Modeling Medicine Propagation in Tissue: Generalized Statement

Селезов, І. Т.; Kryvonos, Iu. G.

doi:10.1007/s10559-017-9955-1

Cited by 4 publications

(4 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note the method of numerical inversion presented in [21]. This method has been used in [22] to solve a new IBV problem on a finite interval for a hyperbolic equation with relaxation parameter (parabolic operator). The original is determined by the formula where , ,…”

Section: Other Approaches and Some Recent Onesmentioning

confidence: 99%

Somapplicationsofnumericalinversionofthelaplacetransforminproblemsofpropagationofwaveoscillations

Селезов¹

2018

Visn. Zaporiz. nacuniv.Fiz.-mat. nauki

View full text Add to dashboard Cite

Three algorithms for the numerical inversion of the Laplace transform are considered, for solving specific applied problems of wave dynamics. Comparing the algorithm based on the shifted Lagendre polynomials with the standart solutions shows that there exists an optimal number of terms in expansions. It is also established from the consideration of various algorithms, including modern ones, that the accuracy of all algorithms of numerical inversion decreases with increasing time t (with decreasing in the transformation parameter p in the complex plane). These two conclusions are a consequence of the incorrectness of the inversion Laplace transform problem. The application of the expansion method in the sine arcs to the solution of the initial-boundary value problem (IBV problem) of the study of the propagation of pulse pressure waves in blood vessels is presented. It is based on the equations of the cylindrical shell and blood pressure, and includes the matching conditions at the junction of the vessels, excitation of the pulse pressure wave, its propagation to the junction, reflected and transmitted waves. Application of the same method is presented for the problem of evolution of the free surface of water waves due to local bottom excitation sources that are repeated in time.

show abstract

Section: Other Approaches and Some Recent Onesmentioning

confidence: 99%

Somapplicationsofnumericalinversionofthelaplacetransforminproblemsofpropagationofwaveoscillations

Селезов¹

2018

Visn. Zaporiz. nacuniv.Fiz.-mat. nauki

View full text Add to dashboard Cite

show abstract

“…The first term in (5) is the main part of the operator, the second term remains as part of the operator. In (6), the term f j is an operator of lower order than the first term. It is assumed that the coefficients a ilq and b jlq are constants, but they can depend on a small parameter ε r ≪ 1.…”

Section: Hyperbolic Degeneration and The Finiteness Of The Velocity Omentioning

confidence: 99%

“…If the system of equations (5) is of hyperbolic type, then in the case of the well-posed Cauchy problem for (5), (6), solutions exist in the region in the form of weak propagating discontinuities (discontinuities of derivatives of the highest order in the differential operator). This corresponds to reality in actual physical media or systems, any perturbation propagates at a finite rate determined by the properties of the medium or system.…”

Section: Hyperbolic Degeneration and The Finiteness Of The Velocity Omentioning

confidence: 99%

“…After Maxwell, generalized hyperbolic models describing the propagation of heat, diffusion, and others have been developed, cited in (Selezov and Krivonos, 2015) [5]. We also note the latest study on the injection of a medical preparation into tissue, where a new generalization of the diffusion equation to a hyperbolic equation is presented (Selezov & Kryvonos, 2017) [6]. From the mathematical point of view, in essence, a second-order parabolic operator (predicting the perturbation propagation with infinite velocity) was generalized to a hyperbolic operator of the second order (but now describes the perturbation propagation with finite velocity).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalization and application of the Cauchy-Poisson method to elastodynamics of a layer and the Timoshenko equation

Селезов¹

2018

Math. Model. Comput.

View full text Add to dashboard Cite

The Cauchy-Poisson method is extended to n-dimensional Euclidean space so that to obtain partial differential equations (PDEs) of a higher order. The application in the construction of hyperbolic approximations is presented, generalizing and supplementing the previous investigations. Restrictions on derivatives in Euclidean space are introduced. The hyperbolic degeneracy by parameters and its realization in the form of necessary and sufficient conditions are considered. As a particular case of 4-dimensional Euclidean space, keeping operators up to the 6th order, we obtain a generalized hyperbolic equation of transverse (bending) vibrations of plates with coefficients depending only on the Poisson number. Numerical calculations are carried out and presented. This equation includes, as special cases, all the known equations of Bernoulli-Euler, Kirchhoff, Rayleigh, Timoshenko. It should be noted that the refined equation of bending oscillations of a beam, firstly presented by Timoshenko, must be considered as the development of Maxwell's and Einstein's investigations on the perturbation propagation with finite velocity in media. For the first time, the conformity with the Cosserat theory is noted.

show abstract

Development and Application of the Cauchy–Poisson Method to Layer Elastodynamics and the Timoshenko Equation

Селезов

2018

Cybern Syst Anal

View full text Add to dashboard Cite

Modeling Medicine Propagation in Tissue: Generalized Statement

Cited by 4 publications

References 10 publications

Somapplicationsofnumericalinversionofthelaplacetransforminproblemsofpropagationofwaveoscillations

Somapplicationsofnumericalinversionofthelaplacetransforminproblemsofpropagationofwaveoscillations

Generalization and application of the Cauchy-Poisson method to elastodynamics of a layer and the Timoshenko equation

Development and Application of the Cauchy–Poisson Method to Layer Elastodynamics and the Timoshenko Equation

Contact Info

Product

Resources

About