Alexander A. Cherevko

Cerebral aneurysms and arteriovenous malformations are life-threatening hemodynamic pathologies of the brain. While surgical intervention is often essential to prevent fatal outcomes, it carries significant risks both during the procedure and in the postoperative period, making the management of these conditions highly challenging. Parameters of cerebral blood flow, routinely monitored during medical interventions or with modern noninvasive high-resolution imaging methods, could potentially be utilized in machine-learning-assisted protocols for risk assessment and therapeutic prognosis. To this end, we developed a linear oscillatory model of blood velocity and pressure for clinical data acquired from neurosurgical operations. Using the method of Sparse Identification of Nonlinear Dynamics (SINDy), the parameters of our model can be reconstructed online within milliseconds from a short time series of the hemodynamic variables. The identified parameter values enable automated classification of the blood-flow pathologies by means of logistic regression, achieving a balanced accuracy of 74%. Our results demonstrate the potential of this model for both diagnostic and prognostic applications, providing a robust and interpretable framework for assessing cerebral blood vessel conditions.

In this paper we consider the coefficient inverse problem for a second-order nonlinear ODE surrogate model describing hemodynamic parameters during intraoperative neurosurgical measurements. This mathematical model of cerebral hemodynamics is based on the generalized Van der Pol–Duffing equation and described the local interaction of the velocity and pressure of blood flow in cerebral vessels. For each patient, the coefficients of this equation are individual and are determined from clinical data in real-time by solving the coefficient inverse problem. We apply the gradient method for optimization of the cost functional with the analytical finding of initial guess to get the coefficients by clinical data obtained during neurosurgical operation in the vicinity of arterial pathologies. A good initial guess is based on the analytical Fourier method. Statistical analysis of clinical data has shown that the surrogate model equation is sensitive to different types of pathology, which allows intraoperative monitoring of the patient’s condition and assessment of the type of pathology in real time. Numerical results are presented and it is shown that the proposed mathematical model and numerical method predict clinical data well.

INTRODUCTION: Idiopathic normal pressure hydrocephalus (NPH) is a condition characterized by enlargement of the cerebral ventricles and an isolated disturbance of cerebrospinal fluid dynamics, the etiology and pathogenesis of which are still not fully determined.OBJECTIVE: To evaluate changes in hemo- and cerebrospinal fluid dynamics in idiopathic normal pressure hydrocephalus according to phase-contrast MRI data.MATERIALS AND METHODS: Three groups of subjects were formed: patients with NPH (12 people), elderly volunteers with atrophic ventriculomegaly (15 people), a group of healthy volunteers (15 people). For each subject, the data from a routine MRI study, the volumes of gray, white matter and cerebrospinal fluid were assessed, and the volume-velocity characteristics of CSF and blood flows at several levels were calculated.Statistics: For quantitative indicators of cerebrospinal fluid dynamics, the median (Me), 25% and 75% percentiles, and interquartile range were calculated. An intergroup assessment of the significance of differences was carried out using the Mann-Whitney U test and nonparametric multivariate analysis of variance MANOVA.RESULTS: Individual neuroimaging markers of IGT were determined, as well as an increase in the volume-velocity characteristics of CSF flow at the level of the cerebral aqueduct (pDISCUSSION: The data obtained show a significant impairment of cerebrospinal fluid dynamics in patients with NPH, in contrast to elderly volunteers with age-related atrophy and replacement expansion of the cerebrospinal fluid spaces at the level of the brain aqueduct, and also indicates the importance of the venous link in maintaining intracranial volumetric interactions.CONCLUSION: The combined use of a routine protocol and phase-contrast MRI techniques made it possible to identify a number of neuroimaging, hemo- and CSF dynamic changes in patients with NPH in comparison with healthy volunteers, and also, most importantly, with patients of comparable age with the presence of replacement ventriculomegaly against the background of atrophy.

The accuracy of the CABARET scheme (of second order) is compared with the accuracy of the WENO5 and A-WENO schemes (of fifth order in space and fourth order in time) as applied to the computation of various Riemann problems for a nonconvex system of conservation laws describing two-phase porous medium flow with an active additive. It is shown that CABARET is much more accurate than the WENO schemes, especially in exact-solution domains where centered rarefaction waves adjoin shock waves.

The study derives an equation and solves for the first time the problem on the formation and radiation dynamics of a quasi-empty pulsating spherical cavity in a cavitating liquid under the influence of variable sound velocity in a cavitation and cavitation nuclei concentration zone. The data on the cavity dynamics, radiation, and collapsing velocity for a spectrum of initial internal pressures show that, at a maximum gas phase concentration, pulsations are different in the degree of their compression. They have almost identical character: after the first collapse, only a single half-cycle is completed to attain different constant equilibrium radii. The condition of equality between the pressures in a cavitation zone and inside a spherical cavity at its boundary makes it possible to establish a dynamic relation between the volumetric concentration (sound speed) in the cavitation zone and the radius of this spherical cavity for the first time. When calculating and constructing the solution, the condition that the initial cavity size takes a value corresponding to the initial pressure is changed. The dependences of radiation amplitudes over the entire range of applied pressures are plotted. It turns out that the radiation amplitude increases by five orders of magnitude, when the initial pressure inside a cavity changes by three orders of magnitude from 10^–2 to 10^–5 atm.

Aim: To adapt a mathematical model describing the interaction between fluid media and brain matter for the purpose of definition of the dependence between brain ventricle size and capillary pressure in laboratory animals of two genotypes, BALB/c and C57BL/6. Material and methods. The study included 4 male mice of each inbred strain C57BL/6 and BALB/c at the age of 12 weeks. The brain and cerebrospinal fluid system images were obtained using an 11.7 T horizontal MR scanner (Bruker, BioSpec 117/16 USR, Germany). An axial section at the level of -0.5 mm from bregma was chosen as the geometry for mathematical modelling. To describe the data obtained, the mathematical model was adapted by selecting a scale factor based on the known values of the cerebrospinal fluid formation rate for humans and mice. Results and discussion. The same qualitative pattern of relationship between capillary pressure and mean ventricular wall displacement was observed for all animals considered. Although the selected genetic strains of BALB/c and C57Bl mice differ significantly in terms of cerebral ventricle size, these differences in animal genotype did not affect the nature of this relationship. Changing the parameters of the fluid media interaction in the area of compression or moderate ventricular dilation almost does not lead to an exit from the physiologically acceptable capillary pressure value. In this case, the size of the ventricles changes significantly. In the area of large ventricular dilation, in contrast, there is little change in ventricular size, and this is accompanied by a dramatic increase in capillary pressure far beyond physiologic limits. Thus, the change in ventricular size is an adaptive process associated with pressure fluctuations caused by changes in intracranial fluid flow. The mere fact that some of the values reach the zone of physiologically unacceptable pressures associated, in fact, with death, provided that there is practically no change in ventricular size indicates that such a situation is rarely realized and is possible in case of violation of intracranial fluid media flows associated with the fact that the increase in ventricular size limits adaptive capabilities. Conclusions. The presented animal model will further increase the understanding of the pattern we have established and allow us to move on to attempts at prediction.

Aim of the study was to compare the results of mathematical modelling of the dependence between brain ventricle size and capillary pressure for humans and animals based on the equations of multicomponent poroelastic filtration for brain parenchyma. Material and methods. The study included two groups of animals - 4 male mice of each inbred line C57Bl/6 and BALB/C at the age of 12 weeks – and 4 healthy volunteers. The brain and cerebrospinal fluid system images of mice were obtained using an 11.7 T horizontal MR scanner, group of humans were examined using the Ingenia 3.0 T MRI scanner. An axial section at the level of –0.5 mm from bregma in the mouse groups and a frontal slice at the level of the middle of the bodies of the lateral and third ventricles, posterior to the foramen of Monroe in the human group were chosen as the geometry for mathematical modelling. Mathematical modelling is based on the stationary mathematical model of multicomponent poroelastic filtration. Multiple linear regression of mean ventricular wall displacement on fluid media interaction parameters was constructed to compare results obtained. Regression coefficients were compared using nonparametric analysis of variance based on the Kraskell–Wallis criterion and post-hoc Dunn’s criterion with Hill’s correction Results. A qualitative coincidence in the behavior of capillary pressure and mean ventricular wall displacement was demonstrated for the human and mouse groups. No significant differences were found between the two animal lines. For the animals characterized by small ventricular size (BALB/c), greater similarity to humans is observed than for the genetic line with hypertrophied ventricles (C57Bl/6). A significant difference between humans and mice is observed only for capillary-venous interaction. Conclusions. The low variance within groups and insignificant discrepancy between groups indicate the possibility of further accumulation of empirical data to establish correction coefficients of the animal model, which will bring it more in line with the model for humans. Thus, the analyzed models are sufficiently comparable with each other.

An approach is proposed to model hemodynamics in an arteriovenous malformation and its vascular environment during neurosurgical embolization. This approach is based on a combination of the filtration flow model for blood and embolic agent in the malformation and the hydraulic approximation for the vessels surrounding the malformation. The model is described mathematically by a system of integrodifferential hyperbolic equations. The parameters and functions included in the model are determined using clinical data from real patients. Based on this model, the problem of optimal control of multistage embolization was formulated and studied numerically in a special class of controls. Optimal embolization regimes were found for which there is good agreement between the calculated and clinical data. The proposed approach can be used to develop preoperative recommendations about the optimal surgical intervention tactics.

Highlights. An increase in the pulsatility index of intracranial venous blood flow and cerebrospinal fluid flow at the foramen magnum level, and a decrease in arteriovenous delay and an intracranial compliance index indicate disturbances in the pulse wave distribution, and a decrease in compliance/extensibility of the brain due to increased intracranial pressure.Aim. To assess the parameters of hemodynamics and cerebrospinal fluid dynamics in patients with idiopathic intracranial hypertension syndrome according to phase-contrast MRI.Methods. The study included 18 patients with idiopathic intracranial hypertension syndrome and 20 controls, all patient were examined using the Ingenia 3,0T MRI scanner. The analysis was performed using phase-contrast MRI to assess quantitative parameters of hemodynamics and cerebrospinal fluid (CSF) dynamics in 14 different structures. The blood and CSF volumes, pulsatility index (PI), arterio-venous delay, and intracranial compliance index were calculated. The Mann-Whitney U-test reliability was used to assess the differences between the controls and patients.Results. The group of patients had an increased CSF systolic peak at the foramen magnum without significant changes in CSF volume, and significantly increased CSF PI at the cervical level by 11.88% (p˂0,05). There was a tendency toward an increase in the intracranial venous blood volume, as well as a tendency toward significant increase in PI at the straight and superior sagittal sinuses by 1,3 times (p˂0,01, p˂0,05). Moreover, there was a reduction of intracranial arterio-venous delay by 1,9 times (p˂0,05), and a significant decrease in the intracranial compliance index by 1,2 times (p˂0,05).Conclusion. We have assessed the parameters of hemodynamics and CSF dynamics in patients with idiopathic intracranial hypertension and revealed disturbances in CSF dynamics and pulse wave propagation in the intracranial regions. Such changes may indicate a decrease in compliance/increase in stiffness of the brain tissue due to an increase in intracranial pressure and a possible diffuse stagnation of interstitial fluid.

Разработана модель, объясняющая зависимость сопротивления проводящих графеновых пластин, полученных методом многослойной струйной печати, от поверхностного сопротивления слоя и числа слоёв. Печатная проводящая пластина графена является слоистой, что обусловлено методом изготовления пластины. Проведено сравнение результатов моделирования с экспериментальными результатами, полученными авторами. Пластины печатались двумя типами чернил: графеновыми чернилами (1) и графеновыми чернилами с полимерными добавками (2). Достоверность аппроксимации экспериментальных данных по поверхностной проводимости пластин, напечатанных первым и вторым типом не хуже 99.5 % и 98.5 %. соответственно. Модель позволила оценить эффективную толщину печатных слоев графена, образующих проводящую графеновую пластину. Рассмотрен механизм проводимости слоев.