Numerical estimation of stress and refractive power maps in healthy and keratoconus eyes.

Keratoconus is an eye condition caused by localized thinning of the corneal tissue, which leads to a characteristic cone-shaped protrusion of the cornea. We investigate the mechanical behavior of keratoconus and suspect keratoconus corneas versus healthy corneas by using patient-specific finite element models. Patient-specific geometries of the corneas are obtained from diagnostic images provided by corneal topographer, transformed into solid models, and discretized in hexahedral elements. For the diseased corneas, a suitable reduction of the stiffness is applied within a limited region of the cornea around the conus. After the identification of the stress-free configuration, the models are used to simulate pressurization tests up to 40 mmHg. The material parameters have been estimated within the stress-free configuration identification procedure. As expected, numerical results reveal a more compliant behavior for the diseased corneas in terms of apex displacement plots as a function of the intraocular pressure, with diseased corneas experiencing up to 44% increase in apex displacement compared to healthy corneas. The maps of the stress confirm, for the diseased corneas, a marked increase of the maximum tensile stress, on both anterior and posterior surfaces, to be ascribed mainly to the reduction of the corneal thickness. Stress maps also show, for keratoconus corneas, a marked increase of the ratio between posterior and anterior tensile stress in the conus. Numerical analyses are used to construct the refractive power maps, revealing clearly that the maximum dioptric power in keratoconus corneas is at the center of the cone-shape rather than at the apex.

Non-invasive evaluation of skin tension lines with elastic waves.

BACKGROUND: Since their discovery by Karl Langer in the 19th Century, Skin Tension Lines (STLs) have been used by surgeons to decide the location and orientation of an incision. Although these lines are patient-specific, most surgeons rely on generic maps to determine their orientation. Beyond the imprecise pinch test, there remains no accepted method for determining STLs in vivo. METHODS: (i) The speed of an elastic motion travelling radially on the skin of canine cadavers was measured with a commercial device called the Reviscometer® . (ii) Similar to the original experiments conducted by Karl Langer, circular excisions were made on the skin and the geometric changes to the resulting wounds and excised samples were used to determine the orientation of STLs. RESULTS: A marked anisotropy in the speed of the elastic wave travelling radially was observed. The orientation of the fastest wave was found to correlate with the orientation of the elongated wound (P<0.001, R2 =74%). Similarly, the orientation of fastest wave was the same for both in vivo and excised isolated samples, indicating that the STLs have a structural basis. Resulting wounds expanded by an average area of 9% (+16% along STL and -10% across) while excised skin shrunk by an average area of 33% (23% along STL and 10% across). CONCLUSION: Elastic surface wave propagation has been validated experimentally as a robust method for determining the orientation of STLs non-destructively and non-invasively. This study has implications for the identification of STLs and for the prediction of skin tension levels, both important factors in both human and veterinary reconstructive surgery.

Deficiencies in numerical models of anisotropic nonlinearly elastic materials.

Incompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial finite element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a 'compressibility parameter' (or 'penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a 'bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in 'Poisson's ratio' close to the perfect incompressibility limit of 1/2 are made.