Tropocollagen springs allow collagen fibrils to stretch elastically.

The mechanical properties of connective tissues are tailored to their specific function, and changes can lead to dysfunction and pathology. In most mammalian tissues the mechanical environment is governed by the micro- and nano-scale structure of collagen and its interaction with other tissue components, however these hierarchical properties remain poorly understood. In this study we use the human cornea as a model system to characterise and quantify the dominant deformation mechanisms of connective tissue in response to cyclic loads of physiological magnitude. Synchronised biomechanical testing, x-ray scattering and 3D digital image correlation revealed the presence of two dominant mechanisms: collagen fibril elongation due to a largely elastic, spring-like straightening of tropocollagen supramolecular twist, and a more viscous straightening of fibril crimp that gradually increased over successive loading cycles. The distinct mechanical properties of the two mechanisms suggest they have separate roles in vivo. The elastic, spring-like mechanism is fast-acting and likely responds to stresses associated with the cardiac cycle, while the more viscous crimp mechanism will respond to slower processes, such as postural stresses. It is anticipated that these findings will have broad applicability to understanding the normal and pathological functioning of other connective tissues such as skin and blood vessels that exhibit both helical structures and crimp. STATEMENT OF SIGNIFICANCE: The tropocollagen spring mechanism allows collagen fibrils from some tissues to elongate significantly under small loads, and its recent discovery has the potential to change our fundamental understanding of how tissue deforms. This time-resolved study quantifies the contribution of the spring mechanism to the local strain in stretched tissue and compares it to the contribution associated with the straightening of fibril waviness, the widely accepted primary low-load strain mechanism. The spring mechanism contributed more to the local tissue strain than fibril straightening, and was found to be elastic while fibril straightening was more viscous. The results suggest that the viscoelastic behaviour of a biomaterial is controlled, at least in part, by the relative amount of fibril-scale crimp and tropocollagen supramolecular twist.

Analysis of X-ray scattering microstructure data for implementation in numerical simulations of ocular biomechanical behaviour.

This study aimed to analyse microstructure data on the density and orientation of collagen fibrils in whole eye globes and to propose an effective method for the preparation of data for use in numerical simulations of the eye's biomechanical performance. Wide-angle X-ray scattering was applied to seven healthy ex-vivo human eyes. Each eye was dissected into an anterior and a posterior cup, and radial incisions were used to flatten the tissue before microstructure characterisation. A method was developed to use the microstructure data obtained for the dissected tissue to build realistic 3D maps of fibril density and orientation covering the whole eye globe. At the central cornea, 61.5±2.3% of fibrils were aligned within 45° sectors surrounding the two orthogonal directions. In contrast, more than one-third of the total fibril content was concentrated along the circumferential direction at the limbus (37.0±2.4%) and around the optic nerve head (34.8±2.1%). The insertion locations of the four recti muscles exhibited a preference in the meridional direction near the equator (38.6±3.9%). There was also a significant difference in fibril density between the limbus and other regions (ratio = 1.91±0.45, p <0.01 at the central cornea and ratio = 0.80±0.21, p <0.01 at the posterior pole). Characterisation of collagen fibril density and orientation across the whole ocular surface has been possible but required the use of a technique that involved tissue dissection and hence caused tissue damage. The method presented in this paper aimed to minimise the effect of dissection on the quality of obtained data and was successful in identifying fibril distribution trends that were compatible with earlier studies, which concentrated on localised areas of the ocular globe.

A viscoelastic anisotropic hyperelastic constitutive model of the human cornea.

A constitutive model based on the continuum mechanics theory has been developed which represents interlamellar cohesion, regional variation of collagen fibril density, 3D anisotropy and both age-related viscoelastic and hyperelastic stiffening behaviour of the human cornea. Experimental data gathered from a number of previous studies on 48 ex vivo human cornea (inflation and shear tests) enabled calibration of the constitutive model by numerical analysis. Wide-angle X-ray scattering and electron microscopy provided measured data which quantify microstructural arrangements associated with stiffness. The present study measures stiffness parallel to the lamellae of the cornea which approximately doubles with an increase in strain rate from 0.5 to 5%/min, while the underlying stromal matrix provides a stiffness 2-3 orders of magnitude lower than the lamellae. The model has been simultaneously calibrated to within 3% error across three age groups ranging from 50 to 95 years and three strain rates across the two loading scenarios. Age and strain-rate-dependent material coefficients allow numerical simulation under varying loading scenarios for an individual patient with material stiffness approximated by their age. This present study addresses a significant gap in numerical representation of the cornea and has great potential in daily clinical practice for the planning and optimisation of corrective procedures and in preclinical optimisation of diagnostic procedures.

Ex vivo testing of intact eye globes under inflation conditions to determine regional variation of mechanical stiffness.

BACKGROUND: The eye globe exhibits significant regional variation of mechanical behaviour. The aim of this present study is to develop a new experimental technique for testing intact eye globes in a form that is representative of in vivo conditions, and therefore suitable for determining the material properties of the complete outer ocular tunic. METHODS: A test rig has been developed to provide closed-loop control of either applied intra-ocular pressure or resulting apical displacement; measurement of displacements across the external surface of the eye globe using high-resolution digital cameras and digital image correlation software; prevention of rigid-body motion and protection of the ocular surface from environmental drying. The method has been demonstrated on one human and one porcine eye globe, which were cyclically loaded. Finite element models based on specimen specific tomography, free from rotational symmetry, were used along with experimental pressure-displacement data in an inverse analysis process to derive the mechanical properties of tissue in different regions of the eye's outer tunic. RESULTS: The test method enabled monitoring of mechanical response to intraocular pressure variation across the surface of the eye globe. For the two eyes tested, the method showed a gradual change in the sclera's stiffness from a maximum at the limbus to a minimum at the posterior pole, while in the cornea the stiffness was highest at the centre and lowest in the peripheral zone. Further, for both the sclera and cornea, the load-displacement behaviour did not vary significantly between loading cycles. CONCLUSIONS: The first methodology capable of mechanically testing intact eye globes, with applied loads and boundary conditions that closely represent in vivo conditions is introduced. The method enables determination of the regional variation in mechanical behaviour across the ocular surface.

In vivo study of corneal responses to increased intraocular pressure loading.

BACKGROUND: The cornea is responsible for two-thirds of the eye's refractive power which is a function of the shape and refractive index. The aim of this present study is to examine human eyes in vivo for corneal shape changes in response to short-term elevation in intraocular pressure. METHODS: Videokeratographic and tonometric assessments at baseline were compared with the same assessments when intraocular pressure was elevated to approximately double (199 ± 22 %) the baseline levels using ophthalmodynamometer applanation of the sclera. Composite maps of the cornea and limbus were created by combining topographical assessments for central, nasal, temporal, inferior and superior fixation. Numerical finite-element simulations were custom built for each subject and the stiffness distribution across corneal surface modified to achieve matches between simulated and experimental data. RESULTS: The stiffness distributions required to achieve simulation-experimental matches showed a consistent trend with the 2.5 mm annulus bounded by the limbus showing a mean stiffness reduction of 47.3 ± 10.8 % compared with the central cornea (P = 0.001). CONCLUSIONS: Corneal structure appears to provide the central cornea with a greater stiffness compared with the peripheral cornea and associated greater tolerance to elevation in intraocular pressure, consistent with the need for stable corneal refraction and vision. The method adopted to examine corneal biomechanical performance in vivo may have applications in additional studies.

Evaluation of the relationship of corneal biomechanical metrics with physical intraocular pressure and central corneal thickness in ex vivo rabbit eye globes.

The relationship of corneal biomechanical metrics provided by the Ocular Response Analyzer (ORA) and Corvis ST (CVS) with physical intraocular pressure (IOPp) and central corneal thickness (CCT) was evaluated. Thirty fresh enucleated eyes of 30 rabbits were used in ex vivo whole globe inflation experiments. IOPp was measured with a pressure transducer and increased from 7.5 to 37.5 mmHg in steps of 7.5 mmHg while biomechanical data was acquired using the ORA and CVS. At least 3 examinations were performed at each pressure level, where CCT and twelve biomechanical metrics were recorded and analyzed as a function of IOPp. The biomechanical metrics included corneal hysteresis (CH) and corneal resistance factor (CRF), obtained by the ORA. They also included the applanation times (A1T, A2T), lengths (A1L, A2L) and velocities (A1V, A2V), in addition to the highest concavity time (HCT), peak distance (PD), radius (HR) and deformation amplitude (DA), obtained by the CVS. The variation of CCT and the twelve biomechanical metrics for the 30 rabbit eyes tested across the 5 pressure stages considered (inter-pressure differences) were statistically significant (P = 0.00). IOPp was highly to moderately correlated with most biomechanical metrics, especially CRF, A1T, A1V, A2V, PD and DA, while the relationships with CH, A2T, A1L and HCT were poor. IOP has important influences on most corneal biomechanical metrics provided by CVS and ORA. Two biomechanical metrics A1V and HR were influenced by CCT after correcting for the effect of IOP in most pressure stages, while the correlation with others were weak. Comparisons of research groups based on ORA and CVS with different IOPs and CCTs may lead to possible misinterpretations if both or one of which are not considered in the analysis.

Biomechanical model of the human cornea: considering shear stiffness and regional variation of collagen anisotropy and density.

A numerical model based on continuum mechanics theory has been developed which represents the 3D anisotropic behaviour of the corneal stroma. Experimental data has been gathered from a number of previous studies to provide the basis and calibration parameters for the numerical modelling. The resulting model introduces numerical representation of collagen fibril density and its related regional variation, interlamellar cohesion and age-related stiffening in an anisotropic model of the human cornea. Further, the model incorporates previous modelling developments including representation of lamellae anisotropy and stiffness of the underlying matrix. Wide angle X-ray scattering has provided measured data which quantifies relative fibril anisotropy in the 2D domain. Accurate numerical description of material response to deformation is essential to providing representative simulations of corneal behaviour. Representing experimentally obtained 2D anisotropy and regional density variation in the 3D domain is an essential component of this accuracy. The constitutive model was incorporated into finite element analysis. Combining with inverse analysis, the model was calibrated to an extensive experimental database of ex vivo corneal inflation tests and ex vivo corneal shear tests. This model represents stiffness of the underlying matrix which is 2-3 orders of magnitude than the mechanical response representing the collagen fibrils in the lamellae. The presented model, along with its age dependent material coefficients, allows finite element modelling for an individual patient with material stiffness approximated based on their age. This has great potential to be used in both daily clinical practice for the planning and optimisation of corrective procedures and in pre-clinical optimisation of diagnostic procedures.

Assessment of corneal biomechanical behavior under posterior and anterior pressure.

PURPOSE: To determine the biomechanical response of the rabbit cornea to inflation under posterior and anterior pressure. METHODS: Twelve Japanese white rabbits were included in the study. A randomly selected eye from each animal was subjected to posterior pressure in an inflation test rig, and the other eye was subjected to anterior pressure after manually reversing its curvature. Specimens were loaded by cycles of pressure up to 40 mmHg, and the experimentally obtained pressure-deformation data were used to derive the stress-strain behavior of each eye using an inverse modeling procedure. RESULTS: The differences between the two groups in corneal thickness, diameter, and intraocular pressure (IOP) were not statistically significant (P=.935, .879 and .368, respectively). Corneas tested under posterior pressure displayed significantly higher stiffness (as measured by the tangent modulus) than those inflated by anterior pressure (P<.001). CONCLUSIONS: Cornea is a nonlinear viscoelastic tissue that presents different mechanical properties when tested under posterior and anterior pressure. The determination of the behavior under both forms of pressure could contribute to the construction of accurate finite element simulations of corneal behavior and the correction of tonometric IOP measurements. The difference in mechanical behavior between anteriorly and posteriorly loaded corneas in the study, although significant, could have been partly affected by the changes in microstructure possibly caused by changing corneal form to enable anterior loading.

Stress free configuration of the human eye.

Numerical simulations of eye globes often rely on topographies that have been measured in vivo using devices such as the Pentacam or OCT. The topographies, which represent the form of the already stressed eye under the existing intraocular pressure, introduce approximations in the analysis. The accuracy of the simulations could be improved if either the stress state of the eye under the effect of intraocular pressure is determined, or the stress-free form of the eye estimated prior to conducting the analysis. This study reviews earlier attempts to address this problem and assesses the performance of an iterative technique proposed by Pandolfi and Holzapfel [1], which is both simple to implement and promises high accuracy in estimating the eye's stress-free form. A parametric study has been conducted and demonstrated reliance of the error level on the level of flexibility of the eye model, especially in the cornea region. However, in all cases considered 3-4 analysis iterations were sufficient to produce a stress-free form with average errors in node location <10(-6)mm and a maximal error <10(-4)mm. This error level, which is similar to what has been achieved with other methods and orders of magnitude lower than the accuracy of current clinical topography systems, justifies the use of the technique as a pre-processing step in ocular numerical simulations.