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Electroconvulsive therapy (ECT) is a procedure performed under general anaesthesia involving triggering an intentional brief seizure through small electrical currents through the brain. The anaesthetic depth should be adequate prior to shock and measured with BIS, a processed electroencephalogram (EEG) monitor. Adjusting the hypnotic dose allows to decrease the ictal threshold and thus improve the response to treatment and decrease side effects.
Our goal is detecting elements such as spontaneous epileptiform activity after ECT without tonic-clonic activity with the spectral density matrix (SDM).
Our patient: an 87-year-old woman, diagnosed with F20.2 catatonic schizophrenia and under antipsychotic treatment since her youth. She has required multiple hospital admissions due to psychopathological decompensations until starting monthly maintenance ECT sessions in 2014. Since then she no new hospital admissions have been required.
Images 1D and 1E shows the SDM, a spectrogram of the EEG. The X axis show time (minutes), the Y axis shows the frequency (Hz) and the Z axis shows the energy or intensity of that electrical activity in the frequency bands replaced by colors: warm colors (red) reflecting high intensity electroencephalographic activity and cool colors (yellow, blue and green), low activity. Images 2 and 3’s EDM shows spontaneous epileptiform activity after electroconvulsive therapy without tonic-clonic activity. We observed an initial EDM of an awake patient, with warm colours in practically all frequency bands, including the beta band (13-30 Hz), characteristic of waking states. Around 9:50 anaesthetic induction occurs, activity increases in slow frequencies (red colours in alpha, theta and delta), plus an increase of cold colours in beta, reflecting the disappearance of brain activity in that frequency. The asterisk reflects the EEG response to the electrical discharge, followed by a postcritical state with brain activity exclusively in slow waves and high amplitude (delta and some theta) and absence of activity in other frequencies (blue colour in the beta and alpha bands) around 9:57. At about 10:00 there is an abrupt appearance of high intensity brain activity (warm colours) in beta and alpha and delta, mainly, reflecting spontaneous epileptiform activity after treatment and clinically reflected as a patient absent and disconnected from the environment, but without tonic-clonic activity. New postcritical state in which blue colour predominates, reflecting little brain activity, and warmer colours reappear in all frequency bands, including beta, reflecting the progressive recovery of wakefulness.
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Image 2:
Image 3:
Psychiatric pathology can be reflected in the SDM, which allows to observe changes in the EEG, correcting the electrical stimulus of the shock and the dose of anesthetic appropriate to the patient to trigger an intentional brief seizure under general anesthesia.
None Declared
We develop a Thom–Mather theory of frontals analogous to Ishikawa's theory of deformations of Legendrian singularities but at the frontal level, avoiding the use of the contact setting. In particular, we define concepts like frontal stability, versality of frontal unfoldings or frontal codimension. We prove several characterizations of stability, including a frontal Mather–Gaffney criterion, and of versality. We then define the method of reduction with which we show how to construct frontal versal unfoldings of plane curves and show how to construct stable unfoldings of corank 1 frontals with isolated instability which are not necessarily versal. We prove a frontal version of Mond's conjecture in dimension 1. Finally, we classify stable frontal multigerms and give a complete classification of corank 1 stable frontals from $\mathbb {C}^3$
to $\mathbb {C}^4$
.
We consider the relative Bruce–Roberts number $\mu _{\textrm {BR}}^{-}(f,\,X)$
of a function on an isolated hypersurface singularity $(X,\,0)$
. We show that $\mu _{\textrm {BR}}^{-}(f,\,X)$
is equal to the sum of the Milnor number of the fibre $\mu (f^{-1}(0)\cap X,\,0)$
plus the difference $\mu (X,\,0)-\tau (X,\,0)$
between the Milnor and the Tjurina numbers of $(X,\,0)$
. As an application, we show that the usual Bruce–Roberts number $\mu _{\textrm {BR}}(f,\,X)$
is equal to $\mu (f)+\mu _{\textrm {BR}}^{-}(f,\,X)$
. We also deduce that the relative logarithmic characteristic variety $LC(X)^{-}$
, obtained from the logarithmic characteristic variety $LC(X)$
by eliminating the component corresponding to the complement of $X$
in the ambient space, is Cohen–Macaulay.
