الفهرس 
Chapter 3 | Mathematical Modelling for Corneal Viscoelastic BehaviorOnly 14 pages are availabe for public view
 |  | from | 124 |  |  |
| | | from | 124 | | |
Abstract
A stable shape for corneas experiencing refractive surgery has to be sustained so as to elude post-refractive surgery de-compensation. This de-compensation leads to visual complications and unsatisfactory procedure recovery. Variation in corneal lamellae and collagen fibres is induced by recent LASER refractive surgical procedures utilizing LASER ablation and disruption techniques. Conserving a steady response of central apex flattening and peripheral steepening in an elastic cornea pre- and post- procedure is the ultimate purpose of successful refractive surgery. Early diagnosis of ectatic corneal disorders and better understanding of corneal pathogenesis is achieved by assessment of corneal biomechanical properties.
The ultimate objective of this research is to estimate the biomechanical properties for both normal and pathogenic corneal tissue pre- and post-operative refractive surgery. This achieved using ultrasonic acoustic radiation force impulse as a non-invasive method accounting for its high localization. Induced displacement tracking methods will be utilized for assessment of soft tissue biomechanical properties related to the investigated soft tissue. Ultrasound probe simulations will be carried out to optimize the probe design. FEM simulations will take place to precisely estimate in-situ corneal tissue biomechanics.
In this research, corneal biomechanical properties are studied and estimated using acoustic radiation force impulse. This is achieved either by estimating the focal peak axial deformation value or by estimating the shear wave speed for the resulting propagating deformation wave. This is accomplished by means of three steps. Firstly, a mathematical model is derived based on standard linear solid model to study the viscoelastic behavior of corneal tissue in response to an acoustic radiation force in either loading situation of constant or transient loading situation.
Secondly, based on the mathematical model outcomes a 3D FEM simulation is performed to study the corneal tissue in 3D and in response to an acoustic radiation force impulse. FEM simulations are carried out for two major case studies, the pre-refractive and the post-refractive case study. The corresponding corneal biomechanical properties for each case study from these two major case studies are obtained from relevant experimental research studies. The availability to estimate corneal biomechanics using estimated shear wave speed resulting from application of acoustic radiation force impulse is investigated by eleven different elastic moduli 3D FEMs. FEMs’ biomechanical properties are chosen to cover a wide range of human corneal biomechanics in both normal and pathogenic states. For simulating normal post-refractive surgery cornea, six different FEMs are investigated with elastic moduli of 3, 30, 140, 300, 600 and 800 KPa respectively. For simulating the pathogenic pre-refractive surgery cornea, five different FEMs are investigated with elastic moduli of 1, 1.5, 2, 2.5 and 3 MPa respectively. At this stage of research, two ultrasonic tissue deformation estimation methods are utilized, the radial shear wave speed (rSWS) method and the focal peak axial deformation method (FPAD). For rSWS method, two B-mode frame rates are used, 10 KHz and 100 KHz, while for the FPAD method only 100 KHz frame rate is used. For FPAD method, two mathematical curve fitting formulae are used in order to include all non-involved elastic moduli values in this experiment.
Thirdly, ultrasound transducer model in conjunction with two other models, namely, the FEM and the scatterrers model, is used to study the behavior of corneal tissue deformation in response to acoustic radiation force impulse as imaged by high-frequency B-mode ultrasound probe. At this step of research, the ultrasound transducer model is simulated to generate acoustic radiation force map to be applied on the 3D FEM and is simulated to image the resulting deformation wave using high-frequency B-mode imaging as well. Nine FEMs are used to be investigated and to cover both normal and pathogenic cornea states for both pre- and post-refractive surgeries. For post-refractive surgery cornea four elastic moduli are used, 140KPa, 300KPa, 600KPa and 800KPa respectively. For pre-refractive surgery cornea five elastic moduli are used, 1MPa, 1.5MPa, 2MPa, 2.5MPa and 3MPa respectively. Time-To-Peak (TTP) deformation, deformation amplitude (DA), deformation amplitude ratio at 2 mm (DA at 2 mm) and shear wave speed (SWS) are all estimated for the involved different nine FEMs. These parameters are used as metrics to assess corneal biomechanics before and after corneal refractive surgeries.
Simulation results show that, rSWS is optimum for high-frequency ultrasound imaging. Maximum accuracy of 99.8% with a range of 2.4% is achieved with 100 KHz frame rate while for 10 KHz frame rate the achieved maximum accuracy is 95.5% with a range of 29%, with a nearly stable accuracy at 100 KHz on contrary to highly fluctuating accuracy at 10 KHz. Also, FPAD show that logarithmic formula is optimum with mean square value of 0.006 compared to 0.09 for power formula. Results have shown that, FPAD is optimum with low frame rate transducers. TTP results have shown decreasing values for increasing corneal elastic modulus. DA values are decreasing with increasing elastic modulus as well. Difficulty of corneal tissue to deform uniformly at higher elastic moduli is reflected by decreasing DA ratio values at increasing elastic moduli. Obtained SWS shows an estimation accuracy of 98%.