Applications of stereology to the mechanics of soft tissues.

Quantification of microstructure in conjunction with mechanical testing and modeling may provide new insight into problems of soft tissue mechanics with potential clinical significance. Some general observations concerning this as well as brief discussions of specif examples are presented.

An alternate formulation of blood vessel mechanics and the meaning of the in vivo property.

In an effort to bridge the gap between theoretically based vascular mechanics and simpler, clinically relevant compliance models, an alternative complementary energy formulation as well as an improved experimental method are proposed. This formulation generalizes the uniaxial compliance models to multiaxial stretch and twist and clarifies the role of the total in vivo force (measured in biaxial vascular testing) in vessel stability. The measurement of wall thickness when incompressibility is assumed, and the assumption of the existence of an unloaded state are unnecessary. Scattered results from both clinical and mechanical literature are reinterpreted in view of this new understanding of vascular mechanics. Canine saphenous veins (4-5 mm in diameter) conform to the behavior expected from the analysis. Their in vivo property is shown to be a passive property, independent of smooth muscle tone. Redundant particle tracking, control of force and pressure values and the use of papaverine, result, respectively, in strain measurements accurate to within 0.002, experimental control accurate to 0.5% of full range, and repeatable experiments over a few days. The validated system and the new formulation show great potential for exploiting the benefits of innovative experimental design and statistically reliable data analysis.

On large periodic motions of arteries.

The large, radial periodic motion of an artery subjected to a dynamic inner pressure is studied through the use of finite deformation theory of elastic materials. The artery is assumed to behave as an isotropic, homogeneous and incompressible elastic material. Expressions for intramural pressure and wall stresses are obtained as a function of the large periodic motion. Dynamic effects are shown to both increase the diastolic pressure and decrease the systolic pressure. It is also shown that, under certain conditions, the artery may experience a negative intramural pressure, in which case the artery may collapse. The present study predicts very large circumferential stress and stress gradients which might lead the artery to arteriosclerosis.

Quantification of strains in biaxially tested soft tissues.

A technique for the quantification of the strain field in the central region of biaxially tested planar soft tissues is presented. A vidicon-based image analysis system interfaced to a PDP 11/34 minicomputer is employed to track particles affixed to the specimen surface in real-time, from which the strains are inferred. Illustrative results are given for tests on excised canine pleural specimens on which four particles were affixed. The technique is applicable, however, to any planar soft tissue and any number of tracking particles. This procedure is recommended over previously used methods when testing anisotropic tissues.

The distribution of strain in the human cornea.

Experimental data on the mechanics of human cornea is meager and sometimes flawed. Moreover, questions regarding the correct material symmetry and the role of the fibrous microstructure are usually glossed over when mechanical models of the cornea and corneal shape changing procedures are presented. Accordingly, the deformation of 14 intact human corneas was measured for five pressures in the physiologic range (0, 5, 10, 25 and 45 cmH2O) by tracking small, self-adherent particles placed on their anterior surfaces. The meridional strains, calculated in five regions assuming axisymmetric deformation, are small; the average strain in the apical region being 1.14% at 45 cmH2O. Results also indicate that the strain distribution is unexpectedly nonuniform with statistically significant (p < 0.01, typical) variations between regions and a minimum occurring approximately half-way between apex and limbus. To better understand these results, a finite-element model (FEM) of the cornea was constructed and used to simulate the experiment. The heterogeneous model shows that our data may reflect the changing fiber orientation along a meridian suggested in the literature. The implications of a link between microstructure and mechanics are discussed in light of clinical procedures, such as radial keratotomy, the outcomes of which are dependent on corneal mechanical properties.

The effects of cryopreservation on the biaxial mechanical properties of canine saphenous veins.

The experimental and analytical methods presented in the companion paper [1] are used here to study the effects of cryopreservation on the in vitro biaxial random-elastic mechanical properties of canine saphenous veins. The properties of specimens tested in their physiological range of loadings immediately after thawing were not significantly different from their properties before cryopreservation. However, they stiffened significantly in the few hours following thawing. This effect was not observed for aging fresh specimens, nor for cyanide-poisoned specimens, indicating that the static tone of the venous smooth muscle may be affected by cryopreservation and thawing, but the elastin and collagen fibers are most likely unaffected.

Mechanisms for rupture of pancreatic pseudocysts. A biomechanical evaluation.

Considerable morbidity and mortality continue to attend the rupture of pancreatic pseudocysts. If the mechanism responsible for rupture were known, it is conceivable that patients with impending rupture could be identified and appropriate measures taken. In an effort to determine whether pseudocysts rupture from increased internal pressure, in vivo pressure measurements and stress calculations were performed in 10 intact pseudocysts. Next, fresh strips of pseudocyst wall tissue from seven patients were placed in a tensile testing machine, and ultimate strength (peak stress capacity) was determined. The average in vitro peak stress prior to yield and separation was 12.30 +/- 2.75 Kg-F/cm2. Both this value, and calculated internal pressures required to achieve this level of wall stress, are more than 100 times greater than the corresponding values ever measured in humans. In all likelihood, pseudocysts rupture from diminished wall thickness resulting from immaturity and/or enzymatic debridement.

A model for estimating corneal stiffness using an indenter.

A finite element model that simulates indentation of the cornea was generated to examine the feasibility of using indentation data to determine mechanical properties. A layered model which included geometric nonlinearities was necessary to characterize the indentation process. Results indicate that a secant modulus could be determined by measuring indenter force and contact area.

Finite element based mechanical models of the cornea for pressure and indenter loading.

BACKGROUND: In this article, we examine the finite element method and its use in mechanical modeling of the cornea. METHODS: Both linear elastic and geometrically nonlinear models are considered. The effects of corneal geometry, boundary conditions, thickness, and the number of layers in the model are determined. RESULTS: Results indicate that, for intraocular pressure loading, the thickness and the choice of boundary conditions at the limbus are significant. CONCLUSIONS: A model of tonometry showed that simulating the layered nature of the cornea and including the increased flexibility of large deformation are critical.

Two-dimensional stress-strain relationship for canine pericardium.

Two-dimensional pseudoelastic mechanical properties of the canine pericardium were investigated in vitro. The pericardium was assumed to be orthotropic. The material symmetry axis was determined a priori and aligned with the stretching axis. Various biaxial stretching tests were then performed and a set of data covering a wide range of strains was constructed. This complete data set was fitted to a new exponential type constitutive model, and a set of true material constants was determined for each specimen. Using the constitutive model and the true material constants, the results from constant lateral force tests and constant lateral displacement tests were predicted and compared with experiment.

A new approach to mechanical testing and modeling of biological tissues, with application to blood vessels.

The collection and processing of data from mechanical tests of biological tissues usually follow classical principles appropriate for studying engineering materials. However, difficulties specific to biological tissues have generally kept such methods from producing quantitative results for statistically-oriented studies. This paper demonstrates a different approach linking testing and data reduction with modern statistical tools. Experimental design theory is used to minimize the detrimental effects of collinearity on the stability of the parameters in constitutive equations. The numerical effects of time-dependent biasing factors such as viscoelasticity are reduced by randomizing the order of collection of data points. Some of the parameters of the model are allowed to vary from specimen to specimen while the others are computed once from a database of designed experiments on several specimens. Finally, a new self-modeling algorithm based on principal component analysis is used to generate uncorrelated parameters for a model that is linear in its specimen-dependent parameters. The method, associated with a recently published complementary energy formulation for vascular mechanics, is illustrated with biaxial canine saphenous vein data. Results show that three specimen-dependent linear parameters are enough to characterize the experimental data and that they can be repeatedly estimated from different data sets. Independently collected biaxial inflation data can also be predicted reasonably well with this model.

Mechanical behavior of excised canine visceral pleura.

A computer-controlled optical electromechanical biaxial test system was employed to study the mechanical response of excised sheets of canine visceral pleura. Three classes of tests were performed: uniform biaxial stretching tests and tests in which the specimen was cyclically stretched along one axis while either the load or dimension was maintained at a prescribed level in the orthogonal direction. The tests were defined completely within the software. Strain was inferred from tracking four particles affixed to the central region of the specimen surface. The visceral pleura was found to behave similarly to other biological soft tissues and required preconditioning to yield repeatable responses. In addition, the visceral pleura appeared to possess in-plane transverse isotropic material symmetry and to exhibit strong in-plane mechanical coupling at lower loads. The data presented herein is sufficient for determination of certain three-dimensional constitutive laws which are essential for further biomechanical analyses of the visceral pleura's role in lung response.

Pseudoelasticity of excised visceral pleura.

A pseudostrain-energy function is proposed for describing the behavior of excised sheets of canine visceral pleura. Pseudoelastic material constants are determined from experimental biaxial data by employing a nonlinear least-squares algorithm. The agreement between theory and experiment is shown to be quite good. Furthermore, the visceral pleura studied appears to be inelastic and to exhibit in-plane isotropy. Comparison with previous works is discussed.

A mechanical model of the cornea: the effects of physiological and surgical factors on radial keratotomy surgery.

A finite element-based computer simulation of radial keratotomy surgery was conducted to study, in particular, curvature changes of the central clear zone in human cornea under various physiological and surgical conditions. Corneal tissue was assumed to behave as a nearly incompressible, linear elastic, homogeneous, isotropic material undergoing small deformation. The Young's modulus was determined by using the model to predict the surgical outcome of a representative patient. The results of the simulation are in qualitative agreement with clinical experience indicating the potential of finite element modeling as an aid to the surgeon in evaluating variables.