This variation has been attributed to differingdegrees of S/X anion disorder. For X = {Cl,Br}, the S/X anions aresubstitutionally disordered, while for X = I, the anion substructureis fully ordered. To better understand the role of substitutionalanion disorder in enabling fast lithium-ion transport, we have performeda first-principles molecular dynamics study of Li6PS5I and Li6PS5Cl with varying amountsof S/X anion-site disorder. By considering the S/X anions as a tetrahedrallyclose-packed substructure, we identify three partially occupied lithiumsites that define a contiguous three-dimensional network of face-sharingtetrahedra. The active lithium-ion diffusion pathways within thisnetwork are found to depend on the S/X anion configuration. For anion-disorderedsystems, the active site–site pathways give a percolating three-dimensionaldiffusion network; whereas for anion-ordered systems, critical site–sitepathways are inactive, giving a disconnected diffusion network withlithium motion restricted to local orbits around S positions. Analysisof the lithium substructure and dynamics in terms of the lithium coordinationaround each sulfur site highlights a mechanistic link between substitutionalanion disorder and lithium disorder. In anion-ordered systems, thelithium ions are pseudo-ordered, with preferential 6-fold coordinationof sulfur sites. Long-ranged lithium diffusion would disrupt thisSLi6 pseudo-ordering, and is, therefore, disfavored. Inanion-disordered systems, the pseudo-ordered 6-fold S–Li coordinationis frustrated because of Li–Li Coulombic repulsion. Lithiumpositions become disordered, giving a range of S–Li coordinationenvironments. Long-ranged lithium diffusion is now possible with nonet change in S–Li coordination numbers. This gives rise tosuperionic lithium transport in the anion-disordered systems, effectedby a concerted string-like diffusion mechanism.The rational developmentof fast-ion-conducting solid electrolytesfor all-solid-state lithium-ion batteries requires understanding thekey structural and chemical principles that give some materials theirexceptional ionic conductivities. For the lithium argyrodites Li One possible solution is toinstead use solid electrolytes, which ideally should be electrochemicallyinert, mechanically robust, have negligible electronic transport,and have high lithium-ion conductivities.4Lithium-ion-conducting solid electrolytes are considered candidatematerials for use in future all-solid-state lithium-ion batteries.6 Identifying new solid lithium-ion electrolytes isan active area of research,3 with strategiesranging from targeted chemical modification of known solid electrolytes,to improve their conductivities,11 to high-throughput screening of new materials.15 In both cases, it is useful tounderstand why some materials are highly conducting, yet others arenot.20 Such an understanding can help inform chemical strategiesfor optimizing the ionic conductivities of known materials, or canprovide selection criteria for identifying new promising electrolytes.Particular insight can be gained from studying families of solid electrolytesthat are superficially similar—such as those that share a commonstructural motif—but that exhibit quite different ionic conductivities,19 as this can help reveal the fundamental mechanisms and key materialcharacteristics that govern fast-ion conduction.Although a number of highly conducting solid lithium-ion electrolytesare known, none meet all the criteria for general commercial use.6PS5X .25 While Li6PS5Cl and Li6PS5Br exhibit high room-temperature ionic conductivities(σRT ≈ 10–3 S cm–1), Li6PS5I is considerably less conductive(σRT ≈ 10–6 S cm–1).27 The large difference between X = {Cl,Br}and X = I is notable because these three materials have topologicallyidentical crystal structures, suggesting the same lithium-ion diffusionpathways should exist in each system. This inverse correlation betweenanion size and ionic conductivity also runs counter to the trend seenin other families of solid electrolytes, for example, thio-LISICONand NASICON, in which larger, more polarizable, less-electronegativeanions are associated with increased ionic conductivities2—with this relationship often attributedto a combination of larger anions giving an increased accessible volumefor the diffusing lithium ions and weaker lithium–anion electrostaticinteractions.One familyof promising lithium-ion solid-electrolytes are thelithium argyrodites Li6PS5X argyrodites comes fromthe observation thatin these materials, high conductivities are correlated with substitutionalS/X anion disorder.27 In Li6PS5I, the anions are fully ordered, and S and I atoms fully occupy crystallographicallydistinct 4c and 4a Wyckoff positions, respectively. In Li6PS5Cl and Li6PS5Br, the S and Cl,or S and Br, atoms are substitutionally disordered, which has beenattributed to their similar ionic radii28 giving a low formation energy for S/X antisites.30 Molecular dynamics simulations of Li6PS5Xin which the degree of S/X disorder has been systematically variedprovide additional evidence for a causal link between anion substitutionaldisorder and fast lithium-ion transport.34A partial explanation for the ionic conductivitytrend in the Li6PS5X modelswithfully ordered S/X atoms predict low lithium diffusion coefficientsand highly localized lithium motion, with lithium ions restrictedto discrete “cages” surrounding the S atoms. In contrast,simulations performed on S/X-disordered models predict high lithiumdiffusion coefficients, with lithium ions moving through a contiguousthree-dimensional diffusion network. Despite this experimental andcomputational evidence linking lithium-ion conductivities in Li6PS5X argyrodites with the degree of S/X disorder,a mechanistic model that explains this relationship is currently lacking.Simulations performed on Li6PS5I and Li6PS5Cl with varying amounts of S/X anion-site disorder.We find that the lithium substructure can be generally described interms of partial occupation of three crystallographically distincttetrahedral sites that define a contiguous three-dimensional network.The pattern of active and inactive lithium-ion diffusion paths withinthis network, however, depends on the degree of S/X disorder. In anion-orderedsystems, lithium site positions are displaced toward neighboring sulfursites because of electrostatic S–Li attraction, giving an orderedpattern of “inactive” site–site paths. In anion-disorderedsystems, however, the lithium site positions are statically disordered,and the set of active site–site paths forms a percolating three-dimensionalnetwork that permits long-ranged lithium diffusion.To address this question, we have performed a first-principlesmolecular dynamics study of Li6 units is frequent,lithium exchange between SLi6 units is rare on a simulationtimescale. We explain this by considering lithium exchange as a formof “defect formation”, which is energetically disfavored.In the anion-disordered systems, however, strong Coulombic interactionsbetween nearby lithium ions frustrate the otherwise preferable 6-foldS–Li coordination, producing a range of disordered SLix (x ≥ 6) coordinationenvironments. Lithium movement between coordination polyhedra is nowpossible without a net change in S–Li coordination, makinglong-ranged lithium diffusion a viable low-energy process. Furtheranalysis of the dynamical correlations between mobile lithium ionsreveals a concerted string-like “superionic” diffusionmechanism in the anion-disordered argyrodites. These results providea mechanistic explanation for the exceptional ionic conductivitiesof anion-disordered Li6PS5X argyrodites, andshow how configurational framework disorder in solid electrolytescan cause static disorder amongst mobile ions, which consequentlyfacilitates superionic conductivity.We alsohave analyzed our simulation trajectories by consideringclusters of lithium ions as “coordination polyhedra”located around S anions. This perspective provides insight into thespatial correlations and collective dynamics in these groups of lithiumions. In the anion-ordered systems, the lithium-ions are pseudo-ordered,and preferentially form 6-coordinate polyhedra around sulfur atoms.While lithium movement within these SLi26PS5X argyroditestypically adopt a cation-disordered cubic aristotype in the F4̅3m space group, which can be consideredto be derived from the MgCu2 cubic Laves phase (Fd3̅m space group).37 In MgCu2, the Mg sites(8a) form a diamond-structured array, and the Cu sites (16d) forman interpenetrating corner-sharing network of tetrahedra  are fully occupied by S, forming a face-centered cubic arrayof PS4 tetrahedra, and the “Mg” sites (nowsplit into 4a and 4c) are occupied by an equal ratio of S and X anions or mobile lithium ions.In MgCu2, the Mg and Cu positions define the vertices ofthree crystallographically distinct tetrahedral sites. The lower crystalsymmetry of the argyrodites splits these into six distinct tetrahedraltypes, which are listed in 36 In Li6PS5X, one set oftetrahedra (type 0) is occupied by phosphorus, while the remainingtetrahedra (types 1–5) are available to potentially accommodatelithium. The type 3 tetrahedra are centered on the 4d Wyckoff positionswith four 16e sites as vertices, which they share with the type 0PS4 tetrahedra. The remaining tetrahedra types 1, 2, 4,and 5 form face-sharing cages around the 4a and 4c S/X sites. Thesecages each contain 28 tetrahedra, and each tetrahedron representsone lithium interstitial site  > 6.50 A general mechanistic description of lithium conduction in lithium-argyroditesthat describes the role of different lithium sites and that can explainthe relationship between substitutional anion disorder and fast lithiumtransport, however, is currently lacking.Thecapacity for nontype 5 tetrahedra to accommodate lithium may,therefore, determine the degree to which lithium can diffuse throughthe structure. Some computational evidence for the role of nontype5 tetrahedra in lithium diffusion in Li36PS5I andLi6PS5Cl, we have performed a series of ab initiomolecular dynamics simulations using the Vienna ab initio simulationpackage.52 For all calculations, we have used the revisedPerdew–Burke–Ernzerhof generalized gradient approximationPBEsol exchange–correlation functional.53 Interactions between core and valence electrons were describedusing the projector augmented wave (PAW) method,54 with cores of [He] for Li, [Ne] for P, [Ne] for S, [Ne]for Cl, and [Kr] for I. Zero-pressure volumes were calculated forordered Li6PS5I and Li6PS5Cl, with the 4c sites occupied by S, and the 4a sitesoccupied by I or Cl. These calculations consisted of full geometryoptimizations for a single unit cell (52 atoms) starting from theMaterials Project structure ID-985592,55 with a cutoff of 700 eV, and a 2 × 2 × 2 Monkhorst–Pack k-point mesh. The optimized lattice parameters were thenused to construct 2 × 2 × 2 supercells (416 atoms) for thesubsequent molecular dynamics simulations.To simulate lithium dynamics in Lik-space sampling.All MD simulations were performed at 500 K, and used a time-step of2 fs. For both Li6PS5I and Li6PS5Cl, we have considered three different S/X configurations:0% site-inversion, with S fully occupying the 4c sites and X fullyoccupying the 4a sites, corresponding to the experimentally reportedordered Li6PS5I structure; 50% site-inversion,with a random S/X configuration that approximates the experimentallyreported disordered Li6PS5Cl structure; and100% site-inversion, with S fully occupying the 4a sites and X fullyoccupying the 4c sites. The same randomly generated 50% site-invertedS/X configuration was used for the Li6PS5I 50%and Li6PS5Cl 50% simulations. For each system,the lattice parameters were kept fixed to the zero-pressure 0% optimizedvalues. For each MD simulation, two equilibration stages were performed,first using a 2 ps NVE run with temperature rescaling every 50 steps,followed by a 2 ps NVT run. For each simulation,the production runs were 70 ps.The molecular dynamicssimulations used a plane-wave cutoff of280 eV and only the gamma point for 58 from each simulation trajectory by performing conjugate-gradientgeometry optimizations for configurations selected every 50 time-steps.Each inherent structure represents a local minimum on the corresponding3N-dimensional potential energy surface, and the sequences of inherentstructures from a given simulation describe the nontrivial motionof lithium ions as they move between these local minima.The analysis of MD simulationtrajectories is often complicatedby “trivial” thermal motions of the mobile ions andof the host framework. Here, we are interested in nontrivial lithiumdisplacements that contribute to net lithium diffusion, rather thanshort-timescale vibrational motion. To help resolve the lithium-diffusionprocesses in our simulations, we have extracted a series of “inherent”structures59 All codes used to analyze the simulation trajectories andto generate the corresponding figures are available as a series ofJupyter notebooks60 under the MIT license.Our analysis used the Matplotlib,61 NumPy,62 Pymatgen,64 SciPy,65 tqdm,66 vasppy,67 site-analysis,68 polyhedral-analysis,69 Kinisi,70 and crystal-torture71 Python packages.A datasetcontaining inputs and outputs for all DFT calculationssupporting this study is available under the CC BY-SA 4.0 licensefrom the University of Bath Research Data Archive.44.1726PS5I and Li6PS5Cl with 0, 50, and 100% S/X site inversion. For both X = I and X= Cl, for the anion-ordered systems (0 and 100% site inversion), theMSD initially increases, before plateauing at longer times, givingan effective lithium diffusion coefficient of zero. These plateausindicate that in the anion-ordered systems the lithium ions do notdiffuse freely, but instead are confined to small disconnected regionsof space. The MSDs of the anion-disordered systems (50% site inversion)show qualitatively different behavior: these MSDs continually increaseat long times, corresponding to nonzero diffusion coefficients andlong-ranged lithium diffusion. These results are consistent with datafrom previous molecular dynamics simulations,32 and highlight two interesting points. First, thediffusion behavior is qualitatively the same for X = I and X = Cl,as noted previously by Stamminger et al.30 Second, lithium caging is observed for both 0 and 100% site inversion,showing that long-ranged lithium diffusion is not a first-order consequenceof occupying 4a sites with sulfur, but that instead anion disorderacross the 4a and 4c sites is the necessary prerequisite.The rate at whichindividual lithium ions diffuse through a solidelectrolyte is described by the lithium self-diffusion coefficient,which can be calculated from molecular dynamics simulations as theslope of the lithium mean-squared displacement (MSD) versus time,in the long time limit.4.26PS5X suggests that thearrangement of anions in each system directs the microscopic lithiumdiffusion mechanism. To examine the relationship between the anionconfiguration and diffusion behavior, we can calculate the time-averagedtetrahedral site-type populations for each simulation trajectory.To assign lithium ions to specific sites at each time-step, we usethe instantaneous positions of the S/X anions to define the tetrahedravertices. A lithium ion is deemed to occupy a particular tetrahedron,if it sits inside the volume defined by these vertex positions.74Thequalitative difference in diffusion behavior between anion-orderedand anion-disordered Li6PS5I (anion-ordered)and Li6PS5Cl (anion-disordered), which haveassigned lithium as predominantly occupying two positions associatedwith the type 5 tetrahedra: the 48h positions located inside eachtype 5 tetrahedron, and the 24g positions (type 5a sites) in the trigonalfaces shared by type 5 tetrahedra pairs.756PS5I, lithium partially occupies tetrahedra types 5 and 2. Inall the other systems, lithium is distributed over tetrahedra types5, 2, and 4. The possibility of lithium occupying nontype 5 tetrahedrain Li6PS5X argyrodites has been discussed indetail by Deiseroth et al.,36 who notedthat lithium ions must pass through nontype 5 tetrahedra for long-rangedlithium transport to occur.45In all six systems, we find someproportion of lithium ions locatedat nontype 5 tetrahedra. For 0% site-inverted Li6PS5Br and Li6PS5Cl,which have reported partial occupation of type 2 tetrahedra.47 The study of Minafra et al. also reported data for Li6PS5I,46 with lithium assignedonly to type 5 and type 5a sites, in apparent contradiction to thesimulation results presented here. Experimental samples of Li6PS5I are fully anion-ordered, and are approximatedby our 0% site inversion model. For this system, our simulations predictonly 2.5% of Li occupies type 2 sites, which is unlikely to be resolvedin diffraction experiments. Similarly, we predict very low numbersof lithium ions occupy type 4 sites, making direct experimental observationchallenging.Theobservation of partial occupation of nontype 5 tetrahedra isqualitatively consistent with recent neutron diffraction studies ofLi6PS5I also exhibit partial type 4 tetrahedral occupation,which further increases the connectivity of the three-dimensionaltetrahedral network . In eachmatrix, each row corresponds to a different initial site type  and each nonblank entry in that row gives the observed probabilityof moving to a given adjacent site type. For 0% anion site-inversion,only 5 → 5, 5 → 2, and 2 → 5 transitions occur.With no 2 → 2 or 5 → 4 transitions, no long-ranged diffusionis possible, and lithium motion is restricted to closed “cages”around the 4c sites , for specific pairs of these per-site averagelithium positions, are shown in As discussed in For the 0% site-inverted systems,the site–site rdfs showsharp peaks, indicating a degree of ordering by the lithium ions,and a clear hierarchy of site separations: the shortest 5–5separation is ∼1.2 Å, corresponding to pairs of adjacenttype 5 tetrahedra. The next-nearest separation is 5–2 at ∼1.5Å, and the first 2–2 site separation peak is at >2Å.The 100% site inverted systems also show sharp rdf peaks and distinctshort and long site–site separations. Now, the nearest-neighbordistances increase in the order 2–2 < 5–4 < 5–2< 5–5, with the first 5–5 peak at > 2 Å.Comparingthe positions of the nearest-neighbor first peak for each site-pairto the corresponding site–site transition probabilities above5 shows lIn each system, the hierarchyof site–site distances 7 is corrThis correlationbetween short or long site–site distancesand active or inactive lithium-site-transitions suggests a model whereinfast long-ranged lithium diffusion in the anion-disordered systemsis associated with a percolating network of short lithium site separations,while nondiffusive motion in the anion-ordered systems is associatedwith a nonpercolating disconnected network. To test this model, foreach system we have calculated the minimum site–site separationdistance at which the average lithium positions at each site forma percolating network 7. We fin4.52– ions than to X– ions. Thisasymmetry in anion–lithium coordination is larger for X = Ithan for X = Cl because of the additional difference in anion ionicradii. Because the S and X anions are crystallographically orderedin these systems, a decrease of Li-site distances to S-occupied 4cor 4a sites corresponds to an increase of Li-site distances to X-occupied4a or 4c sites, respectively. This pattern of short S–Li andlong X–Li distances, combined with the S/X ordering over 4cand 4a sites, explains the Li–Li site distances discussed inthe previous section –Liand X(4a/4c)–Li radial distribution functions 8. In the section 7, which  section 6. This e6PS5Cl, the S–Li and X–Li nearest-neighborpeaks coincide. In an anion-disordered system, the Li sites experiencea range of local coordination environments with different permutationsof S and X neighboring anions. The average position of each Li sitenow depends on the specific local anion environment. Because the Sand X anions are disordered, the arrangement of long Li site–sitedistances, which correspond to inactive diffusion paths, is also disordered,allowing a percolating network of shorter active diffusion paths , wefind an average of n = 6 lithium ions around the4c or 4a S atoms, respectively, suggesting the structure can be describedas 4c or 4a-centered SLi6 subunits, with X occupying theremaining 4a or 4c sites. For the 50% systems, we find an averageof n > 6 Li ions associated with each S atom,suggestinga more complex lithium arrangement. Because the ratio of lithium to4a/4c sulfur is consistently 6 Li to 1 S in all cases, an averagecoordination number of n > 6 Li ions indicatesthatsome Li contributes to coordination of more than one S center.The averagenumbers of lithium ions around the S/X 4a and 4c sitescan be calculated by integrating the rdf data 9. For Li4.6x coordination polyhedra. We consider a “coordination polyhedron”to consist of a single S atom residing at a 4c or 4a site plus theset of lithium ions within a spherical cutoff rcoord, with the cutoff distance chosen to lie in the firstplateau region from 77 The CSM can be thought of as a normalized “distance”between two polyhedral geometries: larger CSM values indicate largerdeviations from the reference geometry. Here, we classify each coordinationpolyhedron geometry by computing CSM values with respect to a setof common polyhedral coordination motifs78 and selecting the “most similar” motif—givenby the smallest CSM.For amore detailed description of the local S–Li coordinationenvironments, we have classified the local lithium coordination aroundeach 4a or 4c sulfur according to the degree of geometric similaritywith respect to a set of reference SLi79 as suggested by the average S–Li coordination numbers data.The relative proportions of different coordinationpolyhedral geometries are shown in berscf. 9. Inthe4.7x coordinationpolyhedra provide a schema for classifying the lithium dynamics ineach system. For each polyhedron, we consider two features: the firstis the set of lithium ions that define the polyhedron vertices, andthe second is the set of edges that connect these vertices, whichthen defines the polyhedron topology. In our simulation trajectories,each lithium ion is assigned an integer index. The set of lithiumions that define a specific coordination polyhedron  can be describedby a vertex list of these ion indices, for example, . The edge topology connecting these ions is describedby an undirected edge graph, where we consider an edge formed betweenany two vertices of a polyhedron with a separation smaller than athreshold distance redge. These featuresallow us to define three classes of lithium motion:1.Neither the vertexlist nor the edgegraph change, but the polyhedron undergoes a “rigid”rotation in space.2.Onlythe edge graph changes. The vertexlist remains unchanged. This corresponds to some internal reorganizationof lithium ions that changes the polyhedron topology.3.rcoord), or joining a new polyhedron, or both.The vertex list changes . This corresponds to a lithium ion leavinga polyhedron  argyrodites.48The conventionalmodel for ionic diffusion in solid electrolytesassumes that ion transport is effected by a sequence of single-ion“hops” between discrete sites,6 coordinationpolyhedra is highly concerted—octahedral rotations and trigonal-prismaticreorganizations both involve synchronous motion of groups of lithiumions. For the anion-disordered systems, however, the more complexlithium dynamics means that this local “lithium-coordination”analysis is less useful in distinguishing between individual or concertedlithium motion.Our site–sitetransition analysis, above, allowed a characterization of the connectivityof active diffusion pathways within the argyrodite structure, andhow the topology of the diffusion network varies with the 4a/4c S/Xanion configuration. That analysis, however, cannot distinguish betweena single-particle hopping mechanism, and a collective “superionic”diffusion mechanism. In the anion-ordered system, we have alreadyobserved that the internal dynamics of SLi6PS5X systems diffuse via individual or collectiveprocesses, we have identified groups of lithium ions that are involvedin cooperative string-like motions.97 Wedefine strings that form on a timescale Δt byconnecting two mobile ions i and j ifTo determine whether the lithium ions in anion-disorderedLiThis corresponds to selecting pairs of mobile ions where oneionhas moved into a position previously occupied by the second ion. Toconstruct strings, we then connect ion pairs that occur within thesame time window that contain one common mobile ion.t. For a stochastic hoppingprocess, the number of hops in time window Δt, and hence the distribution of string lengths, samples a Poissondistribution.98 Observing a probabilitydistribution of string lengths that strongly deviates from a Poissondistribution is, therefore, evidence for ion displacements that areclustered in time.The identificationof strings of mobile ions, via P(n), from our simulations, for Δt = 5 ps. For the anion-ordered systems, we find high probabilitiesof strings with lengths 2–4, corresponding to the concertedmotions of ions within SLi6 coordination polyhedra describedabove. For the 50% site-inverted systems, we observe a range of stringlengths, with P(n) following anapproximate geometric distribution. This mirrors the behavior observedin supercooled glassy liquids97 where string-likediffusion is often associated with dynamic heterogeneity,101 whereby spatially correlatedsubsets of particles exhibit much faster dynamics than the systemaverage. A geometric distribution of string lengths is consistentwith a mechanistic model consisting of string “initiation”,followed by string “propagation” with the probabilityof a string increasing in length from N particlesto N + 1 particles is independent of N. Our analysis here indicates that lithium mobility is effected byconcerted ion motions in all our systems. In the anion-ordered systems,these motions are “closed-loops” typically consistingof groups of four or three lithium ions undergoing local cyclic motions sites,with lithium diffusion decomposed into classes of direct 5 →5 transitions.103 This simplified perspectiveneglects the different tetrahedra types defined by the close-packedanion substructure, and obscures their roles in the lithium diffusionprocesses in different argyrodite compositions. For Li6PS5X systems, these nontype 5 tetrahedra are not simplyhigh-energy intermediates that define local potential energy maximaalong lithium diffusion 5 → 5 pathways. Instead, we find stableLi configurations, corresponding to local potential-energy minima,in which nontype 5 sites are occupied. This illustrates the importanceof these sites when describing the relevant potential energy surfacefor lithium diffusion. Occupation of nontype 5 tetrahedra has beenidentified in experimental samples for x(Li) >6argyrodites50 as well as in recent neutron diffraction studiesof Li6PS5Br and Li6PS5Cl.47 The tetrahedrally close-packed geometrydefined by the MgCu2-structured anion sites is common toall argyrodites, and we, therefore, expect analyses that considerdiffusion in terms of ion motion between these different tetrahedrato provide useful insight into the transport mechanisms operatingin argyrodite stoichiometries beyond Li6PS5X.We first analyzed the lithium distributionin each simulation interms of occupation of the different tetrahedral sites within theclose-packed anion substructure. We find that lithium ions predominantlyoccupy type 5 tetrahedral sites; particularly so for the fully orderedS(4c)/X(4a) systems; which broadly agrees with previous diffractionexperiments.6PS5X systems, an analysisin terms of occupation of spatially discrete lithium sites also allowsthe active lithium diffusion pathways in each system to be resolved.While the partial site-occupations for these anion-ordered and anion-disorderedsystems might equally suggest the existence of a contiguous lithium-diffusionpathway, via a network of face-sharing tetrahedra, lithium does notalways move freely between these partially occupied tetrahedra. Foranion-ordered systems, there are regular “blocked” pathwaysbetween specific neighboring tetrahedral sites, giving a noncontiguousdiffusion network. Our analysis of the time-average lithium positionswithin each partially occupied tetrahedral site shows that “blocked”pathways correspond to large average Li–Li separations, whilethe set of short “active” pathways forms closed orbitsaround the 4c or 4a S anions, producing the restricted “cage-like”lithium diffusion reported in previous studies.34 This can beconsidered a form of lithium ordering, induced by the configurationalanion order, that arises from a preference for shorter S–Lithan X–Li distances. In the anion-disordered systems, conversely,we find no systematic pattern of short–long average lithiumseparations between adjacent sites: the set of short “active”pathways is disordered and forms a percolating three-dimensional network,that facilitates long-ranged lithium diffusion.In the case of the Lix polyhedraaround the 4c or 4a sulfur atoms. This “pseudo-ordering”corresponds to an effective crystal symmetry where the regular 6-coordinateSLix motif is invariant under integerlattice-vector translations, even though the lithium ions are crystallographicallydisordered over the available tetrahedral sites.The idea thatthe lithium ions are, in some sense, ordered whenthe S/X anions are substitutionally ordered, but that lithium ionsare disordered when these anions are disordered, and that this differencedirects the lithium diffusion behavior, also emerges from our analysisof the local lithium coordination environment around the 4a and 4cS anions. In the anion-ordered systems, the lithium substructure canbe considered as 6-coordinate SLi2– than X– anions, because of the larger formal charge of S, which encouragesLi to adopt cage-like configurations around the 4a or 4c S ions. Therepulsive Li–Li Coulombic interactions, however, tend to maximizeLi–Li separations within each coordination cage. In an anion-orderedsystem, these two factors can be simultaneously optimized by arrangingexactly six Li ions around each 4a or 4c S anion  in a nonstoichiometric conventional crystal.98In the S/X-disordered systems, we canagain understand the behaviorby considering the interplay of anion–Li and Li–Li Coulombinteractions. Li ions again preferentially coordinate S, rather thanX anions. We have seen in the anion-ordered system that if these SLiS anions 15b: SLi6ral site 15c. Lith108 and studies of various solid electrolyte families have revealeda range of mechanisms that can contribute to this substructural disorder.113 The results presented here provide another example of this generalprinciple. In this instance, superionic conductivity arises as a consequenceof substitutional disorder within the immobile ion host-substructure,via induced mobile-ion disorder. Enhanced conductivities have beenreported in other materials with configurational host-framework disorder,118 and the same underlying mechanism of induced mobile-ion disordermay be responsible in these cases. This raises the question of theextent to which substitutional framework-disorder might be usefulas a general design strategy to obtain superionic conductivity inother families of solid electrolytes?Superionic conductivity in solid electrolytesis often associatedwith some form of disorder within the mobile-ion substructure,6PS5X mightsuggest design strategies for optimizing the ionic conductivity of x(Li) ≠ 6 argyrodites? Our results indicate thatin the case of Li6PS5X, substitutional aniondisorder, and the resulting lithium disorder, are key to achievingfast Li diffusion. This suggests that substitutional disorder; eitherdue to mixed anions, or to partial substitution of P with elementssuch as Ge, might have a similar positive effect in x(Li) ≠ 6 systems. A disordered potential energy surface maypromote fast diffusion by causing concerted “superionic”diffusion mechanisms,119 rather than slowerindependent-hopping diffusion mechanisms. A second, contrasting, interpretationcomes from noting that in Li6PS5X systems, S/Xanion disorder gives S occupying adjacent 4a and 4c sites, which contributesto lithium disorder because of Coulombic frustration of otherwiseregular SLix units. This perspective suggeststhat in x(Li) ≠ 6 argyrodites, fast lithium-iondiffusion might be achieved in compositions in which the S/X ratiodiffers from one, making, for example, Li7PS6 an interesting end-member case.In the case of the lithiumargyrodites, we can ask the more specificquestion of how these results for Lix(Li) > 6, such as Li6.6P0.4Ge0.6S5I11 and Lix6+MxSbx1–S5I .48 In the latter case, lithiumhas been shown tooccupy nontype 5 sites, which was attributed to the x(Li) > 6 lithium stoichiometry, with this lithium “site-disorder”suggested as the origin of the observed fast lithium-ion conduction.48 This suggestion is consistent with the generalprinciple that lithium disorder (in some form) is necessary to achievefast lithium diffusion, and raises the possibility of doing so directlythrough control of lithium stoichiometry; in contrast to the inducedlithium disorder arising from substitutional framework disorder, asfor the anion-disordered Li6PS5X systems. Attributing the exceptional ionic conductivity of theseexperimental x(Li) > 6 systems to a single mechanisticorigin is challenging. The excess Li stoichiometry is a consequenceof aliovalent substitution of host-framework atoms occupying the 4bsite, which introduces a new source of substitutional disorder withinthe host framework. These materials also exhibit small amounts ofS/I disorder, which may also contribute to Li disorder and enhanceLi diffusion.11 Resolving the interplaybetween stoichiometry, structure, and lithium dynamics, and usingthis understanding to further optimize the ionic conductivities ofthis family of solid electrolytes presents an intriguing challenge.The complexity of these issues suggests that a full understandingwill only be reached by combining data from systematic experimentalstudies of controlled stoichiometries with insight from correspondingcomputational studies.Finally, we note that thehighest room-temperature ionic conductivitiesfor lithium argyrodites have been reported for “Li excess”systems with


Acceptable insertion without perforation or <2-mm lateral/cranial position was more frequent in ECD (67.1%) than in non-ECD (56.9%) (p = 0.02). Critical ≥5-mm medial/caudal malposition was not seen in ECD (0.0%) but in non-ECD (2.4%) (p = 0.02). The perforation distance was shorter in ECD (2.2 ± 1.1 mm) than in non-ECD (2.6 ± 1.7 mm) (p = 0.01). Results involve small sample size, selection, performance, and learning curve biases; nevertheless, ECD could be useful for more accurate and safer pedicle screw placement in severe syndromic/neuromuscular scoliosis.An electrical conductivity-measuring device (ECD) has recently been developed to support pedicle screw placement. However, no evidence exists regarding its efficacy for syndromic/neuromuscular scoliosis with extremely difficult screwing. We retrospectively reviewed 2010–2016 medical records of 21 consecutive syndromic/neuromuscular scoliosis patients undergoing free-hand segmental fixation surgery at our institution and compared the pedicle screw insertion accuracy and safety between 10 with a conventional non-ECD probe (2010–2013) and 11 with an ECD probe (2014–2016). We analyzed preoperative pedicle shape and postoperative screw placement in computed tomography. There were no significant differences between ECD and non-ECD groups in demographic, clinical, and treatment characteristics including scoliosis severity and pedicle diameter. The abandonment rate due to liquorrhea or perforation was lower in ECD (12.3%) than in non-ECD (26.7%) ( While idiopathic scoliosis is the most common, definite causes including congenital scoliosis and syndromic/neuromuscular scoliosis account for 20% to 25% [Instrumentation of the posterior spine with pedicle screw is currently the most common surgical technique to stabilize, fix, and correct pathological changes of the spine caused by degenerative disease, developmental scoliosis, trauma, and tumors ,2,3. How% to 25% . Pedicle% to 25% ,9,10.Various methods have currently been utilized to insert screws into the pedicle accurately. Traditional free-hand pedicle screw placement based on the anatomical landmarks is often used ,3. HowevA probe with an electrical impedance conductivity-measuring device (ECD) has recently been developed to improve the accuracy of pedicle screw placement ,19. The This was a retrospective case–control study. Data were collected from historical medical records under the approval and guidance of the Institutional Review Board (IRB) at Kobe University Graduate School of Medicine . Considering the nature of the retrospective study design to review medical records of patients who completed the treatment, IRB waived the requirement to obtain informed consent. However, for the use of personal information and images of patients, written informed consent for publication was obtained from each patient in accordance with the principles of the Declaration of Helsinki and the laws and regulations of Japan.n = 5).Twenty-three consecutive patients with syndromic/neuromuscular scoliosis who underwent posterior segmental fixation surgery from 2010 to 2016 at our university hospital were included in this study. Anterior surgery and revision surgery were excluded. Surgical indications were generally progressive scoliosis with the Cobb angle of >60° and/or difficulty to stay in a sitting position requiring pelvic fixation. Clinically, pulmonary function was also taken into account. In fact, we surgically treated all consecutive cases of referred patients with syndromic/neuromuscular scoliosis fulfilling surgical indications and did not refuse surgery because of the worsened general condition or high risk of anesthesia. In Japan, preoperative and postoperative scans of computed tomography (CT) were still acceptable when needed with minimized radiation exposure, which was therefore performed in all scoliosis cases without any selection bias. Demographics of patients regarding age, sex, underlying diseases, clinical characteristics regarding the preoperative Cobb angle and pedicle diameter in images of standing or sitting (difficult to stand up in many cases) thoracic and lumber spine radiography and CT, and treatment characteristics regarding the postoperative Cobb angle, correction rate, number of fixed vertebrae, operation time, and blood loss were investigated. Two patients were excluded because of one case with anterior fusion surgery and one case with revision surgery. Consequently, 21 patients  were finally included. Underlying diseases of these patients are listed in ® Deformity Spinal System; K2M/Stryker, Leesburg, VA, USA). Ponte osteotomy was performed at six periapical intervertebral segments. If necessary, fixation down to the pelvis using iliac or S2 alar–iliac screws was applied. Intraoperative monitoring of spinal cord function was conducted by motor evoked potentials. Even in pedicles with the outer diameter of <4.5 mm, we attempted screw placement based on the pedicle expansion concept and in-out-in screw insertion technique [®; SpineGuard, Vincennes, France) was used. The use of ECD was approved from 13 August 2013 in Japan and from 1 November 2013 at our institution; therefore, we tested and decided to apply it for all cases of syndromic and neuromuscular scoliosis surgery from 1 January 2014. Further, we compared findings between patients whose pedicle screws were inserted with a conventional probe by a free-hand technique as the non-ECD group (2010–2013) and those whose screws were placed with PediGuard® as the ECD group (2014–2016). Consequently, the non-ECD group comprised 288 pedicles from the initial consecutive cases of 10 patients  while the ECD group consisted of 284 pedicles from the last consecutive cases of 11 patients .Free-hand posterior segmental pedicle screw fixation was performed by the single board-certified senior surgeon using the single instrumentation system with the minimum 4.5-mm screw diameter . Further, the position of inserted pedicle screws was assessed through axial, sagittal, and coronal plane images to determine whether pedicle wall breaches occurred medially, laterally, caudally, or cranially and then considered correct if screws were completely placed within the pedicle (intrapedicular position). If not within the pedicle, screw placement was categorized based on the deviation direction and distance. Based on the ECD primary nature of avoiding neural injury, laterally or cranially deviated screws of <2 mm were considered as in a relatively acceptable position whereas laterally or cranially deviated screws of ≥2 mm were determined as in a mechanically threatening malposition based on the low fixability. Meanwhile, any medially or caudally deviated screws were judged as in a neurologically threatening malposition. Regarding the degree of deviation, pedicle breaches were classified by grades based on 2-mm or 3-mm increments and pedicle screws with breaches <2 mm were recognized as in a safe zone in prior studies ,29. Therp-value of <0.05. The Student’s t-test after normality assumption and the Pearson’s chi-squared test or Fisher’s exact test were used for the comparison between ECD and non-ECD groups of continuous variables and of categorical variables, respectively. In addition, the intra-class correlation coefficient was calculated to clarify the intra-observer and inter-observer reliability for CT measurements.All statistical analyses were performed using IBM SPSS Statistics 23.0  with significance set at a n = 11) and non-ECD (n = 10), there were no significant differences in the patient age, sex, preoperative Cobb angle, postoperative Cobb angle, correction rate, and blood loss  (p = 0.09) (p = 0.02) (p = 0.20). However, mechanically threatening pedicle screw misplacement located ≥2 mm laterally or cranially was observed in 37 pedicles (14.9%) of the ECD group but in 48 pedicles (22.7%) of the non-ECD group (p = 0.03) (p = 0.04) (p = 0.53) (p = 0.28) (p = 0.01) (p = 0.02). In fact, there were no patient cases requiring revision surgery due to pedicle screw misplacement.The preparation of pilot screw holes was performed at 288 pedicles of the non-ECD group with a free-hand technique and at 284 pedicles of the ECD group with the aid of electrical conductivity-measuring PediGuard < 0.01) A,B. Post = 0.09) C. Regard = 0.02) D. There  = 0.03) . Mechani = 0.04) E. Regard = 0.53) . Neurolo = 0.28) F. Howeve = 0.01) G. In addA 20-year-old man with the Sotos syndrome presented at pre-operation right-curved scoliosis with the Cobb angle of 64° and severe kyphosis with the Cobb angle of 85° at Th5–L1 A,B. We pIn scoliosis surgery, the use of all-pedicle screw constructs has become common. The frequency and accuracy of pedicle screw placement are essential for acquiring satisfactory surgical outcomes. Most scoliosis studies regarding the accuracy and safety of pedicle screw insertion represent idiopathic scoliosis. The perforation rate of free-hand pedicle screw placement ranged from 3.7% to 65% ,30. A ren = 28), syndromic (n = 2), and congenital (n = 1) scoliosis also demonstrated an acceptable accuracy and prevention from critical misplacement of the ECD, which was comparable with the three-dimensional model and intraoperative navigation system [Prior reports studying the ECD probe in scoliosis have shown its efficacy during surgery. The ECD increased pedicle screw placement accuracy and decreased insertion time and radiation exposure in posterior adolescent idiopathic scoliosis surgery . A studyn system . HoweverIn our study series, pedicle screws were inserted using either with a free-hand technique or with the ECD assistance, which can help surgeons to detect pedicle breaches. In both groups, subjects had severe deformity with the mean thoracic pedicle diameter of <3.5 mm and the mean preoperative Cobb angle of >80°. Under these severe circumstances, more than half of pedicle screw placement by a free-hand technique led to the pedicle perforation in every direction. Inserted pedicle screws with breaches <2 mm were considered as a safe zone in many studies . HoweverThis study has several limitations. First, this study cases and controls were retrospectively collected from not randomly distributed, consecutive case series; therefore, potential selection bias exists despite no significant differences in patient demographics and clinical and treatment characteristics related to screw placement between ECD and non-ECD groups. In addition, the learning curve would affect results because we selected patients who underwent surgery before the appearance of the ECD probe as the historical control; consequently, performance bias could overestimate the efficacy of ECD. Second, the enrolled subjects were relatively small in number and heterogeneous in patient demographics and clinical characteristics because of the rarity of diseases and nature of the retrospective design. Third, the comparison in the ECD efficacy with other surgery-supporting methods capable of facilitating accurate pedicle screw placement, e.g., intraoperative navigation systems and three-dimensional printed models , was notThis retrospective case–control study provides only limited evidence because of a high-risk involvement of bias with the small sample size and learning curve effects; nevertheless, the ECD probe could be a helpful support tool to provide more accurate and safer pedicle screw placement, leading to substantial reductions in mechanical instability, critical malposition, and then potential neural damage, even during challenging syndromic/neuromuscular scoliosis spine surgery. Future prospective clinical trials are warranted to clarify the efficacy of ECD.


Categorical neural responses underlie various forms of selection and decision-making. Such binary-like responses promote robust signaling of the winner in the presence of input ambiguity and neural noise. Here, we show that a ‘donut-like’ inhibitory mechanism in which each competing option suppresses all options except itself, is highly effective at generating categorical neural responses. It surpasses motifs of feedback inhibition, recurrent excitation, and divisive normalization invoked frequently in decision-making models. We demonstrate experimentally not only that this mechanism operates in the midbrain spatial selection network in barn owls, but also that it is necessary for categorical signaling by it. The functional pattern of neural inhibition in the midbrain forms an exquisitely structured ‘multi-holed’ donut consistent with this network’s combinatorial inhibitory function for stimulus selection. Additionally, modeling reveals a generalizable neural implementation of the donut-like motif for categorical selection. Self-sparing inhibition may, therefore, be a powerful circuit module central to categorization. Decision making is facilitated by categorical neuronal responses, which robustly signal a winner despite input noise. In this study, the authors demonstrate that a donut-like inhibition motif effectively generates such categorical responses. Neural responses that are explicitly categorical4, have been reported across brain areas and animal species in a variety of perceptual and decision-making contexts13. Such response profiles, which involve a large and abrupt change in firing rate across the category boundary  and several nuclei in the midbrain tegmentum, referred to as the isthmic nuclei21 22. These neurons fire at a high rate when the stimulus inside their spatial receptive field (RF) is the highest priority, but switch abruptly to a lower firing rate when a distant, competing stimulus becomes the highest priority one 22.An excellent site in the brain at which to investigate neural circuit mechanisms of categorization is a vertebrate midbrain network that plays a causal role in controlling gaze and spatial attentioni21 Fig. . In the 27. In parallel, responses of OTid neurons to multiple competing stimuli are controlled by inhibitory neurons of the isthmi pars magnocellularis (Imc)  pathway as well as the indirect (Imc→Ipc→OTid) pathway , which exhibit point-to-point recurrent connectivity with the OT Fig. -orange25mc) Fig. -purple2832, we investigate how categorical neural responses in the barn owl OTid are generated by computations in the OT-Imc-Ipc network. We demonstrate that a donut-like pattern of spatial inhibition in this network causally controls categorization by OTid, and also that this inhibition is implemented with an intricate multi-holed donut-like pattern across interconnected brain areas in support of categorization across space. These results suggest that donut-like inhibition may be a fundamental circuit motif for generating categorical neural responses, a function central to spatial selection, perception, and decision making34.Here, using a combination of neurally grounded computational modeling, dual electrophysiological recordings, and focal iontophoretic neural inactivation37  options45. Therefore, in our model, we introduced feedback inhibition as reciprocal inhibition between the two model Imc neurons  at distant spatial locations (or to distinct “channels” in the model). The relative strength of the S1 and S2 (controlled by their loom speed) was systematically varied, resulting in two well-defined stimulus strength-dependent categories8: S1 > S2 and S1 < S2; Fig. n = 50 “neurons”; Methods). The values of the parameters of these sigmoids, as well as the value of response fano factor used in the models , were obtained from a series of previous experimental  measurements of input-output functions in the barn owl midbrain network49.The eight circuit models that arise from different combinations of these three proposed circuit motifs are illustrated in Fig. 8 Fig. . This pr8. This index, defined as the average difference in responses between categories divided by the average difference in responses within categories, is insensitive to simple multiplicative scaling of the responses  between categories divided by the average difference within categories . This result was largely independent of the strength of feedback inhibition , the strength of amplification . The magnitude of improvement was inversely related to the strength of “self”- inhibition, reaching the maximum when self-inhibition was zero, i.e., when the pattern of inhibition was fully donut-like . Whereas the presence of either or both recurrent excitation and feedback inhibition enhanced the impact of the donut-like motif , without the donut-like motif, they were nearly ineffective, either individually or together, at signaling the strongest stimulus categorically , and simulated 324 circuit models representing different combinations of parameter values Fig. . We founDonut-like inhibition, therefore, emerged as the most powerful single circuit motif (among the three proposed in the literature) for producing categorical neural responses Fig. .31 have indicated that the direct projections from Imc neurons to the OT spare the portion of the OT providing input to Imc, supporting a donut-like motif in the direct inhibitory pathway , and Ipc provides substantial amplification of OTid responses to single stimuli25.To examine the potential role of donut-like inhibition in controlling categorical neural responses in the avian midbrain, we first investigated experimentally whether a donut-like inhibitory motif even operates in the owl midbrain selection network. As we pointed out above, anatomical tracing studies32 (Methods).To determine whether the Imc-Ipc-OT circuit implements a functional donut-like pattern of competitive inhibition, we measured experimentally the strength of the net inhibition delivered by Imc neurons onto OTid neurons, due to both the direct as well as the indirect pathways. Specifically, we compared the strength of net inhibition from Imc neurons onto ‘misaligned’ OTid neurons encoding for stimuli at distant, non-matched azimuthal locations .To measure the strength of net “other”-inhibition, we first recorded the responses of OTid neurons to a stimulus (S1) inside the receptive field RF; Fig. -right, a50, and this suppression is known to be abolished upon focally inactivating the portion of Imc representing S233. Therefore, any increase in OTid responses to the paired presentation of S1 and S2 following Imc inactivation would represent other-inhibition provided by Imc n = 19 paired neurons; p = 9.43e-9, t test against 0; mean distance between centers = 26.74°). We verified that the results were specifically due to Imc inactivation by observing that OTid responses to paired S1 and S2 returned to pre-drug levels after recovery from iontophoresis  presented inside the RF . We verified that these results were not due to ineffectiveness of iontophoresis by observing that the suppression of Imc responses by kynurenic acid was substantial . Therefore, strength of net self-inhibition in the OTid was substantially weaker than the strength of net other-inhibition . Additionally, the average strength of net self-inhibition from Imc to OTid was not significantly different from zero .We found that Imc neurons exerted no significant inhibition onto OTid neurons encoding for overlapping spatial locations  space map; operating necessarily along both the direct and indirect pathways. Notably, they attest to the presence of a functional donut-hole of inhibition in Imc→OTid projections, as well as in Imc→ Ipc projections.51; Fig. 51.Imc neurons are strikingly asymmetric in their encoding of elevational vs. azimuthal space. The majority (67%) exhibit RFs with multiple discrete firing fields (“lobes”) distributed along the elevation, but not the azimuth . If so, we next measured the strength of gap inhibition by positioning a second electrode in the OTid such that the spatial RF of the OTid neuron was centered within the gap between Imc RF lobes . Imc was inactivated effectively in both sets of experiments , operating along both the direct and indirect pathways. Each Imc neuron’s net inhibitory action in the OTid creates a spatial pattern complementary to its (multilobed) RF structure Fig. .Considering the complexity of the multi-holed donut-like connectivity between Imc (and Ipc) and OT Fig. , we nextTo resolve this apparent conundrum, we stepped back and considered the specialized anatomical connectivity of the avian midbrain selection network Fig. . We obseThis observation led us to reason that we could achieve the goal of experimentally introducing self-inhibition onto OTid neurons not by activating the (likely non-existent) self-projections from Imc to the aligned Ipc neuron in the dominant indirect pathway Fig. , but ratTo test if this logic was sound, we first simulated this latter model Fig. , and fou22.Using these insights, we proceeded to test experimentally, the functional consequence of filling-in the donut hole on categorization by barn owl OTid neurons. We focally (and reversibly) inactivated Ipc neurons by the iontophoresis of the pan-glutamate receptor blocker, kynurenic acid Fig. ; MethodsCatI of 104.7% . These results reinforce the dominance of the indirect Imc-Ipc-OT pathway over the direct Imc-OT pathway (the donut-like inhibition there remained intact in these experiments). Thus, the midbrain spatial selection network not only contains a specialized donut-like inhibitory circuit motif, but also critically depends on it for categorical signaling by OTid.We found that disrupting the donut-like inhibitory motif caused a substantial reduction in categorical signaling in the OTid . Although not effective for producing categorical responses, feedback inhibition and recurrent amplification have been linked to other important functions related to selection, namely, the implementation of a flexible selection boundary (feedback inhibition52), and evidence accumulation (recurrent amplification42). Selection circuits may, therefore, need to include these motifs for other reasons than categorization. If present as well, they heighten the efficacy of the donut-like inhibitory motif in producing categorical response profiles , that inhibit one other, and that deliver pooled inhibition uniformly (rather than in a donut-like manner) to the output elements . The midbrain spatial selection network (OT-Imc-Ipc), in which categorical neural responses have been reported, does not implement pooled divisive normalization for selection across space: past work has shown that the inhibitory Imc neurons receive selective input51, and our results . Thus, the normalization mechanism is not effective for generating categorical responses . Indeed, it was the presence of self-inhibition, specifically, that caused this circuit to be ineffective: a modified version of the circuit which did not include self-inhibition , 0.34 (filled orange)). Nonetheless, the feedforward implementation of the donut-like motif , and no matter what the sensory modality is 61. In other words, categorical neural responses are not idiosyncratic to a specific stimulus feature, but are in fact, general, representing the neural basis of stimulus competition and selection across space in the barn owl21. Notably, the categorical responses measured in the owl OTid have been shown to be capable of accounting for behavioral deficits in target selection for spatial attention in monkeys following focal perturbation of the homologous SCid14. These observations, together with the fact that the midbrain tecto-isthmic selection network is conserved across all vertebrates63, point to the potential generality of the donut-like motif across the vertebrate midbrain for spatial selection.This study revealed the donut-like inhibitory motif as the engine of categorization in the avian midbrain network for spatial selection, a network conserved across vertebratesMight this motif also generalize to other forms of categorical selection (beyond selection across space), mediated by other cortical and subcortical areas (beyond the midbrain)? If so, how might it generalize, implementation-wise? Below, we examine these two questions in order.67. These models successfully account for neural as well as behavioral responses in a wide array of decision-making tasks –perceptual decision-making, delayed-match-to-sample decision-making, sensory categorization, etc. Examination of the circuit architectures in these models reveals that nearly all of them contain a (seemingly hidden) donut-like inhibitory motif34. Some include a feedforward implementation67 , we draw upon the extensive literature of computational modeling of categorical decision-making by various cortical  areas23. This readily generalizes to other instances of selection in which stimulus options are encoded with neural activity that is proportional to their net attractiveness or importance: for instance, subjective-value of an option in the case of value-based decision-making76, degree of membership of a stimulus in the case of perceptual categorization77, etc. Second, in this network, long-range suppression across spatial locations is the substrate upon which the donut-like inhibitory motif is sculpted, and is implemented by inhibitory neurons with far-reaching projections across the space of stimuli. Alternatively, such inhibition could also be implemented, for instance, in cortical circuits, through long-range excitation contacting local inhibitory neurons. Third, in the midbrain network, the donut-like motif is instantiated via a feedforward implementation. As we saw in Fig. 78 is also effective. Fourth, in the midbrain network, the donut-like motif aids spatial selection by operating across a well-organized topographic map of space. However, for many forms of selection, such organized functional maps do not exist, with olfactory categorization being an extreme example79. In the case of olfactory decision-making, there is some evidence suggesting self-sparing, combinatorial lateral inhibition across mouse glomeruli80, of the kind found in the owl Imc. In most of these cases, however, a detailed description of the large-scale connectivity diagrams of inhibitory neurons in the corresponding brain areas is yet to be worked out; this study suggests that a search for donut-like inhibitory connectivity might be a fruitful endeavor.To address the second question of how it might generalize (issues of implementation), we highlight four key characteristics of the donut-like motif in the avian midbrain selection network and discuss plausibly generalizable implementations of each. First, in the midbrain selection network in which the donut-like motif operates, individual stimuli are encoded with neural activity that is proportional to their net priority82.More generally, the donut-like motif described here does not rely on mechanisms of plasticity for its operation. It is able to dynamically generate categorical neural responses from continuously varying inputs, on the fly, and dynamic categorization is critical to various behaviors . However, conceptually, this motif could also be introduced into a circuit through plasticity mechanisms, thereby aiding in the generation of categorical response profiles that are learned with experience61. . Our past modeling work (which forms the basis of this work) has shown that not including precise timing descriptions—for instance, timing of the arrival of excitation vs. inhibition, does not impact the ability of these models to capture phenomena at the level of average firing rates44. Separately, several experimental studies have also reported temporal aspects of decision-making—time courses of neural activity as well as behavioral reaction times. We recall that leading classes of models of selection/decision-making contain the donut-like inhibitory motif83. Consequently, because those models account for experimentally measured reaction times of animals during the selection tasks , the donut-like motif is consistent with such temporal aspects and dynamical features of categorical decision-making as well. It will be valuable for future studies (involving behavior) to explore these links explicitly.In this study, we were interested, particularly, in mechanisms that could generate categorical profiles of average firing rates  as a function of relative stimulus strength, as reported experimentally in the barn owl midbrain13, psychometric profiles (of accuracy) are often not. To clarify, whereas the animal or subject must (and does) make a discrete choice on each trial, which results in the task being referred to commonly as a “categorical” decision-making task, behavioral performance, when assessed as a function of a continuous task parameter, is often not actually step-like85. It does not exhibit a large, abrupt change across the category boundary, but instead, varies more gradually across it. These two facts, however, are not in conflict: in line with previous findings, neurons can encode information more effectively than the animal as a whole, with behavior being a result of (noisy) aggregation of activity across neurons86. Consequently, the central prediction of this study is that causally perturbing donut-like neural inhibition in a relevant brain area during a decision-making task, will cause loss of categorical neural responses, and in turn cause psychometric response curves to become shallower  than in the intact condition, independently of their original shape, with selection performance worsening particularly around the selection boundary.The central proposal of this study is that donut-like inhibition underlies categorical neural responses. Whereas neural response profiles underlying decision-making and selection tasks are frequently categoricalIn closing, we propose that the donut-like inhibitory motif Fig.  may be aTyto alba). Both male and female birds were used; the birds were shared across studies. All procedures for animal care and use were carried out following approval by the Johns Hopkins University Institutional Animal Care and Use Committee, and in accordance with NIH guidelines for the care and use of laboratory animals. Owls were group housed in flight runs within the aviary, each containing up to 6 birds. The light/dark cycle was 12 hr/12 hr.We performed experimental recordings in 7 head-fixed awake adult barn owls viewing a visual screen passively  were used to record single and multi-units extracellularly in the OTid. Multi-barrel glass electrodes  filled with kynurenic acid  were used to record from and inactivate neurons in the Imc and Ipc. Inactivation was performed using micro iontophoresis by ejecting kynurenic acid with an eject current of −450 nA to −500 nA; data were collected starting 15 min after drug ejection commenced. A retain current of +15 nA was used to prevent leakage of the drug from the tip of the electrodes when drug was not being iontophoresed. Recovery data were measured 15 min after drug ejection was ceased. Microiontophoresis, the technique we use here, is an established technique for focal delivery of drugs that has been used extensively for this purpose in the literature91. Prior published work has demonstrated that microiontophoresis of kynurenic acid is spatially specific in the Imc-OT circuit32, and that it offers a reliable approach to quantify Imc inhibition onto OTid neurons32. Additionally, it is preferable to the alternative of electrical microstimulation of Imc neurons for measuring the strength of Imc-OT inhibition because, (a) it avoids the confound that can arise from potentially activating fibers of passage from Ipc to OT as well (which are known to course through the Imc region31), and (b) it measures the strength of physiological inhibition evoked by a stimulus rather than that evoked by ectopic electrical activation.Experiments were performed following protocols that have been described previously92), and then navigated to the Imc using the OT’s topographic space map as reference. The Imc is an oblong structure that is 2.8 mm rostrocaudally and 0.35 mm dorsoventrally, appearing as a 700-μm × 350-μm elliptical disk in coronal sections. It lies parallel to the rostrocaudal axis of the OT, located ~16 mm ventral to the surface of the brain, and ~500 μm medial to the medial-most part of the OT. We targeted the Imc following published methods32. Imc targeting has been validated previously using dye injections and lesions51. Dorsoventral penetrations through the Imc were made at a medial-leading angle of 5˚ from the vertical to avoid a major blood vessel in the path to the Imc. The Ipc lies roughly 500–700 um medial to the Imc and its targeting was confirmed based on the neural response characteristics of the neurons (characteristic bursty responses61).We navigated to the OT  following stimulus onset.93. We included only those units for analysis for which fewer than 5% of the recorded spikes were within 1.5 ms  of each other.The automated “wave-clus” spike-sorting toolbox was used for spike sortingModel details :The excitatory neurons were simulated using the following parameters (which are consistent with the parameters obtained by fitting a sigmoid to response functions of OTid neurons44):The inhibitory neurons were simulated using the following parameters (which are consistent with the parameters obtained by fitting a sigmoid to response functions of Imc neurons48):The excitatory neurons that provide recurrent amplification in Fig. 44.din and dout are parameters that control the strength of input and output division and The inhibition sent from the inhibitory neurons onto excitatory neurons is modeled using input and output divisive factors as below using previously published methodsdin = 0 and dout = 0.25 consistent with previously published methods .The value of these parameters chosen were see Fig.  in44.44.In models in which the inhibitory neurons inhibit each other . The time course of reverberant activity due to this feedback connectivity has been plotted in our previously published workThe values of the feedback parameters used were In models in which the excitatory neuron receives inhibition from more than one inhibitory neuron . We also vary the amplification factor The value of the parameter is chosen as 0.01 to yield results consistent with the amplification effect of Ipc on OT responses as reported in previously published work  of the inhibitory neurons are set to their baseline level, and of the excitatory neurons are calculated from the stimulus inputs without any divisive inhibition.For the models with recurrent amplification Fig. , the out8. We presented stimulus S1 at location 1 and stimulus S2 at location 2. As the strength of the first stimulus was increased, the strength of the second stimulus was decreased . We measured the boundary discriminability (bd’) of the responses of neuron 1 by calculating the d-prime between the responses of neuron to stimuli pair straddling either side of the selection boundary and at a distance of 3 units from the boundary as:8) (a) the mean within-category d-prime (WCD’) between the responses of the neuron to pairs of stimulus-pairs (S1 and S2) that are in the same category, and (b) the mean between-category d-prime (BCD’) between the responses of the neuron to pairs of stimulus-pairs that are in different categories. The pairs are chosen while ensuring that (i) the number of pairs used to calculate both these metrics are the same, and (ii) the distribution of the distances between the chosen pairs for calculating both the metrics are the same. The categorization index is calculated from these two metrics as:To compute the categorization index, we compared two quantities: , and a spatially misaligned “other” OTid neuron (with a tungsten electrode) as described below; we ensured that the half-max of the RF of the OTid neuron lay outside (did not overlap with) the half-max of the Imc RF.Tuning curve (TC) centered at the OTid RF peak: A 1-dimensional spatial tuning curve centered at the peak of the OTid RF. The stimulus had a loom strength of 9.6°/s.49.Tuning curve centered at the OTid RF peak + competing stimulus centered at the Imc RF peak (TCC): The same curve as in a), but along with a (distant) competitor positioned at the peak of the Imc RF. The strength of the competing stimulus was chosen to be 19.2°/s. This second competing stimulus drives the Imc neuron, which sends strong competitive inhibition to the OTid neuron. Since the competing stimulus was more salient than the stimulus driving the OTid neuron, the responses of the OTid neuron were strongly suppressed consistent with previous published resultsTuning curve (TC) centered at the Imc RF peak: 1-dimensional spatial tuning curve centered at the Imc RF. The loom strength of the stimulus was chosen to be 9.6°/s.For measuring “other” inhibition, we recorded the following data curves together in an interleaved manner.We measured the above 3 curves both when the Imc neuron is intact (“baseline” condition) and focally inactivated (“inactivation” condition) and compare the responses as below. In a subset of the data, we also measured the curves after the responses of the Imc neurons recovered  and TCC (curve b); Fig. 9.First, a distant competing stimulus is known to typically suppress OTid responsesp = 3.8e-6, sign test, n = 19).Next, to measure the amount of Imc inactivation, we compared the responses of the Imc neurons to the TC measured at the Imc RF peak (curve c) in the baseline condition vs. the inactivation condition. Kynurenic acid was able to effectively shut down Imc responses:  in the baseline condition and the inactivation condition. In the baseline condition, the Imc neuron was intact, driven by the competing stimulus and sent strong inhibition to the OTid neuron. In the inactivation condition, the Imc neuron was silenced, as a result of which the OTid neuron was released from inhibition and exhibited an increase in responses.2.“Self” inhibition:To measure the strength of “self” inhibition sent from an Imc neuron to a matched location in the OTid space map, we simultaneously recorded from the Imc neuron (with a multi-barrel glass electrode filled with the kynurenic acid), and a spatially aligned “self” OTid neuron (with a tungsten electrode) as described below; we ensured that the half-max of the RF of the OTid neuron overlapped with the half-max of the Imc RF.We recorded a spatial tuning curve centered at the peak of the OTid  RF. The loom speed of the stimulus used was 9.6°/s; this stimulus drives both the OTid and the Imc neuron.We compared the responses of the OTid neuron in the Imc-intact (baseline) and Imc inactivated condition and the difference quantified the strength of “self” inhibition Fig. , blue.p = 7.5e-9, sign test).To measure the amount of Imc inactivation, we compared the responses of the Imc neuron in the baseline and the inactivation condition as before. Kynurenic acid was able to effectively shut down Imc responses: , we simultaneously recorded from the Imc neuron (with a multi-barrel glass electrode filled with the kynurenic acid), and “gap” OTid neuron (with a tungsten electrode), the RF  of which was located in the gap between the half-max of the lobes of the Imc RF Fig. . We recoAs pointed out in the Neurophysiology subsection above, microiontophoresis is a focal technique for manipulating neural activity. This minimizes concerns about potentially broad spread of kynurenic acid in this experiment causing inactivation of Imc neurons encoding for the gap location as well. Notably, even if such widespread inactivation were to occur, it would not affect our interpretations for the following reason. Consider that an Imc neuron that encodes for the gap location /responses in Imc off condition. To obtain an accurate estimate of the % change, we considered the responses to stimulus S1 (in the two conditions) at all locations inside the RF as follows. We fit a straight line to the plot of OTid responses to S1 in the Imc intact vs. Imc of conditions Fig. , calculaTo measure the strength of inhibition sent “from” locations within one lobe of an Imc neuron with a multilobed RF to the locations in the OTid space map within other lobes of the Imc RF (“different lobe” inhibition), we simultaneously recorded from a multilobe Imc neuron (with a multi-barrel glass electrode filled with the kynurenic acid), and an OTid neuron (with a tungsten electrode), the RF  of which overlapped with one of the lobes of the Imc RF Fig. . Then weAn OTid neuron in this configuration was defined as a “different lobe” OTid neuron; the half max of its RF overlapped with the half max of one of the lobes of the Imc RF, but not of other lobes. .II.Paired OTid and Ipc data collection Figs.  and S4We applied similar analyses as in the “other” case to the data from “different lobe” OTid neurons and quantified the strength of “different lobe” inhibition.8. Briefly, we presented one stimulus (S1) inside the RF of the OTid neuron . Simultaneously, we presented a competing stimulus (S2) 30˚ away along azimuth from S1. As the strength of the S1 decreased, the strength of S2 stimulus increased  categorization, we made paired recordings at spatially aligned Ipc and OTid neurons. We used a strength morphing stimulus protocol described in previously published worksed Fig. .We applied the same analyses described above for the model in Fig. corr command in MATLAB with the “Pearson” option).All analyses were carried out with custom MATLAB code. Parametric or non-parametric statistical tests were applied based on whether the distributions being compared were Gaussian or not, respectively . The Holm-Bonferroni correction was used to account for multiple comparisons; the abbreviation “with HBMC correction” in the text stands for “with Holm-Bonferroni correction for multiple comparisons”. All tests were two-sided. Data shown as a ± b refer to mean ± standard deviation, unless specified otherwise. The “*” symbol indicates significance at the 0.05 level . Correlations were tested using Pearson’s correlation coefficient (Further information on research design is available in the Supplementary InformationSupplementary DatasetReporting Summary


The diagnosis, prognosis, and control of chronic kidney disease rely on an understanding of the glomerular filtration rate (GFR). The renal clearance of the cystatin-C is closely associated with the GFR. Cystatin-C is a more suitable GFR marker than the commonly used creatinine. General techniques for cystatin-C calculation, such as particle-enhanced turbidimetric and nephelometric assay, are time-consuming and tedious. Here, we propose a rapid, quantitative immunoassay for the detection of cystatin-C. A fluorescence-based lateral-flow kit was developed in a sandwich format by using a monoclonal antibody. A Linear calibration was obtained over the clinical diagnostic range of 0.023–32 µg/mL and the limit of detection (LOD) was 0.023 µg/mL and the limit of quantification (LOQ) was 0.029 µg/mL. Average recoveries from spiked urine samples ranged from 96–100% and the coefficient of variation was less than 4% for both intra and inter-day assays with excellent repeatability. With the comparison with an ELISA kit, the developed kit is highly sensitive, performs well over the detection range, provides repeatable results in a short time, and can easily be used at point-of-care (POC), making it an ideal candidate for rapid testing in early detection, community screening for renal function disorders. Shinde 3 months . Finally3 months .Untreated CKD progress can lead to acute kidney failure (stage V)  and mortCystatin-C is mostly quantified in urine by using a particle-enhanced turbidimetric immunoassay (PETIA) or nephelometric immunoassay (PENIA) ,15,16. DNitrocellulose membranes (HiFlow135plus) were procured from Merck Millipore . Sample and conjugation pad (CF4 and Standard 17) and absorbent pad (CF6) were obtained from Whatman . The anti-cystatin-C capturing antibody (Cyst24), the anti-cystatin-C detecting antibody (Cyst28), and recombinant protein cystatin-C  were obtained from Hytest Ltd., Turku, Finland. Goat anti-mouse IgG H & L, Alexa Fluor™ 647 NHS Ester (Succinimidyl Ester) was obtained from Thermofisher . Centrifugal filters were procured from Millipore . Sephadex G20 column was obtained from GE Healthcare  and PBS, NaOH, Sucrose, BSA, and Tween-20 were procured from Sigma-Aldrich .The key methods used in the development of the cystatin-C LFIA kit are explained in the following sections.g for 5 min and collecting the labelled antibody in 1× PBS buffer. The synthesized conjugate was mixed with an equal volume of glycerol to the final concentration of 10 µg/mL and stored at −20 °C until use.The monoclonal antibody used for the detection (clone cyst68 for cyst C) was conjugated with a fluorescent organic dye. Alexa Fluor 647 dye (excitation wavelength of AF647 is 633 nm and the emission wavelength is 650 nm) possesses a succinimidyl ester that acts with primary amines on the antibody. Briefly, the detection antibody at 1 mg/mL in 10 mM phosphate solution (pH 7.4) containing 140 mM NaCl (PBS) was reacted with the organic dye (20 molar excess) dissolved in DMSO for 1 h at room temperature. The reaction mixture was separated by Sephadex G20 gel chromatography column by centrifuging at 1300× The buffer solutions used were as follows: Sample pad buffer , conjugate pad buffer , nitrocellulose membrane blocking buffer , washing buffer , and assay running buffer .The LFIA membrane strip consisted of four types of pads arranged in a connected manner with limited overlapping. The four membranes were: A sample application pad for the analyte, a conjugate pad made of polyester fiber to hold the conjugated mixture of detection antibody and dye, a nitrocellulose test membrane for the generation of the signals, and finally, the absorbent membrane to promote the capillary flow of the assay. The sample pad was dipped in the sample buffer for 5 min and dried overnight at room temperature. The conjugate pad was immersed in the conjugation buffer and dried overnight; after drying, it was dipped in the conjugation mixture diluted from the original stock (10 µg/mL) to different concentrations  and dried at 37 °C for 1 h. The dye–conjugate solution was diluted in a conjugation buffer. The capture antibody (at 1 mg/mL) and the goat anti-mouse IgG (at 1 mg/mL), both diluted in 1× PBS, were dispensed onto the nitrocellulose membrane using an Easy printer and dried at 37 °C for 1 h. Thereafter, the nitrocellulose membrane was blocked by using 1% BSA with a blocking buffer (50 mL) for 5 min, and washed twice with the washing buffer and dried at 40 °C for 1 h. Finally, the membranes were assembled and cut to a width of 3.2 mm and stored at 4 °C.R) value was plotted vs. the cystatin-C concentration to get the calibration curve.In this proposed study, the cystatin-C recombinant protein was spiked into the human urine sample (45 first morning (morning void) urine samples) that had been diluted to the ratio of 1 μL of urine: 74 μL of the buffer. The samples were collected and stored at 4 °C and used for the experiment immediately. The urine samples were collected in sterile containers and used directly (no centrifugation steps). They were prepared in a dilution of cystatin-C of 0, 0.015, 0.03, 0.06, 0.12, 1, 2, 4, 8, 16, and 32 µg/mL in 0.1 M PBS with 1% BSA and 0.1% Tween-20. For the assay development, 75 μL of the spiked sample were dropped in the sample pad packed in the cartridge. The data was acquired from the ImageQuant  immunoan280 − (A650 × 0.03) × dilution factor/11,000, where 11,000 is the molar extinction coefficient of cystatin-C and 0.03 is a correction factor to account for the absorption of the dye at 280 nm.The fluorescent pixel map was processed using the NI LabView software mentioned in our previous work by Malay et al. ,28. The The LoB and LoD were estimated according to the CLSI EP-17A2 guidelines . For LoBThe glomerular filtration rate (GFR) was calculated by using the cystatin-C formula given by Stevens et al. :GFR = In ten aluminium foil pouches, three strips of each concentration of the cystatin-C were prepared. Five pouches were kept at 4 °C for 0 and 90 days and the remaining were stored at 37 °C for 0, 2, 6, and 8 days. All the pouches were taken from the oven and the fridge on days 0 and 90; the strips were tested for determining the cystatin-C concentration.Human Cystatin-C ELISA Kit (ab119589) KIT was purchased from Abcam, UK. The procedure was followed according to the manufacturer’s protocol.All quantitative data of the assay were calculated by Graph Pad Prism 6.0  for determining its sensitivity (Se) and specificity (Sp). Each parameter was calculated using a 95% confidence interval (CI) and the (CoV) of COI values was also analyzed for the assay data. The values for the (LOB) and (LOD) were obtained by using the 1.645 × SD of the negative samples and LOD = LOB + 1.645 (SD lower level of the sample), respectively . A urineThe principle of a sandwich fluorescent LFIA is illustrated in The fluorescent lateral flow immunoassay was developed and optimized to estimate the cystatin-C value to calculate the glomerular filtration rate. R of the LFIA strip. According to the results shown in p > 0.05); hence, 1 mg/mL was finalized.For coating the capture antibody at the nitrocellulose membrane, the capture antibody solution was diluted into concentrations of 0.2, 0.5, 1, 1.5 µg/mL. The amount of capture antibody on the test line has a large influence on the sensitivity of the test strip assay. If the concentration of the antibody is too high, it could lead to nonspecific adsorption. The results showed that inadequate amounts of antibodies in the nitrocellulose membrane led to the low volume ratio and that increasing the antibody concentration improved the VR) recorded in R) with the increase in the amount of Alexa fluor labeled mAb and a peak was recorded at approximately 0.3 μg/mL, and then, it decreased gradually. Based on this observation, the amount of labelled antibody of 0.3 μg/mL was chosen as the optimum amount for the strip.Glynou et al.  recordedLateral flow immunoassay performance was evaluated in the sense of pre-treatment given to the sample pad. Many reports showed that when the sample pad was pre-treated with a dilution buffer with surfactants, such as Tween 20 or PEG, it increased the sample flow, eliminated the background, and increased the sensitivity and stability of the LFIA . In our For the nonspecific binding, mainly to avoid false-positive results, we characterized the different blocking solutions for the nitrocellulose membrane. For this, we used five different blocking buffer compositions, containing BSA, a commonly used blocking agent, and the surfactant Tween-20 was used to reduce the hydrophobic effect and surface tension of the sample buffer, and the reaction was carried out at pH 7.4. R) of T line to C line is illustrated in R ratio increased rapidly in the first 15 min and then changed only slowly after 15 min. Finally, we selected 15 min as the most suitable incubation time for further experiments . The calculated limit of quantification (LOQ) was 0.023 µg/mL and the limit of detection (LOD) was 0.029 µg/mL. Analytical validation was studied by spiking the cystatin-C recombinant protein samples into urine samples, whose initial cystatin-C concentrations were 0.015, 0.03, 0.06, 0.12, 0.21, 1, 2, 4, 8, 16, and 32 μg/mL. The calibration curve was assessed by plotting the observed cystatin-C concentration against the VR ratio . The assTo determine the within run and between run variances, we analyzed five replicates from the concentration between 0.015 and 32 µg/mL on each of the six days. The precision was calculated using the one-way analysis (ANOVA). Data from the replicates for the consecutive six days are compiled in The assay recovery was determined by the measured concentration of cystatin-C divided by the theoretical concentration. Control urine samples were spiked with three various concentrations of cystatin-C standard samples with the low, medium, and high concentration, respectively , for analysis, and the recovery rates of the four selected samples were 92, 117, 102, and 105%, respectively .The accelerated ageing test was done to evaluate the stability of the strips by storing the strips at 37 °C for 7 days. For the determination of the stability, control strips were stored at 4 °C until the end of the experiment. On the other hand, experimental strips were kept at 37 °C until the completion of the experiment and then transferred to a 4 °C fridge. As shown in To investigate the potential clinical application of our Quantitative-lateral flow immunoassay, we compared its analytical performance with that of a commercially available ELISA assay kit . Eleven different concentrations  of cystatin-C were prepared and tested using both methods. As shown in A cystatin-C antibody-based lateral flow immunoassay was successfully developed, optimized, and verified. The calculated limit of quantification (LOQ) was 0.029 µg/mL and the limit of detection (LOD) for cystatin-C standard solutions spiked in urine samples was 0.023 µg/mL. The precision of the assay determined by the CV from the intra-assay and inter-assay was less than 10%, which comes under the acceptance level for the LFIA. The cystatin-C LFIA strips showed stability for one year at 4 °C. The stability test showed that, after a week at 37 °C, the volume ratio of the strips had not significantly changed, which means that the strips are stable at 4 °C for one year. The recovery level of the LFIA for the cystatin-C in the spiked urine samples was almost 100% for 10 µg/mL of cystatin-C. This new LFIA for cystatin-C shows increased sensitivity. The comparative study was done with the ELISA KIT to identify the significance of the fluorescent LFIA and demonstrate that the agreement with our kit cystatin-C rapid test card meets the requirements of clinical applications .