Biorheology

This paper summarizes the recent findings of our laboratory on the mechanical properties of parallel fibered soft connective tissues. Using the improved experimental methodology developed in recent years, it is possible to overcome some of the past experimental difficulties and as a result, more reliable data on the stress-strain relationships for the digital flexor and extensor swine tendons and the medial collateral ligaments of the swine and dog were obtained. Furthermore, the experimental data was used in conjunction with a nonlinear viscoelastic theory to determine the time and history dependent properties of these tissues. A detailed example using the canine medial collateral ligament is reported to illustrate this combined approach.

The primary goal of this investigation is to study whether soft tissue homeostatic responses secondary to decrease or increase in physiological stress levels and range of motion are a change of mechanical properties or a change of mass, or both. Two experimental animal studies are presented. One is a stress and motion deprivation study by immobilization of a rabbit knee, and the other is an increase in stress and motion study by running exercise of the miniature swine. The findings are that changes in stress and motion significantly altered the tissue properties as well as mass in the case of ligaments and digital extensor tendons. Whereas, no significant changes in properties and mass were detected for the digital flexor tendons. Possible mechanisms of the difference in tissue responses to stress and motion are discussed, and nonlinear relationships between stress and tissue remodeling are suggested.

For the description of the mechanical properties of the arterial wall, a number of different models and mathematical approaches of varying complexity have been used. Most investigations based on the elastomeric approach have been related to the elastic properties of arteries, while relatively little is known about the arterial wall viscosity (η _w) and its dependence on circumferential wall stress (σ _t) and smooth muscle tone. For this reason we have examined these relationships on segments of the abdominal aorta, the carotid artery, and the tail artery of normotensive rats in vitro under the condition of strong smooth muscle activation induced by norepinephrine (NE), and during smooth muscle relaxation induced by papaverine (PAP).

This paper deals with the three different approaches which we have employed to study the mechanical properties of cardiovascular tissues. They are: (1) Multiaxial constitutive laws, (2) Uniaxial tensile properties, and (3) Parametric expression for practical use. A lot of results obtained from these different analyses suggest to us that we should evaluate the mechanical properties of natural tissues in different ways depending on practical problems and applications.

This paper reviews the structure (fran molecular to macroscopic level) of collagen, elastin and glycosaminoglycans, with special reference to their functional properties and to how their behavior can be elucidated from in vitro manipulations of the tissues by biochemical means. Modes to analyse the mechanical behavior are briefly discussed and examplified by data from reconstituted collagenous “tissue”. It is concluded that the basic equation for the “non-linear elasticity” component in Fung’s law (and for the reconstituted “tissue” a modification of it) is a powerful tool for analysis of the physiological range of the stress-strain curve. Further, enzymatic “dissection” of one tissue element at a time provides a valuable method for the analysis of tissue element interactions. This approach is illustrated with data fran aortic tissue. It is shown that the mechanical properties of the aorta depend on an interaction between elastic and collagenous elements and that the strength of the tissue is not derived from its collagen fibers per se.

Erythrocytes are unusual in that the cell membrane plays a large and direct role in observed rheological properties. The cell membrane is not a three dimensional material or tissue in the usual sense but being only two molecules thick. It behaves like a liquid sheet of constant thickness and surface area with some elastic properties due in part to protein networks of spectrin and actin on the interior face of the cell membrane. Packed red cells form a viscoelastic fluid which can be sheared, but exhibits a considerable elastic response. The elastic component decreases as the hematocrit is reduced, but is present at all hematocrits. Leukocytes also exhibit viscoelasticity but the properties are primarily dependent on the cell cytoplasm. The cell membrane plays a role only when it is stretched taut. The normal white cell properties have been explored over a wide range of osmolarities, becoming much less viscous and less elastic as the fluid content of the cell increases. White cells also may show spontaneous deformation during which the rheological properties become much stiffer than in the normal passive state.

A characterization of the passive nonlinear thermorheological response of incompressible, curvilinearly orthotropic arterial tissue is presented in the framework of modern continuum thermodynamics. The stress tensor, the specific entropy, the specific internal energy and the heat flux vector are expressed as functionals of the histories of local deformation, temperature and temperature gradient. These functionals are systematically reduced by subjecting them to the requirements of Clausius-Duhem inequality and material frame indifference. The reduced functionals are then specialized to reflect the material symmetry characterizing the tissue by using the histories of the joint invariants of the Green-St. Venant strain tensor and temperature as the independent argument functions. The functionals are expressed in terms of series of multiple integrals and terms upto and including second order integrals are retained. An approach toward experimental determination of the 14 constitutive functions to describe two stress differences is outlined. It is believed that the characterization presented here will provide a rational basis for simpler thermorheological descriptions and experimental programs to include important thermorheologic considerations.

Mechanical properties of human intracranial arteries were studied with regard to their aging changes as well as cerebral vasospasm. There exists a considerable difference in the development of sclerosis between the intracranial and the extracranial arteries. Intracranial arteries are already stiff at birth and become stiffer with age. Their increase in stiffness is attributable to the marked thickening of their walls, which compensates for the decrease of their elastic modulus with age. The pressure-diameter curve of the intracranial vertebral arteries subjected to subarachnoid hemorrhage is biphasic and has a sharp flexion at the pressure of 180 mmHg when their smooth muscle is activated. Pressure elevation yields little change of diameter in the strongly constricted vessel up to the pressure level at the flexion point, above which the constriction is released abruptly. The existence of flexion point at a high pressure level is an important mechanical feature in considering the development of cerebral ischemia produced by the vasospasm.