Nonlinear fourth‐order elastic characterization of the cornea using torsional wave elastography

Measuring the mechanical nonlinear properties of the cornea remains challenging due to the lack of consensus in the methodology and in the models that effectively predict its behaviour. This study proposed developing a procedure to reconstruct nonlinear fourth-order elastic properties of the cornea based on a mathematical model derived from the theory of Hamilton et al. and using the torsional wave elastography (TWE) technique. In order to validate its diagnostic capability of simulated pathological conditions, two different groups were studied, non-treated cornea samples (n=7), and ammonium hydroxide (NH4OH) treated samples (n=7). All the samples were measured in-plane by a torsional wave device by increasing IOP from 5 to 25 mmHg with 5 mmHg steps. The results show a nonlinear variation of the shear wave speed with the IOP, with higher values for higher IOPs. Moreover, the shear wave speed values of the control group were higher than those of the treated group. The study also revealed significant differences between the control and treated groups for the Lamé parameter ���� (25.9–6.52 kPa), third-order elastic constant A (215.09–44.85 kPa), and fourth-order elastic constant D (523.5–129.63 kPa), with p-values of 0.010, 0.024, and 0.032, respectively. These findings demonstrate that the proposed procedure can distinguish between healthy and damaged corneas, making it a promising technique for detecting diseases associated with IOP alteration, such as corneal burns, glaucoma, or ocular hypertension

Torsional wave elastography to assess the mechanical properties of the cornea

Corneal mechanical changes are believed to occur before any visible structural alterations observed during routine clinical evaluation. This study proposed developing an elastography technique based on torsional waves (TWE) adapted to the specificities of the cornea. By measuring the displacements in the propagation plane perpendicular to the axis of the emitter, the effect of guided waves in platelike media was proven negligible. Ex vivo experiments were carried out on porcine corneal samples considering a group of control and one group of alkali burn treatment ( NH 4OH) that modified the mechanical properties. Phase speed was recovered as a function of intraocular pressure (IOP), and a Kelvin-Voigt rheological model was fitted to the dispersion curves to estimate viscoelastic parameters. A comparison with uniaxial tensile testing with thin-walled assumptions was also performed. Both shear elasticity and viscosity correlated positively with IOP, being the elasticity lower and the viscosity higher for the treated group. The viscoelastic parameters ranged from 21.33 to 63.17 kPa, and from 2.82 to 5.30 Pa s, for shear elasticity and viscosity, respectively. As far as the authors know, no other investigations have studied this mechanical plane under low strain ratios, typical of dynamic elastography in corneal tissue. TWE reflected mechanical properties changes after treatment, showing a high potential for clinical diagnosis due to its rapid performance time and paving the way for future in vivo studies.Ministerio de Educacion, Cultura y Deporte Grant DPI2017-83859-R DPI2014-51870-R UNGR15-CE-3664 EQC2018-004508-PSpanish Government DTS15/00093 PI16/00339Instituto de Salud Carlos III y Fondos FederJunta de Andalucia PI-0107-2017 PIN-0030-2017 IE2017-5537MCIN/AEI - European Social Fund "Investing in your future" PRE2018-086085Consejeria de economia, conocimiento, empresas y universidad SOMM17/6109/UGR B-TEP-026- IE2017-5537 P18-RT-1653European Commission SOMM17/6109/UGR B-TEP-026- IE2017-5537 P18-RT-165

Healthy human skin Kelvin‑Voigt fractional and spring‑pot biomarkers reconstruction using torsional wave elastography

This paper presents a novel method for reconstructing skin parameters using Probabilistic Inverse Problem (PIP) techniques and Torsional Wave Elastography (TWE) rheological modeling. A comprehensive examination was conducted to compare and analyze the theoretical, time-of-flight (TOF), and full-signal waveform (FSW) approaches. The objective was the identification of the most effective method for the estimation of mechanical parameters. Initially, the most appropriate rheological model for the simulation of skin tissue behavior was determined through the application and comparison of two models, spring pot (SP) and Kevin Voigt fractional derivative (KVFD). A numerical model was developed using the chosen rheological models. The collection of experimental data from 15 volunteers utilizing a TWE sensor was crucial for obtaining significant information for the reconstruction process. The study sample consisted of five male and ten female subjects ranging in age from 25 to 60 years. The procedure was performed on the ventral forearm region of the participants. The process of reconstructing skin tissue parameters was carried out using PIP techniques. The experimental findings were compared with the numerical results. The three methods considered (theoretical, TOF, FSW) have been used. The efficacy of TOF and FSW was then compared with theoretical method. The findings of the study demonstrate that the FSW and TOF techniques successfully reconstructed the parameters of the skin tissue in all of the models. The SP model’s the skin tissue η values ranged from 8 to 12 Pa ⋅ s, as indicated by the TOF reconstruction parameters. η values found by the KVFD model ranged from 4.1 to 9.3 Pa ⋅ s. The µ values generated by the KVFD model range between 0.61 and 96.86 kPa. However, FSW parameters reveal that skin tissue η values for the SP model ranged from 7.8 to 12 Pa ⋅ s. The KVFD model determined η values between 6.3 and 9.5 Pa ⋅ s. The KVFD model presents µ values ranging between 26.02 and 122.19 kPa. It is shown that the rheological model that best describes the nature of the skin is the SP model and its simplicity as it requires only two parameters, in contrast to the three parameters required by the KVFD model. Therefore, this work provides a valuable addition to the area of dermatology, with possible implications for clinical practice.Ministerio de Educación, Cultura y Deporte grant numbers DPI2017-83859-R, and EQC2018-004508-PMinisterio de Ciencia e Innovación grant numbers PID2020-115372RB-I00, PYC20 RE 072 UGRMinisterio de Sanidad, Servicios Sociales e Igualdad grant numbers DTS15/00093 and PI16/00339Instituto de Salud Carlos III y Fondos Feder; Junta de Andalucía grant numbers PI-0107-2017, PIN-0030- 2017 and IE2017-5537Consejería de Universidad, Investigación e Innovación de la Junta de Andalucía - proyecto P21.00182Listen2Future funding by 101096884 in HORIZON-KDT-JU-2021-2-RIA and by PCI2022-135048-2 by Ministerio de Ciencia e InnovaciónConsejería de economía, conocimiento, empresas y universidad and European Regional Development Fund (ERDF) SOMM17/6109,B-TEP- 026-IE2017-5537 and P18-RT-1653Proyectos Intramurales IBS. Granada INTRAIBS-2022-05. MCIN/AEI 10.13039/501100011 033 grant number PRE2021-096978 (Co-funded by European Social Fund “Investing in your future”)Ministerio de Universidades Ayudas para la recualificación del sistema universitario español, MS2022-96 (Co funded by European Union NextGenerationEU/PRTR)Open access charge: Universidad de Granada / CBUA