A wavelet neural operator based elastography for localization and quantification of tumors.

BACKGROUND AND OBJECTIVES: The application of intelligent imaging techniques and deep learning in the field of computer-aided diagnosis and medical imaging have improved and accelerated the early diagnosis of many diseases. Elastography is an imaging modality where an inverse problem is solved to extract the elastic properties of tissues and subsequently mapped to anatomical images for diagnostic purposes. In the present work, we propose a wavelet neural operator-based approach for correctly learning the non-linear mapping of elastic properties directly from measured displacement field data. METHODS: The proposed framework learns the underlying operator behind the elastic mapping and thus can map any displacement data from a family to the elastic properties. The displacement fields are first uplifted to a high-dimensional space using a fully connected neural network. On the lifted data, certain iterations are performed using wavelet neural blocks. In each wavelet neural block, the lifted data are decomposed into low, and high-frequency components using wavelet decomposition. To learn the most relevant patterns and structural information from the input, the neural network kernels are directly convoluted with the outputs of the wavelet decomposition. Thereafter the elasticity field is reconstructed from the outputs from convolution. The mapping between the displacement and the elasticity using wavelets is unique and remains stable during training. RESULTS: The proposed framework is tested on several artificially fabricated numerical examples, including a benign-cum-malignant tumor prediction problem. The trained model was also tested on real Ultrasound-based elastography data to demonstrate the applicability of the proposed scheme in clinical usage. The proposed framework reproduces the highly accurate elasticity field directly from the displacement inputs. CONCLUSIONS: The proposed framework circumvents different data pre-processing and intermediate steps utilized in traditional methods, hence providing an accurate elasticity map. The computationally efficient framework requires fewer epochs for training, which bodes well for its clinical usability for real-time predictions. The weights and biases from pre-trained models can also be employed for transfer learning, which reduces the effective training time with random initialization.

Biomechanical modelling and computer aided simulation of deep brain retraction in neurosurgery.

BACKGROUND AND OBJECTIVES: Surgical simulators are widely used to promote faster and safer surgical training. They not only provide a platform for enhancing surgical skills but also minimize risks to the patient's safety, operation theatre usage, and financial expenditure. Retracting the soft brain tissue is an unavoidable procedure during any surgery to access the lesioned tissue deep within the brain. Excessive retraction often results in damaging the brain tissue, thus requiring advanced skills and prior training using virtual platforms. Such surgical simulation platforms require an anatomically correct computational model that can accurately predict the brain deformation in real-time. METHODS: In this study, we present a 3D finite element brain model reconstructed from MRI dataset. The model incorporates precisely the anatomy and geometrical features of the canine brain. The brain model has been used to formulate and solve a quasi-static boundary value problem for brain deformation during brain retraction. The visco-hyperelastic framework within the theory of non-linear elasticity has been used to set up the boundary value problem. Consequently, the derived non-linear field equations have been solved using finite element solver ABAQUS. RESULTS: The retraction simulations have been performed for two scenarios: retraction pressure in the brain and forces required to perform the surgery. The brain was retracted by 5 mm and retained at that position for 30 minutes, during which the retraction pressure attenuates to 36% of its peak value. Both the model predictions as well as experimental observations on canine brain indicate that brain retraction up to 30 minutes did not cause any significant risk of induced damage. Also, the peak retraction pressure level indicates that intermittent retraction is a safer procedure as compared to the continuous retraction, for the same extent of retraction. CONCLUSIONS: The results of the present study indicate the potential of a visco-hyperelastic framework for simulating deep brain retraction effectively. The simulations were able to capture the dominant characteristics of brain tissue undergoing retraction. The developed platform could serve as a basis for the development of a detailed model in the future that can eventually be used for effective preoperative planning and training purposes.

An embedded element based 2D finite element model for the strength prediction of mineralized collagen fibril using Monte-Carlo type of simulations.

A computationally efficient statistical model for the prediction of the strength of mineralized collagen fibril (a basic building block of bone) is presented by taking into account the uncertainties associated with the geometrical and material parameters of collagen and mineral phases. The mineral plates have been considered as one-dimensional bar elements embedded in the two-dimensional plane stress collagen matrix. The mineral phase is considered as linear elastic and a hyperelastic material model is adopted for the collagen phase. Further, the crack initiation and propagation in the collagen phase have been modeled using a damage plasticity approach. Different realizations of the arrangement of mineral plates have been generated to account for the associated geometrical uncertainties using an in-house MATLAB® code. Monte-Carlo type simulations have been performed on the different realizations of mineralized collagen fibril to predict its characteristic stress-strain response under tensile load. The characteristic strength of 3.64 GPa is obtained for mineralized collagen fibril using Weibull's analysis which is found to be in agreement with the molecular dynamics simulation data and numerical studies reported in the past. A parameter sensitivity analysis concluded that mineral modulus has a significant effect on the overall tangent modulus of mineralized collagen fibril in large strain regime.

Monte Carlo Type Simulations of Mineralized Collagen Fibril Based on Two Scale Asymptotic Homogenization.

A multiscale model for mineralized collagen fibril (MCF) is proposed by taking into account the uncertainties associated with the geometrical properties of the mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli of bone's nanostructure at two hierarchical length scales, namely: microfibril (MF) and MCF. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes and structural arrangements. A total of 100 realizations for the MCF model with random distribution have been generated using an in-house MATLAB code, and Monte Carlo type of simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small (≤10%) and large (≥10%) strain regimes. The stress transformation mechanism has also been explored in MF which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for MF under small and large strains have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as an input for the upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the MCF in the small and large strain regimes are obtained as 4.08 ± 0.062 and 12.93 ± 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics (MD) simulations in the literature with a significant reduction in the computational cost.