To clarify the complex interaction between mechanical and biological processes in natural or artificial (surgical) phenomena, the knowledge of the properties of biological tissues is required. It is also of interest for biochemistry, biophysics, cardiology, radiology, physiology, surgery, and pathology. In particular we require a constitutive formulation to be capable of reflecting an actual experimental data over the wide range of deformation and stresses. The constitutive equations should ideally be relatively simple, involving a few parameters, capable to predict the material response of biological tissue subject to a static or dynamic load.

Almost 30 years ago Y. C. Fung and co-authors proposed the algorithm, which became classical and popular nowadays, using in vitro measurements to identify the stress-strain relationship of the arterial wall. The method is based on two integral static equilibrium conditions, comprising the load factors (internal pressure and axial force), radial distributions of strain tensor components, and material constants of the Fung’s pseudo-elastic model. Using the set of measured outer diameters for the combinations of internal pressure and an axil force loads, as well as an empirical distribution of strain components, the integral equations have been discretized, and solved for the four unknown hyperelastic constants.

The new algorithm, proposed in the present work, is based on a 3D theoretical model, and does not require a priori empirical knowledge of any distributions. The two measurements of the principal stretch ratios at the internal and external radii of the arterial vessel cross section serve as boundary conditions for the utilized 3D theoretical model, accounting for an arbitrary hyperelasticity and finite deformations. Applying the least square methodology to provide the best fit between available set of measurements and theoretical prediction, the material constants of the arbitrary nonlinear anisotropic constituent model are identified. As a side effect of this approach the residual stress in artery is identified as well.

Two algorithms serving for in-vivo approaches are developed to identify the stress- strain relationship of the arterial wall based on PPG (photoplethysmography) measurements of the pulse wave velocity (PWV) propagation, or the strain tensor components, based on ultrasound measurements. Examples of applications of a hyperelastic finite deformation 3D nonlinear model, and 2D thin walled membrane shell model to in-vivo identification of biological tissues properties are presented.

Library of Congress Subject Headings

Arteries--Mechanical properties--Mathematical models; Strains and stresses--Mathematical models; Anisotropy

Publication Date


Document Type


Student Type


Degree Name

Mechanical Engineering (MS)

Department, Program, or Center

Mechanical Engineering (KGCOE)


Alexander Liberson

Advisor/Committee Member

Stephen Boedo

Advisor/Committee Member

Hany Ghoneim


Physical copy available from RIT's Wallace Library at QP106.2 .M47 2016


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