Some Algebraic and Algorithmic Problems in Acoustocerebrography

Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human health but not for all. In this article we describe how the mathematics of acoustocerebrography has become one of the most important applications of mathematics to the problems of brain monitoring as well we will show some algebraic problems which still have to be solved. Acoustocerebrography ([4, 1]) is a set of techniques of visualizing the state of (human) brain tissue and its changes with use of ultrasounds, which mainly rely on a relation between the tissue density and speed of propagation for ultrasound waves in this medium. Propagation speed or, equivalently, times of arriving for an ultrasound pulse, can be inferred from phase relations for various frequencies. Since, due to Kramers-Kronig relations,the propagation speeds depend significantly on the frequency of investigated waves, we consider multispectral wave packages of the form W (n) = ∑Hh=1 Ah · sin(2π ·fh · n/F + ψh), n = 0, . . . , N – 1 with appropriately chosen frequencies fh, h = 1, . . . ,H, amplifications Ah, h = 1, . . . ,H, start phases ψh, h = 1, . . . , H and sampling frequency F. In this paper we show some problems of algebraic and, to some extend, algorithmic nature which raise up in this topic. Like, for instance, the influence of relations between the signal length and frequency values on the error on estimated phases or on neutralizing alien frequencies. Another problem is finding appropriate initial phases for avoiding improper distributions of peaks in the resulting signal or finding a stable algorithm of phase unwinding which is resistant to sudden random disruptions

Detecting cerebrovascular changes in the brain caused by hypertension in atrial fibrillation group using acoustocerebrography.

Acoustocerebrography is a novel, non-invasive, transcranial ultrasonic diagnostic method based on the transmission of multispectral ultrasound signals propagating through the brain tissue. Dedicated signal processing enables the estimation of absorption coefficient, frequency-dependent attenuation, speed of sound and tissue elasticity. Hypertension and atrial fibrillation are well known factors correlated with white matter lesions, intracerebral hemorrhage and cryptogenic stroke numbers. The aim of this study was to compare the acoustocerebrography signal in the brains of asymptomatic atrial fibrillation patients with and without hypertension. The study included 97 asymptomatic patients (40 female and 57 male, age 66.26 ± 6.54 years) who were clinically monitored for atrial fibrillation. The patients were divided into two groups: group I (patients with hypertension) n = 75, and group II (patients without hypertension) n = 22. Phase and amplitude of all spectral components for the received signals from the brain path were extracted and compared to the phase and amplitude of the transmitted pulse. Next, the time of flight and the attenuation of each frequency component were calculated. Additionally, a fast Fourier transformation was performed and its features were extracted. After introducing a machine learning technique, the ROC plot of differentiations between group I and group II with an AUC of 0.958 (sensitivity 0.99 and specificity 0.968) was obtained. It can be assumed that the significant difference in the acoustocerebrography signals in patients with hypertension is due to changes in the brain tissue, and it allows for the differentiating of high-risk patients with asymptomatic atrial fibrillation and hypertension

Treatment data.

<p>Treatment data.</p

Receiver operating characteristic plot of the gbm classifications: The features of the ACG data for 97 patients with asymptomatic atrial fibrillation (40 female, 57 male, age 66.26 +- 6.54 years) were combined using a gradient boosting machine to classify if a patient has hypertension (positive result of the test) or if a patient does not have hypertension (negative result of the test).

<p>The AUC was 0.958 (sensitivity 0.99, specificity 0.968).</p

An outline of the process of forming a multidimensional phase bundle: The compound multispectral signal is being emitted at one side of a patient’s head, and after transversing skull bones and the brain tissue, it is being received on the other side.

<p>Then, the received signal is being decomposed into sine waves with base frequencies equal to the ones included in the original signal, and their phases φ1, …, φH (here H = 10) are reconstructed.</p

Time of flight and attenuation measured for three different frequencies.

<p>The differences between the mean values of the two groups examined were checked using Kruskall-Wallis test.</p

Effects of arachidonyl-2’-chloroethylamide (ACEA) on the protective action of various antiepileptic drugs in the 6-Hz corneal stimulation model in mice

<div><p>Accumulating evidence indicates that cannabinoid CB₁ receptor ligands play a pivotal role in seizures, not only in preclinical studies on animals, but also in clinical settings. This study was aimed at characterizing the influence of arachidonyl-2′-chloroethylamide (ACEA–a selective cannabinoid CB₁ receptor agonist) co-administered with phenylmethylsulfonyl fluoride (PMSF) on the anticonvulsant potency of various antiepileptic drugs (clobazam, lacosamide, levetiracetam, phenobarbital, tiagabine and valproate) in the 6-Hz corneal stimulation model. Psychomotor seizures in male albino Swiss mice were evoked by a current (32 mA, 6 Hz, 3 s stimulus duration) delivered via corneal electrodes. Potential adverse effects produced by the antiepileptic drugs in combination with ACEA+PMSF were assessed using the chimney test (motor performance), passive avoidance task (remembering and acquisition of learning), and grip-strength test (muscular strength). Brain concentrations of antiepileptic drugs were measured by HPLC to exclude any pharmacokinetic contribution to the observed effect. ACEA (5 mg/kg, i.p.) + PMSF (30 mg/kg, i.p.) significantly potentiated the anticonvulsant potency of levetiracetam (<i>P</i><0.05), but not that of clobazam, lacosamide, phenobarbital, tiagabine or valproate in the 6-Hz corneal stimulation model. Moreover, ACEA+PMSF did not significantly affect total brain concentrations of levetiracetam in mice. No behavioral side effects were observed in animals receiving combinations of the studied antiepileptic drugs with ACEA+PMSF. In conclusion, the combined administration of ACEA+PMSF with levetiracetam is associated with beneficial anticonvulsant pharmacodynamic interaction in the 6-Hz corneal stimulation model. The selective activation of cannabinoid CB₁ receptor-mediated neurotransmission in the brain may enhance levetiracetam-related suppression of seizures in epilepsy patients, contributing to the efficacious treatment of epilepsy in future.</p></div