Jurgen Kurths
Humboldt Universität zu Berlin, Institut für Physik, Faculty Member
The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the... more
The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the brain waste removal system (BWRS), caused an active discussion on both the criticism of some of the perspectives and our intensive study of new experimental facts. It was especially found that the intensity of the metabolite clearance changes significantly during the transition between sleep and wakefulness. Interestingly, at the cellular level, a number of aspects of this problem have been focused on, such as astrocytes–glial cells, which, over the past two decades, have been recognized as equal partners of neurons and perform many important functions. In particular, an important role was assigned to astrocytes within the framework of the glymphatic hypothesis. In this review, we return to the “astrocytocentric” view of the BWRS function and the expl...
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The global number of people with Alzheimer’s disease (AD) doubles every 5 years. It has been established that unless an effective treatment for AD is found, the incidence of AD will triple by 2060. However, pharmacological therapies for... more
The global number of people with Alzheimer’s disease (AD) doubles every 5 years. It has been established that unless an effective treatment for AD is found, the incidence of AD will triple by 2060. However, pharmacological therapies for AD have failed to show effectiveness and safety. Therefore, the search for alternative methods for treating AD is an urgent problem in medicine. The lymphatic drainage and removal system of the brain (LDRSB) plays an important role in resistance to the progression of AD. The development of methods for augmentation of the LDRSB functions may contribute to progress in AD therapy. Photobiomodulation (PBM) is considered to be a non-pharmacological and safe approach for AD therapy. Here, we highlight the most recent and relevant studies of PBM for AD. We focus on emerging evidence that indicates the potential benefits of PBM during sleep for modulation of natural activation of the LDRSB at nighttime, providing effective removal of metabolites, including a...
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The deposition of amyloid-β (Aβ) in the brain is a risk factor for Alzheimer’s disease (AD). Therefore, new strategies for the stimulation of Aβ clearance from the brain can be useful in preventing AD. Transcranial photostimulation (PS)... more
The deposition of amyloid-β (Aβ) in the brain is a risk factor for Alzheimer’s disease (AD). Therefore, new strategies for the stimulation of Aβ clearance from the brain can be useful in preventing AD. Transcranial photostimulation (PS) is considered a promising method for AD therapy. In our previous studies, we clearly demonstrated the PS-mediated stimulation of lymphatic clearing functions, including Aβ removal from the brain. There is increasing evidence that sleep plays an important role in Aβ clearance. Here, we tested our hypothesis that PS at night can stimulate Aβ clearance from the brain more effectively than PS during the day. Our results on healthy mice show that Aβ clearance from the brain occurs faster at night than during wakefulness. The PS course at night improves memory and reduces Aβ accumulation in the brain of AD mice more effectively than the PS course during the day. Our results suggest that night PS is a more promising candidate as an effective method in preve...
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The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the Adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional... more
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the Adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values for the clustering coefficient. Here we study the effects of cycles or order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectrum distribution of the network Adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Furthermore we show that cycles of order three have a weak influence on the Laplacian eigenvalues, fact that explains the recent controversy on the dynamics of clustered networks. Our findings can shed light in the study of how pa...
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2020 and 2021 have been unprecedented years due to the rapid spread of the modified severe acute respiratory syndrome coronavirus around the world. The coronavirus disease 2019 (COVID-19) causes atypical infiltrated pneumonia with many... more
2020 and 2021 have been unprecedented years due to the rapid spread of the modified severe acute respiratory syndrome coronavirus around the world. The coronavirus disease 2019 (COVID-19) causes atypical infiltrated pneumonia with many neurological symptoms, and major sleep changes. The exposure of people to stress, such as social confinement and changes in daily routines, is accompanied by various sleep disturbances, known as ‘coronasomnia’ phenomenon. Sleep disorders induce neuroinflammation, which promotes the blood–brain barrier (BBB) disruption and entry of antigens and inflammatory factors into the brain. Here, we review findings and trends in sleep research in 2020–2021, demonstrating how COVID-19 and sleep disorders can induce BBB leakage via neuroinflammation, which might contribute to the ‘coronasomnia’ phenomenon. The new studies suggest that the control of sleep hygiene and quality should be incorporated into the rehabilitation of COVID-19 patients. We also discuss persp...
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Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people and development of Alzheimer’s disease (AD). Blood–brain barrier (BBB) leakage is a key pathophysiological mechanism of amyloidal CSVD. Sleep... more
Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people and development of Alzheimer’s disease (AD). Blood–brain barrier (BBB) leakage is a key pathophysiological mechanism of amyloidal CSVD. Sleep plays a crucial role in keeping health of the central nervous system and in resistance to CSVD. The deficit of sleep contributes to accumulation of metabolites and toxins such as beta-amyloid in the brain and can lead to BBB disruption. Currently, sleep is considered as an important informative platform for diagnosis and therapy of AD. However, there are no effective methods for extracting of diagnostic information from sleep characteristics. In this review, we show strong evidence that slow wave activity (SWA) (0–0.5 Hz) during deep sleep reflects glymphatic pathology, the BBB leakage and memory deficit in AD. We also discuss that diagnostic and therapeutic targeting of SWA in AD might lead to be a novel era in effective therapy of AD. Moreover, we ...
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In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of... more
In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of state-coupled dynamical networks. We will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks. Some generic mean square stability criteria are derived in terms of algebraic conditions, which guarantee that the whole state-coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes. An effective method is given to select the nodes which should be controlled at each impulsive constants. The proportion of the controlled nodes guaranteeing the stability is explicitly obtained, and the synchronization region is also derived and clearly plotted. Numerical simulations are exploited to demonstrate the effectiveness of th...
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Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general... more
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general situation (but with a constraint) where all the coefficients of the error equation corresponding to the synchronization manifold are time dependent. These analytical results are also confirmed by the numerical simulation of paradigmatic examples.
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Research Interests: Engineering, Mathematics, Physics, Medicine, Coupled Oscillator, and 12 moreNumerical Simulation, Mathematical Sciences, Physical sciences, Piecewise Linear, Phase Synchronization, Chaotic System, Recurrence Quantification Analysis, Lyapunov exponent, Chaotic, attractor, chaotic dynamical system, and Time delay system
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Research Interests: Earth Sciences, Computer Science, Statistical Mechanics, Information Theory, Statistical Physics, and 15 moreCausality, Time series analysis, Entropy, Mathematical Sciences, Physical sciences, Electromagnetic Emissions, Symbolic Dynamics, Permutation Entropy, QC, Holocene Climate Variability, Tsallis Entropy, Entropy Measures, Recurrence Plots, Transfer Entropy, and Non-Extensive Statistical Mechanics
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the... more
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey–Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlati...
Research Interests: Mathematics, Applied Mathematics, Algorithms, Physics, Nonlinear dynamics, and 15 moreSystems Theory, Medicine, Coupled Oscillator, Chaos, Numerical Simulation, Computer Simulation, Piecewise Linear, Phase Synchronization, Chaotic System, Autocorrelation, Recurrence Quantification Analysis, Lyapunov exponent, Autocorrelation Function, attractor, and chaotic dynamical system
Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also... more
Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown that the same general asymptotic stability condition obtained using the Krasovskii–Lyapunov functional theory can be valid for the cases where (i) both the coefficients of the Δ(t) (error variable) and Δτ=Δ(t−τ) (error variable with delay) terms in the error equation corresponding to the synchronization manifold are time independent and (ii) the coefficient of the Δ term is time independent, while that of the Δτ term is time dependent. The existence of different kinds of synchronization is corroborated using similarity function, probability of synchronization, and also from changes in the spectrum of Lyapunov exponents of the coupled time-delay systems.
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In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and... more
In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite ...
Research Interests: Mathematics, Applied Mathematics, Computer Aided Design, Finite element method, Finite Element, and 15 moreMedicine, Hysteresis, Chaos, Computer Simulation, Industry, Motion, Multiple Linear Regression, Conditional Expectation, Linear Regression, Materials Testing, Modular Design, Equipment Design, Equipment Failure Analysis, Control of Chaos, and Machine Tool
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Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to... more
Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to uncover its physical mechanisms for system stability and/or instability (oscillation). In this paper, we first establish a nonlinear model of a multi-converter power system within the DC-link voltage timescale, from the first principle. Then, we obtain a linearized model with the associated characteristic matrix, whose eigenvalues determine the system stability, and finally get independent subsystems by using symmetry approximation conditions under the assumptions that all converters’ parameters and their susceptance to the infinite bus (Bg) are identical. Based on these mathematical analyses, we find that the whole system can be decomposed into several equivalent single-converter systems and its small-signal stability is solely determined by a simp...
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Recent research has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. A challenging task is to understand the implications of such network structures on the functional organization of the... more
Recent research has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. A challenging task is to understand the implications of such network structures on the functional organization of the brain activities. This is studied here basing on dynamical complex networks. We investigate synchronization dynamics on the cortico-cortical network of the cat by modelling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that this network of networks displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the anatomical network. This kind of mesoscopic modelling seems to be a promising approach for understanding brain dynamics. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.
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The emergence of various power electronic devices, including voltage source converters (VSCs), has greatly changed the dynamics of power systems. It is a great challenging to put forward new theories for modeling, analysis, and... more
The emergence of various power electronic devices, including voltage source converters (VSCs), has greatly changed the dynamics of power systems. It is a great challenging to put forward new theories for modeling, analysis, and understanding of power-electronic-based power systems. In this paper, we first establish a detailed nonlinear model of multiple VSC systems, and then, by using the singular perturbation technique, obtain a reduced-order nonlinear model within the DC-link timescale. The latter model consists of differential algebraic equations (DAEs) and keeps slow dynamics in transient processes, showing a balance between computational accuracy and system complexity. Furthermore, the model is compared with the traditional electromechanical dynamical model of power systems, which are dominated by synchronous generators (SGs). Our model of multi-converter systems can be put into a similar diagram to the traditional power system dynamics, with which most of power electrical engineers are familiar. Finally, wide simulation results verify the efficiency of the proposed model.
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The photodynamic (PD) effect has been reported to be efficient for the opening of the blood-brain barrier (BBB), which provides a new informative platform for developing perspective strategies towards brain disease therapy and drug... more
The photodynamic (PD) effect has been reported to be efficient for the opening of the blood-brain barrier (BBB), which provides a new informative platform for developing perspective strategies towards brain disease therapy and drug delivery. However, this method is usually performed via craniotomy due to high scattering of the turbid skull. In this work, we employed a newly-developed optical clearing skull window for investigating non-invasive PD-induced BBB opening to high weight molecules and 100-nm fluid-phase liposomes containing ganglioside GM1. The results demonstrated that the BBB permeability to the Evans blue albumin complex is related to laser doses. By two-photon imaging and confocal imaging with specific markers of the BBB, we noticed PD-related extravasation of rhodamine-dextran and liposomes from the vessels into the brain parenchyma. The PD induced an increase in oxidative stress associated with mild hypoxia and changes in the expression of tight junction (CLND-5 and ...
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The enhanced transport of particles by roughness in a tilted rough ratchet potential subject to a Lévy noise is investigated in this paper. Due to the roughness, the transport process exhibits quite different properties compared to the... more
The enhanced transport of particles by roughness in a tilted rough ratchet potential subject to a Lévy noise is investigated in this paper. Due to the roughness, the transport process exhibits quite different properties compared to the smooth case. We find that the roughness on the potential wall functions like a ladder to provide the convenience for particles to climb up but hinder them to slide down. The mean first passage time from one well to its right adjacent well and the mean velocity are, respectively, calculated versus the roughness, the external force, and the Lévy stability index. Our results show that the roughness is able to induce an enhancement on the mean velocity of particles and accelerate the barrier crossing process. The general conditions require a small external force and a small Lévy stability index. We find that with increasing external forces, the enhancement areas of roughness and Lévy stability index both shrink. However, for the Lévy stability index withi...
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Stroke has a large physical, psychological, and financial burden on patients, their families, and society. Based on functional networks (FNs) constructed from resting state fMRI data, network connectivity after stroke is commonly... more
Stroke has a large physical, psychological, and financial burden on patients, their families, and society. Based on functional networks (FNs) constructed from resting state fMRI data, network connectivity after stroke is commonly conjectured to be more randomly reconfigured. We find that this hypothesis depends on the severity of stroke. Head movement-corrected, resting-state fMRI data were acquired from 32 patients after stroke, and 37 healthy volunteers. We constructed anomaly FNs, which combine time series information of a patient with the healthy control group. We propose data-driven techniques to automatically identify regions of interest that are stroke relevant. Graph analysis based on anomaly FNs suggests consistently that strong connections in healthy controls are broken down specifically and characteristically for brain areas that are related to sensorimotor functions and frontoparietal control systems, but new links in stroke patients are rebuilt randomly from all possibl...
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In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling... more
In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.
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Most of the existing methods for the robustness and targeted immunization problems can be viewed as greedy strategies, which are quite efficient but readily induce a local optimization. In this paper, starting from a percolation... more
Most of the existing methods for the robustness and targeted immunization problems can be viewed as greedy strategies, which are quite efficient but readily induce a local optimization. In this paper, starting from a percolation perspective, we develop two strategies, the relationship-related (RR) strategy and the prediction relationship (PR) strategy, to avoid a local optimum only through the investigation of interrelationships among nodes. Meanwhile, RR combines the sum rule and the product rule from explosive percolation, and PR holds the assumption that nodes with high degree are usually more important than those with low degree. In this manner our methods have a better capability to collapse or protect a network. The simulations performed on a number of networks also demonstrate their effectiveness, especially on large real-world networks where RR fragments each of them into the same size of the giant component; however, RR needs only less than 90% of the number of nodes which ...
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We consider a network topology according to the cortico-cortical connec- tion network of the human brain, where each cortical area is composed of a random network of adaptive exponential integrate-and-fire neurons. Depending on... more
We consider a network topology according to the cortico-cortical connec- tion network of the human brain, where each cortical area is composed of a random network of adaptive exponential integrate-and-fire neurons. Depending on the parameters, this neuron model can exhibit spike or burst patterns. As a diagnostic tool to identify spike and burst patterns we utilise the coefficient of variation of the neuronal inter-spike interval. In our neuronal network, we verify the existence of spike and burst synchronisation in different cortical areas. Our simulations show that the network arrangement, i.e., its rich-club organisation, plays an important role in the transition of the areas from desynchronous to synchronous behaviours.
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The classic equal-area criterion (EAC) is of key importance in power system analysis, and provides a powerful, pictorial and quantitative means of analysing transient stability (i.e. the system's ability to maintain stable operation... more
The classic equal-area criterion (EAC) is of key importance in power system analysis, and provides a powerful, pictorial and quantitative means of analysing transient stability (i.e. the system's ability to maintain stable operation when subjected to a large disturbance). Based on the traditional EAC, it is common sense in engineering that there is a critical cleaning time (CCT); namely, a power system is stable (unstable) if a fault is cleared before (after) this CCT. We regard this form of CCT as bipartite. In this paper, we revisit the EAC theory and, surprisingly, find different kinds of transient stability behaviour. Based on these analyses, we discover that the bipartite CCT is only one type among four major types, and, actually, the forms of CCT can be diversified. In particular, under some circumstances, a system may have no CCT or show a periodic CCT. Our theoretical analysis is verified by numerical simulations in a single-machine-infinite-bus system and also in multi-...
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A new application of the photodynamic treatment (PDT) is presented for the opening of blood-brain barrier (BBB) and the brain clearing activation that is associated with it, including the use of gold nanoparticles as emerging... more
A new application of the photodynamic treatment (PDT) is presented for the opening of blood-brain barrier (BBB) and the brain clearing activation that is associated with it, including the use of gold nanoparticles as emerging photosensitizer carriers in PDT. The obtained results clearly demonstrate 2 pathways for the brain clearing: (1) using PDT-opening of BBB and intravenous injection of FITC-dextran we showed a clearance of this tracer via the meningeal lymphatic system in the subdural space; (2) using optical coherence tomography and intraparenchymal injection of gold nanorods, we observed their clearance through the exit gate of cerebral spinal fluid from the brain into the deep cervical lymph node, where the gold nanorods were accumulated. These data contribute to a better understanding of the cerebrovascular effects of PDT and shed light on mechanisms, underlying brain clearing after PDT-related opening of BBB, including clearance from nanoparticles as drug carriers.
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Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be... more
Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the...
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We have introduced a multiplex recurrence network approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on... more
We have introduced a multiplex recurrence network approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on coupled map lattices and a typical example from palaeobotany research. In both examples, topological changes in the multiplex recurrence networks allow for the detection of regime changes in their dynamics. The method goes beyond classical interpretation of pollen records by considering the vegetation as a whole and using the intrinsic similarity in the dynamics of the different regional vegetation elements. We find that the different vegetation types behave more similarly when one environmental factor acts as the dominant driving force.
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We study the dynamics of a discrete-time tritrophic model which mimics the observed periodicity in the population cycles of the larch budmoth insect which causes widespread defoliation of larch forests at high altitudes periodically. Our... more
We study the dynamics of a discrete-time tritrophic model which mimics the observed periodicity in the population cycles of the larch budmoth insect which causes widespread defoliation of larch forests at high altitudes periodically. Our model employs q-deformation of numbers to model the system comprising the budmoth, one or more parasitoid species, and larch trees. Incorporating climate parameters, we introduce additional parasitoid species and show that their introduction increases the periodicity of the budmoth cycles as observed experimentally. The presence of these additional species also produces other interesting dynamical effects such as periodic bursting and oscillation quenching via oscillation death, amplitude death, and partial oscillation death which are also seen in nature. We suggest that introducing additional parasitoid species provides an alternative explanation for the collapse of the nine year budmoth outbreak cycles observed in the Swiss Alps after 1981. A deta...
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Photodynamic treatment (PDT) causes a significant increase in the permeability of the blood-brain barrier (BBB) in healthy mice. Using different doses of laser radiation (635 nm, 10-40 J/cm2) and photosensitizer (5-aminolevulinic acid -... more
Photodynamic treatment (PDT) causes a significant increase in the permeability of the blood-brain barrier (BBB) in healthy mice. Using different doses of laser radiation (635 nm, 10-40 J/cm2) and photosensitizer (5-aminolevulinic acid - 5-ALA, 20 and 80 mg/kg, i.v.), we found that the optimal PDT for the reversible opening of the BBB is 15 J/cm2 and 5-ALA, 20 mg/kg, exhibiting brain tissues recovery 3 days after PDT. Further increases in the laser radiation or 5-ALA doses have no amplifying effect on the BBB permeability, but are associated with severe damage of brain tissues. These results can be an informative platform for further studies of new strategies in brain drug delivery and for better understanding of mechanisms underlying cerebrovascular effects of PDT-related fluorescence guided resection of brain tumor.