A new method of increasing the durability and reliability of polymer dielectrics has been proposed by designing a composite structure of the micro and nano particles. The synergistic effects of the micro particles and nano particles are found to enhance the resistance to electrical tree and extend the lifetime of polymer dielectrics for insulations. Epoxy loaded with the micro and nano SiO2 particles at different concentrations are prepared as micro-nano composites. The micro particles show the blocking effects on the electrical tree channel and the interfaces of the nano particles lead to the inhibiting effects on the tree inception and propagation. The lifetime of the micro-nano composite samples in the experiments extends to 4 times of the neat epoxy. The new type of micro-nano composites can be widely applied in future electronic and electrical energy areas. Polymer degradation and electrical tree growth arise from the creation of intense electric fields at the tips of conducting inhomogeneity, discharge channels and sites of stress concentration5. The intense electric field leads to localized breakdown, creating cavities and tree channels6 which influence the long term degradation of the polymer dielectrics. If the growth these electrical tree could be avoided, the lifetime and reliability of the insulation could be greatly increased.The reliability of electrical equipment and electronic devices becomes a big issue right now since once the insulating materials break down, the equipment can no longer serve on line further more. The durability of the polymer dielectrics is essential to the lifetime of the electrical equipment and electronic devices such as capacitors, batteries and cables8. High concentration (50 wt%) of micro inorganic particles are first applied in improve the resistance to the electrical tree12. However, the high loading of the micro particles usually causes the insulation problems such as increased dielectric loss and decreased breakdown strength13. Recently, similar improvements of the resistance have been found using less amount (<10 wt%) of the nano particles in many researches. The nano particles are believed to expand the width of the electrical tree15, inhibit the charges injection17, capture the mobile charges with deep traps20, act against the partial discharge erosion23 and enhance the bonding strength of the polymer24.Using fillers to enhance the performance of polymer dielectrics has attracted widespread attention2 composites with certain proportions of micro/nano particles are tested to evaluate the resistance to electrical tree breakdown. The dielectric parameters are measured to study the interfacial polarizations of the composites which are related to the effects of the nano particles. The electrical tree growth in the composites with low particles concentrations (<1 wt%) are observed under a stereomicroscope to study the effects of the micro particles on enhancing resistance to electrical tree. The synergistic effects of the micro and nano particles are proposed as well as the blocking effects of the micro particles and the inhibiting effects of the nano particles, which explain the high performance of the micro-nano composites for long-term electrical insulations.In this paper, the big volume of the micro particles and the large surface area of the nano particles are both found to contribute to enhancing the resistance to electrical tree. Although there are many researches on the electrical tree behaviors of the micro composites, nano composites and the comparison of two, few has investigated into the resistance to electrical tree of the micro-nano composites containing both micro and nano particles. A feasible way to combine the advantages of both micro and nano particles is to design a structure which has not only big volume but also large surface area. However, these two features are usually contradictory for traditional particle structures. Here, a composite structure of micro particle covered by nano particles is proposed to have the two advantages. This structure can be achieved by blending surface modified micro and nano particles in solvent. Epoxy/SiOTo study the properties of the micro-nano composites, epoxy/SiO2 composites with different total SiO2 concentrations and different micro/nano proportions were prepared for the followed experiments. In this paper, the neat epoxy resin samples are labelled as EP, and epoxy/SiO2 composites are labelled as CX-X/X. For example, C10-1/3 represents the composite with a total SiO2 concentration of 10 wt%, while the micro/nano proportion is 1/3, which means there are 2.5 wt% micro SiO2 and 7.5 wt% nano SiO2 in the composite. The incorporation of SiO2 can be seen from the TGA curves and NMR spectrums  curves. The incorporation of nano particles decreases the trap level density of the composite, which is similar to the results in previous research41. Because the origin of depolarization current is the injection of electrons/holes, the less trap level density detected indicates the less injection of charges, which is caused by the interface introduced by the nano particles. The average trap depths of the samples can be estimated through the half-width method42, which gives the average trap depths of EP, C10-4/0, C10-1/3 and C10-0/4 as 0.74 eV, 0.77 eV, 0.96 eV and 1.02 eV (Supplementary Information 5). Trapping sites exist in the interfaces between nano SiO2 particles and epoxy polymer matrices. Lewis43 described two kinds of trapping. One is at the chain ends, the chain kinks or the crosslinking sites. The other kind is the sites where activation to a higher energy state is necessary to maintain a continuous path in the interfaces along the field direction. From the results of trap depths, it can be inferred that nano SiO2 introduce the second kind of traps into the composite by their interfaces with polymer matrices and this kind of traps is deeper than the first kind in epoxy. The deeper trap depths introduced by the nano particles will hinder the movement and the transport of the charge carriers, which contributes to the enhancing the stability of polymer against the attack of the charge carriers.Figure 44 indicates that under AC voltage, the charge injection and extraction break the bonding of the polymer and lead to the tree initiation. Repeated charge injection and extraction may cause substance degradation and electron avalanche breakdown to form the tree channels. The electron avalanche is affected by the energy and the mobility of the electrons. In the nano composites, the electrons will be affected by the nano particles and the electron avalanche is restrained21. It is believed that tree initiation must be influenced by some potential barrier formed near the tip of the needle electrode37. This barrier is connected to the field formed around nano particles. Later researches pointed out that this potential barrier may be due to the homocharges trapped around needle tip20. The equivalent needle tip radius is increased by these homocharges, so the actual electric field strength near needle tip is mitigated and the voltage required for charge injection is raised. In this case, the mobility of the electrons decrease and the electrons gain insufficient energy. Then it will be hard for electron avalanche to form and this will therefore lower the tree inception probability. Tanaka45 indicated that high energy electrons must not interact directly with nano particles, but with electronic states in the interfaces between nano particles and polymer matrices. The travelling electrons are affected by these electronic states and shown as trapping. The deeper traps are more likely to play a role in the interaction because of their trapping capability. They can decelerate electrons to retard the formation of tree channels.Shimizu’s tree initiation theoryIt can be concluded that the inhibition of the charges injection and movement will reduce the probability of breaking the molecular chains which causes the polymer degradation, the electrical tree inception and the electrical tree growth. The interfacial polarizations and traps are all directly related to the polymer-particle interfaces in the nano composites. As a result, the inhibition of the electrical tree inception shown in Fig. Both the blocking effects of the micro particles and the inhibiting effects of the nano particles have been demonstrated in the micro-nano composites. It should be pointed out that these two effects are not linear combined due to the composite structure of micro particle covered by nano particles. As shown in Fig. 13It should be noticed that with this kind of composite structure of the micro and nano particles, the resistance to the electrical tree is stronger when the nano particles are more than the micro particles theoretically. The micro/nano proportion is set to be When the electrical tree reaches a micro particle, the particle act as an obstacle at only two dimensions. The blocking effects do not work at the dimension along the electrical field but at the two dimensions vertical to the electrical field. Therefore, the dimension of the blocking It is shown in the photograph to prove the blocking effects of the micro particles because of the bigger scale than the tree channel. It can be concluded that the inhibiting effects of the nano particles are due to the large number of polymer-particle interfaces which inhibit the charges injection and movement by enhancing the interfacial polarizations and increasing the polymer active energy and the average trap depth. Thus, both incorporation of the micro particles and the nano particles will increase the resistance to electrical tree. It has been demonstrated that the difference in resistance to electrical tree of the micro-nano composites is due to the synergistic effects of the composite structure of the micro and nano particles, which not only reduce the chance of tree inception but extend the electrical tree breakdown time. This research provides a strategy to improve the durability and reliability of polymer dielectrics and extend the lifetime of electrical equipment and electronic devices. The proposed synergistic effects of the micro and nano particles shall exist in other performances of mico-nano composites and be applicable for other types of particles and polymers. Therefore, the new micro-nano composites will find a wide application in future electronic and electrical energy areas.Micro SiO2 (20 um) and nano SiO2 (30 nm) were purchased from Beijing DK nano technology Co., LTD  and then modified with silane coupling agent KH-550 purchased from Kunshan Lvxun electronic material Co., LTD . 0.6 g KH-550 was dissolved in 200 ml 95% alcohol under stirring for 5 min, then 6 g micro SiO2 or nano SiO2 were added into the solution and the mixture was stirred under room temperature for 2 h. Finally after the slurry was dried at 70 °C for 24 h and 130 °C for 12 h, the KH-550 modified SiO2 micro particles and nano particles were obtained.Epoxy/SiO2 composites were prepared by solution blending method. The SiO2 particles were first dispersed in chloroform and treated with ultrasound for 3 min at room temperature before the sample preparation. For each composite, a predetermined amount of SiO2 and epoxy were dissolved in chloroform. After stirring for 5 min, the mixture was degassed for 30 minutes at 40 °C and then cured for 2 h at 80 °C followed by 12 h at 100 °C according to a standard curing procedure for this epoxy system. The synthesized composite films were prepared for the dielectric parameters measurement. The cubic samples with pre-embedded steel needle electrode were prepared by curing and sized by a tetrafluoroethylene mould. A piece of conductive rubber was penetrated by the needle electrode and embedded at one side of the sample to provide a conductive contact with the external electrode. The tip of the needle electrode was located near the other side of the 30 × 30 × 3 mm cubic sample .The electrical treeing experiments were performed with alternating voltage, the samples were clamped between a high voltage plate electrode and a ground plate electrode which were in good contact with the needle electrode and grounding surface of the samples, respectively, and AC high voltage of 15 kV  was applied to the samples. The development of the electrical tree was observed under a stereomicroscope at 100× magnification. The dielectric constants and the dielectric losses of the composites were measured by a broadband dielectric spectrometer with 1 V from 1 Hz to 1 MHz at 0 °C, 25 °C, 50 °C and 75 °C. The samples were 2 mm thick and had diameters of 20 mm. In TSC tests, the tested samples were first polarized under 300 V/mm at 25 °C for 30 min then cooled down to −20 °C in the speed of −10 °C/min. Then, the samples were depolarized for 10 min to release the polarization charges. Finally, the samples were linearly heated in 3 °C/min with the depolarization current recorded.Supplementary Information


An uncertain version of the permutation flow-shop with unlimited buffers and the makespan as a criterion is considered. The investigated parametric uncertainty is represented by given interval-valued processing times. The maximum regret is used for the evaluation of uncertainty. Consequently, the minmax regret discrete optimization problem is solved. Due to its high complexity, two relaxations are applied to simplify the optimization procedure. First of all, a greedy procedure is used for calculating the criterion’s value, as such calculation is NP-hard problem itself. Moreover, the lower bound is used instead of solving the internal deterministic flow-shop. The constructive heuristic algorithm is applied for the relaxed optimization problem. The algorithm is compared with previously elaborated other heuristic algorithms basing on the evolutionary and the middle interval approaches. The conducted computational experiments showed the advantage of the constructive heuristic algorithm with regards to both the criterion and the time of computations. The Wilcoxon paired-rank statistical test confirmed this conclusion. The paper develops a minmax regret approach as a special case of uncertain (non-deterministic) discrete optimization with reference to selected flow-shop problem when processing times are given in the form of intervals. The contribution and significance of results can be considered both from the minmax regret discrete optimization and from flow-shop problems points of view. In general, dealing with any non-deterministic discrete optimization has to be focused on three fundamental issues: the representation of uncertainty, the evaluation of feasible solutions (optimization variables) and the development of solution algorithms  and C / K represents the degree of uncertainty as the less is its value the less is the uncertainty’s significance. The above method is applied to all uncertainty intervals of the problem, thus, to obtain a new random problem instance, four parameters are required; n, m, K, and C. Whenever a random problem instance is referred to, it is denoted by a 4-tuple in the form {n, m, K, C}. If any element of the tuple needs to be randomized, it is generated according to the discrete uniform distribution from a set of integers denoted in braces or from an interval of integers denoted in brackets. For example, {20, {3,5}, 100, } describes an instance with 20 jobs, random number of machines from the set {3,5} where C is randomly selected integer from the interval .For the deterministic flow shop, there are in the literature known benchmark problems Taillard . It is an, m, 100, 50} where n, m, 100, 50}, and corresponding values of both performance indices  and the evident middle interval algorithm (MIH). The value of maximum regret, as well as the computational time has been the basis for the comparison. The new algorithm CVE substantially outperforms EVO and MIH for both bases of the comparison. It turned out that CVE not only is faster than EVO, but it also is substantially better in terms of the value of minmax regret , and, coThe elaboration of a branch and bound based exact algorithm is now in progress to have the more credible basis for the evaluation of heuristic algorithms. Moreover, searching for new more efficient heuristic approaches for the considered in the paper minmax regret flow-shop with interval processing times is still under development. It mainly concerns the approximation of the criterion value which is itself an NP-hard issue. The usefulness of other heuristics for the flow-shop like CDS  will also be verified Pinedo . The ide


MJRM) representing the joint response to errors in the Cartesian work space. The decomposition of the linear matrix indicates the separation of path planning in terms of the direction of the reaching motion and the synergies of joint coordination. Once the MJRM is numerically obtained, the feedfoward planning of reaching direction allows us to provide asymptotically stable, linear trajectories in the entire work space through rotational transformation, completely avoiding the use of inverse kinematics. Our dynamics-driven control law suggests an interesting framework for interpreting human reaching motion control alternative to the dominant inverse method based explanations, avoiding expensive computation of the inverse kinematics and the point-to-point control along the desired trajectories.A new dynamics-driven control law was developed for a robot arm, based on the feedback control law which uses the linear transformation directly from work space to joint space. This was validated using a simulation of a two-joint planar robot arm and an optimisation algorithm was used to find the optimum matrix to generate straight trajectories of the end-effector in the work space. We found that this linear matrix can be decomposed into the rotation matrix representing the orientation of the goal direction and the joint relation matrix ( Path planning for reaching tasks is a fundamental problem both in roboticset al.Human reaching motions have characteristic properties that distinguish them from those of robots, the most visible being that they are near-straight in the work spaceSome have stated that inverse dynamic models are a necessity for the control of the human body, arguing that it is the only way to execute specific motions with such a complex system10Many researchers have utilised vision as a basis for controlling robots, either transforming visual data into feedback for a conventional robot controller Our study considered whether it is possible to cause an arm to generate a straight path with its end effector by correcting visual path deviations as they arise during movement. This does not require a precise kinematic model and is thus much less sensitive to erroneous or incomplete data on the robot’s link lengths and joint states. This method relies on the robot’s nature as a dynamic system moving in the work space, as opposed to being derived from the system’s statics, like the Jacobian transpose method. We thus also aim to demonstrate that this method is energy efficient compared to the Jacobian transpose method, based on this distinction.It has been established that a control law based on a linear transformation of visual information can enable a robot end effector to converge on a target within a specific area of the work spaceM is used to complete the sensory-motor loop of a simulated robot arm, with the aim of creating straight movements in the end effector. The matrix M is reminiscent of the concept of a ‘body schema’, a dynamic representation of the body’s behaviour. In humans this is the element of body representation that allows an understanding of how the body’s elements will coordinate16M encodes a dynamic relationship between the arm’s components that results in a stereotyped movement. Because M defines how the dynamics of the arm’s joints interact, rather than acting as a computational model of the dynamics themselves, it is much simpler than the kinematic and dynamic models typically employed in the field of robotics.In this paper, a control law based on a static linear transformation matrix The control law used in this study aims to coordinate the dynamics of the robot’s individual joints such that its end effector moves in a straight line. To this end, a linear transformation matrix is applied to visual feedback to constrain the joint’s motion with respect to the work space, as can be seen in the system block diagram in M is a static transformation matrix applied to the visual information to alter the arm’s trajectory behaviour. τ is the vector of joint torques and x is the work space position of the end effector. xd is the target in the work space. Kp is a proportional gain matrix for the work space error, while Kv is a velocity gain matrix.where M becomes a 2 × 2 matrix composed of four parameters that must be optimised to produce direct, straight line trajectories. We used a simplex optimisation algorithm to optimise M automatically to produce desirable motions, defined as those with a low Linear Index (LI). The LI , and appears to be the product of a 2D rotation matrix T(−θ) and a constant matrix. At the angular origin of 0 radians on the X axis of the workspace the optimal matrix is In order to eliminate the confounding effects of very large or small effective gains, each matrix produced by the optimisation algorithm was normalised by dividing it by its largest element. The optimised matrix was dependent on the orientation of the straight path from start point to target , encoding the relationships between the motion of each joint in the arm and a 2D rotation matrix (T(−θ)) that aligns the coordinates of the target radial trajectory with the X1 axis of the work space:In M for any given orientation of movement, it was possible to post-multiply the final value by T(−θ) to find if the value of MJRM was invariant.Thus, for the optimum M could be decomposed into the components MJRM and T(−θ), the path generation procedure in MJRM was set to T(θ). If our hypothesis was correct, the combination of these two matrices would be the optimum M matrix for movements with the radial coordinate θ.In order to confirm that MJRM by a rotation matrix rotates this region by the specified number of radians in the opposite direction, as hypothesised.The test results are shown in In order to see whether the stability of the control law would be improved or worsened by the inclusion of joint space feedback, q is the vector of joint rotations and qd is the joint space target calculated using the arm’s inverse kinematics (qd = f−1(xd)). The variable k is a dimensionless scalar in the range 0 ≤ k ≤ 1 controlling the proportion of kinematic feedback used by the control law. The effect of including kinematic feedback can be seen by comparing where MJRM) can be understood in terms of the arm’s geometry and dynamics, instead of a coordinate transformation. Any movement of a revolute joint causes a curve in the trajectory of the end effector, deviating from the desired straight path. The JRM connects the torque at the joints to the motion of the end effector such that any deviation caused by one joint is compensated by the other. In this way, the motions of the two joints coordinate and the end effector remains on a straight trajectory.The fact that the control law defined in X1 axis, with the second joint below it as pictured in M is equal to the MJRM. The optimal MJRM matrix in this case has the form This section considers the simplest case of an arm with links of equal length where the end effector approaches a target on the positive MJRM, it is useful to decompose the movement of the end effector into two superimposed movements, as illustrated in r1 in r2 in r1). These two sub-movements are governed by the first and second rows of MJRM, respectively.In order to understand the effect of the optimal T1 and T2 caused by the first and second sub-movements, respectively, in order to explain how the control law described by Here we consider the tangential displacements T1 and T2 must cancel, leaving a net horizontal movement of the end effector. Because the angle between T1 and T2 changes as the arm extends, in order to follow the X1 axis the velocity of joint 2 must change over time in order to maintain this balance. If it does not, the end effector will diverge from the straight path as seen in the solid line in MJRM) are correct, the end effector will eventually be drawn onto the line connecting the arm origin to the target. As the first joint ‘extends’ the arm by accelerating in a positive direction, it causes the vertical component of T1 to grow, meaning that joint 2 must respond by accelerating in a negative direction to maintain balance. This is also why the transformation T(−θ) is required in MJRM have the same magnitude is a reflection of the fact that the links have the same length; the optimal MJRM gives the closest match in joint velocities over the course of the movement, requiring smaller reactive corrections.In order for the end effector to remain on a straight path, the vertical components of the tangents MJRM is set to the 2 × 2 identity matrix. In this case, the second joint reacts to the deviations caused by the first, but the speed of this correction is fundamentally limited by the response time of the joints  used by the MJRM (set at The trol law . Our papJTF = τ). The justification for this use is based on the relationship between end effector forces and joint torques defined by the virtual work principle:The Jacobian transpose is often used in closed loop control of robot manipulators as a means of transforming desired end effector forces into joint torques  iff:Kv > 0where Kv is a positive diagonal matrix. Simplifying, and using the knowledge that Kv = kvI, the second inequality becomes:The first inequality is always true, as Kv to a sufficiently large positive value will ensure that V is positive definite.Thus, setting V with respect to time gives:Differentiating R is the positive-definite, symmetric inertial matrix and S is a matrix of Coriolis forces. where and thus in matrix form:where:B is not a symmetric matrix, but the Schur complement of its Hermitian part can be calculated yielding Kp > 0.Kp > 0 and thus applies to any diagonal gain matrix of the form Kv = kvI. The second inequality holds if (KvMJ + JTMTKv) > 0, both Kv and Kp are sufficiently large and Kv is sufficiently larger than Kp. In particular, since S and The first inequality is true for all This study demonstrates that the otherwise complex task of planning a straight path for an end effector can be solved without explicitly defining the path itself. This is achieved by exploiting the dynamic relationship between an open chain robot’s components. The fact that the movement of any link affects all others further down the chain allows the implementation of a visual-motor loop that continuously corrects deviations from the desired path without relying on accurate kinematics, which are not available for all robotic systems.This study demonstrates that the otherwise complex task of planning a straight path for an end effector can be solved without explicitly defining the path itself. This is achieved by exploiting the dynamic relationship between an open chain robot’s components. The fact that the movement of any link affects all others further down the chain allows the implementation of a visual-motor loop that continuously corrects deviations from the desired path without relying on accurate kinematics, which are not available for all robotic systems.A consequence of this is that not all standard means of comparison can be used in this case, as the tests rely on assumptions that are not applicable to our study. Tracking tests, for example, cannot be properly applied because the control is optimised for a cost function calculated over an unconstrained trajectory as no true reference trajectory exists, only a start point and target.MJRM matrix and the wide area rendered stable by any given value also allow stable reaching motions to be achieved much more simply than in the classical robot model. The transformation matrix can easily be generalised over the entire work space by applying a rotational transformation. This transformed visual feedback can be linearly combined with conventional inverse-kinematics based error to add more stability, but if accurate encoder or visual sensors are available it is unlikely to be necessary.The simplicity of the MJRM method exerts less torque (and thus uses less energy) to move when in a non-equilibrium state than the Jacobian transpose. This could render it useful in situations where sufficient control gain to rigidly track a moving equilibrium point is not possible.Furthermore, the In future work we hope to apply the same self-correcting behaviour to arbitrary motions within the work space, allowing true global stability to be achieved. The degree to which this method can be extended to systems with many degrees of freedom is a matter of continued investigation. There is preliminary evidence that redundant arms controlled using this method experience continual self-motion unless appropriate joint limits are imposed.The control scheme developed in this study was tested using a numerical simulation of a two-joint planar robot arm. This is the simplest form of an arm capable of executing the ‘reaching’ motions the study aims to optimise. This reduced to a minimum the number of parameters that had to optimised while retaining the classical robot arm form.The model was implemented in Simulink, using a third-order ordinary differential equation solver with a constant step size of 0.005 s. The primary components of the simulation are the arm’s dynamics and the control law described by The reaching target is simply modeled as a constant Cartesian coordinate vector.j = ml2/3 (where m is the link mass and l is the link length) and their centre of mass halfway along their length. In the case we are modeling, the links have the same mass (m1 = m2) and equal length (l1 = l2). The arm is considered to be supported by a parallel plane, reducing the gravity term to 0. This restriction to a fixed plane replicates the constraints placed upon human subjects in many reaching experiments8The links of the arm are modeled as thin, uniform rods with the moment of inertia The dynamics of the simulation are derived by solving the Lagrange equation for a driven robotic system:τ is the vector of joint torques, q is the vector of joint angles and L = V − U where V and U are the kinetic and potential energy, respectively. Because no gravity is experienced by the arm, U is set to 0.where xcn1, and xcn2, are the x1 and x2 coordinates of the nth joint’s centre of mass, respectively.where Solving with the inertial matrix:and a Coriolis force vector with the form below.Cn = cos qn and Sn = sin qn. MJRM we used the widely-known simplex algorithm defined by Nelder and MeadM in MJRM for a specific start/endpoint pair. Unlike the original formulation of the simplex algorithm, the algorithm used here does not include the ‘contraction’ step that reduces the simplex’s deviation around the mean if the projected new value has a sufficiently high error. Not including this step improved the algorithm’s likelihood of finding a good solution in all the experiments performed.In order to optimise the transformation matrix The initial simplex to be optimised was generated by pseudo-randomly perturbing a ‘seed’ matrix. When performing individual ‘runs’ of experiments optimising for radial movements at a series of angles, this matrix was randomly chosen and kept constant throughout.M are inter-related, but without knowing this relationship, it was not possible to design a problem-specific algorithm. This limited the choice of algorithms to general optimisers. The simplex optimisation algorithm created by Nelder and MeadBecause the end effector position is based on the angle of both joints, it was assumed that the components of How to cite this article: Eberle, H. et al. Integration of Visual and Joint Information to Enable Linear Reaching Motions. Sci. Rep.7, 40869; doi: 10.1038/srep40869 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


We propose a minimal model for the spontaneous and persistent generation of polarity in a spherical cell based on dynamic microtubules and a single mobile molecular component. This component, dubbed the polarity factor, binds to microtubules nucleated from a centrosome located in the center of the cell, is subsequently delivered to the cell membrane, where it diffuses until it unbinds. The only feedback mechanism we impose is that the residence time of the microtubules at the membrane increases with the local density of the polarity factor. We show analytically that this system supports a stable unipolar symmetry-broken state for a wide range of parameters. We validate the predictions of the model by 2D particle-based simulations. Our model provides a route towards the creation of polarity in a minimal cell-like environment using a biochemical reconstitution approach. The unraveling of the subtle molecular mechanisms underlying these phenomena is an active field of biological research . At the However, it appears that the cytoskeleton, the dynamic network of protein filaments that performs a host of structural and mechanical roles in all eukaryotic cells, is often implicated in polarity mechanisms . A well-by itself a sufficient mechanism to generate robust cell polarity. We do so by formulating a model that achieves the two desirable features of spontaneous symmetry breaking and steady-state persistence, using a minimal number of components. It is based on the proven ability of microtubules to bind and directionally transport proteins.Here we show that the latter idea—positive feedback on membrane insertion through stabilisation of transporting structures—is The key ingredient of the model is that the molecules acting as polarity factors, having been delivered to membrane by dynamical microtubules, stabilize the latter against detaching from the membrane. At the same time, a locally increased concentration of the polarity factors on the membrane depletes the finite pool of this species present in the cell providing a global inhibitory effect on the propensity of similar stable patches to develop elsewhere. Conceptually this model thus belongs to the generic class of activator-depletion models  are nucleated from a point-like centrosome in the cell center covered with a constant density of m nucleation sites per unit of solid angle, each of which can support a single MT. When unoccupied, these sites can “fire” with a rate rn, creating a new MT. The MTs obey the standard two-state dynamical instability model [v+, shrinking speed v−, catastrophe rate r+ and rescue rate r−. When the microtubules hit the cell boundary they stall, after which they switch to the shrinking state with a rate σ, which interpolates the unbinding rate between the (higher) value ru(0) when no PFs are present and the (lower) saturation value ru(∞) depends on the reduced density γ ≡ cb/c*, where c* sets the relevant density scale parameter. Although the specific choice for σ is not very critical  diffusion constant D = Db/R2, until they unbind and are recycled into the interior of the cell with rate ku. The total number of PFs in our model thus is conserved and denoted by the parameter C. The mathematical details of this model can be found in the The PFs in the cell interior freely diffuse and can bind to the MTs on a time scale much shorter than the MT dynamics. We therefore assume that they are in equilibrium with the instantaneous MT configuration, and their degree of binding only depends on the total length of MTs isotropic solution for any total number of PFs C. For details and the properties of this isotropic solution please refer to anisotropic solutions, we perform a standard stability analysis. We thus determine whether a small anisotropic perturbation ru(∞)/ru(0) and the number of MTs at the boundary, here represented by the dimensionless factor μb.In order to understand whether our model allows for spontaneous polarization, we study its steady-state behaviour. As it turns out, the steady state distribution of MT properties can be analytically determined for arbitrary distribution of PFs in the cell boundary. The details of all the relevant derivations can be found in At this point we have identified the four (effective) parameters that are involved in governing the propensity of the system to polarize.C, which in turn monotonically determines the relative mean membrane density The number of available polarity factors δ ≡ D/ku,The mean square angular displacement of PFs on the membrane before unbinding p, used in the definition of σ(γ), which governs the steepness of the dependency of the MT residence time on the PF density, and,The Hill coefficient η, whose role we return to below.the composite parameter d of n = 1. This mode can exist wheneverA necessary requirement for η, γ and δ for the case p = 5 is presented in The full phase boundary that separates the region where the unipolar solution is stable, from the one where only the isotropic solution can exists can be obtained by numerically solving In summary, on the basis of these results, we can say that spontaneous polarization will occur whenever:γ) to selectively promote the lifetime of MTs at the membrane.There is a sufficient number of PFs available (governed by increasing η), because they stay much longer at the boundary than non-stabilized ones /ru(0)) and/or the probability of reaching the boundary is small to begin with  so that there are also fewer competitors for the finite supply of PFs.The competitive advantage of MTs stabilized at the boundary is high enough (governed by decreasing p).The density dependence of the residence time enhancement of MTs is steep enough to have a more switch-like behaviour distinguishing the stabilized MTs from the non-stabilized ones (governed by increasing δ).After insertion the PFs unbind from the membrane before influencing other MTs at farther away locations —and hence in other directions—  can be found above which spontaneous symmetry breaking to a unipolar steady state occurs. However, as the pool of available PFs is increased, inevitably the polarization inducing mechanism breaks down: When the monotonically increasing average density of PFs in the membrane rises significantly above c*, the lifetime of all membrane-bound MTs becomes ≃ ru(∞)−1 independent of position, so that the differential stabilization mechanism is saturated and the system will revert back to the isotropic state. We thus expect that as a function of the number of available PFs we can distinguish three regimes: At low values of γ there are insufficient PFs bound to membrane to activate localized regions of longer-lived MTs. At high values of γ, the surfeit of available PFs precludes any localized increase of PFs to inhibit its accumulation at other locations, and MTs are equally stabilized everywhere. Only in the intermediate regime, where activation balances inhibition can sustained polarization be achieved. η and suitably small δ any line parallel to the γ axis pierces the ordered region at two locations.For fixed values of shorter than in the saturated case. This decreases the fraction of MTs reaching the boundary, and hence decreases the parameter ηenhancing the propensity to polarize. At the same time, however, the number of active microtubules decreases, but our model can be made robust against smaller MT numbers as shown by the analysis in In our model we have assumed that the amount of tubulin is not a limiting factor. However, since we are considering a finite volume, it is reasonable to ask to what extent our results would be influenced by potential finite tubulin pool size limitations. Indeed, recent experiments  have shon2 in 2D vs. n(n + 1) in 3D). For simplicity’s sake, we therefore choose to provide proof-of-principle of our mechanism by simulations of a 2D stochastic version of our model in which both PFs and MTs are explicitly modelled as particles. Since the theoretical model is of a mean field nature, and implicitly assumes a continuous density of MTs, we first focus on a relatively large number of M = 103 MTs.In order to validate the results of the theoretical model described above, and to test its viability in the light of known data on relevant cellular parameters we turn to simulations. We first note that the dimensional dependence of the model is in fact very weak, and essentially only enters through the eigenvalue of the angular laplacian  or of insufficient inhibition (∼factor of 2 larger than at M = 1000). To estimate the magnitude of these effects we performed additional simulations in which we keep the total number of PFs in the membrane equal to that of the original simulations, but artificially maintain an isotropic unpolarized state by “homogenizing” the membrane density of PFs at each time step. This results in the lower curves in Although the peaks of the two curves appear to be fairly close, it is obvious that finite particle number effects are much more prominent at D stochastic simulation in a circular cell geometry with a radius R. The control parameter in the simulations is the total number C of PFs in the system. A point-like centrosome in the center of the disc has M nucleation sites and the boundary of the disc is divided to M equal segments, each subtending an angle Δθ = 2π/M around one of the nucleation directions. The number of PFs in the m’th segment is denoted by C, an approximation reasonable in view of the specific parameters chosen in the simulation.We implement a 2kuΔt, where Δt is the time step and ku is the unbinding rate. Correspondingly, the probability of diffusing on the membrane is given by 1 − kuΔt. To determine the angular displacement δθ of a diffusing PF, we sample from the analytical form of the cumulative probability of diffusion on the unit circleAt the boundary, a PF can either diffuse or unbind thus recycling back into the cell interior. The probability of unbinding from the membrane in a single time step is given by As expected, the location of the maximum of the distribution (if this exists) can slowly drift over the unit circle. To obtain meaningful averages, we therefore corrected for this phase-drift, by extracting the phase through Fourier analysis and shifting the distribution accordingly.Where available, we have used simulation parameters consistent with generic experimental values reported in the literature  proteins such as Mal3 and the kinesin Tea2 to ensure the polar localization of cell growth . RecentlIt is of course also interesting to consider how the current model can be coupled to polarized cell growth to further elucidate the biologically highly relevant interplay between cell shape, microtubule organisation and polarization.S1 File(PDF)Click here for additional data file.


Due to the fine spatial fractionation dosimetry of these beams is a challenging and complicated problem. In this proof-of-concept work, we present a fibre optic dosimeter that uses plastic scintillator as the radiation conversion material. We claim an ideal one-dimensional resolution of 50 μm. Using plastic scintillator and fibre optic makes this dosimeter water-equivalent, a very desirable dosimetric property. The dosimeter was tested at the Australian Synchrotron, on the Imaging and Medical Beam-Line. The individual microbeams were able to be resolved and the peak-to-valley dose ratio and the full width at half maximum of the microbeams was measured. These results are compared to a semiconductor strip detector of the same spatial resolution. A percent depth dose was measured and compared to data acquired by an ionisation chamber. The results presented demonstrate significant steps towards the development of an optical dosimeter with the potential to be applied in quality assurance of microbeam radiation therapy, which is vital if clinical trials are to be performed on human patients.Synchrotron microbeam radiation therapy is a novel external beam therapy under investigation, that uses highly brilliant synchrotron x-rays in microbeams 50  These quantities are important for characterising the radiobiological effect on the tissue to be treated in the peaks9 and the tissue to be spared in the valleys, which receives dose via Compton scattered electrons11. In addition the peak-to-valley dose ratio (PVDR) has major implications for the efficacy of the MRT. It is therefore necessary to have dosimeters with high enough resolution to measure these quantities. Dosimetry methods currently exist that have the required resolution for this purpose. Radiochromic film is commonly used for this purpose but take several hours to develop and process, and can be inaccurate by up to 15%12. Semiconductor devices such as metal-oxide semiconductor field-effect transistors (MOSFET)13 and silicon strip detectors (SSD)15 have excellent resolution and can resolve microbeams. Silica core optical fibers can also be doped (with molecules of hydroxide or fluoride) to produce light under irradiation. They have been demonstrated to show radiation hardness, with an approximately 25% increase in light absorbance after 1000 Gy dose16. However a major disadvantage of these dosimeters, as well as nearly all conventional dosimeters, is that they lack water-equivalence, meaning the dose measured by the dosimeter must be converted to the equivalent dose deposited in water, which can be a complicated function of radiation type and energy. This is necessary for clinical applications as the radiation dose deposited in tissue is the primary quantity of concern, and a water-equivalent dosimeter measures this dose.Synchrotron microbeam radiation therapy (MRT) is a type of external beam radiation therapy that comprises of highly collimated planes of 70 keV median energy x-rayssee Fig.  of typic17 but their application to high-resolution dosimetry has not been explored in great depth. A crystal scintillator dosimeter, which demonstrated a resolution of 100 μm has been described by Belley et al.18. However as the scintillator is crystalline, it is not water-equivalent and so must be calibrated against an ionisation chamber, is only valid at calibrated energies, when the crystal is completely inside the microbeam. This means any measurements in the edges of microbeams may not result in the correct dose, and calculations of microbeam width may not be accurate.Scintillators are one of the older radiation detectorset al20. for photon beams. In these articles the authors demonstrate that this dosimeter is highly water-equivalent, has excellent dose linearity and radiation hardness (2.8% response decrease for 10 kGy accumulated dose), and is energy independent. It also shows only very small changes in response under temperature and pressure variations. These qualities make it a very suitable dosimeter. In this work we improve upon this design by increasing the resolution of the probe from centimeters to 50 micrometers, allowing individual microbeams to be resolved.The dosimeter presented in this work uses a BC-400 plastic scintillator optically coupled to an Eska CK-40 plastic optical fiber and coated in BC-620 reflective paint. The scintillator is the radiation conversion material, converting the energy of the x-ray secondary electrons to visible light  TiO 21. The x-ray microbeams generated at the Australian Synchrotron, in the present case, have a peak flux at about 66 keV (this depends on the beam defining aperture (BDA) used, but the average photon energy remains 66 keV) and the percentage of photons above 175 keV energy is approximately 0.05%, meaning the amount of Cherenkov radiation noise in this system will not contribute greatly to the optical signal. Fluorescence in the fiber optic will therefore be the main contributor to any unwanted signal. The physical mechanism of fluorescence is the same as scintillation, but the intensity is much less per unit incident energy.Because this dosimeter is an optical system, there is no electronic interference. The main sources of unwanted signal are Cherenkov radiation and fluorescence generated in the fiber optic. Cherenkov radiation is generated by charged particles moving through a medium faster than the speed of light in that medium. For the refractive indexes used in this dosimeter, the minimum electron energy required to produce Cherenkov radiation is calculated to be approximately 175 keVμm. This length defines the optimal one-dimensional resolution of the dosimeter, highest along the optical fiber axis. Perpendicular to the axis the resolution is 1 mm, the diameter of the scintillator. By scanning the probe along the fiber axis a lateral resolution of 50 μm can be achieved over a depth of 1 mm. The design of this probe, with a 100 μm resolution was demonstrated in a linear accelerator x-ray field in a previous work22.A diagram of the probe is shown in Fig. μs). The detection efficiency is compared to the BC-400 scintillator photon output spectrum in Fig. The optical signal is measured using a SensL MiniSM Silicon Photomultiplier 10035 (SiPM). This SiPM has a peak sensitivity at 500 nm, with efficiency of 20%, and a typical dark count of 44 kHz  of 2.014 mm, 1.052 mm and 0.532 mm.To demonstrate the ability of this dosimeter to resolve microbeams it was tested at the Australian Synchrotron on the Imaging and Medical Beam-Line (IMBL)  and vertical (z direction) motion. The horizontal motor is a Parker MX80 S Ballscrew Drive with 50 mm range. The motor control allows speed to be controlled between 0.1 mm/s and 40 mm/s, which is within the operational ranges of the stage. The vertical motor is a Parker ZP200 Leadscrew Drive, which has a maximum scanning speed of 20 mm/s and a range of 25 mm. The reliability of this motor speed has been verified using an interferometer by IMBL scientists1.The dosimeter was mounted on the Dynamic MRT stage in the beamline, which has motor controls for horizontal (y axis: perpendicular to both the incident beam and the microbeams. The measurement was performed at a depth of 15 mm under solid water (Gammex 457 Solid WaterTM), and the probe was scanned at a speed of 0.1 mm/s in the +y direction, allowing the entire profile to be measured in 400 s, including the response at the edge and outside of the field. Data points were sampled over a 200 μs interval with a frequency of 2 kHz. The data acquired with the scintillation fibre optic dosimeter (FOD) was compared to an epitaxial silicon strip detector (SSD), also with a one-dimensional resolution of 50 μm, developed by the Centre for Medical Radiation Physics (CMRP), scanned through the beam under identical conditions. The SSD is detailed in Fournier et al14. and Lerch et al.15.A lateral scan of the beam profile was done to record the individual microbeams, allowing the PVDR to be calculated throughout the radiation field. The probe was oriented in edge-on mode, with the fibre axis aligned in the To remove any Cherenkov or fluorescence from the signal, we consider the amount of light generated per unit length of fibre, as this is the source of this unwanted signal. The signals should be identical both before and after the probe has been scanned through the field. However there is an increase in the signal when the probe has passed though the field, but the fibre remains exposed. A steady rise in detector response can also be seen in the valley regions, as more fibre is exposed. By using the background signals on either side of the profile, a linear fit can be made to the Cherenkov/fluorescence signal and subtracted off.z), averaging the response three times at each depth. The probe was mounted in the same orientation as the beam profile. The depth was changed by moving the probe in the + x direction and adding solid water between the beam and the probe. This was done at two scanning speeds, 5 mm/s and 10 mm/s, using each of the three BDAs. These results are compared to a PinPoint N31014 ionisation chamber under identical conditions.The depth dose response of the broad-beam field (without the collimator in place) was also measured by scanning vertically down the field  and the FWHM to be (62.4 ± 0.9) μm.The average PVDR was calculated to be (19 ± 3). The average width  of the peaks was calculated to be (63 ± 2) The results of the PDD scans are presented in Fig. μm across the 1mm diameter cross-section, the response may be different on either side of the scintillator. Secondly, if the fibre is not perfectly aligned perpendicular to the incident microbeam field then this will also create an asymmetry in the response. There is also an asymmetry present in the SSD profile, although it is less significant.The slight asymmetry apparent in the inset of the beam profile Fig.  is due tμm sensitive volume with a 50 μm width microbeam will result in the measured FWHM being larger than the microbeam itself. The average FWHM measured with the scintillator probe is (63 ± 2) μm, which agrees with result from the SSD of (62.4 ± 0.9) μm, which verifies the resolution of the scintillator probe to be 50 μm (the same as the SSD). The PVDR using the scintillator of (19 ± 3) is much lower than the SSD result of (26.9 ± 1.4). This can be explained by the higher response in the valley regions in the scintillator probe than the SSD.The convolution of a 50 The error bars in the valley response in Fig. μs the probe will move a distance of 0.02 μm. Compared to the sensitive length along the fibre axis of 50 μm the blurring caused by sampling while scanning is negligible. The scan speed of the beam profile measurement can be increased, as much more data was acquired than necessary. Increasing the scanning speed and decreasing the sampling frequency will greatly reduce the time taken to acquire the data as well as the quantity of the data.At the scanning speed of 0.1 mm/s and a sample time of 200 The PDD results are of great interest, given the consistent and repeatable over-response at low depths. In a future experiment we will repeat these measurements, taking more values between zero depth and 20 mm to greater characterise this discrepancy.et al19. their dosimeter  saw less than a 3% decrease in responsiveness from 10 kGy dose, justifying this assumption.Radiation damage to the detector was assumed to be negligible for this experiment, as the total dose the probe was exposed to during the PDD measurements was 2 Gy, (which was the experiment where the probe was exposed to the most dose). As was demonstrated by Beddar An improved method for subtraction of Cherenkov and fluorescence background signal is to use an identical fibre running parallel to the probe, but without the scintillator. This provides a source of background light, but no scintillation light. For real time dosimetry in fields of high dose gradients (such as MRT) this method is not very practical, however we intend to measure the background signal separately in future works to compare to the method applied in this work to assess its validity.μm thick, the compromise to water-equivalence may not be justified by the increased light capture. We intend to investigate the effect of replacing the paint layer with an aluminium coating. The advantages of this is twofold: aluminium is a lower Z number material than titanium, and the layer can be applied less than 1 μm thick, reducing the interaction of the aluminium with the ionising radiation. The signal strength with no reflector is also an area to be explored.The water-equivalence of this probe is reduced by the optical paint. As the paint is a diffuse reflector, the expected increase in light capture is not very large, and as the paint forms a layer on the order of 100 μm and 10 μm thickness, to test the limits of possible resolution of this probe design, while maintaining a practical level of sensitivity. Now that we have demonstrated the function of the dosimeter, the data collection methodology will be optimised. For example, the combination of 200 μs sample time and 2 kHz sample rate provides much more data than necessary, increasing digital data processing time and memory. As the sample frequency corresponds to a distance of 50 nm , at 0.1 mm/s, increasing the scanning speed will allow a much quicker measurement of the intrinsic beam profile.The next step for this work is twofold: experimental and computational. We will fabricate a probe of higher spatial resolution, aiming for probes of 20 We will also perform a Geant4 Monte Carlo study to provide a comparison to the experimental results. This will allow validation of the PVDR and peak widths measured using this probe, and will allow the optimal scintillator thickness to be investigated.μm. The individual microbeams have been resolved, and important beam properties, such as the PVDR, have been calculated. The probe has been compared to both a SSD dosimeter and ionisation chamber and the results agree, with a few exceptions. This proof-of-concept work has demonstrated that is is possible to perform microbeam dosimetry with a plastic scintillator probe, and justifies the development of higher spatial resolution probes of this design. The use of an optical system overcomes challenges presented by using electronic dosimeters, and the simple and inexpensive nature of the probe makes this area of research very promising for the challenging area of clinical microbeam dosimetry.This work demonstrates the first water-equivalent plastic scintillator optical dosimeter applied to relative microbeam dosimetry, with the highest spatial resolution found in the literature of 50


Cerebral blood flow (CBF) is regulated over a range of systemic blood pressures by the cerebral autoregulation (CA) control mechanism. This range lies within the lower and upper limits of autoregulation , beyond which blood pressure drives CBF, and CA function is considered impaired. A standard method to determine autoregulation limits noninvasively using NIRS technology is via the COx measure: a moving correlation index between mean arterial pressure and regional oxygen saturation. In the intact region, there should be no correlation between these variables whereas in the impaired region, the correlation index should approximate unity. In practice, however, the data may be noisy and/or the intact region may often exhibit a slightly positive relationship. This positive relationship may render traditional autoregulation limit calculations difficult to perform, resulting in the need for manual interpretation of the data using arbitrary thresholds. Further, the underlying mathematics of the technique are asymmetric in terms of the results produced for impaired and intact regions and are, in fact, not computable for the ideal case within the intact region. In this work, we propose a novel gradient adjustment method (GACOx) to enhance the differences in COx values observed in the intact and impaired regions. Results from a porcine model (N = 8) are used to demonstrate that GACOx is successful in determining LLA values where traditional methods fail. It is shown that the derived GACOx indices exhibit a mean difference between the intact/impaired regions of 1.54 ± 0.26 (mean ± SD), compared to 0.14 ± 0.10 for the traditional COx method. The GACOx effectively polarizes the COx data in order to better differentiate the intact and impaired zones and, in doing so, makes the determination of the LLA and ULA points a simpler and more consistent task. The method lends itself to the automation of the robust determination of autoregulation zone limits. Cerebral blood flow (CBF) is regulated over a range of systemic blood pressures (BPs) by the cerebral autoregulation (CA) control mechanism, which acts through complex myogenic, neurogenic, and metabolic mechanisms . This ra2) and mean arterial (blood) pressure (MAP).The correlation between the pressure drop across the brain-cerebral perfusion pressure (CPP)—and cerebral blood flow (CBF) may be quantified using a linear regression. The derived correlation coefficient, Mx , provide2 and MAP signals. The data within this window are plotted against each other (plot B). The window length is chosen to capture the characteristic periodicity of the physiological slow waves present in the blood pressure signal [X, σy denote standard deviations: replacing X and Y by MAP and rSO2 defines the COx measure . The window is then slid over the signal in incremental steps and the process repeated. In practice, this time step is around 5–10 s, which is chosen to filter out low frequency components (including cardiac and respiratory modulations). At each step, a COx value is calculated and added to an aggregated COx plot  to be zero. In this ideal case, we therefore expect a step change in the binned COx values when transitioning from intact to impaired regions at the LLA or ULA. In practice, however, the binned data are generally noisy and a COx threshold value somewhere between 0 and +1 is used to differentiate the correlating and non-correlating portions of the plot. Values used in studies reported elsewhere in the literature for this threshold are 0.3 [The method for calculating COx is presented in Fig. e signal . In prace signal –6, althoe signal –10. Line are 0.3 , 12, 0.4 are 0.3 , 14 and  are 0.3 .Fig. 2ThThe pressure-flow curve may not contain a central ‘flat’ region of zero gradient during intact CA as depicted in the ideal case of Fig. 2 trend strongly with each other. However, during the intact region we expect the two signals to be decoupled. Thus, for some time periods, both signals may be trending in the same direction, showing an apparent correlation; and in other time periods the two signals may be trending in the opposite direction, showing a negative apparent correlation. Further, there may be many periods where the two have a mix of trending and anti-trending behaviour in the same time window. We thus expect the COx value during intact CA to vary from +1 to −1 randomly over time, with only the average value over time tending to zero .The correlation method itself has a fundamental characteristic that makes it less suitable for clearly defining the two regions (even if an intact CA region of zero slope is present in the data). We expect a strong correlation near unity for the impaired region as MAP and rSOTaking the above into account, we propose a new method for partitioning the intact and impaired CA zones. The technique employs a gradient adjustment prior to performing the correlation analysis, which shifts the expectation from a strong value at unity and a mean value near zero for the calculated correlation coefficients (COx) to strong values at +1 and −1, corresponding to impaired and intact regions respectively. This facilitates partitioning of the data and hence aids determination of the LLA and ULA boundaries. The new method better discriminates correlating and non-correlating signal segments in data used to determine the status of cerebral autoregulation. However, the technique could find general applicability in the analysis of any other signals where regions of correlation and non-correlation require identification.There are, however, fundamental problems with the correlation method described above in two distinct areas: physiological and mathematical. We describe these in turn:2 values before calculating the correlation. This is carried out by calculating the regression line of the rSO2–MAP curve, shown in Fig. 2 signal. The regression line is an equation given byy corresponds to rSO2 values, x to MAP values, m is the slope of the line and b the intersection of the line with the y axis. The gradient-adjusted rSO2 is then calculated asxi is the MAP value for the corresponding i-th element in the data array and y(xi) is the corresponding value of rSO2 on the regression line. As we expect the overall gradient to be greater than that of region B and less than A and C, this gradient adjustment results in a strong negative slope of the data in region B, while maintaining positive slopes in regions A and C  plot. The GACOx method effectively polarizes the COx data in order to better differentiate the intact and impaired zones and, in doing so, makes the determination of the LLA and ULA points a simpler and more consistent task. This polarization of the data to the +1 and −1 values is shown schematically in Fig. The gradient adjustment (GA) method significantly enhances the delineation between impaired and intact autoregulation zones in the COx plot by manipulating the underlying relationship so that the intact region is forced to have a distinct negative gradient while leaving the impaired regions with a distinct positive gradient. In the method, which is illustrated schematically in Fig. Figure Manual method The COx plots were printed out for eight data sets and three of the authors  were asked independently to determine the LLA from the plot. In the event of a disagreement, the manual LLA value for each animal was defined as the median of the three evaluations.Automated algorithm 1 A value of 0.5 was set as the limiting value for the transition between the low-impaired region and the intact region. The binned data was inspected, starting with the lowest blood pressure bin, moving up a 5 mmHg bin at each increment. The LLA was determined as the MAP value corresponding to the first binned COx below 0.5.Automated algorithm 2 The same procedure as Algorithm 1 but requiring at least 3 consecutive binned values below the 0.5 threshold before the LLA was determined. This was done to mitigate against false detections due to erroneous noisy data points below the threshold.The GACOx LLAs were then determined using both a manual and automated algorithm. For the automated algorithm the threshold was simply set to zero and the first point below was determined as the LLA.Three reference methods were employed for the calculation of the limits of autoregulation for comparison with GACOx: manual inspection and two automated algorithms. These are described below:The analysis of the method presented here was performed retrospectively based on data from an animal study originally designed to investigate the characterization of cerebral autoregulation. The study consisted of a healthy porcine model , aged 8.4 ± 0.5 weeks (mean ± SD), with a weight of 13.3 ± 1.7 kg (mean ± SD). The protocol was reviewed and approved by the PCRS Animal Care and Use Committee. The study was conducted in GLP like fashion accordance with 21 CFR Part 58 at an Association for Assessment and Accreditation of Laboratory Animal Care (AAALAC) accredited site. The following standards in terms of appropriate use of animals for biomedical research and/or training were adhered to: The U.S. Animal Welfare Act amendment of 1976  and the current U.S. National Institute of Health’s Guide for the Care and Use of Laboratory Animals published by the National Research Council.2 signal) and a blood pressure signal were collected. The animal was ventilated with a tidal volume of 6–8 mL/kg, FiO2 was adjusted to maintain 95 % arterial saturation and PEEP was 3 cmH2O. Respiratory rate was adjusted to maintain end-tidal CO2 between 38 and 45 mmHg. Heating pads were used to maintain normal body temperature as necessary.Fentanyl, isoflurane, propofol and vecuronium were used as anaesthetic agents and heparin as an anticoagulant. NIRS sensors (INVOS SAFB-SM) were placed on the animals’ head between the ears. These were attached to the monitor ). NIRS cerebral signals .The signals used in the analysis were acquired during episodes of induced haemorrhagic shock and vasoconstriction using an α-agent (norepinephrine). The protocol allowed mostly for blood pressure variations which resulted in multiple crossings of the LLA. A few high pressure spikes were seen in the data but not enough to adequately define a ULA in most of the cases, hence only LLAs were considered in this study. The MAP was calculated from the raw blood pressure signal by an in-house peak detection algorithm which determines systolic and diastolic blood pressure on a beat-by-beat basis. This is averaged over 10 s and output synchronously with rSO2 signals. This was incremented along the signals in a series of 10 s steps. The calculated COx metric values were binned in 5 mmHg blood pressure increments, and the reference LLAs calculated using the three methods described in 2.1.1. Bins with fewer than three data points were not considered as representative and were excluded from the analysis. Box plots were used to show the relative (aggregated) distributions of the COx and GACOx data either side of the determined LLAs. The difference in the median values of the COx and GACOx data was taken as a measure of the separation of the intact and impaired data.A moving 300 s window was employed to analyse the MAP and rSO2 data, used to adjust the indices, can also be seen in the top row plots. It may be observed from the figure that all GACOx plots exhibit a clear transition from positive to negative values. This is in contrast to the traditional COx plots, where many of the transition regions are difficult to discern, hence making LLA identification problematic. A summary of the calculated LLAs using GACOx and the reference methods is provided in Table Figure Figure 2–MAP plot. Mathematically two issues exist: the asymmetric data clustering in the intact and impaired zones; and the computation of a correlation coefficient for the intact region with idealised data  is mathematically impossible. The gradient adjusted method detailed in this paper was applied to data where the traditional COx method failed to identify an LLA in most of the data sets studied—even when a reasonably high threshold value of 0.5 was employed. A manual assessment of the data did find LLAs for all data sets, but this was critically dependent on the subjective interpretation of the reviewers and required a ‘user-defined’ threshold well above those currently used in the literature.The use of traditional correlation measures for the identification of the intact and impaired regions of autoregulation has inherent physiological and mathematical limitations. Physiologically, there is an inability to differentiate between intact and impaired regions when a slightly positive slope exists in the intact region of the rSO2–MAP relationship so that the intact region exhibits a negative slope while the impaired regions retain a positive slope. In this way, the revised GACOx plot exhibits a clear grouping of the data tending to +1 for impaired and −1 for intact autoregulation. This allows for a more robust and reliable method for detecting the decision boundary at the LLA. In fact, in many cases, the method facilitates the evaluation of otherwise undefinable limits using algorithms based on the traditional method . The work described here is part of a wider study by the authors to investigate alternative and adjunct techniques for traditional correlation-based methods for CA. The method, for example, could prove useful for the calculation of PRx where some studies have reported difficulties in differentiating between intact and impaired regimes exhibiting very small difference  [It is obvious that the GA method may be applied to other correlation-based measures of autoregulation: for example, a blood volume signal, an ICP signal or a measure of flow velocity could be used in place of rSOulation) –24.In previous work , the autAlthough we have considered the case where the intact region displays a positive slope and is therefore a confounder to the traditional correlation-based COx approach, it should be noted that distinct  negative slopes have also been observed in intact regions  for cardNote that application of the GACOx method to a real time algorithm would require a sufficient number of points to establish a linear fit with statistical meaning. It is necessary to have a minimum number of points spanning through a range of blood pressures in order for the method to be able to discern the main autoregulation function regions.The study suffers from a number of limitations. These are described as follows:The method requires data in both the impaired and intact regions to successfully alter the gradient so that the intact region after gradient adjustment is of a negative slope. This was not a problem for the current study, where the whole data set was analysed retrospectively. However, in practice, in order to develop a real-time implementation, this needs to be considered. As the COx curve is built up, the data may initially only be confined to one region (intact or impaired). In this case, gradient adjustment could, for example, be based on a historical knowledge of the expected gradients of impaired and intact regions.2 curve is larger in the high pressure impaired region than in the intact region. However, this will require data sets containing distinct ULAs to test the hypothesis that the method is agnostic to whether a ULA or LLA is considered.Another disadvantage of the reported study is the lack of ULA data with which to test the method. This was due to the nature of the study. It is expected that the method will work for the identification of this upper limit given that the slope of the MAP versus rSOAnother disadvantage of the study was that the results could not be compared directly to an independent reference signal, as the historical data used had no useful reference signal for cerebral blood flow , hence no Mx could be calculated (nor the corresponding GAMx). However, the LLAs could be compared with the standard COx measure derived using various approaches, including recently developed data clustering methods. Although less than ideal, it is worth noting that many of the reference signals that are used in other studies suffer from their own issues. For example Transcranial Doppler, which is required to calculate the Mx measure, requires manual intervention, does not work for some patients and/or works intermittently, and can be very noisy .2 and MAP during intact autoregulation regimes. The proposed gradient adjustment technique is simple to implement and significantly aids in the automatic extraction of the limits of autoregulation. We successfully applied the method to a pig study, with noticeable improvement in terms of successfully determining lower limit boundaries of autoregulation with values very close to those determined by manual inspection. The GACOx method appears promising as a technique for the robust automation of the identification of the limits of autoregulation.It is now recognised that real data behaves in a much more complex way than the traditional Lassen curve indicates, with both positive and negative correlations having been observed in practice between rSO


These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the  potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective ( The design of experimental methods based only on first principles to measure chemical properties is an important research topic of physical chemistry. Isomerization reactions take place within the bound energy region of a molecular system; the measurement of molecular eigenenergies is such a first principles related experimental method. It does not follow the usual predict, measure, and compare methodology: the multi-dimensional eigenvalue equation of the molecular system is extremely simple to formulate but it is impossible to solve1Classical spectroscopic experiments collect data that mainly sample only one type of stationary point on the PES: local minima. These minima describe the isomers of the molecular system and define the concept of the molecular structure. For example, the PES of the  molecular system formed from the atoms C, N and H has two minima corresponding to the molecules HCN and HNC. Between the collected spectroscopic information and the near-minimum region of the potential there is a textbook-based relationship. In this way a complete set of molecular eigenenergies collected at low molecular excitations457The PES of a molecule has another type of stationary points that is very important in chemistry: the saddle points. Saddle points correspond to chemical processes through transition state theory. In contrast to the near-minimum regions, standard textbooks provide no guidance how the potential connecting the two minima is encoded in the eigenstates6ωc(E) times ħ at the total excitation energy E must match approximately the energy spacing The correspondence principleFor systems where this correlation is valid we can gain a physical insight regarding the structure of the energy eigenvalues for a bound quantum system based on purely classical calculations. There are only a few quantum models where analytical solutions for the energy eigenvalues can be given. The correspondence principle allows us to study systems where there is no analytical solution for the quantum problem but where we can find an analytical solution for the classical problem.En(En) and compare it with the result obtained in the classical limit. In any region of the classical phase space where dramatic changes in the system dynamics take place, there will be a significant change in the corresponding ΔEn(En) quantum frequency. We expect that these ΔEn curves show specific quantum signatures.To obtain a visualization of the quantum dynamics in the frequency domain we can represent the spacing of a set of eigenenergies Δħωc(E) is the classical frequency scaled with ħ and ΔEn(En) is the quantum frequency. For practical reasons we consider ħωc as the classical frequency and use energy related dimensions to describe both frequencies. In the ħωc(E) = ΔEn(En) if we consider the following correspondence between the quantum mechanical eigenenergies En and classical total energy EThere are two physical quantities involved here: ωe harmonic frequency. This is a very intuitive result: The zero point energy correction must be evaluated according to the small amplitude classical oscillation frequency.Even if the Morse potential is a fundamentally anharmonic potential the calibration of the mean spectroscopic eigenenergies to the classical oscillation frequencies must be performed based on the The symmetric double-well quartic potential121314E < Eb, where Eb is the barrier height, is given ashas a saddle point between two symmetric minima; for this potential an analytic solution of the classical motionE > Eb it isand for K(k) is the normal elliptic integral of the first kind. For small energy E the oscillations for a system with mass m are harmonic with the frequency ω0 around the positions centered at x = ±xm. To compare the classical and quantum frequencies we factored out where x > 0 and the exact classical trajectories as the energy asymptotically approaches the top of the barrier. As the excitation energy converges to the barrier height Eb the system spends a larger fraction of the oscillation period in the neighborhood of the saddle point. The increasing spatial localization at the saddle point correlates with the decrease to zero of the oscillation frequency.Eb and thereby tuning the position of the eigenstates to the neighborhood of the barrier. The classical frequencies for potentials with increasing barrier heights Eb = i × E0 with i = 11, 111, 221, 441, 881, 1811, 2911 and the corresponding quantum frequencies calculated using the Fourier grid Hamiltonian methodWe can study the classical to quantum correspondence (1) by increasing the barrier height It is possible to set up an analytical model for the eigenenergy spectrum for the quartic potential when the eigenenergies are knownħωc(E) allows adjustment of the experimental data and obtain a fit for the Eb parameter of the quantum mechanical system.This model based on the classical frequency Rovibrational molecular spectroscopy is based on the existence of eigenenergy patterns related to the internal molecular dynamics. We see these patterns in high resolution spectra and they represent our “spectroscopic view” of the molecular system. One special type of pattern we expect to see in molecular spectra is related to the existence of a saddle point on the potential energy surface.ν2 bending mode is coupled to the ν1 HC/HN stretch mode and represents the reaction coordinate. The CN stretch vibration is a spectator mode only slightly coupled to the isomerization.The  molecular system is an ideal candidate to study the eigenstates in the neighborhood of a saddle point. The saddle point corresponds to the transition state of the simple HCN ↔ HNC hydrogen shift isomerization reaction between the HCN and HNC linear isomers. In the isomerization reaction the En eigenenergies correspond to the wavenumbers of the rovibrational eigenstates and the ωc frequency of the classical oscillations corresponds to the classical motion in the molecular Born-Oppenheimer potential energy surface. Correlation (1) has important consequences regarding the energy eigenstates of molecules. To study it for a polyatomic molecule a complete set of assigned energy eigenstates, En up to very high excitation energies is needed.For molecules the et al.The basic concepts of the 0.5CNH0.5The first column of curves in To model the bending quantum frequency curves we can try to set up simple analytical models. Considering the correspondence principle the general method to obtain analytical models for quantum frequency curves is to solve the oscillation frequency of the classical problem analytically. In general the quantum frequencies have different excitation energy dependence because the effective potentials differ for each dynamical isomerization path and molecule. This means that we can expect to find only approximate models. On the other hand even approximate analytical models are still very important. They can be used to set up the effective spectroscopic Hamiltonian in the energy region of the saddle point; this Hamiltonian represents the internal dynamics in the saddle point region of the phase space.et al.E(n) of the eigenenergies for a one-dimensional potential allows to obtain the analytical model for the quantum number dependence of the effective frequency. In the absence of such a formula for a potential with a saddle point region they propose an ansatz type effective frequency formula expressed in the excitation energy. The formula is based on the analysis of the physical mechanism of the diatomic potentials and their typical effective frequency dependence. In this work, we use this as an ansatz type quantum frequency formula in a slightly changed formBaraban where we included the classical to quantum frequency correspondence 2; The three-parameter dependent ansatz type model has been testedThe quantum frequency curves fitted with the analytical models are shown in 0.5CNH0.5As the pure bending eigenstates pass through the energy of the isomerization barrier, the hydrogen atom no longer “belongs” to one of the ends of the CN fragment. These vibrational states are extremely important for chemistry as they correspond to a third type of molecule that we can form from the H, C and N atoms: HThe theoretical description within the adiabatic approximation of bond-breaking states is based on the assumption that the stretch quantum numbers remain well-defined for bond-breaking + stretch mixed states. This is not a straightforward result and the validity of this model still requires an experimental verification. We assigned all states -without exception- to one of the bond-breaking + stretch eigenenergy progressions based on visual inspection of the wavefunctions. The majority of these states are strongly mixed from the viewpoint of the eigenstates below the barrier.P along the bending coordinate for the HCN and HNC molecular wavefunction for some γH–CN = 76° transition state. The eigenenergies of these states give the position of the The quantum frequency curves shown in The localization at the saddle point in the case of the  molecular system does not occur by chance, the localization is a general feature of the eigenenergy spectrum of any system with saddle points. The  molecular wavefunctions near the x and p. A measurement of the position or momentum can yield any result however the multiplicative factor of the root mean square deviations The spatial localization is a general feature of wavefunctions in the neighborhood of saddle points and can be intuitively understood based on the classical trajectories shown in Even if this quantum localization is a very fundamental and general property of the energy eigenstates, it seems that their importance and emergence have not been previously recognized. To our knowledge the localization of the eigenstates at the potential saddle point has been mentioned in two works: in the work of Dutta and BhattacharyyaThe functional form of the localization probability at the saddle point for these wavefunctions corresponds to a minimum Gaussian wavepacket see  and S8.ωloc = 150 cm−1. This means that the position of the bending Q-branches that decrease in wavenumber as v2 increases in a HCN ν2 wavenumber region spectrum will be limited to a minimum of 150 cm−1. We expect to see the existence of this limit at low wavenumbers in molecular spectra as the unique spectroscopic pattern of a saddle point localized eigenstate.Another important property of these states is the existence of a minimum quantum frequency as expected from a semiclassical viewpoint. J = 0 saddle point localized wavefunctions suggests that we may assign these states to any of the HCN or the HNC molecule. Indeed, from the point of view of the internal dynamics this state seems to be “degenerated”. The effective potential barrier heights match the barrier heights of the quantum frequency analysis . For each molecule, the eigenenergies and transitions between the eigenstates define a complex spectroscopic networkv2 = 12, 13, 14 states determined form the newly assigned P,Q and R bands of a HCN emission spectrum in the pure bending region. The spectroscopic constants of these states are given in 6The analysis of the  molecular system presented in this work is based on two complete rovibrational eigenenergy data sets that one of the authors developed over the last fifteen years. The first is based on experimental eigenenergies determined through the spectroscopy of hot molecular gases3456242526−1 above the isomerization barrier. This ab initio spectrum18326−1 above the saddle point and stored the complete set of the state vectors. Our calculation improved on the previously reported69The second data set is the list of the complete, full dimensional Born-Oppenheimer rovibrational eigenenergies282930How to cite this article: Mellau, G. C. et al. Saddle point localization of molecular wavefunctions. Sci. Rep.6, 33068; doi: 10.1038/srep33068 (2016).


The inclusion of a healing chamber in dental implants has been shown to promote biological healing. In this paper, a novel numerical approach to the design of the healing chamber for additive-manufactured dental implants is proposed. This study developed an algorithm for the modeling of bone growth and employed finite element method in ANSYS to facilitate the design of healing chambers with a highly complex configuration. The model was then applied to the design of dental implants for insertion into the posterior maxillary bones. Two types of ITI® solid cylindrical screwed implant with extra rectangular-shaped healing chamber as an initial design are adopted, with which to evaluate the proposed system. This resulted in several configurations for the healing chamber, which were then evaluated based on the corresponding volume fraction of healthy surrounding bone. The best of these implants resulted in a healing chamber surrounded by around 9.2% more healthy bone than that obtained from the original design. The optimal design increased the contact area between the bone and implant by around 52.9%, which is expected to have a significant effect on osseointegration. The proposed approach is highly efficient which typically completes the optimization of each implant within 3–5 days on an ordinary personal computer. It is also sufficiently general to permit extension to various loading conditions. Dental implant has been an important surgical component in recent years. A well-designed dental implant is able to benefit patients with improved appearance, comfort, and speech, as well as stopping the bone loss , 2 and eMost studies on the design of healing chambers have focused on the shape of the threads, the thread pitch , 10, 11,Circumferential troughs within the region between threads can also serve as a healing chamber. In an in vivo study, Berglundh et al.  demonstrThe design of the healing chamber is also greatly affected by the manufacturing techniques. Dental implants are typically fabricated using Ti6Al4V. The complexity of the implant shape is limited by machining techniques . The macExtending the applicability of design methods to include cases with a wider range of loading conditions would require that researchers to take into account the remodeling of bone after implantation. The mechanism underlying bone remodeling is described by Wolff's Law  and the In this work, which is extended by the authors' previous model , a numerWhile conventional dental implants typically adopt the same shape of healing chambers throughout the entire implant, the modified finite element approach can generate a biomimetic dental implant which allows the diversity of the shape of the healing chamber across different regions between threads. This complex shape of the healing chamber is the result of the complicated local boundary conditions and is particularly suitable for the additive manufacturing. In the following sections, the algorithm of the bone remodeling and the corresponding 3D finite element model will be described. The power of this method with detailed study of the dental implants used in posterior maxillary bones is then illustrated. The approach is sufficiently general to permit extension to other types of bone as well as various of loading conditions.ε. It is assumed that a decrease in the equivalent strain accelerates bone resorption when ε < εdu, such that the formation of bone would occur at an accelerated rate following an increase in ε when εol ≤ ε. The two strain ranges are known as the disuse window (DW) and overuse window (OW), respectively. When εpl ≤ ε < εpu, the strain range is referred to as a physiological window (PW), in which bone formation and resorption are assumed to occur stochastically according to the degree of nonuniformity in local stress.The proposed numerical model is based on the methods outlined by Kwon et al. , 36, whec on the bone surface, where the equivalent strain of the corresponding bone element is εc. The probability of adding or removing a new bone element at point c which is denoted by f∗ is written as follows [f(Гc) is the probability of bone resorption and formation at point c, which is a function of nonuniformity (Гc) in the stress distribution in the bone near point c.Now consider point  follows :(1)f∗Гc,In the following, the algorithm used to design the trough-type healing chamber in dental implants is outlined. The cross-section of the healing chamber is initially set as a simple rectangle, as illustrated in The implant is then subjected to specific loads and boundary conditions. The equivalent stress and strain states of each bone element in contact with implant elements at the surface of the healing chamber are substituted into Equation  to deterГc tends to remove bone elements from inside the healing chamber to achieve a more uniform stress state in the bone tissue. This makes it inevitable that after several iterations the healing chamber will be entirely filled with implant elements. Thus, the configuration of the healing chamber in its final iteration is not necessarily the best implant design for the given load. Thus, the configurations generated in every iteration are regarded as candidates to be evaluated according to the volume fraction of the healthy surrounding bone in the region of interest. Healthy bone is defined as bone tissue under a strain state similar to that caused by normal physical activities, ranging between 400 με and 1500 με [It is natural that the bone elements within a healing chamber be subjected to stress and strain conditions lower than those outside the healing chamber. The mechanism of nonuniformity  1500 με . The canIn the following, the proposed numerical method is applied to the design of implants with healing chamber for implantation in the posterior maxillary bone. Two types of implant are studied here: (1) a commercial ITI  solid cylindrical screwed implant number 033.512S  and (2) The initial configuration of both types of implant was based on the design of the ITI devices with an added circumferential trough. The depth of the trough is chosen to be the half of spacing between pitches. μm, which corresponds to the size of the bone elements used in previous bone models [The corresponding finite element model was constructed and meshed using ANSYS Workbench 15.0. The element type SOLID 185 was used for all implant and bone elements. The model for the case of type (1) implant is shown in e models . This ise models . Figure Z-axis on the top surface of the abutment, as shown in The parameters used in the model follow those outlined by Kwon et al. .  Table Now consider type (1) implant (ITI number 033.512S). μm, and thus seven distinct colors (red-deep purple) are used here to indicate their depth. Now consider type (2) implant (ITI number 033.563S). The changes on the shape of the area between threads of the initial implant and implants I–IX generated in each iteration of the design process for type (2) implant are illustrated in 2, which exceeds type (1) ITI commercial implant by almost 53%.The volume fraction values of healthy surrounding bone for both types (1) and (2) implants are presented in 2, which exceeds type (2) ITI commercial implant by about 42%. The improvements for both types (1) and (2) implants would undoubtedly enhance the osseointegration [Consider the case of type (2). The volume fractions of healthy surrounding bone for all the implants, illustrated as a red line with square markers in egration , 42, whiegration . Thus, iμε. The strain contour of these elements forms a pattern of square shapes and bands beneath the threads, which shrink toward the crestal region. This is an indication that bone elements close to the crestal region are in higher strain states. Nonetheless, the strain state of bone elements within the healing chamber remains low, in terms of the bone remodeling criteria. This can also be seen in the second data point of the black line in Next, the strain state of the surrounding bone for both cases (1) and (2) is examined in order to reveal the effect of the design of the healing chambers. με can be found above and beneath the threads close to the sinus floor. Most of the bone elements in the design region of the initial implant are at strain states in the range of 200 με and 400 με. In the next iteration, the resulting implant I gives the strain contour as shown in με and 600 με, where the bone is in a healthy status and is less likely to be absorbed.Now consider the case of type (2). μm. This decrease in depth can be attributed to the fact that bone elements in the middle of the implant are subjected to less strain than those close to the crestal region. The bottom of the healing chamber tapers down to a depth of 150 μm with a height of 350 μm in a trapezoidal configuration  and sufficiently general to enable application to any type of implant, for any type of bone structure, under any load conditions. This is an ideal tool for the customization of dental implants and improvement of the design process.