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Bio-thermo-mechanics behavior in living viscoelastic tissue under the fractional dual-phase-lag theory

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Abstract

Viscoelasticity is a natural property of biological tissue that is often used as a diagnostic parameter of cancer diagnosis. Recently, it was discovered that the fractional calculus accurately describes the experimental effects of viscoelastic materials. In this work, the model of the thermo-viscoelasticity theory of fractional dual-phase-lag heat conduction law with rheological properties of the volume is constructed to investigate one-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue. The model is applied to the one-dimensional problem of the skin tissue layer with an arbitrary thickness. The bounding plane of the skin tissue is subjected to three different types of thermal loading. The method of transforming Laplace was used and the reversal was measured using the Tzuo process. The influences of fractional dual-phase-lag relaxation parameters and rheological properties of the volume on the distributions of temperature, displacement and stress are obtained and illustrated graphically.

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Abbreviations

λ, μ :

Lamé’s constants

λ, ρ :

Density of tumor tissue

λ, ρ b :

Blood mass density

λ, ω b :

Blood perfusion rate

t :

Time

c :

Specific heat of tumor tissue

L :

Characteristic length

K :

=λ+(2/3)μ, bulk modulus

k :

Thermal conductivity of the tumor tissue

T :

Temperature

T b :

Blood temperature

S ij :

Components of stress deviator tensor

σ ij :

Components of stress tensor

e ij :

Components of strain deviator tensor

ε ij :

Components of strain tensor

u i :

Components of displacement vector

α T :

Coefficient of linear thermal expansion

c o :

=[(λ+2μ)/ρ]1/2, speed of propagation of isothermal elastic waves

c b :

Specific heat of blood

η o :

=ρc/k

γ :

=3KαT

θ :

=T − T0, such that |θ/T0| ≪ 1

e :

=εii, dilatation

T o :

Reference temperature

ε :

Thermoelastic coupling parameter

τ q, τ θ :

Phase-lags

R(t), R y(t):

Relaxation functions

λ, A 0, β, α * :

Empirical constants

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Qassim University, Al Bukairiyah, Saudi Arabia

    Magdy A. Ezzat

  2. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

    Magdy A. Ezzat

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Correspondence to Magdy A. Ezzat.

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Ezzat, M.A. Bio-thermo-mechanics behavior in living viscoelastic tissue under the fractional dual-phase-lag theory. Arch Appl Mech 91, 3903–3919 (2021). https://doi.org/10.1007/s00419-021-01984-4

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