Emília Tóth
(Supervisor: Dr. István Ulbert) totem@digitus.itk.ppke.hu
Abstract— Electrical stimulation is frequently performed in concurrence with electrocorticogram recording for functional mapping (or electrical stimulation mapping-ESM) of the cortex and identification of critical cortical structures. In medically refractory epilepsy surgical candidates, intracranial electrodes are necessary to localize the epileptogenic focus prior to surgical resection. This electrodes are used to record the underlying brain activity and also for electrical stimulation of the cortex. Electrical stimulation mapping (ESM) is the gold standard for identifying functional and pathological areas of the brain. Although the procedure remains unstandardized, and limited data support its clinical validity nevertheless, electrical stimulation mapping for define language areas has likely minimized postoperative language decline in numerous patients, and has generated a wealth of data elucidating brain-language relations [3]. Our aim was to study another way of cortical stimulation, so called single pulse electrical stimulation (SPES) to map pathological and functional networks in the brain.
Keywords-component; biomedical signal processing, electrodes, brain networks, electrocorticography, epilepsy, in vivo, human
Abbreviations- ESM=electrical stimulation mapping;
SPES=single pulse electrical stimulation; CT=computed tomography; DCES= direct cortical electrical stimulation;
CCEP=cortico-cortical evoked potential; BA=Brodmann area;
ROC curves=receiver operating characteristic curves
INTRODUCTION
Mapping of functional areas in the human brain is crucial in epilepsy and tumor surgery. There are several non-invasive methods to identify eloquent cortices, such as functional Magnetic Resonance Imaging (fMRI) or Positron Emission Tomography (PET), but the gold standard is direct high frequency cortical electrical stimulation. In this study we used single pulse electrical stimulation evoked late responses to map language and motor networks and to better understand the electrophysiological mechanisms of the cortico-cortical evoked potentials.
Single pulse electrical stimulation is a new method to investigate the cortico-cortical connections in vivo in the human language, motor and sensory system which can provide insight into the mechanisms of higher-order cortical functions and the connections between functional areas [1]. When using a crown configuration, a handheld wand bipolar stimulator may be used at any location along the electrode array. However, when using a subdural strip, stimulation must be applied
between pairs of adjacent electrodes due to the nonconductive material connecting the electrodes on the grid. Electrical stimulating currents applied to the cortex are relatively low, between 2 to 4 mA for somatosensory stimulation, and near 15 mA for cognitive stimulation. The functions most commonly mapped through DCES are primary motor, primary sensory,
and language. The patient must be alert and interactive for mapping procedures, though patient involvement varies with each mapping procedure. Language mapping may involve naming, reading aloud, repetition, and oral comprehension; somatosensory mapping requires that the patient describe sensations experienced across the face and extremities as the surgeon stimulates different cortical regions.[2]
High frequency electrical stimulation is the gold standard in neurosurgery for mapping brain functions, but the exact mechanisms behind the effect and parameters used need to be further studied. There is also some risk associated with the
Figure 1. Reconstructed MRI picture with the implanted electrode array, colored lines represent the functions revealed with ESM.
stimulation, due to its proepileptic effect and the limits imposed by the fact that the cortex has to be exposed using some type of surgery.
During the development of epilepsy, the connections between nerve cells are also strengthen or weakening because of various reasons (neuronal cell death, proliferation, brain stem injury, etc). We hypothesized, this cause changes in the number of significant evoked potentials between the areas showing epileptic activity compared to other areas.
153
(a) A sparse realization (b) The dense realization
Figure 1: Different, dynamically equivalent realizations of the Lorenz-system.
the proposedl1-norm based sparse search can complete this task in 0.0166 seconds.
The dense realization was also successfully computed by all the three algorithms. The MILP based algorithm can complete it in 5.3477 seconds,Element-wise LP consumes 0.2524 seconds and the LP-MAX algorithm needs 0.0446 seconds to compute the solution.
Two different, dynamically equivalent realization of the Lorenz-system can be seen in Fig. 1.
B. Computing alternative realizations of the ErbB network As it was mentioned before, we would like to use our methods to study the possible structures of large scale, biologically relevant networks. As a case study the ErbB network described in [2] was investigated.
In our representation theErbBsignalling pathway model consists of 504 species, 1082 complexes and 1654 reactions.
The model description was originally a sparse representa-tion. With the help of the LP-MAX algorithm introduced in Section III-B the dense realization is computed. It contains 1683 reactions: 29 mathematically possible extra reactions compared to the published model originating from 15 different complexes. The overall computational time was 4993 seconds.
The sparse realization was also extracted from the dense realization with the help of thel1-norm based sparse search.
The resulting network had the same structure as the original sparse representation. The computational time was around 430 seconds.
V. Conclusion
In this work linear programming based methods were presented to compute alternative realizations of CRN. By analysing the properties of the system model and the MILP-based description, simplified algorithms were developed which have polynomial complexity. The algorithms can be easily applied in a parallel framework, too.
Acknowledgements
This research has been supported by the Hungar-ian National Research Fund through grant NF104706.
The first and second authors were also supported by the projects TÁMOP-4.2.1./B-11/2/KMR-2011-002 and TÁMOP-4.2.2./B-10/1-2010-0014.
References
[1] A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints.Automatica, 35:407–427, 1999.
[2] William W. Chen, Birgit Schoeberl, Paul J. Jasper, Mario Niepel, Ulrik B. Nielsen, Douglas A. Lauffenburger, and Peter K.
Sorger. Input-output behavior of erbb signaling pathways as revealed by a mass action model trained against dynamic data.
Molecular Systems Biology, 5, January 2009.
[3] David L. Donoho. For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution. Comm. Pure Appl. Math, 59:797–829, 2004.
[4] David L. Donoho. Compressed sensing. IEEE Trans. Inform.
Theory, 52:1289–1306, 2006.
[5] M. Feinberg. Lectures on chemical reaction networks. Notes of lectures given at the Mathematics Research Center, University of Wisconsin, 1979.
[6] F. Horn and R. Jackson. General mass action kinetics. Archive for Rational Mechanics and Analysis, 47:81–116, 1972.
[7] R. Raman and I.E. Grossmann. Modelling and computational techniques for logic based integer programming.Computers and Chemical Engineering, 18:563–578, 1994.
[8] J. Rudan, G. Szederkényi, and K. M. Hangos. Efficiently computing alternative structures of large biochemical reaction networks using linear programming.MATCH Commun. Math.
Comput. Chem., 2013. submitted.
[9] Thomas L. Magnanti Stephen P. Bradley, Arnoldo C. Hax.
Applied Mathematical Programming. Addison-Wesley, 1977.
[10] G. Szederkényi. Computing sparse and dense realizations of reaction kinetic systems. Journal of Mathematical Chemistry, 47:551–568, 2010.
[11] G. Szederkényi, J. R. Banga, and A. A. Alonso. Inference of complex biological networks: distinguishability issues and optimization-based solutions. BMC Systems Biology, 5:177, 2011.
[12] G. Szederkényi and K. M. Hangos. Finding complex balanced and detailed balanced realizations of chemical reaction net-works.Journal of Mathematical Chemistry, 49:1163–1179, 2011.
[13] G. Szederkényi, K. M. Hangos, and T. Péni. Maximal and minimal realizations of reaction kinetic systems: computation and properties. MATCH Commun. Math. Comput. Chem., 65:309–332, 2011.
[14] G. Szederkényi, K. M. Hangos, and Zs. Tuza. Finding weakly reversible realizations of chemical reaction networks using opti-mization. MATCH Commun. Math. Comput. Chem., 67:193–
212, 2012.
[15] Z. A. Tuza, G. Szederkényi, K. M. Hangos, and J. R. Banga A. A. Alonso. Computing all sparse kinetic structures for a Lorenz system using optimization methods. International Journal of Bifurcation and Chaos, accepted:to appear, 2013.
[16] Michael M. Zavlanos, A. Agung Julius, Stephen P. Boyd, and George J. Pappas. Inferring stable genetic networks from steady-state data. Automatica, 47(6):1113–1122, 2011.
[17] P. Érdi and J. Tóth. Mathematical Models of Chemical Reac-tions. Theory and Applications of Deterministic and Stochastic Models. Manchester University Press, Princeton University Press, Manchester, Princeton, 1989.
Complex Electrophysiological Analysis of the Effect of Cortical Electrical Stimulation in Humans
Emília Tóth
(Supervisor: Dr. István Ulbert) totem@digitus.itk.ppke.hu
Abstract— Electrical stimulation is frequently performed in concurrence with electrocorticogram recording for functional mapping (or electrical stimulation mapping-ESM) of the cortex and identification of critical cortical structures. In medically refractory epilepsy surgical candidates, intracranial electrodes are necessary to localize the epileptogenic focus prior to surgical resection. This electrodes are used to record the underlying brain activity and also for electrical stimulation of the cortex. Electrical stimulation mapping (ESM) is the gold standard for identifying functional and pathological areas of the brain. Although the procedure remains unstandardized, and limited data support its clinical validity nevertheless, electrical stimulation mapping for define language areas has likely minimized postoperative language decline in numerous patients, and has generated a wealth of data elucidating brain-language relations [3]. Our aim was to study another way of cortical stimulation, so called single pulse electrical stimulation (SPES) to map pathological and functional networks in the brain.
Keywords-component; biomedical signal processing, electrodes, brain networks, electrocorticography, epilepsy, in vivo, human
Abbreviations- ESM=electrical stimulation mapping;
SPES=single pulse electrical stimulation; CT=computed tomography; DCES= direct cortical electrical stimulation;
CCEP=cortico-cortical evoked potential; BA=Brodmann area;
ROC curves=receiver operating characteristic curves
INTRODUCTION
Mapping of functional areas in the human brain is crucial in epilepsy and tumor surgery. There are several non-invasive methods to identify eloquent cortices, such as functional Magnetic Resonance Imaging (fMRI) or Positron Emission Tomography (PET), but the gold standard is direct high frequency cortical electrical stimulation. In this study we used single pulse electrical stimulation evoked late responses to map language and motor networks and to better understand the electrophysiological mechanisms of the cortico-cortical evoked potentials.
Single pulse electrical stimulation is a new method to investigate the cortico-cortical connections in vivo in the human language, motor and sensory system which can provide insight into the mechanisms of higher-order cortical functions and the connections between functional areas [1]. When using a crown configuration, a handheld wand bipolar stimulator may be used at any location along the electrode array. However, when using a subdural strip, stimulation must be applied
between pairs of adjacent electrodes due to the nonconductive material connecting the electrodes on the grid. Electrical stimulating currents applied to the cortex are relatively low, between 2 to 4 mA for somatosensory stimulation, and near 15 mA for cognitive stimulation. The functions most commonly mapped through DCES are primary motor, primary sensory,
and language. The patient must be alert and interactive for mapping procedures, though patient involvement varies with each mapping procedure. Language mapping may involve naming, reading aloud, repetition, and oral comprehension;
somatosensory mapping requires that the patient describe sensations experienced across the face and extremities as the surgeon stimulates different cortical regions.[2]
High frequency electrical stimulation is the gold standard in neurosurgery for mapping brain functions, but the exact mechanisms behind the effect and parameters used need to be further studied. There is also some risk associated with the
Figure 1. Reconstructed MRI picture with the implanted electrode array, colored lines represent the functions revealed with ESM.
stimulation, due to its proepileptic effect and the limits imposed by the fact that the cortex has to be exposed using some type of surgery.
During the development of epilepsy, the connections between nerve cells are also strengthen or weakening because of various reasons (neuronal cell death, proliferation, brain stem injury, etc). We hypothesized, this cause changes in the number of significant evoked potentials between the areas showing epileptic activity compared to other areas.
E. Tóth, “Complex electrophysiological analysis of the effect of cortical electrical stimulation in humans,”
in Proceedings of the Interdisciplinary Doctoral School in the 2012-2013 Academic Year, T. Roska, G. Prószéky, P. Szolgay, Eds.
Faculty of Information Technology, Pázmány Péter Catholic University.
Budapest, Hungary: Pázmány University ePress, 2013, vol. 8, pp. 153-156.
Our aim with this study was to find other ways to map functional networks in the brain, using a less invasive method and analyze the network features with this new approach.
Single pulse electrical stimulation (0,5Hz) is much less invasive in terms of seizure generation, and the distribution of the evoked potentials may reveal the intracortical pathways between cortical regions.
METHODS
A. Clinical electrodes and recordings
The electrode implantations and recordings, along with ESM and SPES took place at two well established epilepsy surgical centers in Budapest (National Institute of Neuroscience) and New York (North Shore-LIJ Health System). Patients were implanted with intracranial subdural grid, strip, and in some cases depth electrodes for 5– days.
They were monitored to identify the seizure focus, at which time the electrodes were removed and, if appropriate, the seizure focus was resected. Continuous intracranial EEG was recorded with standard recording systems with sampling rates 1000 or 2000 Hz. The microelectrodes were implanted in eleven cases, perpendicularly to the cortical surface to sample the width of the cortex. This 24 contact laminar electrode has been described previously [4]. Differential recordings were made from each pair of successive contacts to establish a potential gradient across the cortical lamina.
B. Functional Stimulation Mapping
For localization of functional cortical areas, electrical stimulation mapping was carried out according to standard clinical protocol (bipolar stimulation: 2–5 s, 3–15 mA, 20–50 Hz). Areas were defined as expressive language sites when stimulation resulted in speech arrest. When stimulation resulted in a naming deficit based on auditory or visual cues, or an interruption in reading or comprehension, the area was deemed a nonexpressive language site. Sensory and motor areas were identified when stimulation caused movement or changes in sensation.
C. Cortical Electrical Stimulation and Cortico-Cortical Evoked Potentials.
Following implantation of intracranial electrodes, patients were monitored for epileptic activity and during this time, CCEP mapping was performed using single-pulse stimulation.
Systematic bipolar stimulation of each pair of adjacent electrodes was administered with single pulses of electrical current (3 mA-15 mA, 0.5 Hz, 0.2-ms pulse width, 20-25 trials per electrode pair). The associated evoked responses (CCEPs) were measured at all other electrode sites. The current amplitude of 10 mA activated the maximal number of neuronal elements without epileptic afterdischarges or other clinical signs. The 2 seconds interstimulation interval was used to minimize the effect of overlapping evoked responses and to leave enough restitution time for the cortex. Patients were awake and at rest at the time of CCEP recording
D. Analysis of CCEPs.
Electrophysiological data analyses were performed using Neuroscan Edit 4.5 software (Compumedics) and own developed MATLAB scripts. Evoked responses to stimulation
were divided into 2-s epochs (-500 ms to 1,500 ms) time-locked to stimulation pulse delivery. The CCEP consists of two usually negative peaks termed N1, timed at ∼10–30 ms, and N2, which exhibits a broader spatial distribution and occurs between 70 and 300 ms [1]. To quantify the magnitude of the CCEPs in the time window of the N2, the data were low-pass filtered (30 Hz), and baseline correction (−450 to −50 ms) was performed. The SD was computed for each electrode separately using all time points in the -450 to -50 time window, CCEPs were considered significant if the N2 peak of the evoked potential exceeded the baseline amplitude by a threshold of ±6 SD as determined from the receiver operating characteristic (ROC) curves.
E. Electrode localization
To co-register the electrodes to anatomical structures, we used sophisticated imaging techniques, developed by our co-operational research team. We used intraoperative pictures and a postoperative CT scan to localize the electrodes in the skull.
This was co-registered to a high resolution preoperative MRI where we could precisely localize the anatomical structures.
Using these scans and freely available softwares (Bioimagesuite, Freesurfer, FSL, AFNI) we developed a semi – automated co-localizing each electrode to the underlying Brodman area of the brain. Determination of the seizure onset zone was performed by epileptologists [5].
F. Patients
Twentyfive patients (ages 6–53 years, 28±14.84, 14 females) with medically intractable focal epilepsy were enrolled in the study after informed consent was obtained.
These procedures were monitored by local Institutional Review Boards, in accordance with the ethical standards of the Declaration of Helsinki.
Figure 2. This figure shows averaged responses time locked to the bipolar stimulation artefact (-250-600ms). Green line is the significant response, blue line is the absolute value of the significant response, pink line is a non significant response and the red horizontal line is the threshold for the two responses.
G. Pathological and physiological networks
Neurologist defined pathological and non pathological electrode groups. Pathological electrodes were those which showed seizure onset, or early spread (in the first 10 s) The number of significant evoked potentials was divided into four groups, according to pathological or non pathological classification of the stimulate and the recording electrode.
In addition, two type of seizure spreading mechanism were distinguished, according to the consistency of seizure spread.
Consistent seizure spread is when seizure starts always at same places, inconsistent if there were more than one typical seizure spreading mechanism. Network connections were examining from these two aspects.
RESULTS
H. Analysis of the significant signal features.
Due to the artifact caused by the stimulation we only focused on the N2 response, which seemed very reliable and reproducible. The variance of both time and amplitude of the N2 peak was high, but it the largest number of peaks occurred around 150 ms, and showed quasi-normal distribution, with two smaller deflections at around 180 -190 ms and 210-250ms.
Analysis of 892 peaks, the average latency was 152.84 ms, with 58.7 ms standard deviation.
I. Create a graph.
A significant evoked response indicates the relationship between the electrodes which were stimulated and which showed the significant response. Significant CCEPs were converted to a distance matrix and transformed to a graph using multidimensional scaling ( a toolbox from Matlab)
On the one hand the result shows that the functional areas which are close to each other are tightly connected (above somatosensory cortex BA40, BA3, BA2; visual cortex BA17, BA18, BA19 and motor cortex BA6, BA4). On the other hand, those regions which are physically more distant from each other seemed also connected, such as Broca’s (BA 45) and Wernicke’s (BA 21, BA20, BA22) area. Using this methodology we tried to map as many areas of the brain as possible, to be able to map all the connections between regions which were covered with electrodes.
Figure 3. Significant CCEPs were converted to a distance matrix and transformed to a graph using multidimensional scaling. Numbers in squares represent Brodmann areas and lines represent connections. Functional networks are color coded: green sensory, pink visual, red language, blue motor. Lines color coded: thin light pink bidirectional, thin blue unidirectional, darker lines between the elements of functional networks is unidirectional, same color is bidirectional. Stimulating electrodes over Broca’s area showed significant responses in electrodes part of the language network as defined with functional stimulation mapping. Responses to stimulation of the primary motor cortex revealed connections to major hubs involved in motor processing.
J. Analysis of changes taking place in cortical layers. After processing the data from the laminar microelectrode and the implanted macroelectrodes, it can be concluded that after the stimulus, there is a decrease in the power of 15-100 Hz frequency band, and the stimulus elicit deactivation in the middle cortical (3th-5th) layers. This finding is in correlation with previous animal studies, which showed wide band decrease in oscillatory power after stimulation was induced.
K. Analysis of the physiological networks.
We calculated the incoming connections and the outgoing connections of all BAs across all patients (n=25) included in the study. BAs localized on the convexity of the brain were densely covered with electrodes, including primary motor and sensory cortex, temporal lobe and the majority of the frontal
We calculated the incoming connections and the outgoing connections of all BAs across all patients (n=25) included in the study. BAs localized on the convexity of the brain were densely covered with electrodes, including primary motor and sensory cortex, temporal lobe and the majority of the frontal