Doctoral Research Work

Biomechanical Modelling and Computer-Aided Simulation of Deep
Brain Retraction in Neurosurgery

In neurosurgery, the brain retraction technique has become popular in the field of image-guided procedures for intracranial operations, such as in brain tumor, cerebral aneurysms, cerebral hematoma, etc. Brain retraction is performed for adequate exposure during surgeries as such procedure requires consistent retraction. This causes several local brain contusions, which limit the accuracy of the image-guided neurosurgical system. Therefore, there is a need for training in this field to enhance the efficiency of the procedure. In this study, we present a 3D finite element brain model segmented from human head magnetic resonance images in the visco-hyperelastic framework. The numerical model is used to predict the deformation and stress fields within the brain during brain retraction. The brain was retracted by 5 mm and retained at that position for 30 minutes. It was observed that during this period, 33% of the maximum stress level generated due to retraction gets released from the brain. The results show that brain retraction can be performed continuously for up to 30 minutes without any risk of local brain contusions or postoperative complications. Finally, through a combination of judicious retraction and rigorous preoperative planning, a drop in the morbidity rate due to brain retraction is expected in the future. This technique can be used for preoperative effective planning and training, especially in minimally invasive brain surgeries. The work has been published in Computer Methods and Programs in Biomedicine (click here).

MatNLI: An open-source MATLAB-based solver for the
non-linear inversion in elastography

Elastography has emerged as one of the most promising non-invasive clinical tools. In elastography, a stiffness map or elastogram is generated by solving an inverse problem of elasticity utilizing the tissue motion data acquired using magnetic resonance imaging or ultrasound. Among various inverse algorithms devoted to elastography, non-linear inversion coupled with the finite element method has demonstrated excellent applicability in extracting complex physics of the tissue. The development and implementation of such an inverse algorithm are challenging and often unavailable to clinicians. In the present work, we offer an open-source parallel MATLAB implementation of an efficient non-linear inversion algorithm based on the finite element method for different isotropic material models, viz., linear elastic and viscoelastic materials in the regime of compressible and nearly incompressible materials. Additionally, the framework has been extended to account for anisotropy by assuming transversely isotropic material. For the optimization module, the gradient of the objective function to the model parameters has been computed using the Adjoint method. Different case studies involving smooth variations and piece-wise discontinuities in the material property distribution are explored, and the efficacy of the inversion algorithm in reconstructing the stiffness map is discussed. In addition, noise is added to the synthetic data to depict a realistic setup, i.e., to prevent inverse crimes, and enhance the numerical stability and robustness of the current implementation. The present framework with general-purpose computer implementation could be beneficial for academic and clinical uses and may aid researchers in strengthening their existing frameworks and developing new algorithmic ideas. The work has been published in Advances in Engineering Software (click here).

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

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. 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. 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. 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. The work has been published in Computer Methods and Programs in Biomedicine (click here).

Subzone based Non-linear Inversion for 3D Dynamic Elastography

Elastography involves using full-field displacement data to determine the unknown material model parameter field by solving an inverse problem as a PDE-constrained optimization problem. To reconstruct the material field map, iterative solvers are employed that use gradient-based optimization algorithms, with Gauss-Newton and Quasi-Newton methods being the most common. The second-order optimization methods guarantee faster convergence with higher reconstruction accuracy but with a higher computational cost as the number of model parameters increases. To address this, we utilized a sub-domain approach, where the inverse problem is solved on small, independent subzones to reduce the effective number of unknowns. A comparison between the full and subzone-based approaches demonstrated the high efficacy of the subzone method, with an acceleration up to a factor of 20 for the subzone method compared to typical full inversion. The subzone-based framework was also tested on a 3D case study to demonstrate its effectiveness in handling large-scale problems. This work is an extension of the 2D MATLAB inversion algorithm presented in the previous study published in Advances in Engineering Software (click here).

A review of brain injury at multiple time scales and its clinicopathological correlation through in silico modeling 

Ever wondered about the intricate mechanics behind how our brain responds to different types of injuries? Delve into our review article to explore the fascinating intricacies of brain injuries stemming from trauma, treatment, or neurodegenerative mechanisms across various spatiotemporal scales. We explore the potential of in silico modeling, combining physics and clinical data, to uncover new injury pathways and contribute to prevention, diagnosis, and treatment planning. The work has been published as a review article in Brain Multiphysics (click here).