orbitals method, within the atomic sphere approximation (RS-LMTO-ASA)50. Mean field theory is used to describe the ground state of the system, considering an effective intra-atomic Coulomb interaction d-orbital energy levels to reproduce the electronic occupancy obtained by the RS-LMTO-ASA calculations for each layer51. At the end of this process the atomic planes of the non-magnetic substrate close to ferromagnetic layer become also slightly spin polarized due to the proximity effect. Spin-orbit interaction is incorporated within the local (on-site) approximation d-band complex only. All coupling constants The electronic structures of the adsorbate/substrate combinations are described by a multi-orbital tight-binding hamiltonian with nine orbitals (the five 52, and follows through application of the RPA. Due to spin-orbit coupling, the responses of the transverse components of the magnetization are coupled to the longitudinal ones, and we end up with a 4 × 4 susceptibility matrix in spin space whose elements need to be calculated simultaneously54.Our description of the excitations is based on linear response theory using the Kubo formalismA more detailed description of the theory is given in the Supplementary Note Supplementary Information


Internal combustion engines (ICEs) are widely used in many important fields. The valve train clearance of an ICE usually exceeds the normal value due to wear or faulty adjustment. This work aims at diagnosing the valve clearance fault based on the vibration signals measured on the engine cylinder heads. The non-stationarity of the ICE operating condition makes it difficult to obtain the nominal baseline, which is always an awkward problem for fault diagnosis. This paper overcomes the problem by inspecting the timing of valve closing impacts, of which the referenced baseline can be obtained by referencing design parameters rather than extraction during healthy conditions. To accurately detect the timing of valve closing impact from vibration signals, we carry out a new method to detect and extract the commencement of the impacts. The results of experiments conducted on a twelve-cylinder ICE test rig show that the approach is capable of extracting the commencement of valve closing impact accurately and using only one feature can give a superior monitoring of valve clearance. With the help of this technique, the valve clearance fault becomes detectable even without the comparison to the baseline, and the changing trend of the clearance could be trackable. Internal combustion engines (ICEs), as a power source, are widely used in the automobile industry, ship and power equipment. However, the complex structure, and harsh and fickle working conditions usually result in unexpected faults. A serious failure of the ICE may cause loss of production or even human casualties. The techniques of condition monitoring and fault diagnosis have received increasing recognition and proven to be very valuable. Furthermore, the recent achievements of these techniques for industrial applications is well reviewed and summarized in ,2,3. TheThe abnormal clearance fault of an ICE may lead to a decline in the performance and reliability, as well as occurrences of malignant failure such as valve fracture and cylinder hit fault . In factSeveral significant works on detecting the valve clearance fault have been reported. Vibration and acoustic emission analysis techniques are considered to be more suitable for implementation on on-board monitoring systems as their signal acquisitions are non-intrusive and convenient . HoweverIn this work, we study the detection approach of the ICE valve clearance fault using vibration analysis. Vibration signals are measured on the engine cylinder heads of a 12-cylinder ICE. The measurement is conducted at three different fault levels, three different operating speeds and five different operating loads to provide investigative data. The main contribution of this work can be summarized as follows: (1) a fault feature which is sensitive to the valve clearance and insensitive to working conditions is selected through dynamic simulation; (2) a novel impact commencement detection method which is capable of obtaining a sufficiently accurate result is proposed; (3) based on experimental verification, using only one feature can provide superior monitoring and tracking of valve clearance without comparison to the baseline extracted during the healthy condition; and (4) there is potential for applying the fault diagnosis method in real-time mode since it has good adaptability and robustness.The rest of this paper is organized as follows. The test rig and experiment procedure are described in All the experiments will be conducted on a TBD234 twelve-cylinder V-shaped direct injection diesel engine . The major features of the ICE are summarized in As shown in In the ICE, the valve train controls the flow into and out of the combustion chambers. The engine’s manufacturer provides the normal limits of valve clearances or the valve timings. In the normal state of the TBD234V12 diesel engine , the clearance should be between 0.25 and 0.35 mm for the intake valve, and between 0.45 and 0.55 mm for the exhaust valve. The chosen clearance fault levels of the exhaust valve are 0.8 mm and 1.1 mm, i.e., the values of 0.5 mm, 0.8 mm and 1.1 mm will be used for the normal and fault cases studied in this paper.Three sets of measurement experiments were carried out. The first set involves testing at 1500 rpm engine speed at three different engine loads: 700, 1000 and 1300 N m, and testing at 1800 rpm at four loads: 700, 1000 1300 and 1600 N m, and testing at 2100 rpm at five loads: 700, 1000 1300 1600 and 2200 N m during the healthy condition. The second and third sets of measurements are for the fault conditions with the valve clearance in the exhaust valve of the B1-cylinder of 0.8 mm and 1.1 mm in the same operating conditions as the first set. The asynchronous sampling method is adopted, while all channels are kept in synchronization, and data was collected at the sampling frequency of 51.2 kHz per channel in all tests.Feature selection is a key step in the processes of fault diagnosis and prediction. It is generally related to two important aspects: firstly, the selected features should be sensitive to target faults and not sensitive or less sensitive to noises; then, the available signal processing techniques have the ability to extract the selected features with sufficient accuracy, satisfying the requirements of the engineering application. The objective of this work is to develop a method to detect and diagnose the abnormal ICE valve train clearance. The ideal selected features should be sensitive to abnormal valve train clearance and stable to engine operating conditions, because it is usually difficult to achieve the engine loads except for engines used for power generating sets. In order to select good features for diagnosing the valve clearance fault, studies on the influence of valve clearance on the kinetic and dynamic response of the valve train are conducted.Changing this clearance would have an influence on the kinematic and dynamic response of valve lifting. The valve impacts include an opening impact generated from the collision between the rocker and valve cap, and a closing impact generated from the collision between the valve seat and cylinder head. The vibration transmission paths are shown in To study the movement characteristics of the valve train mechanism, ADAMS, a multi-body dynamic simulation tool, is employed to simulate and to obtain the dynamic influence of the valve clearance and operating condition. The solid model used for simulation is shown in Four valve lift curves corresponding to clearances of 0.5 mm , 0.8 mm, 1.1 mm and 1.4 mm are drawn in On the other hand, the simulation results corresponding to different operating conditions  with normal clearance are shown in As shown in The first category includes features such as the peak and the peak-to-peak, the root mean square, etc. These features are extracted directly from the time domain and indicate the overall level, or the peakedness, or the flatness of the vibration signals. The simulation results show that the first category features are connected to the operating conditions. In particular, the valve closing peaks have unpredictable behaviors and even change considerably in a random manner. Therefore, the first category features may not be useful for the valve fault detection. The second category features are extracted from the vibration signal after transformation to the frequency domain usually by means of FFT. These features can often be effective for diagnosing the faults that may have detectable characteristic frequency components of the vibration signal. So, the application of the frequency domain is usually more successful for stationary vibration signals, such as the vibration signals of most rotating machines. However, the vibration signals measured on the upper surface of the cylinder heads are usually non-stationary signals resulting from the variation of the crankshaft angular speed of ICEs. According to previous studies ,17 and tThe representative feature of the third category is mainly the timing of valve closing. The simulation results indicate that the valve would open late and close early when the valve clearance increases. In fact, the theoretical timing of valve closing is mainly determined by the cam profile, the arm length ratio of the rocker, and the valve train clearance. The lift of the valve train can be approximately derived based on these parameters, almost without consideration of the engine operating conditions. Therefore, we select the timing of valve closing as the target feature, i.e., the commencement phase of valve closing impact.To carry out the commencement phase of valve closing impact, the angle-invariant interval sampling mode, rather than the time-invariant interval sampling mode, is usually recommended to collect the vibration signals, in which the variations in ICE speed will have less impact on the measured signals. However, it is well known that the angle-invariant interval sampling approach requires a high-cost analog anti-aliasing filter, while the time-invariant interval sampling has relatively lower requirements and is simple to implement. Therefore, an indirect approach, combining time-invariant interval sampling with soft re-sampling, is employed in this study. The rationale and procedures of the introduced method can be found in ,20. FurtREST. This step is described as follows:In order to improve the accuracy of fault detection and diagnosis methods, the vibration data should be filtered through a high-pass or band-pass filter with a certain cutoff frequency . ConsideIt is well known that thresholding is a frequently used technique to detect the impact region in signal processing. In many cases, the threshold parameters are set manually, leading to risks of unreasonable setting. In this application, an adaptive method-based optimized maximum ascending gradient will be used to extract the start time of an impact. As an impact is the result of a sudden collision between components, the vibration energy will suddenly increase upon commencement of the impact. Then, it will decrease gradually due to the existence of structural impedance. Therefore, theoretically, the energy increase rate may be used to find the commencement of an impact, i.e., the maximum ascending gradient point of vibration energy can verify the impact location. However, the signal energy gradient is usually influenced by many factors. In this work, we further enhanced the impact detection method to overcome this problem by changing the policy of maximum point selection.Calculate the local energy using a sliding window method. The local energy values were calculated by sliding a given window through the vibration signal and calculating the local energy for each data point of the signal. The process can be described mathematically as:Calculate the signal energy gradient. It is calculated with the following equation:kth maximum value in Find the commencement of impact. We find the kth maximum value rather than the first maximum value in The main steps can be summarized as follows:The exhaust valve closing impact region was extracted from the filtered vibration signal in the angle domain. The segmental signal will be used in the subsequent analysis. To confirm the ability of the impact detection method presented in this paper, the test results of the exhaust valve closing commencement phase with different values of k introduced in Equation (5) are shown in In addition, it is also worth noting here that the basic trend of the valve closing phase does not change with the working condition of the engine, as alluded to in the aforementioned analysis.From Note that changing the valve clearance is usually a slow process rather than an instantaneous one, and the valve closing phase is stable when the valve clearance remains unchanged, as previously mentioned. According to the three-sigma rule, singular measurement data can be suggested as an outlier if its error is three times greater than the standard error; singular data can be reasonably deleted and substituted with an arithmetic average value. As the error processing criterion is very simple to implement and widely used in practical engineering applications, it was introduced in this work to enhance the robustness. We used a given detection window to slide through the time series of the valve closing phase extraction results. The value of each point is calculated using:The optimized results are shown in In order to evaluate the performance of the feature extraction method for valve clearance condition monitoring, the abnormal valve clearance fault is introduced into the B1-cylinder, while the other cylinders are kept in normal condition. Three different valve clearances—0.5 mm , 0.8 mm and 1.1 mm (fault conditions)—are used to examine the fault diagnosis and prediction capabilities. To investigate the influence of the operating condition on the detection results, data from all sensors mounted on the engine was collected with three different operating speeds and five different operating loads for each valve clearance condition, as mentioned in The procedures are briefly summarized in the flow chart presented in Hence, our accurate extraction method for the valve closing phase has been proven to be effective, and the fault detection performance based on it has been verified as good enough, as the valve closing phase is sensitive to changes in valve clearance and insensitive to the working condition of the engine.In this study, an effective approach has been developed to detect and diagnose the ICE valve train clearance based on the vibration signal measured on the engine cylinder heads. This presented method is capable of monitoring the clearance accurately with only one feature—the commencement of valve closing impact—since the feature is sensitive to the valve clearance and insensitive to working conditions. Moreover, because this feature has clear physical significance, the baseline acquired during the healthy condition is no longer needed. Subsequently, a novel feature extraction technique was carried out based on a newly proposed impact detection method to meet the feature calculation accuracy requirement. The experimental results proved that the selected feature is indeed ideal for this fault detection, and the feature extraction results are accurate enough. In addition, this method has potential for application in real-time and the trend of the valve clearance may become trackable, as the calculation processes are adaptable and automatic with good robustness, and the implementation is simple. In the future, the new impact detection method will be extended to diagnose other impulse faults, and the valve clearance detection approach will be further studied and finally built into a real-time monitoring system for an engine.