Probing mechanical properties of fully hydrated gels and biological tissues

A longstanding challenge in accurate mechanical characterization of engineered and biological tissues is maintenance of both stable sample hydration and high instrument signal resolution. Here, we describe the modification of an instrumented indenter to accommodate nanomechanical characterization of biological and synthetic tissues in liquid media, and demonstrate accurate acquisition of force-displacement data that can be used to extract viscoelastoplastic properties of hydrated gels and tissues. We demonstrate the validity of this approach via elastoplastic analysis of relatively stiff, water-insensitive materials of elastic moduli E>1000 kPa (borosilicate glass and polypropylene), and then consider the viscoelastic response and representative mechanical properties of compliant, synthetic polymer hydrogels (polyacrylamide-based hydrogels of varying mol%-bis crosslinker) and biological tissues (porcine skin and liver) of E<500 kPa. Indentation responses obtained via loading/unloading hystereses and contact creep loading were highly repeatable, and the inferred E were in good agreement with available macroscopic data for all samples. As expected, increased chemical crosslinking of polyacrylamide increased stiffness (E40 kPa) and decreased creep compliance. E of porcine liver (760 kPa) and skin (222 kPa) were also within the range of macroscopic measurements reported for a limited subset of species and disease states. These data show that instrumented indentation of fully immersed samples can be reliably applied for materials spanning several orders of magnitude in stiffness (E=kPa-GPa). These capabilities are particularly important to materials design and characterization of macromolecules, cells, explanted tissues, and synthetic extracellular matrices as a function of spatial position, degree of hydration, or hydrolytic/enzymatic/corrosion reaction times.     

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

Influence of hydration on nanoindentation induced energy expenditure of dentin

Improved understanding of the effects of hydration and drying in mineralized tissues is highly desirable, particularly for physiologically hydrated biological materials such as dentin. We investigated the influence of hydration on the nanomechanical properties of healthy dentin and hypothesized that drying leads to an increase in indentation induced energy expenditure and hardness. Hydrated and dry dentin were tested with a UMIS set up with a Berkovich indenter at a maximum load of 50 mN. Values representative of the energy expenditure behavior were presented as dissipated energy, U(d), recovered energy, U(e), normalized energy expenditure index, ψ, and hardness, H. Energy expenditure index results, which normalize the energy expenditure for each test and describe the relative energy dissipation-recovery behavior of a material, suggested that, for the relatively severe contact strains about a sharp Berkovich indenter, dissipation dominates the mechanical response of both the hydrated and dry dentin. In support of our initial hypothesis, dry dentin presented a significantly higher energy expenditure index than hydrated dentin (p<0.0001). These results were primarily associated with a lower U(e) that was found upon drying. Hydration also decreased H significantly (p<0.0001). In summary, this study presents the first direct measurements of the energy expenditure behavior of hydrated and dry dentin using instrumented nanoindentation.     

Cloning of matrix Gla protein in a marine cartilaginous fish, Prionace glauca: preferential protein accumulation in skeletal and vascular systems

Matrix Gla protein (MGP) belongs to the family of vitamin K dependent, Gla containing proteins and, in mammals, birds and Xenopus, its mRNA has been previously detected in bone, cartilage and soft tissue extracts, while the accumulation of the protein was found mainly in calcified tissues. More recently, the MGP gene expression was also studied in marine teleost fish where it was found to be associated with chondrocytes, smooth muscle and endothelial cells. To date no information is available on the sites of MGP expression or accumulation in cartilaginous fishes that diverged from osteichthyans, a group that includes mammals, over 400 million years ago. The main objectives of this work were to study the sites of MGP gene expression and protein accumulation by means of in situ hybridization and immunohistochemistry. MGP mRNA and protein were localized as expected not only in cartilage from branchial arches and vertebra but also in the endothelia of the vascular system as well as in the tubular renal endothelium. The accumulation of MGP in non mineralized soft tissues was unexpected and suggests differences in localization or regulation of this protein in shark soft tissues compared to tetrapods and teleosts. Our results also corroborate the hypothesis that in Prionace glauca, as previously shown in mammals, the MGP protein probably also acts as a calcification inhibitor, protecting soft tissues from abnormal and ectopic calcification.J. B. Ortiz-Delgado, D.C. Simes authors contributed equally to this work     

Characterization of the growth plate-bone interphase region using cryo-FIB SEM 3D volume imaging

The interphase region at the base of the growth plate includes blood vessels, cells and mineralized tissues. In this region, cartilage is mineralized and replaced with bone. Blood vessel extremities permeate this space providing nutrients, oxygen and signaling factors. All these different components form a complex intertwined 3D structure. Here we use cryo-FIB SEM to elaborate this 3D structure without removing the water. As it is challenging to image mineralized and unmineralized tissues in a hydrated state, we provide technical details of the parameters used. We obtained two FIB SEM image stacks that show that the blood vessels are in intimate contact not only with cells, but in some locations also with mineralized tissues. There are abundant red blood cells at the extremities of the vessels. We also documented large multinucleated cells in contact with mineralized cartilage and possibly also with bone. We observed membrane bound mineralized particles in these cells, as well as in blood serum, but not in the hypertrophic chondrocytes. We confirm that there is an open pathway from the blood vessel extremities to the mineralizing cartilage. Based on the sparsity of the mineralized particles, we conclude that mainly ions in solution are used for mineralizing cartilage and bone, but these are augmented by the supply of mineralized particles.     

Mechanical characterization of anisotropic planar biological soft tissues using large indentation: a computational feasibility study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.     

Apparatus for measuring the swelling dependent electrical conductivity of charged hydrated soft tissues

This paper describes a new apparatus and method for measuring swelling dependent electrical conductivity of charged hydrated soft tissues. The apparatus was calibrated using a conductivity standard. Swelling dependent specific conductivity of porcine annulus fibrosis (AF) samples was determined. The conductivity values for porcine AF were similar to those for human and bovine articular cartilage found in the literature. Results revealed a significant linear correlation between specific conductivity and water content for porcine AF tissues tested in phosphate buffered saline (PBS).     

Immunohistochemical localization of bone sialoprotein in foetal porcine bone tissues: comparisons with secreted phosphoprotein 1 (SPP-1, osteopontin) and SPARC (osteonectin)

Summary Bone sialoprotein (BSP) is a prominent component of bone tissues that is expressed by differentiated osteoblastic cells. Affinity-purified antibodies to BSP were prepared and used in combination with biotin-conjugated peroxidase-labeled second antibodies to demonstrate the distribution of this protein in sections of demineralized foetal porcine tibia and calvarial bone. Staining for BSP was observed in the matrix of mineralized bone and also in the mineralized cartilage and associated cells of the epiphysis, but was not observed in the hypertrophic zone nor in any of the soft tissues including the periosteum. In comparison, SPP-1 (osteopontin) and SPARC (osteonectin), which are also major proteins in porcine bone, were observed in the cartilage as well as in the mineralized bone matrix, In addition, SPARC was also present in soft connective tissues. Although SPP-1 distribution was more restricted than SPARC, hypertrophic chondrocytes, periosteal cells and some stromal cells in the bone marrow spaces were stained in addition to osteoblastic cells. The variations in the distribution and cellular expression of BSP, SPARC and SPP-1 in bone and mineralizing cartilage indicate these proteins perform different functions in the formation and remodelling of mineralized connective tissues.     

Characteristics of mineral particles in the human bone/cartilage interface

Bone and cartilage consist of different organic matrices, which can both be mineralized by the deposition of nano-sized calcium phosphate particles. We have studied these mineral particles in the mineralized cartilage layer between bone and different types of cartilage (bone/articular cartilage, bone/intervertebral disk, and bone/growth cartilage) of individuals aged 54 years, 12 years, and 6 months. Quantitative backscattered electron imaging and scanning small-angle X-ray scattering at a synchrotron radiation source were combined with light microscopy to determine calcium content, mineral particle size and alignment, and collagen orientation, respectively. Mineralized cartilage revealed a higher calcium content than the adjacent bone (p<0.05 for all samples), whereas the highest values were found in growth cartilage. Surprisingly, we found the mineral platelet width similar for bone and mineralized cartilage, with the exception of the growth cartilage sample. The most striking result, however, was the abrupt change of mineral particle orientation at the interface between the two tissues. While the particles were aligned perpendicular to the interface in cartilage, they were oriented parallel to it in bone, reflecting the morphology of the underlying organic matrices. The tight bonding of mineralized cartilage to bone suggests a mechanical role for the interface of the two elastically different tissues, bone and cartilage.     

Analyzing acoustoelastic effect of shear wave elastography data for perfused and hydrated soft tissues using a macromolecular network inspired model

Shear wave elastography (SWE) has enhanced our ability to non-invasively make in vivo measurements of tissue elastic properties of animal and human tissues. Recently, researchers have taken advantages of acoustoelasticity in SWE to extract nonlinear elastic properties from soft biological tissues. However, most investigations of the acoustoelastic effects of SWE data (AE-SWE) rely on classic hyperelastic models for rubber-like (dry) materials. In this paper, we focus solely on understanding acoustoelasticity in soft hydrated tissues using SWE data and propose a straightforward approach to modeling the constitutive behavior of soft tissue that has a direct microstructural/macromolecular interpretation. Our approach incorporates two constitutive features relevant to biological tissues into AE-SWE: static dilation of the medium associated with nonstructural components (e.g. tissue hydration and perfusion) and finite extensibility derived from an ideal network of biological filaments. We evaluated the proposed method using data from an in-house tissue-mimicking phantom experiment, and ex vivo and in vivo AE-SWE data available in the SWE literature. In conclusion, predictions made by our approach agreed well with measurements obtained from phantom, ex vivo and in vivo tissue experiments.     

The kinetics of chemically induced nonequilibrium swelling of articular cartilage and corneal stroma

An electromechanical model for charged, hydrated tissues is developed to predict the kinetics of changes in swelling and isometric compressive stress induced by changes in bath salt concentration. The model focuses on ionic transport as the rate limiting step in chemically modulating electrical interactions between the charged macromolecules of the extracellular matrix. The swelling response to such changes in local interaction forces is determined by the relative rates of chemical diffusion and fluid redistribution in the tissue sample. We have tested the model by comparing the experimentally observed salt-induced stress relaxation response in bovine articular cartilage and corneal stroma to the response predicted by the model using constitutive relations for the concentration dependent material properties of the tissues reported in a related study. The qualitatively good agreement between our experimental measurements and the predictions of the model supports the physical basis of the model and demonstrates the model's ability to discriminate between the two soft connective tissues that were examined.     

Ultrasonic measurement of depth-dependent transient behaviors of articular cartilage under compression

We previously reported an ultrasound method for measuring the depth-dependent equilibrium mechanical properties of articular cartilage using quasi-static compression. The objective of this paper was to introduce our recent development for nondestructively measuring the transient depth-dependent strains of full-thickness articular cartilage specimens prepared from bovine patellae. A 50 MHz focused ultrasound transducer was used to collect ultrasound echoes from articular cartilage specimens (n=8) and sponge phantoms with open pores (n=10) during tests of compression and subsequent stress-relaxation. The transient displacements of the tissues at different depths along the compression direction were calculated from the ultrasound echoes using a cross-correlation tracking technique. An LVDT sensor and a load cell were used to measure the overall deformation of the tissue and the applied force, respectively. Results showed that the tissues inside the cartilage layer continued to move during the stress-relaxation phase after the compression was completed. In the equilibrium state, the displacements of the cartilage tissues at the depths of 1/4, 1/2, and 3/4 of the full-thickness reduced by 51%+/-22%, 54%+/-17%, and 50+/-17%, respectively, in comparison with its peak value. However, no similar phenomenon was observed in the sponge phantoms. Our preliminary results demonstrated that this ultrasound method may provide a potential tool for the nondestructive measurement of the transient depth-dependent processes involved in biological and bioengineered soft tissues as well as soft biomaterials under dynamic loading.     

An evaluation of three-dimensional diarthrodial joint contact using penetration data and the finite element method

We have developed an approximate method for simulating the three-dimensional contact of soft biphasic tissues in diarthrodial joints under physiological loading. Input to the method includes: (i) kinematic information describing an in vitro joint articulation, measured while the cartilage is deformed under physiological loads, (ii) geometric properties for the relaxed (undeformed) cartilage layers, obtained for the analyses in this study via stereophotogrammetry, and (iii) material parameters for the biphasic constitutive relations used to represent cartilage. Solid models of the relaxed tissue layers are assembled in physiological positions, resulting in a mathematical overlap of the cartilage layers. The overlap distribution is quantified and converted via the biphasic governing equations into applied traction boundary conditions for both the solid and fluid phases for each of the contacting layers. Linear, biphasic, three-dimensional, finite element analysis is performed using the contact boundary conditions derived for each of the contacting layers. The method is found to produce results consistent with the continuity requirements of biphasic contact. Comparison with results from independent, biphasic contact analyses of axisymmetric problems shows that the method slightly underestimates the contact area, leading to an overestimation of the total traction, but yields a good approximation to elastic stress and solid phase displacement.     

Structure and function of the horn shark (Heterodontus francisci) cranium through ontogeny: development of a hard prey specialist

The horn sharks (Heterodontidae: Chondrichthyes) represent one of four independent evolutions of durophagy in the cartilaginous fishes. We used high-resolution computed tomography (CT scanning) to visualize and quantify the mineralized tissue of an ontogenetic series of horn sharks. CT scanning of neonatal through adult California horn sharks (Heterodontus francisci) confirmed that this technique is effective for examining mineralized tissue in even small (<10 mm) specimens. The jaw joint is among the first areas to become mineralized and is the most heavily mineralized area in the cranium of a neonatal horn shark. The hyoid is also well mineralized, although the poorly mineralized molariform teeth indicate that the neonatal animal may be a suction feeder on softer prey. The symphysis of the jaws never mineralizes, in sharp contrast to the condition in the hard prey-crushing stingrays. Digitally reslicing the CT scans along the jaws allowed measurement of the second moment of area (Ina). Assuming that the jaws are made of the same material at all ages, Ina is an indicator of the flexural stiffness of the jaws. In all sizes of shark the lower jaws were stiffer than the upper and the stiffness increased in the area of the molariform teeth. The central region of the jaws, where the rami meet, support cuspidate grasping teeth and has the lowest Ina. The spotted eagle ray (Aetobatus narinari), a hard prey-crushing stingray, shows a different pattern of flexural stiffness, with the peak at the central part of the jaws where the prey is reduced between flattened tooth plates. Although the eagle ray jaws have a higher Ina than the horn shark, they are also far more heavily mineralized. When the relative amounts of mineralization are taken into account, horn sharks do better with what mineral they have than does the eagle ray. With a tight jaw joint and loose mandibular symphysis, as well as nearly opposite patterns of stiffness in the jaws, it is clear that two of the clades of hard prey specialists use very different methods for cracking the hard prey problem.     

The effect of storage on the biomechanical behavior of articular cartilage--a large strain study.

The transplantation of stored shell osteochondral allografts is a potentially useful alternative to total joint replacements for the treatment of joint ailments. The maintenance of normal cartilage properties of the osteochondral allografts during storage is important for the allograft to function properly and survive in the host joint. Since articular cartilage is normally under large physiological stresses, this study was conducted to investigate the biomechanical behavior under large strain conditions of cartilage tissue stored for various time periods (i.e., 3, 7, 28, and 60 days) in tissue culture media. A biphasic large strain theory developed for soft hydrated connective tissues was used to describe and determine the biomechanical properties of the stored cartilage. It was found that articular cartilage stored for up to 60 days maintained the ability to sustain large compressive strains of up to 40 percent or more, like normal articular cartilage. Moreover, the equilibrium stress-strain behavior and compressive modulus of the stored articular cartilage were unchanged after up to 60 days of storage.     

Cloning and characterization of tissue inhibitor of metalloproteinase-3 (TIMP-3) from shark, Scyliorhinus torazame

We cloned the full-length cDNA encoding TIMP-3 from the cartilage of cloudy dogfish, Scyliorhinus torazame. The entire open reading frame was composed of 645 nucleotides and 214 residues including 12 conserved cysteines and asparagine-184, a putative site for N-linked sugars. It showed about 72% identity to those of other species based on the deduced amino acid sequence. The mRNA of shark TIMP-3 were expressed abundantly in brain and cartilage tissues. To investigate the roles of shark TIMP-3, an expression vector was constructed and transfected into HT1080 human fibrosarcoma cells. Overexpression of shark TIMP-3 reduced the activity of MMP-2 in gelatin zymography. Through human Alu PCR based CAM assay, we also confirmed that shark TIMP-3 transfected HT1080 cells had less intravasation effects.     

A study of preconditioned Krylov subspace methods with reordering for linear systems from a biphasic v-p finite element formulation

A study was conducted on combinations of preconditioned iterative methods with matrix reordering to solve the linear systems arising from a biphasic velocity-pressure (v-p) finite element formulation used to simulate soft hydrated tissues in the human musculoskeletal system. Krylov subspace methods were tested due to the symmetric indefiniteness of our systems, specifically the generalized minimal residual (GMRES), transpose-free quasi-minimal residual (TFQMR), and biconjugate gradient stabilized (BiCGSTAB) methods. Standard graph reordering techniques were used with incomplete LU (ILU) preconditioning. Performance of the methods was compared on the basis of convergence rate, computing time, and memory requirements. Our results indicate that performance is affected more significantly by the choice of reordering scheme than by the choice of Krylov method. Overall, BiCGSTAB with one-way dissection (OWD) reordering performed best for a test problem representative of a physiological tissue layer. The preferred methods were then used to simulate the contact of the humeral head and glenoid tissue layers in glenohumeral joint of the shoulder, using a penetration-based method to approximate contact. The distribution of pressure and stress fields within the tissues shows significant through-thickness effects and demonstrates the importance of simulating soft hydrated tissues with a biphasic model.     

Mechanics of biting in great white and sandtiger sharks

Although a strong correlation between jaw mechanics and prey selection has been demonstrated in bony fishes (Osteichthyes), how jaw mechanics influence feeding performance in cartilaginous fishes (Chondrichthyes) remains unknown. Hence, tooth shape has been regarded as a primary predictor of feeding behavior in sharks. Here we apply Finite Element Analysis (FEA) to examine form and function in the jaws of two threatened shark species, the great white (Carcharodon carcharias) and the sandtiger (Carcharias taurus). These species possess characteristic tooth shapes believed to reflect dietary preferences. We show that the jaws of sandtigers and great whites are adapted for rapid closure and generation of maximum bite force, respectively, and that these functional differences are consistent with diet and dentition. Our results suggest that in both taxa, insertion of jaw adductor muscles on a central tendon functions to straighten and sustain muscle fibers to nearly orthogonal insertion angles as the mouth opens. We argue that this jaw muscle arrangement allows high bite forces to be maintained across a wider range of gape angles than observed in mammalian models. Finally, our data suggest that the jaws of sub-adult great whites are mechanically vulnerable when handling large prey. In addition to ontogenetic changes in dentition, further mineralization of the jaws may be required to effectively feed on marine mammals. Our study is the first comparative FEA of the jaws for any fish species. Results highlight the potential of FEA for testing previously intractable questions regarding feeding mechanisms in sharks and other vertebrates.