Igor Szczyrba

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We numerically model the brain dynamics during and after impulsive head translations using linear Partial Differential Equations (PDEs) describing viscoelastic solids and a nonlinear generalization of these PDEs describing incompressible, viscoelastic fluids. The brain matter motion and the sensitivity of the solutions with respect to the skull's geometry(More)
INTRODUCTION For over fifty years the theory of viscoelasticity has played a major role in modeling brain injuries. The main premise of this approach is that the brain is injured when the strain field, created in the brain tissue by shear waves, assumes sufficiently high values. In particular, the linear Voigt PDE system describing the motion of shear waves(More)
INTRODUCTION The Head Injury Criterion limit, HIC 1000T =1000, was developed based on skull fracture data (short time intervals T) and longer duration head translations that lead to Closed Head Injuries (CHI). However, recent results imply that the HIC limits depend on the time interval T and the victim's age [1]. Since the HIC lacks a clear physical(More)
We numerically model the human brain dynamics in realistic 2D cross-sections during traumatic scenarios corresponding to the Head Injury Criterion's critical value HIC 36 =1000. Our simulations are based on the Kelvin-Voigt Partial Differential Equations that treat the brain tissue as a viscoelastic solid and on our nonlinear generalization of these linear(More)
We numerically model the effects of repetitive human head motions in traumatic scenarios that are associated with severe brain injuries. Our results are based on the linear Kelvin-Voigt brain injury model, which treats the brain matter as a viscoelastic solid, and on our nonlinear generalization of that model, which emulates the gel-like character of the(More)
We investigate how a nonlinear stress-strain relation (that leads to a stiffening of the brain matter under strain) influences the brain dynamics in traumatic situations. We numerically simulate rapid rotational accelerations and decelerations of a human head using our generalization of the viscoelastic Kelvin-Voigt brain injury model that includes an(More)
We study generalizations of the sequence of the n-anacci constants that are constructed from the ratio limits generated by linear recurrences of an arbitrary order n with equal integer weights m. We derive the analytic representation of the class C ∞ of these ratio limits and prove that, for a fixed m, the ratio limits form a strictly 1 increasing sequence(More)
We introduce geometric representations of the sequence of the n-anacci constants and generalizations thereof that consist of the ratio limits generated by linear recurrences of an arbitrary order n with equal real weights p > 0. We represent the n-anacci constants and their generalizations geometrically by means of the dilation factors of 1 dilations(More)
— We investigate numerically which properties of the human brain cause Diffuse Axonal Injuries (DAI) to appear in a scattered and pointwise manner near the gray/white matter boundary, mostly in the white matter. These simulations are based on our dually-nonlinear, vis-coelastic, fluid Traumatic Brain Injury model, which includes a nonlinear stress/strain(More)