Flow in arteries in the presence of stenosis.

Of concern in the paper is a study of blood flow in an arterial segment having a stenosis. The artery is modelled as an initially stressed orthotropic elastic tube filled with a viscous incompressible fluid. The analysis is based on the assumption of the presence of a mild stenosis in the artery. Blood is treated as a Newtonian fluid. The effect of the surrounding connective tissues on the motion of the wall has been incorporated. Propagation of small amplitude harmonic waves, generated due to the flow of blood where the wave length is large compared to the radius of the arterial segment, is is considered in detail.

Effect of material damping on bone remodelling.

This paper considers the effect of internal material damping on the stresses, strains, and surface and internal remodelling behaviour in a section of axisymmetrical bone with a force-fitted axially oriented medullary pin. The bone response to several loading situations is modelled using visco-elastic equations. An approximate method is developed to analyse the proposed mathematical model. By considering a numerical example, the effect of material damping on the remodelling stresses is quantified.

A study of rotational brain injury.

Of concern in the paper is an investigation on brain injuries which may occur owing to an input angular acceleration of the head. The study is based on the use of an improved mathematical model for the cranium. The eccentricity of the braincase is incorporated through the consideration of a prolate spheroidal shell as the representative of the skull. Also the dissipative mechanical behaviour of the brain material (as per the observations of experimenters) has been accounted for by considering the material contained in the shell as viscoelastic. The problem is formulated in terms of prolate spheroidal coordinates. The singularities of the governing equations of motion (when expressed in the prolate coordinate system) are removed by a suitable transformation of the concerned dependent variable, viz. the one that stands for the angular displacement of a representative point of the system. In the first place the solution of the boundary value problem is sought in the Laplace transform space, by employing a finite difference technique. Use of the alternating-direction-implicit method together with Thomas algorithm was made for obtaining the angular acceleration in the transformed space. The Laplace inversion is also carried out with the help of numerical procedures (Gauss quadrature formula is used for this purpose). The results of the parametric study are presented through graphs. The plots illustrate the shear stresses and strains in the brain medium. A meaningful comparison of the computational results with those of previous investigations indicate that the eccentricity of the braincase plays a significant role in causing injury to the brain.

Dynamic response of arterial walls in vivo.

By the use of non-linear constitutive equations suitable for the characterization of anisotropic viscoelastic incompressible materials under finite deformations, the paper is devoted to analytical study on the dynamic stress field in arterial walls under the combined action of the pressure of blood on the inner surface and the pressure from the neighbouring components of the body on the outer surface. By using short time range approximations, the magnitudes of the radial and circumferential stresses are examined at various locations of the vascular wall and for different time intervals. It is observed that consideration of the mechanical influence of the external tissues and the inertial forces makes the derived stress field quite close to the experimental results reported recently by Fung et al. (1979), in comparison to the results of Cheung et al. (1972), who did not consider the aforementioned factors. It can thus be concluded that these factors need be considered for the studies of the stress field in arteries in vivo.

A free-vibration analysis for the human cranial system.

The problem of free-vibration of the cranial vault is studied in the paper by taking into account the dissipative material behaviour of both the skull and the brain. Two mathematical models are considered for this purpose. In one model, the layered structure (inner table, diploë and outer table) of the skull is considered, the outer surface of the skull being assumed to be traction-free while the second model assumes the homogeneity of the skull but takes into account the mechanical influence of the scalp. Results of numerical computation show that the dissipative material behaviour of the skull as well as the brain and also the mechanical influence of the scalp have a significant effect on the frequency spectrum of the freely vibrating cranial system.

A non-Newtonian fluid model for blood flow through arteries under stenotic conditions.

This paper presents an analytical study on the behaviour of blood flow through an arterial segment having a mild stenosis. The artery has been treated as a thin-walled initially stressed orthotropic non-linear viscoelastic cylindrical tube filled with a non-Newtonian fluid representing blood. The analysis is restricted to propagation of small-amplitude harmonic waves, generated due to blood flow whose wave length is large compared to the radius of the arterial segment. For the equations of motion of the arterial wall consideration is made of a pair of appropriate equations derived by using suitable constitutive relations and the principle of superimposition of a small additional deformation on a state of known finite deformation. It has been shown through numerical computations of the resulting analytical expressions that the resistance to flow and the wall shear increase as the size of the stenosis increases. A quantitative analysis is also made for the frequency variation of the flow rate at different locations of the artery, as well as of the phase velocities and transmission per wavelength.

Momentum integral method for studying flow characteristics of blood through a stenosed vessel.

Taking into consideration the slip velocity at the wall of a blood vessel, a mathematical model is developed in the paper for the study of blood flow through a mammalian blood vessel in the presence of a stenosis. By employing the momentum integral technique, analytical expressions for the velocity profile, pressure gradient and skin-friction are derived. The condition for an adverse pressure gradient is also deduced. It is observed that the slip velocity bears the potential to influence the velocity distribution of blood to a remarkable extent and to reduce considerably the pressure-gradient as well as the skin-friction.

Formation of a boundary layer in steady-state blood flow.

This paper is devoted to a study of boundary layer formation in the steady flow of blood through the human aorta. Blood is treated as an incompressible fluid. Consideration is given to a flat-top velocity profile which combines the potential flow with the boundary layer; expressions for the displacement thickness, skin-friction and pressure in the entry region are derived.

Effect of initial stresses on the wave propagation in arteries.

A theoretical analysis for the problem of wave propagation in arteries is presented. Blood is treated as a Newtonian, viscous incompressible fluid. On the basis of information derived from experimental investigations on the mechanical properties of wall tissues, the arterial wall is considered to be nonlinearly viscoelastic and orthotropic. The analysis is carried out for a cylindrical artery, under the purview of membrane theory, by taking account the effect of initial stresses. The motion of the wall and that of the fluid are assumed to be axisymmetric. Particular emphasis has been paid to the propagation of small amplitude harmonic waves whose wavelength is large compared to the radius of the vessel. By employing the equations of motion of the fluid and those for the wall, together with the equations of continuity, a frequency equation is derived by exploiting the conditions of continuity of the velocity of the arterial wall and that of blood on the endosteal surface of the wall. In order to illustrate the validity of the derived analytical expressions a quantitative analysis is made for the variations of the phase velocities as well as the transmission coefficient with frequency corresponding to different transmural pressures which relate to different initial stresses. Computational results indicate that phase velocities increase with the increase of transmural pressures.

Induced electric and magnetic fields due to wave propagation in a tubular bone.

Electric and magnetic fields in tubular bones induced due to the propagation of travelling axisymmetric torsional waves, are determined in the paper by accounting for the piezoelectricity, inhomogeneity and anisotropy of osseous tissues. Using the derived expressions and experimentally determined values of the involved physical constants, numerical values of the displacement and stress fields, and also the induced fields are computed for points at different locations of the bone specimen.