A data-driven approach to characterizing nonlinear elastic behavior of soft materials.

The Autoprogressive (AutoP) method is a data-driven inverse method that leverages finite element analysis (FEA) and machine learning (ML) techniques to build constitutive relationships from measured force and displacement data. Previous applications of AutoP in tissue-like media have focused on linear elastic mechanical behavior as the target object is infinitesimally compressed. In this study, we extended the application of AutoP in characterizing nonlinear elastic mechanical behavior as the target object undergoes finite compressive deformation. Guided by the prior of nonlinear media, we modified the training data generated by AutoP to speed its ability to learn to model deformations. AutoP training was validated using both synthetic and experimental data recorded from 3D objects. Force-displacement measurements were obtained using ultrasonic imaging from heterogeneous agar-gelatin phantoms. Measurement on samples of phantom components were analyzed to obtain independent measurements of material properties. Comparisons validated the material properties found from neural network constitutive models (NNCMs) trained using AutoP. Results were found to be robust to measurement errors and spatial variations in material properties.

Role of corneal biomechanical properties in applanation tonometry measurements.

PURPOSE: To demonstrate the importance of material properties of the cornea in intraocular pressure (IOP) readings via standard Goldmann applanation tonometry. METHODS: A realistic finite element model of the cornea was developed for the simulation of Goldmann applanation tonometry. A virtual cornea population was generated by randomly sampling material properties, central corneal thickness (CCT), and IOP for comparison with 181 clinical cases. The effect of material properties and CCT on IOP prediction in the virtual population was determined via computational simulation. RESULTS: The results show that corneal biomechanical properties (as characterized in this study by the stiffness parameter Einit) are as important as the CCT in influencing measured (Goldmann) IOP. CONCLUSIONS: This study supports the contention that the observed large scatter in standard correlations of clinical measurements of IOP versus CCT can be largely accounted for by plausible individual variations in corneal biomechanical stiffness properties.

Physics-guided machine learning for 3-D quantitative quasi-static elasticity imaging.

We present a 3D extension of the Autoprogressive Method (AutoP) for quantitative quasi-static ultrasonic elastography (QUSE) based on sparse sampling of force-displacement measurements. Compared to current model-based inverse methods, our approach requires neither geometric nor constitutive model assumptions. We build upon our previous report for 2D QUSE and demonstrate the feasibility of recovering the 3D linear-elastic material property distribution of gelatin phantoms under compressive loads. Measurements of boundary geometry, applied surface forces, and axial displacements enter into AutoP where a Cartesian neural network constitutive model (CaNNCM) interacts with finite element analyses to learn physically consistent material properties with no prior constitutive model assumption. We introduce a new regularization term uniquely suited to AutoP that improves the ability of CaNNCMs to extract information about spatial stress distributions from measurement data. Results of our study demonstrate that acquiring multiple sets of force-displacement measurements by moving the US probe to different locations on the phantom surface not only provides AutoP with the necessary information for a CaNNCM to learn the 3D material property distribution, but may significantly improve the accuracy of the Young's modulus estimates. Furthermore, we investigate the trade-offs of decreasing the contact area between the US transducer and phantom surface in an effort to increase sensitivity to surface force variations without additional instrumentation. Each of these modifications improves the ability of CaNNCMs trained in AutoP to learn the spatial distribution of Young's modulus from force-displacement measurements.

Data-Driven Elasticity Imaging Using Cartesian Neural Network Constitutive Models and the Autoprogressive Method.

Quasi-static elasticity imaging techniques rely on model-based mathematical inverse methods to estimate mechanical parameters from force-displacement measurements. These techniques introduce simplifying assumptions that preclude exploration of unknown mechanical properties with potential diagnostic value. We previously reported a data-driven approach to elasticity imaging using artificial neural networks (NNs) that circumvents limitations associated with model-based inverse methods. NN constitutive models can learn stress-strain behavior from force-displacement measurements using the autoprogressive (AutoP) method without prior assumptions of the underlying constitutive model. However, information about internal structure was required. We invented Cartesian NN constitutive models (CaNNCMs) that learn the spatial variations of material properties. We are presenting the first implementation of CaNNCMs trained with AutoP to develop data-driven models of 2-D linear-elastic materials. Both simulated and experimental force-displacement data were used as input to AutoP to show that CaNNCMs are able to model both continuous and discrete material property distributions with no prior information of internal object structure. Furthermore, we demonstrate that CaNNCMs are robust to measurement noise and can reconstruct reasonably accurate Young's modulus images from a sparse sampling of measurement data. CaNNCMs are an important step toward clinical use of data-driven elasticity imaging using AutoP.

An information-based machine learning approach to elasticity imaging.

An information-based technique is described for applications in mechanical property imaging of soft biological media under quasi-static loads. We adapted the Autoprogressive method that was originally developed for civil engineering applications for this purpose. The Autoprogressive method is a computational technique that combines knowledge of object shape and a sparse distribution of force and displacement measurements with finite-element analyses and artificial neural networks to estimate a complete set of stress and strain vectors. Elasticity imaging parameters are then computed from estimated stresses and strains. We introduce the technique using ultrasonic pulse-echo measurements in simple gelatin imaging phantoms having linear-elastic properties so that conventional finite-element modeling can be used to validate results. The Autoprogressive algorithm does not require any assumptions about the material properties and can, in principle, be used to image media with arbitrary properties. We show that by selecting a few well-chosen force-displacement measurements that are appropriately applied during training and establish convergence, we can estimate all nontrivial stress and strain vectors throughout an object and accurately estimate an elastic modulus at high spatial resolution. This new method of modeling the mechanical properties of tissue-like materials introduces a unique method of solving the inverse problem and is the first technique for imaging stress without assuming the underlying constitutive model.

Accurate intraocular pressure prediction from applanation response data using genetic algorithm and neural networks.

The fact that Goldmann applanation tonometry does not accurately account for individual corneal elastic stiffness often leads to inaccuracy in the measurement of intraocular pressure (IOP). IOP should account not only for the effect of central corneal thickness (CCT) but should also account for other corneal biomechanical factors. A computational method for accurate and reliable determination of IOP is investigated with a modified applanation tonometer in this paper. The proposed method uses a combined genetic algorithm/neural network procedure to match the clinically measured applanation force-displacement history with that obtained from a nonlinear finite element simulation of applanation. An additional advantage of the proposed method is that it also provides the ability to determine CCT and material properties of the cornea from the same applanation response data. The performance of the proposed method has been demonstrated through a parametric study and via comparison with a well known clinical case. The proposed method is also shown to be computationally efficient, which is an important practical consideration for clinical application.