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.     

A microstructurally-based finite element model of the incised human cornea.

A mechanical model of the human cornea is proposed and employed in a finite element formulation for simulating the effects of surgical procedures, such as radial keratotomy, on the cornea. The model assumes that the structural behavior of the cornea is governed by the properties of the stroma. Arguments based on the microstructural organization and properties of the stroma lead to the conclusion that the human cornea exhibits flexural and shear rigidities which are negligible compared to its membrane rigidity. Accordingly, it is proposed that to a first approximation, the structural behavior of the cornea is that of a thick membrane shell. The tensile forces in the cornea are resisted by very fine collagen fibrils embedded in the ground substance of the stromal lamellae. When the collagen fibrils are cut, as in radial keratotomy, it is argued that they become relaxed since there is negligible transfer of load between adjacent fibrils due to the low shear modulus of the ground substance. The forces in the cornea are then resisted only by the remaining uncut fibrils. The cutting of fibrils induces an anisotropy and inhomogeneity in the membrane rigidity. By assuming a uniform angular distribution of stromal lamellae through the corneal thickness, geometric arguments lead to a quantitative representation for the anisotropy and inhomogeneity. All material behavior is assumed to be in the linear elastic regime and with no time-dependency. The resulting constitutive model for the incised cornea has been employed in a geometrically non-linear finite element membrane shell formulation for small strains with moderate rotations. A number of numerical examples are presented to illustrate the effectiveness of the proposed constitutive model and finite element formulation. The dependence of the outcome of radial keratotomy, measured in terms of the immediate postoperative shift in corneal power, on a number of important factors is investigated. These factors include the value of the elastic moduli of the stromal lamellae (dependent on the patient's age), the incision depth, the optic zone size, the number of incisions and their positions, and the intraocular pressure. Results have also been compared with expected surgical corrections predicted by three expert surgeons and show an excellent correspondence.     

Biomechanical and optical characteristics of a corneal stromal equivalent

Cell matrix interactions are important in understanding the healing characteristics of the cornea after refractive surgery or transplantation. The purpose of this study was to characterize in more detail the evolution of biomechanical and optical properties of a stromal equivalent (stromal fibroblasts cultured in a collagen matrix). Human corneal stromal fibroblasts were cultured in a collagen matrix. Compaction and modulus were determined for the stromal equivalent as a function of time in culture and matrix composition. The corneal stromal fibroblasts were stained for alpha-smooth muscle actin expression as an indicator of myofibroblast phenotype. The nominal modulus of the collagen matrix was 364 +/- 41 Pa initial and decreased initially with time in culture and then slowly increased to 177 +/- 75 Pa after 21 days. The addition of chondroitin sulfate decreased the contraction of the matrix and enhanced its transparency. Cell phenotype studies showed dynamic changes in the expression of alpha-smooth muscle actin with time in culture. These results indicate that the contractile behavior of corneal stromal cells can be influenced by both matrix composition and time in culture. Changes in contractile phenotype after completion of the contraction process also indicate that significant cellular changes persist beyond the initial matrix-remodeling phase.     

Biomechanical model of the human shoulder joint--II. The shoulder rhythm

A method to investigate the rhythm of the human shoulder, i.e. the interplay between the motion of constituent parts of the shoulder, has been devised and tested. The method is based upon numerical evaluation of low dose roentgenstereophotogrammetric motion pictures of subjects equipped with radiation dense implantations in the bones. Evaluation of the method shows that it may be used in determining motion patterns and that the employed interpolation techniques can be used to simulate motions not actually performed in the laboratory. The shoulder rhythm has been previously poorly investigated and quantified results published pertain to one plane only. Our results on motion patterns correlate with previous investigations. With this method, we show that the absolute position of the bones varies significantly between individuals while the relative displacement of the bones during motion exhibit similarities. In particular the results show that, under normal conditions, the individual rhythm is very stable and insensitive to small hand-loads.     

A model for the human cornea: constitutive formulation and numerical analysis

The human cornea (the external lens of the eye) has the macroscopic structure of a thin shell, originated by the organization of collagen lamellae parallel to the middle surface of the shell. The lamellae, composed of bundles of collagen fibrils, are responsible for the experimentally observed anisotropy of the cornea. Anomalies in the fibril structure may explain the changes in the mechanical behavior of the tissue observed in pathologies such as keratoconus. We employ a fiber-matrix constitutive model and propose a numerical model for the human cornea that is able to account for its mechanical behavior in healthy conditions or in the presence of keratoconus under increasing values of the intraocular pressure. The ability of our model to reproduce the behavior of the human cornea opens a promising perspective for the numerical simulation of refractive surgery.     

Calculation and application of the anterior surface area of a model human cornea

The macroscopic anterior surface area was calculated for three models of the average human cornea. Two models, a general ellipsoid and a rotational ellipse (rotationally symmetric ellipsoid) gave a surface area of 132 mm2, while a spherical model gave 126 mm2. A general ellipsoidal model having the maximum radius horizontal (with-the-rule corneal astigmatism) has less surface area than a rotational ellipse with the same horizontal radius. For a corneal sagittal height of 2.59 mm, the surface area of an ellipsoidal cornea equals -19.2Q + 16.3R -0.476 which specifies a rotational ellipse (radius R, asphericity Q) of equal surface area. In a cornea with the maximum radius vertical (against-the-rule corneal astigmatism), the ellipsoid has slightly more surface area than a rotational ellipse with the same horizontal radius of curvature. For a given horizontal radius of curvature, the sphere has the lowest surface area. For a corneal sagittal height s of 2.59 mm, the sphere underestimates by 8% the surface area of a rotational ellipse with asphericity -0.5. The anterior corneal surface area of a rotational ellipse model, radius R, asphericity Q is given by 2 pi Rs- 19.2Q. In all three models, the surface area increases with horizontal radius of curvature. In the rotational ellipse model, the rate of increase (slope) is independent of asphericity, and the slope found in with-the-rule astigmatism is less than the slope found with against-the-rule astigmatism. The calculated surface area predicts a precorneal tear volume of 0.86 microliter for a 6.5 micron tear thickness. The apparent, or plane projected are of an epithelial lesion underestimates the curved surface area with a percentage error that increases rapidly with lesion diameter. For a 12 mm diameter lesion on a rotational ellipse model, the apparent area underestimates the surface area by 18%. The average posterior corneal surface in human is not spherical but imitates the anterior surface, and has an area of 137 mm2 or 3.8% greater than the anterior area.     

Progesterone metabolism by human cornea

Human cornea excised from patients with wounded eyes were incubated in vitro for a 5-day period in the presence of [4-¹⁴C]-progesterone. The following C₂₁ steroid metabolites were identified by paper chromatography, derivative formation, and crystallizations to specific activities: 20α-hydroxy-4-pregnen-3-one, 20β-hydroxy-4-pregnen-3-one, and 5α-pregnan-3,20-dione.     

Biomechanical model of the diabetic foot

In this work, a two dimensional (2D) finite element foot model was established from magnetic resonance imaging (MRI) of a male subject. The model comprises first medial planar cross-section through the foot, representing the foot in standing posture. For specified external load, the stress and strain distribution field under foot structure are determined. The material characterization of foot structure components are stronger related to diabetic phenomena. The new material model for soft tissue based on mixture theory is proposed. The linear finite element model replaced by nonlinear counterpart with segment-to-segment contact element.     

Biomechanical characteristics of human ankle-joint muscles

Equivalent biomechanical characteristics of human ankle-joint muscles have been determined by impact and vibration tests. The estimate of the stiffness and damping coefficients has yielded, respectively, (2.67 +/- 0.48) X 10(4) N X m-1 and (811.58 +/- 201.3) N X s X m-1 by impact actions, n = 126; (1.49 +/- 0.35) X 10(4) N X m-1 and (430.1 +/- 36.1) N X s X m-1 -by vibration actions, n = 7. The characteristics of the ankle-joint muscles of subjects representing different kinds of sports have proved to be different.     

Synchrotron x-ray diffraction studies of the cornea, with implications for stromal hydration.

The intermolecular and interfibrillar spacings of collagen in bovine corneal stroma have been measured as a function of tissue hydration. Data were recorded from low- and high-angle x-ray diffraction patterns obtained using a high intensity synchrotron source. The most frequently occurring interfibrillar spacing varied from 34 nm in dry corneas to 76 nm at H = 5 (the hydration, H, is defined as the ratio of the weight of water to the dry weight). The most frequently occurring intermolecular Bragg spacing increased from 1.15 nm (dry) to approximately 1.60 nm at normal hydration (H approximately 3.2) and continued to increase only slowly above normal hydration. Most of the increase in the intermolecular spacing occurred between H = O and H = 1. Over this hydration range the interfibrillar and intermolecular spacings moved in tandem, which suggests that the initial water goes equally within and between the fibrils. Above H = 1 water goes preferentially between the fibrils. The results suggest that, even at normal hydration, water does not fill the interfibrillar space uniformly, and a proportion is located in another space or compartment. In dried-then-rehydrated corneas, a larger proportion of the water goes into this other compartment. In both cases, it is possible to postulate a second set or population of fibrils that are more widely and irregularly separated and therefore do not contribute significantly to the diffraction pattern.     

Biomechanical properties of the human umbilical cord

The umbilical cord is a complex and fascinating structure that connects the fetus to the placenta and encases the umbilical vessels. The response of its tissues to mechanical loading due to fetal movements and uterine contractions is not well understood. The aim of this study is the evaluation of the mechanical properties of the main components of the human umbilical cord. Fresh umbilical cord specimens were collected from neonates born at term of the gestation and submitted to compliance tests. Furthermore, uniaxial tensile and stress-relaxation tests were performed on samples of umbilical vein and Wharton's jelly. Both materials exhibited nonlinear stress-strain response with increasing strain, increasing the elastic modulus (E(high) about 10-20 times E(low)) and significant viscoelastic behavior. In addition, anisotropy of the vein was observed. Although the circumferential properties of the vein (mean E(high) about 2.4 MPa) were similar to those after birth, the longitudinal stiffness of both materials was higher (mean E(high) over 10 MPa) and comparable to that of the ligaments. These findings suggest a mechanism of protection acting against excessive elongations of the cord, which could cause undue restriction of the umbilical vessel area and interference with the fetal blood circulation.     

Proteome of human subcutaneous adipose tissue stromal vascular fraction cells versus mature adipocytes based on DIGE

Adipose tissue contains a heterogeneous population of mature adipocytes, endothelial cells, immune cells, pericytes, and preadipocytic stromal/stem cells. To date, a majority of proteomic analyses have focused on intact adipose tissue or isolated adipose stromal/stem cells in vitro. In this study, human subcutaneous adipose tissue from multiple depots (arm and abdomen) obtained from female donors was separated into populations of stromal vascular fraction cells and mature adipocytes. Out of 960 features detected by 2-D gel electrophoresis, a total of 200 features displayed a 2-fold up- or down-regulation relative to each cell population. The protein identity of 136 features was determined. Immunoblot analyses comparing SVF relative to adipocytes confirmed that carbonic anhydrase II was up-regulated in both adipose depots while catalase was up-regulated in the arm only. Bioinformatic analyses of the data set determined that cytoskeletal, glycogenic, glycolytic, lipid metabolic, and oxidative stress related pathways were highly represented as differentially regulated between the mature adipocytes and stromal vascular fraction cells. These findings extend previous reports in the literature with respect to the adipose tissue proteome and the consequences of adipogenesis. The proteins identified may have value as biomarkers for monitoring the physiology and pathology of cell populations within subcutaneous adipose depots.     

Oxidative stress in diseases of the human cornea

Intense exposure to light, robust metabolic activity, and high oxygen tension render the human eye particularly vulnerable to oxidative damage and the list of ophthalmological disorders implicating reactive oxygen and nitrogen species is rapidly expanding. Here, we review the roles of oxidative stress in the etiopathogeneses and pathophysiology of diseases of the human cornea including pterygium, keratoconus, trauma and chemical injury, and a host of inflammatory, metabolic, degenerative, and iatrogenic conditions. Data from animal and tissue culture experimentation germane to these conditions are also adduced.