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Objective. We aimed to clarify the pathophysiology of epilepsy involving seizures with apparently generalized onset, progressing to focal ictal rhythm through stereotactic EEG (SEEG) implantation, recording, stimulation and highfrequency oscillation (HFO) analysis. Methods. We identified two patients with seizures with bilateral electrographic onset evolving to focal ictal rhythm, who underwent SEEG implantation. Patients had pre‐surgical epilepsy work‐up, including prolonged video scalp EEG, brain MRI, PET, ictal/interictal SPECT, MEG, and EEG‐fMRI prior to SEEG implantation. Results. Both patients had childhood‐onset seizures involving behavioural arrest and left versive head and eye deviation, evolving to bilateral tonic‐clonic convulsions. Seizures were electrographically preceded by diffuse, bilateral 3‐Hz activity resembling absence seizures. Both had suspected focal lesions based on neuroimaging, including 3T MRI and voxel‐based post‐processing in one patient. Electrode stimulation did not elicit any habitual electroclinical seizures. HFO analysis showed bilateral focal regions with high fast‐ripple rates. Significance. “Generalized‐to‐focal” seizures may occur due to a diffuse, bilateral epileptic network, however, both patients showed ictal evolution from a generalized pattern to a single dominant focus which may explain why the focal aspect of their seizures had a consistent clinical semiology. Patients such as these may have a unique form of generalized epilepsy, but focal/multifocal cerebral abnormalities are also a possibility.

Background: The metabolism of [18F]-FDG, an analogue of glucose molecule, is often evaluated by kinetic analysis. Methods: In this study, we compare the performance of the Iterative Two-stage (ITS) algorithm against the standard Weighted Nonlinear Least Squares (WNLS) and the Patlak analysis for PET imaging quantification in control and diseased rats. A full kinetic modelling and graphical analyses were performed on [18F]-FDG PET data (7 controls and 7 Myocardial Infarct (MI) rats). The evaluation of the identifiability of parameters and the goodness of the fit in nonlinear regression wereconducted by statistic measures i.e. the Coefficient of Variation (COV), Akaike Information Criterion (AIC) and the Model Selection Criterion (MSC). Bland-Altman analysis was used to assess the reproducibility of the net influx rate (Ki) constants in the mid-inferoseptal region. The Patlak Ki outcome values were compared to ITS Ki by calculating the percentage changes between their outcomes estimated values. Results: The WNLS and ITS show an excellent identifiability of the parameters (resp. 5.15≤COV≤8.92; 4.12≤COV≤ 10.20) and showed a good reproducibility of the Ki constants in controls. In contrast, in the MI group, WNLS revealed a poor identifiability in the mid-inferoseptal region (17.62≤COV≤38.15) whereas ITS revealed a good identifiability (10.84 ≤COV≤23.54). The Bland Altman analysis showed a large bias in the estimation of the Ki constants in the region of interest e.g. mid-inferoseptal, 0.053 ± 0.017 mL/ min/mL. The Patlak Ki values were underestimated by 6.8% and 7.4% compared to ITS Ki in controls and MI respectively.

Polymicrogyria (PMG) and periventricular nodular heterotopia (PNH) are two developmental brain malformations that have been described independently in multiple syndromes. Clinically, they present with epilepsy and developmental handicaps in both children and adults. Here we describe their occurrence together as the two major findings in a group of at least three cortical malformation syndromes. We identified 30 patients as having both PNH and PMG on brain imaging, reviewed clinical data and brain imaging studies (or neuropathology summary) for all, and performed mutation analysis of FLNA in nine patients. The group was divided into three subtypes based on brain imaging findings. The frontal-perisylvian PNH–PMG subtype included eight patients (seven males and one female) between 2 days and 10 years of age. It was characterized by PNH lining the lateral body and frontal horns of the lateral ventricles and by PMG most severe in the posterior frontal and perisylvian areas, occasionally with extension to the parietal lobes beyond the immediate perisylvian cortex. The posterior PNH–PMG subtype consisted of 20 patients (15 male and 5 female) between 5 days and 40 years of age. It was characterized by PNH in the trigones, temporal and posterior horns of the lateral ventricles, and PMG most severe in the temporo-parieto-occipital regions. The third type was found in 2 females aged 7 months and 2 years, and was characterized by severe congenital microcephaly and more diffuse cortical abnormality. The PNH–PMG subtypes described here have distinct imaging and clinical phenotypes that suggest multiple genetic aetiologies involving defects in multiple genes, and a shared pathophysiological mechanism for PNH and PMG. The frontal-perisylvian and posterior subtypes both had skewing of the sex ratio towards males, which suggests the possibility of X-linked inheritance. Delineation of these syndromes will also aid in providing more accurate diagnosis and prognostic information for patients with these malformations.

Focal cortical dysplasia is a frequent cause of medically intractable partial epilepsy. These lesions are being increasingly identified by high quality images provided by magnetic resonance imaging (MRI), resulting in improved seizure control of surgically treated patients. Small dysplastic lesions are often missed by conventional MRI methods. The identification of subtle structural abnormalities by rectilinear slices is often limited by the complex convolutional pattern of the brain. We developed a method of curvilinear reformatting of three‐dimensional MRI data that improves the anatomical display of the gyral structure of the hemispheric convexities. It also reduces the asymmetric sampling of gray–white matter that may lead to false‐positive results. We present 5 patients in whom conventional two‐dimensional and three‐dimensional MRI with multiplanar reformatting was initially considered normal. Subsequent studies using curvilinear reformatting identified lesions in all. Four patients underwent surgery with histological diagnosis of focal cortical dysplasia. Three patients are seizure‐free and 1 had significant improvement in seizure control. These results indicate that an increase in the detection of subtle focal dysplastic lesions may be accomplished when one improves the anatomical display of the brain gyral structure by performing curvilinear reformatting. Ann Neurol 1999;46:88–94

Focal cortical dysplasia is a frequent cause of medically intractable partial epilepsy. These lesions are being increasingly identified by high quality images provided by magnetic resonance imaging (MRI), resulting in improved seizure control of surgically treated patients. Small dysplastic lesions are often missed by conventional MRI methods. The identification of subtle structural abnormalities by rectilinear slices is often limited by the complex convolutional pattern of the brain. We developed a method of curvilinear reformatting of three-dimensional MRI data that improves the anatomical display of the gyral structure of the hemispheric convexities. It also reduces the asymmetric sampling of gray–white matter that may lead to false-positive results. We present 5 patients in whom conventional two-dimensional and three-dimensional MRI with multiplanar reformatting was initially considered normal. Subsequent studies using curvilinear reformatting identified lesions in all. Four patients underwent surgery with histological diagnosis of focal cortical dysplasia. Three patients are seizure-free and 1 had significant improvement in seizure control. These results indicate that an increase in the detection of subtle focal dysplastic lesions may be accomplished when one improves the anatomical display of the brain gyral structure by performing curvilinear reformatting. Ann Neurol 1999;46:88–94

Whether temporal lobe epilepsy is the result of an isolated, early injury or whether there is ongoing neuronal dysfunction or loss due to seizures is often debated. We attempt to address this issue by using magnetic resonance techniques. Proton magnetic resonance spectroscopic imaging can detect and quantify focal neuronal dysfunction or loss based on reduced signals from the neuronal marker N-acetylaspartate (NAA), and magnetic resonance imaging (MRI)-based measurements of hippocampal volumes (MRIvol) can quantify the amount of atrophy in this structure. We performed magnetic resonance spectroscopic imaging and MRIvol in 82 consecutive patients with medically intractable temporal lobe epilepsy to determine whether there was a correlation between seizure frequency, or type or duration of epilepsy, with NAA to creatine (Cr) values or hippocampal volumes. Volumes and spectroscopic resonance intensities were categorized as to whether they were measured from the temporal lobe ipsilateral or contralateral to the predominant electroencephalographic focus. Ipsilateral and contralateral NAA/Cr was negatively correlated with duration of epilepsy. Hippocampal volumes were negatively correlated with duration ipsilaterally but not contralaterally. Frequency of complex partial seizures was not correlated with any of the magnetic resonance measures. However, patients with frequent generalized tonic–clonic seizures had lower NAA/Cr bilaterally and smaller hippocampal volumes ipsilaterally than patients with none or rare generalized tonic–clonic seizures. The results suggest that although an early, fixed injury may cause asymmetric temporal lobe damage, generalized seizures may also cause progressive neuronal dysfunction or loss. Ann Neurol 1999;45:568–576

Based on Peano kernel technique, explicit error bounds (optimal for the highest order derivative) are proved for the derivatives of cardinal spline interpolation (interpolating at the knots for odd degree splines and at the midpoints between two knots for even degree splines). The results are based on a new representation of the Peano kernels and on a thorough investigation of their zero distributions. The bounds are given in terms of Euler–Frobenius polynomials and their zeros.

Whether temporal lobe epilepsy is the result of an isolated, early injury or whether there is ongoing neuronal dysfunction or loss due to seizures is often debated. We attempt to address this issue by using magnetic resonance techniques. Proton magnetic resonance spectroscopic imaging can detect and quantify focal neuronal dysfunction or loss based on reduced signals from the neuronal marker N‐acetylaspartate (NAA), and magnetic resonance imaging (MRI)‐based measurements of hippocampal volumes (MRIvol) can quantify the amount of atrophy in this structure. We performed magnetic resonance spectroscopic imaging and MRIvol in 82 consecutive patients with medically intractable temporal lobe epilepsy to determine whether there was a correlation between seizure frequency, or type or duration of epilepsy, with NAA to creatine (Cr) values or hippocampal volumes. Volumes and spectroscopic resonance intensities were categorized as to whether they were measured from the temporal lobe ipsilateral or contralateral to the predominant electroencephalographic focus. Ipsilateral and contralateral NAA/Cr was negatively correlated with duration of epilepsy. Hippocampal volumes were negatively correlated with duration ipsilaterally but not contralaterally. Frequency of complex partial seizures was not correlated with any of the magnetic resonance measures. However, patients with frequent generalized tonic–clonic seizures had lower NAA/Cr bilaterally and smaller hippocampal volumes ipsilaterally than patients with none or rare generalized tonic–clonic seizures. The results suggest that although an early, fixed injury may cause asymmetric temporal lobe damage, generalized seizures may also cause progressive neuronal dysfunction or loss. Ann Neurol 1999;45:568–576

To our knowledge, petit mal status lasting longer than 2‐3 days has been documented only once [1]. We report a 66 year‐old man with well‐documented, idiopathic generalized epilepsy who developed petit mal status lasting 6 weeks. Valproate levels remained low because of interactions with phenytoin. When phenytoin was discontinued, valproate levels increased, and he progressively improved. Chronic ischemic changes in the white matter may have been an additional factor in the causation and, most likely, in the duration of his status. Exceptionally long status and stupor increase the risk of medical complications. Valproate remains the medication of choice for the treatment of petit mal status. Despite the extraordinary course in this patient, complete recovery took place, confirming the benign nature of even such a prolonged episode.

BACKGROUND: Magnetic resonance imaging (MRI)—based volumetric measurements of the hippocampal formation are useful in detecting unilateral hippocampal sclerosis (HS) in patients with temporal lobe epilepsy. In this pathologic entity, volumetric MRI analysis shows the epileptogenic structure to be atrophic when compared with the normal, nonepileptogenic side. Some authors have suggested that the radiological features of atrophy of medial temporal lobe structures are common in patients with complex partial seizures, but also are seen frequently in other seizure types and can occur even in patients with out epilepsy. OBJECTIVE: To determine if seizures originating in extrahippocampal sites cause gliosis, cell loss, and atrophy of medial temporal lobe structures (ie, HS). METHODS: We studied 110 patients with chronic epilepsy using volumetric MRI measurements of the hippocampal formation. Seventeen patients had pathologically proven HS, 27 patients had seizures due to extratemporal structural lesions, 15 patients had seizures caused by extrahippocampal temporal lobe lesions, 29 patients had primary generalized epilepsy, and 22 patients had secondary generalized epilepsy. RESULTS: All 17 patients with HS showed significantly reduced absolute hippocampal formation volumes of greater than 2 SDs below the mean of the control groups. The preoperative hippocampal formation volume measurements correlated well with the severity of HS on pathological examination. Hippocampal volumes were within the normal range in all patients with primary generalized epilepsy, secondary generalized epilepsy, extratemporal structural lesions, and extrahippocampal temporal lobe lesions. CONCLUSIONS: Seizures originating at extrahippocampal sites do not cause gliosis, cell loss, or atrophy of medial temporal structures. Significant reduction in hippocampal volumes is a specific marker for HS.

The standard form of the principle of mathematical induction (PMI) is well known. Here we compare the standard form to the Cauchy's form of PMI. We present some results proved by the Cauchy's form of PMI. Finally we indicate the relation between the two forms of PMI and the well-ordering principle.

Magnetic resonance imaging (MRI)-based volumetric measurements of thehippo campus and amygdala (AM) are useful in detecting unilateral hippocampal and amygdaloid sclerosis in patients with temporal lobe epilepsy. In these pathologic entities, volumetric MRI analysis shows the epileptogenic structures to be atrophic as compared with the normal, nonepileptogenic side. Some researchers have suggested that the radiological features of atrophy of medial temporal lobe structures are common in patients with complex partial seizures but also are frequently observed in other seizure types and can occur even in patients without epilepsy. We prospectively studied 22 consecutive patients with secondary generalized epilepsy using volumetric MRI measurements of the AM and hippocampal formation (HF). AM and HF ratios (smallerside/larger side) were calculated to assess side-to-side asymmetry. Hippocampal and amygdaloid volumes and ratios were within the normal range in all our patients as compared with those of our normal control population. Significant reduction in hippocampal and amygdaloid volumes is a specific marker for hippocampal and amygdaloid sclerosis.

In this paper we present an extension of Bauer's work about u -means. We consider a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible function φ(x) . This construction allows us to define (u,φ) -means. When φ(x)=x , the (u,φ) -means are the u -means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases.

In this paper we present an extension of Bauer's work about u-means. We consider a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible function ϕ(x). This construction allows us to define (u,ϕ)-means. When ϕ(x)=x, the (u,ϕ)-means are the u-means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases.

We define a periodic quartic spline s from its nodal values. We show existence and uniqueness of such splines and obtain error bounds of the form $${\Vert {f}^{\left(k\right)}-{s}^{\left(k\right)}\Vert }_{\infty }\tilde{-}o\left({h}^{5-k}\right)\left(k=0,\mathrm{...},4\right).$$.