A layered agarose approach to fabricate depth-dependent inhomogeneity in chondrocyte-seeded constructs

Inspired by the depth-dependent inhomogeneity of articular cartilage, it was hypothesized that a novel layered agarose technique, using a 2% (wt/vol) top and a 3% (wt/vol) bottom layer, would create an inhomogenous tissue construct with distinct material properties in conjoined regions. The biochemical and mechanical development of these constructs was observed alongside uniform 2% and 3% constructs. Initially, uniform 3% agarose disks had the highest bulk Young's modulus (E(Y) approximately 28 kPa) of all groups. After 28 days of culture in 20% FBS-containing media, however, uniform 2% chondrocyte-seeded constructs achieved the highest Young's modulus compared to bilayered and 3% agarose disks. Though all three groups contained similar GAG content ( approximately 1.5% ww), uniform 2% agarose disks on day 28 possessed the highest collagen content ( approximately 1% ww). Unlike in either homogeneous construct type, microscopic analysis of axial strain fields in bilayered constructs in response to applied static compression revealed two mechanically disparate regions on day 0: a softer 2% layer and a stiffer 3% layer. With time in culture, this inhomogeneity became less distinct, as indicated by increased continuity in both the local displacement field and local E(Y), and depended on the level of FBS supplementation of the feed media, with lower FBS concentrations (10%) more closely maintaining the original distinction of material properties. These results shed positive light on a layered agarose technique for the production of inhomogeneous bilayered chondrocyte-seeded agarose constructs with applications for investigations of chondrocyte mechanotransduction and for possible use in the tissue engineering of inhomogeneous articular cartilage constructs.

Removal of the superficial zone of bovine articular cartilage does not increase its frictional coefficient

OBJECTIVE

To investigate the role of the superficial zone in regulating the frictional response of articular cartilage. This zone contains the superficial protein (SZP), a proteoglycan synthesized exclusively by superficial zone chondrocytes and implicated in reducing the friction coefficient of cartilage.

DESIGN

Unconfined compression creep tests with sliding of cartilage against glass in saline were carried out on fresh bovine cylindrical plugs (slashed circle Ø6 mm, n=35) obtained from 16 bovine shoulder joints (ages 1-3 months). In the first two experiments, friction tests were carried out before and after removal of the superficial zone ( approximately 100 microm), in a control and treatment group, using two different applied load magnitudes (4.4 N and 22.2 N). In the third experiment, friction tests were conducted on intact surfaces and the corresponding microtomed deep zone of the same specimen.

RESULTS

In all tests the friction coefficient exhibited a transient response, increasing from a minimum value (mu(min)) to a near-equilibrium final value (micro(eq)). No statistical change (P>0.5) was found in micro(min) before and after removal of the superficial zone in both experiments 1 and 2. However, micro(eq) was observed to decrease significantly (P<0.001) after removal of the surface zone. Results from the third experiment confirm that micro(eq) is even lower at the deep zone. Surface roughness measurements with atomic force microscopy (AFM) revealed an increase in surface roughness after microtoming. Immunohistochemical staining confirmed the presence of SZP in intact specimens and its removal in microtomed specimens.

CONCLUSIONS

The topmost ( approximately 100 microm) superficial zone of articular cartilage does not have special properties which enhances its frictional response.

Single-cell elastography: probing for disease with the atomic force microscope

The atomic force microscope (AFM) is emerging as a powerful tool in cell biology. Originally developed for high-resolution imaging purposes, the AFM also has unique capabilities as a nano-indenter to probe the dynamic viscoelastic material properties of living cells in culture. In particular, AFM elastography combines imaging and indentation modalities to map the spatial distribution of cell mechanical properties, which in turn reflect the structure and function of the underlying cytoskeleton. Such measurements have contributed to our understanding of cell mechanics and cell biology and appear to be sensitive to the presence of disease in individual cells. This chapter provides a background on the principles and practice of AFM elastography and reviews the literature comparing cell mechanics in normal and diseased states, making a case for the use of such measurements as disease markers. Emphasis is placed on the need for more comprehensive and detailed quantification of cell biomechanical properties beyond the current standard methods of analysis. A number of technical and practical hurdles have yet to be overcome before the method can be of clinical use. However, the future holds great promise for AFM elastography of living cells to provide novel biomechanical markers that will enhance the detection, diagnosis, and treatment of disease.

Dynamic osmotic loading of chondrocytes using a novel microfluidic device

Many cells exhibit disparate responses to a mechanical stimulus depending on whether it is applied dynamically or statically. In this context, few studies have examined how cells respond to dynamic changes of the extracellular osmolality. In this study, we hypothesized that the cell size change response of cultured articular chondrocytes would be dependent on the frequency of applied osmotic loading. To test this hypothesis, we developed a novel microfluidic device, to apply hydrostatic pressure-driven dynamic osmotic loading by applying composition modulated flow, adapted from Tang and co-workers. This microfluidic device was used to study osmotic loads of +/-180 mOsm at a frequency up to 0.1 Hz with a constant minimal fluid-shear stress, and permit real-time monitoring of cell responses. Bovine articular chondrocytes were observed to exhibit increasing changes in cell volume with decreasing osmotic loading frequency. When the cell volume response was modeled by an exponential function, chondrocytes exhibited significantly different volume change responses to dynamic osmotic loading at 0.0125 Hz and static osmotic loading applied for a period of four minutes (Delta = +/-180 mOsm relative to the isotonic 360 mOsm). The intracellular calcium response at 0.0125 Hz was also monitored and compared with the response to static loading. Coupled with phenomenological or constitutive models, this novel approach could yield new information regarding cell material properties in response to dynamic loading that may contribute new insights into mechanisms of cellular homeostasis and mechanotransduction.

Creating alignment and anisotropy in engineered heart tissue: role of boundary conditions in a model three-dimensional culture system

Electrical and mechanical anisotropy arise from matrix and cellular alignment in native myocardium. Generation of anisotropy in engineered heart tissue will be required to match native properties and will provide immediate opportunities to investigate the genesis and structural determinants of functional anisotropy. We investigated the influence of geometry and boundary conditions on fibroblast alignment in thin collagen gels. Consistent with previous reports, we found that human dermal fibroblasts align parallel to free edges in partially constrained gels; in contrast to at least one report, fibroblasts in fully constrained gels remained randomly aligned independent of geometry. These experiments allowed us to distinguish between two possible mechanisms for such alignment. Mean orientations that followed the shape of the free edges and stronger alignment nearest the free edges in gels with a variety of geometries suggested that cells align parallel to a local free boundary rather than to local lines of tension. These findings focus attention on the presence of voids and free surfaces such as the endocardium and epicardium, cleavage planes, and blood vessels in governing cell and fiber alignment in developing and remodeling myocardium, myocardial scar tissue, and engineered heart constructs.

Buckling of actin stress fibers: a new wrinkle in the cytoskeletal tapestry

Intracellular tension is considered an important determinant of cytoskeletal architecture and cell function. However, many details about cytoskeletal tension remain poorly understood because these forces cannot be directly measured in living cells. Therefore, we have developed a method to characterize the magnitude and distribution of pre-extension of actin stress fibers (SFs) due to resting tension in the cytoskeleton. Using a custom apparatus, human aortic endothelial cells (HAECs) were cultured on a pre-stretched silicone substrate coated with a fibronectin-like polymer. Release of the substrate caused SFs aligned in the shortening direction in adhered cells to buckle when compressed rapidly (5% shortening per second or greater) beyond their unloaded slack length. Subsequently, the actin cytoskeleton completely disassembled in 5 sec and reassembled within 60 sec. Quantification of buckling in digital fluorescent micrographs of cells fixed and stained with rhodamine phalloidin indicated a nonuniform distribution of 0-26% pre-extension of SFs in non-locomoting HAECs. Local variability suggests heterogeneity of cytoskeletal tension and/or stiffness within individual cells. These findings provide new information about the magnitude and distribution of cytoskeletal tension and the dynamics of actin stress fibers, and the approach offers a novel method to elucidate the role of specific cytoskeletal elements and crosslinking proteins in the force generating apparatus of non-muscle cells.

Contribution of laminar myofiber architecture to load-dependent changes in mechanics of LV myocardium

The ventricular myocardium consists of a syncytium of myocytes organized into branching, transmurally oriented laminar sheets approximately four cells thick. When systolic deformation is expressed in an axis system determined by the anatomy of the laminar architecture, laminar sheets of myocytes shear and laterally extend in an approximately radial direction. These deformations account for ~90% of normal systolic wall thickening in the left ventricular free wall. In the present study, we investigated whether the changes in systolic and diastolic function of the sheets were sensitive to alterations in systolic and diastolic load. Our results indicate that there is substantial reorientation of the laminar architecture during systole and diastole. Moreover, this reorientation is both site and load dependent. Thus as end-diastolic pressure is increased and the left ventricular wall thins, sheets shorten and rotate away from the radial direction due to transverse shearing, opposite of what occurs in systole. Both mechanisms of thickening contribute substantially to normal left ventricular wall function. Whereas the relative contributions of shear and extension are comparable at the base, sheet shear is the predominant factor at the apex. The magnitude of shortening/extension and shear increases with preload and decreases with afterload. These findings underscore the essential contribution of the laminar myocardial architecture for normal ventricular function throughout the cardiac cycle.

Relating myocardial laminar architecture to shear strain and muscle fiber orientation

Cardiac myofibers are organized into laminar sheets about four cells thick. Recently, it has been suggested that these layers coincide with the plane of maximum shear during systole. In general, there are two such planes, which are oriented at +/-45 degrees to the main principal strain axes. These planes do not necessarily contain the fiber axis. In the present study, we explicitly added the constraint that the sheet planes should also contain the muscle fiber axis. In a mathematical analysis of previously measured three-dimensional transmural systolic strain distributions in six dogs, we computed the planes of maximum shear, adding the latter constraint by using the also-measured muscle fiber axis. Generally, for such planes two solutions were found, suggesting that two populations of sheet orientation may exist. The angles at which the predicted sheets intersected transmural tissue slices, cut along left ventricular short- or long-axis planes, were strikingly similar to experimentally measured values. In conclusion, sheets coincide with planes of maximum systolic shear subject to the constraint that the muscle fiber axis is contained in this plane. Sheet orientation is not a unique function of the transmural location but occurs in two distinct populations.

Mechanism underlying mechanical dysfunction in the border zone of left ventricular aneurysm: a finite element model study

BACKGROUND

The global left ventricular dysfunction characteristic of left ventricular aneurysm is associated with muscle fiber stretching in the adjacent noninfarcted (border zone) region during isovolumic systole. The mechanism of this regional dysfunction is poorly understood.

METHODS

An anteroapical transmural myocardial infarct was created by coronary arterial ligation in an adult Dorset sheep and was allowed to mature into left ventricular aneurysm for 10 weeks. The animal was imaged subsequently using magnetic resonance imaging with simultaneous recording of intraventricular pressures. A realistic mathematical model of the three-dimensional ovine left ventricle with an anteroapical aneurysm was constructed from multiple short-axis and long-axis magnetic resonance imaging slices at the beginning of diastolic filling.

RESULTS

Three model simulations are presented: (1) normal border zone contractility and normal aneurysmal material properties; (2) greatly reduced border zone contractility (by 50%) and normal aneurysmal material properties; and (3) greatly reduced border zone contractility (by 50%) and stiffened aneurysmal material properties (by 1000%). Only the latter two simulations were able to reproduce experimentally observed stretching of border zone fibers during isovolumic systole.

CONCLUSIONS

The mechanism underlying mechanical dysfunction in the border zone region of left ventricular aneurysm is primarily the result of myocardial contractile dysfunction rather than increased wall stress in this region.

Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.

Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium

Previous studies suggest that the laminar architecture of left ventricular myocardium may be critical for normal ventricular mechanics. However, systolic three-dimensional deformation of the laminae has never been measured. Therefore, end-systolic finite strains relative to end diastole, from biplane radiography of transmural markers near the apex and base of the anesthetized open-chest canine anterior left ventricular free wall (n = 6), were referred to three-dimensional laminar microstructural axes reconstructed from histology. Whereas fiber shortening was uniform [-0.07 +/- 0.04 (SD)], radial wall thickening increased from base (0. 10 +/- 0.09) to apex (0.14 +/- 0.13). Extension of the laminae transverse to the muscle fibers also increased from base (0.08 +/- 0. 07) to apex (0.11 +/- 0.08), and interlaminar shear changed sign [0. 05 +/- 0.07 (base) and -0.07 +/- 0.09 (apex)], reflecting variations in laminar architecture. Nevertheless, the apex and base were similar in that at each site laminar extension and shear contributed approximately 60 and 40%, respectively, of mean transmural thickening. Kinematic considerations suggest that these dual wall-thickening mechanisms may have distinct ultrastructural origins.

Three-dimensional residual strain in midanterior canine left ventricle

All previous studies of residual strain in the ventricular wall have been based on one- or two-dimensional measurements. Transmural distributions of three-dimensional (3-D) residual strains were measured by biplane radiography of columns of lead beads implanted in the midanterior free wall of the canine left ventricle (LV). 3-D bead coordinates were reconstructed with the isolated arrested LV in the zero-pressure state and again after local residual stress had been relieved by excising a transmural block of tissue. Nonhomogeneous 3-D residual strains were computed by finite element analysis. Mean +/- SD (n = 8) circumferential residual strain indicated that the intact unloaded myocardium was prestretched at the epicardium (0.07 +/- 0.06) and compressed in the subendocardium (-0.04 +/- 0.05). Small but significant longitudinal shortening and torsional shear residual strains were also measured. Residual fiber strain was tensile at the epicardium (0.05 +/- 0.06) and compressive in the subendocardium (-0.01 +/- 0.04), with residual extension and shortening, respectively, along structural axes parallel and perpendicular to the laminar myocardial sheets. Relatively small residual shear strains with respect to the myofiber sheets suggest that prestretching in the plane of the myocardial laminae may be a primary mechanism of residual stress in the LV.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: II--Prolate spheroidal coordinates

A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I--Cylindrical and spherical polar coordinates

A three-dimensional Galerkin finite element method was developed for large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent savings in solution time for inflation of a thick-walled cylinder). Generalized tensor products of linear Lagrange and cubic Hermite polynomials permitted custom elements with improved performance, including 52 percent savings in degrees of freedom and 66 percent savings in solution time for compression of a circular disk. Such computational efficiencies become significant for large scale problems such as modeling the heart.

Finite element stress analysis of left ventricular mechanics in the beating dog heart

A three-dimensional finite element model was used to explore whether or not transmural distributions of end-diastolic and end-systolic fiber stress are uniform from the apex to the base of the canine left ventricular wall. An elastance model for active fiber stress was incorporated in an axisymmetric model that accurately represented the geometry and fiber angle distribution of the anterior free wall. The nonlinear constitutive equation for the resting myocardium was transversely isotropic with respect to the local fiber axis. Transmural distributions of end-diastolic fiber stress became increasingly nonuniform from midventricle toward the apex or the base. At a typical diastolic left ventricular pressure (1 kPa), the differences between largest and smallest fiber stresses were only 0.5 kPa near midventricle, compared with 4.6 kPa at the apex, and 3.3 kPa at the base. Transmural fiber stress differences at end-systole (14 kPa) were relatively small in regions from the base to the midventricle (13-22 kPa), but were larger between midventricle and the apex (30-43 kPa). All six three-dimensional end-diastolic strain components were within or very close to one standard deviation of published measurements through the midanterior left ventricular free wall of the passive canine heart [Omens et al., Am. J. Physiol. 261, H918-H928 (1991)]. End-systolic in-plane normal and shear strains also agreed closely with published experimental measurements in the beating dog heart [Waldman et al., Circ. Res. 63, 550-562 (1988)]. The results indicate that, unlike in the midventricle region that has been studied most fully, there may be significant regional nonhomogeneity of fiber stress in the normal left ventricle associated with regional variations in shape and fiber angle.

Physiological interpretations based on lumped element models fit to respiratory impedance data: use of forward-inverse modeling

Respiratory impedance (Zrs) data at lower (less than 4 Hz) and higher (greater than 32 Hz) frequencies require more complicated inverse models than the standard series combination of a respiratory resistance, inertance, and compliance. In this paper, a forward-inverse modeling approach was used to provide insight on how the parameters in these more complicated inverse models reflect the true physiological system. Forward models are set up to incorporate explicit physiological and anatomical detail. Simulated forward data are then fit with identifiable inverse models and the parameter estimates related to the known detail in the forward model. It is shown that inverse fitting of low frequency data alone will not allow a distinction between frequency dependence due to airway inhomogeneities and frequency dependence due to tissue viscoelasticity. With higher frequency data, a forward model based on an asymmetric branching airways network was used to simulate Zrs from 0.1-128 Hz with increasing amounts of nonuniform peripheral airway obstruction. Here, inverse modeling is more amenable to sensibly separating estimates of airway and tissue properties. A key result, however, is that changes in the tissue parameters of an inverse model (which provides an excellent fit to Zrs data) will appropriately occur in response to inhomogeneous alterations in airway diameters only. The apparent altered tissue properties reflect the decreased communication of some tissue segments with the airway opening and not an explicit change at the tissue level. These phenomena present a substantial problem for the inverse modeler. Finally, inverse model fitting of low and high frequency Zrs data simultaneously with a single model is not helpful for extracting additional physiological detail. Instead, separate models should be applied to each frequency range.